Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020) [2, 1 ed.] 3030548163, 9783030548162

Table of contents :
Preface
Contents
Justification of Textured Wheels Arrangement in Combined Tool and Modeling the Workpiece Temperature During Grinding
1 Introduction
2 The Tool for the Combined Grinding by Coarse- and Fine-Grained Textured Wheel
3 Modeling Technique of Workpiece Temperature at the Combined Grinding by the Textured Coarse- and Fine-Grained Wheel
4 Modeling Results of Temperature of Processed Surface and Their Analysis
5 Conclusion
References
Hydrodynamic Streams of Coolant at Internal Grinding by Textured Wheel
1 Introduction
2 Design of the Textured Grinding Wheel and the Device for Coolant Giving
3 Technique of Studies of Hydrodynamic Coolant Streams
4 Hydrodynamic Streams, Which Flow via the Textured Grinding Wheel
5 A Hydrodynamic Coolant Veil for Neutralization of Face Aerodynamic Streams
6 Coolant Pressure Upon the Processed Surface of Workpiece
7 Conclusion
References
Peculiarities of Assembly of Bevel and Hypoid Gears with Curved Teeth
1 Introduction
2 Structure
3 Finishing Treatment
4 Conclusion
References
On Issue of Evaluating the Effectiveness of the Driver-Car-Road-Environment (DCRE) System
1 Introduction
2 Methods and Materials
3 Results
4 Conclusions
References
Computer-Aided Algorithm for Nonlinear Optimization of Finishing Operations in Machining Using Precision Cutting Tool
1 Introduction
2 Mathematical Model of the Cutting Process
3 MS Excel as a Solver
4 The Practical Implementation
5 Conclusion
References
Calculation of Technological Dimensional Chains by Probability Method
1 Introduction
2 The Calculation Algorithm
3 Examples of Calculation
4 Conclusion
References
Study of Influence of Magnetic-Pulse Hardening on Cutting Tools Strength and Wear Resistance
1 Introduction
2 The Modeling and Discussion
3 The Experimental Research and Results
4 Conclusions
References
Solid Modeling of Involute Bevel Gears
1 Introduction
2 Theoretical Part
3 Practical Significance
4 Conclusion
References
Application of Modal Analysis to Building Simulation Models of Thermal Processes in Machine Tools
1 Introduction
2 Modal Analysis
3 Building Multimodal Simulation Model of the Machine Tool
4 Full-Scale and Machine Experiments
5 Discussion of the Results
6 Conclusions
References
Software Development for the Optimal Parts Location in the Bath Space with the Purpose to Reduce the Non-uniformity of the Coating Thickness
1 Introduction
2 Mathematical Model and Optimization Problem
3 Database Composition
4 Software Algorithm
5 Materials and Methods
6 Results and Discussion
7 Conclusion
References
Methodology of Measuring Cutters by Using Coordinate Measuring Machine in Automatic Mode
1 Introduction
2 Methodology
3 Conclusions
References
Adaptation of PLM Information System in Industry 4.0 Concept at Stage of Technological Production Preparation
1 Introduction
2 Tool Stock Level Calculation Model
3 Conclusion
References
Research of Forming Process of Surface Quality During Machining with Free Abrasive
1 Introduction
2 Importance and Scientific Novelty of the Research
3 The Researching of Gas-Dynamic Processing
4 The Result of Research
References
Study of Reactive Power Compensation Efficiency for Asynchronous Motors of Metal-Cutting Machine Electric Drives
1 Introduction
2 Formulation of the Problem
3 Main Part
4 Research Results
5 Conclusion
References
Influence of Technological Inheritance on Accuracy of Assembly of Axisymmetric Shells
1 Introduction
2 Factory Technology Analysis
3 Statistical Processing of Experimental Data
4 Conclusion
References
The Investigations of Surface Micro-Hardness of Experimental Hard Alloy Grades
1 Introduction
2 The Experimental Part
3 Results and Discussion
4 Conclusions
References
About One Approach to the Study of Heat Fluxes in the Processes of Drilling Deep Holes Machining
1 Introduction
2 Statement of the Problem
3 Description of the Approach and Derivation of the Basic Equations
4 Conclusions
References
Simulation Modeling of the Choice of Metal Cutting Tool Coating
1 Introduction
2 Methodological Support of Simulation Modeling
3 Discussion of the Results
4 Conclusion
References
Investigation of Electrochemical Machining Using Nanosecond Voltage Pulse Packets
1 Introduction
2 Mathematical Model
3 Results and Discussion
4 Conclusions
References
Modeling Electrical Discharge Machining of Deep Micro-Holes by Rotating Tool-Electrode
1 Introduction
2 Mathematical Model
3 Results and Discussion
3.1 Results of Modeling
3.2 Experimental Studies for Model Validation
4 Conclusion
References
FEM Analysis of Carbide Insert Strength for Milling Application
1 Introduction
2 Methodology
3 Conclusions
References
Study and Evaluation of Stability of Technical Processes for Machine-Building Products at Stage of Serial Production
1 Introduction
2 Reasons for Deviations of End Products from the Requirements of the Standard Process Documentation
3 A Study of the Stability of a Technical Process According to the Accuracy of a Product Manufactured
4 Quality Forms for the Individual Values of the Parameters Measured
5 Conclusions
References
Studying the Impact the Microrelief of Teeth Surface Has on Gear Operational Parameters
1 Introduction
1.1 Structure Gears Operation Process
1.2 Tables
2 Micro-Cutting Gear
3 Roughness of the Surface
4 Micropitting Morphology
5 Sliding Gears
6 Equations
References
How the Parameters of an Agricultural Machine and Tractor Unit Affect the Wear of Friction Pairs in a Diesel Engine When Used for Transport
1 Introduction
2 Method
2.1 Analytical Expressions to Find the Wear Rates of Friction Pairs in an MTU Diesel Engine in Transport Operations
2.2 Transport-Mode Wear Rate of the Friction Pairs in an MTU Diesel Engine
3 Results and Discussion
References
Oil Consumption Through Burning in Heavy-Duty Operation of an Agricultural Machine and Tractor Unit
1 Introduction
2 Method
2.1 Analytical Expressions to Find Oil Consumption Through Burning in Plowing
2.2 MTU Diesel Engine: Oil Consumption Through Burning in Plowing
3 Results and Discussion
References
Modeling of Turbine Rotor Journal Machining with Location on Bearing and with Center Pregrinding
1 Introduction
2 Modeling of Preparatory Machining of Rotor Journal with Location on the Center Hole and on the Adjacent Cylindrical Surface
3 Computer Modeling of Preparatory Machining of the Shaft Journal with Location on the Center Hole and on the Adjacent Cylindrical Surface and of Following Machining with Location on the Machinable Surface
4 Conclusions
References
Industrial Manipulating Robot Finite Element Mesh Generation Based on Robot Voxel Model
1 Introduction
2 Methodology of Developing Small-Sized Finite Element Model
3 Development of Voxel and Finite Element Models of Industrial Manipulating Robot Equivalent Part
4 Conclusions
References
Axis Determination Based on Regression for Calculation of Virtual Pitch Thread Diameter Using a Point Cloud from CMM
1 Introduction
2 The Methodology to Determine Regression Equation of Part Thread Surface Axis
2.1 Problem Statement
2.2 Calculation of Regression Equations’ Coefficients
2.3 Determination of Thread Surface Curved Axis Equation
3 Computer Modeling of Threads with Various Axis Types, Determination of Thread Location and of VPTD
4 Results and Discussion
5 Conclusion
References
Improving Technology of Manufacturing Preparations for Brackets of Heavy Truck Cars
1 Introduction
2 Setting a Research Problem
3 Development of a New Design for Transfer Case Suspension Bracket Parts
4 The Method of Calculation
5 Conclusion
References
Methodology and Tools for Computer-Aided Calculation of Characteristics of Electromechanical Clamping Drive Actuated by Induction Motor
1 Introduction
2 The Purpose of the Research
3 Research
4 Conclusions
References
Road Fuel Consumption by Dump Truck in Mountain Conditions
1 Introduction
2 Experimental Study
3 Mathematical Model
4 Results
5 Conclusions
References
Very Hard Titanium Carbosilicide Coatings to Protect Parts of Energy Machines
1 Introduction
2 Research Results
3 Conclusions
References
Marking Metal Products by Anodic Etching by Means with Semiconductor Electrode Tools
1 Introduction
2 Theoretical Analysis
3 Experimental Part
4 Conclusion
References
Features of Design and Practical Application of Digital Twin of Internal Grinding Operation with CNC
1 Introduction
2 Features of Design and Practical Application of the Digital Twin of the Internal Grinding Operation Realized on the CNC Machine
3 Conclusions
References
Assessing Cutting Force: A Study of Varying Internal Grinding Wheels
1 Introduction
2 Review of Existing Methods for Developing Models of the Cutting Force Occurring During Internal Grinding
3 Analytical Model of the Cutting Force that Occurs During Internal Grinding
4 Experimental Studies of the Cutting Force in Internal Grinding with Wheels with Various Performance Indicators
5 Conclusions
References
Analysis of the Influence of Installation Deformations of Diesel Cylinder on Its Operating Indicators
1 Introduction
2 Investigation of Elastic Properties and Level of Mounting Deformations of Cylinders
3 The Research of the Effect of Mounting Deformations of the Diesel Cylinder on Its Performance
4 Conclusion
References
Studies on the Effect of Output Parameters on Productivity When Turning Titanium Alloys
1 Introduction
2 Materials and Methods
3 Results and Discussion
4 Conclusion
References
The Study of Stress State Uniformity Along with the Thickness of the Constructive Element of Housing High-Pressure Vessels Deformed by Conjugated Elements of Physical Separation of Heating Elements Embedded in the Vessel Housing
1 Introduction
2 Test Problems and Verification of the Simulation Method
3 Numerical Research
4 Conclusions
References
Modeling Metal Removal in Automatic Circular Grinding Cycles Taking into Account Process Dynamics
1 Introduction
2 Dynamic Displacement Modeling
3 Results and Discussions
4 Conclusions
References
Development of a Method for Verification of API Thread Measurement Results by Comparing Them with Measurement Results of Reference Measuring Instruments
1 Introduction
2 Standard System Accuracy and Production Requirements
3 Development of a Method to Verify the Thread Measurement
4 Conclusion
References
Calculation of Contact Tensions in the Process of Thermofrictional Treatment
1 Introduction
2 Main Text
3 Conclusion
References
Effect of Mode Amplitude on Power Consumption in Vibrating Mixer
1 Introduction
2 Study Objects and Methods
3 Results and Discussion
4 Conclusion
References
Multi-stages to Ensure Quality Control of Designing and Production at External Cylindrical Grinding Machines
1 Introduction
2 Model of Stages of a Relationship Between Stages at External Cylindrical Grinding
3 Conclusion
References
Design of High-Efficiency Device for Gas Cleaning from Fine Solid Particles
1 Introduction
2 Study Objects and Methods
3 Results and Discussion
4 Conclusion
References
Geometry of Six-Dimensional Space for Engineering
1 Introduction
2 Modern Problems of Representation Geometric Configuration of Products and Their Components
3 The Fundamental Provisions Geometry of the Six-Dimensional Space
4 The Configuration of the Actual Parts and Its Display
5 Discussion
6 Conclusion
References
Providing the Working Accuracy of CNC Metal-Cutting Machine
1 Introduction
2 The Formation of Defects in the Form of Toolholders
3 Using Finite Element Analysis to Assess the Accuracy of the Axial Location of the Tool Holder and the Angular Stiffness of the Spindle-Tool Subsystem
4 Conclusion
References
Performance Study of Mills with Amorphous Silicon-Carbon Coatings
1 Introduction
2 Relevance and Setting of the Problem
3 Determination of Temperatures on the Surface of Parts During Final Plasma Hardening
4 Possibility of Using Ion Implantation
5 Setting Up and Conducting an Experiment
6 Calculation Results
7 Conclusion
References
Fatigue Test Optimization for the Aircraft Engine Based on the Life Cycle Information Support and Modeling
1 Introduction
2 Problem Definition and Big Data Concept Applying
3 The Life Cycle Model Building
4 An Example of the Assessment of the Fatigue Test Parameters
5 Conclusion
References
Reduction of Static Elastic Displacements During Processing on Vertical Milling Machines
1 Introduction
1.1 State of the Art in Modern Mechanical Engineering
1.2 Relevance
1.3 Statement of Problem
2 Determination of the Rigidity Axes in the Working Space of a Vertical Milling Machine
3 Mathematical Model for Optimization of Cutting Modes
4 Testing the Adequacy of the Developed Mathematical Model
5 Conclusions
References
Effect of Wire Arc Additive Manufacturing Process Parameters on Deposition Behavior of Steel
1 Introduction
2 Materials and Experimental Techniques
3 Results
4 Discussion
5 Conclusions
References
Study of the Axial Contact Points Method Applied When End-Milling Titanium Alloys
1 Introduction
2 Equipment and Methods
3 Results and Discussion
4 Conclusion
References
Investigation of the Effect on the Efficiency of Hot Die Forging Operations Cutting Off and Heating Blanks from Rolled Round Bar
1 Introduction
2 Calculation of the Metal Consumption During the Manufacturing Process and Heating Blank
3 Influence Analysis of the Rolled bar Precision, Cutting Methods, and Heating Blank on Its Mass
4 Effectiveness Evaluation of the Standard HDF Process on CHDFP for Round Forging Depending on the Mass of Blank
5 Summary
References
The Express-Method for Determining the Workability of Structural Steels Using the Indicator of Specific Cutting Work
1 Introduction
2 Purpose of Research
3 Results and Discussion
4 Conclusion
References
Digital Space of Small Enterprises in Engineering
1 Introduction
2 The Information Environment of the Enterprise
3 Design Preparation of Production
4 Engineering of Parts and Assemblies
5 Technological Preparation of Production
6 PLM Strategy
7 Conclusions
References
Some Features of the Pisarenko–Lebedev Generalized Strength Criterion Application for Long-Term Strength Calculations
1 Introduction
2 Research Goal
3 Materials and Methods
4 Experimental Results
5 Conclusions
References
Evaluation of the Impact of the Actual Geometry of the Planetary Gearing on Its Capabilities in the KISSSYS Program
1 Introduction
1.1 Problem Statement
1.2 The Source Data of the Design Stage
2 Instrumental and Metrological Support
3 Simulation of Planetary Gear Operation
4 Conclusion
References
Predictive Simulation Tool for Control Over Precision of Geometrically Complex Mould Making at Preproduction Engineering Stage
1 Introduction
2 Key Method Provisions
3 Method Implementation
4 Conclusions
References
A Tool Management System Design Using Object-Oriented and Functional Modeling
1 Introduction
2 Functional and Object-Oriented Modeling
3 Evaluation of Information Processing Efficiency
4 Results and Discussion
References
Classification of Technologies for Obtaining Geometric Configuration of Parts
1 Introduction
2 Classification of Manufacturing Techniques for Parts
3 The Results of Grouping of Technologies According to the Proposed Classification
4 Discussion
5 Conclusion
References
Methods of Designing Technological Trajectories of Single Layer of Laser Powder Cladding on Flat Surfaces of Part Model in CAM
1 Introduction
2 Problem Statement
3 Preparation of a Three-Dimensional Polygon Model
4 Design of Technological Trajectories of LRPC on a Flat Surface
5 Design of Technological Trajectories LRPC on a Flat Surface with the Rotation of the Part in the Positioner
6 Conclusion
References
Aeroacoustic Cartography as Method of Non-destructive Testing of Turbine Blades Based on Fiber Optic Sensor Systems
1 Introduction
1.1 Locational Sensing Equipment
2 Acoustoelectric Method
3 Gas Dynamics Method as an Addition to the Acoustic Method
4 Fiber Optic Systems of Aeroacoustic Cartography
References
Exploratory Design of Technical Systems with Fluid and Gas Working Body Based on Heuristic Modeling of Physical Operating Principles
1 Introduction
2 Modeling of Physical Principles of Action
3 Heuristic Modification of PPA Models
4 Conclusions
References
Computer-Aided Design of Precast End Mills Based on the Parametric Model
1 Introduction
2 Materials and Methods
3 Results
4 Conclusion
References
Modeling Cutting Force During Internal Grinding with Different Wheel Characteristics
1 Introduction
2 Modeling the Cutting Force During Internal Grinding by the Wheels of Different Characteristics
3 Conclusions
References
Fuzzy Formalization of Individual Quality Criteria for Quality Level Evaluation by Using Two-Level Optimization Model
1 Introduction
2 A Mathematical Model for Assessing of the Product Quality
3 Formalization of Unique Criteria for a Model for Assessing of Quality of Instrument-Making Products
4 Calculating the Quality Level Using a Two-Level Optimization Model
References
Programming Industrial Robots for Wire Arc Additive Manufacturing
1 Introduction
2 Materials and Equipment
3 Case Study
4 Discussion
5 Conclusion
References
Metrology Assurance of Assembling DESY’s XFEL Free-Electron Laser Accelerator of Elementary Particles
1 Introduction
2 Measurements During Installation of the Waveguide Distribution System
2.1 Object of Measurement
2.2 Methodology for Measurement and Adjustment
3 Introduction
4 Conclusion
References
Modeling Geometric Obstacles in the Assembly of Complex Products
1 Methods of Geometric Solvability
1.1 Separability of Geometric Sets
1.2 Combinatorial Methods of Geometric Solvability
1.3 Collision Detection Methods
1.4 Graph Methods of Geometric Solvability
1.5 Motion Planning Methods
2 Game-Theoretic Model of Geometric Solvability
2.1 Geometric Situations
2.2 Geometric Inheritance
2.3 Correct Colorings of Ordered Sets
3 Conclusion
References
Information Model of the Automated System of Assembling Plant Identification and Traceability
1 Introduction
2 The Theoretical Studies
3 Practical Implementation
4 Conclusion
References
Modeling of Production Process Energy Characteristics in Mechanical Engineering
1 Introduction
2 Mathematical Modeling
3 Simulation Modeling
4 The Performance of the Experiment
5 Results and Discussion
References
Control Algorithm for Compensated Tripod-Based Manipulators
1 Introduction
2 Mathematical Manipulator-Dynamics Model
3 Synthesizing the Programmed Control Forces
4 Programmed Control Force: A Calculation Example
5 Conclusion
References
Modeling and Assessment of Production Cycle Information Entropy Under Joint Activities
1 Introduction
2 Collaborative Strategy Development
3 Creation of a Model of Trust in Operational Processes
4 Modeling Results
5 Conclusion
References
Ensuring Stability of Wheeled Vehicles When Driving on Slopes
1 Introduction
2 Theoretical Justification
3 Research Results
4 Conclusion
References
Conceptual Design Methodics of Hybrid Car Traction Drive
1 Introduction
2 Scheme of the Proposed Drive
3 Justification of the Conceptual Design Methodology
4 Calculation Example According to the Proposed Methodology
5 Conclusion
References
Results of Computer Simulation of a Braking Vehicle Energy Recovery System
1 Introduction
2 Materials and Methods
3 Results
4 Conclusion
References
Investigation into Operational Reliability of Vehicle Electronic Systems
1 Introduction
2 Methods
3 Results and Discussion
4 Conclusion
References
Numerical Modeling of a Railway Wheel Profile in a Fillet Radius Space Using the Uniform Search Method
1 Introduction
2 Algorithm of Uniform Search Method
3 Results of Variant Computational Experiments
4 Conclusions
References
Features of Development of Structures of Extruders
1 Introduction
2 The Main Part
3 Conclusions
References
Research of Dynamics of Seat Air Suspension with Possibility of Vibration Energy Recuperation Under Action of Typical Harmonic Disturbances
1 Introduction
2 Model Description
3 Research Results
4 Conclusions
References
Functional Tuning of Car Suspension
1 Introduction
2 Relevance
3 Formulation of the Problem
4 Theoretical Part
5 Practical Significance
6 Conclusions
References
Approaches to Formation of Car Service Modes in Case of Complete or Insufficient Information on Operational Reliability of Car Elements
1 Introduction
2 Research Methods
3 Research Results
References
Vibration Diagnostics of Swivel Suspension Elements of Automotive Vehicles
1 Introduction
2 Problem Formulation
3 Theoretical Part
4 Experimental Studies
5 Conclusions
References
Indicator Analysis of Injection Process of Different Composition Mixtures of Diesel Fuel and Palm Oil at Changing of Speed Mode of Diesel Engine
1 Introduction
1.1 The Purpose and Objectives
2 Object and Methods of Research
3 Results and Discussion
4 Conclusion
References
Selection of Air Cooled Diesel Engine Boosting Level Considering Process Deviations of Parameters
1 Introduction
2 Object of Research
3 Impact of Process Variety of Pressure Charging on Thermal Condition of Cylinder Head
4 Impact of Variety in Process Characteristics on Temperature Field of Cylinder Head
5 Conclusion
References
Analysis of Constructive Reliability and Maintainability of the Contemporary Electronic Control Units of the Active Safety Systems
1 Introduction
2 Basic Faults of the Unit
3 Maintainability Analysis
4 Technology of Repair
References
Simulation of Change in Reliability of Rope System Motion Mechanism in Mobile Ropeway Complex
1 Introduction
2 Statement of the Research Task
3 Mathematical Model
4 Test Analysis of the Mathematical Model
5 Conclusion
References
Interaction of a Large Tire with the Soil
1 Introduction
2 Justification of Selection of Research Object
3 Description of the Model and Experimental Installation
4 Conclusion
References
Improving Technical Readiness of Wheeled and Tracked Vehicles in Severe Climatic Conditions
1 Introduction
2 Relevance, Scientific Significance with a Brief Overview of Literature
3 Setting a Task
3.1 Structure
4 Practical Significance, Suggestions, and Results of Pilot Research
5 Conclusions
References
Modeling the Equipment for Mechanical Bulk Products Sorting
1 Introduction
2 Materials and Methods
3 Results and Discussion
4 Conclusions
References
Method of Calculating the Stress–Strain State of the Cylinder Head of a Liquid-Cooled Transport Diesel Engine
1 Introduction
2 Purpose of Research
3 The Proposed Method of Research
4 Conclusion
References
Specifics of Rock Excavation Process Using Open-Pit Excavator
1 Introduction
2 The Goal and Tasks of the Research
3 Solution of the Research Tasks
4 Conclusion
References
Temperature Condition of Car Exhaust System at Low Ambient Temperatures
1 Introduction
2 Experimental Procedure
3 Experimental Results
4 Analysis of the Experimental Results
5 Conclusion
References
Analysis of a Quarry Mobile Diesel Generator Station During the Moving of an Excavator
1 Introduction
2 Analysis of the “Mobile Station—Excavator” System
2.1 Calculation of the Power of the Station When Moving the Excavator
2.2 Functional Diagram of the “Mobile Station—Excavator” System
2.3 Electrical Safety During the Operation of a Mobile Station
3 Conclusion and Direction of Further Work
References
Experimental and Theoretical Approach for Evaluation of Thermal Loading of Car Brake Discs
1 Introduction
2 Theoretical Approach
3 Experimental Approach
References
Opportunities for Increasing the Operability of Heavy Vehicle Transmissions by Using Thermodynamically Stable Power Semiconductor Devices
1 Introduction
2 General Provisions
3 The Use of Power Semiconductor Devices in Mining Trucks
4 Experiment
5 Conclusion
References
Development of Operational Opportunities for Two-Stage Torque Converters
1 Introduction
2 Problem Statement
3 Results of Engineering
4 Conclusion
References
Conveyor Belt Vibrations
1 Introduction
2 Theoretical Part
3 Conclusion
References
Property-Based Identification and Separation of Rocks in the Drilling Process and Shipment
1 Introduction
2 Analysis of the Problem of Useful Ore Components Loss and Dilution at Extremely Different Ore Quality
3 Evaluation of the Ores Identification Possibility for Further Separation of Various Physical and Mechanical Properties
4 Development of Principles for Evaluating the Strength and Density of Drilled Rocks
5 Methodology for Evaluating Areas of Specific Types of Rocks While Drilling, Milling (Explosion), and Shipment
6 Control System of the Addressed Portioned Shipment of Various Types of Rocks
7 Quality of Addressed Portioned Shipment of Certain Types of Rocks
7.1 CSAPS Performance Verification System
7.2 Intelligent System Performance Evaluation
References
Development of Control Systems for Screw Propellers
1 Introduction
2 Solution of the Problem
3 Conclusion
References
Management of Transport and Logistics System Based on Predictive Cognitive and Fuzzy Models
1 Introduction
2 Cognitive Model for Predictive Assessment of Emergency Situations During Cargo Transportation
2.1 Application of Cognitive Modeling in the Management of Transport Systems
2.2 Fuzzy Cognitive Model-Building for Predictive Assessment of Emergency Situations During Cargo Transportation
3 Predictive Estimation of the Duration of Cargo Transportation and Selection of the Optimal Route
4 Methodological Example of Predictive Assessment of Emergency Situations in the Process of Cargo Transportation
5 Conclusion
References
The Study of Influence of Hole Diameter Within the Inclined-Corrugated Contact Elements on the Hydraulic and Heat-Mass Transfer Characteristics of Cooling Toweraper
1 Introduction
2 Description of the Device and Its Operation
3 Description of the Study and Its Results
4 Conclusion
References
Foamed Heat-Insulating Materials
1 Introduction
2 Main Part
2.1 Technology for Producing Foam Glass
2.2 Thermal Calculation of an Oil Pipeline with Foam Glass Insulation
3 Conclusion
References
Computer Simulation of Microprofile Strain Under Orthogonal Impact at Constrained Load. Part 1
1 Introduction
2 Materials and Methods
3 Results and Discussion
4 Conclusion
References
The Algorithm for Calculating the Milling Error by Mathematical Modeling Method When Machining the Parts
1 Introduction
2 Theoretical Justification
3 Research Results
4 Conclusion
References
Improving Surface Quality in Honing Low-Carbon Steels Pre-treated by Hydrogen Absorption
1 Introduction
2 Relevance
3 Purpose and Objective
4 Theoretical Relevance
5 Practical Relevance
6 Conclusions
References
Research on the Process of Forming Cylindrical Surfaces of Holes During Milling Finish with End Mills Using a Circular Interpolation Strategy
1 Introduction
2 Method
3 Results and Discussions
4 Conclusions
References
Cutting Forces and Roughness During Ball End Milling of Inclined Surfaces
1 Introduction
2 Model of Cutting Forces and Vibrations
3 Experimental Details
4 Results and Discussion
5 Conclusions
References
Optimization Criteria for Modeling of Gear Hone Tooth Engagement and Processed Gear in Terms of Specific Sliding and Contact Pattern Size
1 Introduction
2 Relevance of Deformation Accounting
3 Theoretical Analysis of Gearing Conditions
4 Analytical Research Results
5 Analysis of the Results
6 Conclusions
References
Twist Drilling FEM Simulation for Thrust Force and Torque Prediction
1 Introduction
2 Analysis of Factors Affecting the Cutting Forces During Drilling
3 3D FEM Model Description
4 Results of Numerical Simulation
5 Conclusion and Further Research
References
Modeling Abrasive Grain Interaction with Machined Surface
1 Introduction
2 Problem Statement
3 Theoretical
4 Results
5 Conclusion
References
On the Formation of Groove Geometry Defects Due to Transverse Vibrations of End Mills
1 Introduction
2 Structure
3 Conclusions
References
Peculiarities of Process Conditions and Rail Grinding Modes
1 Introduction
2 Main Part
3 Conclusions
References
Thermal Processes in Surface Plastic Deformation of Difficult-to-Cut Materials
1 Introduction
2 Determination of Maximum Contact Temperatures
3 Conclusion
References
Nonlinear Matching Between Forming Motions as the Basis for Machining Composite Surfaces with Simple Shape Tools
1 Introduction
2 Problem Statement
3 Theoretical
4 Conclusions
References
Chip Formation Analysis in Finish Turning of Alloy and PM Hardened Tool Steels Using Coated and Uncoated PBCN Tools
1 Introduction
2 Experimental Approach
2.1 Workpiece Materials
2.2 Investigation Method and Tools
3 Results and Discussion
3.1 Chip Shape
3.2 Characteristics of the Chip Formation Zone
4 Conclusions
References
Numerical Modeling of Metal Thin Layer Upset Forging with Extrusion into in Forging Cavity Under Stiffening Rib
1 Introduction
2 Main Part
3 Conclusions
References
Calculation of the Stress–Strain State of the Polymer Material in the Cutting Zone
1 Introduction
2 Stresses in the Cutting Zone
3 Shrinkage Coefficient
4 Conclusion
References
Research on Formation of Microgeometry of Work Surface of Grinding Wheel
1 Introduction
1.1 Theoretical Part
1.2 Experimental Part
References
Possibilities of Technology Grinding Steel Parts
1 Introduction
1.1 Theoretical and Experimental Party
References
Calculation of Allowance Value for Grinding with Flap Wheels of Shot-Treated Surface to Ensure Required Roughness
1 Introduction
2 Formation of Model of Allowance for Desired Roughness
3 Conclusion
References
Phasechronometric Turning Monitoring System Testing in Industrial Conditions
1 Introduction
2 Method Description
3 Experimental Results
4 Conclusion
References
Optimizing the Design of a Grooving Tool Plate
1 Introduction
2 Criteria and Their Limit Values to Optimize the Design of a Prefabricated Shaped Grooving Tool
2.1 Choosing the Position of the Plate According to the Type of Installation Relative to the Workpiece
2.2 Choosing a Plate Shape
2.3 Choosing the Plate Mounting System
2.4 Coefficient of Volume Compactability
2.5 Labour Intensity in Plate Production
3 Choosing the RPP Design
4 Conclusion
References
Mathematical Modeling of Cutting Process Output Parameters for Production Technological Preparation and Adaptive Control of Turning and Milling in Digital Production Systems
1 Introduction
2 Relevance
3 Setting of the Problem
4 The Theoretical Part
5 Practical Significance
6 Conclusions
References
Study of Caprolon Turning Using Cutting Fluid
1 Introduction
2 New Method Description
3 Methods of Experimental Research
4 Results of Experimental Studies
5 Conclusions
References
Modeling and Optimization of Tools for Machining Helical Grooves
1 Introduction
2 Mathematical Model
3 Simulation
4 Conclusion
References
Increase in Accuracy of Calculation of Cut Thickness Parameters at Profile Milling
1 Introduction
2 The Reason of Quite Low Accuracy of the Known Formulas for Calculation of Cut Thickness at Machining
3 Influence of Workpiece Feed on Calculation Error of the Maximum Values of the Cut Thickness
4 Conclusion
References
Mathematical Modeling of Energy Characteristics at Profile Milling of Substandard Workpieces
1 Introduction
2 The Time of a Single Cut in the Profile Milling of a Workpiece with a Runout and the Geometric Interpretation of the Main Component of the Cutting Force
3 Graphic Interpretation of the Main Component of the Cutting Force When Milling a Workpiece with a Positive Increment of the Over-Measure
4 Graphical Interpretation of the Main Component of the Cutting Force When Milling a Workpiece with a Negative Increment of the Over-Measure
5 Models of the Main, Radial Components of the Cutting Force and the Power of Profile Milling of the Workpiece with a Runout
6 Conclusion
References
Regression Modeling of Machining Processes
1 Introduction
2 Methods of Measurement and Evaluation of Surface Microrelief
3 Technique of Contactless Evaluation Microrelief Parameters
4 Conclusion
References
Research into the Influence of the Planetary Ball Mill Rotation Frequency on the Limiting Value of the Specific Surface Area of the WC and Co Nanopowders Caused by the Coalescence or Hardening of Particles
1 Introduction
2 Experiment
3 Results and Discussions
4 Conclusion
References
Analytical Simulation of Relations Between Cutting Force and Elastic Distortion of Process System During Plane Grinding
1 Introduction
2 Analytical Simulation of the Relations Between the Cutting Force and the Elastic Distortion of a Process System During Plane Grinding
3 Practical Significance, Proposals and Implementation Results, Experimental Results
4 Conclusions
References
Study of “Burr” Defect Cases in the Bolt Production
1 Introduction
2 Model Development
3 Conclusions
References
Reflection and Refraction Features of Sound Waves at Oblique Incidence on the Interface “Porous Medium–Gas”
1 Introduction
2 Basic Equations
3 Border Conditions
4 Calculation Results
5 Conclusion
References
Forced Cooling Modeling in Grinding
1 Introduction
2 Literature Review
3 Research Methodology
4 Results
5 Conclusions
References
Theory of Energy Conservation as the Basis for the Design of Wire Drawing
1 Introduction
2 Energy Theory of the Drawing Process
3 Configuration Drawing Sequences Providing High Mechanical Properties of the Wire
4 Principles of Building Resource-Saving Wire Drawing Sequences
5 Conclusion
References
Accuracy Assessment of Setting Pressure Change Speed in Aircraft Control Systems of Air-Speed Flight Parameters
1 Introduction
2 Development of an Algorithm for Setting Air Pressure Change Speed and Setting Speed Accuracy Assessment
3 Conclusion
References
Hydrodynamics of Flow in a Flat Slot with Boundary Change of Viscosity
1 Introduction
2 Literature Review
3 Research of Flow in a Flat Slot with Boundary Change of Viscosity
4 Conclusions
References
Increased Measurement Accuracy of Average Velocity for Turbulent Flows in Channels of Ventilation Systems
1 Introduction
2 Literature Review
3 Determination of the Radii of the Average Velocity for Turbulent Flows in the Circular and Ring-Shaped Cylindrical Channels of Ventilation Systems
4 Conclusions
References
Actuation Control System of a Hydraulic Machine Drive Locking Device
1 Introduction
2 Topicality, Scientific Significance of the Issue with a Brief Overview of the Literature
3 Task Statement
4 Theoretical Part
5 Practical Relevance, Suggestions and Results of Implementation, Results of Experimental Investigations.
6 Conclusion
References
Re-engineering of Equipment to Feed the Melting Furnace with Aluminum Charge
1 Introduction
2 The RIFAR CJSC Casting and Melting Complex
3 Equipment to Feed the Melting Furnace with Aluminum Charge
4 Re-engineering of Equipment to Feed the Melting Furnace with Aluminum Charge
5 Conclusion
References
Comprehensive Diagnostics of the State of Metallurgical Equipment
1 Introduction
2 Problem
3 Solution Approach
4 System of Current Diagnostics
5 Method of Solution
References
Research of a Mathematical Model of a Pneumatic Actuator with Energy Recovery
1 Introduction
1.1 The Main Part of the Research
2 Conclusions
References
Adaptive Vibration Protection Systems for Pipelines
1 Introduction
2 Actuality of the Research
3 Statement of the Problem
4 Constructive Solution of the Problem
5 Control Algorithm of Adaptive Vibration Protection Systems for Pipelines
6 Sensor Installation and Error Estimate for Automated Control Systems
7 Calculation Results
8 Novelty, Practical and Scientific Significance of Research
9 Conclusions
References
Hybrid Hydraulic Systems in Technological Processes
1 Introduction
2 Actuality of the Research
3 Statement of the Problem
4 Constructive Solution of the Problem
5 Calculation of Dynamics of Ferrofluid Control Elements
6 Control Algorithm for Mixing and Dosing System with Ferrofluid Control Elements and Its Realization as Program Code
7 Calculation of Required Flow Rate Characteristics in Working Channels
8 Calculation Results
9 Novelty, Practical and Scientific Significance of Research
10 Conclusions
References
Determination of the Main Structural Parameters of the Device for Creating a Two-Layer Annular Flow
1 Introduction
2 Theoretical Basis for the Design of a Device for Creating an Annular Flow
3 Methodology for Determining the Structural Dimensions of the Device to Create a Stable Annular Flow
4 Experimental Evaluation of the Effectiveness of the Device to Create a Two-Layer Annular Flow
4.1 Objects of Study and Their Characteristics
5 Analysis of the Results of Experimental Studies
References
Positional Hydraulic Drive of Rotary Dividing Gears with Increased Speed and Exactitude
1 Problem Statement
1.1 Main Part
2 Result
3 Output
References
The Calculation of Pneumatic Actuator Pipelines
1 Problem Statement
2 Main Part
References
Mathematical Model of Hydraulic Shock Absorber with Feedback
1 Introduction
2 Mathematical Sample Piece
3 Results of Mathematical Simulation
4 Conclusion
References
Making up Model for Forced Cathode Cooling of Casing Powerful Aluminum Electrolyzer with Prebaked Anodes
1 Introduction
2 Setting of the Problem
3 The Results of Experiments
4 Conclusions
References
Heat System for Rigid Wedge Valves
1 Introduction
2 Problem Statement
3 Development of Mathematical Models
4 Calculation of the Heating System Parameters
5 Determination of Inductor Parameters
6 Conclusion
References
Mathematical Modeling of Gas Transportation System Using Graph Theory
1 Introduction
2 Theoretical Part
3 Mathematical Description of Floyd Algorithm
4 Software Implementation of an Algorithm for Building a Directed Graph (Digraph)
5 Computer Modeling of Gas Transportation System Facility Management
6 Conclusion
References
Diagnostics of a Pressure Transmitter Based on Output Signal Noise Characteristics
1 Introduction
2 A Pressure Transmitter and Its Fault Modes
3 Experiment and Results
4 Discussion and Conclusions
References
Environmental Issues of the Railway Transport and Solutions Thereto
1 Introduction
2 Problem Statement
3 Research Questions
4 Theoretical Section
5 Findings
6 Conclusion
References
Disposal of Spent Coolant by Dynamic Membrane
1 Introduction
2 Methods
3 The Results of the Study of the Properties and Parameters of Ultrafiltration with a Composite Membrane PTFEg-PSd
4 Conclusion
References
Effectiveness of the Plasma Neutralization Technology for Supertoxicants
1 Introduction
2 Technique of Researches
3 Results of Research and Their Discussion
4 Conclusions
References
State of the Nickel Alloy Surface Layer After Grinding with a Minimum Quantity Lubrication
1 Introduction
2 Research Methods
3 Results and Discussion
4 Conclusions
References
Comparative Analysis of the Performance of Oscillating and Propeller Stirrers
1 Introduction
2 The Stirring Device Design and Operating Mode
3 Experimental Unit
4 The Study Objects and Their Characteristics
5 Analysis of the Experimental Study Results
References
Environmental Aspects of Trucks Transition to Alternative Type of Fuel
1 Introduction
2 Problems of Environmental Pollution by Transport
3 Computer Simulation of Truck Movement in the AVL CRUISE Program
4 Structural Scheme for Computer Simulation of a Truck
5 The Results of Modeling the Movement of a Car on Diesel and Gas Engine Fuel
6 The Results of Modeling the Environmental Performance of ICE on Different Types of Fuel
7 Conclusion
References
Analysis of Experience of Actual Operation of Gas Turbine Units Capstone C1000. Issues of Concern and Methods for Problem-Solving
1 General Information
2 Analysis of Operational Experience
3 MTU Malfunctions
4 The Problem of Burnout of the Combustion Chamber
5 Repair of Combustion Chambers
6 Results
References
Folding Wind Turbines with Vertical Axis of Rotation as Way to Ensure Safe Operation in Emergency Situations
1 Introduction
2 Ensuring the Safety of Wind Turbines
3 Components of a Folding Rotor
4 Calculation of Generated Power
5 Conclusion
References
New Type of Energy-Saving Oil Treatment Plant
1 Introduction
2 Energy-Saving Oil Separation Units
3 Separator Performance Improvement Proposal
References
Electric Heating of Non-conductive Dispersed Raw Materials in Activated Carbon Production
1 Introduction
2 The Main Part
3 Equations
References
Biofuel Produced From Larch Dry Debarking Waste
1 Introduction
2 Characteristics of Larch Dry Debarking Wastes
3 Biofuel Based on Briquettes Produced from Dry Debarking Wastes
4 Smokeless Biofuel Based on Briquettes Produced from Dry Debarking Wastes
5 Conclusion
References
Improving the Technology of Wood Glued Materials Production
1 Introduction
2 Physical Representations
3 Experiment
4 Discussion
5 Conclusion
References
Hydropower Potential as a Resource for Improving the Water Management Situation in Crimea
1 Introduction
2 Methods and Materials
3 Results
4 Conclusion
References

Citation preview

Lecture Notes in Mechanical Engineering

Andrey A. Radionov Vadim R. Gasiyarov Editors

Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020) Volume II

Lecture Notes in Mechanical Engineering Series Editors Francisco Cavas-Martínez, Departamento de Estructuras, Universidad Politécnica de Cartagena, Cartagena, Murcia, Spain Fakher Chaari, National School of Engineers, University of Sfax, Sfax, Tunisia Francesco Gherardini, Dipartimento di Ingegneria, Università di Modena e Reggio Emilia, Modena, Italy Mohamed Haddar, National School of Engineers of Sfax (ENIS), Sfax, Tunisia Vitalii Ivanov, Department of Manufacturing Engineering Machine and Tools, Sumy State University, Sumy, Ukraine Young W. Kwon, Department of Manufacturing Engineering and Aerospace Engineering, Graduate School of Engineering and Applied Science, Monterey, CA, USA Justyna Trojanowska, Poznan University of Technology, Poznan, Poland Francesca di Mare, Institute of Energy Technology, Ruhr-Universität Bochum, Bochum, Nordrhein-Westfalen, Germany

Lecture Notes in Mechanical Engineering (LNME) publishes the latest developments in Mechanical Engineering—quickly, informally and with high quality. Original research reported in proceedings and post-proceedings represents the core of LNME. Volumes published in LNME embrace all aspects, subfields and new challenges of mechanical engineering. Topics in the series include: • • • • • • • • • • • • • • • • •

Engineering Design Machinery and Machine Elements Mechanical Structures and Stress Analysis Automotive Engineering Engine Technology Aerospace Technology and Astronautics Nanotechnology and Microengineering Control, Robotics, Mechatronics MEMS Theoretical and Applied Mechanics Dynamical Systems, Control Fluid Mechanics Engineering Thermodynamics, Heat and Mass Transfer Manufacturing Precision Engineering, Instrumentation, Measurement Materials Engineering Tribology and Surface Technology

To submit a proposal or request further information, please contact the Springer Editor of your location: China: Dr. Mengchu Huang at [email protected] India: Priya Vyas at [email protected] Rest of Asia, Australia, New Zealand: Swati Meherishi at [email protected] All other countries: Dr. Leontina Di Cecco at [email protected] To submit a proposal for a monograph, please check our Springer Tracts in Mechanical Engineering at http://www.springer.com/series/11693 or contact [email protected] Indexed by SCOPUS. All books published in the series are submitted for consideration in Web of Science.

More information about this series at http://www.springer.com/series/11236

Andrey A. Radionov Vadim R. Gasiyarov •

Editors

Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020) Volume II

123

Editors Andrey A. Radionov South Ural State University Chelyabinsk, Russia

Vadim R. Gasiyarov Mechatronics and Automation Department South Ural State University Chelyabinsk, Russia

ISSN 2195-4356 ISSN 2195-4364 (electronic) Lecture Notes in Mechanical Engineering ISBN 978-3-030-54816-2 ISBN 978-3-030-54817-9 (eBook) https://doi.org/10.1007/978-3-030-54817-9 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

International Conference on Industrial Engineering took place on May 18–22, 2020. The spread of the coronavirus COVID-19 made adjustments to our lives that year, including the organization of the ICIE conference. ICIE was held as a virtual conference. Both oral sections and poster sections were organized by online. Oral sections were implemented as video conferences. Poster sections were in a chat mode. The conference was organized by four universities—South Ural State University (national research university), Moscow Polytechnic University, Platov South-Russian State Polytechnic University, and Volgograd State Technical University. The conference was carried out under financial support of the South Ural State University (national research university). The conference was really large-scaled and international. The international program committee has selected more than 500 reports. The conferees represented 83 Russian cities from the western and central parts to the Far East regions. International participants represented 43 cities and 17 countries. These are countries such as Bulgaria, China, Egypt, France, Germany, India, Iraq, Israel, Italy, Kazakhstan, Malaysia, Poland, Portugal, Tajikistan, Ukraine, Uzbekistan, and Vietnam. The conference participants submitted papers reflecting recent advances in the field of Industrial Engineering, in Russian and English. The conference was organized in 13 sections, including: Part 1. Mechanical Engineering (Machinery and Mechanism Design; Dynamics of Machines and Working Processes; Friction, Wear, and Lubrication in Machines; Design and Manufacturing Engineering of Industrial Facilities; Transport and Technological Machines; Mechanical Treatment of Materials; Industrial Hydraulic Systems; Green Manufacturing); Part 2. Materials Engineering and Technologies for Production and Processing (Polymers, Composites and Ceramics; Steels and Alloys, Metallurgical and Metalworking Technologies; Chemical and Hydrometallurgical Technologies; Surface Engineering and Coatings; Processing and Controlling Technologies).

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vi

Preface

The international program committee has selected 311 papers for publishing in the Lecture Notes in Mechanical Engineering (Springer International Publishing AG). The organizing committee would like to express our sincere appreciation to everybody who has contributed to the conference. Heartfelt thanks are due to authors, reviewers, participants, and to all the team of organizers for their support and enthusiasm which granted success to the conference. Chelyabinsk, Russia

Prof. Andrey A. Radionov Conference Chair

Contents

Justification of Textured Wheels Arrangement in Combined Tool and Modeling the Workpiece Temperature During Grinding . . . . . . . . V. G. Gusev, A. V. Morozov, and E. V. Sobolkov

1

Hydrodynamic Streams of Coolant at Internal Grinding by Textured Wheel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. G. Gusev

10

Peculiarities of Assembly of Bevel and Hypoid Gears with Curved Teeth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. S. Kalashnikov, Yu. A. Morgunov, and P. A. Kalashnikov

19

On Issue of Evaluating the Effectiveness of the Driver-Car-Road-Environment (DCRE) System . . . . . . . . . . . . . A. M. Umirzokov, K. T. Mambetalin, and S. S. Saidullozoda

30

Computer-Aided Algorithm for Nonlinear Optimization of Finishing Operations in Machining Using Precision Cutting Tool . . . . . . . . . . . . M. G. Galkin and A. S. Smagin

39

Calculation of Technological Dimensional Chains by Probability Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. G. Galkin and A. S. Smagin

48

Study of Influence of Magnetic-Pulse Hardening on Cutting Tools Strength and Wear Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L. G. Nikitina and A. V. Volchenkov

59

Solid Modeling of Involute Bevel Gears . . . . . . . . . . . . . . . . . . . . . . . . B. Lopatin, S. Plotnikova, and V. Bruzhas Application of Modal Analysis to Building Simulation Models of Thermal Processes in Machine Tools . . . . . . . . . . . . . . . . . . . . . . . . A. N. Polyakov and I. P. Nikitina

66

75

vii

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Contents

Software Development for the Optimal Parts Location in the Bath Space with the Purpose to Reduce the Non-uniformity of the Coating Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. S. Solovjev, I. A. Solovjeva, and V. V. Konkina

85

Methodology of Measuring Cutters by Using Coordinate Measuring Machine in Automatic Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. P. Nikitina, S. V. Kamenev, and A. N. Polyakov

94

Adaptation of PLM Information System in Industry 4.0 Concept at Stage of Technological Production Preparation . . . . . . . . . . . . . . . . A. Markov, S. Babaev, and I. Yunakov

105

Research of Forming Process of Surface Quality During Machining with Free Abrasive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. A. Kulkov, A. Y. Popov, and A. Y. Korytov

112

Study of Reactive Power Compensation Efficiency for Asynchronous Motors of Metal-Cutting Machine Electric Drives . . . . . . . . . . . . . . . . L. E. Shvartsburg and S. I. Gvozdkova

122

Influence of Technological Inheritance on Accuracy of Assembly of Axisymmetric Shells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. S. Yamnikov, E. N. Rodionova, and I. A. Matveev

130

The Investigations of Surface Micro-Hardness of Experimental Hard Alloy Grades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. V. Fominov, A. A. Ryzhkin, and C. G. Shuchev

141

About One Approach to the Study of Heat Fluxes in the Processes of Drilling Deep Holes Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L. Mironova and L. Kondratenko

148

Simulation Modeling of the Choice of Metal Cutting Tool Coating . . . B. Mokritskii, A. Morozova, and E. J. Sitamov

156

Investigation of Electrochemical Machining Using Nanosecond Voltage Pulse Packets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Lyubimov, V. Krasilnikov, and V. Volgin

163

Modeling Electrical Discharge Machining of Deep Micro-Holes by Rotating Tool-Electrode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Nguyen, V. Volgin, and V. Lyubimov

171

FEM Analysis of Carbide Insert Strength for Milling Application . . . . V. G. Shalamov, S. D. Smetanin, and I. S. Boldyrev Study and Evaluation of Stability of Technical Processes for Machine-Building Products at Stage of Serial Production . . . . . . . . M. P. Kukhtik, A. M. Makarov, and N. V. Fedorova

180

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Contents

Studying the Impact the Microrelief of Teeth Surface Has on Gear Operational Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. G. Karavanova and A. S. Kalashnikov How the Parameters of an Agricultural Machine and Tractor Unit Affect the Wear of Friction Pairs in a Diesel Engine When Used for Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. P. Antipin, M. Ya. Durmanov, and O. A. Mikhailov

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207

Oil Consumption Through Burning in Heavy-Duty Operation of an Agricultural Machine and Tractor Unit . . . . . . . . . . . . . . . . . . . M. Ya. Durmanov, B. G. Martynov, and S. V. Spiridonov

216

Modeling of Turbine Rotor Journal Machining with Location on Bearing and with Center Pregrinding . . . . . . . . . . . . . . . . . . . . . . . A. V. Shchurova

224

Industrial Manipulating Robot Finite Element Mesh Generation Based on Robot Voxel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. I. Shchurova

232

Axis Determination Based on Regression for Calculation of Virtual Pitch Thread Diameter Using a Point Cloud from CMM . . . . . . . . . . . I. A. Shchurov

240

Improving Technology of Manufacturing Preparations for Brackets of Heavy Truck Cars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. V. Shaparev and I. A. Savin

248

Methodology and Tools for Computer-Aided Calculation of Characteristics of Electromechanical Clamping Drive Actuated by Induction Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Prydalnyi, Y. Kuznetsov, and V. Lyshuk Road Fuel Consumption by Dump Truck in Mountain Conditions . . . A. M. Umirzokov, K. T. Mambetalin, and S. S. Saidullozoda

256 267

Very Hard Titanium Carbosilicide Coatings to Protect Parts of Energy Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. R. Shekhtman, N. A. Sukhova, and M. Sh. Migranov

278

Marking Metal Products by Anodic Etching by Means with Semiconductor Electrode Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . V. V. Glebov

285

Features of Design and Practical Application of Digital Twin of Internal Grinding Operation with CNC . . . . . . . . . . . . . . . . . . . . . . A. V. Akintseva, A. V. Prokhorov, and S. V. Omelchenko

292

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Contents

Assessing Cutting Force: A Study of Varying Internal Grinding Wheels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. V. Akintseva, A. V. Prokhorov, and A. A. Kopyrkin

300

Analysis of the Influence of Installation Deformations of Diesel Cylinder on Its Operating Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . I. E. Agureev, R. N. Khmelev, and K. Yu. Platonov

308

Studies on the Effect of Output Parameters on Productivity When Turning Titanium Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. V. Savilov and A. G. Serebrennikova

316

The Study of Stress State Uniformity Along with the Thickness of the Constructive Element of Housing High-Pressure Vessels Deformed by Conjugated Elements of Physical Separation of Heating Elements Embedded in the Vessel Housing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Elovenko and V. Kräusel Modeling Metal Removal in Automatic Circular Grinding Cycles Taking into Account Process Dynamics . . . . . . . . . . . . . . . . . . . . . . . . P. P. Pereverzev, A. D. AlMawash, and M. K. Alsigar Development of a Method for Verification of API Thread Measurement Results by Comparing Them with Measurement Results of Reference Measuring Instruments . . . . . . . . . . . . . . . . . . . . D. S. Lavrinov

323

335

344

Calculation of Contact Tensions in the Process of Thermofrictional Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. Pokintelitsa and E. Levchenko

353

Effect of Mode Amplitude on Power Consumption in Vibrating Mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. Dubkova, V. Kharkov, and B. Ziganshin

362

Multi-stages to Ensure Quality Control of Designing and Production at External Cylindrical Grinding Machines . . . . . . . . . . . . . . . . . . . . . M. K. Alsigar, P. P. Pereverzev, and A. D. AlMawash

370

Design of High-Efficiency Device for Gas Cleaning from Fine Solid Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Zinurov, A. Dmitriev, and V. Kharkov

378

Geometry of Six-Dimensional Space for Engineering . . . . . . . . . . . . . . V. E. Lelyukhin, O. V. Kolesnikova, and E. V. Ruzhitskaya

386

Providing the Working Accuracy of CNC Metal-Cutting Machine . . . . O. Yu. Kazakova and L. B. Gasparova

395

Contents

xi

Performance Study of Mills with Amorphous Silicon-Carbon Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Vlasov, V. Vlasova, and A. Zentsov

403

Fatigue Test Optimization for the Aircraft Engine Based on the Life Cycle Information Support and Modeling . . . . . . . . . . . . . . . . . . . . . . N. Kondratyeva and S. Valeev

410

Reduction of Static Elastic Displacements During Processing on Vertical Milling Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R. M. Khusainov, A. R. Sabirov, and V. V. Lozinsky

419

Effect of Wire Arc Additive Manufacturing Process Parameters on Deposition Behavior of Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. A. Kulikov, A. E. Balanovskii, and M. V. Grechneva

426

Study of the Axial Contact Points Method Applied When End-Milling Titanium Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. V. Nikitenko, A. V. Savilov, and A. S. Pyatykh

436

Investigation of the Effect on the Efficiency of Hot Die Forging Operations Cutting Off and Heating Blanks from Rolled Round Bar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. V. Telegin The Express-Method for Determining the Workability of Structural Steels Using the Indicator of Specific Cutting Work . . . . . . . . . . . . . . . A. V. Karpov Digital Space of Small Enterprises in Engineering . . . . . . . . . . . . . . . . V. F. Bulavin, T. G. Bulavina, and A. S. Stepanov

445

453 462

Some Features of the Pisarenko–Lebedev Generalized Strength Criterion Application for Long-Term Strength Calculations . . . . . . . . A. V. Belov, A. A. Polivanov, and N. G. Neumoina

469

Evaluation of the Impact of the Actual Geometry of the Planetary Gearing on Its Capabilities in the KISSSYS Program . . . . . . . . . . . . . A. V. Plyasov and N. N. Trushin

477

Predictive Simulation Tool for Control Over Precision of Geometrically Complex Mould Making at Preproduction Engineering Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Lukina, S. Ivannikov, and M. Krutyakova A Tool Management System Design Using Object-Oriented and Functional Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Krylov, N. Kozlovtseva, and V. Barabanov

485

493

xii

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Classification of Technologies for Obtaining Geometric Configuration of Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. E. Lelyukhin and O. V. Kolesnikova Methods of Designing Technological Trajectories of Single Layer of Laser Powder Cladding on Flat Surfaces of Part Model in CAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Rodionov, A. Lyukhter, and V. Prokoshev Aeroacoustic Cartography as Method of Non-destructive Testing of Turbine Blades Based on Fiber Optic Sensor Systems . . . . . . . . . . . V. Yu. Vinogradov, O. G. Morozov, and R. Z. Gibadullin Exploratory Design of Technical Systems with Fluid and Gas Working Body Based on Heuristic Modeling of Physical Operating Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. A. Yakovlev, S. G. Postupaeva, and N. V. Fedorova

502

509

520

529

Computer-Aided Design of Precast End Mills Based on the Parametric Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. V. Bogoyavlensky and A. V. Shatilo

538

Modeling Cutting Force During Internal Grinding with Different Wheel Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. V. Akintseva and P. P. Pereverzev

548

Fuzzy Formalization of Individual Quality Criteria for Quality Level Evaluation by Using Two-Level Optimization Model . . . . . . . . . . . . . . G. Pipiay, L. Chernenkaya, and V. Mager

557

Programming Industrial Robots for Wire Arc Additive Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. A. Kulikov, A. V. Sidorova, and A. E. Balanovskii

566

Metrology Assurance of Assembling DESY’s XFEL Free-Electron Laser Accelerator of Elementary Particles . . . . . . . . . . . . . . . . . . . . . . Hristo Radev, Dimitar Diakov, and Hristiana Nikolova

577

Modeling Geometric Obstacles in the Assembly of Complex Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Bozhko

584

Information Model of the Automated System of Assembling Plant Identification and Traceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Nosenko, A. Silaev, and S. Grednikov

596

Modeling of Production Process Energy Characteristics in Mechanical Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Salnikov and Yu. Frantsuzova

606

Contents

Control Algorithm for Compensated Tripod-Based Manipulators . . . . V. Zhoga, V. Dyashkin-Titov, and N. Vorob’eva Modeling and Assessment of Production Cycle Information Entropy Under Joint Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R. Fatkieva, E. Evnevich, and A. Vasiliev

xiii

618

627

Ensuring Stability of Wheeled Vehicles When Driving on Slopes . . . . . I. N. Starunova, A. V. Starunov, and S. Yu. Popova

635

Conceptual Design Methodics of Hybrid Car Traction Drive . . . . . . . . A. Ch. Khatagov, S. B. Adzhimanbetov, and Z. A. Khatagov

643

Results of Computer Simulation of a Braking Vehicle Energy Recovery System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. I. Posmetev, V. O. Nikonov, and V. V. Posmetev

652

Investigation into Operational Reliability of Vehicle Electronic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Y. V. Bazhenov, V. P. Kalyonov, and M. Y. Bazhenov

662

Numerical Modeling of a Railway Wheel Profile in a Fillet Radius Space Using the Uniform Search Method . . . . . . . . . . . . . . . . . . . . . . . L. B. Tsvik and E. V. Zenkov

670

Features of Development of Structures of Extruders . . . . . . . . . . . . . . V. Kushnir, N. Gavrilov, and I. Koshkin Research of Dynamics of Seat Air Suspension with Possibility of Vibration Energy Recuperation Under Action of Typical Harmonic Disturbances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Lyashenko, P. Potapov, and A. Iskaliev Functional Tuning of Car Suspension . . . . . . . . . . . . . . . . . . . . . . . . . . D. Kushaliyev, L. T. Shulanbayeva, and B. A. Ermanova Approaches to Formation of Car Service Modes in Case of Complete or Insufficient Information on Operational Reliability of Car Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Grigoriev and V. Zenchenko Vibration Diagnostics of Swivel Suspension Elements of Automotive Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. N. Novikov, M. D. Tebekin, and S. V. Kolpakova Indicator Analysis of Injection Process of Different Composition Mixtures of Diesel Fuel and Palm Oil at Changing of Speed Mode of Diesel Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. V. Kurapin, E. A. Salykin, and K. E. Tshibanda

678

686 694

702

712

720

xiv

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Selection of Air Cooled Diesel Engine Boosting Level Considering Process Deviations of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. N. Ilyushin, A. M. Lartsev, and E. A. Fedyanov Analysis of Constructive Reliability and Maintainability of the Contemporary Electronic Control Units of the Active Safety Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Dygalo, M. Lyashenko, and O. Kosov Simulation of Change in Reliability of Rope System Motion Mechanism in Mobile Ropeway Complex . . . . . . . . . . . . . . . . . . . . . . . A. V. Lagerev, V. I. Tarichko, and I. A. Lagerev Interaction of a Large Tire with the Soil . . . . . . . . . . . . . . . . . . . . . . . A. V. Vasilenko, S. A. Ivanov, and V. I. Gilmutdinov Improving Technical Readiness of Wheeled and Tracked Vehicles in Severe Climatic Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. A. Gorbunov and A. M. Burgonutdinov Modeling the Equipment for Mechanical Bulk Products Sorting . . . . . L. V. Konchina, M. G. Kulikova, and A. V. Borisov Method of Calculating the Stress–Strain State of the Cylinder Head of a Liquid-Cooled Transport Diesel Engine . . . . . . . . . . . . . . . . . . . . A. N. Gotz and V. S. Klevtsov Specifics of Rock Excavation Process Using Open-Pit Excavator . . . . . O. Lukashuk, K. Letnev, and A. Komissarov

730

737

745 755

762 771

778 787

Temperature Condition of Car Exhaust System at Low Ambient Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. G. Boyarshinov and N. I. Kuznetsov

795

Analysis of a Quarry Mobile Diesel Generator Station During the Moving of an Excavator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. I. Malafeev and S. S. Malafeev

803

Experimental and Theoretical Approach for Evaluation of Thermal Loading of Car Brake Discs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Dygalo and I. Zhukov

811

Opportunities for Increasing the Operability of Heavy Vehicle Transmissions by Using Thermodynamically Stable Power Semiconductor Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. Savin, R. Polyakov, and Fu Sheng-ping Development of Operational Opportunities for Two-Stage Torque Converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. N. Trushin

821

828

Contents

Conveyor Belt Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G. G. Kozhushko, M. D. Lukashuk, and O. A. Lukashuk Property-Based Identification and Separation of Rocks in the Drilling Process and Shipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. A. Shigina, A. O. Shigin, and A. A. Stupina Development of Control Systems for Screw Propellers . . . . . . . . . . . . . Y. Liberman, N. Shonokhova, and O. Lukashuk Management of Transport and Logistics System Based on Predictive Cognitive and Fuzzy Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Asanov and I. Myshkina The Study of Influence of Hole Diameter Within the InclinedCorrugated Contact Elements on the Hydraulic and Heat-Mass Transfer Characteristics of Cooling Toweraper . . . . . . . . . . . . . . . . . . A. Dmitriev, I. Madyshev, and A. Khafizova Foamed Heat-Insulating Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. A. Smoliy, E. A. Yatsenko, and A. A. Chumakov

xv

837

845 857

864

874 883

Computer Simulation of Microprofile Strain Under Orthogonal Impact at Constrained Load. Part 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . N. V. Vulykh and A. N. Vulykh

891

The Algorithm for Calculating the Milling Error by Mathematical Modeling Method When Machining the Parts . . . . . . . . . . . . . . . . . . . N. I. Oleynik, E. V. Malkova, and S. Yu. Popova

900

Improving Surface Quality in Honing Low-Carbon Steels Pre-treated by Hydrogen Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . O. A. Kursin, X. B. Pham, and A. A. Zhdanov

909

Research on the Process of Forming Cylindrical Surfaces of Holes During Milling Finish with End Mills Using a Circular Interpolation Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. A. Stelmakov, M. R. Gimadeev, and D. D. Iakuba Cutting Forces and Roughness During Ball End Milling of Inclined Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. R. Gimadeev, V. A. Stelmakov, and V. V. Gusliakov Optimization Criteria for Modeling of Gear Hone Tooth Engagement and Processed Gear in Terms of Specific Sliding and Contact Pattern Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yu. Bagaiskov Twist Drilling FEM Simulation for Thrust Force and Torque Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. S. Boldyrev and D. Y. Topolov

917

926

938

946

xvi

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Modeling Abrasive Grain Interaction with Machined Surface . . . . . . . A. M. Kozlov, S. K. Ambrosimov, and A. A. Kozlov On the Formation of Groove Geometry Defects Due to Transverse Vibrations of End Mills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. A. Dyakonov, S. V. Sergeev, and A. V. Baev Peculiarities of Process Conditions and Rail Grinding Modes . . . . . . . I. Yu. Orlov, S. A. Krukov, and N. V. Baydakova

953

961 969

Thermal Processes in Surface Plastic Deformation of Difficult-to-Cut Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. Papsheva and O. Akushskaya

977

Nonlinear Matching Between Forming Motions as the Basis for Machining Composite Surfaces with Simple Shape Tools . . . . . . . . S. K. Ambrosimov and A. M. Kozlov

984

Chip Formation Analysis in Finish Turning of Alloy and PM Hardened Tool Steels Using Coated and Uncoated PBCN Tools . . . . . M. Ociepa, M. Jenek, and O. V. Yagolnitser

991

Numerical Modeling of Metal Thin Layer Upset Forging with Extrusion into in Forging Cavity Under Stiffening Rib . . . . . . . . . O. A. Nikitina and T. M. Slobodyanik

999

Calculation of the Stress–Strain State of the Polymer Material in the Cutting Zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1006 O. Erenkov, I. Lopushanskii, and D. Yavorskii Research on Formation of Microgeometry of Work Surface of Grinding Wheel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1013 T. N. Ivanova and Witold Biały Possibilities of Technology Grinding Steel Parts . . . . . . . . . . . . . . . . . . 1022 T. N. Ivanova Calculation of Allowance Value for Grinding with Flap Wheels of Shot-Treated Surface to Ensure Required Roughness . . . . . . . . . . . 1029 V. P. Koltsov, V. B. Rakitskaya, and E. V. Tardybaeva Phasechronometric Turning Monitoring System Testing in Industrial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1036 D. D. Boldasov, A. S. Komshin, and A. B. Syritskii Optimizing the Design of a Grooving Tool Plate . . . . . . . . . . . . . . . . . 1045 S. V. Grubyi and P. A. Chaevskiy

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xvii

Mathematical Modeling of Cutting Process Output Parameters for Production Technological Preparation and Adaptive Control of Turning and Milling in Digital Production Systems . . . . . . . . . . . . . 1055 A. R. Ingemansson Study of Caprolon Turning Using Cutting Fluid . . . . . . . . . . . . . . . . . 1064 O. Erenkov, I. Lopushanskii, and D. Yavorskii Modeling and Optimization of Tools for Machining Helical Grooves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1071 A. A. Troshin, A. V. Kochetkov, and O. V. Zakharov Increase in Accuracy of Calculation of Cut Thickness Parameters at Profile Milling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1080 A. A. Fomin, R. G. Safin, and N. M. Terekhin Mathematical Modeling of Energy Characteristics at Profile Milling of Substandard Workpieces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1088 A. A. Fomin, R. V. Yudin, and D. G. Riabushkin Regression Modeling of Machining Processes . . . . . . . . . . . . . . . . . . . . 1101 Yu. L. Tchigirinsky, N. V. Chigirinskaya, and Z. S. Tikhonova Research into the Influence of the Planetary Ball Mill Rotation Frequency on the Limiting Value of the Specific Surface Area of the WC and Co Nanopowders Caused by the Coalescence or Hardening of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1109 M. Dvornik and E. Mikhailenko Analytical Simulation of Relations Between Cutting Force and Elastic Distortion of Process System During Plane Grinding . . . . . . . . . . . . . . 1116 P. Pereverzev and S. Yudin Study of “Burr” Defect Cases in the Bolt Production . . . . . . . . . . . . . . 1124 S. A. Kurguzov, M. V. Nalimova, and A. A. Kalchenko Reflection and Refraction Features of Sound Waves at Oblique Incidence on the Interface “Porous Medium–Gas” . . . . . . . . . . . . . . . . 1131 L. F. Sitdikova and I. K. Gimaltdinov Forced Cooling Modeling in Grinding . . . . . . . . . . . . . . . . . . . . . . . . . 1140 N. V. Lishchenko, V. P. Larshin, and I. V. Marchuk Theory of Energy Conservation as the Basis for the Design of Wire Drawing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1150 L. V. Radionova, R. A. Lisovsky, and V. D. Lezin Accuracy Assessment of Setting Pressure Change Speed in Aircraft Control Systems of Air-Speed Flight Parameters . . . . . . . . . . . . . . . . . 1164 A. Markov

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Hydrodynamics of Flow in a Flat Slot with Boundary Change of Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1172 V. Sokolov Increased Measurement Accuracy of Average Velocity for Turbulent Flows in Channels of Ventilation Systems . . . . . . . . . . . . . . . . . . . . . . . 1182 V. Sokolov Actuation Control System of a Hydraulic Machine Drive Locking Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1191 N. A. Fomenko, S. V. Aleksikov, and S. G. Artemova Re-engineering of Equipment to Feed the Melting Furnace with Aluminum Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1198 A. V. Nefedov, V. V. Svichkar, and O. N. Chicheneva Comprehensive Diagnostics of the State of Metallurgical Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1205 S. N. Rednikov, E. N. Akhmedyanova, and D. M. Zakirov Research of a Mathematical Model of a Pneumatic Actuator with Energy Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1212 A. N. Sirotenko and S. A. Partko Adaptive Vibration Protection Systems for Pipelines . . . . . . . . . . . . . . 1219 K. V. Naigert and V. A. Tselischev Hybrid Hydraulic Systems in Technological Processes . . . . . . . . . . . . . 1228 K. V. Naigert and V. A. Tselischev Determination of the Main Structural Parameters of the Device for Creating a Two-Layer Annular Flow . . . . . . . . . . . . . . . . . . . . . . . 1237 L. A. Ilina, M. S. Krasnodubrovsky, and N. A. Dukov Positional Hydraulic Drive of Rotary Dividing Gears with Increased Speed and Exactitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1245 V. S. Sidorenko, D. A. Korotych, and S. P. Prikhodko The Calculation of Pneumatic Actuator Pipelines . . . . . . . . . . . . . . . . . 1252 D. D. Dymochkin, D. A. Korotych, and A. N. Kharchenko Mathematical Model of Hydraulic Shock Absorber with Feedback . . . 1262 V. I. Grishchenko, M. S. Kilina, and G. A. Dolgov Making up Model for Forced Cathode Cooling of Casing Powerful Aluminum Electrolyzer with Prebaked Anodes . . . . . . . . . . . . . . . . . . 1271 I. A. Sysoev Heat System for Rigid Wedge Valves . . . . . . . . . . . . . . . . . . . . . . . . . . 1277 A. A. Bazarov, N. V. Bondareva, and A. A. Navasardyan

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xix

Mathematical Modeling of Gas Transportation System Using Graph Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1288 K. Syzrantseva, V. Rumyantsev, and M. Alfyorova Diagnostics of a Pressure Transmitter Based on Output Signal Noise Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1298 E. S. Tugova, D. D. Salov, and O. Yu. Bushuev Environmental Issues of the Railway Transport and Solutions Thereto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1308 A. V. Muratov and V. V. Lyashenko Disposal of Spent Coolant by Dynamic Membrane . . . . . . . . . . . . . . . . 1314 D. D. Fazullin, G. V. Mavrin, and L. I. Fazullina Effectiveness of the Plasma Neutralization Technology for Supertoxicants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1323 S. V. Anakhov, A. V. Matushkin, and Yu A. Pyckin State of the Nickel Alloy Surface Layer After Grinding with a Minimum Quantity Lubrication . . . . . . . . . . . . . . . . . . . . . . . . . 1331 A. P. Mitrofanov, A. A. Isaeva, and V. A. Nosenko Comparative Analysis of the Performance of Oscillating and Propeller Stirrers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1340 L. A. Ilina, A. A. Shagarova, and I. O. Goncharov Environmental Aspects of Trucks Transition to Alternative Type of Fuel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1348 A. G. Vozmilov, R. Yu. Ilimbetov, and D. V. Astafev Analysis of Experience of Actual Operation of Gas Turbine Units Capstone C1000. Issues of Concern and Methods for Problem-Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1358 A. S. Rychkova, V. Y. Sokolov, and S. A. Naumov Folding Wind Turbines with Vertical Axis of Rotation as Way to Ensure Safe Operation in Emergency Situations . . . . . . . . . . . . . . . 1367 A. Miroshnichenko, A. Kulganatov, and E. Sirotkin New Type of Energy-Saving Oil Treatment Plant . . . . . . . . . . . . . . . . . 1376 B. H. Gaitov, A. V. Samorodov, and V. A. Kim Electric Heating of Non-conductive Dispersed Raw Materials in Activated Carbon Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1384 V. Kushnir, I. Koshkin, and S. Ibragimova Biofuel Produced From Larch Dry Debarking Waste . . . . . . . . . . . . . . 1393 Yu.Ya. Simkin and S. A. Voinash

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Improving the Technology of Wood Glued Materials Production . . . . . 1402 S. Isaev, O. Erenkov, and I. Galanina Hydropower Potential as a Resource for Improving the Water Management Situation in Crimea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1409 R. Y. Zakharov and N. E. Volkova

Justification of Textured Wheels Arrangement in Combined Tool and Modeling the Workpiece Temperature During Grinding V. G. Gusev(B) , A. V. Morozov, and E. V. Sobolkov Vladimir State University Named After Alexander and Nikolay Stoletovs, 87, Gorky Street, Vladimir 600000, Russia [email protected]

Abstract. The article considers the perspective of combined grinding by textured wheels. It offers to unite technological capabilities of the combined processing with the advantages of the textured grinding wheels. It is established that the elastic displacements of the spindle axis at static unbalance of the combined tool is significantly higher than those with the moment unbalance, so to reduce the vibration level of the spindle, it is recommended to place a coarse- and finegrained wheel on the spindle so that the angle between the main vectors of the unbalances of these wheels is equal to 180. Workpiece temperature at simultaneous grinding by the textured coarse- and fine-grained wheel and by usual wheels with the continuous cutting surface was made using modern Cosmos Works software product. It allowed comparing the temperature of workpieces processed by the known and offered grinding tools. The results of modeling showed that the lowest surface temperature is generated at the simultaneous processing by the textured coarse- and fine-grained wheel at the same time temperature of the processed surface increases slightly, if to carry out process of the combined grinding by the textured coarse- and a fine-grained wheel with the continuous cutting surface. Simultaneous preliminary and final processing of workpiece on one machine tool by the textured wheels with various markings of abrasive material open new ways of reduction of thermal tension in a cutting zone, roughness of the processed surface, and increase in productivity of grinding operations. Keywords: Combined grinding · Textured wheel · Main unbalance vector · Elastic displacement · Temperature modeling

1 Introduction Grinding processes provide high details about the quality of mechanical engineering [1, 2]. Further increase in grinding efficiency is possible by creation of new abrasive materials [3], combined [4], single-component [5], high-porous [6], discrete [7–12], textured [13–15] grinding wheels, by effective cooling of a cutting zone [16, 17], dynamics management of grinding [18–20], etc. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_1

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Russia, England, China, USA, Japan, Sweden, Kazakhstan, Ukraine, and other countries made researches of the textured abrasive and diamond wheels [13–15]. There is a significant benefit comparing to usual grinding tools that have a continuous cutting surface. Great Britain and China created the international association [13] and made a research of grinding processes by the textured wheels of metals, alloys, of high-precision optical lenses, and other responsible products. The success of this research direction is caused by the positive technological effects reached by using these tools. Besides, works for increasing in productivity of grinding operations by the uniting of preliminary and final processing on one machine tool without replacement of a coarse on the fine-grained wheel are carried out [4]. The combined grinding by textured wheels in scientific and technical literature was not considered. Realization of the combined processing by coarse- and fine-grained textured wheel [7–11] opens new ways of increasing in productivity of grinding operations.

2 The Tool for the Combined Grinding by Coarseand Fine-Grained Textured Wheel The tool for the combined grinding consists of fine-grained 1, coarse-grained 2 wheel between which is located a laying 3 (Fig. 1a) [21]. Wheels 1 and 2 are fixed on a spindle 4 of machine tool for flat peripheral grinding. On the cutting surface of both grinding wheels by high concentrated energy streams (a laser beam or a hydro-abrasive stream of high pressure) the radial holes 5 and 6 are executed. The workpiece 7 is fixed on a machine tools’s table (number 8 at Fig. 1). Coarse-grained grinding wheel 2 is used for preliminary processing of workpiece. Diameter Dpr of cutting surface of the wheel 2 (Fig. 1b, view A) on (10–20) micrometers is less than diameter Do of fine-grained wheel 1 which is carrying out final processing.

Fig. 1. The combined tool with textured coarse- and fine-grained wheels.

While a fine-grained wheel produces allowance measured by micrometers, a coarsegrained wheel produces allowance measured by tenths of millimeter. Therefore a workpiece (number 7 Fig. 1) temperature increases significantly. In order to decrease the temperature in both cases, a radius of holes (number 5 and 6 at Fig. 1) should be calculated

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by the formula: r < 0.5L,

(1)

where L—a length of contact arch of a grinding wheel with workpiece. The fine-grained wheel 1 is intended for formation of low roughness and waviness of the processed surface and owing to removal of a small allowance, thermal emissions in workpiece at grinding by this wheel are insignificant. The radius of radial holes in a finegrained wheel is less than in coarse-grained because an arch length of contact of wheel 1 with workpiece 7 is less than of wheel 2. Before installation on a spindle of machine tool the wheels 1 and 2 have to be balanced by use of a stand or balancing machine tool, and because of impossibility of balancing with an absolute accuracy each of wheels has a residual main unbalance vector. As a balancing of coarse- and fine-grained grinding wheel is carried out with use of the same balancing means, the residual main unbalance vector for each of wheel will be same and equal Dst . The main unbalance vector Dst at rotation of a grinding wheel leads to the centrifugal force determined by the formula: Q = Dst ω2 ,

(2)

where ω—angular velocity of grinding wheel. Vibration level of a spindle at the combined grinding depends on a type of unbalance which arise after installation and fixing both wheels on a spindle. Static unbalance is, if the angle α between the vectors Dst1 and Dst2 (Fig. 1c) is equal 0, moment unbalance – at α = 180° (Fig. 2a), and dynamic unbalance – at 180° < 0 < α < 180° and 180° ym . Thus, for reduction of vibration level of a spindle an angle between vectors Dst of both wheels should be equal 180° (Fig. 1a, b). At such angular arrangement of coarse- and fine-grained wheels instead of the greatest possible main unbalance vector of the tool 2Dst arises a main unbalance moment determined by a formula: RA = RB =

MD = Dst h = 0.5Dst (Bo + Bpr + 2lk ),

(8)

where h—is a shoulder of vectors Dst (the same vectors Q) couple; Bo , Bpr , respectively, a height of fine- and coarse-grained wheel; lk— a thickness of laying 3 (Fig. 1a). The combined grinding tool works as follows. Operator 9 serving the machine tool moves a workpiece 7 in direction of an arrow A under a coarse-grained wheel 2. Include rotation of a spindle 4 in the direction of an arrow Dr and lower the tool until easy contact of the workpiece with a coarse-grained wheel (until emergence of a small spark). Bring the tool out of contact with workpiece by moving a Table 8 in the longitudinal direction on an arrow Dspr . Adjust the machine tool on the required cutting mode (cutting depth, longitudinal, and cross-feed). The grinding process is carried out at the rotating instrument and movement of workpiece in the longitudinal Dspr and cross Dsp directions. At the included cross-feed a workpiece 7 discretely moves to operator 9 (to the left). First, the workpiece is processed by a coarse-grained wheel 2, then a fine-grained wheel 1 comes into operation, which forms the required microgeometry of the surface. The combined grinding comes to end at machining of a workpiece by a fine-grained wheel 1.

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3 Modeling Technique of Workpiece Temperature at the Combined Grinding by the Textured Coarse- and Fine-Grained Wheel When the surface is simultaneously treated with a coarse-and fine-grained wheel, heat flows occur which differ from the heat flows in traditional grinding. This circumstance leads to the need for temperature analysis for combined grinding, which can be carried out by continuous and textured wheels, which allow you to use different characteristics of the abrasive material. Taking this into account temperature studies of the treated surface were carried out with three schemes of combined grinding: • coarse- and fine-grained grinding wheel has a continuous cutting surface (the first scheme); • coarse-grained wheel is textured, fine-grained wheel has a continuous cutting surface (the second scheme); • coarse- and fine-grained grinding wheels are textured (the third scheme). Textures of grinding wheels formed by cutting the radial holes 1, located on the short 2 and long 3 lines, parallel to an axis of the tool [8]. Radial holes have a diameter 2r, are displaced relative each other on a half of an axial step T os (Fig. 3) and are located in the district direction with a step T o (section A-A).

Fig. 3. The cutting surface of a textured grinding wheel.

Modeling of temperature of the processed surface carried out at the following geometrical characteristics of the combined tool: height of the wheel for preliminary grinding Bpr = 20 mm, height of the wheel for final grinding Bo = 10 mm, thickness of laying 3 δ = 2 mm (Fig. 1a), diameter of the cutting surface of wheel for preliminary grinding Dpr = 250 mm, for final grinding—Do = 250.01 mm. The sizes of the processed workpiece: length—100 mm, width—100 mm, height—10 mm.

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Temperature was modeled in the Solid Works CAD-system by method of the final and element analysis (DEM) which provides a splitting of solid-state model of workpiece into separate final elements-tetrahedrons and creation of a grid. The solid-state model of workpiece consisted of elements 1-mm long and width equal to the sum of threefold length of contact arch of a grinding wheel with workpiece. A full length of solid-state model was determined by summation of heights of wheels for preliminary and final grinding. The heat flux q is generated by coarse- and fine-grained wheels. The surfaces which are not contacting with grinding wheels were cooled as a result of the convective heat exchange determined by heat-transfer coefficient. Used heat-physical characteristics of the processed steel 9HS: density ρ = 7830 kg/m3 ; heat conductivity coefficient λ = 27 W/m*K; the specific heat c = 640 J/kg*K. The maximum contact areas of a coarse- and fine-grained grinding wheel with the workpiece, the heating and cooling time of the cutting zone, and the density of the heat flow entering the workpiece are determined by calculation. The workpiece was processed in the following cutting modes: longitudinal feed Dspr = 15 m/min, transverse feed Dsp = 3 mm/table pass, cutting speed v = 35 m/s; allowance removed by a wheel for pre-grinding zpr = 60, for final grinding zo = 5 micrometers.

4 Modeling Results of Temperature of Processed Surface and Their Analysis As a result of modeling the temperature at the first scheme, when the coarse- and finegrained grinding wheels are made continuous, maximum surface temperature in contact with coarse-grained wheel, made 309,1 °C, and with fine-grained wheel −102,2 °C. In the second scheme of processing by a textured coarse-grained wheel, the maximum temperature was 264 °C which is 15% less than the temperature of 309.1 °C formed in the first scheme. The maximum temperature of the workpiece when grinding by finegrained wheel according to the second scheme was 90 °C (Fig. 4a, b) which is 12% lower than the temperature 102 °C formed during the first scheme. At the third scheme with use of textured fine-grained wheel the maximum temperature of the processed surface was 85.9 °C (Fig. 5a, b) that is 5% less than temperature 90.9 °C (Fig. 4a, b) received at the second scheme. Thus, results of modeling showed that the minimum temperature of the processed surface arises at the combined grinding by textured coarse- and fine-grained wheels. Temperature at grinding by the textured fine-grained wheel insignificantly is less in comparison with grinding by fine-grained wheel with a continuous cutting surface therefore for processing of workpieces it is recommended to use simultaneous grinding by textured coarse-grained and fine-grained wheel with continuous cutting surface. Observance of this recommendation will allow not only to reduce significantly thermal tension of the combined flat peripheral grinding, but also to provide small roughness of the processed surface.

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Fig. 4. The surfaces processed by a textured coarse- and continuous fine-grained wheel (a). Temperature field (b).

Fig. 5. The surfaces processed by both textured grinding wheels (a) and a field of temperature (b).

5 Conclusion 1. A prior information analysis determined the important directions of improvements of grinding processes and wheels designs, among which the textured wheels differ in a number of advantages in comparison with the known grinding wheels. The new grinding tool is worked out, that allows to carry out at the same time preliminary and final processing of workpieces by textured wheels. 2. Elastic displacements of a spindle axis under the influence of main unbalance vector of combined tool is much more, than under of main unbalance moment. For reduction of vibration level of a spindle an angle between the main unbalance vectors of both textured wheels should be equal to 180°. At such angular arrangement of coarse- and fine-grained wheels instead of the greatest possible main unbalance vector arises in combined tool a main unbalance moment.

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3. Minimum temperature arises at using textured coarse- and fine-grained wheels. The simultaneous use of the coarse-grained textured wheel and fine-grained wheel with the continuous cutting surface leads to increasing of surface temperature no more, than 5%. For decrease of temperature and providing the minimum roughness of the processed surface it is recommended to use the combined grinding by coarse-grained textured wheel and a usual fine-grained wheel with the continuous cutting surface. 4. Simultaneous realization of preliminary and final processing of workpiece on one machine tool by combined textured tool opens new ways in decrease of thermal tension in a cutting zone, roughness of the processed surface, and increase in productivity of grinding operations.

References 1. Kremen Z, Yuryev V, Baboshkin A (2007) Technology of grinding in mechanical engineering. Publication House of Polytechnic University, St. Petersburg 2. Koltunov I, Stepanov Iu, Tarapanov A (2007) Raise of accuracy and quality of grinding of internal curvilinear surfaces. Mech Eng 1, Moscow 3. Kremen Z, Iuryev V (2013) Grinding by super abrasives of highly plastic alloys. Publication House of Polytechnic University, St. Petersburg 4. Gusev VG, Morozov AV, Shvagirev PS (2016) Grinding method. RU Patent 2606143, Sept 2016 5. Poljanchikov Ju (2002) Scientific bases of creation and application of the single-component abrasive tool formed by pulse pressing and high-temperature sintering. Dissertation, RU, University of Saratov 6. Starkov V (2007) Grinding by high-porous wheels Moscow. Mech Eng, Moscow 7. Gusev V, Morozov V (2007) Plane discrete grinding technology. RU, Vladimir State University Publishing, Vladimir 8. Gusev V, Morozov A (2012) Flat peripheral grinding with discrete wheels. RU, Yoshkar-Ola Pub. House 9. Morozov A, Gusev V (2016) Discrete plane face grinding. Pen Publ House, Moscow 10. Gusev VG, Morozov AV (2017) Discretization technology of abrasive wheels operating surfaces with laser and hydro-abrasive jet. RU J Sci Int Tech Mech Eng 9(73):20–27 11. Gusev VG, Morozov AV, Shvagirev PS (2009) Discrete structure of the cutting surface of a grinding wheel. J Rus Eng Res 29(9):940–943 12. Morozov AV (2016) Deterioration of the diamond tool at editing of discrete grinding wheels. RU J Sci Eng Ind Bul 3:59–64 13. Li H, Axinte D (2016) Textured grinding wheels: a review. Int J Mach Tools Manuf 109:8–35. https://doi.org/10.1016/j.ijmachtools.2016.07.001 14. Daneshi A, Azarhoushang B (2016) Cylindrical grinding by structured wheels. Mat Sci Forum Trans Tech Publ Switzerland 874:101–108 15. Blurtsyan D (2016) Centrifugal internal grinding by assembled wheel with radially mobile segments. Mat Sci Forum Trans Tech Publ Switzerland 874:85–91 16. Khudobin L, Babichev A, Bulyzhev E (2006) Lubricant-cooling technological means and their application at machining by cutting. Mech Eng Moscow 17. Dolganov AM (2006) The perspective grinding tool with vortex cooling. In: All-RU sci tech pr conference Novosibirsk

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18. Zubarev Iu, Priemyshev A (2016) Process stability of grinding taking into account its dynamic characteristics. Publication House of Polytechnic University, St. Petersburg 19. Gusev VG, Morozov AV, Shvagirev PS (2009) Evaluating discrete wheels and their influence on grinding dynamics. J Sci Rus Eng Res 29(8):835–837 20. Novoselov Iu (2012) Dynamics of surfaces forming at abrasive machining. RU, Nat Tech Univ, Sevastopol 21. Gusev VG (2018) Discrete tool for combined grinding. RU Patent 2664997, Aug 2018

Hydrodynamic Streams of Coolant at Internal Grinding by Textured Wheel V. G. Gusev(B) Vladimir State University Named Under Alexander and Nikolay Stoletovs, 87, Gorky Street, Vladimir 600000, Russia [email protected]

Abstract. In the article the guaranteed delivery of lubricant cooling liquid (LCL) in a cutting zone is considered. For this purpose, the designs of the textured grinding wheel and the device for LCL giving are developed. The liquid is directed into a quickly rotating tool, from where it instantly goes out under the influence of centrifugal forces on the processed surface. The streams flow on the processed surface with a high speed, causing intensive cooling of workpiece. Pressure of LCL on the processed surface is also investigated. A maximum pressure arises on the entrance to a cutting zone, and for the textured grinding wheel is equal to 7.8·10ˆ4 Pas, that is 3.4–3.5 times more in comparison with a standard wheel. In the axial direction the pressure of LCL is distributed unevenly, decreasing from the center of a wheel to end faces. The hydrodynamic veil by use of coolant near end faces of wheel is applied for alignment of its pressure on all cutting surface. At a higher pressure and speed of coolant current on the processed surface and at uniform distribution of coolant pressure, it is possible to eliminate thermal damage to the processed details. Keywords: Grinding · The textured wheel · Coolant · Pressure · Cutting zone · Hydrodynamic stream

1 Introduction The textured grinding wheels are characterized by a number of advantages before standard wheels [1–5], together with it they generate more powerful aerodynamic streams, having negative influence on delivery of coolant in a cutting zone [6–8]. Neutralization of aerodynamic streams may be carried out by isolation of a cutting zone, placement of a grinding wheel and workpiece in the cavity [9], which is filled with LCL. Streams neutralization may be carried out by giving LCL via the rotated tool [10] and also by using of combinatory way of coolant giving [11, 12]. In work [13] increase in efficiency of grinding is reached by application of a vortex way of cooling. Grinding by standard wheels is characterized by negative LCL pressure (depression) [14, 15], what leads to thermal damage of the processed layer. The best results in decrease of workpiece temperature are achieved at the greatest speed of the LCL current [16–20]. For today these questions did not find the solution, therefore it is necessary to carry out further research works on creation of more effective tools and devices for LCL giving. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_2

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2 Design of the Textured Grinding Wheel and the Device for Coolant Giving At grinding by the textured wheel (Fig. 1a, b) arise powerful district aerodynamic streams, which interfere with passing of the lubricant cooling liquid (LCL) to a cutting zone, spray and push aside is from a zone of contact of a wheel with workpiece. Negative impact of aerodynamic streams can be excluded, if to direct the LCL along these streams. The textured grinding wheel with an internal cavity for reception LCL and the device for direction of LCL along the generated aerodynamic streams are developed. A case 1 has longitudinal grooves, into which abrasive segments 2 are inserted. An axial movement of abrasive segments in a grinding wheel by the cover 3, fixed on case 1, is eliminated. The grinding wheel is established on a spindle 4 of machine tool and fixed by a bolt 5. The device for LCL giving consists of flange 6, on which the conic nut 7 is screwed. At the turn of a conic nut 7 leads to a changing of a ring gap 8, and a LCL volume, coming in the textured wheel. Between a cylindrical surface 9 and motionless flange 6 there is a gap δ1 , and between covers 3 and 7—a gap δ2 . The LCL from the pump via holes 10, executed in the flange 6, passes through a ring gap 8 and comes to a reception cavity 11 of the wheel. Under the influence of centrifugal forces the LCL instantly goes out through holes 12 on the processed surface of workpiece 13 with the formation of a ring 14 of a liquid, moving with a high angular speed ω (Fig. 1c). A grinding wheel rotates with a cutting speed on an arrow Dr , and moves with a speed of longitudinal feed on an arrow Dsp (Fig. 1a). The workpiece moves with a speed of radial feed on an arrow Dsr (Fig. 1c) and rotates with a circular feed on an arrow Dsk .

3 Technique of Studies of Hydrodynamic Coolant Streams Studies of a movement trajectory of the hydrodynamic coolant streams during a work of the textured grinding wheel, established on a spindle of grinding machine tool 3A227V, have been conducted. Characteristic data of the textured grinding wheel: diameter of the cutting surface—63 mm, diameter of a central case hole—20 mm, a segment height— 20 mm, a segment quantity in a wheel—6 pieces (Fig. 1b), the relation of length of the cutting surface of an abrasive segment to an air interval between the segments— 2:1, abrasive material of segments—25AF60L6V5, a rotation frequency of a wheel— 13600 min-1 . In experiences are used the developed device for CLC giving (Fig. 1a) and the stroboscopic tachometer. Also is studied a coolant pressure on workpiece during the work of a usual grinding wheel. The difference of the experiments, made with use of the textured and standard wheels, consisted in a way of coolant giving and its minute expense. In the first case a coolant direct to an internal reception cavity 11 (Fig. 1a) with an expense of 10−4 m3 /s, and in the second via the pipeline to an entrance of a cutting zone, between the cutting surface of a wheel and the processed surface, with an expense of 2· 10−4 m3 /s. Pressure of the CLC on the processed surface was measured by piezometers, which connected to measurement points, located along the workpiece by means of unions 15 (Fig. 1c), what allowed to define values of pressure also in the axial direction. For assessment of

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Fig. 1. The constructive scheme of the textured grinding wheel with the device for coolant giving (a), its real wheel model (b) and hydrodynamic streams (c) at wheel rotation.

pressure distribution in district direction of the processed surface the unions 15 were situated at an angle ϕ, which was changed from 0 up to 360 degrees.

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4 Hydrodynamic Streams, Which Flow via the Textured Grinding Wheel At the motionless and rotating textured grinding wheel height h1 , h2 and CLC streams, following from abrasive segments and holes 12, differ from each other (Fig. 2a).

Fig. 2. Scheme of hydrodynamic streams of CLC (a), streams from a motionless wheel (b), from the rotating wheel with a protection: 1—a wheel; 2—the device for CLC giving; 3, 4, and 5—streams of CLC; 6—the device for workpiece fixing.

At not rotating wheel h1 ≈ (1 –2) mm, h2 ≈ ( 70–80) mm. Considerable volume of CLC comes in a textured grinding wheel and under the influence of gravitational forces goes out via holes 12 in the low half of a wheel, a little smaller volume passes through gaps δ1 , and δ2 (Fig. 2b, positions 3, 4, and 5), and the smallest volume via abrasive segments. Smaller values h1 and h2 correspond to width 1.5 mm of a ring gap 8 (Fig. 1a) and great values to width 2.0 mm. At the CLC current from an internal cavity 11 there are two hydrodynamic streams. First stream leaves a cavity 11 via radial holes 12 (Fig. 1a) and passes through an air interval 16 between adjacent segments 2 and 18 (Fig. 2a). Streams 17 move on a curvilinear trajectory from abrasive segment 18 and catch up with a segment 2, located ahead. After achievement of segment 2 the streams 17 lag behind the rotating tool. Such unusual trajectory of the movement of streams 17 is explained by the fact, that at wheel rotation on an arrow Dr the segment 18 create a high air pressure, which rejects streams 17 in direction to a segment 2. The second hydrodynamic stream leaves

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a reception cavity 11 through abrasive segments in the form of curvilinear streams 19 and 20. In dynamics at an operating frequency of a wheel rotation n = 13600 minˆ(−1) are created the powerful streams 3 and 4 (Fig. 2c), which pass in the radial direction through gaps of cylindrical parts of device for workpiece fixing. At the same time h2 ≈ (30–40) mm, h1 ≈ (15–30) mm, and coolant streams follow from a wheel evenly on all height of the tool. The described movement trajectory of the hydrodynamic coolant streams is characteristic of each of abrasive segments and an air interval between them. The device for CLC giving has to provide a control of CLC flow, at passing through a ring gap 8 (Fig. 1a). In this regard, the schedule (Fig. 3) of change of coolant volume depending on an angular position of a cover 7 has a grate practical impotence. Curves 1, 2, and 3 are constructed, respectively, for a coolant expense Q = 2.3· 10−4 ; 1.8· 10−4 , and 1.0· 10−4 m3 /s.

Fig. 3. Influence of a turn angle of a cover of device for coolant giving on its expense.

5 A Hydrodynamic Coolant Veil for Neutralization of Face Aerodynamic Streams It should be noted, that the streams, flowing from the grinding wheel, connect in the general stream of liquid, being located on the middle of abrasive segments. As a result in the field of segment ends the quantity of CLC is decreased, but in the middle of segments CLC is increased, what is explained by influence of the aerodynamic streams, generated by rotating textured grinding wheel. Pushing off of coolant from end faces of the wheel to the center by aerodynamic streams leads to uneven distribution of a coolant on height of segments, what can lead to thermal damage to the processed surface. To eliminate a thermal damage of workpiece the aerodynamic streams need to be neutralized. For example, influence elimination of air flows 1 and 2 (Fig. 4) can be reached by cover by a water-proof layer of ends of abrasive segments. The effective way, by means of which it is possible to neutralize the pushing of a coolant to the tool center, is creation of a hydrodynamic veil 3 and 4 near of both ends of segments 5. For this purpose on both sides of a case 6 the radial holes 7 near of each end of abrasive segments are carried out. The effective way, by means of which it is possible to neutralize the pushing of a liquid to the tool center, is a creation of a hydrodynamic

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Fig. 4. An isometry of the rotating grinding wheel with hydrodynamic coolant veils.

veil 3 and 4 near of both ends of segments 5. For this purpose on both sides of a case 6 the radial holes 7 near of each end of abrasive segments are carried out. The coolant, arriving in the textured grinding wheel, via pipelines 8 and 9 instantly flows out under the influence of centrifugal force on the length of segments and in district direction of grinding wheel, protecting a coolant from action of aerodynamic streams.

6 Coolant Pressure Upon the Processed Surface of Workpiece Processes of round internal grinding by the standard and textured wheel are characterized by formation of hydrodynamic wedges of CLC: the standard wheel generates during the work only one wedge, located before of a contact zone of the tool and workpiece, the textured wheel generates two hydrodynamic wedges, one of which is situated before a cutting zone, the second wedge—directly behind a contact zone. Pressure of CLC upon the processed surface during the work of the standard and textured wheel is distributed unevenly, i.e., pressure depends on an angular position of union 15 (Fig. 1c) concerning a contact zone. The minimum pressure of CLC between the tool and workpiece is observed during the work of a standard wheel at giving of coolant from a pump via a tube in a cutting zone (Fig. 5a, lines 1–5). At grinding by the textured wheel the CLC moves through quickly rotating tool, therefore the speed of a current and pressure of CLC on the processed surface considerably increases (lines 6–10). At the change of angular coordinate ϕ from 30 to 300° CLC pressure at working of a standard wheel equal p = + 1,2·104 Pas, but at working of the textured wheel – p = + 3.3· 104 Pas. In the narrowed space between workpiece and the wheel (ϕ = 300 ÷ 355°) CLC pressure increases for both tools, reaching of maximum at ϕ = 355°. The maximum pressure during the work of a usual (standard) wheel equal p = + 0.022 MPas, and during the work of the textured wheel – p = +0.078 MPas (Fig. 5a). The given peak values of pressure are characteristic of the hydrodynamic wedge, located above a contact arch of the tool and workpiece. At values ϕ = 0 ÷ 30° pressure of CLC during the work of both wheels decreases: for an usual wheel pressure sharply falls up

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Fig. 5. Coolant pressure, generated by the tool in a district direction (a) and along a height of a segment (b).

to depression p = –0.018 MPas, for the textured wheel pressure decreases to positive value p = +0.012 MPas. Thus, at grinding by usual wheel arises a positive (at ϕ = 355°), and negative pressure (depression at ϕ = 0 − 30◦ ), but during the work of the textured wheel arises a positive pressure not only before, but also after a contact zone. This fact is very important, because at the removal of metal temperature of a processed surface increases, and for excluding the structural changes in a blanket of detail, the coolant presence in a cutting zone is very necessary. At grinding by the textured wheel a processed blanket is cooled by liquid continuously, what cannot be told about standard wheel. Except much bigger speed of the CLC current on the processed surface, of a more high extreme pressure p = (7.5–7.8)·104 Pas, the textured wheel provides the guaranteed presence of cooling liquid within a full angle ϕ = (0–360)°. For a standard wheel extreme of CLC pressure p = 2,2·104 Pas less in 3.4–3.5 times in comparison with the textured wheel. Pressure is present only before a contact zone (ϕ = 350–355)°. At ϕ = (0–30)° there is a depression, i.e., CLC is absent, and at ϕ = (30–350)° pressure is equal 1,2· 104 Pas, that is 2.75 times less in comparison with the textured wheel. Told above demonstrates advantages of the textured wheel before standard wheel. Along height B of wheel pressure of CLC is distributed unevenly for both tools (Fig. 5b). Curves 1–3 characteristic the textured wheel, curves 5–7— the standard wheel at ϕ = 355°, 330° and (5–30)° respectively. Alignment of CLC pressure on height B of the textured wheel is possible by the use of a hydrodynamic veil 3, 4 (Fig. 4), neutralizing end faces aerodynamic streams 1 and 2. Thus, the research of the hydrodynamic CLC streams, arising during the work of the textured and usual grinding wheels, showed, that the textured wheel provides higher pressure, and a current speed of CLC on the processed surface and allows to align a pressure on tool height, what has a positive impact on quality of processed details.

7 Conclusion 1. At grinding by the textured wheel appear powerful aerodynamic streams, which complicate a passing of the lubricant cooling liquid (LCL) to a cutting zone, what leads to thermal damage of details. For elimination of negative impact of aerodynamic streams the textured grinding wheel and the device for LCL giving are developed.

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2. Movement trajectories of the hydrodynamic CLC streams during a work of the textured wheel are experimentally investigated. It is established, that the powerful coolant streams follow from wheel holes on a curvilinear trajectory in direction to ahead located abrasive segment. Having reached abrasive segment, the hydrodynamic streams lag behind the rotating wheel. 3. Pressure of hydrodynamic streams is distributed along a height of the textured and standard wheel unevenly. Pressure increases in direction from the end faces surfaces to a middle of the wheel. In the district direction the maximum pressure of CLC arises on an entrance of a cutting zone. In hydrodynamic wedge pressure during the work of the textured wheel 3.4–3.5 times more than pressure formed by usual wheel. Directly behind a cutting zone the textured wheel forms a positive CLC pressure, while the usual wheel forms a depression, that have a negative impact on removal of heat from workpiece. 4. To eliminate a decreas of coolant in the end faces and to align pressure along a height of abrasive segments a hydrodynamic veils, which are formed by the coolant and which protect the end faces of segments from action of the aerodynamic streams, are worked out. Significant increase in speed of the CLC current on the processed surface and increase its pressure with simultaneous alignment along the height of the textured wheel allow to intensify heat removal from a cutting zone and to decrease the probability of thermal damage of the processed details.

References 1. Li HN, Axinte D (2016) Textured grinding wheels. J Mach Tools Manuf 109:8–35. https:// doi.org/10.1016/jijmachtools201607001 2. Daneshi A, Azarhoushang B (2016) Cylindrical grinding by structured wheels. In: Materials science forum, vol 874. Trans Tech Publications, Switzerland, pp 101–108 3. Blurtsyan D (2016) Centrifugal internal grinding by assembled wheel with radially mobile segments. In: Materials science forum, vol 874. Trans Tech Publications, Switzerland, pp 85–91 4. Gusev V, Morozov A (2017) Discretization technology of abrasive wheels by laser beam and hydro-abrasive stream. RU J Int Sci Tech Mech Eng 9(73):20–27 5. Morozov A (2016) Deterioration of the diamond tool at editing of discrete grinding wheels. RU J Mess Mech Eng 3:59–64 6. Gusev V, Shvagirev P, Morozov A (2004) Aerodynamic streams, generated by a discrete face grinding wheel. Int Sci Tech Conf RU Tula St Univ 2:74–79 7. Morozov A, Gusev V (2016) Discrete plane face grinding. Pen Pub House, Moscow 8. Vasilenko Yu (2008) Current state of the giving technology of coolant when grinding. RU J Chief Mech Eng 2:14–19 9. Blurtsyan DR, Trifonova JV, Blurtsyan IR et al (2002) Way of internal grinding. RU Patent 2,182,531, 14 May 2002 10. Gusev VG, Kirichek AV, Borisov IV (1990) Grinding way. SU Copyright certificate 1,604,585, 8 Jul 1990 11. Tyukhta A (2012) Combinatorial method for cooling Lubricating fluid supply at flat grinding with periphery wheel. In: The 13th joint Chi-Ru symposium, pp 63–68

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12. Tyukhta A (2012) Mathematical model of particle interaction of waste by a curtain from coolant at flat grinding by the wheel periphery. RU J Fundam Appl Prob Equip Techol 3– 2(293):60–67 13. Dolganov AM (2006) The perspective grinding tool with vortex cooling. In: All-RU Sci Practical Conf., Novosibirsk, pp 72–74 14. Oliveira E, Silva C, Hashimoto G (2009) Industrial challenges in grinding. CIRP Annals Man Tech 58(2):663–680 15. Daneshi A, Azarhoushang B (2016) Cylindrical grinding by structured wheels. Mat Sci Forum 874:101–108 16. Khudobin L et al (2006) Lubricant cooling technological means and their application when processing by cutting. Mech Eng, Moscow 17. Kremen Z, Yuryev V, Baboshkin A (2007) Technology of grinding in mechanical engineering. Polyequipment, St Petersburg 18. Kremen Z, Iur’ev V (2013) Grinding by super abrasives highly plastic alloys. Politekhn Unversity Pub House, St Petersburg 19. Starkov V (2007) Grinding by high-porous wheels. Mech Eng, Moscow 20. Jackson M, Hitchiner M (2012) High performance grinding and advanced cutting tools. Springer pub house

Peculiarities of Assembly of Bevel and Hypoid Gears with Curved Teeth A. S. Kalashnikov(B) , Yu. A. Morgunov, and P. A. Kalashnikov Moscow Polytechnic University, 38 Bolshaya Semenovskaya Ul, Moscow 107023, Russia [email protected]

Abstract. The author provides comparative characteristics of various processes of finishing treatment of thermally reinforced curved teeth in bevel and hypoid gears. The paper analyzes the geometrical precision and roughness of teeth lateral surfaces reached by the following processes: gear lapping, gear honing, gear hobbing with the help of cutter heads having hard-alloy cutters and gear grinding. The author considers a possibility to obtain complete interchangeability of the main gear and driven wheel in bevel and hypoid gears during the use of considered processes. Gear lapping and honing are conducted after chemical and thermal treatment to obtain the 6th and 8th degree of precision under GOST 1643-81, decrease of roughness of teeth surface (up to Ra 0.6–2.0 um) and insignificant stabilizing of the spot form and location on the teeth. As gear lapping and honing correction capabilities are insignificant, that is why it is impossible to obtain completely interchangeable pairs, one needs to conduct pairing and marking of key gear parameters. Gear hobbing and grinding allow significantly increasing the precision of teeth after chemical and thermal treatment, especially on the radial beam of a gear ring (kinematic precision norm) and on pitch deviation (norm of operation smoothness). It is very important to guarantee complete interchangeability of gear and wheel teeth interfacing in the gearing unit after gear hobbing and grinding. At the assembly of fully interchangeable parts of the interface of bevel and hypoid gears the quality of teeth engagement increases while the labour intensity of the assembly becomes lower (no operations of pairing and marking of key gear parameters). Keywords: Assembly technology · Labour intensity · Teeth lapping · Teeth honing · Gear hobbing · Teeth grinding · Gear

1 Introduction Here introduce the paper. The paragraphs continue from here and are only separated by headings, subheadings, images and formulae. The first paragraph after a heading is not indented (Bodytext style).

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_3

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2 Structure Bevel and hypoid gears with curved teeth serve for transmitting mechanical energy between intersecting and crossing shaft axes. High-performance coefficient (50–95%), possibility to transmit driving torques at the angle  = 0–180° between shaft axes with a high range of gear ratio (u = 1–100) and circumferential velocities up to 125 m/sec facilitated their widespread occurrence in industry. These gears are applied in complex assemblies of the mechanisms of air and vessel engines, railway electrical and diesel locomotives, wind electrical units, car drive axles, tractors, agricultural and road cars, general-purpose gearboxes. They are applied for operation under significant loads and high circular velocities, they are generally made of alloyed, low-carbon steel grades and subject to chemical and thermal treatment (CTT) including carburizing (nitro-carburizing) and hardening [1–3]. If the teeth surface hardness is HRC 58-63 and the core hardness is HRC 32-42, gears demonstrate high back-to-back endurance 1,300…1,650 N/mm2 and bending resistance 320…540 N/mm2 . However, during CTT bevel and hypoid wheel are subject to intense deformation, the precision and smoothness of teeth engagement decreases, the form, length and location of the contact spot are not stable from one tooth to another. Figure 1 shows the driven bevel wheel 3 after CTT where the contact spot is located irregularly and circumferentially: in the middle of the tooth 1 and 4, at the tooth inside end (tooth toe) 2 and at the outside end (at tooth heel) 5. The length of the contact spot at tooth toe and heel is significantly smaller than in the middle of the tooth.

Fig. 1. Layout of contact spot location on the teeth.

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3 Finishing Treatment To eliminate the teeth errors, occurring during CTT, bevel and hypoid cog wheels are subject to finishing treatment. For finishing treatment of hardened wheels, the following technological operations are applied most widely: gear lapping, gear honing, gear hobbing with cutting heads, having hard-alloy cutters and gear grinding. Table 1 provides comparative characteristics of the finishing treatment operations for the hardened teeth (HRC 58-63) of bevel and hypoid gears. Table 1. Characteristics of operations of teeth finishing treatment. Ser. No. Technical parameters of finishing operations

Gear lapping Gear ho-ning Gear hobbing with Gear grinding hard-alloy cutters

1

Module of treated wheels, mm

≤16

≤16

1–13

0.7–18

2

Production efficiency

+

++

+/−

+

3

Precision according to GOST 1758-81

6–8

6–7

5–7

4–6

4

Roughness of 1–2 teeth surface according to Ra, um

0.6–1.6

0.4–1.2

0.4–1.6

5

Need of cutting tooth base

_

_

_

+

6

Teeth modifications

_

_

+

+

7

Residual compressing strain on teeth surface

–

+

+

+

8

Treatment of bending radius at teeth base

_

_

_

+

9

Need of pairing

_

±

+

+

10

Process reproducibility

+/−

+/−

+

+

Symbols (+)—positive result; (−)—negative result; (+/−)—possibility of a positive or negative results

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The traditional criteria of evaluation of finishing treatment of bevel and hypoid gears are the following: production efficiency, obtained precision and roughness of teeth surface. The stable quality of gear manufacturing significantly depends on the process reproducibility. Finishing operations can conduct cross-section and longitudinal teeth modifications, generate residual internal compressive strains and treat the bending radius at teeth base. This allows improving bending endurance (resistance to fatigue failure at teeth base) and back-to-back endurance (resistance towards pitting and micropitting as well as wear because of contact stresses). Cutting at teeth base is necessary for creating an enabling environment for tool cutting at finishing, which significantly reduces economic efficiency of pre-treatment and negatively influences teeth bending endurance. Only one operation out of all considered finishing teeth treatment does not require teeth base cutting - teeth grinding. Teeth lapping is conducted after CTT to reduce the roughness of teeth lateral surfaces (up to Ra 1–2 um) and insignificant corrections of the contact spot form and location to guarantee smooth and noiseless teeth engagement. No allowance is left for gear lapping, while metal removal from the most strained sections of tooth surface can reach 0.03 mm. As correcting capabilities of gear lapping are insignificant, after treatment it is necessary to conduct pairing, i.e. define two mating elements—driving and driven gears the quality of engagement corresponds to the drawing requirements. During final control at the inspection and measuring machine lapped gear sets are marked as follows: number of a set 113, lateral gap—B, Z. 0.25 mm between the teeth of the gear and wheel marked by the sign “X”, and the basic gear distance—B.P. 128.1 mm; this distance allows obtaining the best results on the contact spot form and location as well as teeth engagement smoothness (Fig. 2). Gears and wheels from various sets cannot be installed in the gearbox together without additional treatment [4–6].

Fig. 2. Marking of bevel and hypoid gear.

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As the pairs are controlled under load, equal to only 25–50% of maximum load, present in the mechanism under operation, necessary corrections should be made during contact spot evaluation. Gear honing is a high-performance process at which the treatment is performed with the help of metal gear hones with a special structure; one layer of grains of a cubic boron nitride is galvanically fastened on their surface. The treatment is conducted at the machines with strong kinematic connection between a workpiece and tool without coolant supply. Due to a short contact time, the workpiece is not heated and not subject to structural changes in the gear surface. The removal of the allowance of up to 0.1 mm on the tooth lateral side allows reaching the stability of process and complete interchangeability of gears in specific cases [7, 8]. However, process reproducibility at teeth honing significantly depends on CTT quality. At large teeth deformations after CTT gear honing is associated with difficulties, so the required indices of gear precision and engagement smoothness cannot be reached in all cases. In such cases after gear honing the pairing is conducted with the marking of set number, basic distance of gear and the lateral gap of marked teeth. As during gear lapping, and in certain situations during gear honing as well, one cannot completely eliminate the teeth errors, occurring at previous treatment and CTT, that is why, the base distance of the driving gear A1 has a deviation from the required value. This negatively influences the form and location of the contact spot (Fig. 3).

Fig. 3. Gearbox of the car drive axle.

To eliminate this deviation, the base distance of the gear A1 during assembly should precisely correspond to the marked value. This is reached with the help of a highprecision step-type compensator Ak. Besides, the required lateral gap of the marked teeth is obtained due to the shift of the driven wheel along the axis. Such assembly is labour intensive, requires a well-organized workstation, significant time expenditures and a high qualification of the mounter [9–11]. The assembly of the driving gear unit is conducted

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with the help of a hard spacer unit Bk providing for the pre-tension between bevel roller bearings. External rings of bevel bearings are installed with diametral tightness [12]. The finishing of thermally reinforced wheels of bevel and hypoid gears is conducted by gear hobbing with hard-alloy cutter heads and gear grinding at hard kinematic connection between a workpiece and a tool. The allowance, removed from teeth lateral sides, is significantly larger than one at gear lapping and honing. This results in the elimination of most errors in gear engagement. The possibility to conduct cross-section and longitudinal modifications of the teeth allows significantly increasing the quality of the contact spot form and location. Thus, high precision and complete interchangeability are reached of mating elements (gears and wheels) of bevel and hypoid gear. Gear hobbing of the hardened wheels of bevel and hypoid gears with hard-alloy cutting heads allows significantly reducing the beam of a gear ring (kinematic precision norms) and pitch deviation (operation smoothness norms). Gear transmissions, the mate gears of which are cut by this method, have a high engagement smoothness. It is important that the machines for cutting hardened wheels have increased static and dynamic hardness as well as thermal stability. The treatment is conducted only for lateral teeth sides without contacting the bottom land. The mandatory condition is the preliminary treatment of teeth with cutting the base by cutting tools with thickening on the head. To avoid excess cutting of the tooth base and reduction of its bending endurance, characterized by the resistance of gear engagement to fatigue failures under stresses at the tooth base, it is necessary to accurate the thickening on the cutter top for preliminary finishing [13, 14]. The value of the removed allowance is 0.15…0.25 mm on the tooth side. Cutting is conducted with coolant supply at cutting rate 25…35 m/min for one or two operating pitches. The thickness of the removed layer for one operating pitch should be at least 0.1 mm. This method of finishing is widely applied in small- and medium-series where there is a possibility of using the same gear hobbing machine for cutting thermally hardened and unhardened wheels. Gear grinding is one of the processes of high-speed micro-cutting occurring as a result of the action the tools (abrasive wheels) with cutting elements (in most cases, these abrasive grains or grains from cubic boron nitride), having geometrically indefinite cutting edge, on the teeth surface. The characteristic feature of the cutting elements of abrasive wheels is their negative face angle γ (Fig. 4). At the initial micro-cutting moment, when a cutting element penetrates the workpiece 2 with a circumferential speed V, supply S and under the pressure P, the swelling 1 of the workpiece surfaces occurs due to elastic strains 3. During further abrasive wheel motion in relation to the workpiece 2 plastic strains also occur at the front, on the sides and below the cutting element. When the cutting element leaves cut, the workpiece metal starts destroying and one can observe chip formation. Grinding of bevel and hypoid gear teeth is conducted by means of an interrupted method when the cutting process is interrupted after treatment (rough of finishing) of each land, the tool is moved backwards and the workpiece is turned for treating the next

Peculiarities of Assembly

25

Fig. 4. Scheme of chip formation by geometrically indefinite cutting edge.

land. Conventionally, cup cylindrical wheels 3 are used, their axial section is similar to the cutters of cutting heads (Fig. 5). At the treatment of driving gear 1 and the driven wheel 4 the operating surface of an abrasive wheel reproduces the tooth of an imaginary generating wheel 2.

Fig. 5. Scheme of engagement of the cup cylindrical wheel with an imaginary generating wheel 2.

Most bevel and hypoid gears are ground by means of a rolling method. During grinding of rolling gears, the abrasive wheel 3, having the precise dimensions of an imaginary generating wheel 2, is in tight engagement with the gear workpiece 1 or the wheel workpiece 4 and performs rolling motion. The conducted research has shown that the process of gear grinding, as compared with other methods of finishing, have large technological capabilities and provides for

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complete interchangeability of mate bevel and hypoid wheel without pre-pairing, gear grinding may produce the 4–6th degree of teeth precisio (GOST 1758-81) the roughness of lateral teeth sides Ra = 0.3–1.6 um. However, gear grinding is a high-heat process. Heat action, as a rule, is connected with structural changes in the superficial layer of the treated material in the form of spots or burnt strips and thermal micro-cracks reducing the bending and contact wear resistance of bevel and hypoid gear teeth. The heat, emitted during grinding, can cause undesirable changes in the superficial layer structure as well as its physical state alongside with unstable hardness. That is why many manufacturers of bevel and hypoid gears do not apply gear grinding despite its obvious advantages [15–20]. To reduce the risk of burns and thermal micro-cracks at gear grinding this paper studies high-porous (open-structured) abrasive wheels as tools. The structure of such wheels is characterized by the increase of the porous space volume 3 and, correspondingly, by the decrease in the volume of bonding 4 and abrasive grains consisting of electrically produced corundum 1 and micro-crystal corundum 2 (Fig. 6).

Fig. 6. Structure of wheel abrasive materials.

The presence of large pores between abrasive grains provides for a sufficient space of microchips control at a high intensity of material removal as well as supply of a significant coolant amount directly to the cutting area through the wheel porous structure. High-porous wheels are made by a special technology using pore agents which, additionally to natural pores, form large pores 0.08…1.0 mm in a wheel. The volume of large pores is equal to 15…30% of all the wheel volume. Comparing with the normal structure wheels, high-porous ones have the increased distance between the grains by 2–3.5 times, a decreased friction surface at the contact with the workpiece and lowered heating temperature in the grinding area by 300…400 degrees °C. In comparison, high-porous wheels tend more to self-sharpening and less to greasing. Micro-crystal corundum 2 (see Fig. 6) included in the composition of wheel abrasive grains is obtained by means of baking by a special technology. Its grains consist of baked submicrocrystals of high purity of aluminum oxide with the size ≈1 um.

Peculiarities of Assembly

27

At gear grinding a seamy surface of the baked micro-crystal corundum is uniformly crumbles out under high cutting forces thus forming new cutting edges of grains. Selfsharpening effect occurs (the wheel surface seems to be continuously renewed). Perfect cutting properties of micro-crystal corundum allow significantly increasing supply at gear grinding, increase the time of wheel operation between dressings and reduce the consumption rate of a tool. As at gear grinding during final operation pitches the cutting force and pressure on the micro-crystal corundum grains decrease, the self-sharpening effect is also less obvious. That is why a volumetric fraction of micro-crystal corundum in the mix with electrically produced corundum is 10–50%. The grinding of concave and convex sides of curved teeth of hardened bevel gears (z = 11, mte = 9.0 mm, β = 45° 23’, steel 30HGT, hardness HRC 58-63) was conducted separately by means of the interrupted rolling method (Fig. 7). The allowance 0.2 mm with concave and convex lateral sides of teeth was removed for 5 operating pitches with the cutting rate V = 35.0 m/sec. Machine time was equal to Tm = 5.87 min.

Fig. 7. Scheme of curved teeth grinding.

The conducted experimental research showed that high cutting properties are demonstrated by high-porous abrasive wheels 25A 16 CM1(K) 10 K. Thoroughly selected grinding modes allow significantly decrease heat action on the teeth superficial layer (maximum temperature in the cutting area ≈350 °C), obtain the 5th precision degree under GOST 1758-81 and the roughness of lateral surfaces of the teeth Ra ≈ 1.00…1.25 um. The results of metallographic research of the micro-structure showed that after gear grinding of the teeth superficial layer no burns or thermal micro-cracks were revealed. It is important that bevel and hypoid wheels with ground teeth provide for complete interchangeability of interface. In addition, there is no need to conduct pairing and final control with the marking of set, lateral gap of marked teeth and actual base distance of a mate driving gear (see Fig. 2). Due to this, at the assembly of the driving gear 1 (Fig. 3) no adjustment of the base distance A1 with a stepwise compensator is required, for example, in the drive axle

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gearbox. In addition, the driven wheel 2 after CTT is subject not only to gear grinding but also to mounting face grinding that is why a stable high-precision lateral gap is provided, which means there is no need of its adjustment as well. This significantly simplifies the gearbox structure. Inside only one compensator Bk is thus installed, which is located in the internal circuit of a size net and intended for the pre-tension of bearing assemblies. Manufacturing high-precision and completely interchangeable bevel and hypoid gears with gear grinding and cutting by hard-alloy cutting heads after CTT improves the quality of engagement of the gear and wheel, provides high operation indicators and makes labour intensity of assembly lower by 2–3 times.

4 Conclusion 1. Gear lapping and honing processes of bevel and hypoid gear wheels provide for the 6–8th precision degrees (GOST 1758-81). However, gears, treated with these processes, are not completely interchangeable and require additional operations, such as pairing and marking of key parameters of gears. This makes the process of manufacture and assembly much more labour intensive at the setting of a necessary base distance A1 in the gearbox with the help of the stepwise compensator Ak and a necessary lateral gap in the engagement. 2. Gear grinding and cutting with the help of hard-alloy cutting heads after CTT allow obtaining completely interchangeable gears with the 3–6th precision degree that do not require adjustment of the gear base distance and lateral gap setting. This simplified the gearbox structure.

References 1. Zinchenko VM (2001) Engineering of Surface of Cog Wheels by means of Chemical & Thermal Treatment. Publishing House of Bauman Moscow State Technical University, Moscow, p 302 2. Bauch T (2006) Innovative Zahnradfertigung. Expert Verlag Gmbh, D–71268, Reningen, Germani, p 778 3. Kalashnikov AS, Morgunov YuA, Kalashnikov PA (2017) Continuous grinding of tooth by generating planetary transmission gears. Proc Eng 206:1167–1172 4. Shandrov BV, Bulavin IA (2016) Controlling axial position of driving gear in relation to axis of driven wheel at assembly of drive axle gearboxes. Car Ind 9:33–37 5. Voronin AV (1978) Evaluation of precision of assemble of bearing assemblies of vehicle aggregates. Car Ind 4:31–34 6. Shandrov BV, Bulavin IA (2015) Change of mounting height of bevel roller bearings under axial load during force closure of bearing assemblies with pre-tension. Car Ind, No, p 6 7. Kalashnikov AS, Morgunov YuA, Kalashnikov PA (2010) Modern methods of cylindrical gear grinding: reference book. Eng Mag 5:28–31 8. Kalashnikov AS, Morgunov YuA, Kalashnikov PA (2013) Chemical and thermal treatment of cog wheels with the use of gaseous vacuum cementation: reference book. Eng Mag Annex 10(199):12–16

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9. Kalashnikov AS, Morgunov YuA, Kalashnikov PA (2016) Producing of cylindrical gears by high-speed grinding. Russ Eng Res 36(5):400–403 10. Voronin AV, Shandrov BV (1978) Some peculiarities of assembly of axle drive gears. Car Ind 5:36–38 11. Kalashnikov AS, Morgunov YuA, Kalashnikov PA (2012) Modern methods of cog wheel treatment. Publishing House Spektr, p 238 12. Starkov VK (2007) Grinding with highly porous circles. Mashinostroyeniye, Moscow, p 688 13. Shandrov BV, Morgunov YuA, Kalashnikov PA (2007) Experimental research of allowances at continuous generating gear grinding: reference book. Eng Mag Annex 11:17–22 14. Morgunov YuA, Saushkin BP, Shandrov BV (2016) Development of conceptual framework of engineering technology/Yu A. Morgunov: reference book. Eng Mag 4(229):3–7 15. Shandrov BV, Bulavin IA, Samoilova AS (2017) Factors defining quality of gearboxes of drive axles of vehicles. Car Ind 7:25–28 16. Kalashnikov AS, Morgunov YuA, Kalashnikov PA (2018) Decrease of labour intensity of assembly of bevel and hypoid gearboxes. In: Innovative technology in metal treatment, Collection of Papers of All-Russian Research-to-Practice Conference with International Participation. Ulyanovsk, November 25, 2018, pp 26–31 17. Kalashnikov AS, Morgunov YuA, Kalashnikov PA (2010) Analysis of finishing methods for cylindrical gear teeth applied in industry: reference book. Eng Mag Annex 4:21–26 18. Kalashnikov AS, Morgunov YuA, Kalashnikov PA, Khomyakova VN (2018) Hobbing of cylindrical gears without machining fluid. Russ Eng Res 7:529–533 19. Kalashnikov AS, Morgunov YuA, Kalashnikov PA (2016) Improving bending tolerance of bevel and hypoid gears with curved teeth: reference book. Eng Mag Annex 6:8–13 20. Kalashnikov AS, Kalashnikov PA, Khomyakova NV (2017) Cutting-head optimization to improve the reliability of bevel and hypoid gears. Russ Eng Res 37(7):603–607

On Issue of Evaluating the Effectiveness of the Driver-Car-Road-Environment (DCRE) System A. M. Umirzokov1 , K. T. Mambetalin2 , and S. S. Saidullozoda2(B) 1 Tajik National University, 17, Rudaki Avenue, Dushanbe 734025, Tajikistan 2 South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, Russia

[email protected]

Abstract. The article considers a conceptual model for evaluating the effectiveness of the DCRE system. The conceptuality of the proposed research model of the DCRE system is substantiated. The evaluation of the effectiveness of the DCRE system is increasingly recognized by many researchers. However, there are no differential equations of traction balance for calculating the effectiveness of the DCRE system in high-altitude quarries. The proposed model for evaluating the effectiveness of the DCRE system takes into account the complex stochastic nature of the conversion and transfer of energy within a particular subsystem and between subsystems. Therefore, for this case, it is proposed to apply probabilisticstatistical methods for assessing the effectiveness of the DCRE system. Moreover, the DCRE system can be classified as large and complex, because it contains ambiguous relationships and patterns of interconnection between its elements. The processes, taking place in the DCRE system, are stochastic. Its complexity is compounded by the random nature of changes in its performance. Consequently, probabilistic-statistical methods for evaluating the effectiveness of the DCRE system were used. A differential equation is obtained for calculating the efficiency of the DCRE system for the operation of heavy cars in mountain and high mountain quarries. The results of the study can be used to calculate the effectiveness of the DCRE system. Keywords: Car · System · DCRE · Conceptual model · Efficiency · Probability · Career

1 Introduction The mountain roads of the Republic of Tajikistan come close to extreme in complexity and are characterized by sufficiently large longitudinal slopes (in some places up to 10… 12%) of up to 30 km or more, frequent turns (sometimes more than 10 per 1 km of track), with complex geometry and rounding of small radii (up to 8… 10 m on slopes), insufficient width of the carriageway and subgrade, poor visibility and insufficient visibility (50… 100 m) in some areas [1–3]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_4

On Issue of Evaluating the Effectiveness

31

As the main type of open-cast mine transport, widely used in mountain and high mountain quarries of the Republic of Tajikistan (in open-cast mining), automobile opencast mine transport can be distinguished, as well as combined transport, which provides for a different combination of the main modes of transport. Automobile mining transport is cyclical in the nature of cargo flows. Despite the relatively low reliability, the ability to transport rocks with various physical and mechanical properties, the relatively high energy intensity and unit cost of transportation, as well as a significant dependence on climatic conditions, automobile quarry transport in the Republic of Tajikistan has been and remains the most rational mode of transport; There are a number of requirements for heavy-duty mining trucks, the most important of which are Bulleted lists may be included and should look like this • Improved cross • Large capacity • Reliability, as the dominant element that determines the reliability of the DCRE system. The most important properties that determine the reliability of heavy mining dump trucks are reliability, durability, maintainability, and retention • Performance • Security • Maneuverability • Widespread use of automation and electronics in the construction of heavy mining dump trucks, especially in cars operating in mountain and high mountain conditions • Compactness of individual nodes while maintaining the load-bearing capacity • Adaptation to specific operating conditions • Quality indicators (indicator of purpose, ergonomics, etc.). When choosing heavy mining dump trucks for operation on the territory of the Republic of Tajikistan, it is necessary to pay attention to the following factors: the scale of transportation, the condition of roads, preparedness of access roads, features of the quarry, altitude, geometry of the road, climatic conditions—all this determines the choice of the most optimal models. In order for the equipment to be used with maximum effect, the loading rate must correspond to the capacity of the body. At the same time, on the territory of the Republic of Tajikistan, BelAZ-7540B and SHACMAN-384 vehicles are considered the most demanded of heavy-duty mining dump trucks. The modern process of globalization and integration has penetrated into all spheres of the world economy, in particular having influenced the modification of such an industry as automobile transport. With the increase in the level of motorization, each year the level of specialization and automation of cargo transportation increases. To replace generalpurpose trucks, specialized and special vehicles are steadily being introduced, while ensuring cargo safety, vehicle safety and cargo transportation efficiency, and, on the whole, increasing DCRE reliability. Today, dozens of countries and automobile factories producing mining equipment are known around the world. In the Republic of Belarus alone, more than ten series and more than forty modifications of various mining dump trucks are currently being produced. All this provides a wide selection of mining trucks. At the same time, at the moment

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there is no sufficient theoretical basis for an unambiguous interpretation of the nature and features of the operation of heavy-duty mining trucks, which in turn complicates the choice of mining dumpers, taking into account their operational efficiency in specific road and climatic conditions. In connection with the foregoing, in this study, a conceptual model for assessing the effectiveness of the DCRE system was traced, which contributes to a favorable choice in specific operating conditions from a wide variety of them.

2 Methods and Materials DCRE systems are a large and complex system consisting of a set of interacting living and nonliving, natural and artificial objects of various natures, forming a certain integrity and unity [2, 3]. There is an opinion that the concept of “system” is a means of combating complexity, a way to find the simple in the complex. It is noted correctly, however, without defining the properties and attributes of the system it is not possible to find a simple solution to a complex problem. Therefore, the correct and rational classification of the system is a necessary prerequisite for assessing its effectiveness and reliability. The classification of any system is relative. The DCRE system is no exception, where at the same time natural and artificial, as well as discrete and analogous features of its individual elements and processes can take place. In the process of clarifying the properties and characteristics of the DCRE system, the most significant and important of them are selected that contribute to simplifying the creation of adequate and reliable mathematical models, as well as simplifying the tasks associated with increasing the efficiency and reliability of the DCRE system (Fig. 1) [2]. The peculiarity of the DCRE system is that it can be considered both in a narrow and in a broad sense. In the narrow sense of the word, the DCRE system refers to relationships and regular relationships between individual components, i.e., between an individual driver, a car, a stretch of road and the environment. In a broad sense, we are talking about relationships and regular relationships between a large number of drivers, a stream or fleet of cars, a network of roads and the environment. The DCRE system is simultaneously large and complex. The complexity of the DCRE system is that it contains ambiguous relationships and regularities of the relationship between its elements, the multicriteria system and the processes taking place in it are stochastic, and it is difficult to model the DCRE system. The DCRE system can be classified as complex because of its multidimensionality, the diversity of the nature of elements, relationships, heterogeneity of the structure, and also because the system functions under conditions of significant uncertainty of the environmental impact. Its complexity is compounded by the random nature of changes in its performance. Any object of study, in order to be considered a system, must possess four basic properties or attributes: integrity and divisibility; the presence of strong ties; organization; emergence. The DCRE system is not an exception to this rule; all four of these features are fully characteristic of it. Particular note is the property of the organization in the DCRE system, which is characterized by the presence of a certain coordination, which is manifested in a change in the entropy (degree of uncertainty or chaos) of the system.

On Issue of Evaluating the Effectiveness SYSTEM

D

D

D

D

D

D

D

D

D

С

С

С

С

С

С

С

С

С

Driver Environment

Road

DCRE system

Car

Holistic Availability stable connection Organization Emergence With the synerg ism property Material Natural

Artificial Technical Big Complex Multi-criteria Isolated Compatible Adaptive Irreproducible Non-stationary Stochastic (probabilistic) Dynamic

Continuous (analog)

Discrete Open Multiplicative

Non-additive Active (targeted)

Organizational

Social Multidimensional Mixed type system

Heterogeneous

Homogeneous Nonlinear Control system Ergоdic

Fig. 1. Classification of the DCRE system [2].

33

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A. M. Umirzokov et al.

In the DCRE system, as in any other system, entropy is the most important sign that determines its longevity its change obeys the law of conservation and transformation of energy. Any chaos in any system depends on the dynamics of energy conversion. The dynamics of energy conversion is characterized by the modulus, direction, and place of energy conversion. As for the DCRE system, it is closely related to the conversion of thermal energy into mechanical and other types of energy, the conversion of mechanical energy during maneuvers, especially during acceleration, braking and collision of a car, etc. Therefore, what is the measured conversion of energy in elements of the DCRE system or between its elements, then the higher the reliability of the system and its effectiveness. The level of entropy in the DCRE system is supported by timely and highquality maintenance and repair of the car, training and retraining of drivers, repair and restoration of roads, and optimization of traffic management [3, 4]. There is nothing that is not subjected to systematization and does not belong to one or another system. There are a great variety of systems, the study of which, classification helps significantly. Classification is the division of the totality of objects into classes according to some of the most significant signs. At the same time, it is important to realize that classification is just a model of reality. Therefore, it should be treated like this without requiring absolute completeness. There was not and there is no perfect and comprehensive classification of the system; moreover, for today, its principles have not been finalized. The DCRE system is no exception, despite the fact that it has extremely important state, national, economic, environmental, and other values. The proposed classification is aimed at a simpler solution to such important and complex problems associated with evaluating the efficiency and reliability of the DCRE system. Today there is no unambiguous definition of the effectiveness of the DCRE system. Consequently, there is no single and comprehensive conceptual model for evaluating the effectiveness of the DCRE system. The conceptuality of the model can be assessed by having a leading design and main point of view in a certain type of activity [4–7]. What is the conceptuality of the proposed method for studying the effectiveness of the DCRE system? Firstly, it should be noted that today there are many studies related to the assessment and improvement of the reliability of the DCRE system. A more important indicator of the DCRE system is its effectiveness. It should be borne in mind that the reliability of the DCRE system is a fundamental factor in evaluating its effectiveness [8–12]. Secondly, as a leading concept of this model, it is proposed to study the effectiveness of the DCRE system on the basis of fundamental laws of nature, in this case, on the basis of the law of conservation, transformation, and transmission of energy. Thirdly, the conceptuality of the model lies in the fact that the conversion and transfer of energy within a particular subsystem and between subsystems occurs stochastically or has a probabilistic nature. Based on this point of view, it is proposed to apply probabilistic-statistical methods for assessing the effectiveness of the DCRE system [13–15]. Fourthly, the efficiency of the DCRE system is identified by the energy conversion efficiency and is defined as the ratio of the useful work performed by the DCRE system

On Issue of Evaluating the Effectiveness

35

to the total amount of energy expended, i.e., [16, 17]. E=

AU · 100%, Q

(1)

where AU = PT · S · cos α,—amount of useful converted heat in the DCRE system, J; Q = gl · Hi · S—amount of total (total) energy spent on performing useful work, J. Therefore, expression (1) can be rewritten as follows: E =

PT · cos α PT · S · cos α · 100% = · 100%. gl · Hi · S gl · Hi

(2)

In the last expression: PT —vehicle tractive effort, N; S—distance traveled, km; α— angle between the directions of the traction force applied to the car and its movement, deg; gl —linear fuel consumption (nominal), kg/(100 km); H i —lower calorific value of fuel, MJ/kg [18]. According to the equation of power balance, the traction force on the driving wheels of the car is determined from the expression [19, 20]. PT = Pf + Pi + Pj + Pw ,

(3)

where Pƒ —car rolling resistance, N; Pi —drag force when the car is moving up, N; Pj — inertia force of translationally moving and rotating car masses, N; Pw —air resistance force, N. The rolling resistance of a car is determined from the expression. Pf = f · Gc ,

(4)

where f —rolling coefficient, which depends on the type and condition of the road surface, on the type and condition of the tire, the tire structure, the location of the cord layers, the tread pattern, the rigidity of the tire material, and the air pressure in it. The resistance force when the vehicle is moving uphill is determined from the expression. Pi = Gc · sin α,

(5)

where α—rise angle of the road. Usually, with small elevation angles not exceeding 9°, it is taken as. sin α = tgα = i,

(6)

where i—road rise coefficient. For operating conditions of cars in mountain and high mountain quarries, where the elevation angle often reaches 12°, the specified limit is exceeded. In this regard, to calculate the resistance force when the vehicle is moving uphill, it is recommended to conduct according to expression (5).

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For the convenience of calculations, use the total coefficient of road resistance ψ, which takes into account the total energy loss, which depends on the same parameters as the rolling coefficient. The total coefficient of road resistance for the operating conditions of heavy trucksdump trucks in mountain and high mountain quarries is [20]. ψ = f + sin α.

(7)

Then, the strength of the total road resistance can be determined as follows. Pψ = ψ · Gc .

(8)

The inertia force of the translationally moving and rotating masses of the car is determined from the expression. Pj = ±mc · δrm · dv/dt,

(9)

where mc —progressively moving mass of the car, kg; δ rm —coefficient of accounting for the rotating masses of a car. The coefficient of accounting for the rotating masses of a car is determined from the expression. δrm = 1, 04 + 0, 05 · Ug2 .

(10)

It should be noted that at vehicle speeds V ≤ 20 km/h in the calculations it is allowed to neglect the force of air resistance. The average speed of heavy trucks in high mountain quarries, as a rule, does not exceed the specified limit.

3 Results Based on the foregoing, as well as expressions (8) and (9), the equation of traction balance (3) of a heavy vehicle operating in conditions of an alpine quarry can be expressed as follows.     PT = Pψ + Pj = ψ · Gc ± mc · δrm · dv dt = mc ψ · g ± δrm · dv dt . (11) Substituting the value of the car’s traction from expression (11) into formula (2), we obtain a differential equation for calculating the efficiency of the DCRE system.   E = PT · cos α (gl · Hi ) · 100% = mc (ψ · g ± δrm · dv/dt) · cos α (gl · Hi ) · 100%. (12) In relation to the operating conditions of heavy dump trucks in mountain and high mountain quarries, it was found that the indicators characterizing the effectiveness of the DCRE system vary within the following limits [8]: • Car speed—Va = 0 … 20 km/h • Mass of transported cargo (for BelAZ-7540B cars) mc = 23 … 37 tons, the average arithmetic value of the mass of the transported cargo is mav= 32,17 tons, mean square deviation—σ = 1,93 tons, and the coefficient of variation—ν = 6% • Longitudinal slope of the road varies from 0 to 12 degrees.

On Issue of Evaluating the Effectiveness

37

4 Conclusions 1. The conceptuality of the method for studying the effectiveness of the DCRE system is substantiated. 2. It is proposed to study the effectiveness of the DCRE system on the basis of fundamental laws of nature, in this case, on the basis of the law of conservation, transformation, and transfer of energy. 3. The feasibility of applying the probabilistic-statistical method for assessing the effectiveness of the DCRE system is substantiated. 4. The effectiveness of the DCRE system can be assessed by identifying the energy conversion efficiency as the ratio of the useful work performed by the DCRE system to the total amount of energy expended. 5. A differential equation is obtained for calculating the effectiveness of the DCRE system for the operation of heavy cars in mountain and high mountain quarries.

References 1. Tursunov AA, Umirzokov AM (2009) The influence of the metrological conditions of the mountain region on the efficiency of cars. Sci Herald Moscow State Techn Univ Civil Aviat 147(10):64–71 2. Umirzokov AM, Mambetalin KT, Saydullozoda SS, Saibov AA, Abaev AKh, Berdiev AL (2019) Classification of the DCRE system. Polytech Bull Series Eng Res 1(45):161–176 3. Umirzokov AM, Saibov AA, Mazhitov BZh, Berdiev AL, Tursunov FA (2016) Evaluation of the efficiency of car operation in the high mountains of the Republic of Tajikistan. In: Actual problems of operation of vehicles: Materials of the XVIII International Scientific and Practical, Conference of Nov, pp 110–117 4. Rotenberg RV (1986) The basics of reliability of the driver-car-road-environment system. Transport, Moscow 5. Bodrov VA (1977) Fundamentals of differential management of operational reliability of automotive structures. Yaroslavl 6. Bodrov VA, Makhnov AV (2000) The concept of randomness of a change in the technical condition of machines and the effectiveness of the existing control system for their reliability. Krasnodar 7. Kuznetsov ES, Andrianov YuV (1981) Operating conditions and reliability of automobiles. Automot Ind 1:8–9 8. Tursunov AA, Abdulloev MA, Umirzokov AM (2010) Assessment of the influence of the parameters of the mountain environment on the energy performance of power plants of transport vehicles. In: International scientific and technical conference, Tyumen State Oil and Gas University, pp 330–334 9. Bobrov VU et al (1980) The study of the reliability of KamAZ vehicles during operation in mountain conditions. DAN Tajik SSR 23:411–414 10. Dzirkal EV (1974) Selection and evaluation of reliability indicators of complex products. Knowledge, Moscow 11. Reliability of Eng Prod (1990) A practical guide to rationing, validation and support. Publ. house of standard, Moscow 12. Aliev VA, Tursunov AA (1987) Reliability of the brake systems of KamAZ vehicles in the specific conditions of the republic. Horizons Sci 4:23–26

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13. Arinin IN, Konovalov SI, Bazhenov YuV, Bochkov AA (1998) Technical operation of cars. In l GU, Vladimir 14. Aristov AI, Borisenko BC (1983) Application of queuing theory to solve practical reliability problems. Knowledge, Moscow 15. Bednyak MN (1983) Modeling of maintenance and repair car processes. Vishchaschool, Kiev 16. Velikanov D, Levin A (1977) Requirements for design features and type of cars of the southern and mountain performance. Vehicles 9:23–26 17. Brailchuk PL, Sattivaldiev BS (1971) Study of the effect of highlands on the fuel efficiency of a car. Tajik NIIINTI, Tajik NIIINTI Dushanbe, p 4 18. Kolchin AI (2008) Calculation of automobile and tractor engines. Higher school, Moscow 19. Saidov ShV, Saibov AA (2008) Quality and competitiveness management of engines. Dushanbe 20. Avdonkin FN (1985) Theoretical foundations of the technical operation of cars. Transport, Moscow

Computer-Aided Algorithm for Nonlinear Optimization of Finishing Operations in Machining Using Precision Cutting Tool M. G. Galkin and A. S. Smagin(B) Ural Federal University, 19, Mira Street, Yekaterinburg 620000, Russia [email protected]

Abstract. For computer-aided multi-variant design of machining technologies, it is important to optimize the cutting parameters at the final pass in each technological operation. When carrying out designing procedures, there emerge problems relating to the algorithm of choosing the decision-making method, the objective function, and the regions of feasibility at final machining steps. Linear programming is time-consuming for multi-variant and multi-pass machining, if the algorithm is to be clear. It is known that when simulating the optimal metal-cutting process, the optimization criterion and the system of constraints are nonlinear. Therefore, a computational algorithm can be made significantly more efficient if it is a nonlinear algorithm based on the Lagrange multipliers. Such an approach to design helps simplify automating the computational algorithm for multi-pass single-tool machining with a precision cutting tool (a reamer). In this paper, we consider the method of forming a mathematical model of nonlinear optimization of the processing mode and solving this model using the Visual Basic for Application programming environment from Ms Excel. Keywords: Nonlinear optimization · Computer-aid · Precision cutting tool · Lagrange multipliers · Ms excel · Visual basic

1 Introduction The main direction in the development of calculation algorithms to determine the most favorable conditions for the final machining of materials cutting is necessary to use computer technology in combination with special mathematical methods of calculation, automating the search for optimal conditions of the cutting process. When using the same traditional calculation algorithms to determine the most rational cutting conditions requires time-consuming calculations with the need for multiple repetition, which complicates the use of formalized solutions. Consequently, there are no guarantees of the choice of effective parameters at this stage of the design of the machining process.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_5

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2 Mathematical Model of the Cutting Process When forming a mathematical model at its initial stage, it is necessary to determine the criterion of the optimal solution for this technological problem. Rationally as a function of the goal for the elementary technological transition deployment to take the equation of machine time per unit length of cutting [1]. It will have the form: to =

1 , n·s

(1)

where n is the scan speed in rpm; s—feed in mm/rev. From Eq. 1 follows that by providing maximum value the denominator of the productivity of the process of machining will be greatest, as for through and blind holes. This fact allows us to consider as the optimized parameters of the spindle speed of the machine and the working feed of the cutting tool in the form of a machine scan. It is known that the mathematical model in the General form in the optimization problem to be solved, determine the dependence on the selected optimization parameters and the requirements introduced by the system of restrictions in the form of inequalities that determine the real conditions of the technological process. In particular, in the early works on optimization of cutting conditions it was proposed to use up to thirteen restrictions, which to varying degrees determined the conditions of the cutting process when considering the preliminary stage of processing by linear optimization. Given the actual production conditions and traditional methods of selection of processing modes, a mathematical model that describes the production of the hole in the final stage of processing “floating” scan after the drill or countersink, may contain fewer restrictions in the modeling of the cutting process. Therefore, in the mathematical model adopted for consideration, no more than six significant limitations can be taken into account when describing the elementary technological transition performed by machine scanning and implemented on a drilling or boring machine. First of all, the first three restrictions will be determined by the kinematics of the equipment. This is the minimum frequency of rotation of the machine spindle—1, the maximum frequency of rotation of the machine spindle—2, minimum flow reamer per revolution to 3. Next, in order to take a working feed machine scan, which is determined by the size of the hole and the hardness of the workpiece material— 4. The next parameter will characterize the resistance of the scan—5. The last restriction in the context of the description of the power parameter of the processing process will be presented through the drive power of the main motion of the machine—6. The restrictions accepted for consideration are shown in Fig. 1 in the form of graphic dependencies. It is obvious that the area of acceptable solutions in this image is represented as a shaded closed loop.

Computer-Aided Algorithm for Non-Linear Optimization

41

Fig. 1. Constraints for machining with a precision cutting tool.

Analyzing the range of acceptable solutions, we can conclude that both the goal function and the system of constraints are nonlinear. Therefore, to solve the mathematical model of this class, we use the well-known conditional optimization method [2], which includes additional conditions in the form of constraints. Its analytical interpretation, in general, can be represented by the following system of Eq. 2: ⎧ F = f (xi ) → max ⎪ ⎪ ⎪ ⎨ g (x ) ≤ c j i j , (2) ⎪ gj (xi ) ≥ cj ⎪ ⎪ ⎩ i = 1, m; j = 1, k where F—is the target function or optimization criterion; gj (x i )—are the function of the optimized parameters; cj —are basic variables to specify the region of feasible solutions. To solve the system of Eq. 2 it is proposed to use the method of Lagrange multipliers [2], which allows to transform the conditional optimization problem into the unconditional optimization problem. As a result of such transformations, it is rational to use the gradient method to find the optimum in the area of acceptable solutions, since it has a good enough convergence, which allows to determine the extremum for a small number of iterations [3–5].

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The formed restrictions on Eq. 2 in the formalized form for processing by the measuring tool in the form of a machine scan can be represented as follows. 1. For the minimum spindle rotation speed: x1 ≥ nmin = c1

(3)

2. For the maximum spindle rotation speed: x1 ≤ nmax = c2

(4)

x2 ≥ smin = c3

(5)

x2 ≤ f (dhole , σb , znom ) = c4

(6)

3. For the minimum reamer feed:

4. For the operating reamer feed:

where dhole —the size of the processed hole (mm), σb —tensile strength of the processed material (MPa), znom —the value of the nominal allowance at the elementary transition (mm). 5. For the necessary cutter durability y

x1 · x2v ≤

(q −1)

v 318 · Cv · dhole Tnm · t xv

· Kv

= c5

where Cv , Kv —reference factors for cutting speed, Tn —reamer durability (min), T —depth of cut at the elementary transition (mm), qv , m, xv —empirical indicators of the degree of cutting parameters. 6. For the primary-motion engine power constraint:   19, 5 · 105 · Ndv · η yp = c6 x1 · x2 ≤ Cp · dhole · t xp

(7)

(8)

where Ndv —power of the main drive of the machine (kW), η—coefficient useful action of the main drive of the machine, Cp —reference coefficient for the power parameters of the process, yp , xp —regulated exponents for the power parameters. The dependences that form these inequalities are formed in accordance with the formulas described in the works [6–9]. In Eq. 8 C p and all coefficients in exponents are taken as for the longitudinal turning process [8].

Computer-Aided Algorithm for Non-Linear Optimization

43

As the objective function adopted the maximum minute reamer feed. This condition allows to minimize the main processing time at each elementary transition (Eq. 1). Consequently, solvable problem, which has in the calculation of the cutting conditions, three optimized parameters, turned in the two-parameter as the frequency of rotation of the reamer x 1 and feed per revolution x 2 . In this case, the depth of cut t, modeling the third parameter in the process of deployment, is already limited to the minimum allowable allowance zmin . According to this circumstance, the target function can be written as F = x1 · x2 → max.

(9)

Substituting the system of constraints and the function of the target (Eq. 9) into the Eq. 2, we obtain the following system of equations: ⎫ x1 ≥ C1 ⎪ ⎪ ⎪ ⎪ x1 ≤ C2 ⎪ ⎪ ⎪ ⎪ ⎪ x2 ≥ C3 ⎬ (10) x2 ≤ C4 ⎪ ⎪ ⎪ ⎪ y ⎪ x1 · x2v ≤ C5 ⎪ ⎪ ⎪ ⎪ yp ⎭ x1 · x2 ≤ C6

3 MS Excel as a Solver To solve this mathematical model (Eqs. 9–10), we propose a programming environment Visual Basic for Application, which is applied a table processor Ms Excel. The mechanism of application of nonlinear optimization in the implementation of various algorithms for finding the best solutions using Ms Excel, has been described in detail in the works [10–12]. The use of the Visual Basic programming environment in this work allows to significantly minimize the amount of program code through the use of ready-made applications that implement this computational process in the calculation procedures. To visualize the calculation algorithm, a model of a user dialog box is proposed for entering the initial information array and displaying the results of the calculation procedures (Fig. 2). With the use of this window interface input of initial data in the form of kinematic characteristics of the processing equipment is realized (Group № 1), in the form of parameters for selection from the database of table feed of the scan (Group № 2), in the form of power parameters of the cutting process (Group № 3), in the form of kinematic parameters of the processing process (Group № 4). Further, in the last Group number 5 implemented a mechanism for selecting the optimal parameters for the deployment, as well as the definition of the minute feed machine scan when removing the specified technological conditions allowance.

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Fig. 2. Blank dialog box for solving the optimization problem.

At the final stage of the optimization task implementation, it is necessary to create a control mechanism for the window interface developed above (Fig. 2). For this purpose, the effective program code in the programming environment Visual Basic for Application [13] is used. In this formulation of the problem it consists of three control procedures. The first procedure called “begin” implements the view of the dialog box in user mode on the monitor screen and allows you to enter the initial information for the calculation. Sub begin () Sheets("deployment").Select DialogSheets("Windows_deployment").Show ‘Modeling the drop-down lists to select options DialogSheets.DropDowns(1).AddItem "10 … 30 … 60" – durability DialogSheets.DropDowns(2).AddItem "Steel; cast Iron; Copper" – material DialogSheets.DropDowns(3).AddItem to_15; to_20; to_30 – diameter interval DialogSheets.DropDowns(4).AddItem "fine; finishing" – type of treatment End Sub.

The next in the order of implementation of the computational process control procedure called “Calculation” addresses the parameters specified for the calculation in the memory, and then performs the proposed calculation algorithm in accordance with the structure of the mathematical model, followed by the output of the basic variables for each constraint in the user dialog box.

Computer-Aided Algorithm for Non-Linear Optimization

45

Sub Calculation () 'addressing the variables specified in the dialog box (st; dr; x1min; x1max; x2min) = Val(DialogSheets.EditBoxes(j).Text (g_v; y_v; m_; k_v) = Val(DialogSheets.EditBoxes(j).Text (N_d; g_p; y_p; x_p; k_p_d) = Val(DialogSheets.EditBoxes(j).Text 'choice of the filing of the scan and the calculation of the reference variables i=20 j=1 interv_dr = DialogSheets.DropDowns(i+2).Text mat = DialogSheets.DropDowns(i+1).Text vid_ob = DialogSheets.DropDowns(i+3).Text Cells(i+20, j+3) = mat Cells(i+20, j+4) = vid_ob Cells(i+20, j+1) = interv_dr ВПР(mat; R21C2:R38C7; interv_dr) so = Cells(i+14, j+34) ‘table feed per revolution of the reamer c_5 = (318 * c_v * dr^ (g_v - 1) * k_v) / (st ^ m_* t^x_v) c_6 = (1950000 * N_d * k_p_d) / (g_p * dr * t^x_p) 'connection of the table processor with the programming environment Cells(i-1, j+4) = x1min Cells(i, j+4) = x1max Cells(i+3, j+4) = x2min Cells(i+4, j+4) = c_5 Cells(i+5, j+4) = c_6 DialogSheets.Labels(k).Text = c_5 DialogSheets.Labels(k+1).Text = c_6 End Sub

The third procedure, called “Optimization”, implements a nonlinear optimization algorithm and then visualizes the optimal parameters of the cutting mode for an elementary transition in the user dialog box (Group № 5) [14]. Sub Optimization () 'modeling of solution of nonlinear optimization problem SolverOk SetCell:= Cells(i, j), MaxMinVal:= 1, ValueOf:= 0, ByChange:=_ Range("R4C4:R5C4") SolverSolve True End Sub.

In this procedure, the algorithm is conditional optimization of the objective function and basic variables is performed by the application SolverOk connected to the object model of Ms Excel is in customization mode.

4 The Practical Implementation The practical use of the calculation algorithm when choosing the optimal parameters of the cutting process is considered further when deploying a hole with a diameter of 20 mm in a workpiece made of high-quality carbon steel 30 with a processing length of 30 mm. The Regulated resistance of the machine scan 30 min, the type of processing-the final deployment. The treatment process is implemented for vertical drilling machine 2H125L. The window user interface is shown in Fig. 3, visualizes the entered initial parameters of the process, the results of the calculation of constraints, the values of optimized parameters as the frequency of rotation of the sweep and its two types of feed, and the main processing time.

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Fig. 3. The user interface window.

From the above dialog follows that for this transition, the optimum frequency of rotation of the scanner turned out to 184 Rev/min, feed per revolution—0,88 mm/Rev, feed rate—161,7 mm/min. on engine time when the length of the hole 30 mm corresponds to min. of 0.18 was found, the settings from the dialog are passed in an automated manner in operating card template.

5 Conclusion The use of the presented computational model allows you to choose not only the optimal parameters of the cutting process in a given area of machining, but also significantly reduce the regulated design time of the operating technology. Since the choice of cutting modes for each technological transition, especially in the conditions of implementation of multi-processing, is quite a long routine and as a consequence of labor-intensive procedure.

References 1. Komyagin V (1996) Programming in excel on visual basic. Radio i svyaz’ Publisher, Moscow, p 320 2. Tsirlin A (2015) Optimization methods for engineers. Direct-Media Publishing, Moscow, p 214

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3. Spiridonov A (1981) The planning of the experiment in the study of technological processes. Mechanical Engineering Publishing, Moscow, p 184 4. Shoup T (1979) A practical guide to computer methods for engineers. Prentice-Hall, p 255 5. Kuritskiy B (1997) Optimum decisions search by means of Excel. BHV–Sankt-Peterburg Publisher, Sankt-Petersburg, p 384 6. Kosilova A, Meshcheryakov R (1986) Spravochnik tekhnologa-mashinostroitelya. V 2 t. T. 2 Handbook of mechanic engineer technologist, vol 2. Mashinostroenie Publisher, Moscow, p 496 7. Matalin A (2008) Machine-building technology. Mashinostroenie Publ, Moscow, p 512 8. Lasdon L (1970) Optimization theory for Lange system. Macmillan, New York, p 523 9. Pang C-M, Busch-Vishniac IJ, Lasdon LS (2000) Optical sensor design using nonlinear programming. Eng Optim 32(4):523–548 10. Bertsekas D (1987) Constrained optimization and Lagrange multiplier methods. Academic Press, p 395 11. Guzeyev V, Batuyev V, Surkov I (2005) Cutting regimes for turning and drilling-milling-andboring machines with numerical control. Mashinostroyeniye, Moscow, p 368 12. Kosilova A, Meshcheryakov R (1986) Spravochnik tekhnologa-mashinostroitelya. V 2 t. T. 1 Handbook of mechanic engineer technologist, vol 1. Mashinostroenie Publisher, Moscow, p 496 13. Gajulapalli R, Lasdon L (2000) Computational experience with a safeguarded barrier algorithm for sparse nonlinear programming. J Comput Optim Appl (to appear) 14. Averchenkov V, Polsky E (2010) Engineering technology: collection of tasks and exercises. Infra-M Publisher, Moscow, p 288

Calculation of Technological Dimensional Chains by Probability Method M. G. Galkin and A. S. Smagin(B) Ural Federal University, 19, Mira Street, Yekaterinburg 620000, Russia [email protected]

Abstract. Modern approaches to the design of machining processes must reliably guarantee the required accuracy of parts manufacturing. When using preconfigured equipment in automated technological design, it is impossible to ensure the accuracy of technological processes without performing a dimensional and precision analysis of design solutions. The article deals with dimensional accuracy analysis, which evaluates the accuracy of obtaining the design dimensions specified in the working drawing of the part. This assessment is necessary to determine the effectiveness of the designed technology and prevent defects in the process of obtaining the specified dimensions. In addition, it is possible to formulate recommendations for adjusting the adopted project decisions to ensure their quality indicators. In the course of solving the problem, the model of the technological process from the initial bar billet to the finished part is considered. For its description, a probabilistic method for calculating technological dimensional chains is used. This method allows you to expand the tolerance fields of the component links of dimensional chains in comparison with the maximum-minimum method, which makes the processing process more economical. This method is available for the development of automated calculation of technological dimensional chains and can be used in modern automated production. Keywords: Technological process · Probabilistic calculation · Dimensional chain · Closing link · Initial graph · Derivative graph · Tolerance

1 Introduction A feature of technological dimensional chains, where design dimensions are considered as master links, is the minimum number of component links. Therefore, the general method of their calculation is the method of complete interchangeability [1]. One of the disadvantages of this algorithm is the assignment of sufficiently tight tolerances on the technological dimensions to ensure the accuracy of the design dimensions within the specified limits [2].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_6

Calculation of Technological Dimensional

49

It is known that all production errors that occur during the processing of parts are random and independent values. This means that the law of their distribution does not change from the values accepted by each of the errors separately. Therefore, it is possible to use the probability method to calculate linear technological chains, which is based on the basic laws of probability theory [3]. This method expands the tolerances on technological links to economically acceptable values (compared with the method of complete interchangeability) but with the assumption of a certain percentage of reclaimable rejects [4].

2 The Calculation Algorithm Theoretical dependencies of the probabilistic method, which can be used in technological dimensional analysis, contain theorems on theoretical average and standard deviations [5]. In particular, using the theoretical average theorem for the sum of random variables, we can establish the relationship between the average deviation of the master link Ec and the average deviations of the component links EcLi . The formula put forth by Professor N. A. Borodachev, with the gear ratio Ai that takes into account the increasing and decreasing links in the technological chain, is the following: Eci + αi

m+n  Ti TLi = ), Ai (EcLi + αi 2 2

(1)

i=1

where αi is the relative asymmetry ratio of the master link; Ti is the master link tolerance; m is the number of increasing links in the chain; n is the number of decreasing links in the chain; αi is the relative asymmetry ratio of the component link; T Li is the component link tolerance. From Eq. 1, it follows that production errors must be corrected according to the center of their grouping using the ratio αi that characterizes the share of mismatch of the expected value of the designed size in the batch of parts with the middle of the dimension tolerance zone specified by the design drawing. These parameters for each technological dimension can be selected during a numerical experiment using pre-formed equations of dimensional bonds that describe mechanical processing. Ratio α for the design dimensions in the low-link technological chain for practical cases is calculated according to the following formula [1]:  0, 59 m+n i=1 Ai αi TLi α = . (2) m+n i=1 TLi In order for the calculations of parameters of component links to be correct, the following conditions should be met: Esi = Eci +

Tki ≤ [Esi ], 2

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M. G. Galkin and A. S. Smagin

Tki ≥ [Eii ]. (3) 2 where [Esi ] and [Eii ] are acceptable tolerance extremes of the i-th master link specified on the component’s design drawing; Esi and Eii are calculated tolerance extremes of the i-th master link; Eci is the calculated average deviation of the i-th master link. Applying the theorem on mean standard deviations of random variables, one can calculate the tolerance limit of the master link [3]. The formula for a low-link technological chain looks like this [2]:  m+n  1  2,  T = λ2Li TLi (4) λ Eii = Eci −

i=1

where λ is the master link’s relative scatter factor; λLi is a component link’s relative scatter factor. λ could be calculated in the following manner [1]:  ⎛  m+n ⎞ m+n   0, 183 ⎝  1 2 − 2⎠ λ2Li TLi TLi 3 λ = + m+n  3 i=1 i=1 TLi

(5)

i=1

In order to determine λLi , which is a part of Eq. 5, it is necessary to establish a theoretical description of the scattering curve of actual dimensions. In particular, for serial production, it is possible to accurately accept the distribution of actual dimensions according to Simpson’s law [1]. Figure 1 shows the dependence of the probability density of appearance of dimensions for this case.

Fig. 1. Probability density of appearance of actual dimensions.

Therefore, if the scattering of dimensions is close to the Simpson law, then, in the calculated dependence, the factor λ2Li is taken as 1/6 [1].

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51

3 Examples of Calculation The use of the presented theoretical material for conducting technological dimensional analysis to compare the effectiveness of the probabilistic method and the maximumminimum method during machining can be exemplified by the formation of linear dimensions in the manufacturing of an axisymmetric component from a bar stock on preconfigured equipment. The sketch of the component and the numbering of the machined surfaces are presented in Figs. 2 and 3.

Fig. 2. Sketch of a component.

Based on the analysis of the information model in Fig. 2, it follows that the accuracy of linear dimensions (along the X axis) in accordance with the principle diagram of the processing of ferrous metals proposed by Professor V.D. Tsvetkov does not go beyond the accuracy of the first stage [6–8]. It is known that within this stage, tolerance is provided in the range of 14 ÷ 12 grades when one machining step is made on each end surface. Next, it is necessary to develop a model of surface treatment along the horizontal X axis of the workpiece in the form of a dimensional diagram. The mechanism behind its development is described in [9–12], and [13]. The final model is shown in Fig. 4. Technological dimensions are marked as Li, and design dimensions as Ki. Since the initial billet is a bar, it does not have dimensions, and processing begins with the previously prepared fifth surface.

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M. G. Galkin and A. S. Smagin

Fig. 3. Numbering of surfaces.

Fig. 4. Dimensional diagram of processing of a component along the X axis.

The next step is to create mathematical models which describe the process of forming canonical equations of dimensional bonds. They are presented in the form of the original and derived graphs [14–16]. On the initial graph (Fig. 5), the master links of dimensional chains are presented as design dimensions, while on the derived graph (Fig. 6), the component links of dimensional chains are presented as technological dimensions.

Fig. 5. Original graph.

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53

Fig. 6. Derived graph.

Then, canonical equations for dimensional links are put together according to rules set in [9, 17, 18]. The system of equations for this processing is as follows: ⎧ − K1 + L1 = 0, ⎪ ⎪ ⎪ ⎨ − K + L − L = 0, 2 4 1 (6) ⎪ − K3 + L4 − L2 = 0, ⎪ ⎪ ⎩ − K4 + L2 − L3 = 0. Since only design dimensions act as master links, the initial data for solving the problem is given in the corresponding design document (Fig. 2). It is clear from the figure that K1 = 10 ± 0, 075 mm, K2 = 5−0,3 mm, K3 = 4−0,3 mm, and K4 = 7 ± 0, 11 mm. To compare the algorithms of complete and incomplete interchangeability, it is proposed to evaluate the accuracy of the design dimensions in the presented processing model (Fig. 4). In order to solve this problem, the accuracy of obtaining technological dimensions is preliminarily assigned. The focus in this case is on the accuracy of the first stage of processing, and economically acceptable tolerances are taken into consideration [3, 19]. This means that these tolerance limits will not be more accurate than the 12th tolerance grade. In Table 1 containing technological tolerances that correspond to the data from the unified fits and clearances [20]. Table 1. Tolerances for technological dimensions. No.

Dimensions

Processing stage

Assigned tolerance (in mm)

1

L1

I

0.15

2

L2

I

0.18

3

L3

I

0.12

4

L4

I

0.18

It is known that the condition for ensuring the accuracy of design dimensions is as follows: the tolerance of the master link corresponding to the value from the design drawing must be greater than or equal to the tolerance determined by the calculated dependence.

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The calculated dependence describing this rule in the probabilistic method is represented by Eq. 4 and is as follows in the complete interchangeability method [1]: T =

n+m 

TLi .

(7)

i=1

The first two-link Eq. 6 implies the following inequality TK1 ≥ TL1 . By placing set and assigned tolerance values into this inequality, we get 0.15 mm ≥ 0.15 mm. Thus, the accuracy for the dimension K1 is fulfilled in both options. The second equation with a master link K2 is a three-link one. Therefore, it is necessary to first determine the calculated tolerance T2 according to Eqs. 4 and 7 and then compare it with the same parameter for the design drawing. First, for the probabilistic method, it is necessary to calculate the factor λ2 according to Eq. 5, inserting the values from Table 1 into it.     0, 183 1 2 1 2 2 2 (T + TL1 ) − (TL4 + TL1 ) = 0.366. 3 λ2 = + 3 TL4 + TL1 6 L4 After calculating it according to Eq. 4, T2 is calculated and compared to TK2 .  1 2 1 2 ) = 0.26 mm. (T + TL1 T2 = 0, 366 6 L4 Since 0.3 mm ≥ 0.26 mm, then the inequality TK2 ≥ T2 is true. This means that the dimensional accuracy K2 is ensured in this processing mode, and the value of design tolerance TK2 takes the value of TK2 = T2 = 0, 26 mm. The same parameter T2 using the maximum-minimum method according to Eq. 7 takes the value of T2 0.33 mm. This value exceeds the design tolerance from the design drawing. Consequently, the method of complete interchangeability requires tightening tolerances of technological dimensions TL1 and TL4 through the selection of more accurate means of technological preparation of production. When analyzing data from Table 2, it is clear that, when the probabilistic method of calculating dimension chains is used, the tightening of tolerances of technological dimensions L 2 and L 3 in the fourth equation is only necessary for the dimension K 4 , which obviously results in a negative margin of accuracy. Thus, in subsequent calculations, the tolerance for dimension L 2 has been tightened from 0.18 to 0.16 mm in order to eliminate these inconsistencies, but within the range of accuracy of the first machining stage. The use of the method of complete interchangeability requires tightening the accuracy of almost all technological dimensions, since a negative margin of accuracy is obtained in the second, third, and fourth equations. After calculation and subsequent adjustment of the accuracy parameters of all technological dimensions using a more economical method of calculation, then it is necessary to determine the remaining parameters of these links. Since most often the adjustment of automated equipment is carried out to reach the middle value of the tolerance limit of the corresponding technological dimension, it

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Table 2. Provision of accuracy of design dimensions. No.

Dimension tolerances according to design drawing, in mm

Tolerances using the probabilistic method

Tolerances using the maximum-minimum method

Design tolerance value

Accuracy margin

Design tolerance value

1

T K1 = 0.15

0.15

0

0.15

0

2

T K2 = 0.3

0.26

0.04

0.33

– 0.03

3

T K3 = 0.3

0.28

0.02

0.36

– 0.06

4

T K4 = 0.22

0.25

– 0.03

0.3

– 0.08

Accuracy margin

is only rational to determine the average values of the deviations of these components included in Eq. 6. To determine the average values of deviations by the probabilistic method, dependence Eq. 1 is used. Thus, the equations for the processing model under consideration will take the following form:     T1 TL1 = EcL1 + α1 , Ec1 + α1 2 2       T2 TL4 TL1 = EcL4 + α4 − EcL1 + α1 , Ec2 + α2 2 2 2       (8) T3 TL4 TL2 Ec3 + α3 = EcL4 + α4 − EcL2 + α2 , 2 2 2       T4 TL2 TL3 Ec4 + α4 = EcL2 + α2 − EcL3 + α3 . 2 2 2 The deviation EcL1 is determined from the first Eq. 8, the deviation EcL4 from the second one, the deviation EcL2 from the third one, and the deviation EcL3 from the fourth one. During this calculation, it is necessary to simultaneously select the αLi factors for each technological dimension, which determine the rational arrangement of the scattering fields of master links within their tolerance limits, as specified by the design drawing. In particular, for the design dimension K 3 , the scatter plot described by the parameters from the design drawing will take the form of 1 in Fig. 7. As a result of the accuracy assessment, the tolerance field of the master link K 3 was adjusted in accordance with the resulting margin of accuracy equal of 0.02 (see Table 2). This means that the tolerance for this dimension is 0.28 mm, not 0.3 mm. As a result, at zero values of factors αLi , the average value of this dimension will shift by 0.14 mm from the nominal value, which coincides with the maximum value. In this case, the scatter plot will have the position 2 in Fig. 7. Then, assigning, within specified limits, the asymmetry factors αLi for each technological dimension, it is possible to change the position of scattering plots of master links

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M. G. Galkin and A. S. Smagin

Fig. 7. Position of the scatter plot of the dimension K 3 .

obtained by calculation within the tolerance limits of these links, which are indicated in the design drawing. These measures help to rationally determine the adjusting dimensions to minimize the effect of production errors on dimensional accuracy during machining. In particular, to locate the center of the grouping of errors of the dimension K 3 symmetrically relative to its tolerance limit specified in the design drawing, factors αLi chosen through automation means should have values presented in Table 3. Table 3. Cycle asymmetry factors. αL1 αL2 0

αL3

αL4

−0.15 −0.2 0.1

Scatter plot of the dimension K 3 for this case of machining is represented by 3 in Fig. 7. Upon reaching the rational positions of the scatter plots within the tolerance limits specified in the design drawing, the values of adjusting and limiting dimensions of all component links are written down. These values are presented in Table 4.

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Table 4. Calculated values for component links. Dimension item

Nominal value, mm

Adjusting dimension, mm

Upper deviation, mm

L1

10.0

10.0

0.075

– 0.075

L2

11.0

11.016

0.096

– 0.064

L3

4.0

4.016

0.076

– 0.044

L4

15.0

14.865

– 0.045

Lower deviation, mm

– 0.225

To verify the accuracy of adjustment of technological dimension chains, dependencies (Eq. 3) and the system of dimensional constraint Eq. 6 may be used. Results of verification are listed in Table 5. Table 5 Calculated and limit values for master links Dimension item

Maximum limit, in mm

Minimum limit, in mm

Calculated value

Accepted value

Calculated value

Accepted value

K1

10.075

[10.075]

9.925

[9.925]

K2

4.995

[5.0]

4.735

[4.7]

K3

3.989

[4.0]

3.709

[3.7]

K4

7.11

[7.11]

6.890

[6.89]

4 Conclusion After the analysis of dimensional relations, which are formed along the axis of a component, by the probabilistic method during its machining, the following conclusions can be made: 1. This calculation method helps to expand the tolerances of technological dimensions forming dimensional chains by an average of 20%, compared with the method of complete interchangeability, even in low-link technological chains (Table 2). 2. The analyzed calculation algorithm allows for automated dimensional adjustment using the selection of asymmetry factors, which increases the stability of processing.

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References 1. Myagkov V (1982) Tolerance values and fit. Mashinostroenie Publ, Leningrad, p 545 2. Paley M, Romanov A, Braginsky V (2009) Tolerance values and fit. Politekhnika Publ, StPetersburg, p 629 3. Ye Ventsel (1999) Probability theory (Teoriya veroyatnostey), 5th edn. Vyshhaya Shkola publishing house, Moscow, p 376 4. Timiryazev V, Voronenko V, Skhirtladze A (2012) Fundamentals of machine-building technology (Osnovy tekhnologii mashinostroitelnogo proizvodstva): handbook. Lan Publishing House, Saint-Petersburg, p 448 5. Solonin I (1972) Mathematical statistics in machine-building. Mashinostroenie Publ., Moscow, p 216 6. Tsvetkov V (1979) System and structural modeling and automation of the design of technological processes (Sistemno-strukturnoye modelirovaniye i avtomatizatsiya proyektirovaniya tekhnologicheskikh protsessov). Nauka i tekhnika Publ, Minsk, p 264 7. Tsvetkov V (1972) System of automation for designing technological processes (Sistema avtomatizatsii proyektirovaniya tekhnologicheskikh protsessov). Mashinostroyeniye Publ, Moscow, p 240 8. Zhukov E, Kozar I, Rozovsky B, Dektyaryov V, Soloveychik A (2002) Technology of machine-building (Tekhnologiya mashinostroyeniya). Polytechnical University Publishing House, Saint-Petersburg, p 498 9. Ashikhmin V, Zakuraev V (2005) Razmernyy analiz pri tekhnologicheskom proektirovanii (Dimensional analysis in design process). UGTU-UPI, Yekaterinburg, p 93 10. Matalin A (2008) Technology of machine-building (Tekhnologiya mashinostroyeniya). Lan Publ House, Moscow, p 512 11. Ivashchenko I (1975) Technological dimensional calculation and methods of their automation (Tekhnologicheskiye razmernyye raschety i sposoby ikh avtomatizatsii). Mashinostroyeniye Publ, Moscow, p 222 12. Matveyev V, Tverskoy M, Boykov F (1982) Dimensional analysis of technological processes (Razmernyy analiz tekhnologicheskikh protsessov). Mashinostroyeniye Publ, Moscow, p 264 13. Mitrofanov V, Kalachev O, Skhirtladze A et al (1995) CAD in machine-building (SAPR v tekhnologii mashinostroyeniya). Yaroslavl State Technology University, Yaroslavl, p 228 14. Solonin I, Solonin S (1980) Calculation of assembly and technological dimension chains. Mash Publ, Moscow, p 110 15. Bazrov B (2001) Modular technology in machine-building (Modulnaya tekhnologiya v mashinostroyenii). Mashinostroenie Publ, Moscow, p 368 16. Mordvinov B, Ogurtsov Y (1975) Calculation of technological dimensions and tolerances during the design of technological processes of machining (Raschet tekhnologicheskikh razmerov i dopuskov pri proyektirovanii tekhnologicheskikh protsessov mekhanicheskoy obrabotki). Omsk, OmPI, p 160 17. Ashikhmin V, Zakuraev V (2006) Automated design of technological processes (Avtomatizirovannoye proyektirovaniye tekhnologicheskikh protsessov). Novouralsk State Technology Institute, Novouralsk, p 196 18. Korchak S, Koshin A, Rakovich A, Sinitsyn B (1988) Systems of computer-aided design of technological processes, devices, and cutting tools (Sistemy avtomatizirovannogo proyektirovaniya tekhnologicheskikh protsessov. prisposobleniy i rezhushchikh instrumentov). Mashinostroyeniye Publ, Moscow, p 352 19. Kharlamov G, Tarapanov A (2006) Allowances for machining (Pripuski na mekhanicheskuyu obrabotku). Mashinostroyeniye Publ, Moscow, p 256 20. Dalsky A, Suslov A, Kosilova A (2001) Mechanical engineer’s handbook (2001) (Spravochnik tekhnologa-mashinostroitelya). Mashinostroyeniye Publ, Moscow, p 994

Study of Influence of Magnetic-Pulse Hardening on Cutting Tools Strength and Wear Resistance L. G. Nikitina1(B) and A. V. Volchenkov2 1 Vladimir State University, 87, Gorky Street, Vladimir 600000, Russia

[email protected] 2 Murom Institute of Vladimir State University, 23, Orlovskaya Street, Murom 602264, Russia

Abstract. We presented the results of the laboratory studies of pulsed magnetization of blade tools, whose cutting part is made of hard alloy (cutters) and high-speed steel (drills). We described the technique of the laboratory experiment with parameters of treatment modes of cutting, magnetization, the equipment which was used, and introduced tool wear evaluation criteria. It was established that during pulsed magnetization wear resistance of cutting tools increases. The orientation of the domains, enhanced particle cohesiveness largely inhibits the movement of interdomain boundaries. An attempt was made to evaluate the state of the cutting part of magnetized and non-magnetized tool by analyzing analytical dependences of thermal stress which arises in the cutting process and causes brittle fracture of the tool. The analysis of the calculations done with the allowance for the set of physico-mechanical parameters of magnetized tool materials can lead to the conclusion that magnetized tool materials have the effect of thermal stress weakening though it is negligible. Keywords: Strength · Durability · Magnetic hardening · Cutting tool · Drill · Cutter

1 Introduction Increasing the strength of cutting tools is an important task of engineering production. One of the possible methods of increasing the strength of the tool is pulse magnetization of its cutting part. The research on magnetic-pulse hardening, has been conducted for several decades by scientists from different countries. Technological effect in relation to the tool life increase has always been positive and ranged from 30 to 300% [1–7]. Instrumental metals can be attributed to magnets, i.e., substances that can be magnetized. The reason for magnetization is that the movement of electrons within each atom is closed electrical currents, so it can be assumed that they are molecular currents responsible for a substance magnetization. All magnetic phenomena are due to the interaction of currents [8, 9].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_7

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L. G. Nikitina and A. V. Volchenkov

According to modern concepts, the essence of ferromagnetism lies in the fact that a strong orientation of electron magnetic moments occurs in ferromagnetic materials, regardless of the external magnetic field, so that ferromagnetic materials prior to saturation corresponding to a given temperature, are magnetized without any field. However, ferromagnetic materials in the absence of an external field may not be magnetized. To explain this apparent contradiction P.Weis proposed a second major hypothesis that a ferromagnetic material is divided into a large number of small areas (domains) [10, 11]. Each of these areas at temperatures below the Curie temperature is strongly magnetized, but the directions of the magnetization of individual domains are different, namely, the total magnetic moment of the ferromagnetic material is equal to zero. The physical cause of spontaneous magnetization was settled in 1928, by Ya. I. Frenkel and later by Heisenberg V., who showed that a strong orientation of the electron spins is caused by the exchange interaction forces. Thus, the magnetization process is accompanied by the enlargement of domains, a decrease in the amount of cross-domain boundaries, and hence by metal inhomogeneity, domains’ uniform energy distribution by volume. In the presence of the internal field, the domain structure changes and the ferromagnetic material can be deformed. The deformation phenomenon in case of magnetization was discovered by Joel in the middle of the nineteenth century and became known as magnetostriction. These processes of magnetization occur with some delay, that is, the shifting of boundaries and the rotation of the magnetization vector, are behind the field changes, which leads to hysteresis [12–14]. The aim of the research is to study the influence of magnetic hardening of blade tools (drills, cutters) on strength and wear resistance.

2 The Modeling and Discussion An attempt was made to evaluate the state of the cutting part of magnetized and nonmagnetized tool by analyzing analytical dependences of thermal stress which arises in the cutting process and causes brittle fracture of the tool. As we know that for fragile bodies thermal stress value in a certain point x of a cutting part of tool in case of heating and cooling is calculated by equations [15]      √ σθ ∼ (1) = E · α · 1 − ϑ −1 · 1 − l h · (θk − θ0 ) · erf · 1 2 Fox     σθ ∼ =E · α · 1 − ϑ −1 · 1 − l h ·   √  √ 2 , (θk − θ0 ) · erf · 1 2 Fox − eBi ·x+Bi · x · Fox ·efrc · 1 2 Fox + Bi ·x · Fox (2) where: E—elastic modulus; α—coefficient of thermal expansion; ν—Poisson’s ratio; x—coordinate of a given point; θ k—temperature of contact surfaces; θ 0 —ambient temperature; C p —volumetric heat capacity; h—height of tool body; I—distance from cutting tool to neutral line; Bi —Biot number; erf —risk of errors integral.

Study of Influence of Magnetic-Pulse

61

F ox —Fourier number for coordinate x; t , cp

Fox = λ ·

(3)

where: λ—thermal conductivity; 2

efrc · x = 1 − Φ(x) = π·

x

,

(4)

eox dt

o

where Φ(x)—tool material density Φ(x) =

2 π·

x

.

(5)

e−t

o

As the Eqs. (1) and (2) show, thermal stress for a given time moment depends on a set of physical features of tool material and cooling medium. In the cutting process summation of compressive mechanical and thermal stresses occurs in the contact zone. Thermal stresses, at any point at any given time can be stretching or compressing. Outside the contact zone thermal and mechanical stresses can have a different sign [15]. Rapid heating and cooling during intermittent cuts cause thermal “shocks”, the temperature field in the surface layers is characterized by high gradients of temperature and σv at high contact temperatures reaches significant values. If the value of σθ exceeds the strength limit σv , the cracks appear and brittle fracture starts. Let’s use the last recommendation (σθ < σv ) as a criterion of sustainability properties of the tool. It is necessary to calculate the dependencies of thermal stress against temperature θk according to formulae (1) and (2) under familiar parameter values introduced to these formulae after pulse magnetization; then it is necessary to compare the derived thermal stress values to mechanical loading stresses [15]. Calculations are made for hard alloy WCCo4 and high-speed steel R6M5 for the point, located off the cutting edge at depth x = 0,5 mm and under t = 0,01c and temperatures θk = 1273 K, θo = 293 K [16]. The study of physical and mechanical features of hard alloys under magnetic-pulse treatment shows the reduction of coefficient of linear expansion by 1,5…3%, the increase of heat conduction and heat capacity by 10…15% [2]. As for elasticity modulus and Poisson’s ratio, the study shows their little reduction which can be neglected in calculations [16]. The calculated results are given in Fig. 1(a, b, c, d). For hard alloy WCCo4 under heating (Fig. 1a) thermal stresses are reducing under pulse magnetization (straight line 2), the temperature range of tool usage extends by 50…70 °C. The usage of magnetized tool under temperature higher than 370 °C is not advantageous as there isn’t any strength increase effect. Though there is an effect of

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L. G. Nikitina and A. V. Volchenkov

Fig. 1. Dependence of thermal stresses σθ on the temperature of the cutting edge of the tool: a hard alloy WCCo4 under heating, b hard alloy WCCo4 under cooling, c high-speed steel R6M5 under heating, d high-speed steel R6M5 under cooling; where: 1-non-magnetized tool; 2-magnetized tool.

thermal stress reduction (compare straight lines 2 and 1) under cooling (Fig. 1b), the tool usage under temperatures higher than 120 °C is not possible as in this temperature range thermal stresses are higher than mechanical loading stresses. For high-speed steel R6M5 under heating (Fig. 1c) the whole temperature range can be practically used for both non-magnetized and magnetized tool. Thermal stress reduction is observed (straight line 2) which extends temperature range. Under cooling (Fig. 1d) temperature range contracts considerably to 300 °C. The analysis of calculations made with allowance for a set of physico-mechanical parameters of magnetized tool materials makes it possible to draw a conclusion that the effect of thermal stress reduction of magnetized tool materials is present, however, it is negligible (about 10…15% under procedure offered), so the usage of magnetized tools is possible under strict observance of the norms of thermodynamic parameters.

3 The Experimental Research and Results The aim of laboratory tests is to study the magnetic hardening of the wear resistance of the blade tool. Cutters with TiC15Co6 hard metal plates and HSS Ø16 mm drills were chosen for the research. Testing of the cutting tools was conducted in laboratory conditions using vertical 2N135 drilling machine and 16B25P screw-cutting lathe. Wear measurement was performed on the horizontal IZA-2 comparator, which is used for absolute linear measurements. The linear dimensions of the instrument were measured by comparing the

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measured size with a dashed liner scale of the instrument with the help of two microscopes, the distance between which was always constant, and the optical axes were parallel. A scale interval of the spiral ocular microscope was 0,001 mm. Magnetization of the tools was carried out with a special IIM-3 installation. A specific feature of this installation is its ability to magnetize a tool, to demagnetize, and measure magnetic parameters (magnetic field intensity, coercive force, magnetic induction, magnetic permeability). Characteristics of the installation: • magnetic field in the center of the inductor—250–350 kA/m; • power consumption of up to 5 kW. The installation creates a pulsed magnetization with adjustable pulse duration of 0,5–60 s., with a 2 s delay. Power consumption for one instrument with a pulse duration of 2 s and the number of pulses of p = 5 is 0,0138 kW/h. The magnetization technology involves the following procedures: (a) measurement of magnetic parameters prior to magnetization; (b) carrying out the process of magnetization. For this a number of pulses and their duration are selected: • high-speed steel—p = 3–5 pulses, duration = 1,5–2 s, delay = 16–24 h; • solid steel—p = 7–10 pulses, duration = 0,5–1 s, delay = 16–24 h; (c) measurement of the magnetic parameters after magnetization. Operation, layout and installation of pulse magnetization installation are given in the technical description of the installation. One of the important issues in the preparation of test procedure technique is the question of choosing a cutting tool resistance criterion [17, 18]. In laboratory conditions, the absolute criterion, in our opinion, may be a maximum linear wear over the entire duration of the cutting process or a tool wear value of the cutting edge for a cutting time between sharpening. In the first case it is connected with resistance, and in the second case with a period of cutting tool resistance [19, 20]. Laboratory tests were performed on straight-turning cutters with plates made of TiC15Co6 hard alloy in the amount of 6 pieces. Two cutters were control samples, and four were magnetized. The longitudinal turning of the shaft made of 38HS steel was carried out with the cutters on 16B25P screw-cutting lathe. The following cutting modes were appointed: supply S = 0,05 mm/rev and 0.1 mm/rev; depth of cut t = 0,025 and 0,5 mm and the υ = 50, 70, 80 m/min (speed of the spindle is 250, 315, 400 rev/min, respectively) [21]. At the given speed every 10 min the wear of the cutter was measured with a micrometer method. The measurements were summed during the 100 min period of the cutter operating time. Wear results were compared. The effect of wear was calculated according to the formula: Ew % =

h · 100 hmin

,

(6)

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where h = hk − ho hk —wear of the control sample of non-magnetized drill; h0 —wear of the nonmagnetized drill which is in use; hmin —permissible minimum wear value. Laboratory tests were also been performed on Ø16 HSS drills in the amount of 5 pieces. One of the drills—the control sample (non-magnetized), and the remaining four were magnetized. The drills made holes of 30 mm in depth in a steel billet made of 45 steel, the drill geometry: ω = 30°, 2ϕ = 116°, ψ = 55° on 2N135 vertical drilling machine. At a certain cutting mode (supply S = 0,2 mm/rev, length l = 30 mm, the cutting speed υ = 17, 25, 35 m/min (speed 355, 500, 710 rev/min)), respectively, 5 or 10 holes were drilled out and wear was measured [21]. Then we calculated machining time Tm and established the dependency ho = f (Tm ) at υ = const, and t = const. The obtained results of magnetized drills were compared to non-magnetized ones. The effect of wear was calculated according to the above formula. The following results were obtained during the research: • laboratory testing of through-cutters with plates made of hard alloy TiC15Co6 when processing the workpiece such as “shaft” made of 38HS steel showed that the wear of the cutting edge of magnetized cutters (4 pcs.) caused by the field with the strength of 300 kA/m in comparison with the non-magnetized cutters (2 pcs.) decreased by 8,7% (300 min without resharpening), 57% (300 min without resharpening), 6,6% (120 min without resharpening), i.e., on average, it constituted 96%. • laboratory tests on Ø16 mm drills made of R6M5 high-speed steel when drilling billets of 45 steel showed that the wear of the cutting edge of the magnetized drills (4 pcs.) caused by the field with the strength of 300 kA/min comparison with the non-magnetized drills decreased by 51,7% (Tm = 10 min), 71,55% (Tm = 5 min), 35,5% (Tm = 10 min), 25,5% (Tm = 10 min), i.e., on average it constituted 46%.

4 Conclusions • In the process of magnetization, the structure and temperature field change. The orientation of the domains, enhanced particle cohesiveness largely inhibits the movement of interdomain boundaries, thus preventing the movement of dislocations and thereby contributes to the resistance of material to brittle failure. • It was found that magnetic-pulse hardening of the cutter having the plates made of TiC15Co6 hard alloy leads to 96% wear reduction of the cutting edge. • It was found that magnetic- pulse hardening of the Ø16 mm drills made of high-speed steel reduces the wear of the trailing edge by an average of 46%. • The effect of thermal stress reduction of magnetized tool materials is present, however, it is negligible (about 10…15% under procedure offered), so the usage of magnetized tools is possible under strict observance of the norms of thermodynamic parameters.

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References 1. Loladze T (1982) The strength and durability of cutting tools. Engineering, Moscow 2. Maligin B (1989) Magnetic hardening of tools and machine parts. Engineering, Moscow 3. Sokolik N (1993) Increase of durability of details by the combined method of magnetic processing. Dissertation, University of Moscow 4. Mansori M, Lafdy K, Palmer D (2002) Enhanced wear resistance and tools durability using magnetization, metal cutting and high-speed machining. Kluwer Academic, Plenum Publishers, pp 301–310 5. Mohamed M et al (2012) Effect of magnetic field on the friction and wear displayed by the scratch of oil lubricated steel. Int J Eng Technol (IJET-IJENS) 12(6) 6. Borisova E, Zelinskyi V (2015) On the mechanism of ferromagnetic materials wear reduction. Proc Eng 129:111–115 7. Zelinskyi V, Borisova E (2015) About the quantum-mechanical nature of wear on magnetized cutting and deforming tools. In: International conference on mechanical engineering, automation and control systems (MEACS) 8. Kifer I (1969) Ferromagnetic materials testing. Energia, Moscow 9. Landau L, Lifshits E (1969) To the theory of magnetic permeability dispersion. Collected works, Science 10. Kersten M (1956) To the interpretation of temperature dependence of initial permeability. Zs.f Phys, 8, p 382 11. Taylor R, Jakubovics J, Astie D et al (1983) Direct observation of the interaction between magnetic domain walls and dislocations in iron. J Magn Magn Mater:970–972 12. Neel L (1946) Bases d’une champ coercitif. Ann Univ Grenoble 22:299–343 13. Neel L (1949) New theory of coercive force. Physica 15:225 14. Betaneli A (1973) The strength and reliability of cutting tools. Sabchota Sakartvelo, Tbilisi, p 302 15. Loladze T, Tkemaladze N, Tyutchev F (1975) Study of stresses in the cutting part of the tool during transients by the method of photoelasticity. Mess GSSR 3:657–660 16. Nikitina L, Putyrsky V (2014) Effect of pulsed magnetization on the state of cutting tools. Fund Appl Probl Eng Technol 4:65–68 17. Avakov A (1983) Physical basis of the theory of cutting tool resistance. Engineering, Moscow 18. Gurevich D (1980) The wear mechanism of titanium tungsten solid alloy’s. J Mech Eng 1:41–43 19. Rabinowicz E (1995) Friction and wear of materials. Wiley 20. Markov D, Kelly A (2002) Establishment of a new class of wear: adhesion initiated catastrophic wear. Int J Appl Mech Eng:887–901 21. Cosilov F, Meshcheryakova R (1985) Reference technologist-mechanical engineer. Mashinostroenie, Moscow

Solid Modeling of Involute Bevel Gears B. Lopatin(B) , S. Plotnikova, and V. Bruzhas South Ural State University, Zlatoust Branch, 16, Turgenev Street, Zlatoust 456209, Russia [email protected]

Abstract. In some cases, when designing modern transmissions, it is not possible to obtain a rational layout of the drive, to increase its load capacity when using traditional gears (cylindrical, bevel, etc.). The use of gears with involute bevel gears (IBG) allows solving this problem. It is possible to form gears for any arrangement of gears axles in space (crossing, intersecting, parallel axes) from IBG. At the same time, gears with IBG will have improved load and layout characteristics with respect to gears from ordinary cylindrical and bevel gears. However, the problem arises for obtaining solid-state models of involute bevel gears when assessing the stress-strain state of gear teeth with IBG. The paper presents a method for generating 3D models of involute bevel gears (IBG) by modeling machine gearing of an IBG and generating rack. The initial data for obtaining the involute bevel wheel model are: the number of teeth z, the module m, the angle δ, the angle of the tool β, the width of the wheel b, the wheel diameter at the greater end of Da , the distance from the larger end to the zero cross-section b0 , the parameters of the rack (profile angle, height dimensions, radii of filets on the top and hollow of the tooth). In this case, the parameters of the generating rack can be set at the designer’s request. Models of a straight IBG, helical IBG, and an internal IBG are shown. Models of different involute bevel gearings are demonstrated as an example. Keywords: Solid model · Involute bevel gear · Models of gearings · Models of gears · Generating rack

1 Introduction Present-day design of gear trains requires solid modeling. Solid models of gears and generated gearings can be used to evaluate their stress-strain state. While solid modeling of conventional spur gears is facilitated by standard software such as KOMPAS, Inventor, etc., the problem of modeling IBG is more difficult to solve due to their specific geometry. Involute bevel gearings are used to design modern original gear trains which cannot be generated from conventional gears [1–7]. Three-dimensional solid models of IBG are necessary to generate designed IBG trains and study their stress-strain state.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_8

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This is due to the peculiarity of the geometry of the teeth of the IBG. In such a gear, in contrast to the usual helical cylindrical gear, the coefficient of tool displacement in each end section varies linearly. In the train, the width of the gear is limited by the conditions of the sharpening at the larger end and the undercut on the smaller one. For the helical IBG due to the cone angle, the end gearing angles for different sides of the teeth with a symmetrical rake profile are different. All these peculiarities do not allow forming 3D models of IBG with known software tools. The article presents a method for obtaining 3D models of involute bevel gears.

2 Theoretical Part An involute bevel gear is a gear cut by a rack-type tool (rack-type cutter, hob cutter, grinding wheel) with alternating shift along the gear axis [8–11]. It is typical of such gears for each cross section to have a profile with a certain shift coefficient which varies in each section by the amount. x = s · tgδ/m,

(1)

where s is the pitch (the assumed distance between two adjacent sections); x is coefficient of tool displacement; δ is the IBG cone angle; and m is the module. IBG tooth geometry in its cross section is determined by the geometry of the generating rack section cut in the plan perpendicular to the gear axis. In accordance to the notations from [9–11], let us take as the left-hand side of a tooth that side which is visible when the teeth are viewed clockwise from the heel side. Let us call the side of the rack which cuts the right-hand side of a tooth the right side. Values corresponding to the right-hand side of a tooth will be labeled as “R”, and those corresponding to the left-hand as “L”. While the central plane of the rack is angularly inclined to the gear axis, the height dimensions of the cross section increase by 1/cosβ times. While the rack is inclined in the central plane at an angle β, the dimensions along the center line of the rack increase 1/cosβ times in relation to the dimensions in the normal section, therefore mt = m/ cos β.

(2)

The coefficients h*at and c*t which characterize the height of the straight and rounded portions of a rack tooth can be determined with the following assumptions: ht = h∗at · mt = h/ cos δ = h∗a · m/ cos δ.

(3)

h∗at = h∗a · cos β/ cos δ, ct∗ = c∗ · cos β/ cos δ.

(4)

From which

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The process of generating an IBG tooth in an arbitrary cross section (the position of which is determined by the tool shift value x t mt ) can be considered a result of cutting and gear with an asymmetric rack. This makes it possible to apply methods and formulas used for calculating spur gears to determine the IBG dimensions in the cross section. The pitch circle equals r = mt z/2, where z is the number of gear teeth. The addendum circle equals   Ra = mt · z + 2h∗at + 2xt − 2ct∗ /2.

(5)

(6)

The dedendum circle equals   Ri = mt z − 2h∗a + 2xt − 2ct∗ /2.

(7)

The radii of involute base circles which generate the tooth flanks are rbr = r · cos αtr rbl = r · cos αtl

(8)

When β = 0, the tooth flanks are outlined by the involutes of different base circles. The pitch circle thickness of a tooth is determined by St = mt (π/2 + xt · tgαtr + xt · tgαtl ).

(9)

The flank of an IBG tooth is an involute helical surface (involute helicoid). When, the right-hand and the left-hand tooth flanks are different involute helicoids, the base cylinder radii of which are determined by formulas (8), and helix angles on the pitch cylinder are calculated with the expressions: tgβl = tgβ · cos δ + tgα · sin δ/ cos β

(10)

tgβr = tgβ · cos δ − tgα · sin δ/ cos β

(11)

In these formulas, the positive value of angle β corresponds to the right-hand direction of the helix. The above dependencies allow us to determine the principal dimensions of the IBG model. In work [12] presents a method of modeling with a special software package which generates a model by combining several IBG cross sections. When applying this method of IBG modeling, the accuracy of the model depends on the number of combined cross sections, that is, the more sections there are, the more accurate the model is. This paper centers on IBG modeling by simulating cutter-blank mesh of an IBG with a generating rack (Fig. 1). In this case, gears can be modeled with different parameters of the generating rack (α, ha *, hf *, c*, ρ*). Gear teeth were shaped with the computer-aided modeling system KOMPAS-3D. Initial data for IBG modeling were uncut dimensions and rack setting angles β and δ. Figure 2 shows the process of shaping IBG teeth.

Solid Modeling of Involute Bevel Gears

Fig. 1. Diagram of a machine engagement of a bevel gear with a generating rack.

Fig. 2. Shaping IBG teeth.

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3 Practical Significance Figure 3 shows examples of solid models: a straight involute bevel gear (Fig. 3a), a helical involute bevel gear (Fig. 3b), and an internal involute bevel gear (Fig. 3c). Involute bevel gearings can be shaped at any axial position [13]. Involute bevel gears form conjugate meshes not only among themselves, but also with conventional spur gears.

Fig. 3. Models of involute bevel gears: a straight IBG; b helical IBG; c internal IBG.

Figure 4 shows diagrams of spur-bevel gearings with a conventional spur gear [13, 14]. Figure 4a shows a diagram of a gearing on skew axes. It operates smoothly and is less sensitive to interaxial distance errors than a spur gearing. Linear or near-linear contact is possible for one of the rotation directions; this makes it possible to use these gearings in high-speed and heavy-duty drives. For δ 1 = 0; β 1 = 0; β 2 = 0, the gearing degenerates into a spiral gearing (Fig. 4b). Figure 4c shows a diagram of a spur-bevel involute gearing on crossed axes. It is advisable to apply such gearings when crossed axes angles are narrow and generation of conventional bevel gears with a large cone distance is difficult. The gearings are insensitive to crossed axes angle errors. Two involute bevel gears set point-to-point in gearings between parallel axes (Fig. 4, d) allow axial movements to adjust the side clearance or interaxial distance [15–18]; δ 1 = δ 2 and β 1 = – β 2 in such gearing. If we assume that angle δ = 0 in this scheme, the gearing transforms into a conventional spur gearing on parallel axes. Figure 5 shows models of involute bevel gearings [19, 20].

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Fig. 4. Diagrams of cylindro-bevel gearings: a on skew axes; b a spiral gear; c on crossed axes; d on parallel axes.

4 Conclusion Solid IBG models developed by simulating cutter-blank mesh of an IBG and a generating rack most fully reflect the real process of tooth shaping. This method makes it possible to model IBG at various tool height and angle parameters (generating rack parameters), which significantly expands the range of generated gear models. Solid IBG models make it possible to shape various types of gearings (hyperboloid, bevel, spur) when designing gear trains for various purposes. Gearing models can be further used to estimate their strain-stress state. When moving the rack along a curved path, it can get a gear with a non-involute tooth profile [21, 22]. The proposed method for obtaining 3D models of IBG can be used to obtain models of conical gears with non-involute tooth profile by moving the generating rack along a given path the axis of the billet [23–27].

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Fig. 5. Models of gearings: a helical involute bevel gearing on parallel axes; b backlash-free planetary gearing of straight involute bevel gears; c spur-bevel involute gearing on crossed axes; d gearing between parallel axes.

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References 1. Bezrukov VI, Goncharov YuA, Zaynetdinov RI (1983) Planetary transmission. Copyright evidence USSR 10559223, Nov 1998 2. Lopatin BA, Kazartsev DN, Lopatin DB, Bezrukov VI, Rublev VM (1998) A non-gaping planetary gear. RF Patent 2101588, 10 Jan 1998 3. Lopatin BA, Tsukanov ON (2002) Theoretical aspects of the synthesis of helical-bevel gearing in general settings. Proc High Educ Establish Eng 2:37–43 4. Lopatin BA, Tsukanov ON, Plotnikova SV (2003) Cylindro-bevel toothed gears in car drives. Bull Mach Build 8:7–9 5. Tsukanov ON, Lopatin DB, Poluektov EA (2009) Electromechanical drive for mechanisms of the angular turn of objects of space technology. Bull Mach Build 2:14–16 6. Eremin VP, Eremin NV, Kirillin AN et al (2015) Creation of a new generation of electromechanical drives of trans-formed spacecraft systems. In: FSUE GNPRKC TsSKB-Progress, Samara 7. Plekhanov FI, Lopatin BA (2015) Planetary gear. RF Patent 2550598, 10 Apr 2015 8. Litvin FL (2004) A fuentes gear geometry and applied theory, 2nd edn. Cambridge University Press, Cambridge 9. Bolotovsky IA (1986) Handbook on geometric calculation of involute and worm gears, 2nd edn (updated and revised). Mashinostroyeniye, Moscow 10. Lopatin BA, Tsukanov ON (2005) Cylinder-conical gears. Monograph. SUSU, Chelyabinsk 11. Lopatin BA (1998) Development of theoretical bases of design, manufacture and testing of helical bevel gears with small interaxle corners. Dissertation, Kalashnikov ISTU 12. Bruzhas VV, Lopatin BA (2015) Development Of Solid-State Models For The Gears Of Different Geometry. In: International conference on industrial engineering, ICIE 2015, Procedia Engineering Series, pp 369–373. https://doi.org/10.1016/j.proeng.2015.12.125 13. Lopatin BA (2014) Involute-bevel gearings. In: Science SUSU, materials of the 66-th scientific conference, pp 1478–1483 14. Lopatin BA, Tsukanov ON (2012) Cylindro-bevel gearing. Int J Exp Edu 11:34–36 15. Tsukanov ON (2011) Ground rules of design of helical-bevel gearing in homogeneous coordinates. SUSU, Chelyabinsk 16. Lopatin BA, Plotnikova SV, Khaustov SA (2015) Involute helical-bevel gearing. In: International conference on industrial engineering, ICIE 2015. Procedia Engineering, Ser, pp 891–895. https://doi.org/10.1016/j.proeng.2015.12.123 17. Lopatin BA, Bruzhas VV (2015) Features of involute-bevel gearings on parallel axes. In: Materials of the 67th scientific conference. Ministry of Education and Science of the Russian Federation, South Ural State University, pp 1299–1305 18. Lopatin BA, Plotnikova SV (2017) Helical-bevel gearing with small wheel axles angles. In: International conference on industrial engineering, ICIE 2017. Procedia Engineering, Ser., pp 1189–1194. https://doi.org/10.1016/j.proeng.2017.10.616 19. Lopatin BA, Plotnikova SV (2015) Cylindrical gear formed by helical-bevel gearing. Sci Edu Mod Soc 8:120–121 20. Tsukanov ON, Lopatin BA, Bruzhas VV (2015) Planetary gear: patent for utility model RUS 159017 05/15/2015 21. Lopatin BA, Zainetdinov RI (2019) Cutting teeth of non-involute gears of the cylinder-conical internal transmission of internal gearing. Lect Notes Mech Eng 0:1201–1210. https://doi.org/ 10.1007/978-3-319-95630-5_125 22. Poluektov EA, Lopatin BA, Plotnikova SV (2020) Working Surface Calculation of Teeth Bevel Gear Helical-Bevel Gearing at Milling with Hob. In: 5th International conference on industrial engineering, ICIE 2019, Sochi, Russian Federation, pp 9–16. Lecture Notes in Mechanical Engineering. https://doi.org/10.1007/978-3-030-22063-1_2

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23. Lopatin BA, Poluektov EA, Lopatin DB, Zaynetdinov RI, Rublev VM (2009) Method for cutting teeth of a non-involute gear of a cylindro-bevel transmission of internal gearing. RF Patent 2364480, 20 Aug 2009 24. Lopatin BA, Poluektov EA, Khaustov SA (2011) Formation of an internal approximate gearing of the cylindro-bevel gears. Bull SUSU Ser Mech Eng 11(228):62–69 25. Poluektov EA, Lopatin SD (2011) Modification of tooth profiles in cylindro-bevel gear internal engagement. Science SUSU Chelyabinsk Publ. center SUSU, pp 160–164 26. Plotnikova SV, Poluektov EA (2013) The method of teeth profiling of cylindro-bevel gears of internal engagement. Science SUSU Chelyabinsk Publ. Center SUSU, pp 329–332 27. Lopatin BA, Zainetdinov RI (2018) Forming of tooth profiles of non-involute bevel gear on CNC machines. Int Syst Prod 16(1):53–57

Application of Modal Analysis to Building Simulation Models of Thermal Processes in Machine Tools A. N. Polyakov(B) and I. P. Nikitina Orenburg State University, 13, Av. Pobedy, Orenburg 460018, Russia [email protected]

Abstract. In this paper, modal analysis is proposed to building simulation models of thermal processes in machine tools. The technique of building simulation models in Simulink in three ways is described. The first way of modeling uses an analytical solution of the thermal conductivity equation. The second way of modeling uses built-in tools for solving differential equations. The third way of modeling uses the apparatus of transfer functions. An analysis of the structures of the generated simulation models was carried out to solve two typical tasks: building the thermal characteristics of the machine tool under zero and nonzero initial conditions. The first way to build simulation models, based on the use of analytical solutions of the thermal conductivity equation, allows you to build the most compact simulation models of the running machine tools. A feature of building invariant S-models is the formation of modeling parameters in Matlab M-file. For multimodal thermal characteristics of machine tools based on experimental modal analysis, a new algorithm for building them under nonzero initial conditions is proposed. It is based on the redistribution between several modes of the thermal displacement level formed in a previous section of the machine diagrammatic work. From full-scale and computational experiments, it was shown that this uniquely made it possible to increase the accuracy of prediction. Keywords: Thermal characteristics · Machine tool · Thermal error · Experimental modal analysis · Simulation · Diagrammatic work

1 Introduction Today, despite the serious technical and technological solutions implemented in contemporary CNC machine tools, the problem of their thermal stability remains unresolved [1]. As an example, below is a brief overview of several works published during the current year. In [2], the study of thermo-mechanical coupling in the spindle feed system that occurs during milling is presented. It was shown that as the drive warms up, the influence of thermal processes on axial deformations gradually begins to exceed the influence of cutting forces. In [3], the thermal displacements of the spindle system were investigated, © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_9

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due to both fluctuations in the ambient temperature and a change in the power of internal heat sources. According to the authors, they have achieved the stability of the prediction model based on a multi-objective genetic algorithm. In [4], the advantages of physically based model over data-driven model in relation to thermal processes in machine tools were presented. Testing of the proposed solutions for compensating the temperature error of the machine tool was experimentally carried out on a TC500R vertical machining center. Even with a small spindle speed of 1000 rpm, the displacements along the Yaxis were slightly less than 20 microns, after 4 h of operation of the machine. In [5], a new method for thermal error measurement and modeling in CNC machine tools’ spindle was presented. In [6], an analytical prediction model of the cross-rail deflection considering both gravity and thermal effects in a heavy gantry slideway grinding machine was considered. In [7], among the factors affecting the thermal errors in lathes, errors in a ball screw system of a feed drive are considered. In precision grinding machines equipped with thermal error compensation systems, the thermal effect of the coolant is insufficiently taken into account. So in [8], the influence of coolant on the thermal characteristics of the worm gear of a precision grinding machine was experimentally investigated. In [9], the authors proposed the creation of intelligent machine tools that can compensate the thermal errors arising in all axes in real time. Thus, even an incomplete review of recent studies by various scholars shows the significant influence of thermal problems in achieving the machining accuracy and the complexity of the algorithms used in thermal modeling of machine tools.

2 Modal Analysis Today there is a variety of approaches, methods, and algorithms used in thermal modeling of machine tools and their corresponding thermal error compensation systems. At the same time, in world practice, a modal approach continues to be used to solve problems associated with physical processes in machine tools [10–16]. Thus, in [10] thermal modal analysis was used to develop an innovative temperature sensor placement scheme of machine tool. In [11], a new method for the fast identification of the temperature characteristic in a selected point of a machine tool structure is presented. The method is based on operational modal analysis. The theoretical modal approach is associated with the double modal transformation [12, 13]. When describing the thermal processes of any technical system, the thermal conductivity equation is used, which for any one modal coordinate uk will have the form [13] 1 duk (t) = (Tk · qk − uk ) dt Tk

(1)

where Tk is the k-th thermal time constant, min; qk is the modal thermal load, dimensionless quantity; and k is number of the temperature mode or modal coordinate. During the operational phase of the machine tools, experimental modal analysis is significant [14, 17, 18]. Each thermal characteristic of the machine tool, measured at a

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fixed point in its structure, is a sum of exponential functions of the form yi (t) =

n      Yik · 1 − e−t/Tik + y0ik · e−t/Tik

(2)

k=1

where Yik , Tik , and y0ik are modal parameters (k-th component of the amplitude of the sought-for function yi (t), time constant, and initial level of the k-th mode, respectively) and n is the number of temperature modes or modal coordinates. The thermal time constant when using experimental modal analysis has a local character. This explains the appearance of additional indexation in the subscript. Thus, the thermal time constant additionally depends on the measurement point at which the thermal characteristic was formed. We rewrite Eq. 1 in physical coordinates 1 dy1 = (T1 · P1 − y1 ) dt T1

(3)

where y1 is the physical coordinate, microns; T1 is thermal time constant, min; and P1 is thermal load, microns/min. Equation 3 is an ordinary first-order differential equation. The solution to Eq. 6 can be reduced to Eq. (2) [17, 18]. In theory of automatic control, Eq. 6 is a description of the first-order aperiodic link, the transfer function which has the form W (s) =

k T ·s+1

(4)

where s is the complex variable used in the direct Laplace transform; k is the gain coefficient; and T is the time constant. Thus, Eqs. (2)–(4) represent three ways for solving the thermal conductivity equation. Currently, researchers are focusing on Matlab/Simulink when building efficient computer and simulation models and creating various automated error compensation systems in machine tools [4, 9, 15, 17, 19]. Often, the researcher, in the presence of alternative methods for solving a specific problem, faces the problem of choosing the most effective one. This paper presents a procedure for building one thermal model in three ways using the example of solving a simple problem. It is shown that only the solution of a complex problem made it possible to choose the most effective way.

3 Building Multimodal Simulation Model of the Machine Tool The thermal behavior of the machine tool at a fixed speed at a distinguished characteristic point of its structure is described by either a single-mode or multimodal curve called the thermal characteristic [20]. Let us formulate the problem: to build a thermal characteristic for the operation complex mode of the machine tool (with spindle speeds varying over time) using the values of the modal parameters of thermal characteristics obtained on the machine tool with an operation continuous mode at fixed rotational speeds.

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In previous works [17, 21], some variants of the mathematical and simulation models were proposed, which are used for the thermal characteristics of the complex operating mode of the machine tool. The building of a multimodal type of thermal characteristic for the complex operating mode of the machine tool for the second and subsequent sections of the sequence diagram causes some difficulties. This is because it is impossible to determine the values of modal parameters y0ik from the experiment. As the initial level of the sought-for function in the subsequent section of the sequence diagram, the level of the sought-for function formed at the last moment in the previous section should be used. Moreover, in each section of the sequence diagram, starting from the second, the thermal process and, accordingly, the process of forming the temperature error of the machine tool represent the sum of the processes of heating and cooling. For the convenience of identifying the advantages and disadvantages of each of the three modeling ways considered below, we used a test example of a diagrammatic work of the machine tool, consisting of three sections. On the first section with duration of 50 min, the machine tool spindle was rotated at a rotational speed of 250 rpm. On the second section with duration of 110 min, the machine tool spindle was rotated at a rotational speed of 5000 rpm. On the third section with duration of 140 min, the machine tool spindle was again turned on at a rotational speed of 250 rpm. The features of the test example of a diagrammatic work of the machine tool made it possible to distinguish two typical tasks: building a thermal characteristic under zero initial conditions and building a thermal characteristic under nonzero initial conditions. The first typical task: building a thermal characteristic under zero initial conditions. The first modeling way using Simulink is based on the use of analytical solutions of the thermal conductivity equation. In Fig. 1, a Simulink model is presented in the form of a system of graphic block diagrams for the first spindle speed.

Fig. 1. Simulation model of thermal displacements of the spindle cartridge at a rotational speed of 250 rpm: a 1-st way; b 2-nd way.

The second modeling way is based on using built-in tools for solving differential equations in an explicit Cauchy form (Fig. 1b). The fundamental difference between this way of creating a simulation model from the previous one is the use of the Differential Equation Editor block (DEE). This block is used in conjunction with a constant block generating a constant number in the form of relations of the corresponding amplitude and thermal time constant Cik = Yik /Tik

(5)

where i is a fixed point in the structure of the machine tool and k is the mode number.

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The third way is based on the use of the apparatus of transfer functions based on Eq. (2). The structures of simulation models in the implementation of the third and second ways are identical. The second typical task is building a thermal characteristic under nonzero initial conditions. The main difficulty in solving this typical problem is the redistribution between several modes of the level of displacements formed in the previous section of the sequence diagram that are taken as initial conditions in the current section of the sequence diagram (second and subsequent sections of the sequence diagram). Earlier in [17, 21], this problem was solved using the thermal time constant of only one first mode to describe the machine tool cooling process. This approach is justified only if the amplitude of the second and subsequent modes is substantially less than the amplitude of the first mode. In this paper, we propose a special approach to the formation of the initial level for each mode y0ik . It is implemented in three main stages. For each section of the machine tool diagrammatic work, we introduce a superscript (u). At the first stage, the sum of the amplitudes of all modes involved in the formation of the thermal characteristic is found Ai =

n 

Yik(u)

(6)

k=1

The amplitudes of each mode at this stage of modeling are already known after processing the results of full-scale experiment [18]. At the second stage, the proportionality coefficient is calculated (u)

pi

(u)

= E0i /Ai

(7)

(u) is the initial level of the formed displacements, microns. where E0i (u) At the third stage, the initial levels y0ik are calculated for each mode for each section of the sequence diagram (u)

(u)

y0ik = pi

(u)

· Yik

(8)

Thus, the thermal characteristic for each section of the sequence diagram of the machine tool takes on an updated form yi(u) (t) =

n      (u) (u) (u) Yik(u) · 1 − e−t/Tik + y0ik · e−t/Tik

(9)

k=1 (u)

where Tik is the thermal time constant of the corresponding mode in a separate section of the machine tool sequence diagram. In the first way of implementing the simulation model, its structure does not receive fundamental changes, but requires the inclusion of additional blocks for modeling the cooling of the machine tool from the established level E0i . In this case, in parallel with

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the S-model, an M-file is loaded into Matlab, which generates in the system memory the parameters necessary for subsequent modeling described by Eqs. (5)–(9). The second and third modeling ways have an identical structure. A feature of the practical implementation of the model, in contrast to the first method, is a more complicated accounting of time in a separate section of the sequence diagram. This is explained by the following. The time for each section of the sequence diagram should be set locally, and it always starts from zero. When implementing the first simulation way, this is easily provided programmatically in the corresponding fcn blocks. When using the DEE differential equation editor or the transfer function apparatus, the local time in each of the sections of the sequence diagram is implemented using controlled delay blocks, transport delay. The delay time is equal to the duration of the first section of the sequence diagram, i.e., 50 min. Figure 2 shows a model variant of the test example of the sequence diagram. On the third section of the sequence diagram, an algorithm for redistributing (u) according to relations (5)–(9) is implemented. the initial levels y0ik

4 Full-Scale and Machine Experiments To verify the accuracy of the developed simulation models, a series of full-scale and machine experiments were carried out. The full-scale experiment was carried out on a 400 V machine tool (Sterlitamak, Russia). To measure the temperature, a multichannel temperature meter MIT-12TP was used, connected to 12 thermocouples installed in magnetic sensors on the elements of the machine tool structure. Switching between channels was carried out automatically every second. The temperature sensor placement scheme is described in [19]. In addition, a Testo 865 thermal imager and a Testo 830-T2 infrared thermometer were used to measure the temperature field of individual external areas of the machine tool. The thermal displacements of the spindle cartridge were measured using three Norgau NID1201 digital measuring heads connected by direct USB cables to a computer. Data was transferred to the computer using the USB-ITPAK/V2.1 software. Full-scale experiments were conducted for two diagrammatic works of the machine tool. For the second sequence diagram, the S-model is not presented to reduce the volume of the article. Curves 1 in Fig. 3 are experimental thermal characteristics. Curves 2 represent thermal characteristics in which nonzero initial data are taken into account using only the first mode. Curves 3 represent the thermal characteristics, in which a new algorithm of redistribution between several modes of thermal displacement of the spindle cartridge formed in the previous section of the sequence diagram is used. To construct the thermal characteristics for each sequence diagram, two series of experiments were carried out. In the first series of experiments, tests were carried out at separate spindle speeds during continuous operation of the machine tool. Each of the studied spindle speeds was involved in the formation of the corresponding machine tool diagrammatic works. The duration of each test was sufficient to obtain the most accurate result on the identification of modal parameters [21]. For the first test sequence diagram, experiments were performed at rotational speeds of 250 and 5000 rpm. For the second sequence diagram, experiments were additionally carried out at rotational

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Fig. 2. Simulation model of thermal displacements of the spindle cartridge during operation of the machine tool according to the sequence diagram (test example).

speeds: 1000, 2500, and 4000 rpm. In the second series of experiments, the machine tool worked according to the sequence diagram. The machine experiment also consisted of two series of experiments. In the first series of experiments using experimental modal analysis, modal parameters were found and thermal characteristics were constructed that describe the thermal behavior of the machine tool at separate spindle speeds. In the second series of experiments, the thermal characteristics for the given sequence diagrams were constructed using the simulation models proposed above, and the modeling error was determined.

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Fig. 3. Experimental and calculated thermal displacements of the spindle cartridge.

5 Discussion of the Results According to the results of full-scale experiments of the first series, after the implementation of the experimental modal analysis procedures, a group of modal parameters was obtained for all 12 temperature characteristics and 3 thermal displacements. The maximum experimental values of thermal displacements of the spindle cartridge were recorded along the Z-axis. Using three ways of building simulation models allowed to establish the following: • the maximum comparative modeling assessment was about 0,02%; • the first modeling way allows you to create more compact models, and therefore is preferred. The test sequence diagram was used to fine-tune the modal parameters of thermal characteristics. This is because the modal parameters were obtained from solving the identification problem in the extreme tasking. Moreover, according to optimization theory, the found modal parameters allow one to form only a certain local minimum for the sought-for function. This leads to the fact that the definition of model thermal characteristics is carried out with some error. By adjusting the values of the modal parameters for different sections of the sequence diagram, but for one spindle speed (in the test sequence diagram this was done for a rotational speed of 250 rpm), it was possible to significantly increase the accuracy of constructing the thermal characteristics of the sequence diagram. Without tuning the modal parameters, the modeling error of the predicted thermal characteristic exceeded 12 µm. After updating the modal parameters for the thermal characteristic of 250 rpm, the modeling error did not exceed 6 µm. Comparisons of the results of full-scale and machine experiments showed the following: • the use of the redistribution algorithm of thermal displacements formed in the previous section of the sequence diagram between several modes unambiguously allows to increase the accuracy of prediction;

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• the modeling accuracy did not exceed 10%; • higher modeling accuracy, for example, even within 5 micrometers, is practically impossible to provide only by prediction results without additional correction in real time.

6 Conclusions Studies have shown that Simulink allows you to build models with simple logic, but the advantage of the built S-models is their visibility and structure. Three ways of constructing simulation models in Simulink are considered in the work: using an analytical solution of the thermal conductivity equation, using tools for solving differential equations, and using the apparatus of transfer functions. These ways are considered on two typical problems: building the thermal characteristics of the machine tool under zero and nonzero initial conditions. When modeling the diagrammatic works of the machine tools, the way of constructing simulation models based on the use of analytical solutions of the thermal conductivity equation allows us to build the most compact models. To construct invariant models simultaneously with the S-model, the data generated by the Matlab M-file is used. When constructing multimodal thermal characteristics based on experimental modal analysis, a new algorithm for constructing thermal characteristics under nonzero initial conditions is proposed. It is based on the redistribution between several modes of the thermal displacement value formed in the previous section of the machine tool diagrammatic work. From full-scale and machine experiments, it was shown that this uniquely made it possible to increase the accuracy of prediction. Acknowledgements. The study was carried out with the financial support of the RFBR (Russian Foundation for Basic Research) in the framework of the scientific project no. 20-08-00359.

References 1. Jedrzejewski J, Kwasny W (2017) Development of machine tools design and operational properties. Int J Adv Manuf Technol 93:1051–1068. https://doi.org/10.1007/s00170-0170560-2 2. Ye W, Guo Y, Liang R et al (2019) Research on thermo-mechanical coupling deformation for the ball screw of machine tool spindle feed system. J Vib Eng Technol 68. https://doi.org/ 10.1007/s42417-019-00182-5 3. Hou R, Du H, Yan Z et al (2019) The modeling method on thermal expansion of CNC lathe headstock in vertical direction based on MOGA. Int J Adv Manuf Technol 103:3629–3641. https://doi.org/10.1007/s00170-019-03728-9 4. Liu K, Li T, Wang Y et al (2018) Physically based modeling method for comprehensive thermally induced errors of CNC machining centers. Int J Adv Manuf Technol 94:463–474. https://doi.org/10.1007/s00170-017-0736-9 5. Li Q, Li H (2019) A general method for thermal error measurement and modeling in CNC machine tools’ spindle. Int J Adv Manuf Technol 103:2739–2749. https://doi.org/10.1007/ s00170-019-03665-7

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6. Xiang S, Deng M, Li H et al (2019) Cross-rail deformation modeling, measurement and compensation for a gantry slideway grinding machine considering thermal effects. Measur Sci Tech 30(6). https://doi.org/10.1088/1361-6501/ab1232 7. Li TJ, Zhao CY, Zhang YM (2019) Prediction method of thermal errors of the screw system in lathes based on moving thermal network. Precision Eng 59:166–173 8. Shi X, Wang W, Mu Y et al (2019) Thermal characteristics testing and thermal error modeling on a worm gear grinding machine considering cutting fluid thermal effect. Int J Adv Manuf Technol 103(9–12):4317–4329. https://doi.org/10.1007/s00170-019-03650-0 9. Liu K, Liu H, Li T et al (2019) Intelligentization of machine tools: comprehensive thermal error compensation of machine-workpiece system. Int J Adv Manuf Technol 102:3865–3877. https://doi.org/10.1007/s00170-019-03495-7 10. Zhu J, Ni J, Shih AJ (2009) Robust machine tool thermal error modeling through thermal mode concept. J Manuf Sci Eng Trans ASME 130(6):061006–061014. https://doi.org/10. 1115/1.2976148 11. Xia C, Fu J, Xu Y et al (2014) Machine tool selected point temperature rise identification based on operational thermal modal analysis. Int J Adv Manuf Technol 70(1–4):19–31. https://doi. org/10.1007/s00170-013-5239-8 12. Ewins DJ (1984) Modal Testing: theory and practice. John Wiley and Sons Inc, New York 13. Matsuo M, Yasui T, Inamura T et al (1986) High speed test of termal effects for a mashine-tool structure based on modal analysis. Precision Eng 8(2):72–80 14. Peng Y, Li B, Mao X et al (2018) A method to obtain the in-process FRF of a machine tool based on operational modal analysis and experiment modal analysis. Int J Adv Manuf Technol 95:3599–3607. https://doi.org/10.1007/s00170-017-1405-8 15. Li B, Li L, He H et al (2019) Research on modal analysis method of CNC machine tool based on operational impact excitation. Int J Adv Manuf Technol 103(1–4):1155–1174. https://doi. org/10.1007/s00170-019-03510-x 16. Chan YJ, Huang JW (2018) Time-domain operational modal analysis in machine tools: optimal parameters and practical issues. Int J Precis Eng Manuf 19(6):889–897. https://doi.org/ 10.1007/s12541-018-0105-0 17. Polyakov AN, Parfenov IV (2019) Simulation thermal model of CNC machine tool operating with variable modes. In: IOP Conf Ser Mater Sci Eng 560:012034. https://doi.org/10.1088/ 1757-899x/560/1/012034 18. Polyakov AN, Kravcov AG (2005) Prognozirovanie teplovyh harakteristik stanka v usloviyah nepreryvnoj raboty (Prediction of thermal characteristics of the machine in continuous operation). Vestnik mashinostroeniya 10:43–49 19. Hendrawan YM, Farrage A, Uchiyama N (2019) Iterative NC program modification and energy saving for a CNC machine tool feed drive system with linear motors. Int J Adv Manuf Technol 102(9–12):3543–3562. https://doi.org/10.1007/s00170-019-03390-1 20. Polyakov AN, Parfenov IV (1995) Identifikaciya teplovyh processov v metallorezhushchih stankah (Identification of thermal processes in metal cutting machines). Vestnik mashinostroeniya 2:19–22 21. Polyakov AN, Goncharov AN, Parfenov IV (2019) Prognozirovanie teplovyh harakteristik stankov dlya slozhnogo rezhima raboty (Prediction of thermal characteristics of machines for complex operation). Vestnik MGTU Stankin 1(48):93–97

Software Development for the Optimal Parts Location in the Bath Space with the Purpose to Reduce the Non-uniformity of the Coating Thickness D. S. Solovjev1(B) , I. A. Solovjeva2 , and V. V. Konkina2 1 Tambov State University Named After G.R. Derzhavin, 33, Internatsionalnaya, Tambov

392036, Russia [email protected] 2 Tambov State Technical University, 106, Sovetskaya, Tambov 392000, Russia

Abstract. The article provides an analysis of research to reduce the nonuniformity of electroplated coatings, on the basis of which an approach to changing the parts location in the bath space is proposed. To search for the optimal parts location in the bath space, it is necessary to build software. The optimization problem to achieve the minimum criterion for non-uniformity coating is formulated and a stationary mathematical model of the electroplating process in distributed coordinates is developed, based on the laws of Faraday, Ohm, and the Laplace equation. Methods for solving the optimization problem and the mathematical model equations are proposed. The database tables for storing information about the subject area are described. A software algorithm has been developed. The user’s interaction with the software interface is demonstrated by solving the problem of finding the optimal location of 14 volumetric parts of various shapes in the bath space. The decrease in non-uniformity was 34.6% when zinc coating was applied to parts. The results of solving the problem of optimal parts location can be considered as the initial stage for further improving the uniformity of the resulting coating thickness. Keywords: Software · Algorithm · Interface · Database · Cathode location · Coating non-uniformity · Electroplating process · Mathematical model · Optimization problem

1 Introduction Electroplating is the finishing operation for the production of most engineering parts [1]. The quality of the parts obtained and, ultimately, the finished product directly depends on this operation. Uniformity is one of the most significant indicators of the electroplating quality. The non-uniformity can lead to an increase in the consumption of the coating metal, the energy spent on the electroplating, or to the defect of the final product [2]. A © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_10

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lot of research is devoted to the problem of reducing non-uniformity coating. The search for the optimal anode shape and the electroplating bath geometry is carried out in [3, 4] to reduce the non-uniformity of the coating. In the articles [5, 6], search for the location of bipolar electrodes near the part (cathode) surface is described. The use of auxiliary anodes is considered in [7]. In the articles [8, 9], the use of dummy cathodes that distract part of the coating metal is described. The search for the temperature and electrolyte acidity is carried out in [10, 11]. The articles [12–14] search for the optimal function type of changing the current. These researches are aimed at reducing the heterogeneity of the electric field distribution in the electrolyte, which helps to equalize the current density on the cathode surface and, as a result, the thickness of the coating applied. However, the non-uniformity of the applied coating can be reduced by changing the location of cathodes in the electroplating bath. In practice, the location of parts in the plating bath is only a recommendation, and the optimal location of parts can only be obtained experimentally. This method leads to an increase in the cost of the final product. Therefore, for the optimal location of the cathodes (in terms of reducing the coating non-uniformity), the development of appropriate software is necessary. The software should allow the selection of a suitable suspension device and the option of attaching parts to it. The article’s aim is to develop software for the optimal location of cathodes in the electroplating bath to reduce the applied coating non-uniformity.

2 Mathematical Model and Optimization Problem A feature of the developed software is that the results obtained are the solution to the optimization problem. To solve the optimization problem, it is necessary to do a significant amount of computation [15], which is associated with a large number of obtained cathodes’ location options. The following assumptions were made when modeling the process in question. The inner region of the electroplating bath filled with electrolyte is considered as an ideal parallelepiped. A Cartesian coordinate system was used for which the abscissa axis is directed along the length LenX, the ordinate axis along the width LenY, and the applicate axis along the height LenZ of the inner region of the electroplating bath. The electrolyte region is limited by the electrolyte mirror, the bath bottom, the bath inner walls, and the planes passing along the anodes surface. The electroplating bath dimensions, the anode and the cathode dimensions, and shape are known. Electrodes can have various shapes. The cathodes are moved in a plane parallel to the anode plane. This assumption is confirmed by the fact that the bus, on which anode is suspended, is mounted on brackets, and the suspension device, on which the cathodes are placed, is mounted on catcher supports. Thus, the position of the parts is changed along two axes, and not along three axes. The optimization problem is formulated as follows. Find the coordinates of the base points Xi∗ and Zi∗ (i = 1, 2, …, N) for the i-th cathode, which provide the minimum total non-uniformity R of the electroplating coating: R=

N  i=1

(Si )−1

  Sci

δi (x, y, z) − δimin



δimin dSi → min,

(1)

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where S ci is the surface area of the i-th cathode; N is the number of cathodes; δ i (x, y, z) is the coating thickness on the surface of the i-th cathode at a point with coordinates (x, is the minimum coating thickness. y, z); and δ min i The following restrictions apply: δimin ≥ δ set , Xi∗ = Zi∗ =

(2)

min

Xim ,

(3)

max

Zim ,

(4)

m=1,2,...,M

m=1,2,...,M

where δ set is the required coating thickness and M is the number of projection points of the i-th cathode on the cathode plane. The coating thickness of the i-th cathode at a point with coordinates (x,y,z) for the time τ is calculated according to the Faraday law [16]:  (5) δi (x, y, z) = kη(jci (x, y, z))jci (x, y, z)τ ρ, where k, ρ is the electrochemical equivalent and density of the coating metal; η is the current output of the cathode; jci is the current density of the i-th cathode at a point with coordinates (x,y,z); and τ is the electroplating time. The current densities at the cathodes and the anodes are determined from Ohm’s law in differential form [17]: jci (x, y, z) = −χ grad ϕ(x, y, z), (x, y, z) ∈ Sci ,

(6)

jal (x, y, z) = χ grad ϕ(x, y, z), (x, y, z) ∈ Sal ,

(7)

where χ is the electrical conductivity of the electrolyte; gradϕ(x, y, z) is the gradient of the electric field potential at the point with coordinates (x, y, z) in the electroplating bath; jal is the current density at the point of the l-th (l = 1, 2, …, D) anode with coordinates (x, y, z); S al is the surface area of the l-th anode; and D is the number of anodes. The distribution of the electric potential ϕ can be found using the Laplace equation [18]:    ∂ 2 ϕ(x, y, z) ∂x2 + ∂ 2 ϕ(x, y, z) ∂y2 + ∂ 2 ϕ(x, y, z) ∂z 2 = 0, (8) for which there is the following set of boundary conditions: • for areas “electrolyte-insulator” and “electrolyte-air”:   ∂ϕ(x, y, z) ∂ nS = 0, ins

(9)

• for areas “electrolyte-l-th anode”: ϕ(x, y, z) + Fa (jal (x, y, z))|Sal = U ,

(10)

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• for areas “electrolyte-i-th cathode”: ϕ(x, y, z) − Fc (jci (x, y, z))|Sci = 0,

(11)

where n is normal to the insulator surface; S ins is the insulator surface; U is the supply voltage; and F a , F c are the functions of the anodic and cathodic polarizations. The geometric characteristics of the i-th cathode are determined by the dependence function of the cathode surface on its overall dimensions hx (along the x-axis), hy (along the y-axis), hz (along the z-axis); its configuration Fi ,; and the coordinate array Ω i of the cathode nodal points that uniquely determines it location in the bath:

(12) Sci = Sci hx , hy , hz , Φi , Ωi , The following restrictions are imposed on the projection of the cathodes onto the cathode plane: • the distance to the left and right side walls should not be less than L 1 and L 2 : Xi∗ ≥ L1 ,

(13)



LenX − Xi∗ + hx ≥ L2 ;

(14)

• the distance to the electrolyte mirror and to the bath bottom should not be less than L 3 and L 4 : LenZ−Zi∗ ≥ L3 ,

(15)

Zi∗ −hz ≥ L4 ;

(16)

• the distance between the cathodes should not be less than L 5 :  |Xiq −Xpm | ≥ L5 , |Ziq −Zpm | ≥ L5

(17)

where i, p = 1, 2, …, N; m, q = 1, 2, …, M; i = p. The approach proposed in articles [19–21] is used to solve Eqs. (5)–(12) of the developed mathematical model. The equations of the model are replaced by finite-difference analogs, and the search for solutions to the resulting difference equations is carried out by iterative methods. The use of an approach based on the principles of nonlinear programming [22, 23] is proposed as an optimization method. After entering the cathode’s initial location, the implementation of the restrictions (13)–(17) is checked. If the restrictions are satisfied, then the position of (N−1) cathodes is fixed, and the coordinates of the base points (3, 4) for remaining cathodes are changed taking into account restrictions (13)–(17) until the minimum criterion (1) value is reached with the fulfillment of the restriction (2). The change in the coordinates of the base points is repeated for each of the remaining cathodes. The procedure is performed until the change in the value of the criterion (1) is lesser than the specified accuracy.

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3 Database Composition The software must interact with the databases: finished projects, metals and electrolytes, and suspension devices. The database of finished projects contains information on previously calculated and saved projects. The database of metals and electrolytes contains information about the coating metal, electrolyte, and its components, as well as their physical, chemical, and quantitative characteristics. Data on suspension devices are in the database of the same name. The considered databases contain the following tables: finished projects, nodal points of the anodes, cathode model, coatings, electrolytes, electrolyte composition, and suspension devices. The “Finished projects” table is associated with the “Coatings,” “Suspension devices,” and “Electrolytes” tables in a “one-to-one” relationship. In turn, the table “Finished projects” is associated with the tables “Nodal points of the anodes” and “Cathode model” in relation to “one-to-many.” The “Coatings” is associated to the “Electrolytes” in a “one-to-many” relationship. Since electrolytes can include a different number of components, the “Electrolytes” is associated to the “Electrolyte composition” table in a “one-to-many” relationship.

4 Software Algorithm Consider the software algorithm. 1. The user sets the process parameters: coating metal, electrolyte, bath dimensions, required coating thickness, grid options for axes, optimization parameters, supply voltage, and number of anodes and cathodes. The geometry of the electrodes is entered by setting the nodal points of the anodes and projections of the cathodes, and their initial location in the bath is established, from which the search for the optimal location will begin. 2. Check for completeness and correctness of the entered parameters in the database. If a discrepancy is found with the information stored in the database, then the user is supposed to supplement the database with new parameters or edit existing ones. 3. Finding a finished solution based on user input. If no similar project is found, then go to the next step. The input data is saved. 4. A map of the electroplating bath is being formed, that is, its entire area is divided by a grid along the coordinate axes, depending on the entered values of steps along the axes and bath dimensions. 5. The solution to the optimization problem (1) is sought by changing the position of the cathodes taking into account the restrictions (2)–(4), (13)–(17) and calculating the system of mathematical model Eqs. (5)–(12). 6. After finding the optimal location of the cathodes, a search for suitable suspension devices for the implementation of the solution is done. Optimization results and suspension devices are provided to the user. 7. Analysis of the information received by the user. If the result doesn’t meet the requirements for it, then the input data is edited (go to step 2).

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8. Saving the received results to the database “Finished projects.” 9. Formation and visualization of design documentation (isometric and projection drawings).

5 Materials and Methods Let us consider an example of optimizing the location of cathodes by the example of zinc plating in developed software. Filled fields with the plating bath dimensions, coating metal, electrolyte, supply voltage, and required coating thickness are shown in Fig. 1a in the interface of the software central window.

Fig. 1. Software interfaces: a central window; b interact with the database; c setting calculation parameters; d entering the size and location of the anodes; e entering dimensions and initial location of the parts.

The window interface for adjusting process parameters using the example of interact with the database of metals and electrolytes is shown in Fig. 1b. Parameters for solving of the mathematical model Eqs. (5)–(12) and the optimization problem (1) with restrictions (2)–(4), (13)–(17) are entered in the “Settings” window, the interface of which is shown in Fig. 1c. As anodes, D = 4 zinc plates with the dimensions S a1 = S a2 = S a3 = S a4 = 290 x 650 mm are used. The shape of the anodes and their location in the bath are shown in Fig. 1d.

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There are N = 14 volumetric parts of various shapes (S ci = S cp for i = p). The process of setting the initial location of the parts is shown in Fig. 1e. The optimization problem is solved by pressing the “Optimization” button, according to which the specified parts must be located on the suspension so that the criterion for the non-uniformity (1) of the applied zinc coating is minimal. As a result of solving the optimization problem, design documentation is generated.

6 Results and Discussion According to the initial location of the parts, shown in Fig. 1e, the non-uniformity criterion (1) has a value of R = 1.578412 for a required coating thickness δ set = 10 µm deposited over a time τ = 26.5 min. As a result of solving the optimal location problem of the parts, the non-uniformity criterion (1) value R = 1.032569 was obtained with unchanged δ set and τ. Thus, in solving the problem for the considered example, it was possible to reduce the non-uniformity of coating by 34.6%. The design documentation generated for the option of optimal location of the parts is shown in Fig. 2. Figure 2a shows an isometric drawing of an electroplating bath with 4 anodes and an optimal location of 14 parts in it. Figure 2b shows a projection drawing with the coordinates of the base points for the location of the parts in an electroplating bath.

Fig. 2. Design documentation for optimal location of the parts: a isometric drawing; b projection drawing.

Suspension frame 1000×1100 mm in size is selected to implement the found optimal location of the parts in the bath space. This selection is due to the following: • significant capacity in the number and area of the parts fit on a suspension frame compared to a tree-type suspension; • ease of design modernization when using additional devices (insulating screens, dummy cathodes, auxiliary anodes, and so on); and • the parts hanging on the frame are equally oriented with relation to the anodes.

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7 Conclusion The advantage of the considered approach, in contrast to the use of insulating screens, dummy cathodes, auxiliary anodes, and current reversal, is that the optimal configuration of the electric field is carried out by modifying the parameters of the medium itself by changing the location of the cathodes. In this case, the installation of additional electrical equipment and changing the modes of its operation are not required, as well as there is no excessive consumption of electricity. In addition, the application of this approach doesn’t exclude the use of other methods to increase the plating uniformity. Therefore, the results of solving the problem of optimal cathodes location can be considered as the initial stage for further improving the uniformity of the resulting coating.

References 1. Gamburg YD, Zangari G (2011) Electrodeposition of alloys. Theory and practice of metal electrodeposition. Springer, New York, pp 205–232 2. Tan YJ, Lim KY (2003) Understanding and improving the uniformity of electrodeposition. Surf Coat Tech 167(2–3):255–262. https://doi.org/10.1016/s0257-8972(02)00916-7 3. Volgin VM, Lyubimov VV, Gnidina IV, Kabanova TB, Davydov AD (2017) Effect of anode shape on uniformity of electrodeposition onto resistive substrates. Electrochim Acta 230:382– 390. https://doi.org/10.1016/j.electacta.2017.02.015 4. Garich H, Shimpalee S, Lilavivat V, Snyder S, Taylor EJ (2016) Non-traditional cell geometry for improved copper plating uniformity. J Electrochem Soc 163(8):216–222. https://doi.org/ 10.1149/2.0491608jes 5. Parate DS, Sabitha R, Pushpavanam M, John S (1996) Studies on bipolar electrode for preferential deposit build on intricate shaped article. Bull Electrochem 12(05):294–296 6. Anand RK, Sheridan E, Hlushkou D, Tallarek U, Crooks RM (2011) Bipolar electrode focusing: tuning the electric field gradient. Lab Chip 11:518–527. https://doi.org/10.1039/c0lc00 351d 7. Mehdizadeh S, Dukovic J, Andricacos PC, Romankiw LT, Cheh HY (1990) Optimization of electrodeposit uniformity by the use of auxiliary electrodes. J Electrochem Soc 137(1):110– 117. https://doi.org/10.1149/1.2086343 8. Kim NS, Oh HD, Kang T (1995) Optimization of current distributions of electroplating on patterned substrates with the auxiliary electrode. J Korean Inst Surf Eng 25:164–173 9. Park CW, Park KY (2014) An effect of dummy cathode on thickness uniformity in electroforming process. Results Phys 4:107–112. https://doi.org/10.1016/j.rinp.2014.07.004 10. Poroch–Seri M, Gutt Gh, Severin TL (2009) Study on the influence of current density and temperature about electrodepositions of nickel by electrolytes of type Watts. Annals Suceava Univ Food Eng VIII (2):16–23 11. Birlik I, Azem NFA (2018) Influence of bath composition on the structure and properties of nickel coatings produced by electrodeposition technique. J Sci Eng 20(59):689–697. https:// doi.org/10.21205/deufmd.2018205954 12. Dini JW, Johnson HR (1980) The properties of gold deposits produced by DC, pulse and asymmetric AC plating. Gold Bull 13(1):31–34. https://doi.org/10.1007/bf03215127 13. Leisner P, Zanella C, Belov I, Edström C, Wang H (2014) Influence of anodic pulses and periodic current reversion on electrodeposits. T I Met Finish 92:336–342. https://doi.org/10. 1179/0020296714z.000000000210

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14. Dutov AV, Litovka YV, Nesterov VA, Solovjev DS, Solovjeva IA, Sypalo KI (2019) Search for the optimal control over current regimes in electroplating processes with multi anodes at a diversified assortment of treated articles. J Comput Syst Sci Int 58(1):75–85. https://doi.org/ 10.1134/s1064230719010064 15. Druesne F, Afzali M (2003) Electroplating simulation and design tool. Proc Inst Mech Eng B J Eng Manuf 217(5):705–707. https://doi.org/10.1243/095440503322011434 16. Landau U (2009) Current distribution in electrochemical cells: analytical and numerical modeling. In: Schlesinger M (eds) Modern aspects of electrochemistry, vol 44. Springer, New York, pp 451–501. https://doi.org/10.1007/978-0-387-49586-6_10 17. Behagh AM, Tehrani AF, Salimi JH, Hosseiny N, Sadeghy M, Behagh O (2013) Finite element simulation of nickel electroplating process of a revolving part. Galvanotechnik 104:474–483. https://doi.org/10.12850/issn2196-0267.jept4524 18. Popov K, Zivkovic P, Nikolic N (2011) A mathematical model of the current density distribution in electrochemical cells. J Serb Chem Soc 76(6):805–822. https://doi.org/10.2298/jsc 100312079p 19. Solovjev DS, Solovjeva IA, Litovka YuV, Korobova IL (2018) About one counterexample of applying method of splitting in modeling of plating processes. J Phys Conf Ser 1015(032138). https://doi.org/10.1088/1742-6596/1015/3/032138 20. Mesa F, Alzate PPC, Rodriguez Varela CA (2017) Numerical solution of the Laplace equation: electrostatic potential. Adv Stud Theor Phys 11(12):717–723. https://doi.org/10.12988/astp. 2017.71155 21. Atsue T, Tikyaa EV, Nwokike SC (2018) A numerical solution of the 2D Laplace’s equation for the estimation of electric potential distribution. J Sci Eng Res 5:268–276 22. Bonnans JF, Gilbert JC, Lemarechal C, Sagastizábal CA (2006) Numerical optimization. Theoretical and practical aspects. Springer-Verlag, Heidelberg. https://doi.org/10.1007/9783-540-35447-5 23. Rao SS (2009) Engineering optimization: theory and practice. John Wiley & Sons, New Jersey. https://doi.org/10.1002/9780470549124

Methodology of Measuring Cutters by Using Coordinate Measuring Machine in Automatic Mode I. P. Nikitina, S. V. Kamenev, and A. N. Polyakov(B) Orenburg State University, 13, Pobedy Av, Orenburg 460018, Russia [email protected]

Abstract. The aim of the study was to develop a methodology for measuring the structural and geometric parameters of a straight bull-nose cutter. To test the effectiveness of the developed methodology for measuring the structural and geometric parameters of the cutter, a full-scale experiment was conducted. During the experiment, all the structural and geometric parameters of the straight bull-nose cutter were measured using handheld measuring tools and a coordinate measuring machine Wenzel XOrbit 55 (Germany). A comparative analysis of the results of measurements using a universal handheld measuring tool and coordinate measuring machine showed: all the geometrical parameters of the cutter can only be measured using a coordinate measuring machine; the results of measuring geometric parameters using a universal handheld measuring tool do not allow making unambiguous organizational decisions on the further operation of the cutting tool, since the measurement error is comparable with the current size tolerances; however, for such design parameters as length, height, width of the cutter due to large tolerances, the use of a universal handheld tool is sufficient. The practice of measurements using a coordinate measuring machine has shown that, when conducting critical measurements, the use of coordinate measuring machines is not only accurate, but also more productive in comparison with the use of handheld measuring tools. Keywords: Tool · Accuracy control · CMM · Wenzel XOrbit · Metrosoft quartis

1 Introduction Modern engineering production is characterized by high-accuracy requirements for various high-tech products. Most of these products are produced using machining, the quality indicators of which largely depend on the dimensional parameters of the cutting tool used. For this reason, control of the accuracy of the dimensional parameters of the cutting tool should be an integral component of the product life cycle at the production stage.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_11

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Currently, various methods and tools are used to control the geometric parameters of the cutting tool. However, the most effective and economical approach seems to be the use of coordinate measuring machines (CMM), which allow a high degree of accuracy to determine linear and angular dimensions, as well as deviations in the shape and location of various parts of complex geometric shapes [1–3]. Using CMM allows you to: quickly measure the geometric parameters of simple and complex precision parts, the measurement of which is done by traditional means or requires the development of special expensive equipment, or the measurement of which is impossible even theoretically; minimize product rejection, using constant monitoring of the accuracy during machining of the parts and timely correction [4–10]. The control of the elements of the part consists in determining the coordinates of separate points on the surface or contour and then comparing the measured actual values with the theoretical ones given in the drawing. The accuracy of the control depends on the number of measured points [11–21]. Specialized software of machines (CAI system) allows you to perform measurements in various modes, the most convenient of which is the automatic mode, based on the use of the «electronic standard» of the measured part. The correct interpretation of the received data largely depends on the form in which it will be presented. For this reason, the most effective is the use of measuring instruments, which, in addition to a high degree of accuracy, also demonstrates the visualization of the results with the possibility of additional processing. These criteria are fully met by CMMs, which allow high-precision measurements of geometric accuracy standards, and using their software to draw up informative measurement protocols that facilitate the perception of results.

2 Methodology The purpose of the study is the analysis and determination of rational means of monitoring the structural and geometric parameters of the cutters during its manufacture and subsequent regrinding. As an object of research, straight bull-nose cutters of a composite structure with a hard alloy plate were used. The structural and geometrical parameters of the cutters were studied using a Wenzel XOrbit 55 coordinate measuring machine in automatic mode. Nominal sizes, specifications, as well as upper and lower limit deviations are accepted in accordance with GOST 18878-73 “Carbide-tipped straight bull-nose turning tools. Design and dimensions,” GOST 5688-2015 “Carbide-tipped tools. Specifications” and GOST 25347-82 “Basic norms of interchangeability. Unified system of tolerances and fils. Tolerans zones and recommendalle fils.” To measure the geometric parameters of the thread in automatic mode, it is necessary to prepare a solid-state or surface CAD model for any of the systems with geometric modeling on a 1: 1 scale in relation to the object. In this case, to build a model, it is required to use the results of measurements of the cutter in manual mode. Further, the prepared model must be saved in a neutral format file ACIS (extension *.sat) or IGES (extension *.igs) and load it into the database of the current part.

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After loading the CAD model into the current measurement database, it is necessary to perform the alignment procedure. The indicated procedure consists in creating a coordinate system associated with a real part (in this case, a cutter) and simultaneously combining a CAD model with this coordinate system. The need for alignment is explained by the fact that when loading the CAD model, the origin of its coordinate system is placed by default at the center of the calibration sphere, while for measurements it must be connected with a real part, the position and orientation of which in the coordinate system of the machine is generally unknown. In order to create a new coordinate system for a part, it is necessary to first perform a series of measurements of its geometric elements through which this system can be determined. The origin of the CAD system is located at the intersection of its three orthogonal planes, which coincide with the coordinate planes. Therefore, to construct a new coordinate system for the part, it is necessary to first measure these planes (Fig. 1). The following requirements must be met: the first measured plane (PLN_1) must correspond to the working surface of the table; the second measured plane (PLN_2) should correspond to the vertical side surface of the cutter; and the third measured plane (PLN_3) should correspond to the end surface of the tool holder. After measuring the planes and constructing the adjacent flat elements, it is necessary to perform additional transformations on them to obtain their common intersection point, which will be used as the origin of the system being created. Based on the obtained geometric elements, a coordinate system is constructed that is associated with the real part by determining the directions of the two coordinate axes and the zero point.

Fig. 1. Surfaces defining the coordinate system of the cutter.

As a result of the transformations, the coordinate system of the CAD model will be automatically combined with the created coordinate system of the real part, which will allow the use of geometric elements of the CAD model to identify real geometric elements of the part, i.e., use the model as an electronic standard. In the general case, when using an electronic standard for measuring any geometric element of a real part, it is necessary to • choose the orientation of the measuring probe that is suitable for the measurement, calibrated, or create a new orientation of the probe with its subsequent calibration; • run the appropriate measuring command, designed to measure a geometric element of this type;

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• use the mouse on the CAD model displayed in the graphic area and select the geometric element corresponding to the measured element of the real part; • manually or automatically set the number of touch points necessary to determine the measured geometric element and the distribution parameters of these points within the selected element; and • start the automatic measurement procedure and build the necessary adjacent element. The considered turning tool is a body bounded by flat surfaces and their intersection lines. Therefore, to determine all its linear and angular dimensions, it is necessary and sufficient to use adjacent elements of the « Plane» and «Line» types. For example, to determine the dimensions of the tool holder, it is necessary to measure and build four planes, indicated by the identifiers PLN_1, 2, 3, 4, 5 in Fig. 2. At the same time, the PLN_1 plane corresponding to the working surface of the table does not need to be measured, since it was already built in the process of creating the coordinate system. To determine the planes PLN_2, PLN_3, and PLN_4, at least 20 points of contact must be specified, and for the plane PLN_5 at least 10 points (Figs. 3, 4, 5 and 6). After the parameters that control the measurement process are set, the automatic measurement procedure starts. During it, the measuring system sequentially takes the coordinates of all given points on the selected surface, on the basis of which the required planes will be built.

Fig. 2. Surfaces that determine the size of the tool holder.

Fig. 3. Automatic distribution of touch points on the PLN_2 plane.

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Fig. 4. The distribution of points of tangency on the plane PLN_3.

Fig. 5. Distribution of points of tangency on the plane PLN_4.

Fig. 6. Distribution of points of contact on the plane PLN_5.

As a result of the construction, five flat geometric elements should be present in the current measurement database, which should then be used to determine the size of the tool holder. For example, in order to determine the height of the holder (H in Fig. 2), you need to calculate the distance between the planes PLN_1 and PLN_4 along the normal between them (Fig. 7).

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Fig. 7. The result of determining the height of the tool holder.

In a similar way, the width of the holder (W in Fig. 2) and the length of the cutter (with additional measures taken previously) can be found. By measuring the dimensions of the tool holder, determine the geometric parameters of its cutting part. In this case, for this it is necessary and sufficient to build five flat elements designated PLN_6–PLN_10 in Fig. 8.

Fig. 8. Surfaces that determine the size of the cutting part of the cutter.

The construction of these elements is carried out similarly, as was discussed above, using at least five points to define each plane (Fig. 9). When measuring and plotting

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planes PLN_7–PLN_10, it may be necessary to use the orientation of the probe different from normal to the table surface. This means that before measuring the indicated planes, the probe must be rotated through an angle (s), providing free access of the measuring tip to these surfaces. For the changed orientation of the measuring probe, a calibration procedure must be carried out, followed by saving the obtained orientation in the measurement database.

Fig. 9. Touch points on the model surfaces defining the cutting part of the cutter.

After constructing all the geometric elements indicated in the figure to determine the cutting angles, first of all, it is necessary to form lines corresponding to the cutting edges of the cutter (Fig. 10). To obtain these lines, the « Section » , « Projection » commands are used. The lines LIN_7, LIN_8, LIN_9, and LIN_11 were used to calculate the main cutting angles. To determine the main rake angle, LIN_7 and LIN_8 lines were used. The result of calculating the main rake angle is shown in Fig. 11. The lines LIN_4 and LIN_5, obtained as a result of projection and intersection of objects, are used to calculate angles in the cutter plane. To determine the angle at the tip of the cutter, LIN_4 and LIN_5 lines were used. Auxiliary cutting angles were determined on the basis of a number of similar constructions (LIN_12, LIN_13, LIN_14, LIN_15, LIN_16). The auxiliary rake angle was determined based on the selection of a pair of elements LIN_12 and LIN_13. The angle of inclination of the main cutting edge was determined based on the selection of a pair of elements LIN_2 and LIN_4.

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Fig. 10. Geometric elements necessary for determining the cutting angles.

Fig. 11. Results of calculation.

To present the obtained measurement results in visual form, the Metrosoft Quartis CAI system provides a special software module designed for automatic reporting.

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All values of the geometric parameters of the cutter obtained using measuring tools, manual and automatic measurement modes on a coordinate measuring machine are summarized in Table 1. Nominal sizes, specifications, as well as upper and lower limit deviations are accepted on bases of national standards. Table 1. Experimental data and the results of the calculation of the cutter.

3 Conclusions Conclusion on the accuracy of manufacture of the cutter in accordance with GOST 56882015 «Carbide-tipped tools. Specifications» can only be obtained using a coordinate measuring machine, since measuring with a manual measuring tool during repeated measurements gives a scatter of actual size values comparable to the size tolerance field established by the standard. The taper angle and angle of cutting, as well as the auxiliary taper angle on the plate, cannot be measured with a hand tool. The developed technique for measuring the structural and geometric parameters of the cutter can be extended with other modifications to other types of cutting tools, in view of the universality of the geometric parameters of the cutting wedge of the through cutter. The practice of measurements using a coordinate measuring machine showed that when conducting critical measurements, which include measuring the geometric parameters of cutting tools, the use of coordinate measuring machines, even in manual mode, is not only accurate, but also more productive in comparison with the use of handheld measuring tools. This creates the prospect of a wider implementation of control operations

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using coordinate measuring machines in the manufacturing process and the regrinding of cutting tools. Thus, the study showed that the use of coordinate measuring machines in mechanical engineering can significantly reduce the time to control the structural and geometric parameters of the cutting tool, as well as significantly minimize errors in their control due to the rejection of manual measurements and the corresponding huge assortment of templates and measuring instruments. Acknowledgements. The study was carried out with the financial support of the RFBR (Russian Foundation for Basic Research) in the framework of the scientific project no. 20-08-00410.

References 1. Vykhristyuk IA (2010) Coordinate measuring machine with large working volume based on laser technological system. Key Eng Mater 437:453–457. https://doi.org/10.4028/www.sci entific.net/KEM.437.453 2. Ito S, Kodama I, Gao W (2014) Development of a probing system for a micro-coordinate measuring machine by utilizing shear-force detection. Meas Sci Technol 25(6):064011. https:// doi.org/10.1088/0957-0233/25/6/064011 3. Chang HC, Lin AC (2011) Five-axis automated measurement by coordinate measuring machine. Int J Adv Manuf Technol 55:657–673. https://doi.org/10.1007/s00170-010-3092-6 4. He G, Sang Y, Pang K et al (2018) An improved adaptive sampling strategy for freeform surface inspection on CMM. Int J Adv Manuf Technol 96:1521–1535. https://doi.org/10. 1007/s00170-018-1612-y 5. Yu M, Zhang Y, Li Y et al (2013) Adaptive sampling method for inspection planning on CMM for free-form surfaces. Int J Adv Manuf Technol 67(9–12):1967–1975. https://doi.org/ 10.1007/s00170-012-4623-0 6. Poniatowska M (2012) Deviation model based method of planning accuracy inspection of freeform surfaces using CMMs. Meas J Int Meas Confed 45(5):927–937. https://doi.org/10. 1016/j.measurement.2012.01.051 7. Gao C, Cheng K, Webb D (2004) Investigation on sampling size optimisation in gear tooth surface measurement using a CMM. AMT 24:599–606. https://doi.org/10.1007/s00170-0031595-0 8. Lee S, Yang D (2003) Improvement of Product Accuracy in Freeform Surface Machining. Int J Adv Manuf Technol 21:972–979. https://doi.org/10.1007/s00170-002-1419-7 9. Li Y, Nomula PR (2015) Surface-opening feature measurement using coordinate-measuring machines. Int J Adv Manuf Technol 79:1915–1929. https://doi.org/10.1007/s00170-0156968-7 10. Zuikova NA (2000) Measuring complicated surfaces with coordinate-measuring machines. Meas Tech 43:733–734. https://doi.org/10.1007/bf02503643 11. Wo´zniak A, Mayer JRR, Bałazi´nski M, Côté M (2006) Investigation on precise measurement of cutting tool edges using coordinate measuring machines. In: CIRP 2nd international conference on high performance cutting, University of British Columbia, Vancouver, Canada, 12–13 June 2006 12. Zongwei Y, Yuping Z, Shouwei J (2003) Methodology of NURBS surface fitting based on off-line software compensation of errors of a CMM. Precision Eng 27:299–303

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13. Zhang X, Tsang W, Yamazaki K et al (2013) A study on automatic on-machine inspection system for 3D modeling and measurement of cutting tools. J Intell Manuf 24:71–86. https:// doi.org/10.1007/s10845-011-0540-6 14. Surkov IV (2011) Development of methods and means of coordinate measurements for linear and angular parameters of cutting instruments. Meas Tech 54:758–763. https://doi.org/10. 1007/s11018-011-9800-2 15. Krehel R, Pollak M (2016) The contactless measuring of the dimensional attrition of the cutting tool and roughness of machined surface. Int J Adv Manuf Technol 86:437–449. https://doi. org/10.1007/s00170-015-8197-5 16. Siddhpura A, Paurobally RA (2013) Review of flank wear prediction methods for tool condition monitoring in a turning process. Int J Adv Manuf Technol 65:371–393. https://doi.org/ 10.1007/s00170-012-4177-1 17. Chizhov VN, Petrovskaya IM, Trykov YP et al (1990) Instrument for measuring the radius of round-off of the cutting edges of cutting tools and hard alloy plates. Meas Tech 33:560–562. https://doi.org/10.1007/bf00977915 18. Shiou FJ, Lin YF, Chang KH (2003) Determination of the optimal parameters for free form surface measurement and data processing in reverse engineering. Int J Adv Manuf Technol 21:678–690. https://doi.org/10.1007/s00170-002-1390-3 19. Vrba I, Palencar R, Hadzistevic M et al (2015) Different approaches in uncertainty evaluation for measurement of complex surfaces using coordinate measuring machine. Meas Sci Rev 15(3):111–118. https://doi.org/10.1515/msr-2015-0017 20. Jakubiec W, Płowucha W, Starczak M (2012) Analytical estimation of coordinate measurement uncertainty. Measurement 45(10):2299–2308. https://doi.org/10.1016/j.measurement. 2011.09.027 21. Jakubiec W, Płowucha W, Rosner P (2016) Uncertainty of measurement for design engineers. Proc CIRP 43:309–314. https://doi.org/10.1016/j.procir.2016.02.027

Adaptation of PLM Information System in Industry 4.0 Concept at Stage of Technological Production Preparation A. Markov(B) , S. Babaev, and I. Yunakov Baltic State Technical University “VOENMEH” Named After D.F. Ustinov, 1st Krasnoarmeyskaya Str., 1, St. Petersburg 190005, Russia [email protected]

Abstract. The relevance of the proposed research is the transition of the enterprise to the Industry 4.0 concept. This concept ensures information exchange between participants in real time scale, as well as information integration on the example of the uninterrupted receipt of tools for production areas and workshops equipping. Thus, the purpose of the research is to reduce the product production cycle considering the reduction of time losses that occur while waiting for the receipt of nomenclature items of the tools. This research analyzes the capabilities of the PLM information system in the Industry 4.0 concept at the stage of technological production preparation. The research methods include the mathematical modeling of the processes of tool uninterrupted provision to production areas and workshops, based on the theory of mass maintenance systems. The results of mathematical modeling ensure timely replenishment and continuous support of warehouse balances. The proposed methodological recommendations can also be used in the multi-production organization. Keywords: Technological preparation · Production preparation · Industry 4.0 concept · PLM system · Mass maintenance · Maintenance systems

1 Introduction To analyze the capabilities of the PLM information system in the Industry 4.0 concept at the stage of technological production preparation, we consider the operating model of the production enterprise shown in Fig. 1. This model covers product making from product development to product release [1–8]. The presented sequence, in the form of the first-level decomposition, supports the assumption that it takes considerable time to implement the processes. The functional model “must be” allows analyzing the remaining tools in the enterprise in a shorter time and making its immediate purchase following the production requirements [9–11]. The proposed functional model is implemented in the PLM-class information system TechnologiCS 7.7, which allows © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_12

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Fig. 1. The first-level decomposition “available”.

• managing the composition of a product that includes design specifications for each item part. Specifications can be included in each other with any nesting level that forms a product tree in the database; • technological processes developing, both single and standard (group), based on which it is possible to perform labor and material regulation of technologies, as well as to perform various types of technological calculations; • production specifications creating such as a nomenclature production plan, based on which a production cycle schedule is built and technological equipment loading is planned; • monitoring the product creation process considering technological parameters, as well as performing grading by types and reasons of detected production defects. TechnologiCS 7.7 system provides information interaction of the design and production cycle of product creation in a real time scale. The information system is based on a single MS SQL database and a file server for electronic documents storing. TechnologiCS covers the product life cycle, from design and technological preparation to product manufacturing tracking and shipping to a customer (Fig. 2). The information system operation algorithm is shown in Fig. 3. Let’s take a look at the first-level decomposition after converting the stock residue analysis process during the process plan design shown in Fig. 2. In the conditions of modern multi-product production, the main factors are quality and the earliest fulfillment of the order. For production process support, the system must be set up to ensure that production areas and workshops are resourced uninterruptedly.

Adaptation of PLM Information System in Industry

Fig. 2. The first-level decomposition of the functional model “must be”.

Fig. 3. Unified information system.

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2 Tool Stock Level Calculation Model To solve the problem of control of maintaining the constant stock residue of the tool, we use the “Eq. 1” for tool reorder point calculation. Preor =

N × Tp + Bmin , Dper

(1)

where Preor is the reordering point; N—the demand; Ti —the time of tool demand realization, in days; Dper is the number of days in the period; Bmin —the minimum balance— safety stock, taking into account the risk of delivery disruption and changes in periodic demand. The time dependence of the stock level from the order point to the safety stock is shown in Fig. 4.

Fig. 4. Dynamics of the dependence of warehouse stock level on time.

As can be seen from the graph, it is necessary to order the tool before the safety stock point occurs, taking into account the time for creating the requisition, processing the requisition by the supplier, and the time to deliver the tool to the enterprise. The safety stock point is different for each item. It is calculated either based on statistics or based on a production program, which takes into account the tool consumption and the required quantity for the product manufacture. For mathematical modeling, the method is chosen for calculating the level of warehouse stocks from the theory of mass maintenance systems, in which, on the one hand, mass requests (requirements) for the performance of any types of works arise, and, on the other hand, these requests are satisfied. The mass maintenance system includes the following elements: demand source, incoming demand flow, queue, maintaining device, and outgoing demand flow [12–14]. The model for determining the level of stock of the tool in the warehouse is shown in Fig. 5, where the symbols are entered: λ is the intensity of the incoming flow of

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requirements per tool; μ is the tool issue rate; S0 , S1 ,…, Sm is the quantity of the tool in the warehouse (index indicates the quantity of the tool in the warehouse); and m is the maximum tool stock.

Fig. 5. The model for tool stock level determination.

The probabilities of states are determined by “Eq. 2” Pi = where ρ =

λ μ,

ρi P0 , i = 1, 2, . . . , m, i!

(2)

and the probability of P0 is found from “Eq. 3”  P0 =

m  ρi i=0

−1

i!

.

(3)

The average number of tools m3 used to perform process operations can be calculated using “Eq. 4” m3 =

m 

n · Pn .

(4)

n=1

Let’s look at the example of the proposed model application. The storage bin stores three tools. The tool invoices are delivered to the warehouse for certain operations. If the tool is not in stock according to the delivery note, the new order is not accepted. Let the average tool issue time be 3 min. The requesting flow rate is 0.25 (1/min). It is necessary to determine the probability of missing the tool in the warehouse, their average quantity, which is used to perform a specific operation. Given: m = 3, λ = 0,25 (1/min), T serv = 3 (min). Decision: λ = λ · T¯ serv = 3 · 0, 25 = 0, 75; μ  3 −1  −1  ρi 0, 753 0, 752 P0 = + = 1 + 0, 75 + = [2, 1]−1 ; i! 2! 3! ρ=

i=0

ρm 0, 753 1 PQC = P0 = · = 0, 033; m! 3! 2, 1   m m   1 ρn 0, 753 2 = 0, 75 + 0, 75 + ≈ 0, 72. nPn = P0 m3 = (n − 1)! 2, 1 2 n=1

n=1

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The obtained result of theoretical calculation PQC = 0.033; m3 = 0.72 (tool) indicates that the proposed model used to calculate the quantity of the tool in the warehouse in certain operations allows determining the allowable level of the tool safety stock.

3 Conclusion Thus, the adaptation of the PLM-class information system in the Industry 4.0 concept during the stage of technological design allows reducing the cycle of tool purchase, calculating a reorder point, and determining the probability of missing tools for equipment.

References 1. Afanasiev AS, Vishchenko YL, Ivanov KM (2015) Information and system assurance of quality and improvement of reliability of ammunition and small arms cartridges. innovative technologies and technical means of special purpose. In: Works of VII all-russian scientific and practical conference library of the magazine. Military Mechanical Institute BSTU Bulletin, pp 25–30 2. Ivanov KM, Matveev SA, Kireev OL, Ignatenko VV (2016) Methodological foundations of decision support systems in risk management tasks at the stages of the life cycle of special purpose products. News of the Kyrgyz State Technical University named after I. Razzakov (Bishkek) 2(39):80–87 3. Vyashenko YL, Ivanov KM, Athaniev AS, Kireev OL (2015) Support of life cycle of products of responsible purpose. News of the Kyrgyz State Technical University named after I. Razzakov (Bishkek) 3(36):45–48 4. Babaev SA, Nevokshenov GV, Ivanov MV (2017) Development of an instrument to control the readiness of design and technological documentation for the launch of the product on the IT-technology platform. Radio Ind Mag 04(2017):110–115 5. Bichenkova OF, Chernenka LV (2017) APS-level: quality control in planning production stages. In: XXI International scientific-practical conference system analysis in design and management. Collection of scientific works of part 2, pp 368–374 6. Gurylev OA, Chernenka LV (2018) Improvement of automatic control quality in assembly production of printed circuit boards. In: XXII International scientific-practical conference system analysis in design and management. Collection of scientific works, pp 180–184 7. Bichenkova OF, Potapova LG, Chernenka LV (2019) Operational control of discrete production using a polynomial algorithm. In: XXIII International scientific-practical conference system analysis in design and management. Collection of scientific works of part 3 8. Gurylev OA, Chernenka LV (2019) Operational accounting in assembly production of printed circuit boards. In: XXIII International scientific-practical conference system analysis in design and management. Collection of scientific works of part 3, pp 299–304 9. Pereverzev PP (2012) Functional modeling of production organization processes at machinebuilding enterprises. Mod Probl Sci Edu 2:24–32 10. Greiz GM, Pereverzev PP (2017) Development of information and analytical support of industrial enterprise management system based on functional modeling of logistics business processes. In: Materials of the 69th scientific conference science of YURGU, Chelyabinsk, pp 390–397

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11. Markov AV, Shmatko AD (2005) Functional modeling of processes in organizational and technical systems: educational and practical manual for universities. In: BSTU “VOENMEH” named after D. F. Ustinov. St. Petersburg, p 88 12. Markov AV, Shmatko AD (2005) Communication integration of systems: training manual. In: BSTU “VOENMEH” named after D. F. Ustinov, St. Petersburg, p 160 13. Volkomorov VI, Markov AV (2012) Robotic production technology: a manual. In: BSTU “VOENMEH” named after D. F. Ustinov, St. Petersburg, p 119 14. Ventzel ES (2005) Probability theory. Textbook for university students, 10th ed., p 576

Research of Forming Process of Surface Quality During Machining with Free Abrasive A. A. Kulkov(B) , A. Y. Popov, and A. Y. Korytov Russian University of Transport (RUT), 9b9 Obrazcova Ulitsa, Moscow 127994, Russia [email protected]

Abstract. The operation of processing metal surfaces before factory or repair painting is part of the typical technological processes of transport engineering and repair. The complexity of cleaning before staining can be up to 70% of the complexity of the painting operation itself. The cleaning methods used in a typical technological process are based on a combination of chemical and abrasive blasting. This combination leads to a significant increase in the material consumption of the process, the allocation of industrial waste, an increase in the amount of technological equipment used, labor resources, and, as a result, is expressed in the high cost of the technological process. Based on this, improving the efficiency of the process of pre-painting is an urgent task. One of the ways making it possible to reduce cleaning costs is to exclude washing operations from the technological process and replace them with a more rational method for cleaning non-solid contaminants and degreasing. Keywords: Abrasive · Roughness · Surface quality · Degreasing · Protective coatings · Cleaning · Gas dynamics

1 Introduction Technological processes in transport engineering include processing of metal surfaces before painting with a free abrasive to give the required roughness and ensure the quality of the surface, as well as chemical treatment for degreasing the surface and removing organic and inorganic compounds from it. This combination leads to the release of technogenic waste in the form of spent washing liquids and degreasing compounds, and, in general, complicates the technological process [1–3]. During the operation of vehicles, almost all surfaces of their units, assembly units, and parts are covered with various operational contaminants and undesirable layers, which are a variety of multi-component formations that have a variety of physical and mechanical, adhesive and hygroscopic properties and chemical composition. When repairing vehicles it is customary to distinguish the following groups of operational contaminants that require cleaning:

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_13

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• Operational road dust and particles of transported goods (EP)—the main type of contamination of bodies and crew parts of vehicles. EP is a thin (0.01–0.5 mm), but sufficiently strong layer on the surface. It has high adhesion and low wettability. Chemical composition: up to 10%—organic substances, about 90%—inorganic substances. As a rule, it consists of dust, soot, soot, and the smallest particles of transported goods. It is formed by settling dry or wet aerosol particles on the surfaces of vehicles. At the same time, it should be noted that the most durable connections of EP with metal surfaces of parts are formed if there is a presence in its composition of iron-oxide particles—products of wear of running parts (up to 90% of iron oxides in the form of rust). This contamination, especially in the presence of iron-oxide particles in its composition, is difficult to remove from surfaces. • Oil and mud deposits (MGO)—consist of products of oxidation of oil, grease, fuel, as well as dust, sand, particles of transported goods, products of wear and corrosion. MGO occur in the crankcase of a diesel engine, transformer, connecting rod channels, crankshaft, etc. The harmful effect of MGO is manifested in contamination of fresh oil poured during the operation of vehicles, and as a result, in clogging of oil pipelines, filters, etc. The Chemical composition of MGO: up to 30%—organic substances, about 70%—inorganic substances. MGO has low adhesion and strength. All MGO, depending on their consistency, can be divided into oils, resins, oxyacids, asphaltenes, carbenes, and carbonites. Most of these contaminants are easily removed from the surfaces of parts, but require the use of special tools and technologies. • Asphalt-like layers (APN)—are a derivative of MGO. They are formed during longterm operation, usually in places of grease leaks, at high operating temperatures (more than 120 °C). The presence of APN is most characteristic on the surfaces and assemblies of the engine, transmission, axle assemblies, etc. These layers have high adhesion and strength, as a result of which they are quite difficult to remove during cleaning. • Varnish-like deposits (LPO)—carbonaceous substances (films) that look like lacquer coatings. LPO is formed on the metal surfaces of parts that are washed with oil and fuel when exposed to a relatively low temperature (80–100 °C). The presence of this film worsens the thermal conductivity, which contributes to overheating of components and assemblies. LPO have a sufficiently high adhesion, which makes them difficult to remove during cleaning. • Carbon (NG) is a caked mass on metal surfaces consisting of soot (decomposed at high temperature and incomplete combustion of fuel), oil and resins, as well as road dust and metal particles. In their structure, NG is dense, loose, dry, and oily. The chemical composition of NG: 60–90%—organic substances, 10–40%—inorganic substances. Carbon deposits are formed on pistons, valves, and exhaust manifolds. NG has high adhesion and strength, as well as low hygroscopic. NG sharply reduces the thermal conductivity, which leads to zonal overheating of parts, and as a result, burnout and the formation of thermal cracks; in addition, the presence of carbon on the parts causes an increase in fuel consumption, reduced engine power, increased wear, and increased exhaust smoke. • Scale (NC)—solid deposits that are formed when calcium and magnesium salts fall out when water is heated to temperatures above 70–85 °C. These deposits occur in nodes and pipelines of the engine cooling system, in elements of vehicle heating systems, etc. Since the thermal conductivity of the scale is many times lower than the thermal

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conductivity of the metal, its presence sharply worsens the heat exchange conditions, and also sharply reduces the working sections of pipelines, the heat transfer of working planes, etc. NC has a sufficiently high adhesion and strength. • Metal corrosion (CR)—is the spontaneous destruction of metal surfaces due to their chemical or electrochemical interaction with the external environment. Almost all metal surfaces of vehicle bodies and parts are exposed to CR. The main cause of CR is the thermodynamic instability of structural materials to the effects of substances in contact with them. The rate of KR, like any chemical reaction, depends strongly on the temperature, so increasing the temperature by 1000 °C increases the intensity of KR by several orders of magnitude. Corrosion has a sufficiently high adhesion and strength. • Old paint coatings (LCP) are undesirable layers and usually consist of several layers, primers, putty, and paint coatings that were not removed during previous repairs. As a rule, old coatings have high adhesion and strength, so they are difficult to remove during cleaning. Currently, when repairing vehicles, several dozen different methods of cleaning dirt and unwanted layers are used. According to the technological nature of the cleaning process, they can be divided into the following groups: • Mechanical methods (MM)—based on the destruction and removal of dirt from the surfaces of parts by some mechanical action on them directly by the tool or elements of the working environment. MM is successfully used for cleaning large-sized metal structures in construction, shipbuilding, energy, etc. at enterprises that repair vehicles; MM is used to remove contaminants that have high strength and adhesion, such as NG, NK, KR, APN, and LCP. Depending on the applied technological effects on pollution, MM is divided into the following: locksmith, blade, abrasive, etc. • Impact methods (UM)—based on the destruction and removal of dirt from the surface of parts by some dynamic impact on the elements of the external working environment. Depending on the technological impacts on the pollution, it is divided into the following: tumbling, sand blasting, shot blasting, and waterjet processing. • Chemical methods (XM)—based on the destruction and removal of contaminants as a result of chemical reactions occurring on the surfaces to be cleaned between the contamination and the chemical reagent. Depending on the chemical composition of the pollution, the chemical effects can be organic and inorganic, solid, liquid, gaseous (aerosol vapors), and melts. In addition, they are alkaline, acidic, and neutral, as well as single- or multi-component. XM is widely used in the enterprises of instrument making, automobile manufacturing, production of household appliances, etc. At the same time, despite the high efficiency of XM, their use in enterprises that repair vehicles is sharply limited, according to the requirements of fire safety, labor protection, and ecology. • Physical methods (FM)—based on the principles and features of the course of physical reactions, as a result of which contamination is destroyed and removed from the surfaces of parts. The main physical methods include ultrasonic cleaning, ion bombardment, and laser irradiation.

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• Electrochemical and electrophysical methods (ECFM)—based on the fact that the destruction and removal of contaminants occur as a result of chemical reactions or physical effects occurring under the influence of an electric current. These methods include electrochemical etching, electrochemical polishing, and electrochemical cleaning. • The hydraulic method (GM) is the cleaning of the surface of parts from dirt and unwanted layers using cleaning solutions—water or water with detergents containing surfactants (surfactants). According to the method of implementation, the sink can be jet (hydro-air), submersible, hydro-circulation hydrodynamic, and boiling and steam jet. • Thermal methods (TM)—based on removing contaminants by heating them to a temperature at which they either burn or lose their mechanical strength and are separated from the base metal. In this case, the main sources of temperature influence on pollution can be used, such as gas-flame, furnace, gas-dynamic, plasma-arc, and induction and electric contact method.

2 Importance and Scientific Novelty of the Research The technological process of painting metal surfaces when repairing vehicles is a complex, multi-stage step-by-step process. Depending on the production conditions, the painting process may include not only surface cleaning operations, but also additional chemical transformation of the surface by creating conversion coatings (oxide, chromate, phosphate, etc.). The quality of surface preparation before painting plays an important role in obtaining a high-quality and durable paint coating. Basic recommendations for surface preparation before painting are defined by interstate standard with GOST 9.4022004 ESZKS “paint coatings. Preparation of metal surfaces for painting.” At the same time, surface preparation for painting is the most difficult and time-consuming stage of the entire painting process, which is up to 70% of the entire painting operation [4]. Currently, at vehicle repair companies, a serious problem with repair and restoration painting is the cleaning of metal surfaces from operational contamination and old paintwork. At the same time, this area is worked out and studied much less than the painting process itself. The main purpose of preparing the surface of the part before painting is to remove substances from it that prevent staining or accelerate corrosion processes, as well as to form a surface condition that provides the required adhesion to the paint coating. In addition, when choosing the method of surface preparation for painting, it is necessary to take into account the shape, size, and initial state of the surface, and the material and operating conditions of the part. Let’s analyze the main problems associated with cleaning and preparing the surface for painting: • when cleaning from solid contaminants, the task is to clean the surface to a metallic luster in accordance with grade I or grade II; • it is necessary to give the surface to be cleaned the necessary roughness. Different paint materials require different roughness values when painting. Roughening the surface is an important technological stage of the entire painting process. The surface

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roughness significantly increases the adhesive properties of the coating applied to this surface. Roughness values for various coatings are regulated by the standard; • the next requirement for surface preparation before painting is degreasing [5, 6]. Various operational contaminants, including oil-mud and asphalt-like ones, may be present on the surface of parts after prolonged use. Their removal is usually performed by chemical methods, which significantly complicates the technological process of the entire color. One of the most versatile and highly effective methods of preparing the surface of parts before painting is the gas-dynamic method, which successfully solves all of the above problems. This method is a surface treatment with a stream of heated gas mixed with accelerated particles of free abrasive. In this case, the abrasive stream destroys solid contaminants, gives the surface roughness and the required quality, and the thermal stream degreases it. This eliminates the complex, waste-intensive, and environmentally harmful operation of classical chemical degreasing and generally optimizes the process. Implementation of this method is possible due to the use of the experimental installation “GDA” (gas-dynamic apparatus). Brief technical characteristics of the model used in the research in this work: the working pressure in the combustion chamber is 3–8 bar; operating temperature inside the combustion chamber is 1000–1500 °C; operating temperature in the treatment area is 90–100 °C; air consumption is 4,5–6,0 m3 /min; diesel fuel consumption is 6,0–15,0 l per hour; fuel pressure is 15–25 bar; conditional flow power is 150 kW; cleaning capacity is 5–30 m2 /hour; abrasive consumption is 8–12 kg/m2 ; maximum size of abrasive particles is 2.0 mm; and total electric power consumption is 15 kW. The use of GDA in vehicle repair enterprises requires study and scientific justification of the parameters of the impact of the free abrasive flow on the treated surface. This paper presents the results of studies of the gas-dynamic cleaning process and obtained parameters of the flow effect on the metal surface, the actual cleaning speed and performance of the process, the temperature in the processing zone, the roughness of the metal surface after processing and other technological parameters, as well as the justification of the effectiveness of the gas-dynamic method in transport engineering. On the example of a typical design of a gas-dynamic apparatus [7, 8], presented in Fig. 1, we can consider the basic principles of generating a gas-dynamic flow of free abrasive. Through the fitting (Pos. 4) into the combustion chamber (Pos. 1), the fuel is injected, and through the fitting (Pos. 3) compressed air is supplied. In the combustion chamber, a combustible mixture is created, which is under pressure, and tends to exit through the critical section of the nozzle (Pos. 6). Before this, the mixture is ignited by a spark (Pos. 5) and forms a thermal flow torch (Pos. 9), which is accelerated by narrowing the nozzle diameter before the critical section (Pos. 6). At the exit from the critical section, the nozzle expands again, so as not to create obstacles to the expiration of the accelerated thermal flow. After exiting the accelerating nozzle into the flow through the ejector (Pos. 8) abrasive is supplied. Thus, a hot gas-dynamic flow of free abrasive is created at the outlet of the device [9–11]. There are several basic parameters of gas-dynamic treatment with a free abrasive: processing capacity. This is the actual mass of the material being removed (metal, dirt, and paint) per unit of time. Productivity can be expressed in direct dimension (kg/s), or by

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Fig. 1. Schematic diagram of the installation for the implementation of the gas-dynamic method.

reference to the area of the treated surface (m2 /hour), surface quality. The quality of the surface consists in its “safety” after exposure to free abrasive. It can be expressed by the thickness of the layer deformed by the abrasive (mm), degree of purification. The degree of cleaning before painting is regulated by GOST 9.402-80 and is divided into two main groups: full and partial. The degree can be estimated as the ratio of the areas of cleaned and untreated zones, visually or using a metallographic microscope, roughness. This is a trace of free abrasive treatment expressed in terms of Ra , Rz , or Rmax . The average height of the profile before painting should be a quarter of the thickness of the paint coating; local heating temperature of the treated surface; and free abrasive consumption (kg/hour).

3 The Researching of Gas-Dynamic Processing It is based on the process of the gas-dynamic method of free abrasive treatment based on the model of deformation of the surface as a result of multiple collisions of abrasive particles with it. The process of processing free particles is the destruction of solids in micro-impact collisions. To quantify the destruction in the collision zone of each particle, we apply an ideal model of pressing the sphere into an elastic semi-infinite plane. The main regularities of this process were laid down in theoretical physics, which solved the problem of contact of two elastic bodies with curved surfaces. This result is still the basis of the mechanics of contact interaction. A theoretical model of the collision of an abrasive particle with the treated surface is presented in Fig. 2. Before the collision, an abrasive particle in free flight has kinetic energy, which, when it collides, performs work on deforming and destroying the surface. The parameters of the trace left mainly depend on the mass and velocity of the particle at the moment of collision, as well as on the mechanical properties of the particle material and the material being processed. Theoretical and practical studies have shown that the depth and diameter of the trace left by the particle increase with the speed and mass of the particles and are 20–30% of the particle diameter at calculated speeds of 50 m/s, if the abrasive is quartz sand. When using a harder abrasive, such as steel or cast iron shot, the depth and diameter are already 50% of the particle diameter at the same design speeds. The most commonly used types of free abrasives were studied: quartz sand, electro corundum, silicon carbide, microsteclospheres, and crushed and cast steel and cast iron

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Fig. 2. The model of surface deformation by a free abrasive particle.

shot. The average fractions of the studied free abrasives are from 0.1 to 1 mm. Large particles are more inert and are more heavily dispersed in the flow. The fraction of an average fraction of 1 mm is accelerated to no more than 30 m/s. The sand mixture is accelerated to 60–70 m/s and leaves a better mark on the treated surface. To ensure a high rate of removal of the material, it is advisable to use harder abrasives, and when finishing—softer and more brittle. Smaller abrasive grains give less rough surfaces, but the use of small grains is accompanied by a decrease in the volume rate of removal of the material. When processing with maximum modes, the depth of the defective layer does not exceed 0.2 mm when using a sand mixture and 0.4 mm when using a fraction. In general, the sand mixture provides a softer effect on the metal surface, due to its natural properties. The surface roughness is formed as a trace from collisions with particles and is within the range of Rz 25–60 microns. Due to the multidirectional roughness of the treated surface and controlled material removal, the removal of the surface defective layer is ensured with the elimination of future stress and cracking concentrators; in addition, during gas-dynamic processing, favorable compressive stresses are obtained in the surface layer. One of the most important issues studied was the increase in processing performance, i.e., the increase in the removal of material from the treated surface per unit of time. It was found that the performance of gas-dynamic processing is affected by the size and hardness of abrasive particles, the angle of attack, air pressure, and distance from the treated surface. The performance of the processing process is determined by the average design speed of the particles and their mass. Studies have shown that even when optimal working conditions are provided, the maximum processing capacity that can be realized by a person does not exceed 35 m2 /hour. The process is simply limited by the speed of human hands, and even with powerful processing modes, the energy invested is consumed inefficiently. When the nozzle is moved automatically by a robot using the CNC program, the installation of a closed-cycle system with abrasive recovery, and the presence of an automatic table for moving and rotating products, the processing capacity can reach 75–90 m2 /hour [12, 13]. Simultaneous exposure to abrasive and heat flow helps to heat the surface to temperatures that ensure degreasing of surfaces for painting. The degree of purification

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achieved by the gas-dynamic method is in accordance with GOST 9.402-80, which assumes complete destruction of contaminants and removal of organic compounds from the metal surface. In this case, the maximum local heating temperature of the metal does not exceed 200 °C. The operating temperature is 120–140 °C, which is completely safe for rolling stock parts when heated locally. Temperature is 300 mm from the cleaning zone of 60–70 °C, and in 1 m from the cleaning zone of 30–40 °C. This is possible due to the powerful heat sink of the massive structure of the part. When processing small parts and components, the heating is much more intense [14–16].

4 The Result of Research The consumption of free abrasive in medium modes is approximately 60 kg/hour, while, due to recovery, part of the abrasive can be reused. The sand mixture loses about 30-40% of the mass in one cycle, which turns into dust. Fraction and type of an abrasive have a larger resource and in one cycle lose 7% and 15% of the mass, respectively. From the point of view of quality, the sand mixture has better indicators because it has a softer effect on the treated surface, but, turning into dust, it negatively affects the health of the person working near the cleaning zone. Fraction and type of an abrasive strongly deform the surface, but split in a collision does not form dust. Technical and economic analysis showed that the cost of processing one square meter using the gas-dynamic method is lower than when using a typical technology by 13–17%, and the payback period for its implementation can be less than 1 year. The main effect is achieved by replacing chemical degreasing with thermal [17, 18]. In this case, the roughness obtained on the metal surface after processing is shown in the graph (Fig. 3).

Fig. 3. Graph of the dependence of the surface roughness Rz on the velocity of abrasive particles in the flow.

Practical testing of the results of these studies was carried out at the Kaluga plant “Remputmash” JSC during the repair of track car bodies. Studies have shown that the use of the gas-dynamic method for preparing the surface before painting allows to ensure high quality of the cleaned surface up to Sa-3; roughness from Rz 40 to Rz 20; smooth processing of complex and shaped open surfaces;

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ability to process both metal and non-metal materials; there is no need to firmly fix the workpiece; ability to control the degree of mechanical and thermal effects on the treated surface; minimum consumption of the main material to be cleaned; removal of operational pollution without deformations, with minimal work hardening of the surface; and increased adhesion of paint and varnish materials compared to traditional methods of surface preparation (up to 20 MPa). A comparative analysis of typical cleaning methods in transport engineering has shown that the gas-dynamic method provides not only increased adhesion and service life of the applied paint and varnish coating, but also allows you to optimize the process and achieve greater productivity, reduce material consumption and the volume of manmade waste, reduce production areas and reduce the range of equipment used in the production, and repair of technological equipment.

References 1. Kulkov AA, Popov AY, Korytov AY (2019) Automated Quality Control Systems for Paint Coatings in Industry. IT&QM&IS, pp 277–279 2. Kulkov AA, Inozemtsev VE (2018) Ultrasonic liquid matting of metal surfaces. Bull Bryansk State Techn Univ: 40–43 3. Kulkov AA, Larionov MA (2018) Characteristics of the abrasive-blasting of metal surfaces before application. High Technol Mech Eng 90:15–20 4. Kulkov AA (2017) Technological modes of ultrasonic liquid matting of metal surfaces. Metalworking 102:51–53 5. Kulkov AA, Inozemtsev VE (2017) The formation of the surface quality of the metal at thermoabrasive processing. Proceedings of the VI International conference design-technological informatics, pp 38–39 6. Evseev DG, Kulkov AA, Korytov AY (2016) Evaluation of the effectiveness of the process of surface treatment of wagons prior to painting metal. Metalworking 96:66 7. Evseev DG, Kulkov AA, Korytov AY (2015) Study of the process of surface quality formation in the processing of cars by gas-dynamic method. Metalworking 90:39 8. Evseev DG, Kulkov AA (2009) Shot blasting gas-dynamic method of surface cleaning. Transp Sci Technol Manag:32–34 9. Evseev DG, Kulkov AA (2009) The Influence of gas-dynamic parameters of the shot peening treatment on the performance of the cleaning of surfaces during the repair of cars. Science and technology transport. Sci Infor Collection 2:24–26 10. Kulkov AA, Larionov MA, Krukovich MG (2018) The study of the processing of metals by a loose abrasive on the basis of analysis of particle velocity. IT&QM&IS 2018:254 11. Kulkov AA, Korytov AY (2014) How to assess the quality of capital repairs. The world of Transport 51:110–113 12. Kulkov AA, Korytov AY (2012) Assessment of the quality of capital repairs of rolling stock. The world of transport 10:130–133 13. Galchenko VP, Gulak VA, Evseev DG, Kulkov AA, Prokofiev YA (2007) System for thermoabrasive cleaning and galvanizing of railway carriage surfaces. Utility model patent RUS 68952 14. Kulikov MY, Inozemtsev VE (2016) Electrochemical-mechanical shaping as a high-potential technology in the field of metal processing. Metalworking 94:63–65 15. Evseev DG, Kulikov MY, Inozemtsev VE (2016) Progressive ways of finishing components of the rolling stock. The world of transport 60:40–49

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16. Kopachev SV, Nugumanova AA (2015) Optimization of production costs for maintenance of rolling stock based on the use of toilet systems with bioreactor. Materials of the third all-Russian scientific and technical conference with international participation in three parts, pp 198–204 17. Kopachev SV (2012) Improvement of the organization of repair of rolling stock on the basis of mathematical modeling of labor intensity of technological preparation of production. Moscow University Transport Engineering 18. Vereschaka AA, Grigoriev SN, Vereschaka AS, Popov AY, Batako AD (2014) Nano-scale multilayered composite coatings for cutting tools operating under heavy cutting conditions. Proc CIRP: 239–244

Study of Reactive Power Compensation Efficiency for Asynchronous Motors of Metal-Cutting Machine Electric Drives L. E. Shvartsburg(B) and S. I. Gvozdkova Moscow State University of Technology “STANKIN”, 1, Vadkovsky, Moscow 127055, Russia [email protected]

Abstract. The purpose of the study is to reduce power consumption in a production system. The issues of economical and rational use of electric energy by reducing energy losses in the process of its consumption, transmission, and conversion have been discussed. The analysis of the main sources of energy losses of asynchronous motors for electric drives of metal-cutting machines has been carried out. The approach of reducing energy losses by decreasing the reactive power and increasing the power factor has been discussed. One of the ways to solve the problem of decreasing the reactive power and increasing the power factor of electric drives of automated systems is the phase-shift compensation. Experimental studies have been conducted to evaluate the efficiency of reactive power compensation for electric drives of metal-cutting machines. The purpose of the experimental studies was to evaluate the reactive power compensation efficiency for asynchronous motors of lathe electric drives by determining the relationship between the power consumption parameters and such parameters of the machining process as cutting depth and rotation speed. The results of the experimental studies enabled it to establish the dependence of power consumption on the article machining modes, as well as the efficiency of reducing energy losses by decreasing the reactive power and increasing the power factor based on the use of the phase-shift compensation method. Keywords: Metal-cutting machines · Energy saving · Power factor · Reactive power · Electric drive

1 Introduction Electric energy is widely used in all industries: it is converted into other types of energy (mechanical, thermal, light) for the purpose of actuating machines and mechanisms, and generation of heat and light [1–4]. Mechanical engineering offers the increased requirements for management of the processes and safety of the processes [5, 6]. A modern electric drive carries out almost all process operations related to the conversion of electric energy into mechanical energy [7, 8]. However, generation, transmission, and conversion of electric energy are accompanied by energy losses [9, 10]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_14

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The issue of economical use of resources is one of the most important ones for management of production and environmental protection [11, 12]. Economical rational use of electric energy, and maximum reduction of losses during its consumption, transmission, and conversion are the most important tasks of the modern production process [13–15].

2 Formulation of the Problem Loss of energy in a motor is justified by the fact that electric energy is not completely converted into mechanical energy: a part of electric energy is converted into thermal energy [16, 17]. The energy used is characterized by apparent power S. Apparent power can be represented through active and reactive power. An increase in reactive power consumption by an electric motor is accompanied by an increase in energy losses and a decrease in the power factor, cos ϕ. Active power P is determined as follows (1): P = UI cos ϕ

(1)

where the multiplier cos ϕ—the power factor, U—nominal voltage, I—nominal current. The reactive component Q of apparent power is determined as follows (2): Q = UI · sin ϕ = S · sin ϕ

(2)

where S—apparent power, U—nominal voltage, I—nominal current. A reduction of energy losses is characterized by a decrease in the proportion of reactive power Q [18, 19]. One of the ways to solve the problem of energy saving for electric drives of production equipment is the development and implementation of automated systems for electric drives that reduce energy losses by decreasing reactive power based on phase-shift compensation.

3 Main Part The reduction of energy losses is characterized by a decrease in the proportion of reactive power P, which corresponds to a more efficient use of the energy source [20, 21]. There is a relationship between an increase in the power factor and a decrease in reactive power Q consumption: a decrease in reactive power contributes to an increase in the power factor, cos ϕ. Given that the active power is a constant (P = const), a decrease in the reactive power will result in a decrease in apparent power S. This will reduce power consumption. Electromechanical power converters are designed for a certain nominal voltage U determined by the insulation of these devices, and for a certain nominal current I determined by heating of the device conductors. Accordingly, the highest use of the equipment is possible in the case when the power factor, cos ϕ = 1.

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For electromechanical converters of metal-cutting machines, the condition of current resonance achieved by using compensation capacities is the absence of any phase shift between current and voltage at the circuit terminals. This means that current resonance allows to provide for an angle between the direction of current and voltage ϕ = 0 and, therefore, cos ϕ = 1. Thus, current I coincides with voltage U in terms of phase. Conductivity of the circuit must be purely active and the reactive conductivity must be equal to zero. Current resonance can be obtained by changing frequency, inductance, and capacitance. Vector diagram of the circuit currents is shown in Fig. 1.

Fig. 1. Vector diagram of the circuit currents.

The current in a branch with a coil IL has two components: IL , shifted in the direction of lag behind voltage U by the angle π2 and active IaL in the same phase with U. Current in a branch with a capacity has a component IC shifted in the direction of advance relative to U by the angle π2 . Current vectors IL and IC are equal in magnitude, directed relative to each other at an angle π and mutually compensated. Current vector of circuit I is equal to the sum of the current vectors of the branches and is purely active, and it is in the same phase with voltage vector U. One of the ways to solve the problem of energy saving for electric drives of production equipment is the development and implementation of automated systems for electric drives that reduce energy losses by decreasing reactive power based on phase-shift compensation [22, 23]. Thus, reduction of power consumption by reducing energy losses in the process of its conversion can be carried out through the use of compensating elements that contribute to the decrease of reactive power and increase of the power factor of metal-cutting machines [24, 25].

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4 Research Results The purpose of the experimental studies was to evaluate the reactive power compensation efficiency for asynchronous motors of lathe electric drives by determining the relationship between the power consumption parameters and such parameters of the machining process as cutting depth and rotation speed. Parameters of current consumption I, active power P, reactive power Q, apparent power S, and power factor cos φ were considered as the power consumption parameters. To assess the efficiency of the energy loss reduction process, the measurements were made for two modes: • With compensation of the reactive component of the consumed power of the asynchronous motor (mode I) and • Without compensation of the reactive component of the consumed power of the asynchronous motor (mode II). Experimental studies were conducted for a lathe using an experimental energy-saving system. This energy-saving system consists of a block of capacitors, a programmable controller, a block of switching devices, and a block of control and measuring devices, including the meters for current and voltage, active, reactive and apparent power, and power factor. Phase-shift compensation is provided by parallel connection of capacitor banks. Lathes are used for a wide variety of operations: machining with cutters of external and internal cylindrical, conical and shaped surfaces, end surfaces, cutting of external and internal threads, etc. The operation of machining the external cylindrical surfaces with cutters is discussed below. Stage I of the experimental study included evaluating the efficiency of reactive power compensation, as well as determining the relationship between the parameters of current consumption I (A), active power P (W), reactive power Q (VAr), apparent power S (VA), power factor, and cutting depth (mm) for the two analyzed modes. Measurements were performed at a rotation speed of 1,000 rpm. The results of the experimental study of stage I are presented in the form of graphs of dependencies between the parameters of reactive power Q (VAr) and cutting depth t (mm) for the two analyzed modes (Fig. 2). The results of stage I enabled it to evaluate the efficiency of reactive power compensation, as well as to establish the relationship between the power consumption parameters and the cutting depth at a rotation speed of 1,000 rpm, and • current consumption values for Operation Mode I (with compensation) are significantly lower than for Operation Mode II (without compensation); • the active power values are not changing significantly for Operation Modes I and II, but depend on the load; • the reactive power values for Operation Mode I are significantly lower than those for Operation Mode II; • the apparent power values for Operation Mode I are significantly lower than those for Operation Mode II;

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Fig. 2. Experimental dependencies between the parameters of reactive power Q (VAr) and cutting depth t (mm) for the two analyzed modes.

• the power factor values for Operation Mode I are significantly lower than those for Operation Mode II; and • direct proportional relationship between the increase in the depth of cutting and the values of current consumption, active power, reactive power, apparent power, and power factor for each of the analyzed modes is determined. Stage II of the experimental study included evaluating the efficiency of reactive power compensation and determining the relationship between the parameters of current consumption I (A), active power P (W), reactive power Q (VAr), apparent power S (VA), power factor and cutting depth (mm) for the two analyzed modes. Measurements were performed at a rotation speed of 500 rpm. The results of the experimental study of Stage II are presented in the form of graphs of dependencies between the parameters of the current consumption I (A) and cutting depth t (mm) for the two analyzed modes (Fig. 3).

Fig. 3. Experimental dependencies between the parameters of the current consumption I (A) and cutting depth t (mm) for the two analyzed modes.

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The results of Stage II enabled it to evaluate the efficiency of reactive power compensation, as well as to establish the relationship between the power consumption parameters and the cutting depth at a rotation speed of 500 rpm. In addition, experimental studies of Stages I and II enabled it to determine the relationship between the increase in the value of rotation speed and power consumption parameters, such as current consumption I (A), active power P (W), reactive power Q (VAr), apparent power S (VA), and power factor for the two analyzed modes. Figure 4 shows the graphs of dependencies between the power factor cos φ and depth of cutting t (mm).

Fig. 4. Experimental dependencies between the power factor cos φ and depth of cutting t (mm).

The results of Stages I and II of experimental studies enabled it to establish a direct proportional relationship between the value of rotation speed and the values of the parameters of current consumption I (A), active power P (W), reactive power Q (VAr), apparent power S (VA), and power factor; increasing the value of the rotation speed increases the values of the power consumption parameters. The analysis was carried out in the course of the studies for lathes: • Dependence of power consumption on the article machining modes; • Reducing energy losses by reducing the reactive power and increasing the power factor by using the phase-shift compensation method. The analysis has shown that in order to achieve the optimal result of resolving the issue of energy saving for electric drives of the production equipment, it is required to implement all of the above methods of reducing energy losses by means of automation. Reducing energy losses will help reduce overall power consumption and resolve the issue of rational use of energy resources for production equipment.

5 Conclusion One of the ways to solve the problem of energy saving for electric drives of production equipment is the development and implementation of automated systems for electric drives that reduce energy losses by decreasing reactive power based on phase-shift compensation. For electromechanical converters of metal-cutting machines, the condition

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of current resonance achieved by using compensation capacities is the absence of any phase shift between current and voltage at the circuit terminals. Reduction of power consumption by reducing energy losses in the process of its conversion can be carried out through the use of compensating elements that contribute to the decrease of reactive power and increase of the power factor of metal-cutting machines. Experimental studies have been conducted to evaluate the efficiency of reactive power compensation for electric drives of metal-cutting machines. The purpose of the experimental studies was to evaluate the reactive power compensation efficiency for asynchronous motors of lathe electric drives by determining the relationship between the power consumption parameters and such parameters of the machining process as cutting depth and rotation speed. The results of the experimental studies enabled it to establish the dependence of power consumption on the article machining modes, as well as the efficiency of reducing energy losses by decreasing the reactive power and increasing the power factor based on the use of the phase-shift compensation method.

References 1. Shvartsburg LE, Ivanova NA, Ryabov SA, Gvozdkova SI, Zmieva KA (2012) Automation of maintenance of indicators safety for machine-building technologies formation of the form. Sci Pract Edu Methodical J Life Saf S2:1–24 2. Ryabov SA, Ivanova NA, Shvartsburg LE (2014) Assessment, analysis and managing occupational risks in the industry. Chief Mech Eng 12:21–26 3. Bukeihanov NR, Cmir IM, Hairo DA, Sergeev VN (2010) Heuristic methods of modernization of machine-building enterprises manufactures. Vestnik MSTU STANKIN 3:75–79 4. Bukeihanov NR, Cmir IM (2008) Innovative approaches to solving resource problems in engineering. Vestnik MSTU STANKIN 4(4):161–166 5. Rodriguez PE, Shvartsburg LE, Artemyeva MS (2017) Methodological design and commissioning of an experimental stand for the study of the spread of harmful substances in the air of work areas during the processing of metals in industry. Proc Eng 206:588–593. https://doi. org/10.1016/j.proeng.2017.10.521 6. Shvartsburg LE, Butrimova EV, Yagolnitser OV (2017) Quantitative evaluation of the effectiveness of best available technologies of form-shaping. MATEC Web Conf 129:01027. https:// doi.org/10.1051/matecconf/201712901027 7. Bukeikhanov NR, Gvozdkova SI, Butrimova EV (2020) Automated resource-saving system for the use and regeneration of epilam-based lubricating-cooling technological liquid. Lecture Notes Mech Eng: 1435–1442. https://doi.org/10.1007/978-3-030-22063-1_151 8. Shvartsburg LE, Butrimova EV, Drozdova NV (2012) Experimental research of distribution vibroacoustics factors in the environment for forecasting of their levels in the certain point of space. Sci Pract Edu Methodical J Life Saf 2:27–30 9. Ivanova NA, Ryabov SA, Shvartsburg LE (2016) The role of information technology in rotor balancing. Russ Eng Res 36(3):235–238. https://doi.org/10.3103/S1068798X16030096 10. Gvozdkova S (2015) Analysis of provision methods of environmental safety by minimization of energy losses by the example of industrial vibration and noise. Ecology Ind Russ 19(3):14– 17. https://doi.org/10.18412/1816-0395-2015-3-14-17 11. Egorov SB, Kapitanov AV, Mitrofanov VG, Shvartsburg LE, Ivanova NA, Ryabov SA (2016) Formation of the integral ecological quality index of the technological processes in machine building based on their energy efficiency. Int J Environ Sci Edu 11(11):4065–4078

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12. Shvartsburg LE (2008) Environmental ensuring of forming technology. Vestnik MSTU STANKIN 1:38–43 13. Shvartsburg LE, Butrimova EV, Yagolnitser OV (2019) Assurance of quality indices of technological processes of form-shaping during preproduction stage. Lecture Notes in Mechanical Engineering, pp 1575–1582. https://doi.org/10.1007/978-3-319-95630-5_168 14. Shvartsburg LE, Yagolnitser OV, Butrimova EV (2020) Development of integrated criterion to select environmentally sound cutting fluids and relevant application systems in shape-forming processes. Lecture Notes in Mechanical Engineering, pp 281–288. https://doi.org/10.1007/ 978-3-030-22063-1_31 15. Butrimova EV, Yagolnitser OV, Shvartsburg L (2017) Automation of management of ecological parameters of the technological processes of cutting on the basis of forecasting their negative impact on the person and environment. Int J Eng Sci Res Technol 6(11):379–383. https://doi.org/10.5281/zenodo.1054609 16. Shvartsburg LE, Butrimova EV, Drozdova NV (2014) Development of an algorithm for automated prediction of vibration and noise in the technological environment. Vestnik MSTU STANKIN 4(31):187–190 17. Shvartsburg LE, Zvenigorodskij UG, Bukeihanov NR (2001) Methodology of resource saving projects development. Vestnik MSTU STANKIN 2(14):14–17 18. Shvartsburg LE, Butrimova EV, Yagolnitser OV (2017) Energy efficiency and ecological safety of technological processes of form-shaping. Proc Eng 206:1009–1014. https://doi.org/ 10.1016/j.proeng.2017.10.586 19. Gvozdkova SI, Shvartsburg LE (2019) Analysis of methods for increase of soundproofing structure efficiency for noise reduction during technological processes of machinery production. Lecture Notes in Mechanical Engineering, pp 1311–1319. https://doi.org/10.1007/9783-319-95630-5_138 20. Gvozdkova SI, Shvartsburg LE (2020) Experimental Studies of Steady-State Sources of Vibrations of Machinery Production Process Equipment to Substantiate Choice of Vibration Protection Methods. Lecture Notes in Mechanical Engineering, pp 141–149. https://doi.org/10. 1007/978-3-030-22063-1_16 21. Gvozdkova SI, Shvartsburg LE (2017) Analysis of sources and methods for reducing noise by minimizing vibrations of engineering technological processes. Proc Eng 206:958–964. https://doi.org/10.1016/j.proeng.2017.10.578 22. Shvartsburg LE (2008) Human and environmental protective ensuring of automated engineering. Vestnik MSTU STANKIN 3(3):19–21 23. Zmieva KA, Shvartsburg LE (2009) Automated Energy and Resource Saving Systems for Industrial Enterprises. Ecology Ind Russ 11:7 24. Shvartsburg L (2015) Ecoenergetics of Cutting Manufacturing Processes. Ecology Ind Russ 19(3):4–9. https://doi.org/10.18412/1816-0395-2015-3-4-9 25. Gvozdkova SI, Shvartsburg LE (2012) Ruduce of loss of energy by increase the coefficient of power. Vestnik MSTU STANKIN 2(20):32–36

Influence of Technological Inheritance on Accuracy of Assembly of Axisymmetric Shells A. S. Yamnikov1(B) , E. N. Rodionova1 , and I. A. Matveev2 1 Tula State University, 92, Lenin Avenue, Tula 300012, Russia

[email protected] 2 Deputy Head of the Production Department, JSC NPO SPLAV named after A.N. Ganicheva,

33, Shcheglovskaya Ulitsa, Tula 300004, Russia

Abstract. In the manufacture of thin-walled shells, it is important to increase the accuracy of processing. On the basis of this, a decision was made to conduct research. The technology of manufacturing a long shell from a thick-walled hot-rolled pipe using rotational drawing is considered, which provides a greater accuracy of the form and less significant influence of the properties of the initial workpiece type in comparison with the technology for producing shells by stamping from sheet metal blanks. It has been established that the variation in the diameter of the shell opening during workpiece basing at the operation of rotational pulling is mirrored to the accuracy of the hole in the shell, and the maximum runout of the central part of the shell, obeying the Rayleigh distribution law, fits into the tolerance with a double margin. Experimental studies have shown that an increase in the accuracy of manufacture of extended shells can be achieved by reducing the technological tolerance on the internal base hole of the workpiece for rotational drawing. Keywords: Rotational · Pulling · Size errors · Shape errors · Correlation · Basing

1 Introduction In mechanical engineering, in the processing of various products, thin-walled shells are widely used, consisting of thin-walled cylindrical parts with an outer diameter of 80– 320 mm, a length of 220–3000 mm, and a wall of 1–5 mm. With a small wall thickness and, accordingly, a relatively small mass, the designs of these shells have the necessary accuracy and strength. These two parameters contradict the manufacturing technology of the products, since with a decrease in the mass of the shell its rigidity decreases.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_15

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2 Factory Technology Analysis In the used manufacturing process for the manufacture of shell blanks, including cutting blanks from sheet metal, convolution, and a number of extrusion transitions alternating with heat treatment, the resulting errors of the blanks are 0.75÷1.5 of the tolerance on the diametric dimensions [1, 2]. When machining, these errors are reduced, according to the laws of copying errors [3–8]; however, the anisotropy of the material of the initial workpiece leads to the appearance of shape errors—ovality and curvature of the pipe. In most cases, a shell with a length of more than 1500 mm and a wall thickness of 1.5–5 mm is difficult to manufacture as a single part, and therefore it is made of several pipes of shorter length. At the same time, the geometric errors of the shell increase, since the connection of parts is impossible without mutual skewness of the axes. Two basic requirements presented to prefabricated shells can be distinguished: straightforwardness of the product and tightness. These requirements are guaranteed by the design of the product and the accuracy of its manufacture. Such a prefabricated casing (Fig. 1) is obtained by screwing long pipes with a length/diameter ratio L/D from 10 to 30. The main functional requirement for prefabricated casing is their free connection with given diameters and curvature, estimated by the radial runout of the prefabricated casing, which is normalized drawing (p ≤ 0.5 mm), as well as the tightness of the connection, determined in this case by the accuracy of the mutual position of the mating ends after tightening, normalized by the size of the one-sided end gap mm.

Fig. 1. The prefabricated shell of the product with a threaded connection pipes 1 and 2: 1, 2, 3—centering thickenings on pipes.

Another parameter regulated under technical conditions is the deviation of the shape of threaded and adjacent surfaces in the form of non-circularity, in particular, ovality, which is significant for thin-walled parts with a wall thickness of 1.5–3 mm (in 1.2÷1.5 times the tolerance on the diametric size). However, when assembling thin-walled shells, shape deviations are somewhat corrected. This is known during design, and therefore the average diameter of a smooth cylindrical surface is normalized and an ovality greater

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than the tolerance of the average diameter is allowed. For example, for a centering bulge with a diameter of 121.6 mm on pipe 2 (see Fig. 1), the size tolerance is mm, and the shape tolerance (ovality). Often, products have inflated radial and end runout of mating surfaces, as well as the ovality of the basic structural elements. The circumstance that the manufacture of products according to a single technological process on the same equipment and with frequent adjustment leads to their different qualities, which indicates the presence of hidden technological hereditary ties. The radial runout of the prefabricated shell reaches p = 1, 2 ÷ 1, 5 mm (for a given 0.5 mm), and the number of rejected products is on average from 20 to 30%. Earlier studies were conducted on the formation of the output characteristics of prefabricated shells taking into account the parameters of pipes manufactured by the existing technology [9]. It was found that the scattering fields of all output quality parameters exceed the existing tolerances: radial runout of the assembled shell—1.3 times and ovality of the middle centering thickening (3)—2.15 times. At the same time, only the pipes included in the assembly, checked by the department of technical control of the enterprise with the help of industrial measuring devices and various calibers, were included. Measurements of deviations in the manufacture of the base surfaces of the pipes showed that their scattering fields exceed their tolerance fields: runout of pipe mating ends is 1.5 times, the ovality of the threads is 1.33 times, and the ovality of the belts is 1.62 times. In addition, the radial runout of the belts relative to the axis of the threads is 2.46 times, runout of the ends of complex threaded gages is 2.58 times, and the ovality of the outer base surfaces is 1.848 times. Thus, the manufacturing process of prefabricated shells using initial blanks from sheet metal does not provide the necessary reliability [10]. At present, when processing thin-walled axisymmetric shells for various purposes, rotational hoods are increasingly used, in particular, rollers with closed and open calibration, as well as with separation of the deformation zone. This allows you to get the shell is not prefabricated, as when using blanks stamped from sheet metal (see Fig. 1), but integral, which reduces the weight of the product and reduces the complexity of the assembly. For the manufacture of integral long axisymmetric shells, hot-rolled thick-walled pipes are used as the initial billet. The operations are performed in the following sequence [11, 12]: • • • • • • •

cutting pipes into measured billets; machining by cutting (boring, turning); heat treatment (hardening, tempering); machining (fair boring and turning); rotational pulling (first and second transition); crimping the thickening of the shell; and low-temperature annealing.

An analysis of the manufacturing technology of extended axisymmetric shells, taking into account previous studies [13–15], made it possible to assume that the internal base

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diameter of the workpiece has a great influence on their accuracy parameters. During rotational pulling, the workpiece is based on the base hole on the mandrel fixed in the machine chuck and preloaded by the center. The pipe 1 (Fig. 2) is based on the internal base diameter on the mandrel 2. On the one hand, the pipe is pressed by the rear rotating center entering the centering hole 3; on the other hand, it is installed in the base 4, which is fixed directly with six studs 5 in the spindle of the machine. If it is necessary to eliminate the runout, the mandrel is set through the clamping ring 6 by selective retraction of eight bolts 7 depending on the indications of the clock-type indicator. At both junctions, the blank hole Ø116 + 0.35 mm serves as a double guide base [16] and determines the accuracy of the relative position of the system of machined surfaces relative to unprocessed ones (Fig. 3).

Fig. 2. The scheme of basing the workpiece with a rotary hood: 1. pipe; 2. mandrel; 3. centering hole; 4. base; 5. hairpin; 6. a clamping ring; 7. a bolt.

In the technological process of manufacturing thin-walled shells, using rotational stretching depending on the deformation modes, the base hole diameter can either decrease or increase [17]. Since during rotational drawing, the deformation zone moves from one end of the workpiece to the other along the helix during its rotation, it can be assumed that the drawing is a bifurcation point of the technological process in which there is no influence of previous operations on dimensions and property blanks [18].

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Fig. 3. Sketches of the pipe at the first (a) and second (b) transitions of rotational drawing.

3 Statistical Processing of Experimental Data For the study, a batch of 96 shells was made and the actual deviations of the diameter of the base hole from the nominal value before and after rotational pulling were measured using an indicator number with a division price of 0.01 mm. The maximum variation in the dimensions of the diameter of the base bore of the workpiece to the hood x was 0.12 mm (from 116.19 to 116.31 mm), and the diameter of the base hole of the workpiece after stretching y was 0.14 mm (from 116.1 to 116.24 mm). For the convenience of data processing, the accepted interval value is Cx = Cy = 0.02 mm. The boundaries of the intervals are indicated in Table 1. The frequency of hit sizes for each interval is given in Table 1. The authors of [19] established that the diameters of the base hole of the workpiece x—before drawing (Ø 116.15 + 0.15 ) and y after drawing (Ø 116 + 0.35 )—obey the normal distribution law, and statistical characteristics that reflect a linear relationship between x and y are also determined, which can be written as a straight line equation. (¯x, y¯ x —the average value of the diameter of the base hole of the workpiece before and after drawing in the considered interval; x ,y —new variables with the help of which it is possible to significantly simplify the calculation procedure. The transition to new variables is carried out according to the formulas: x =

y − ay x − ax  ;y = , Cx Cy

(1)

where ax and ay are the new beginning of the reports, and in our case this is the nominal diameter of the base hole: ax = ay = 116 mm).

116,13

116,15

116,17

116,19

116,21

116,23

116,12÷116,14

116,14÷16,16

116,16÷116,18

116,18÷116,2

116,2÷116,22

116,22÷116,24

i=1

nxi = 96

116,11

116,1÷116,12

l 

y¯ x –average the diameter of the base hole of the workpiece after drawing in the considered interval

Interval values y of the diameter of the base hole of the workpiece after drawing

y—diameter of the base hole of the workpiece after drawing

5

–

–

1

–

3

1

–

116,2

15

–

2

3

–

3

5

2

116,22

23

–

3

2

2

6

4

6

116,24

33

–

5

8

9

6

2

3

116,26

12

–

4

5

–

2

1

–

116,28

8

1

3

2

–

2

–

–

116,30

x¯ —The average value of the diameter of the base hole of the workpiece before drawing in the considered interval

116,19÷116,21 116,21÷116,23 116,23÷116,25 116,25÷116,27 116,27÷116,29 116,29÷116,31

X-interval

x—diameter of the base hole of the workpiece before drawing

Table 1. Frequency of values falling into the interval.

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The correlation coefficient that establishes the strength (tightness) of the correlation relationship with a linear relationship between two variables: random values of the diameter of the base hole of the workpiece after stretching y and the diameter of the base hole of the workpiece before stretching xi : rxy =

Cxy 0, 0003 = = 0, 364, Sx Sy 0, 025 · 0, 033

(2)

where Cxy is the covariance value of two random variables x and y; S x and Sy are the sample dispersion, respectively, of the diameter of the base hole of the workpiece before drawing x and after drawing y statistical characteristics [20]. The correlation relation of the dependent variable y with respect to the independent variable xi was ηy =

Sy¯ x 0, 716 = 0, 431, = Sy 1, 663

(3)

where Sy¯ x is the variance of group means (the variance of the theoretical values of the productive attribute, which reflects the influence of factor x on the variation of y) and Sy is the total variance y . The regression equation is obtained in the form: y˜ x = 0, 48x + 60, 37 , (1)

(4)

where y˜ x is the expected value of the diameter of the base hole of the workpiece after drawing, depending on the current value of x which is the diameter of the base hole of the workpiece before drawing. Figure 4 shows a graphical interpretation of the experimental results. On the correlation field, the number of points in each cell corresponds to the frequency values indicated in the table. Figure 4 also shows the points corresponding to the average values of the base hole of the workpiece after stretching in the considered interval y¯ x ; in each interval, connecting them by segments, we obtain an empirical regression line according to Eq. (1), i.e., the theoretical regression line. In order to evaluate the reliability of this model, it is necessary to know the total and inter-interval variance. Determine the variance y˜ x (the statistically expected value of the diameter of the base hole of the workpiece after drawing, depending on the current value of x which is the diameter of the base hole of the workpiece before drawing): 2   nxi y˜ xi − y¯ x 1399367, 731  = 14576, 747 mm2 . = (5) Sy˜2x = nx 96 Fisher criterion determined by the formula F=

Sy2 Sy¯2x

=

5060, 873 = 0, 347. 14576, 747

(6)

According to the results of the above data, for the number of degrees of freedom r1 = r2 = f−1 = 6, where f is the number of intervals, and confidence probability,

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Fig. 4. Graphical interpretation of the experimental results: ● - data array; ▬ and - - - -, respectively, the theoretical and empirical regression lines, x the diameter of the base hole of the workpiece before drawing, y the diameter of the base hole of the workpiece after drawing, the statistically expected value of the diameter of the base hole of the workpiece after drawing, depending on the current value of x which is the diameter of the base hole of the workpiece before drawing.

the table value of the Fisher test FT = 3.7. Since the calculated value is F = 0.347 < FT = 3.7, the resulting model is adequate, i.e., using the regression equation, one can predict the value of y depending on the change in the value of x with the required accuracy. Confidence intervals were also determined for the mathematical probability of the diameter of the base hole of the shell after stretching in the considered limit M (y), for probability β = 0, 95 and the table value of the student criterion are determined from the condition: 116, 17 − 0, 01 < M (y) < 116, 17 + 0, 01, M (y) = 116, 17 ± 0, 01.

(7)

Validation of the obtained model in the “Statistics” program [21] confirmed the possibility of predicting the output parameter by the value of the input parameter, and the best forecast was obtained for the average value of the parameter interval. Thus, a statistically significant effect of technological heredity in the modern manufacturing technology of long axisymmetric shells has been established. In the study, it was shown that the beating of a central thickening is of great importance for the functioning of the combined shell of the product. In our case, this is a monolithic shell (Fig. 5), the runout of the central part of which also needs to be checked.

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Fig. 5. Sketch of the shell with the norms of accuracy of the relative position of the surfaces.

In a specific case, the runout tolerance is 1.5 mm. A total of 48 blanks were measured. It is accepted that the distribution of beats obeys the Rayleigh law. The program “Statistics” processed the results of the experiment and based on the obtained statistical data, a histogram of the distribution of the actual beating of the central part of the shell was constructed (Fig. 6), showing that all measurements are within the tolerance field, and also obey the Rayleigh distribution law (Fig. 7).

Fig. 6. The histogram of the distribution of the actual values of the beats of the central part of the shell:  and  are the experimental and theoretical values, respectively.

4 Conclusion Thus, the foregoing shows that the modern technological process under consideration provides a significant margin in accuracy and in the runout of the central part of the shell. 1. The manufacture of prefabricated shells using the initial blanks from sheet metal does not provide the necessary reliability. 2. The manufacture of monolithic shells using initial billets from a hot-rolled pipe provides a large margin in the accuracy of the dimensions and shape of the metal.

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Fig. 7. Rayleigh distribution curve of value beats of the central part of the shell.

3. Rotary drawing does not eliminate the influence of the errors of previous operations on the dimensions and properties of the workpiece. So, the errors of the base diameter of the workpiece are copied on the shell with a refinement coefficient of 0.48, corresponding to the coefficient in the regression equation. 4. Experimental studies reflect that to increase the accuracy of the manufacture of shells, it is necessary to reduce the maximum tolerance on the base diameter of the workpiece for rotational drawing. The ratio of the allowance for the diameter of the hole to the field of its actual scattering should be 1.786, which is guaranteed to be greater than the value 1.2 required by the criteria of technological reliability obtained in previous studies.

References 1. Vasilyev A, Yamnikov A, Yamnikova O, Matveev I (2019) Influence of hereditary technological errors in the manufacture of the base pipe on the parameters of the assembled jet engine. Ferrous metals 1:67–71 2. Semin V, Logunov V, Yamnikov A (1991) Influence of deformations of thin-walled threaded parts on assembly accuracy. Problems of mechanical engineering and machine reliability 2:74–82 3. Krasilnikov V, Yamnikov A (1993) The formation of accurate threaded surfaces on parts of complex shape in mass production. Sat. materials RSTC “Resource-saving technology, p 95–97 4. Matveev I (2018) The accuracy of pipe shells-shells taking into account technological inheritance during processing and assembly. Dissertation, Tula State University 5. Bakhno A, Yamnikov A, Vasilyev A, Chuprikov A (2019) More Precise Reaming of Holes in Welded Components. Russ Eng Res 39:990–992 6. Yamnikova O, Yamnikov A, Chuprikov A, Matveev I (2018) Elastic deformation of blanks of hollow axisymmetric housings when secured in three-jaw chucks. Ferrous metals 6:25–30 7. Yamnikov A, Matveev I, Rodionova E (2019) The manifestation of technological inheritance during turning of non-rigid pipe blanks. Ferrous metals 5:36–40

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8. Yamnikov A, Chuprikov A (2015) Chucks for Thin - Walled Blanks. Russ Eng Res 35:838–840 9. Yamnikov A, Rodionova E, Yamnikova O, Matveev I (2019) The Effect of Errors of the Form and Position of the Base Surfaces of a Composite Axisymmetric Body on the Size of an Adjacent Contour. Meas Tech 62:692–696 10. Yakovlev S, Tregubov V, Pilipenko O (2015) Rotational extraction of axisymmetric shells from anisotropic materials with separation of the deformation zone. Bulletin of mechanical engineering 1:73–78 11. Tregubov V, Yakovlev S, Osipova E (2013) Innovative technological processes of rotational drawing of complex-profile axisymmetric parts. Forging and stamping. Processing of materials by pressure 11:9–16 12. Yamnikov A, Yamnikova O, Chuprikov A, Kharkov A (2018) Influence of a back angle and parameters of a strengthening facet of ceramic threaded cutters on resistance. Nonferrous metals 12:88–91 13. Vasiliev A (1997) Statistical model of the transformation of product properties in technological environments. Vestnik MSTU. Engineering 4:19–20 14. Dalsky A (1998) Hereditary relations of procurement and mechanical assembly production. Bulletin of mechanical engineering 1:34–36 15. Matveev I, Yamnikov A, Yamnikova O (2015) Statistical analysis of the accuracy of the preliminary turning of the tube stock. Bulletin of the TulSU. Technical science 11:111–120 16. Matveev I, Yamnikov A (2016) The accuracy of the boring operation of extended axisymmetric cases. Bulletin of the TulSU. Technical science 8:9–15 17. Matalin A (2008) Technology of mechanical engineering. St. Petersburg 18. GOST 27.202–83 (2002) Reliability in technology. Technological systems. Methods for assessing reliability by the quality parameters of manufactured products. Moscow 19. Borovikov V (2013) A popular introduction to modern data analysis in the STATISTICA system. Moscow 20. Gromyko G (2001) Theory of statistics. Moscow 21. Korolkov V (2005) A method of manufacturing axisymmetric bodies. RU Patent 2295416C1, June 27 2005

The Investigations of Surface Micro-Hardness of Experimental Hard Alloy Grades E. V. Fominov(B) , A. A. Ryzhkin, and C. G. Shuchev Don State Technical University, Gagarin Sq 1, Rostov-on-Don 344000, Russia [email protected]

Abstract. The article is dedicated to evaluation of surface dynamic microhardness of experimental hard alloy grades with modified binder constructed on the base of standard single-carbide grade VK8. Connections between micro-hardness and absolute thermo-EMF together with thermal entropy of an alloy as integrated characteristics of its chemical composition and surface properties also were investigated. Micro-hardness measurements on the surfaces of samples made of six experimental hard alloy grades with two types of binder (Co-Fe-Cu and Co-MoTi) were performed using scratching by diamond micro-indenter and assessing micro-hardness by the width of a scratch. It was experimentally confirmed that the highest values of micro-hardness and the highest resistance to abrasive wear are characteristic to hard alloy grades which have the lowest values of absolute thermo-EMF together with the highest values of thermal entropy. It was ascertained that experimental grade 2.22 (binder composition: 5,65%Co + l,8%Mo + 0,6%Ti) has the highest value of surface micro-hardness. The addition of more than 5% Mo to binder results in decreasing of surface micro-hardness compared with basic grade VK8. It was recommended that in the process of new hard alloy grades construction preference must be given to compositions with high values of thermal entropy as having the highest resistance to abrasive wear. Keywords: Hard alloys · Micro-hardness · Abrasive wear · Thermo-EMF · Entropy

1 Introduction Among the modern trends in improving performance and cutting properties of hard alloys (HA), used as inserts to equip the cutting tools (CT) for different machining operations, the direction associated with improving binding phase compositions and the search of new materials for binders can be selected 0. The search for new binding phase compositions is conditioned both by the desire to improve the tribological and operational characteristics of the HA, as well as by economic considerations. For example, cobalt, used as a binder for single-carbide HA of WC-Co type, despite its advantages, is an expensive, and most importantly, insufficient to meet a demand metal [1, 2]. To estimate wear rates J of CT, the dependency may be used which was obtained on the basis of © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_16

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entropy balance equations for couples “tool versus work peace” considering as an open thermodynamic systems [3–6]:   h (P[S] − Φ[S])dx J =

0

v·S

· k,

(1)

where P[S]—entropy production; F[S]—entropy flux; v—cutting (sliding) speed; S— entropy of cutting material (CM); and k—coefficient, taking into account the share of energy spent on wear. From (1) it follows that the greatest wear resistance will be possessed by CM with higher values of the entropy S. Existing CMs are multi-component heterogeneous structures, consisting, if we are talking about HA, of two phases: hard carbides phase and binding metal phase. These components differ in mechanical and physical-chemical properties. All thermodynamic potentials of multi-component systems have the property of additiveness. Thus, the entropy is a structurally sensitive characteristic of the material at the micro-level, and can be calculated as [7–10] follows: Si,j = ηi · Si + ηj · Sj ,

(2)

where S i,j —entropy of each alloy component and ηi,j —molar part of each component Σηi,j = 1. The theoretical relationship between thermal entropy and absolute thermo-EMF has been established: the greater value of the entropy of the material corresponds to the lower value of its absolute (relative) thermo-EMF. The resulting dependence has been confirmed experimentally for different groups of CMs [3, 11]. Thus, high-entropy CMs, which have low absolute (relative) thermo-EMF, are more resistant to oxidative wear, which is especially important for HA tools operating under conditions of active heat generation on contact surfaces. Experimental HA grades developed at the Chair of “Metal-cutting machines and tools” of Don State Technical University were based on standard single-carbide HA grade VK8, where Co as binder was partly substituted by Fe, Cu, Mo, and Ti. Double and triple alloys of these pure metals have lower values of absolute (relative) thermo-EMF than cobalt. As a result of the change in the composition of the binder, the cost of the HA is reduced against the background of the improvement of operational and tribological properties of experimental HA in comparison with the base grade VK8 [3, 12–14]. Thus, the smaller relative thermo-EMF of the proposed binders in relation to the carbide phase increases the resistance of HA to gas corrosion [12]. Wear resistance of CMs is in great measure determined by the complex of their mechanical and physical-chemical properties, between them the important role belongs to the micro-hardness of surface layers [15–18]. One of the best methods of microhardness evaluation is dynamical measuring performed by using scratching by diamond micro-indenter and assessing micro-hardness by the width of a scratch. This method is more informative than quasi-static measurement methods and is widely used to assess the wear resistance of materials and deposited coatings [19–21]. Surface micro-hardness values permit to assess the change in surface micro-relief of a specimen after dynamical interaction with counter-body and its resistance to abrasive wear.

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The aim of the work is the evaluation of surface dynamic micro-hardness of experimental hard alloy grades with modified binder of two types (Co-Fe-Cu and Co-Mo-Ti) in comparison with standard single-carbide grade VK8. Connections between microhardness and absolute thermo-EMF together with thermal entropy of an alloy as integrated characteristics of its chemical composition and surface properties also were investigated.

2 The Experimental Part Micro-hardness was measured on the surfaces of square section samples (5 × 5 mm2 ) made of six experimental HA grades and standard single-carbide grade VK8 for which chemical composition and properties are listed in Table 1. Table 1. Composition and physical-mechanical properties of hard alloys grades. Grade Composition Carbide phase Binding phase 2.19

92,63% WC

7,37%[1,52%Co + 5,03%Fe + 0,82%Cu]

2.20

92,38% WC

7,62%[3,6%Co + 3,2%Fe + 0,82%Cu]

2.21

92,45% WC

7,55%[5,3%Co + l,43%Fe + 0,82%Cu]

2.22

91,95% WC

8,05%[5,65%Co + l,8%Mo + 0,6%Ti]

2.23

91,59% WC

8,41%[5,1%Co + 2,7%Mo + 0,61%Ti]

2.24

90,62% WC

9,38%[3,34%Co + 5,44%Mo + 0,6%Ti]

VK8

92% WC

[1, 2, 4, 5] %Co, Fe ≤ 0,3%

Surface grinding was carried out at the STRUERS LaboPol-2 installation, an average roughness of surfaces after preparation was Ra 0.1–0.11 µm. Measurements were made on the scanning nano-hardness meter NanoSCAN-01 (Russia) equipped by piezoresonant scanning probe (diamond micro-indenter) deposited on the highly stiff console (Fig. 1a). The use of a resonant oscillation mode allows monitoring of the contact of the probe’s point with the specimen surface on two parameters: the change in the amplitude and the frequency of vibrations of the probe. Experiments were conducted in feedback mode on the frequency of probe vibrations, i.e., the probe’s point was in elastic contact with the specimen surface. For micro-indenting, several 35 µm × 35 µm plots were randomly selected on the surface of the sample, which were applied to 3–5 scratches which are 20–30 µm long with a different force of F s = 5, 10,…25 N, and then the width of each scratch in five sections was analyzed (Fig. 1b). The statistical processing of the data was carried out by an algorithm composed of standard MathCAD functions for analysis of variance (ANOVA) using the methodology [22].

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Fig. 1. Scanning nano-hardness meter NanoSCAN-01: a working zone with set specimen; b scratch width measurement on one of five sections.

3 Results and Discussion The micro-hardness comparison for different HA samples was carried out by measuring the width of the scratch h left by the diamond micro-indenter on the surface of the sample. The higher values of surface micro-hardness of the material correspond to the smaller width of the scratch h with a given constant effort of scratching F s . The h(F s ) dependencies for HA grades with the first kind of binder (Co-Fe-Cu) are shown in Fig. 2a.

Fig. 2. Scratch width h versus normal load F s for HA grades with different binders: a Co-Fe-Cu; b Co-Mo-Ti.

Partial cobalt replacement in a binder of Fe-Cu group of metals increased the surface micro-hardness of all the samples. The highest micro-hardness value was recorded for 2.20 grade (3.6%Co + 3.2%Fe + 0.82%Cu), and for grades 2.19 and 2.21 values of this parameter based on the results of analysis of variance can be considered statistically

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indistinguishable. In the case of additives Mo and Ti (Fig. 2b), the largest micro-hardness value belongs to the grade 2.22 (5.65%Co + l.8%Mo + 0.6%Ti). The introduction of more than 5% metallic molybdenum into the binder resulted in a significant reduction of micro-hardness for alloy 2.24. Thus, the highest surface micro-hardness values were recorded for grades 2.22 and 2.23, and the smallest for 2.24 and the standard singlecarbide grade VK8. As mentioned above, dynamic surface hardness is an important parameter that determines the stability of the material when interacting with solid particles of secondary structures. The durability of the material under the conditions of abrasive wear can be assessed by the classical formula of M.M. Khrutsov I = b · H,

(3)

where H—the hardness of the material; b—dimensional proportionality ratio, m2 /N. The hardness H of material is closely related to its composition, and therefore to structurally sensitive parameters—absolute thermo-EMF E and thermal entropy S of material. Then, taking into account the dependence of the hardness of the material on its absolute thermo-EMF [23], the expression (3) can be presented in the following form: 2  E·WF KC ·T + KC + KH 1 + KH 2 , (4) I = b A + WF · e where W F —Fermi’s energy; K H1 and K H2 —variable kinetic coefficients; K C —the energy of atoms in a free state, T —absolute temperature; and A—a constant. From (4), it follows that greater hardness and resistance to abrasive wear will have TM, characterized by low absolute thermo-EMF, and therefore high thermal entropy values. This conclusion is well consistent with previous results of micro-indentation of the surfaces of fast speed steels with different values of thermal entropy and absolute thermo-EMF [24]. The results of this study also confirm dependence (4). The width of the scratch h, obtained from the micro-indentation of the surface, is a characteristic by which it is possible to judge the resistance of the material to the abrasive form of wear when force of scratching is constant F S = const (Fig. 3).

Fig. 3. The dependence of the width of the scratch h on the absolute thermo-EMF E for various HA with the effort of scratching F S = 25 N.

From Fig. 3 it is clear that when the absolute thermo-EMF E of the material increases the width of the scratch h also increases, and therefore the resistance of the material to

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abrasive wear is reduced. Also, the high micro-hardness of surface roughnesses contributes to better retention of secondary structures on the surface of the material—the “third body” in the case of dry friction and boundary shielding delayed layer of lubricant during friction with lubricant [13, 14, 16, 24].

4 Conclusions As a result of the determination of the surface dynamic micro-hardness of experimental HA grades with a modified cobalt binder, the greatest value of this parameter was recorded for grade 2.22 (binder: 5.65%Co + l.8%Mo + 0.6%Ti). Somewhat smaller and close in value micro-hardnesses were recorded for alloys 2.23 (binder: 5.1%Co + 2.7%Mo + 0.61%Ti) and 2.20 (binder: 3.6%Co + 3.2%Fe + 0.82%Cu). The introduction of more than 5% metallic molybdenum into the binder resulted in a significant reduction of micro-hardness for alloy 2.24 and this parameter was lower than value recorded for the standard single-carbide basic grade VK8. High micro-hardness of HA contributes to high resistance to abrasive wear. Resistance to abrasive wear is greater in HA with lower absolute thermo-EMF E and high thermal entropy S values, which is experimentally confirmed. Thus, thermal entropy S, the calculation of which is not difficult under the rule of additives, can be used to predict a priori the some tribological characteristics of newly developed HA, including the durability under conditions of abrasive wear.

References 1. Genga RM et al (2013) Effect of Mo2C additions on the properties of SPS manufactured WC–TiC–Ni cemented carbides. Int J Refract Met Hard Mater 41:12–21 2. Correa EO et al (2010) Microstructure and mechanical properties of WC–Ni–Si based cemented carbides developed by powder metallurgy. Int J Refract Met Hard Mater 28:572–575 3. Ryzhkin AA et al (2016) Determination of the efficiency of high-entropy cutting tool materials. J Friction Wear 37:47–54 4. Ryzhkin AA et al (2016) Structurno-termodinamicheskie aspekti povischenia rabotosposobnosti IRM (Structural and thermodynamic aspects of efficiency of cutting tool materials). Maschinostroeniye, Moscow 5. Ryzhkin AA (2011) Termodinamicheskiy podhod k raschiotu intensivnosti okislitel’nogo iznaschivaniya (Thermodynamic approach to calculating the intensity of oxidative wear of hard alloys) Mehanica i tribologia tranportnih system, pp 195–203 6. Ryzhkin AA (2016) Techniko-economicheskie i termodinamicheskie aspekti optimizacii lezviynoiy obrabotki (Technical, economic and thermodynamic aspects of blade processing optimization). Vestnik DGTU 16:41–50 7. Karapet’yanc MH (1975) Himicheskaya termodinamica (Chemical thermodynamic). Himiya, Moscow 8. Moran MJ (1999) Engineering Thermodynamics. CRC Press LLC 9. Guchman AA (2010) Ob osnovah termodinamiki (The grounds of thermodynamic). LKI, Moscow 10. Prigozhin I, Kondepudi D (2002) Sovremennaya termodinamika ot teplovih dvigateley do dissipativnich structur (Modern thermodynamic from heat engines to dissipative structures). Mir, Moscow

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11. Ryhkin AA et al (2017) Otsenka triboelectricheskich haracteristic bistrorezhushtih staley (Estimation of triboelectrical properties of high-speed steels). Vestnik DGTU 2:20–29 12. Ryzhkin AA et al (2018) Wear and performance of hard alloys. Russ Eng Res 38(6):438–441 13. Beskopylny AN, Fominov EV et al (2019) Tribological characteristics of experimental hard alloy grades with modified cobalt binder under conditions of dry friction on titaniumaluminum alloy VT-3. In: Proceedings of 16th International conference on tribologySERBIATRIB’19, University of Kragujevac, Serbia, 15–17 May 2019, pp 49–58 14. Fominoff EV, Shuchev CG (2018) Tribological Properties of Experimental Hard Alloys in Conditions of Friction on Structural Steel without Lubricant. MATEC-Web Conf 226:01006 15. Liu R, Li D (2001) Modification of Archard’s equation by taking account of elastic/pseudoelastic properties of materials. Wear 251:956–964 16. Kregelskiy IV et al (1977) Osnovi raschetov na trenie i iznos. (Basis of calculation for friction and wear) Mashinostroenie, Moscow 17. Hatt O et al (2017) On the mechanism of tool crater wear during titanium alloy machining. Wear 374–375:15–20. https://doi.org/10.1016/j.wear.2016.12.036 18. Buse H, Feinle P (2016) Model system studies of wear mechanisms of hard metal tools when cutting CFRP. Proc Eng 149:24–32 19. Blau PJ (2009) Friction science and technology: from concepts to applications. Taylor & Francis Group LLC 20. Blau PJ (1985) Relationship between Knoop and scratch micro-identation hardness and implications for abrasive wear. Microstruct Sci 12:293–313 21. Vencl A et al (2013) Abrasive wear resistance of the iron-and WC-based hardfaced coatings evaluated with scratch test method. Tribol Ind 35:123–127 22. Montgomery DC (2013) Design and analysis of experiments. John Wiley & Sons 23. Ryzhkin AA (2000) O svyasy mezdu iznosostoykostyu I fizicheskimi svoystvami instumentalnih materialov (Relationship between wear resistance and physical properties of metal cutting tool materials). Vestnik Maschinostroeniya 12:32–40 24. Ryzhkin AA et al (2018) Study on the tribological characteristics of high entropy high speed steels in conditions of dry friction on structural steel. In: Proceedings of the 4th International conference on industrial engineering ICIE. Lecture notes in mechanical engineering, Springer, pp 1819–1827. https://doi.org/10.1007/978-3-319-95630-5_195

About One Approach to the Study of Heat Fluxes in the Processes of Drilling Deep Holes Machining L. Mironova(B) and L. Kondratenko Moscow Aviation Institute (State National Research University), 4, Volokolamskoe Sh, Moscow 125993, Russia [email protected]

Abstract. The article describes an approach to the study of heat fluxes in the processes of drilling deep holes machining, taking into account the features of manufacturing technology. The features of drilling deep holes machining are outlined. It is noted that the classical equations of the theory of thermal conductivity do not fully describe the process of heat transfer in the system “machine-cutting tool-part”. The analysis is performed of internal and external heat sources in the formed heat chains due to the mechanical interaction of the tool with the part and forced cooling of the cutting zone. As the main factor of influence on the formation of internal heat sources, the overall moment of resistance, arising from the mechanical interaction of the cutting part of the gun drill on the surface being machined, was adopted. It is proposed to evaluate the fluxes of heat by the coefficient of friction, taking into account the dynamics of the deep-drilling process. Keywords: Holes drilling · Cutting forces · Cutting tool · Cutting edge · Resistance moment · Heat source · Heat flux · Heat resistance · Friction force · Coefficient of friction

1 Introduction The manufacture of deep holes machining is a rather laborious and demanding technological cutting operation. The complexity of this process is due to the presence of a long mechanical line (metal stem, drilling pipe), perceiving axial, torsional, and bending loads, Fig. 1 [1]. This leads to the problem of the functioning of the cutting tool, remote from the machine spindle at a considerable distance. Due to the uneven rotation of the tool, due to the elasticity of the line and variable moment and axial cutting force, various dynamic phenomena occur in the “machine-cutting tool-part” system, which lead to a loss in the accuracy of the dimensions and location of the surfaces, as well as to a decrease in the quality of the machined surface of the part. In addition, when developing a deepdrilling machining technological operation, specialists have to solve issues related to © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_17

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Fig. 1. Deep hole machining scheme: 1—cutting part with cutting and support plates, 2—drilling pipe, 3—work spindle, 4—aligning bushing, 5—machine support stand, 6—machined part.

the formation and removal of chips from the hole, supply of cutting fluid (coolant) to the cutting zone, reduction of torsional longitudinal vibrations of the cutting tool, deformation of the drill bit, etc. In this regard, two characteristic causes of the emerging dynamic phenomena in the operation of deep-drilling machining should be distinguished. For the first reason, we attribute the dynamic processes due to the mechanical interaction of the cutting part of the tool (Fig. 1, position 1) with the workpiece surface in the technological system “machinecutting tool-part.” The second reason should be associated with thermal processes caused by internal and outer heats sources during the interaction of the cutting part of the tool with the part and forced cooling of the cutting zone. At present, a sufficient number of works are devoted to the optimization of the technology for manufacturing deep holes machining and to improve the quality indicators of the finished part. For example, works [2–5] are devoted to the analysis of dynamic processes when drilling deep holes machining. However, there are still unanswered questions related to the study of the dynamics of a mechanical system. The study of thermal processes due to the mechanical interaction of the tool with the part and the resulting frictional forces and the fluxes of heat in the technological system is associated with great mathematical difficulties. Whereas the Mathematical Theory of Conductivity and Mass Transfer is quite well developed. This is due, first of all, to the difficulty of setting up an adequate experiment and obtaining experimental data that make it possible to compare the results of analytical calculations with experimental data. This article sets out an approach to the study of thermal processes in the technological subsystem “tool-part” as applied to the process of deep hole drilling machining and related dynamic processes. Hereinafter, following the work of Professor A. Reznikov, we will operate with the concept of “technological subsystem,” which is one of the components of the overall technological system that ensures the performance of specified technological processes or operations [6].

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2 Statement of the Problem It is known that in any technological subsystem heat sources can be internal or external. Internal sources arise in the subsystem itself as a result of the working process, for example, during the operation of equipment and the directly proceeding cutting process. In the latter case, heat is generated due to the forces of friction between the material and the tool, as well as the deformation of the processed material. External sources (or heat sinks) are supplied to the subsystem independently of internal sources. In the process of drilling, forced cooling of the material and tool is carried out, i.e., drains of heat occur. As a result of this, in the technological subsystem “tool-part” under consideration, heat exchange between components is carried out by at least two existing methods: thermal conductivity and convection. We believe that there is no thermal radiation here. Heat sources during metal cutting occur on the front surface of the tool, on the surface of the workpiece immediately proximate to the tip point and in the chips removed [6, 7]. For a detailed discussion of heat transfer methods, we distinguish the following heat chains: “heat source-workpiece”; “heat source-chips”; heat source-tool”; “heat sourcecooling liquid.” Each of them is enumerated as follows—1, 2, 3, 4 correspondingly. In the first three heat chains, heat sources are internal sources. Heat exchange between the components is carried out by thermal conductivity. In the last heat chain, heat energy is transferred from the cooling medium to the tool and vice versa by convective heat transfer. It is external to the heat source. Thus, in the study of thermal processes, one should consider the differential equation of conduction of heat for a solid and the system of differential equations describing convective heat transfer in an incompressible fluid (i.e., heat propagation in forced convection). Since the cutting edges of the tool rotate when drilling along the radius of the hole, it is advisable to consider the one-dimensional problem conduction of heat. The main relations are taken in the following form. The differential equation of conduction of heat is given by [8, 9] ∂ 2 T (ξ, τ ) 1 ∂T (ξ, τ ) = 0. − ∂ξ 2 a ∂τ

(1)

Here T is the temperature; ξ is coordinate in the direction of the cutting edge of the drill, Fig. 1; a is the coefficient of thermal diffusivity; τ is time. Convective of heat transfer is described by a system of equations [6]   ∂T (x, τ ) du ∂ 2u ∂ 2 T (x, τ ) 1 ∂T (x, τ ) ∂p + u = 0; ρ = ρgx − + μ 2 . (2) − 2 ∂x a ∂τ ∂x dτ ∂x ∂x Here u is the fluid velocity in the x-axis direction; ρ is the density of the liquid; p is the pressure at a given point in the flow; μ is dynamic coefficient of viscosity of a fluid. On solving Eqs. (1) and (2) the initial and boundary conditions are stated. Differential Eq. (1) is satisfied by several types of solutions. These are the source solution, the error function solution, the solutions in exponentions, etc. [8]. An analytical solution to the system of differential Eq. (2) is associated with mathematical difficulties and can be obtained for simple cases that are far from real heat

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transfer conditions in technological systems [6]. However, this problem can be considered using the theory of regular thermal regime developed by Kondratyev [10]. In this theory, the assumption is made that the temperature of any point on the body changes exponentially for the period of the regular cooling regime T (x, τ ) = T (x) exp(−m0 τ ) m0 = ψλ

S V

(3)

Here T (x) is the temperature of the point along the x-coordinate at the moment corresponding to the beginning of the regular mode process (τ = 0), m0 is the cooling rate, 1/s; ψ is coefficient of non-uniformity of the temperature field; λ is the coefficient of thermal conductivity of the medium; S and V are the surface area and volume of the cooled body, respectively.

3 Description of the Approach and Derivation of the Basic Equations The considered relations (1)–(3) cannot be applied to the study of thermal processes in the operation of deep holes machining drilling. They do not take into account the features of the technology for manufacturing such holes, which include the following fundamental differences. • The power spent on heat transfer should be determined taking into account the assessment of the dynamics of the mechanical drive of the machine in the subsystem “cutting part-machine spindle.” This is explained by the presence of a long force line (from the machine spindle to the interaction surface of the cutting part of the tool with the part) and the oscillations arising in the system as a result of variable actions [4, 5]. • In the system under consideration, frictional forces of various nature and values arise, which include hydraulic friction, boundary friction, dry friction, etc. Therefore, friction losses will be different [11]. • The influence of foreign particles (chips, metal particles, abrasive particles, etc.) that fall between the support elements and the wall of the hole and affect the friction process should be taken into account. The friction process will be variable. • Coolant enters the radial clearance between the cylindrical surfaces of the tool head and the hole. Thus, lubrication and heat removal from the contacting surfaces of the tool and the metal layer, which is removed in the form of chips, are carried out. Taking into account that in the process of mechanical interaction of the cutting part of the tool with the metal of the part, the prevailing force factor is the friction force, which is converted into heat flux; the heat flux can be estimated by the friction coefficient taking into account the dynamics of the deep-drilling process. The methodology for studying the dynamic phenomena of this process is described in [1, 4, 5, 12, 13]. We write the equation of the total resistance moment acting on the cutting part of the drill as the sum of functions depending on all the characteristic cutting parameters and the forces acting on the cutting part, in the form [4] 







Mr (Φ) = Φ + Φ0 + Φ0 + Φ0 .

(4)

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Here M r is the moment of resistance; F , F 0 , F 0 , F 0 are functions depending on all specific cutting parameters and forces acting on the cutting part. In the process of drilling, power is consumed N, which can be determined by the formula [4] N = Mr Ω,

(5)

where is angular speed of the head rotation. In addition, the power in the cutting zone (N T ) is spent on heat transfer in different directions. We write the ratio of the power in the cutting zone spent on heat transfer in these directions NT =

k  Ti i=1

Ri

,

(6)

Here T i is a temperature drop in each heat transfer channel; Ri is thermal resistance in each i-th channel. It means that any channel absorbs as much heat as its heat transfer resistance allows for. According to [4, 11, 14], the heat resistance during the heat transfer without formation of any protective films can be found by Ri =

i , fi · λ i

(7)

where i is a distance of the heat wave or depth of the layer in question; f i is area of the contact; λi is coefficient of heat conductivity of the channel. The depth of the layer can be evaluated by comparing it with the depth of the heat wave penetration [4], which variation can be accepted exponentially  aτ exp(ν). (8) i = π Here ν is a share of the heat fluctuations amplitude at the depth i ; a is thermal diffusivity, which is definable by a standard equation a = λ/(cp ρ) via heat conductivity λ, specific heat capacity c and metal density ρ; and τ is time of propagation of the heat front. The Eq. (8) allows to define the border of the heat effect propagation during τ, s. Supposingν = 0, and inserting the thermal and physical parameters of the steel into the Eq. (8) √ (9) i = 0, 02 τ , m. Supposing that they are arranged radially, the contact time of blades with each radial line of contact in the heat chain of “heat source-workpiece” shall be evaluated as follows: τ1 =

h , Ωr

(10)

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where h is blade thickness; r is radius of the actual point of the cutting edge. In accordance with this, the thermal resistance of the heat transfer channel to the part can be rewritten in the form √ hrΩ . (11) R1 = 0, 002 λ The heat resistance of the channel “heat source-cooling liquid” can be defined on the assumption that the liquid, cooling the heat source, absorbs energy as [9] Q = ρcool ccool qcool T ,

(12)

Here ρcool , ccool , and qcool are density, heat capacity, and flow of the cooling liquid correspondingly. Taking into account, that Q = T /R, and equalizing these relations, the required value can be found R4 =

1 ρcool ccool qcool

.

(13)

The Eq. (13) is true in case of absence of any films on the cooled surfaces and for the liquid without air or gaseous bubbles, which change density and heat capacity of the medium. In real conditions, the cooling liquid in the cutting zone interacts with the heated surface and forms oxides films. The gaseous phase appears in the cooling liquid at the very moment of the contact. Jointly, these factors can significantly change the heat resistance of the heat transfer channel. For the heat chains “heat source-chips” and “heat source-tool,” the relation between the contact time τ2,3 and contact area f 2,3 for the chips and tool can be written as follows with their equality evident: τ2 = τ3 =

η , f2 = f3 = bζ Ωr

(14)

Here η is the coefficient of the chips thickness shrinkage; ζ is the length of the contact line of the chips with the lead surface of the cutting part; b is the width of the contact or total length of the cutting edges. These quantities are known and are determined from the geometrical parameters of the drill. It is known that a necessary condition for the distribution of heat is the presence of a temperature gradient [9]. Since during the cutting process the heat in the part spreads over the volume surrounding the contact point with the cutting edge, it is advisable to describe the heat transfe,r in this case, using the Fourier’s law of thermal conductivity: q = −λ grad T. Here q is density of the heat flux; i.e., the quantity of heat through in unit area per unit time. Then for a unidirectional flow of the heat and one-dimensional temperature field, we can write the following equality [4, 14]: dT c dT = −λ . f dτ dξ

(15)

Here f is an area of contact of the cutting edge with the workpiece; ξ is a coordinate of actual point of the heat propagation line.

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After integration (5) in reference to the coordinate ζ and appropriate transformations taking into account (7), (8), (11), the dependence between the heat propagation velocity and rotation speed of the drill (spindle). The final formula is of the form  √ λ π h dT =− T . (16) dτ c aΩ r Here, T is a temperature drop along the line of propagation of the heat front; h is the thickness of the blade; τis the contact time of the blade with a point on the surface to be treated. Variable effects cause mechanical oscillations in the system “cutting part-spindle.” After stronger oscillations, assessment of the dynamic aspects of the mechanical drive of the machine is a must. A summary of this issue is provided in the articles [11, 14].

4 Conclusions It is obvious that upon contact of the cutting edge of the tool with the surface of the hole at each point, an unsteady temperature field occurs, i.e., there is a heat flow variable in time. If we consider its value to be maximum when the cutting edge passes at a strictly fixed point, then attenuation will occur with distance from it in any direction along the generatrix of the curved surface. Comparing the foregoing with the arguments of Reznikov [7] that in a cutting process the initial temperature is assumed to be constant at each point on the surface of the hole, the following can be said. This approach is not entirely correct in conditions of drilling deep holes machining, although we explain the sufficiency of cooling. However, even with small dimensions of the part, and even more so when drilling, cooling may not be enough. In these cases, there will be a constant increase in the temperature of the part, which should be aggravated by the friction of the guide elements of the drill having a large contact area. Due to the fact that the blade movements are not uniform, dynamic phenomena lead to pulsation of the heat flux, which affects the friction coefficients, and hence the cutting forces. The study of the dependence of the coefficient of friction and heat fluxes during deep hole drilling is outlined briefly in [11]. The authors are ready to present a more detailed presentation of this issue in a full-length article.

References 1. Mironova L, Kondratenko L, Terekhov V (2019) On issue of verifying new method for studying dynamics of deep hole machining. In: 5th International conference on industrial engineering (ICIE 2019). Lecture notes in Mechanical Engineering (LNME) II, pp 151–162. https://doi.org/10.1007/978-3-030-22063-1_17 2. Kondratyuk OA (2005) The stability of the deep hole drilling process on small rotary indexing machines. J Equip Tools Profess 6:22–23 3. Messaond A, Weis C (2009) Monitiring a deep holl drilling process bu nonlinear time series modeling. J. Sound Vibr 326(3-5):620–630

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4. Kondratenko LA (2005) Vibrations and speed regulation methods of movement of technological objects. MRSU, Moscow 5. Kondratenko LA (2008) Calculation of velocity variations and stresses in machine assemblies and components. Sputnik, Moscow 6. Reznikov AN, Reznikov LA (1990) Thermal processes in technological systems. Mashinostroenie, Moscow 7. Reznikov AN (1981) Thermal physics processes of metal machining. Mashinostroenie, Moscow 8. Carslaw HS and Jaeger JC (1959) Conduction of heat in solids. Oxford 9. Lykov AV (1967) Theory of heat conductivity. Vysshaya shkola, Moscow 10. Kondratyev GM (1954) Regular heat. GITTLB, Moscow 11. Kondratenko L and Mironova L (2019) On the influence of thermal processes on the dynamics of a drill during deep hole machining. In: International conference on modern trends in manufacturing technologies and equipment: mechanical engineering and materials science (ICMTMTE 2019). MATEC Web of Conferences, Vol. 298, 00008. Published online: 18 Nov 2019. https://doi.org/10.1051/matecconf/201929800008 12. Kondratenko L, Mironova L, Terekhov V (2017) On the question of the relationship between longitudinal and torsional vibrations in the manufacture of holes in the details. In: 26th Conference in St. Petersburg, June, 2017 Vibroengineering Procedia 12:6–11. https://doi.org/ 10.21595/vp.2017.18461 13. Mironova L, Kondratenko L (2019) Mathematical modeling of the processing of holes on CNC machines. Mater Today Proc (Online 14 Aug 2019). https://doi.org/10.1016/j.matpr. 2019.07.691 14. Terekhov V, Smirnov A, Mironova L (2019) Thermal phenomena and dynamic features of deep holes fabrication for connections of heat exchange tubes, J. Mater Today Proc (Online 31 July 2019). https://doi.org/10.1016/j.matpr.2019.07.077

Simulation Modeling of the Choice of Metal Cutting Tool Coating B. Mokritskii1 , A. Morozova2(B) , and E. J. Sitamov1 1 Komsomolsk-Na-Amure State University, 27, Lenin Av., Komsomolsk-on-Amur 681013,

Russia 2 Bryansk State Technical University, 7, 50 Years of October Boul., Bryansk 241035, Russia

[email protected]

Abstract. The aim of the study is to reduce material and time costs when choosing a rational tool material as well as when designing a new tool material for the given operating conditions of the tool. In relation to this goal, the article shows the solution to the problem of choosing a rational tool coating for turning specialized 09Kh17N7Y grade stainless steel using simulation modeling in the Deform software environment. To solve the problem, a computer numerical experiment based on simulation was used. The results of it are compared with the results of a full-scale experiment during cutting. The adequacy of the results is proved. The novelty of the solution lies in the fact that the simulation was performed on the example of turning specialized 09X17H7YU grade stainless steel, which has no analogs abroad, and previously available domestic recommendations are outdated due to the fact that there is no longer the metal-cutting equipment the recommendations were worked out for. The main result of this article is the proof of the possibility of using the Deform software environment for the goal and the problem being solved, as well as the creation of a certain bank of recommendations to be used in modern production conditions. Keywords: Simulation modeling · Tool wear · Tool coatings

1 Introduction The relevance of the work is associated with the use of simulation modeling for the selection of a rational coating of a turning tool on the example of specialized stainless steel 09X17H7YU. The choice of simulation modeling method is due to the low level of economic efficiency in the implementation of such a choice with the help of experimental methods, especially in situations of processing rare or specialized materials. The scientific significance of the work lies in the established connection of the metal-cutting tool parameters selected for the analysis with the tool performance. The appropriateness of the chosen simulation method application in the Deform medium for the selection and design of the coating for the substrate for the given operating conditions of the metal cutting tool was proved by the comparative analysis of the testing experiment results both in real conditions and in a virtual environment. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_18

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An analysis of the state of the issue of the reasoned selection and design of the turning tool coating for processing highly corrosion-resistant specialized stainless steel 09X17H7YU showed [1–3] that the information presented in the scientific literature is not relevant, and the previous recommendations, oriented on machines suitable for the use in modern production, are not used as a rule. For modern high-performance CNC machines, there are no scientifically based recommendations on the choice of a rational tool cover for turning specialized materials, which necessitates their development by creating an up-to-date data bank of research results that are economically more profitable to carry out by simulation modeling method for various types of tools and specialized materials. Some results of creating such a data bank are given in [4–6].

2 Methodological Support of Simulation Modeling The simulation modeling method can be implemented in several versions using various software environments. The authors implemented a version of computer modeling in the Deform software environment, which is a special case of the ANSYS software environment. The Deform software environment allows us to determine significant factors by which we can choose a rational metal-cutting tool, for example, wear rate, cutting temperature, cutting force, stress, strain rate, etc. The disadvantage of working in such an environment is only the short duration of the analyzed process. Five different tool materials (VK8 substrate) of standard turning boring cutters, differing in the number of layers in the coating, layer thicknesses, their structure, and composition, having the following coatings: 1—TiC (0.5 µm) + TiN (1 µm); 2—Al2O3 (2 µm) + TiCN (5 µm) + (TiAl) N (3 µm) + TiN (3 µm); 3—TiCN (5 µm) + (TiAl) N (3 µm) + Al2O3 (5 µm) + TiC (5 µm); 4—TiCN (2 µm) + TiC (3 µm) + TiN (1.5 µm); 5—TiC (3 µm) + TiN (3 µm) + (TiAl) N (2 µm) were analyzed. For the selected cutting mode by simulation modeling, the rationality (in terms of wear) of tool materials was identified, a randomometric series in descending order of tool performance was made: the material, which showed the minimum amount of wear, was placed first in a row; the material that showed the maximum value of wear of the cutter along the rear face was the last. At the same time, under real cutting conditions, tests on turning tools having various coatings were performed. The obtained results were used to form a range of wear values for an equal operating time; the amount of wear 0.1 mm, 0.2 mm, 0.3 mm was taken into account. The randomness was the same for all three wear values. A comparative analysis of the obtained sequence of arrangement of instrumental materials in the randomometric series during simulation and in the randomometric series during the full-scale experiment showed their complete coincidence, which allowed us to conclude that the results of simulation are adequate. The next stage of the study was “designing” several theoretically possible other instrumental materials with the aim of conducting a simulation of their operational characteristics and a theoretical assessment of their performance; the tool material TiN (3 µm) + TiC (3 µm) + TiN (3 µm) + TiC (3 µm) was successfully “designed”.

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3 Discussion of the Results Under the conditions of the modern technological structure [7–9], the development of the metrological infrastructure of highly efficient instrumental support for machine-building enterprises is inevitable [10]. From this perspective, the task is considered and the following are the individual results of its solution. Figures 1 and 2 are illustrations of the relationship between the amount of wear (over a certain conditional cutting time interval of the cutting tool) of the cutting edge of the turning boring tool and the stresses arising in the cutting tool with different coatings on the same tool material (substrate—hard alloy of BK8 grade), in Fig. 1 and 2 it is conditionally shown by the symbol WC). The following coating options were considered: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

BK8 + TiC (0.5 µm) + TiN (1 µm); BK8 + TiC (0.5 µm) + TiN (1 µm); BK8 + Al2O3 (2 µm) + TiCN (5 µm) + (TiAl)N (3 µm) + TiN (3 µm); BK8 + TiCN (5 µm) + (TiAl)N (3 µm) + Al2O3 (5 µm) + TiC (5 µm); BK8 + TiCN (2 µm) + TiC (3 µm) + TiN (1.5 µm); BK8 + TiC (3 µm) + TiN (3 µm) + (TiAl)N (2 µm); BK8 + TiC (1.5 µm) + TiN (3 µm); BK8 + TiN (2 µm) + TiC (5 µm); BK9+TiN (3 µm) + TiC (3 µm) + TiN (3 µm) + TiC (3 µm); BK8; BK8+(TiAl) N (3 µm) + Al2O3 (3 µm) + (TiAl) N (3 µm) + Al2O3 (3 µm).

The data in Figs. 1 and 2 was obtained for the cutting mode of steel grade 09X17H7YU: cutting speed 50 m/ min, feed 0.21 mm/ turn of the work-piece, cutting depth 0.5 mm. Similar diagrams were built for other cutting mode and for different simulation modeling parameters, for example, cutting temperature, strain value, cutting force, etc. From the data in Fig. 1 and 2, a definite relationship between the amount of wear and stress can be traced. It is not so obvious because the data were obtained only for the first moments of the cutting process but these results are already enough to see the following: the Deform software environment is able to identify the effect of the coating on the tool operational parameter (wear of the cutting edge). Moreover, it is able to respond to minor changes in the architecture [11–13] of the coating. Similar studies aimed at establishing correlation relationships while complicating the entry of parameters into the Deform software environment can be obtained by simultaneously changing several parameters studied: • building a three-coordinate nomogram of the dependence of the wear value of different tool materials by the parameter “cutting time” or by the parameter “cutting force”; • building the dependence of the value of one parameter of one instrumental material on two other parameters.

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Fig. 1. Nomogram illustration of the required parameters (amoumt of wear) of simulation modeling for analysis (comparison) of different instrumental materials (the WC symbol marks the substrate grade VK8 of the instrumental material)

Fig. 2. Nomogram illustration of the required parameters (strain) of simulation modeling for analysis (comparison) of different instrumental materials (the WC symbol marks the substrate grade VK8 of the instrumental material)

Figure 3 shows the kinetics of the turning process obtained by simulation using the “cutting temperature” parameter. This diagram shows the results of a study of a turning tool with the coatings presented in Figs. 1 and 2. The analysis of the data presented in Fig. 3 allows us to draw a number of conclusions not only on the kinetics of temperature over time, but on the comparability of the temperature growth rate for specific instrumental materials as well. 1. The thickness of the coating layers in tool materials affects the cutting temperature less than the number of these layers. 2. Coatings close in architecture, for example, containing an Al2O3 layer, differ in cutting temperature both at the initial cutting moment and for some time. 3. The maximum cutting temperature and the maximum rate of its growth were noted in the tool material without any coating (in the diagrams-WC-without coating). 4. The higher the temperature of the coating at the initial cutting moment, the higher the rate of its growth during operation. Moreover, in some studied instrumental materials,

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the maximum temperature on the instrument surface is reached in the shortest time, while in others it continues to grow with a decrease in the growth rate. In addition, it was found that an increase in the consumption of metal cutting tools (which already reached $ 40 billion in 2021 [14]) inevitably requires a reduction in the share of tool costs in the cost structure of manufactured products; therefore, any decision to predict highly efficient tool material is also relevant and potentially in great demand in conditions of rapidly developing production. The selection of a rational coating for a metal-cutting tool in the scientific literature is also analyzed for high-performance milling [15–17]; the work aimed at “designing” effective coatings at the atomic level [18–23] is underway, which is aimed at providing defect-free tool materials for specified operating conditions.

Fig. 3. The results of changing the cutting temperature by various tool materials by simulation modeling for different cutting times: (the nearest first row in 60 s; the second row in 120 s; the third row in 300 s; the last fourth row in 600 s)

4 Conclusion The capabilities of the Deform software environment are sufficient to solve the problems of choosing rational instrumental materials for given operating conditions. The results of the predictive (robust) choice or design of the tool coating material architecture are confirmed experimentally within the experimental error. The study of the various operational properties of tool materials according to various parameters by the simulation method makes it possible to choose competitive options for tool materials, to “design” an even more effective tool material.

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References 1. Vereschaka A, Mokritskii B et al (2017) Two-component end mills with multilayer composite nano-structured coatings as a viable alternative to monolithic carbide end mills. Mech Ind 18:705 2. Vereschaka A, Oganyan M et al (2018) Increase in Efficiency of tnd Milling of titanium alloys die to tools with miltilayered composite nano-structured Zr-ZrN-(Zr, Al)N and Zr-ZrN-(Zr, Cr, Al)N coatings. Coating 8:395 3. Mokritsii BJa, Morozova AV, Usova TJ (2017) Results in composite hard-allow and milts design basset on simulation of their operation conditions. Series Books Proc Eng 206:1093– 1098 4. Mokritsky BY, Sitamov ES, Serebrennikova AG (2019) Improving the health performance of carbide cutting tools due to coating. Vestnik IrGTU 23(2):246–251 5. Sitamov ES, Mokritsky BY (2019) Evaluation of wear resistance of carbide tools in stainless steel processing. Uchenie zapiskai KnAGU 3–1(39):109–112 6. Mokritsky BY, Shakirova OG et al (2019) Evaluation of the results of predictive modeling of the choice of rational instrumental material. Technol Metals 9:20–26 7. Chirkov AP (2013) The role of methodological support in innovation. Chief Technol 1:20–24 8. Chirkov AP (2013) Infrastructure support for the implementation of high technology. In: Alisov AA et al (ed) Socio-economic aspects of technological modernization of modern engineering production. Pub. house Spectrum, Moscow, pp 78–120 9. Chirkov AP (2013) Quantitative assessment of the impact of metrology on the economy Handbook. Eng J 8:45–51 10. Zavodinsky VG, Gorkusha OA (2019) Energetics and electronic structure of amorphous metals and coating. Comput Nanotechnol 1:26–29 11. Vereschaka AA, Volosova MA et al (2013) Development of wear-resistant complex for highspeed steel tool when using process of combined cathodic vacuum arc deposition. Proc CIRP 9:8–12 12. Vereschaka AA, Volosova MA et al (2016) Development of wear-resistant coatings compounds for high-speed steel tool using a combined cathodic vacuum arc deposition. Int J Adv Manuf Technol 84:1471–1482 13. Vereschaka AA, Vereschaka AS et al (2016) Development and research of nanostructured multilayer composite coatings for tungsten-free carbides with extended area of technological applications. Int J Adv Manuf Technol 87:3449–3457 14. Gonyalin SI (2015) Russia on the world market of metalworking tools. http://www.rusexp orter.ru/partner-materials/2639/. Accessed 14 Nov 2019 15. Vereschaka AS (1993) Working capacity of the cutting tool with wear resistant coatings. Mashinostroenie, Moscow 16. Bouzakis KD, Michailidis N et al (2012) Cutting with coated tools: coating technologies, characterization methods and performance optimization. CIRP Ann Manuf Technol 61:703– 723 17. Fox-Rabinovich GS, Endrino JL et al (2006) Impact of annealing on microstructure, properties and cutting performance of an AlTiN coating. Surf Coat Technol 201:3524–3529 18. Zavodinsky VG, Kabaldin YuG (2018) Modeling study of adhesion in the TiN/Ti, TiN/ZrN, TiN/Ti/ZrN, and TiN/Zr/ZrN layered systems. J Adhesion (online 14) 19. Zavodinsky VG, Kabaldin YuG (2018) Adhesion and mechanical properties of layered nano films TiN/ZrN and TiN/Ti/ZrN: pseudopotential simulation. Compos Interfaces 26(2):97–106 20. Zavodinsky VG (2018) Electronic states of nanostructured systems: titanium and zirconia. Phys Solid State 60(10):1903–1907

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21. Gorkusha OA, Zavodinsky VG (2019) On the calculation of the interaction potential in multiatomic systems. Comput Mathem Mathem Phys 59(2):313–321 22. Zavodinsky VG, Kuz’menko AP (2019) Electronic states of nanosystems based on cadmium sulfide in the zinc-blende form. Semiconductors 53(10):1380–1384 23. Zavodinsky VG, Kuz’menko AP (2019) Initial stages of metal films growth on a SiO2cristobalite surface. J Mater Sci Technol Res 6:16–21

Investigation of Electrochemical Machining Using Nanosecond Voltage Pulse Packets V. Lyubimov(B) , V. Krasilnikov, and V. Volgin Tula State University, 92, Pr. Lenina, Tula 300012, Russia [email protected]

Abstract. The paper studies the electrochemical machining using packets of voltage pulses with the individual pulses from 10 to 100 ns, the interelectrode gap of 10 to 30 microns, the different duty cycle of pulses and various duty cycle of packages. Typical cyclograms of cyclic and pulse-cyclic machining for working conditions using and not using the flushing interelectrode gap are given. The simulation of the dimensional electrochemical machining process using nanosecond voltage pulses for the conditions of competition of the double electric layer charging and anodic dissolution of metal is performed. The local one-dimensional approximation is used in the simulation. The influence of the processes of charge of the double electric layer and anodic dissolution on the process parameters are shown. The change of anode potential depending on the voltage pulse number in the package and processing conditions is investigated. The influence of the duty cycle of the voltage pulses in the package on the residual charge of the double electric layer in the subsequent voltage pulses of the package is estimated. The ratio of processing time and flushing time is considered. The time of single flushing is estimated. Process performance evaluation is performed. Keywords: Electrochemical machining · Packets pulses · Nanosecond pulses

1 Introduction Dimensional electrochemical machining (ECM) is an effective method of processing difficult to cut materials [1–3]. Improvement of ECM methods is associated with an increase in processing accuracy and process reliability (elimination of short circuits) [4–8]. Improving the accuracy is based on the implementation of the ECM with the minimum achievable interelectrode gaps (IEG) [9]. The decrease in the IEG is associated with an increase in the current density, the amount of reaction products, the temperature of the electrolyte, and its gas filling. These factors have a destabilizing effect on the ECM process and require complex control systems for the anode dissolution process.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_19

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ECM at the beginning of its development was carried out in a continuous mode of energy supply and rapprochement of the electrodes as the anode dissolves [6]. This mode turned out to be difficult to implement when using small IEG (less than 30÷50 microns) and at high current densities (over 200÷300 A/cm2 ). This led to the need to periodically restore the initial processing conditions and to control the process parameters. Cyclic and pulse-cyclic ECM schemes have arisen and developed. In the cyclic mode, the IEG is periodically monitored by the electrodes touching in a de-energized state. In a single cycle, processing is carried out at a constant voltage (t cp = 30 ÷ 60 s). The pulse mode ECM is carried out using pulse voltage and a constant feed rate of the electrode tool. The considered mode makes it possible to restore the properties of the interelectrode medium during pause between voltage pulses. Monitoring of the IEG is not carried out and its maintenance is provided only by the correct choice of the speed of movement of the electrode-tool. The cyclograms of modern pulse-cyclic schemes of ECM are shown in Fig. 1. The methods of evaluating the state of the process at small durations of voltage pulses and small interelectrode gaps are developed [9]. Special attention is paid to the use of voltage pulses of nanosecond duration [10–15]. The decrease of the duration of the voltage pulses led to the need to take into account the transient charging of the double electric layer and faradic current density on the rate of anodic dissolution and the reducing of initial inaccuracy [16–19]. The aim of this work is to study the efficiency of the pulse-cyclic ECM process at ultra-small IEG and nanosecond voltage pulses. The substantiation of the parameters of the voltage pulses in the pulse packet and the duty cycle of the packets are performed.

2 Mathematical Model The most important element of the study of a single nanosecond pulse is the analysis of the competition between the charging processes of the double electric layer (DL) and anodic dissolution of the metal. When obtaining a mathematical model, we will take into account the capacity of the DL on the workpiece, the ohmic resistance of the electrolyte, and the resistance of the electrochemical reaction. To simplify the mathematical description, we will use a locally one-dimensional approximation. In this case, the ohmic losses in the interelectrode gap can be determined as follows: i·S , (1) σ where S is the interelectrode gap; i is the current density; σ is the specific conductivity of the electrolyte solution. If we ignore the DL on the cathode, then the mathematical model of the ECM with nanosecond pulses will be reduced to the following differential equation:      dϕ (1 − α)nF αnF U (t) − ϕ C + i0 exp ϕ − exp − ϕ =σ , (2) dt RT RT S ϕR =

where ϕ is the overpotential on the anode; C is the specific capacitance of the double layer; i0 is the exchange current density; n is the charge number; α is the charge transfer

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coefficient; R is the gas constant; F is the Faraday‘s constant; T is the temperature; t is the time; U is the applied voltage. The initial condition for Eq. (2) can be given by the following relation: ϕ|t=0 = 0.

(3)

Fig. 1. Timeline of displacement of the electrode-tool (a, b) and voltage (c, d, e): a ECM without flushing IEG; b ECM with flushing IEG; c constant duty cycle of pulses in the package and U i = const; d variable duty cycle of pulses in the package and U i = const; e constant duty cycle of pulses in the package and U i = var; S is working interelectrode gap; S fl is flushing gap; U is voltage; Y is coordinate of the electrode-tool movement; t pp is the duration of the pulse packet; t p is pulse duration; t off is the duration of the pause between pulses; t gc is the duration of the gap correction; t c is the duration of the pulse period; t cp is the duration of the single cycle; had is the anode dissolution in a single cycle; V e is the electrode rate in the working cycle:V e > 0 is rate when the electrode-tool is removed from the anode surface, V e = 0 is rate when the electrode-tool is stationary, V e < 0 is rate when the electrode-tool is fed to the anode surface.

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If the potential of the electrode is significantly less than the applied voltage, then the electrode potential on the right side of Eq. (2) can be omitted. In this case at α = 0.5 and without taking into account the front edge of the voltage pulse, Eq. (2) can be written as follows: C

dϕ + 2i0 sinh(Aϕ) = iF∞ , dt

(4)

where iF∞ = σ U /S is the current density of anodic dissolution at a fully charged double layer; A = nF/(RT ) is parameter. The analytical solution of the differential Eq. (4) that satisfies the initial condition (3) is as follows:      ∞  iF − 2i0 exp(Aϕ0 ) At 1 1 ∞ tanh , (5) B − artanh B + iF ϕ(t) = ln A 2i0 2C B   2 where B = iF∞ + 4i02 is the parameter. From Eq. (5), the initial rate of change of the overpotential is equal iF∞ C, and the steady-state value of the overpotential of the fully charged DL is equal φ ∞ = and the equation for the time constant of the DL charging is as follows: τ=

i∞ C ln F . ∞ AiF i0

∞

1 iF A ln i0

,

(6)

The capacitive current density (charge-discharge current density of the DL) is determined as follows: iDL = C

dφ . dt

(7)

The faradic current density (anode dissolution current density) is determined as follows: iF = iF∞ − iDL .

(8)

During a pause, the current density is zero, so the capacitive current density is equal in magnitude and opposite in sign of the current density of the anodic dissolution: iF = −iDL .

(9)

The amount of the metal removed from the workpiece during a single pulse repetition period can be determined by the value of the integral of the anode dissolution current density and the electrochemical equivalent.

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3 Results and Discussion The numerical solution of the equations was carried out at the following parameter values: σ = 5 1/Ohm*m, U = 4 V, t p = 100 ns, t off = 10÷100 ns, α = 0.5, n = 2, C = 0.2 F/m2 , i0 = 100 A/m2 , S = 10÷30 μm; duty cycle q = 1÷10 and the number of pulses in the packet N = 5. The results of numerical simulation are shown in Figs. 2 and 3. For a better representation of the results, only the first three pulses were shown (Figs. 2 and 3). The results of mathematical modeling are analyzed in the following areas: • change in the ratio of currents in the charging of DL and Faraday currents when changing the duration of single current pulses, their duty cycle in the package of current pulses, depending on the number of current pulses in the package; • the nature of the change in overvoltage (anode potential) during the flow of the current pulse packet; • influence of packet pulse parameters on the rate of initial error equalization and performance. In addition, the duty cycle analysis of pulse packets was qualitatively performed depending on the parameters of the technological system. Processing in two main modes is considered: 1. unit voltage pulses; 2. packets of voltage pulses. When processing single voltage pulses, it is most effective from the point of view of the leveling intensity of the initial error to use short voltage pulses t p = 50 ns. In this case, at large gaps, there is a long process of charging the DL and a very small Faraday current (Fig. 2). When using large durations of voltage pulses t p > 50÷100 ns, the process of charging the DL is significantly accelerated on large IEG and the advantage of short pulses is leveled. From the point of view of productivity of the ECM when using a large duty cycle, there is a significant decrease in the average current density over the processing period. A decrease in the start time of the anodic dissolution in the current pulse (for the second and all subsequent current pulses in the packet) indicates a residual charge of the DL after the first current pulse in the packet and a decrease in the intensity of charging of the DL. Such a phenomenon is characteristic for the entire range of the considered t p and t off , i.e., in (2 ÷ i) current pulses, the anodic dissolution is more intense than the first current pulse in the packet. The duty cycle of the current pulses in the packet is the most important parameter of the packet, affecting the technological parameters of the ECM. With a decrease in the duty cycle of the current pulses in the packet (t off = 100÷10 ns), the influence of the residual charge on subsequent pulses is enhanced. The values of charging currents and the delay times of the onset of growth of the Faraday current decrease (Fig. 2). Thus, in the package of current pulses, the efficiency of the anodic dissolution process increases from the point of view of productivity. However, the

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Fig. 2. Dependences of current densities i on time: iF is the Faraday current density, iDL is the charge-discharge current density of a double electric layer, i is the total current density; (a, d, g) S = 30 μm; (b, e, h) S = 20 μm; (c, f, i) S = 10 μm; (a, b, c) t off = 100 ns; (d, e, f) t off = 50 ns; (g, h, i) t off = 10 ns.

process of equalizing the initial error is slowed down, since the development delay time for the Faraday current decreases most significantly in the zone of large interelectrode gaps (Fig. 2). The reliability of the voltage pulse packets depends on the values of the flushing interelectrode gaps, the hydrodynamic characteristics of the interelectrode space, and the velocity. Previous research [20] showed that the speed of movement of the electrode-tool in the mode of flushing the interelectrode space (IES) should be in the range V fl = 60÷100 mm/min, which avoids large speed errors at the electrodes-tools touching at the time of control of the actual spatial position of the anode surface. The value of the flushing IEG is determined by the necessary value of the hydrodynamic resistance of the IES to the electrolyte flow. Studies of this process have shown the feasibility of increasing the working gap to the flushing gap by 6÷10 times. When using S = 5÷50 μm, the flushing IEG should be equal to 30÷500 μm. Then the time of a single flushing of the gap and time control of the gap will be tgs =

2 · Sfl = 0.06 ÷ 0.6 s Vfl

(10)

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To achieve an acceptable performance of the process, a packet duty cycle of 2 is desirable, that is, t pp = t gc . In the process of processing, there is a change in the overvoltage at the electrodes (Fig. 3), which leads to a change in the delay time of the start of anodic dissolution, the amplitudes of the charging currents and Faraday currents (Fig. 2). Only at a very large duty cycle of the voltage pulses in the package (t off > 100÷400 ns) is the return to the initial value of the voltage. Thus, the influence of each of the pulses in the package on the technological parameters (processing accuracy, performance) is different. From the point of view of productivity of the processing process when using a large duty cycle, there is a significant decrease in the average current density over the processing period.

Fig. 3. The dependence of potentials ϕ on time: (1) t off = 10 ns, (2) t off = 50 ns, (3) t off = 100 ns; a S = 10 μm; b S = 30 μm.

A decrease in the start time of the anodic dissolution in the current pulse (for the second and all subsequent current pulses in the packet) indicates a residual charge of the DL after the first current pulse in the packet and a decrease in the intensity of charging of the DL. Such a phenomenon is characteristic for the entire range of the considered t p and t off , i.e., in (2 ÷ i) current pulses, the anodic dissolution is more intense than the first current pulse in the packet.

4 Conclusions The study of pulse-cyclic electrochemical machining using nanosecond voltage pulses was performed. The competing nature of the charging processes of the double electric layer and the anodic dissolution is shown. The different character of the current pulse is set depending on its number in the pulse packet. A method for estimating the duty cycle of pulse packets depending on the characteristics of the kinematic system of the machine is proposed. The influence of current pulse packet parameters on the accuracy and performance of the electrochemical machining is analyzed. Acknowledgments. The results of the research project are published with the financial support of Tula State University within the framework of the scientific project № NIR_2019_16.

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References 1. El-Hofy HAG (2005) Advanced machining processes: nontraditional and hybrid machining processes. McGraw Hill, NY 2. Rajurkar KP, Sundaram MM, Malshe AP (2013) Review of electrochemical and electrodischarge machining. Proc CIRP 6:13–26 3. Kibra G, Bhattacharyya B, Davim JP (2017) Non-traditional micromachining processes: fundamentals and applications. Springer, Berlin 4. Schuster R, Kirchner V, Allongue P et al (2000) Electrochemical micromachining. Science 289(5476):98–101 5. Kock M, Kirchner V, Schuster R (2003) Electrochemical micromachining with ultrashort voltage pulses—a versatile method with lithographical precision. Electrochim Acta 48:3213– 3219 6. Davydov AD, Volgin VM, Lyubimov VV (2004) Electrochemical machining of metals: fundamentals of electrochemical shaping. Russ J Electrochem 40(12):1230–1265 7. Kenney JA, Hwang GS (2006) Etch trends in electrochemical machining with ultrashort voltage pulses. Electrochem Solid ST 9(1):D1–D4 8. Lyubimov VV, Volgin VM, Venevtsev AYu et al (2016) Microelectrochemical machining at the ultrasmall interelectrode gaps with the use of the packets of nanosecond voltage pulses. Proc CIRP 42:831–836 9. Rajurkar KP, Wei B, Kozak J (1995) Modelling and monitoring interelectrode gap in pulse electrochemical machining. Ann CIRP 44(1):177–180 10. Ahn SH, Ryu SH, Choi DK et al (2004) Electro-chemical micro drilling using ultra short pulses. Precis Eng 28(2):129–134 11. Kenney JA, Hwang GS (2005) Electrochemical machining with ultrashort voltage pulses: modeling of charging dynamics and feature profile evolution. Nano-technology 16:S309– S313 12. Kenney JA, Hwanga GS, Shin W (2004) Two-dimensional computational model for electrochemical micromachining with ultrashort voltage pulses. Appl Phys Lett 84:3774–3776 13. Lee ES, Baek SY, Cho CR (2007) A study of the characteristics for electrochemical micromachining with ultrashort voltage pulses. Int J Adv Manuf Tech 31(7–8):762–769 14. Hotoiu EL, Van Damme S, Albu C et al (2013) Simulation of nano-second pulsed phenomena in electrochemical micromachining processes—effects of the signal and double layer properties. Electrochim Acta 93:8–16 15. Volgin VM, Lyubimov VV, Gnidina IV (2019) Simulation of ion transfer during electrochemical shaping with the use of ultrashort pulses. In: Radionov A, Kravchenko O, Guzeev V, Rozhdestvenskiy Y (eds) Proceedings 4th international conference on industrial engineering (ICIE 2018). Lecture Notes in Mechanical Engineering. Springer, Cham, pp 1147–1159 16. Mithu MAH, Fantoni G, Ciampi J (2011) The effect of high frequency and duty cycle in electrochemical microdrilling. Int J Manuf Technol 55:921–933 17. Cagnon L, Kirchner V, Kock M et al (2003) Electrochemical micromachining of stainless steel by ultrashort voltage pulses. Z Phys Chem 217(4):299–314 18. Kozak J, Rajurkar KP, Gulbinowicz D et al (2007) Investigations of micro electrochemical machining using ultrashort pulses. In: Proceedings of the 15th international symposium on electromachining (ISEM’07). Pittsburgh, pp 319–324 19. Koyano T, Hosokawa A, Furumoto T (2008) Analysis of electrochemical machining process with ultrashort pulses considering stray inducrance of pulse power supply. J Adv Mech Des Syst Manuf 12(5):JAMDSM0098 20. Lyubimov VV (1973) Investigation of increasing of accuracy of electrochemical machining on small interelectrode gaps. Dissertation, Tula Polytechnic Institute

Modeling Electrical Discharge Machining of Deep Micro-Holes by Rotating Tool-Electrode D. Nguyen, V. Volgin(B) , and V. Lyubimov Tula State University, 92, Lenin Avenue, Tula 300012, Russia [email protected]

Abstract. In order to improve the machining characteristics of electrical discharge machining of deep micro-holes, rotational electrodes have been widely used. This paper is devoted to the theoretical and experimental investigation of the process of evacuation of debris particles from the interelectrode gap during electrical discharge machining of deep micro-holes. Mathematical modeling of hydrodynamic processes in the interelectrode gap is carried out on the basis of numerical solution of the equations of motion of incompressible viscous fluid, which allows one to estimate the influence of the shape and size of the tool-electrodes and their rotation on the evacuation of debris particles from the interelectrode gap. It was found that the use of tool-electrodes with a non-circular cross section enables one to accelerate the evacuation of debris particles. An experimental study of the process of electrical discharge machining of deep micro-holes is performed, and the simulated results are compared with the experimental data. Keywords: Micro-hole · Electrical discharge machining · Rotating tool-electrode · Debris particles · Simulation

1 Introduction Electrical discharge machining (EDM) is an effective method of machining hard materials, producing complex-shaped surfaces, and holes with various cross sections [1– 3]. Unlike the mechanical machining, in the case of EDM, the material is removed from the workpiece surface with no force effect on the workpiece. This enables one to machine low-rigid workpieces and to form the elements with a high aspect ratio. EDM is widely used for the production of various micro-objects, and, in particular, micro-holes. Thus, according to SCOPUS over the past three years, the ratio of articles devoted to micro-EDM to all articles devoted to EDM is almost 50%. EDM is a widely used method for machining deep micro-holes. However, with an increase of the micro-hole depth, the produced discharge debris particles cannot be removed from the interelectrode gap (IEG) quickly enough. A localized discharge or short circuit can arise leading to difficult machining [4–7].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_20

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The productivity of EDM of the deep micro-holes under fixed working conditions directly depends on the intensity of the evacuation of debris particles from IEG. Since it is very difficult to organize the pumping of the dielectric fluid through the narrow IEG during EDM of micro-holes, the evacuation is carried out in a natural way, which is based on an electric discharge. After an electric discharge at the tip of tool-electrode, vapor-gas bubbles almost immediately fall into the vertical side of IEG, where they rise up by the lifting Archimedean force. At the same time, the upward moving vapor-gas bubbles carry with them dielectric fluid and erosion products, creating a flow. Since solid products in the studied process are microparticles ranging in size from several micrometers to several nanometers, the mechanism for their removal from the IEG is based on the flotation method, when microparticles are captured by the wall of the gas bubble. Natural evacuation of debris particles from IEG is not sufficient for a stable flow of the process. In order to improve EDM performance of holes machining, the removal efficiency of the discharge debris particles from narrow interelectrode gap must be improved. At present, many methods have been adopted to promote the removal efficiency of the discharge debris particles, such as pumping of dielectric fluid [8–10], electrode jump motion [11], electrode ultrasonic vibration [12, 13], electrode rotation [7, 14, 15], and their various combinations [3–6]. When using the flow of dielectric fluid requires the use of tubular electrodes-tools [8], through which the working fluid is pumped under high pressure. However, when machining of deep micro-holes (conventionally referred to holes with a diameter of less than 0.2 mm) there is a problem of manufacturing tubular electrodes. The positive effect of ultrasonic vibrations is due to the following factors: (a) decrease in the diameter of vapor-gas bubbles; (b) increase in the number of vapor-gas bubbles and speed of their movement in the lateral IEG [12]. However, the use of tool-electrode vibration is not always appropriate. For example, if the machining of deep holes (up to 5 to 8 diameters), when the evacuation of debris particles from IEG is hampered, the vibrations may reduce the performance, because the periodic change of IEG reduces the number of normal discharges due to the increased number of the short-circuit pulses. Especially strongly this phenomenon is manifested during EDM at small gaps and large amplitudes of vibration. Rotating tool-electrodes are widely used in EDM in order to improve the evacuation of debris particles from the treatment area [7, 14, 15]. The simplest tool-electrode for EDM of micro-holes has a cylindrical shape. When using a cylindrical electrode, it is possible to ensure stable hole processing only at a rather low depth. The rotation of the electrode allows to use tool-electrodes with non-circular cross section [16–20] for hole producing. The use of such electrodes can increase the amount of interelectrode space and thereby significantly facilitate the evacuation of debris particles. Therefore, the using of electrodes with a non-circular cross section (Fig. 1) provides the capability of producing micro-holes with a large aspect ratio. The experimental study of the effect of rotation and cross-sectional shape on the efficiency of EDM is very difficult, so methods of mathematical modeling are widely used [21–24]. In view of the great complexity of the physical processes occurring in EDM, when modeling the evacuation of debris particles, approximate models are used

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Fig. 1. Tool-electrodes various cross sections for EDM deep micro-holes: a cylinder; b triangular; c rectangle; d with spiral grooves.

that take into account only the most significant processes. Therefore, the simulation results require experimental confirmation. This work is devoted to the theoretical and experimental study of EDM of deep micro-holes to assess the impact of the shape and size of the tool-electrode and the working conditions on the evacuation of debris particles from the interelectrode gap to ensure the possibility of improving the technological performance and the quality of the deep micro-holes.

2 Mathematical Model As a mathematical model to describe the flow of dielectric fluid in the interelectrode space, which is a region bounded by the bottom and side surfaces of the micro-hole and the surface of the rotating tool-electrode, we will use the equations of motion of incompressible viscous fluid and the continuity equation [25]:   ∂u + u · ∇u = −∇p + μu + Fb ρ (1) ∂t ∇ ·u =0

(2)

where u is the velocity vector of fluid motion; p is the pressure; ρ is the density of the dielectric fluid; μ is the dynamic viscosity of the dielectric fluid; ∇ is a vector differential operator; Δ is the Laplace operator; t is the time; F b is the body force. The debris particles in the interelectrode space were affected by the dielectric fluid, and their motion followed Newton’s second law. The motion equation for the debris particles is as follows: mp

∂v = FD + Fg + Fext ∂t

(3)

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where mp is the particle weight; v is the particle velocity; F D is the drag force; F g is the gravitational force; and F ext is any other external force. The drag force is determined as follows: FD =

mp (u − v) τp

(4)

where τp is the particle velocity response time. When the relative Reynolds number between the particles and fluid is small, as is the case here, the particle velocity response time can be written as τp =

ρp dp2 18μ

(5)

where ρp is the particle density; d p is the particle diameter. During machining, the debris particles are formed at the bottom of the hole, which go into the gap between the side surface of the hole and the tool-electrode and rise up under the action of lifting Archimedean force: Fg = mp

ρp − ρ g ρp

(6)

where g is the gravitational acceleration. The solution of the equations of the mathematical model (1)–(6), supplemented by the corresponding initial and boundary conditions allows to determine the distribution of hydrodynamic velocities of the dielectric fluid and the trajectories of the debris particles.

3 Results and Discussion 3.1 Results of Modeling The Comsol was used for numerical simulation. On the basis of the results of preliminary experimental studies, the dimensions of the micro-hole (diameter and depth), as well as the shape and size of tool-electrode were set. The scheme of the computational domain is shown in Fig. 2. When modeling, the surface of the tool-electrode rotates relatively to the hole axis. To ensure satisfactory accuracy of the solution, a finite element mesh with an optimal mesh element size of 50 μm is formed in the computational domain (Fig. 2c, d). In the calculations, the rotation frequency of the electrode-tool was taken to be n = 3000 rpm. On the surface of the outer cylinder (the surface of the hole) the no-slip boundary condition is applied, and on the end surfaces—sliding of the liquid without friction. The free debris particles uniformly distributed over the end surface are given. The simulation results show that the highest flow rate of dielectric fluid is observed in the lateral gap (Fig. 3). There is also a local increase in the velocity of the dielectric fluid between the side surfaces of the electrode-tool and the machined hole. The results of modeling the motion of debris particles in IEG during EDM with the rotating electrode showed that the shape of cross section of tool-electrode significantly

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Fig. 2. Scheme of the computational domain and finite element mesh: a, b computational domain; c, d finite element mesh; a, c cylindrical tool-electrode; b, d rectangular tool-electrode; (1) a rotating tool-electrode; (2) the fixed surface of the hole; (3) boundary wall.

Fig. 3. Distributions of the dielectric fluid velocity module at EDM by electrodes of different shapes: a, b cylindrical; c, d rectangular.

affects the evacuation of debris particles. In particular, for the cylindrical tool-electrode the free space does not change over time (Fig. 4), therefore, the particles move only in this narrow gap. Figure 5 shows that, when rotating rectangular tool-electrode, debris particles move in free space, which varies over time. Thus, in comparison with the cylindrical electrode, the rectangular tool-electrode can significantly improve the conditions for the evacuation of debris particles from the treatment area through the lateral gap between the tool-electrode and the hole surface. EDM technology for producing deep holes through the use of sheet tool-electrode was proposed and implemented. 3.2 Experimental Studies for Model Validation Experimental studies of the effect of profile tool-electrodes on the performance of EDM with rotating tool-electrode were carried out on the experimental setup (Fig. 6) at room temperature 20 ± 2 °C. For experimental studies of electrical discharge machining were used: aluminum sheet as workpiece; copper wire with circular (diameter 1 mm), and square (0.7 × 0.7 mm) cross section as tool-electrode; packages of high-frequency pulses with pulse duration in the package t on = 2.5 μs; pulse amplitude U 0 = 80 V; the number of pulses in the package N = 4 (Fig. 7); kerosene was used as a working fluid. The conditions under which the experiments were carried out are presented in Table 1.

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Fig. 4. Debris particles trajectories in IEG during EDM by rotating cylindrical electrode at various time: a t = 20 μs, h = 0.5 mm; b t = 35 μs, h = 1.4 mm; c t = 47 μs, h = 2.5 mm; d t = 100 μs.

Fig. 5. Debris particles trajectories in IEG during EDM by rotating electrode with rectangular cross-section at various time: a t = 20 μs, h = 0.5 mm; b t = 35 μs, h = 1.4 mm; c t = 47 μs, h = 2.5 mm; d t = 100 μs.

Fig. 6. Experimental setup for micro EDM: (1) drives the z- and x-axis; (2) the rotational drive of tool-electrode; (3) table; (4) collet chuck; (5) tool-electrode; (6) workpiece; (7) bath of dielectric fluid.

As a result of experimental studies micro-holes in EDM with a rotation of toolelectrode were obtained (Fig. 8).

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Fig. 7. Waveforms of voltage pulse packets.

Table 1. Basic parameters that ensure stable EDM-drilling of micro-holes in aluminum (electrode diameter is 1 mm). EDM parameters

Value

Current I, A

0.5

Open circuit voltage U 0 , V 80 Discharge voltage U gap , V 40 Pulse duration t on , μs

2.5

Puase duration t off , μs

2.5

Number pulses in packet N 4

Fig. 8. Longitudinal cross sections of micro-holes obtained by EDM with rotation of toolelectrode: (1, 3, 5) cylindrical electrode; (2, 4, 6) rectangular electrode; A at t = 2.5 min; B at t = 5 min; C at t = 8.5 min.

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4 Conclusion As a result of the research, it was shown that the performance of electrical discharge machining using the rotating rectangular tool-electrode is much higher than using the rotating cylindrical electrode. Thus, the use of electrodes with a non-circular cross section allows to improve the conditions of evacuation of debris particles by increasing the volume of interelectrode space filled with dielectric fluid, reducing the hydrodynamic resistance. The comparison of the results of modeling and experimental data shows that they are in good agreement. Acknowledgements. The study was funded by Russian Foundation for Basic Research and Tula region according to the research project № 19-48-710009.

References 1. Eliseev LS, Boitsov AG, Krymov VV et al (2003) Tekhnologiya proizvodstva aviacionnykh gazoturbinnykh dvigatelei (Technology of production of aviation gas turbine engines). Mashinostroenie, Moscow 2. Hocheng H, Tsai HY (2013) Advanced analysis of non-traditional machining. Springer, London 3. Kibria G, Jahan MP, Bhattacharyya B (2019) Micro-electrical discharge machining processes. Springer, Singapore 4. Shabgard MR, Gholipoor A, Baseri H (2016) A review on recent developments in machining methods based on electrical discharge phenomena. Int J Adv Manuf Technol 87(5):2081–2097 5. Raju L, Hiremath SS (2016) A State-of-the-art review on micro electro-discharge machining. Proc Technol 25:1281–1288 6. Prakash V, Kumar P, Singh PK et al (2019) Micro-electrical discharge machining of difficultto-machine materials: a review. P I Mech Eng B J Eng 233(2):339–370 7. Feng G, Yang X, Chi G (2019) Experimental and simulation study on micro hole machining in EDM with high-speed tool electrode rotation. Int J Adv Manuf Tech 101:367–375 8. Yilmaz O, Okka MA (2010) Effect of single and multi-channel electrodes application on EDM fast hole drilling performance. Int J Adv Manuf Technol 51:185–194 9. Kliuev M, Baumgart C, Büttner H, Wegener K (2018) Flushing velocity observations and analysis during EDM drilling. Proc CIRP 77:590–593 10. Kliuev M, Baumgart C, Wegener K (2018) Fluid dynamics in electrode flushing channel and electrode-workpiece gap during EDM drilling. Proc CIRP 68:254–259 11. Wang J, Han FZ, Cheng G, Zhao FL (2012) Debris and bubble movements during electrical discharge machining. Int J Mach Tools Manuf 58:11–18 12. Zhao W, Wang Z, Di S et al (2002) Ultrasonic and electric discharge machining to deep and small holes on titanium alloys. J Mater Process Technol 120:101–106 13. Goioganaa M, Sarasuaa J, Ramosb J (2018) Ultrasonic assisted electrical discharge machining for high aspect ratio blind holes. Proc CIRP 68:81–85 14. Wang CC, Yan BH (2000) Blind-hole drilling of Al2O3/6061 Al composite using rotary electro-discharge machining. J Mater Process Technol 102:90–102 15. Aliakbari E, Baseri H (2012) Optimization of machining parameters in rotary EDM process by using the Taguchi method. Int J Adv Manuf Technol 62(9–12):1041–1053 16. Masuzawa T, Tsukamoto J, Fujino M (1989) Drilling of deep microholes by EDM. CIRP Ann 38(1):195–198

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17. Habel MJ, Peterson LA (1997) Method and apparatus for fast hole electrical discharge machining. US Patent 5614108 18. Li H, Wang Z, Wang Y, Liu H, Bai Y (2017) Micro-EDM drilling of ZrB2-SiC-graphite composite using micro sheet-cylinder tool electrode. Int J Adv Manuf Technol 92(5):2033– 2041 19. Wang K, Zhang Q, Zhu G, Liu Q, Huang Y (2017) Experimental study on micro electrical discharge machining with helical electrode. Int J Adv Manuf Tech 93(5–8):2639–2645 20. Hung JC, Lin JK, Yan BH, Liu HS, Ho PH (2006) Using a helical micro-tool in microEDM combined with ultrasonic vibration for micro-hole machining. J Micromech Microeng 16(12):2705–2713 21. Pontelandolfo P, Haas P, Perez R (2013) Particle hydrodynamics of the electrical discharge machining process. Part 2: Die sinking process. Procedia CIRP 6:47–52 22. Wang Z, Tong H, Li Y, Li C (2018) Dielectric flushing optimization of fast hole EDM drilling based on debris status analysis. Int J Adv Manuf Tech 97(5–8):2409–2417 23. Upadhyay L, Aggarwal ML, Pandey PM (2018) Comparative analysis of magneto rheological fluid assisted electrical discharge machining at stationary and rotating conditions of tool. J Adv Manuf Syst 17(3):277–290 24. Liu Y, Chang H, Zhang W et al (2018) A simulation study of debris removal process in ultrasonic vibration assisted electrical discharge machining (EDM) of deep holes. Micromachines 9(8):378 25. Pozrikidis C (2017) Fluid dynamics: theory, computation, and numerical simulation. Springer, New York

FEM Analysis of Carbide Insert Strength for Milling Application V. G. Shalamov(B) , S. D. Smetanin, and I. S. Boldyrev South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, Russia [email protected]

Abstract. Tool with inserts is the most common in metalworking, providing cost reduction and improving the quality of manufacturing. Typical failure modes of interchangeable inserts are chipping and micro-dyeing of the cutting edge. Therefore, for each prefabricated tool design, the analysis of stressed-deformed condition and strength is important. Moreover, the stresses that arise significantly depend on both the clumping force of the interchangeable inserts and the cutting force. Despite the presence in the tool catalogs of recommendations on the choice of alloy of inserts, they lack guidance on choosing the optimal design and the purpose of clumping force of interchangeable inserts. The article shows the stages of solving the problem of determining of stressed-deformed condition of a disk mill and finding the relationship between the clumping force of interchangeable inserts and cutting force. Keywords: Stressed-deformed condition · Disk mill · Cutting insert

1 Introduction Cutters are a universal widespread tool that provides high-performance machining. Depending on the position of the axis relative to the machined surface, milling cutters are disc, end and finger, and in construction—integral and prefabricated. When using the cutting part of a hard alloy as a material, only small-sized tools are manufactured. Most of the carbide milling structures are prefabricated, which provides increased durability and reduced tooling costs. A wide range of inserts causes a variety of both the conceptual diagrams of their installation in the housing, and the variants of realizations in concrete structures. The main reasons for the deterioration of cutting insert are [1] high power and temperature loads, low strength and wear resistance of hard alloy, non-optimal structural and geometric parameters. This makes it necessary to determine the stress-strain state and strength, i.e., in the study of the distribution of dangerous stresses, leading to destruction. A lot of work has been devoted to the study of the stress-deformed state of the cutting wedge, but they practically do not consider the design of the tool as a whole, which leads to a lack of understanding of the behavior of its various components. Therefore, it © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_21

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will be useful from a scientific and practical point of view, the study and coordination of stress-deformed state on the surfaces of the components of the mill design. Designing a new design requires considerable time and money. Simulation is used to reduce them. Modeling is an effective and now universally applicable method of creating any objects, processes, and phenomena. The main purpose of the model is to make it possible to predict the behavior of the projected object with permissible changes in its structure and parameters (comparative analysis of alternative design options) and environmental conditions (research of the object in various situations). The purpose of modeling the stressed-deformed state of the milling design is to synthesize the amount of tightening of the insert when a cutting force is applied to the cutting element.

2 Methodology The efficiency of the assembly tool is largely determined by the cutting insert installation scheme, the accuracy of manufacturing the mating surfaces and loading conditions. Production experience [1] has shown that, when milling, the destruction of the insert is fragile, and the widespread types of destruction of the cutting blade are chipped and micro-dyeing. In this regard, in order to increase the reliability of the tool, it is desirable to provide the most uniform distribution of stresses in the cutting blade at the initial time. Also, practical experience shows that the operability of cutters with indexable inserts essentially depends on the adopted scheme of basing, the binding force and the joint influence of the binding force and external force. The finite element method (FEM) is widely used in the study of cutting processes. The most common case is orthogonal cutting. The paper [2] presents 2D thermo-mechanical FEM model of orthogonal cutting. The stresses in the primary and secondary deformation zone are simulated. Concluded that the variation of friction coefficient affects thrust force component and temperatures more than it affects cutting force. The greatest amount of research is devoted to turning [3–11]. The authors have explored stress, strain, temperature, chip formation mechanisms, and other characteristics of turning process. Several studies show the modeling of the broaching process [12, 13]. The FEM was applied [14] for understanding and predicting the residual stress values during ball-burnishing, allowing to determine the optimal process parameters. Modeling and simulation of the laser cutting process [15] using the analysis of heat transfer and general energy balance analysis made it possible to determine the temperature and stress distribution along with heat-affected zone. In the research of the deep twist drilling process, the authors [16] simulated the light drilled structure and the conventional welded structure and analyzed their behavior under compression loads. The von Mises stresses and the displacement of the models are determined. Much research has also been devoted to modeling the milling process. With the help of finite element analysis, the effect of the cutting speed on the cutting force, the temperature, width, and curl radius of chip, and the wearing depth of tool are investigated over the milling process [2, 17–21]. In all these works, the finite element method is used to model the interaction of the tool with the workpiece. The integrated model proposed by the authors [22] takes into account the clamping preloads, machining forces, locator–workpiece contact interaction, fixture

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compliances, machine table stiffness, and forced vibrations. The FEM in study [11] creates spindle, holder, and tool models, and is used to simulate the contact conditions of tool and workpiece as well as spindle and tool holder and contact of tool-workpiece. In the paper [23], the authors illustrate the analysis of tooltip positioning error along the three coordinate axes in a CNC machine. This study takes into account only static loads, neglects the dynamic effect during milling, and assumes that the tool and the workpiece deform to their static equilibrium positions at any milling instant. At the same time, in open access there is no information on modeling and optimization of the design of mills with the finite element modeling. In [24], the authors investigate the effect of fastening schemes of inserts, their shape, and linear dimensions on stresses, deformations, and temperature fields in the insert. However, the simulation is carried out in the plane and with reference to turning. In the designs of prefabricated milling cutters, a circular form is often used. The round insert has the advantage associated with the lack of corner areas, which are stress concentrators. In addition, when turning the insert after the wear of the cutting edge, it is possible to use practically the entire perimeter of the cutting edge, increasing the total resistance and reducing costs. However, the circular cutting edge determines the various deformations of the cutting layer associated with the direction of the outgoing chip removal, causing a different amount of cutting force. Therefore, modeling the design of cutters with round inserts requires consideration of specific features. For the analysis of stressed-deformed state, a 3D model of a disk milling cutter (Fig. 1) consisting of a housing 1, a cassette 2 with a pressed pin 4, a cutter insert 3, a ring 5, a washer 6 and a screw 7 is created. When the screw 7 is screwed, the cassette 2 moves radially, thanks to which the insert 3 is pressed against the base surface of the housing 1. This design corresponds to the fastening system of the plate, designated according to the ISO 518 standard by the letter P: the basing of the insert in the tool body along the support and side surfaces with a pin clamped through the central hole. The method provides a guaranteed pressure against the surface of the body, high accuracy of positioning of the main cutting edge, good chip removal, coincidence in the direction of cutting forces and fastening. The cutter can cut through the grooves with a depth greater than the radius of the insert, which imposes a limit on the thickness of the shell. In this paper, we consider a round insert with a clearance angle. At the base of the conical lateral surface of the insert, two circuits are possible in the cutter body (Fig. 2): in the first scheme (Fig. 2a), the contact of the conical surface of the insert with the body is carried out by a smaller cone diameter, and in the second scheme (Fig. 2b)—larger. Evaluation of stressed-deformed state in both cases requires modeling of two versions of the housing, the remaining elements of the design remain unchanged. The developed design scheme (Fig. 2c) takes into account the application scheme of the componencts of the cutting force and subsequent modeling (clearances 1 and 2). Due to the symmetry of the cutting edge, the axial component of the cutting force (in the X-axis direction) is not taken into account, but only the radial Py and the tangential Pz components are taken into account. Also, an assumption has been made that the component cutting forces are distributed evenly along the entire cutting edge (in a halfcircle). The clamping force of the Pc is directed parallel to the cassette’s reference plane.

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Fig. 1. 3D model of milling cutter.

Fig. 2. Basing schemes of insert: a first scheme; b second scheme; c schematic view of a simplified model of a disk mill.

Pressing the pin into the holder allows, when performing calculations, to accept them as a single component (cassette). The methodology for calculating the stressed-deformed state includes three successive steps that correspond to the actual construction of the mill. Step 1—ensuring the specified relative arrangemen¯t of the structural elements. The housing is rigidly fixed, i.e., there is no movement along the coordinate axes. At this point, there are gaps between the assembly components: 1—between the pin and the

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insert and 2—between the insert and the housing. When performing calculations at this step, the absence of interference (interference) between the components whose criterion is the magnitude of the stresses is checked (theoretically it should be zero). Before performing the calculations, it is necessary to spatially sample the calculated area, i.e., replacement of the solid model by a net of finite elements (FE). This requires a reasonable choice of the type and size of the FE. The type of FE is due to the studied properties of the object, its shape, and dimensions. Among the volume elements, the best convergence conditions for the solution are provided by the FE in the form of a cube and a regular tetrahedron. We take as the FE the type SOLID185 used for threedimensional modeling of volumetric constructions. It is determined by 8 nodes (cube) in 3 degrees of freedom in each. The element has the properties of plasticity, hyperelasticity, hardening, creep, deformations, and displacements. It can take the form of a 6 (prism), 5 (pyramid), or 4 (tetrahedron) node element, if it is necessary to coordinate the mesh with the partition. The size of the FE is chosen on the basis of a trade-off between sampling errors and the required computing power resources. When choosing the size of FE for prefabricated structures, it is desirable to observe the proportionality of different components. Therefore, the size of the FE for the housing is taken equal to 1 mm, and for cassette and insert—0.5 mm. The model should include the minimum necessary part of the design, allowing to obtain an adequate solution at the minimum cost of the calculation time. Since the design is axisymmetric, to create a finite element mesh and accelerate the calculation in the computer-aided engineering system, it is sufficient to have one sector of the enclosure containing one cassette with the insert (Fig. 3).

Fig. 3. a The mill sector; b its representation by a finite element mesh.

The initial data include the properties of materials: the Young’s modulus E and the Poisson’s ratio µ. As the material of the housing and the cassette, structural steel is adopted, and the insert is a hard alloy. The boundary conditions are as follows: Step 1—rigid fixation of the housing in all coordinates; limit the movement of the cassette along the X- and Z-axes; no gaps between the cassette and the housing. We accept contact interactions with a friction coefficient of 0.25: between the flat surfaces of the housing of mill and the cassette; between the conical surface of the

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insert and the housing; between the lower surface of the insert and the plane of cassette; between the hole in the insert and the cylindrical surface of the pin. Step 2—clamp the cassette. Corresponds to the assembly of the mill before starting work or changing the insert after wear. To do this, the Pc clamping force is applied to the end face of the cassette in the direction of the Y-axis. As a result, the screw presses the insert to the base surface in the housing, creating a certain interference. The corresponding stresses appear on the components of the structure. Step 3—modeling the cutting process. A uniformly distributed cutting force is applied to the cutting edge of the insert. The value of the tangential component of the cutting force is assumed equal to 500; 1000; 1500; 2000; 2500 N, and radial—equal to half of the tangential component. There is a redistribution of stresses resulting from the clamping of the cassette. The resulting tension in the cassette is concentrated on the cylindrical surface of the pin (Fig. 4a). As a result of the application of the components of the cutting force, the insert is clamped to the support plane of the cassette, which causes the appearance of stresses on it (Fig. 4b). After the application of the cutting force, the redistribution of stresses between the pin and the reference plane occurs: a decrease on the pin and an increase in the plane (Fig. 4c).

Fig. 4. Stress change with increasing cutting force.

In general, the magnitude of the stresses on the surface of the pin and the support surface of the cassette are different. But with a certain clamping force, it is possible to determine such a cutting force at which the stresses on the pin and the support plane are aligned. This condition can be reflected graphically: the interrelation of the clumping force and the cutting force (Fig. 5). Therefore, for a given cutting force, it is possible to determine the clamping force, which ensures equal stresses on the holder and the pin. If necessary, it is possible to ensure the equal strength of these elements, taking into account their geometrical parameters and the type of loading. It can be noted that with insufficient clumping force, the calculation fails. The excessive clamping force leads to stress in the structural elements of the cutter above the conventional yield strength of structural steel (Fig. 6a), which leads to plastic deformation and violation of proper functioning. Also, with an increase in the clumping force the stress at the point of contact of the insert become higher than the stresses at the cutting edge (Fig. 6b), which can cause brittle fracture of the insert not in the cutting zone.

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Fig. 5. Interconnection of cutting and clumping forces.

Fig. 6. Von Mises stress in the elements of the cutter design: a maximum stresses 0.3 * 1010 Pa; b stresses in the insert 0.121 * 1010 Pa.

An analysis of the graphs of the relationship of cutting and clumping forces shows that the basing scheme affects the magnitude of the required clumping force. With small cutting forces (up to 3000 N) basing according to the first scheme requires the application of a smaller clamping force. In addition, this scheme provides a closure to the linear relationship of forces.

3 Conclusions In the article, the stressed-deformed state of a cutting blade of a disk mill is considered taking into account the insert scheme of basing, clamping force, and cutting force. If the clamping force of the cassette is insufficient after loading, even with the minimum cutting force, infinitely large displacements of the insert occur, leading to a failure in the calculation. In practice, this means dropping the insert from the housing of mill.

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The excess clamping force causes the occurrence of stresses above the conditional yield strength of the structural materials of the components. In practice, this will cause plastic deformation of proper functioning. The brittle destruction of insert may not occur in the cutting zone. The clamping force can be assigned depending on the expected cutting force, which will ensure in the process of work of the equality of the stresses on the holder and the pin. The basing of the first scheme with low cutting forces is preferable from the point of view of lower stresses in the holder and pin. Continuation of the research can be done by comparing the stressed-deformed state with other types of disk milling constructions, examining various insert materials, changing the insert geometry and the direction of cutting force, taking into account temperature deformations. Acknowledgements. South Ural State University is grateful for financial support of the Ministry of Education and Science of the Russian Federation (grant No 9.5589.2017/8.9).

References 1. Indexable inserts and tools Sandvik-MKTS (2000) Solid tool 2. Yuan Y, Jing X, Ehmann KF et al (2018) Modeling of cutting forces in micro end-milling. J Manuf Process 31:844–858 3. Markopoulos AP, Vaxevanidis NM, Manolakos DE (2015) Friction modeling in finite element simulation of orthogonal cutting. Tribol Ind 37:440–448 4. Yan H, Hua J, Shivpuri R (2005) Numerical simulation of finish hard turning for AISI H13 die steel. Sci Technol Adv Mater 6:540–547 5. Bassett E (2014) Belastungsspezifische Auslegung und Herstellung von Schneidkanten fu¨r Drehwerkzeuge, Hannover 6. Ma Y, Zhang J, Feng P et al (2018) Study on the evolution of residual stress in successive machining process. Int J Adv Manuf Technol 96:1025–1034 7. Ortiz-de-Zarate G, Madariaga A, Garay A et al (2018) Experimental and FEM analysis of surface integrity when broaching Ti64 Proc CIPR 71:466–471 8. Peirovi S, Pourasghar M, Nejad AF et al (2017) A study on the different finite element approaches for laser cutting of aluminum alloy sheet. Int J Adv Manuf Technol 1:1–15 9. Lopez de Lacalle LN, Fernandez A, Olvera D et al (2011) Monitoring deep twist drilling for a rapid manufacturing of light high-strength parts. Mech Syst Signal Process 25:2745–2752 10. Rai JK, Xirouchakis P (2008) Finite element method based machining simulation environment for analyzing part errors induced during milling of thin-walled components. Int J Mach Tools Manuf 48:629–643 11. Pour M, Ghorbani H (2017) Improving FEM model of low immersion milling process using multi-objective optimization of tool elastic support dynamic properties. Int J Adv Manuf Technol 92:2279–2297 12. Rodríguez A, López de Lacalle LN, Celaya A et al (2012) Surface improvement of shafts by the deep ball-burnishing technique. Surf Coat Technol 206:2817–2824 13. Zhang P, Wang Y (2018) A study on chip and microstructure of 7055 aluminum alloy’s 3D HSC based on FEM and experiment. Vacuum 152:205–213 14. Bermudo C, Sevilla L, Martín F et al (2016) Study of the tool geometry influence in indentation for the analysis and validation of the new modular upper bound technique. Appl Sci 6:1–16

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15. Xiong Y, Wang W, Jiang R et al (2018) Mechanisms and FEM simulation of chip formation in orthogonal cutting in-situ TiB2/7050Al MMC. Materials 606:1–19 16. Biermann D, Menzel A, Bartel T et al (2011) Experimental and computational investigation of machining processes for functionally graded materials. Proc Eng 19:22–27 17. Xie LJ, Schmidt C, Biesinger F et al (2009) Wear progress prediction of carbide tool in turning of AISI1045 by using FEM. In: Proceedings of CIST2008 & ITS-IFToMM2008, pp 372–375 18. Krajinovi´c I, Daves W, Tkadletz M et al (2016) Finite element study of the influence of hard coatings on hard metal tool loading during milling. Surf Coat Technol 304:134–141 19. Liao YG, Hu SJ (2001) An integrated model of a fixture-workpiece system for surface quality prediction. Int J Adv Manuf Technol 17:810–818 20. Zhang Q, Zhang S, Li J (2017) Three dimensional finite element simulation of cutting forces and cutting temperature in hard milling of AISI H13 steel. Proc Manuf 10:37–47 21. Yanda H, Ghani JA, Rizal M et al (2015) Performance of uncoated and coated carbide tools in turning FCD700 using FEM simulation. Int J simul model 14:416–425 22. Klocke F, Lung D, Buchkremer S (2013) Inverse identification of the constitutive equation of Inconel 718 and AISI 1045 from FE machining simulations. Proc CIRP 8:212–217 23. Afkhamifar A, Antonelli D, Chiabert P (2016) Variational analysis for CNC milling process. Proc CIRP 43:118–123 24. Artamonov EV, Pomigalova TE, Tverykov AM et al (2013) Mehanika razrusheniya i prochnost smennih rezhuschih plastin iz tverdyh splavov (Mechanics of destruction and strength of replacement cutting inserts from solid alloys). Tyumen

Study and Evaluation of Stability of Technical Processes for Machine-Building Products at Stage of Serial Production M. P. Kukhtik(B) , A. M. Makarov, and N. V. Fedorova Volgograd State Technical University, 28 Lenin Av, Volgograd 400005, Russia [email protected]

Abstract. The article represents the materials on the stability evaluation of the technical processes for machine-building products at the stage of serial production. Various deviations from the standard process documentation, when serial products are produced, have been considered. The main reasons and factors, which result in deviations in the parameters set up in the standard process documentation, have been described. The general approach to the stability evaluation of the technical processes has been considered, which is based on the accuracy assessment of the details manufactured. Functional relationships to explore the stability of a technical process have been presented and graphs in the form of curved trajectories have been plotted according to them. The maximum distance between the curves in a certain segment is determined according to these graphs, which allows to assess the manufacturing accuracy of a product. Quality forms, which clearly reflect the course of the manufacturing process and detect a technological violation, are introduced in the practice of manufacturing of complex machine-building products with the purpose of statistical regulation of the production process. Quality forms for the individual parameter values are generally used for complex machine-building products. This is due to the fact that the parts, units or devices of these products are manufactured in small lots and the most critical parameters, which influence the efficiency of the products, are subject to inspection. Keywords: Stability of technical processes · Serial production · Manufacturing accuracy · Quality forms

1 Introduction The challenge of detecting the reasons and factors, which influence the stability of the technical processes, as well as the manufacturing accuracy of parts, units and devices of products in serial production, becomes pressing when complex technical products are developed [1–6]. A critical task is to provide the stability of the technical processes through the quality control of the end products. With the purpose of solving the challenge set up in this article, it was necessary to present the main reasons and factors, which influence the stability of the technical © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_22

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processes; develop the functional relationships to determine the accuracy of manufacturing parts, units and devices of the products; specify the quality control of the products output through quality forms for the most critical technical parameter, which influences the product efficiency [7–12].

2 Reasons for Deviations of End Products from the Requirements of the Standard Process Documentation Various deviations from the requirements of the standard process documentation in end products are possible in the course of technical processes, both when the production output is to be mastered and when the production has already been established [13–17]. The reasons for such deviations are quite multiple. There are two groups of factors, which result in these deviations. The first group of factors includes as follows: • the drawings and necessary instructions to carry out technical operations are absent at the workplaces; • specific types of works (operations) are not attached to certain performers; • the sequence of operations, which are set up in the flow process charts, is not observed; • the first part (operation) is presented for the inspection out of time; • fixturing, cutting and measuring tools, test equipment, etc., are used, which are not set out in the flow process charts; • materials, semi-finished products, and accessories are used, which are not provided by the technical processes; • operations, methods and modes of processing and testing products, which are approved in the standard process documentation, are not observed; • uncertified control means and jigs, fixtures and tools with expired effective life are used; • the jigs, fixtures and tools, repair tools, test equipment, etc., are in poor condition. These factors are of a random character and they are removed in the course of administrative and technical measures. The second group of factors, which are also of a random character, include various deviations caused by a spread in • the parameters (physical, geometrical, weight, etc.) of the materials, semi-finished products and accessories; • the characteristics of the parameters and jigs, fixtures and tools, gauge devices, cutting and measuring tools, test-bench and test equipment, etc.; • the tolerances (their random unfavourable combinations) in the dimensional process chains. The second group of factors is described by certain statistical laws, which can be taken into account when the stability of the technical processes is studied.

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3 A Study of the Stability of a Technical Process According to the Accuracy of a Product Manufactured The general approach to the evaluation of the stability of technical processes is based on the assessment of the manufacturing accuracy of a product [18, 19]. Herewith, the manufacturing accuracy of a product is assessed according to both “instant” and integral parameter dispersion for a certain period of time. The accuracy of a technical process deteriorates in direct ratio to its flow time. It means that if the accuracy of a technical process was characterized by value δ0 at certain moment of time t 0 , then, at next moment of time t 1 , which lags from moment of time t 0 by value t, the accuracy shall be characterized by value δ1 , which is related to δ0 through a linear relationship [20–22]: δ1 = δ0 + kt,

(1)

where k is the proportionality factor. The correlation ratio between random values δ0 and δ1 is determined by formula [23] r δ0 , δ1 = 

σδ21 σδ21 + σk2 t 2

≥ 0,

(2)

where σδ1 and σk are the average quadratic deviations of random values δ1 and k. The industrial process management is provided with the purpose of manufacturing high-quality products. In such cases, the correlative relationship between random values δ0 and δ1 shall inevitably weaken with the increase of time interval t. The correlation ratio can be negative with certain values of the parameters measured of the technical processes in period of time t. Let us use the diagrams (Fig. 1) to explore the stability of the technical process according to the accuracy of a product manufactured. At segment [t 0 , t 1 ], which normally represents some curved trajectory, we can use the distance between the two curves, which are set by functions δ0 and δ1 (Fig. 1a) [20]. δ0 and δ1 are the required and actual accuracies of the technological process, respectively.  δ0 = φ0 (t) , where [t0 ≤ t ≤ t1] (3) δ1 = φ1 (t) Let us denote the maximum distance between these curves at segment [t 0 , t 1 ] by l (Fig. 1b), which equals to absolute difference value |ϕ0 (t) – ϕ1 (t)|. Let us construct a strip with the width of 2δ on either side of curve δ = ϕ(t) (Fig. 1 a). Then the distance from curve δ1 = ϕ1 (t) to δ0 = ϕ0 (t) will be half of minimum width δ0 = ϕ0 (t), which comprises curve δ1 = ϕ1 (t). In a particular case, when δ0 = ϕ0 (t) represents a right line, which is parallel to axis 0t, this corresponds to the width of the strip equal to maximum deviation l of curve δ1 = ϕ1 (t) from right line δ0 = ϕ0 (t) (Fig. 1b).

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Fig. 1. Diagrams to determine the distance: a—between two curves −δ1 and δ, δ0 and δ; b— between right line and curve −δ1 and δ, δ0 and δ; c—between two primary curves −δ1 and δ0 .

More accurate distances l between curves δ0 = ϕ0 (t) and δ1 = ϕ1 (t), for which continuous derivatives exist up to the n-th order inclusively, are found by means of difference of peaks between the derivatives from expressions [20, 24]: ⎧ φ0 (t) − φ1 (t) ; ⎪ ⎪ ⎪ ⎨ φ 1 (t) − φ 1 (t) ; 0 1 ⎪ ......... ⎪ ⎪ ⎩ n φ0 (t) − φ1n (t)

(4)

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at segment [t 0 ≤ t ≤ t 1 ], i.e. ⎧ 0 l = max|φ0 (t) − φ1 (t)| ; ⎪ ⎪ ⎪   ⎪ ⎪ ⎨ l 1 = maxφ 1 (t) − φ 1 (t) ; 0 1 ⎪ ⎪ ......... ⎪ ⎪ ⎪   ⎩ n l = maxφ n (t) − φ n (t) 0

(5)

1

at this segment [t 0 ≤ t ≤ t 1 ], where l 1 , and l n are the 1-st and n-th order derivatives. The maximum value of the absolute difference value—max|ϕ0 (t) – ϕ1 (t)|—at time interval [t 0 , t 1 ] is called  the 0-th order  distance, the maximum value of the absolute difference value—maxφ01 (t) − φ11 (t)—at certain moment of time t i is the 1-st order distance. The geometrical sense of this definition is the distance between the tangents in point t i of curves φ0 (ti ) and φ1 (ti ) (see Fig. 1c). In this regard, the 1-st order distance can be considered as a measure, which characterizes the maximum distance between curves δ0 = φ0 (t) and δ1 = φ1 (t) in certain point t i at segment [t0 ≤ t ≤ t1 ].

4 Quality Forms for the Individual Values of the Parameters Measured Quality forms, which clearly reflect the course of the production process and detect violations in the techniques, are introduced into the practice of manufacturing complex machine-building products with the purpose of statistical regulation of the production process. There are quality forms for measurable (quantitative) and unmeasurable (qualitative) quality features, depending on whether a feature is subject to quantitative measuring or it only allows a qualitative evaluation [25, 26]. Quality forms of individual parameter values are used for complex machine-building products in general. This is due to the fact that parts, units and devices of these products are manufactured in small lots, and the most critical parameters, which influence the product efficiency are subject to inspection. An individual parameter quality form is characteristic of measuring the parameter of each unit, device or part, which is manufactured on a machine-tool or other equipment. The parameter value obtained is recorded in the form as a point, a cross or a star. An individual parameter form is used, mainly, to observe the technical process. This form has the disadvantage that, by using it, one cannot conclude at once about the reason for a violation in the technical process after one or two overshoots beyond the control limits. The control limits of an individual value form are determined by proceeding from the normal distribution of a parameter measured. On the one hand, the width of the control interval of a parameter measured is set with maximum error α of 0,27% by the expression a − 3δ ≤ x ≤ a + 3δ ,

(6)

where a is the nominal value of a parameter under the documentation; δ is an average quadratic deviation of random value X; x is the actual value of the parameter measured.

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On the other hand, the tolerance limit with the dimension to control is determined in equation TL = a + δ1 ≤ x ≤ a + δ2 = TH ,

(7)

where δ1 and δ2 are the tolerances of parameter a, which do not exceed limit deviations T L and T H . The tolerance limit shall be TH − TL = δ2 − δ1 .

(8)

Tolerance limits T L = a + δ1 and T H = a + δ2 are set up in a drawing. The nominal value of parameter measured a and limit deviations T L and T H , which are set out in a drawing, are filled in the individual value quality form of a parameter measured (Fig. 2). If measuring result x for a parameter to control moved beyond the tolerance limits, the part is rejected. A part is considered to be accepted, if value x lies within the tolerance, i.e. condition (7) is satisfied. The narrower is the tolerance limit, the higher is the quality of a part. However, when the tolerance limit is narrowed down, the requirements, which are imposed on the production process tooling, increase. Therefore, a tolerance specified must, on the one hand, guarantee the efficiency of a part, a unit or a device, and, on the other hand, comply with the existing manufacturing capabilities.

Fig. 2. Quality form of individual values of a parameter measured: n—number of parts or assembly units checked up.

Therefore, the stability control of the technical processes through individual value forms of a parameter measured allows to ensure high quality of parts, units and devices of a product. Thus, e.g. individual value forms of the parameters measured are introduced for the most critical parts of executive units and devices, e.g. a hoister device, an adjustable jack, a load gear, a block system, clutches, hydraulic cylinders, hydraulic valves, etc. The random inspection method became widespread in the practice of producing serial and mass-manufacture products, with the purpose of ensuring the stability of the technical processes. This method is based on checking up the quality of a certain number of finished parts, units or devices from some lot (e.g. month, quarter, semi-annual and annual) of parts, units or devices, which were output.

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5 Conclusions The main reasons and factors, which influence the stability of the technical processes at the stage of serial manufacturing of machine-building products have been presented. Functional dependences have been developed, on whose base curved trajectories of alterations in the accuracy of the technical parameters of manufacturing parts, units and devices of machine-building products have been built when their serial production takes place. Quality forms for individual values of the parameters measured in parts, units and devices are introduced with the purpose of ensuring the stability of the technical processes. The results of the studies obtained have been implemented at some machinebuilding industry enterprises, e.g. at FGUP “PO” “Barrikady” (Volgograd), JSC “Zavod No. 9” (Ekaterinbourg), and a number of other factories and plants. Acknowledgements. The results of the study presented in the article were obtained under the sponsorship as part of the scientific project RFFI no. 17-08-00018.

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10. Ostanina NG, Bredikhin SG, Petrov IM (2015) Teoreticheskie osnovy analiza stabil’nosti i obespechenie nadezhnosti ZHRD (The theoretical basis for analyzing the stability and reliability LRE). Aktual’nye problemy aviatsii i kosmonavtiki 1(11):98–99 11. Edvabnik VG, Fartyshev YM, Gautzel AK, Kuznetsov MM (2013) Ob otsenke stabil’nosti proizvodstvennykh protsessov v usloviyakh edinichnogo i melkoserijnogo proizvodstva (About the stability evaluation of manufacturing processes under the conditions of custom and small volume manufacturing). Interekspo Geo-Sibir’ 5(1):195–200 12. Fartyshev YM, Kuznetsov MM, Gautzel AK, Yazykov VY (2015) Kontrol’ tekhnologicheskoj distsipliny kak uslovie stabil’nosti proizvodstvennogo protsessa (Technical discipline inspection as a condtion for a stable production process). Interekspo Geo-Sibir’ 5(3):214–218 13. Dalski AM (1975) Tekhnologicheskoe obespechenie nadezhnosti vysokotochnykh detalej mashin (Engineering support for the reliability of highly precise machine parts). Mashinostroyenie, Moscow 14. Trukhanov VM, Matveenko AM (2016) Nadezhnost’ slozhnykh sistem na vsekh ehtapakh zhiznennogo tsikla (Reliability of complex systems at any lifecycle stages). Izdatel’skij dom “Spektr”, Moscow 15. Trukhanov VM, Sultanov MM (2019) Nadezhnost’ energeticheskogo oborudovaniya teplovykh elektrostantsij (Reliability of power engineering equipment in thermal stations). Izdatel’skij dom “Spektr”, Moscow 16. Birolini A (2017) Reliability engineering: theory and practice. Springer, New York, London 17. Kapur KC, Pecht M (2014) Reliability engineering. Wiley & Sons Inc, Hoboken, New Jersey 18. Kernytskyy A, Motyka I, Nestor N (2007) Models for the analysis of accuracy of technological processes. In: Proceedings of the 9th international conference the experience of designing and application of CAD Systems in Microelectronics (CADSM 2007), Lviv–Polyana, 19–24 Feb 2007, pp 303–304 19. Batmanov EZ, Guseinov RV (2016) Veroyatnostnoe modelirovanie v issledovaniyakh tochnosti izgotovleniya izdelij mashinostroeniya (Probabilistic modelling in studies of manufacturing accuracy of machine-building products). Vestnik DGTU. Tekhnicheskie nauki 40(1):46–52 20. Apollonov IV (eds) (1989) Kachestvo i nadezhnost’ v proizvodstve (Quality and Reliability in Production). In: Nadezhnost’ i ehffektivnost’ v tekhnike (Reliability and Efficiency in Engineering), vol 7. Mashinostroyenie, Moscow 21. Pronikov AS (1978) Nadezhnost’ mashin (Reliability of Machines). Mashinostroyenie, Moscow 22. Burdun GD, Volosov SS (eds) (1975) Tekhnologicheskoe obespechenie kachestva produktsii v mashinostroenii (Aktivnyj kontrol’) (Engineering support of product quality in machinebuilding (active process control)). Mashinostroyenie, Moscow 23. Wentzel ES (2018) Teoriya veroyatnostej (The theory of probability). Justitia, Moscow 24. Trukhanov VM (2017) Nadezhnost’ v tekhnike (Reliability in engineering). Izdatel’skij dom Spektr, Moscow 25. Bezprozvannych GV, Roginskiy AV (2017) The stability monitoring of the manufacturing process of electrical insulating systems of traction electric machines. Electr Eng Electromech 6:65–68 26. Nechaev VI, Nechaev YV (2013) Vybor metoda monitoringa tekhnologicheskogo protsessa (Selection of a monitoring method for a technical process). Izvestiya TulGU. Tekhnicheskie nauki 4:216–225

Studying the Impact the Microrelief of Teeth Surface Has on Gear Operational Parameters A. G. Karavanova(B) and A. S. Kalashnikov Moscow Polytechnic University, 16/1, Bolshaya Semenovskaya St., Moscow 115280, Russia [email protected]

Abstract. The article studies the issues arising in gear manufacturing, i.e., noise and their vibrations which depend on the roughness of the lateral teeth surface. The rolling and sliding speeds on the teeth of the driving and driven gears. The modified tooth shape and manufacturing error are the main causes of the difference in the angular velocities of the mating gear elements. Since during the rotation of the gear transmission, the angular position of one gear changes periodically relative to another wheel mated to it, and angular acceleration occurs. It affects the reduction of the load capacity, and as a result of the formation of micropitting on the surface of the teeth in the region of the vertices of micro-roughness under the action of plastic deformation, the bending stresses in the mating area of the side surface and the bottom of the tooth cavity increase. Keywords: Gear grinding · Tooth surface roughness · Microrelief structure · Pitting · Micropitting · Tooth polishing · Hydrodynamic lubrication

1 Introduction Micropitting is the area of the micro-roughness peaks and the mating of the tooth lateral surface under the action of plastic deformation and stress on the part (Fig. 1). Macropitting is a cavity of wear on a part or a crack structure on a part that grows in the opposite direction to the sliding direction on the surface of the gears. The microrelief of the tooth surface has a significant impact on the quality of operation of gears. It primarily affects the decrease in loading ability and the result of the formation of micropitting on the surface of the teeth. Since the region of the tooth peaks has micro-roughness under the action of plastic deformation. Also, an increase in bending stresses together with the conjugation of the lateral surface and the bottom of the tooth depression affects the formation of stress concentrators. Tooth jamming occurs. Tooth jam occurs in connection with the appearance of stable areas of metal contact under the influence of sliding speeds, temperature effects, and plastic deformation of micro-roughnesses. Increased vibration according to GOST 24346 and gear teeth noise levels.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_23

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Fig. 1. Macropitting (a) and micropitting of contact surfaces of gears (b).

1.1 Structure Gears Operation Process Research and operating experience of gears showed that the size and structure of microroughness directly or indirectly affect the operational parameters [1]. The combination of irregularities with relatively small steps, form a microrelief of the tooth flanks, is an important indicator of the quality of gearing gears. 1.2 Tables In order to eliminate manufacturing and assembly errors, as well as deformations during the operation of the gears, make modifications of the teeth (profile and longitudinal line of the tooth, cut off the head and legs of the tooth, profile angle, etc.). The forces acting in meshing are proportional to angular acceleration; they cause vibration, the frequency of which is equal to or multiple of gear rotation speed, i.e., equal to its harmonics. The vibrations that occur when gears mesh cause noise, which is commonly called the noise of gears (Table 1). Table 1. Comparative processes of characteristics parts on the technological manufacturing gears. An example of a column heading

Continuous gear grinding (V, m)

Carbide tapping with carbide worm milling cutters (V, m)

Tooth honing (s)

Gear grinding and subsequent polishing Column B (V, m, s)

Performance

++

+\−

+\−

+\−

The surface roughness of the teeth Ra, microns.

3…6

3…6

6…8

5…8

And another entry

0,3…1,6

0,2…0,8

0,1…0,3

0,08…0,4 (continued)

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Table 1. (continued) An example of a column heading

Continuous gear grinding (V, m)

Carbide tapping with carbide worm milling cutters (V, m)

Tooth honing (s)

Gear grinding and subsequent polishing Column B (V, m, s)

Cutting speed

50…75 m/s

50… 100 m/min

0.5…10.0 m/s

5…10 m/s

Hardness HRC

58…63

≤ 64

58…63

58…63

The need for trimming the tooth cavity (prominence)

+

−

–

–

Possibility of processing the bottom of the tooth cavity

+

−

–

–

Ability to handle closely spaced gears

−

+\−

+

+

The ability to create internal compression stresses on the surface of the teeth

+

+\−

+

+

Possibility of profile and longitudinal modification of teeth

+

+

+\−

+\−

Process reproducibility

+

+

+\−

+

In the broadband frequency spectrum of the sound pressure level, the main frequency (first harmonic), as well as the second and third part of the frequency, which create 98% of the vibrations generated by the gearing of the gears, dominate (Fig. 2). The frequency of the first harmonic 1 is characterized by the frequency of pairing of teeth, its value depends on the design of the gears (the waiters of the total overlap, the width of the ring gear, the angle of inclination, the height of the tooth profile, etc. The second harmonic (doubled fundamental frequency) is determined mainly by the shape of the position of the contact spot when the gears mesh, and also by the accuracy of the geometrical parameters of the teeth. The noise from the third harmonic (arranged by the main frequency) is associated with the roughness of the beech surface of the teeth and can be reduced by reducing the micro-irregularities during the finishing operations of the toothwork. An analysis of the

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existing technological processes and the achieved accuracy of the gears showed that the most effective and widely used methods for finishing the working surfaces of the teeth are gear grinding [2]. The size and structure of micro-roughness depend on the cutting conditions, the size of the cutting elements, and their resistance. Evaluation of the intensity of the grinding process is very often done using the equivalent chip thickness. With continuous roundcut grinding, the equivalent chip thickness is the ratio of the thickness of the removed material layer with one turn of the rough grinding wheel (single and multiple). The value of the equivalent chip thickness microns is determined by the formula.

Fig. 2. The frequency of the vibrational (v) spectrum of the gear based on the processing of parts using grinding and honing wheels (g).

2 Micro-Cutting Gear Grinding refers to the processes of high-speed micro-cutting, resulting from the impact on the work surface of tools (grinding wheels) with a geometrically indefinite cutting edge. A characteristic feature of the cutting elements of grinding wheels is their negative front angle (Fig. 3), [3] .

Fig. 3. The pattern of chip formation is not geometrically defined by the cutting edge (d) on the dependence of the surface roughness of the cured teeth of the equivalent chip (e).

At the initial moment of time during the microcutting process, when the cutting element is introduced into the workpiece 2 with the appropriate peripheral speed, feed and

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pressure, it blasts the surface of the workpiece. The result is three elastic deformations, in front, on the sides and below the cutting element. In addition to elastic deformations, plastic deformations also occur. When the metal cutting from the cut is cut, chips are formed [4]. On the surface of the workpiece forms traces of cuts that are characteristic of gear grinding, which forms a micro-roughness of the tooth flanks.

3 Roughness of the Surface Studies have been conducted that have made it possible to establish the dependence of the roughness of the lateral surface of the teeth on the equivalent chip thickness. The studies were carried out using abrasive highly porous grinding wheels with a grain size of 8–12 (curve one) and 12–20 (curve two). The results obtained make it possible to determine the height of the micro-roughnesses of the tooth surface at the stage of designing the technological process. With continuous bypass gear grinding on the surface of the teeth of the cylindrical wheels, an irregular (stochastic) microrelief can be created with the structure, and detailed structure of the microrelief obtained by gear honing. Systematic grinding tools, characteristic of continuous gear grinding, crush during the diagonal movement of the feed of the worm-grinding wheel, the turns of which were specially edited. Traces of cuts along the length are significantly reduced, and the height of microroughness decreases. With this structure of the lateral surface of the teeth, their bearing surface increases significantly and the smoothness of the engagement of the cylindrical gears increases. An effective means of increasing gear grinding productivity is the use of multi-pass worm-grinding wheels. Multiple worm wheels have two or more producing surfaces; they are widely used in industry, If during one revolution of a single-running worm-grinding wheel near the workpiece, one tooth cavity is machined, then in one revolution of a double-running grinding wheel, two tooth cavities, a three-tooth wheel, three tooth cavities, etc. When using multi-start worm-grinding wheels, it is possible to make various revisions of the turns of the circle. If all branches of the grinding wheel, with the exception of one or two, are corrected by the usual ruling tool, then one or two turns of the circle are corrected by the tool that has undergone special processing. For such ruling instruments smooths the tops of diamonds providing the necessary working profile. The essence of this process is the consequences of the removal of thin layers of approximately 1 micron and a volume of 10…20 microns by diamonds with tools. In order to avoid chipping of the grinding wheel diamonds and the ruling tools, the smoothing speed should not turn 20 m/s. The effective working profile of one or two turns of the abrasive grinding wheel, which have been corrected by smoothing with the surface of the cutting tool instead of with the turns of the wheel tucked with rollers with surfaces without smoothing, when grinding with the corresponding tangential displacement, and allows to obtain a special structure of the tooth lateral surface . In this case, periodic changes in the structure of the ligament of the circle should not cause deviations in the shape of the tooth profile, which affects the increase in noise level. Gear vibration level: one—with an irregular microrelief on the lateral surfaces of the teeth is much lower than that of gears processed by other methods; two—a continuous gear grinding profile and subsequent honing teeth with an abrasive stroke with external gearing on one machine; three—tooth honing with an abrasive hon with internal gearing; four—continuous gear grinding by

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a metal wheel with a single layer coating with cubic boron nitride; five—gearing and running with the removal of nicks after chemical heat treatment. The current operating conditions of mechanisms with gears require an increase in power in the transmission while increasing the load capacity of gears. Pay attention to highly porous materials for gears, their chemical-thermal treatment and complex modification of the flank surfaces of the teeth, which helps to improve the operational properties and duration of gears [5]. At the same time, numerous studies have shown that reducing the roughness of the lateral surface of the tooth reduces power loss in the transmission in the initial period of operation. In this regard, continue theoretical and experimental studies to reduce the roughness of the lateral surface of the teeth. In order to reduce the surface roughness of the teeth after continuous gear grinding, the tooth profiles are polished on the same machine. It is very important that the reduction of the surface roughness of the teeth after polishing occurs without negative impact on the geometric accuracy of the teeth. The method of continuous polishing of teeth is positioned as the last technological operation of tooth processing in which microroughnesses characteristic of grinding and area are removed from the side surfaces of the teeth (Fig. 4).

Fig. 4. Image of the overlay on the direction of the protrusions (h) and sliding (i) the surface roughness of the gears.

4 Micropitting Morphology Micropitting is crucial to determine the root cause of the reduction in gear strength. The micropitting structure of the part is characterized by smoothly extending downward from its beginning on the tooth surface. The gear wheel has a rough surface, a layer which is caused by cracked plastic fatigue. Due to micropitting, the material seems smooth and expressionless, unless it is abraded.

5 Sliding Gears Directions of rolling speeds (r) and sliding (s) on the teeth of the driving and driven gears is shown in Fig. 5. Contact begins near the tooth profile and ends at the end of the

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tooth, which is far from the pitch line of the pinion gear. Contact on the driven tooth starts from the tip of the tooth, rolls down the tooth, and ends near the tooth profile. Like micropitting, micro-rallies have cracks that grow in the opposite direction to the sliding direction on the surface of the gear tooth. Consequently, cracks converge near the pitch line of the driven wheel [6].

Fig. 5. Directions of rolling speeds (r) and sliding (s) on the teeth of the driving and driven gears.

The cross section of the teeth shows that cracks begin on the surface of the gear tooth or near it and grow at a small angle (usually 10–30°, but sometimes up to 45°) to the surface. Direction of sliding changes with the intersection of the dividing line. Micropitting cracks grow in opposite directions above and below the pitch line (Fig. 6).

Fig. 6. Risks (o) after machining and grinding of the gears cause wear of the razor tool based on the determination of the structure of the roughness of the micropitting surface on the part (k).

Gear teeth have a negative slip. The direction of the rolling speed is opposite to the sliding speed. Negative slip contributes to Hertz fatigue and allows for oil to penetrate

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surface cracks where it accelerates crack growth using the hydraulic pressure propagation mechanism. Macropitting starts from high points on the undulation for surfaces of polished gears which have traces of incisors. The surface of the teeth is plastically deformed. After gear grinding, a geometric concentration of micropitting stresses can occur. At the edges of the gear teeth, border of surface defects such as micropitting, dents or marks of incisors. Resistance to micropitting largely depends on the properties of the lubricant, viscosity at operating temperature, viscosity-pressure coefficient, and lubrication [7]. Parts of wear caverns are harmful to micropitting resistance, but they prevent break-in and preserve the surface roughness damaging the micropitting of the surface. However, some additives reduce friction of the parts. Gears have maximum resistance to micropitting in the manufacture of alloy steel with sufficient hardenability to obtain microstructures consisting mainly of hardened martensite. Preserved austenite about 20% is considered useful. More than 30% austenite usually reduces the hardness, strength, and residual compressive stress in the gears and, therefore, adversely affects micropitting resistance. Gears have maximum resistance to micropitting in the manufacture of steel with sufficient hardenability to obtain a hardened martensite microstructure. Preserved austenite about 20% is considered useful. Increased wear, vibration, and noise of the gears are formed as a result of wear of metal particles, and are contaminated with oil. Such an effect on the surface of rotating elements and gears can ultimately lead mowing of the part (Fig. 7).

Fig. 7. Chips (l) when polishing gears to reveal the surface roughness of the gear part (m).

6 Equations In order to avoid the formation of micropitting, you can either use gears with very smooth surfaces treated with finishing operations, change the operating conditions of the equipment, or select a lubricant designed to prevent micropitting of the part. Ra is the arithmetic mean of the absolute values of the deviations of the profile within the base length of 0.026 … 0.012; Ra =

∫0 3000 10 ∫|yi |dx = 9.22 = 0.029993mkm l l 922200

(1)

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In Profiles within width gear, root mean square deviation indicates the root mean square along the sampling length.   5 ∫i=1 |Hi max| − ∫5i=1 |Hi min| Rz = 5 (3 + 4, 5 + 2, 2 + 1 + 11) − (−3, 5 − 3, 8 − 1, 9 − 2 − 5, 5) = 5 =4.4 mkm (2) Gear standard deviation of the profile within the base length.   √ ∫09.22 |3000|2 Ra 10 2 ∫|yi | dx = Rq = = == 9.759 = 3.3mkm l l 922200 0, 8

(3)

For the roughness, profile gear is referred to as root mean square roughness. While its referees are referred to as root mean waviness for the profile.   √ ∫09.22 |3000|2 10 ∫|yi |dx = = 9.743 = 3.321mkm (4) q= l l 922200 Roughness profile is the standard deviation of the profile within the base length of 3.3 . . . 1.15.   √ ∫09.22 |3000|2 10 ∫|yi |dx = Wq = = 9.739 = 3.334mkm (5) l l 922200 The instrument like “Ra. 1” calculated using “Rq. 2” mathematics and using C programming, automatically created a 3D model. Using the model, surface roughness was checked. The result: “l. 800”. According to GOST 2789-73, polishing of gears is required in order to reveal surface roughness of a part. When calculating the detection of surface roughness “Ra. 0.03” and “Rz. 3.4”. Crack edges are machined with a corner between the boundary surfaces of 90 °. Processing is performed to a depth of one-third of the thickness of the metal. To eliminate cracks, composite materials based on epoxy resins are used. After eliminating the cracks, we get “Ra. 0.35”. To eliminate cracks in the details of chromium electro corundum with the addition of chromium oxide with certain ligaments, high precision teeth were achieved according to GOST 1643-81: The accumulated error of the steps of the gear wheel (kinematic accuracy) is “Fpr. 6” degree. Accumulated error of k steps of the gear wheel is “Fpk. 5”. Radial runout of the gear ring is “Frr. 5”. Deviation of the step of the gear wheel is “frr. 6”. Error of the tooth profile of the gear wheel is “Fn. 6”. The error of the gear tooth line is “Fr. 6”. Application polishing of a part consisting of chromium electro corundum with the addition of chromium oxide with a grain size of 8–12 and 12– 20 microns is used for the contact surface hardening of abrasive particles of circles with a surface roughness of “Ra. 0.03”. It also helps in the identification of the relationship of the choice of tools when using the finish machining of gears.

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References 1. Kalashnikov AS, Morgunov YuA, Kalashnikov PA (2012) Modern methods of processing gears. Mechanical engineering, Moscow 2. Shandrov BV, Morgunov YuA, Kalashnikov PA (2007) Experimental studies of allowances during continuous gear grinding. Engineering, Moscow 3. Shandrov BV, Morgunov YuA, Saushkin BP (2013) Development and application of high-tech technologies in the production of aircraft. Engineering, Moscow 4. South J, Blass B (2001) The future of modern genomics. Engineering, London 5. Gorbatsevich AF, Chebotarev VN, Shkred VA, Aleshkevich IL, Medvedev AI (1975) Cours design in engineering technology. Engineering, Moscow 6. Kharlamov GA., Tarapanov AS (2006) Allowances for mechanical processing. Engineering, Moscow 7. Asaeva EV, Ivanyuk AV, Kuzmina SN (2008) Designing engineering production (Guidelines for the implementation of the course project by students of the specialty). Ryazan, Moscow

How the Parameters of an Agricultural Machine and Tractor Unit Affect the Wear of Friction Pairs in a Diesel Engine When Used for Transport V. P. Antipin, M. Ya. Durmanov(B) , and O. A. Mikhailov S.M. Kirov Saint Petersburg State Forest Technical University, 5U, Institutsky Pereulok, St. Petersburg 194021, Russia [email protected]

Abstract. The paper dwells upon how the parameters of an agricultural machine and tractor unit (MTU) affect the wear rate of the liner in the main bearing of a YaMZ-238ND5 diesel engine. The operating parameter in use is the MTU travel speed, while the design parameter used is the suspension stiffness. Transportmode linear wear rates have been determined in association with ascent resistance, MTU inertial forces, MTU suspension vibrations in the longitudinal vertical plane, mechanical losses in the friction pairs, as well as the total loss for various suspension stiffness values. Although an MTU is used for transport only for short periods of time, such usage is energy-intensive; it consumes considerable power and causes faster wear of the friction pairs in a diesel engine. Experimentally obtained frequency response of the volumetric wear rate of friction pairs shows the service life of a diesel engine strongly correlated with the energy consumption. At higher travel speeds, more motor oil is pumped through the friction pairs; this results in burning more oil as well as in a slower wear of the friction pairs. In such cases, the dynamic component of the wear rate becomes lower while the regular component rises. The most significant dynamic wear is associated with the ascent resistance as well as with the suspension vibrations in the longitudinal vertical plane. Keywords: Machine and tractor unit · Diesel engine · Energy consumption · Wear rate · Friction pair · Frequency response

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_24

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1 Introduction To date, there is no consensus on the nature of friction pair wear. However, most researchers [1–10] tend to agree that such wear is mainly caused by the lubrication parameters being inadequate to the loads, speeds, and thermal parameters of a diesel engine. In the cylinder–piston assembly (CPA), this causes the unevaporated fuel to destroy the oil film; in the slider–crank linkage (SCL), this disrupts the lubricant hydrodynamics and causes a rupture of the oil film. Cold welding, fatigue, and abrasive wear occur in either case. Analytical and experimental research [11–15] shows that wear is an energy consumption-related process. In a non-steady state, increasing the fuel feed will speed up the crankshaft and raise the pressure in the main oil-distributing passage, which lags behind the moment-of-load increments by 180° by phase. As a result, semi-dry or boundary friction occurs, triggering an auto-oscillating process associated with increased energy consumption [12, 13]. Experimentally obtained frequency response of the hourly fuel consumption and volumetric wear rate of friction pairs show that the service life of an engine strongly correlates with the energy consumption. Since the oil consumption through burning and the friction pair wear rate depend on the oil pressure in the main oil-distributing passage (MODP), excessive oil consumption and wear rates are caused by [9–11, 16–18]: the inadequacy of MODP oil pressure to the loads and speeds in steady state or the inadequacy of the MODP oil pressure amplitude and phase to the amplitude and phase of the crankshaft load oscillations. The goal hereof was to study how the design and structural parameters of an agricultural MTU could affect the wear rate of the SCL friction pairs, which determines the service life of a diesel engine [3, 5, 7, 12, 17]. The proposed method for calculating the operating performance and residual service life of an MTU is of special relevance when designing the tractor, as it can help improve the design.

2 Method To determine the influence of tractor design parameters on the efficiency of MTU operation in dynamic (unsteady) loading modes, a theoretical and experimental model presented by transfer functions is developed. The transfer functions of the oscillations of the sprung MTU are obtained theoretically. Transfer functions of speed control systems, fuel supply, and engine lubrication are obtained experimentally. The results of calculations of MTU energy consumption, fuel and oil consumption through burning, as well as the wear rate of diesel friction pairs obtained by the section method of frequency response have satisfactory accuracy and reliability and are confirmed by the results of bench studies of engines under dynamic loading modes and MTU operation in real conditions. 2.1 Analytical Expressions to Find the Wear Rates of Friction Pairs in an MTU Diesel Engine in Transport Operations Apparently [3, 7, 12, 17], factory tests only estimate the wear of friction pairs at various regular loads and crankshaft speeds. In the real-world usage, such a unit might have

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to operate both in steady states, where the regular components of loads and speeds may vary, and in non-steady states, where the dynamic load components may vary in a broad range of value and frequency. Therefore, the friction pair wear rate has a regular component Uυ0 and a variable component Uυ (ω), both of which depend on the load, speed, lubrication, and thermal parameters: • for transport mode, Uυt  D3 3 R t a1 Pm0 n0 [ A1 + D1 ( + b1 n0 )]; (1) D1 it η m Pmn eγ t     D3 a U 2 (jω) · { Rω [3At + 4A ω · |U (jω)| + 4f Θ t (jω)]+ M E3 D 4 11 rf n v 11 1 i η t m 1 Uυt (ω) =    · ·· · · ·   D3  R  2 D1 U11 (jω) · { it ηm [At1 + A4 ω · |U11 (jω)| + frf Θvt (jω)]+  2 2 16ω +γ 1 · |G61 (jω)| + 4b1 ω · |U11 (jω)|]} +D1 · [ Pamn ω2 +γ 2 ; ··· |G61 (jω)| ··· 1 |U +D1 [ Pamn ·√ + b · (jω)|]} 1 11 2 2 t Uυ0

= E3

ω +γ

(2) πR where E3 = σmp ; D1 = Vπcτiee ; At1 = mg(sin α + frf cos α); A4 = 30i m. t t The parameters included in the expressions for the regular (1) and variable (2) components of the wear rate of friction pairs and their values are given in [12, 19, 20]. The value D3 for the main-bearing bushing can be found from the equation  3 2 μd π db D3 = ffr Sfr cr , h0 60 Ik

where ffr is the coefficient of friction; Sfr is the area of friction; μd is the kinematic viscosity of oil; hcr 0 is the critical thickness of the oil layer; and db is the diameter of the main bearing. The volumetric wear rate of the main-bearing liner can be calculated by substituting the following data in (1) and (2) [6, 10, 12, 14]: db = 0.11 m; a1 = 0.45; b1 = 0.97·10−3 ; Pmn = 0.6 MPa; the altitude irregularity factor kmp = 0.2; ffr = 0.003; μd = 1.8·10−3 N·s/m2 ; hcr 0 = 0.13 mkm; friction pair wear rate I = 5.0·10-7; and liner yield strength σt = 32 MPa. Note. All the analytical expressions above are for calculating the volumetric wear rate Uυ (ω) of the friction pairs. However, it is linear wear rates that are mainly used in real-world applications, which is why Figs. 1 and 2 and Table 1 give the calculated  wear rates in linear terms U (ω) adjusted for the friction area Sfr , i.e., U (ω) = Uυ (ω) Sfr . The transfer function of the MTU power plant rotation speed in terms of disturbance is [12, 19, 20] U11 (jω) =

ke1 (T22 s2 + 2T2 ξ1 s + 1) (T1 s + 1)(T32 s2 + 2T3 ξ2 s + 1)(T4 s + 1)

,

(3)

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where ke1 is the rotation speed transmission ratio; T1 , T2 , T3 , T4 are the constants of time; and ξ1 , ξ2 are the attenuation coefficients. For a YaMZ-238ND5 engine, ke1 = 1.85; T1 = 0.796 s; T2 = 0.370 s; T3 = 0.199 s; T4 = 0.183 s; ξ1 = 0.200; ξ2 = 0.150 [12, 19, 20]. Note that for the MTU and its mass m, the applied-to-crankshaft moment of inertia Ia and the time constant T1 are written as Ia = Ie +

mR2 π n2n ; T1 = Ia ; 2 30 Nn it

(4)

where Ie is the engine moment of inertia; Nn is the rated power of the engine. The transfer function of the MTU carcass vibrations in the longitudinal vertical plane when running in the transport mode while plow-equipped will depend on the Nyquist plot of tire deformations per disturbance unit of track irregularity at s = jω [12, 19, 20]:   t Θ (jω) = z0 (c1 + jωβ1 ) · [η1 (jω) + η2 (jω)], (5) v where η1 (jω), η2 (jω) are the Nyquist-plot values of front- and rear-tire deformations, respectively, per disturbance unit of track irregularity:  η1 (jω) = m1 ω2 (c1 − m2 ω2 + jωβ1 ) (jω);  η2 (jω) = m2 ω2 (c1 − m1 ω2 + jωβ1 ) (jω). (6) The description of the design, mass, stiffness, and damping parameters of the MTU included in expressions (5) and (6) is presented in [12, 19, 20]. Substitute the expressions (6) in (5) to compute the frequency response of the K744R-05 tractor tires when running in the transport mode while equipped with a PUN8-40 plow; use the following source data [12, 19, 20]: z0 = 0.03 m; mtt = mt + mpl = 13,400 + 2250 = 15,650 kg; It = 44,388 kg·m2 ; Ipl = 24,628 kg·m2 ; Is = 116,400 kg·m2 ; l1 = 1.0 m; l2 = 2.2 m; l = 3.20 m; lt = 0.73 m; lpl = 4.35 m; m1 = 14,670 kg; m2 = √ 15,941 kg; m0 = 7480 kg; m2 = 177.9 ·106 kg2 ; c1 = 1500 kN/m; β1 = 2ν c1 m2 ; ν = 0.1. Transfer function of oil pressure in the main oil-distributing passage by disturbance is [12, 20] G61 (jω) =

km1 , (T1 s + 1)(T32 s2 + 2T3 ξ2 s + 1)

(7)

where km1 is the MODP oil–pressure transmission ratio. For a YaMZ-238ND5 diesel engine, km1 = 1.35 MPa/N·m; T1 = 0.796 s; T3 = 0.199 s; ξ2 = 0.150.   Substitute |U11 (jω)| from (3), Θvt (jω) from (5), and |G61 (jω)| from (7) in (2) to find the state surface of the frequency responses (FR) of friction pair wear rates in a diesel engine of an MTU operated as transport. By sectioning the FR state surfaces vertically for any fixed regular MTU travel speed υ0 over the entire range ω of drive-wheel load oscillations, find the regular (mean) component of the friction pair wear rate; the wear

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rate at dynamic loads as well as its breakdown, see Figs. 1 and 2. In order to quantify the wear rates, substitute the following source data in (1) and (2) [12, 19, 20]: Vc = 1.875 l; ie = 8; τe = 4; a1 = 0.45; b1 = 0.97·10−3 ; Pmn = 0.6 MPa; Pm0 = 0, 9Pmn = 0.54 MPa; nn = 1,900 min−1 ; Nen = 220 kW; Ie = 2.45 kg·m2 ; Men = 1239 N·m; Fca = 0.15 Men ; ηm = 0.8; frf = 0.12; R = 0.8 m; α = 3°. 2.2 Transport-Mode Wear Rate of the Friction Pairs in an MTU Diesel Engine

Fig. 1. FR of the main-bearing linear wear rate, YaMZ-238ND5 diesel engine in an MTU based on a K-744P-05 tractor with a PUN-8-40 plow: breakdown for the transport mode at υ0 = 2.01 m/s: a for a suspension stiffness c1 = 1,500 kN/m; b for a suspension stiffness c1 = 900 kN/m. 1 for wear attributable to the ascent resistance; 2 for wear attributable to inertial forces; 3 for wear attributable to the longitudinal and vertical vibrations of the MTU suspension; 4 for wear attributable to mechanical losses in the friction pairs; 5 for the total dynamic component of the wear rate.

The components of the criteria function (2) were used to calculate the wear rate attributable to the dynamic loads at speeds of 0…20 s−1 as well as the total value for various suspension stiffness values c1 = 1,500, 1,200, or 900 kN/m: 1. for wear attributable to ascent resistance t Uυ1 (ω)

 2 ω=20 ω · U11 (jω) 1, 5R · Mna E3 D3 At1   = ·  d ω; R t 3 U (jω) it ηm ωle D1 D · A 11 D1 it ηm 1 ω=0

(8)

2. for the inertial forces of the MTU

t Uυ2 (ω)

 2 ω=20 ω2 · U11 (jω) 2R · Mna E3 D3 A4  = · d ω; √ D3 R ω it ηm ωle D1 D · A 4 it ηm ω=0 1

(9)

3. for the MTU suspension vibrations in the longitudinal vertical plane t Uυ3 (ω)

 2   ω=20 ω · U11 (jω) · Θvt (jω) 2R · Mna · E3 D3 frf   = ·    d ω; D3 R U (jω) · Θ t (jω) it ηm ωle D1 D f rf v 11 i η ω=0 t m 1

(10)

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Fig. 2. FR of the main-bearing liner wear rate, YaMZ-238ND5 diesel engine in an MTU based on a K-744P-05 tractor with a PUN-8-40 plow: breakdown for the transport mode at υ0 = 5.20 m/s: a for a suspension stiffness c1 = 1,500 kN/m; b for a suspension stiffness c1 = 900 kN/m; for the legend, see Fig. 1.

4. for the mechanical losses in the engine friction pairs

t (ω) = Uυ4

Mna · E3 D3 2ωle

·

  ω=20 U11 (jω)2 · [ Pa1 mn ω=0



16ω2 +γ 2 · |G61 (jω)| + 4b1 ω · |U11 (jω)|] ω2 +γ 2

  |G (jω)| a D3 · U11 (jω) · [ P 1 ·  612 2 + b1 ω · |U11 (jω)|] mn

dω .

(11)

ω +γ

Total friction pair wear rate attributable to dynamic loads at different stiffness values c1 is Uυt (ω)

Ma = n · ωle

ω=20

  t G (jω) d ω, 51

(12)

ω=0

t (jω) is the transfer where ωle is the lowest eigenfrequency of load fluctuations; G51 function of the wear rate of friction pairs in the power unit of an MTU running in the transport mode [12]. t in transport operation with adjustment for The actual friction pair wear rate Uυf dynamic loads at c1 = 1,500, 1,200, or 900 kN/m will be the total t t Uυf = Uυ0 + Uυt (ω).

(13)

Table 1 summarizes the regular and dynamic components of the wear rate with a breakdown as calculated per the Eqs. (8) to (13) in linear terms.

3 Results and Discussion The service life of a tractor engine in a normal-duty operation will be less than what the manufacturer guarantees. This pattern is easy to explain: the current standards only require factory tests in steady states, whether in terms of load or speed. In the real world, MTUs mainly function in non-steady states [12] associated with altered cycled fuel feed, fluctuations of load on the drive wheels and in the power transmission. Meanwhile, the

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Table 1. Calculated main-bearing liner wear rate, YaMZ-238ND5 diesel engine in an MTU based on a K-744R-05 tractor with a PUN-8-40 plow, transport mode. MTA travel speed υ0 , m/s, (transmission Components of the dynamic Dynamic t (ω), gear ratio it ) components Uυt (ω), component Uυi mkm/103 h at stiffness c1 = mkm/103 h as a function of stiffness 1,500 kN/m c1 , kN/m 1

2

3

4

1,500 1,200 900

2.01 (63.4)

5.130 2.170 3.600 1.980 7.130 7.100 7.030

5.20 (24.5)

0.582 0.125 0.669 0.210 0.897 0.866 0.844

t , mkm/103 h Regular component of the wear rate Uυ0

0.930/3.875a

2.01 (63.4)

8.060 8.030 7.960

Actual wear rate t = U t + U t (ω), Uυf υ υ0 mkm/103 h

5.20 (24.5)

4.772 4.741 4.719

a In the numerator at υ = 2.01 m/s; in the denominator, at υ = 5.20 m/s 0 0

lubrication and thermal parameters of the friction pairs in the engine will in most cases be inadequate to the rapidly changing load and speed parameters [2, 3, 5, 17]. Raising the MODP oil pressure will positively affect the friction pair durability regardless of how exactly the engine operates. At the same time, the emergent oil wedge and a hydrodynamic pressure that will prevent the shaft and the liner from interfacing will separate the surfaces in friction [17]. Disruption of lubricant hydrodynamics in plain bearings ruptures the oil film and causes cold welding of the shaft and the liner. This is associated with higher friction, thus with higher temperatures of the oil exiting the bearing, as was observed in [12, 16]. In that case, the MODP oil pressure will barely affect the pressure in the oil layer; on the other hand, it will significantly affect the oil throughput, and thus the thermals of the bearing. Temperature difference may be as significant as dozens of degrees, which ultimately alters the oil viscosity, the pressure curves, and the capacity of the bearing. At higher travel speeds υ0 , more motor oil is pumped through the friction pairs; this results in burning more oil as well as in a slower wear of the friction pairs. In such cases, the dynamic component of the wear rate becomes lower while the regular component rises. The most significant dynamic wear is associated with the ascent resistance as well as with the suspension vibrations in the longitudinal vertical plane. Increasing the travel speed from 2.01 to 5.20 m/s while reducing the MTU suspension stiffness c1 by 40% results in “shrinking” the area bounded by Curve 5 and the coordinate axes, see Fig. 2. This reduces the value of the dynamic wear rate, and its extremes are shifted to the high-frequency region of load fluctuations ω. Acknowledgments. The authors hereof would like to thank Associate Professor Gennady Karshev for his invaluable assistance in writing the manuscript.

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References 1. Denisov AS, Nagorny VI (1980) Iznashivaniye detaley pri peremennykh rezhimach raboty (Wear of parts under variable operating conditions). Dvigatelestroyeniye 1:16–21 2. Antipin VP, Durmanov MYa, Karshev GV, Michasenko VI (2006) Iznos dvigatelya na neustanovivshichsya nagruzochnom, skorostnom I smazochnom rezhimach (The wear of the engine during transient load, speed and lubrication regimes). Dvigatelestroyeniye 1(223):7–9 3. Deryabin AA (1974) Smazka i iznos dizeley (Lubrication and wear of diesel engines). Mashinostroyeniye, Moscow, p 184 4. Suranov GI (1982) Umensheniye iznosa avtotraktornych dvigateley pri puske (Reducing the wear of tractor engines during start-up). Kolos, Moscow, p 143 5. Denisov AS, Baskov VN (1986) Iznashevanie detaley dvigatelya na peremennych rezhimakh raboty (Wear of engine parts in variable operating modes). Dvigatelestroyeniye 1:33–38 6. Drozdov YuN, Pavlov VG, Puchkov VN (1986) Treniye i iznos v ekstremalnykh usloviyakh: Spravochnik (Friction and wear in extreme conditions). Mashinostroyeniye, Moscow, p 324 7. Anilovich VYa, Grinchenko AS, Litvinenko VL et al (1986) Prognozirovaniye nadezhnosti traktorov (Prediction of reliability of tractors). Mashinostroyeniye, Moscow, p 274 8. Smirnov MS, Ocheretyany IT (1972) Vliyaniye razlichnykh dizelnykh topliv i temperatury okhlazhdayushchey zhidkosti na iznos detaley tsilindro-porshnevoy gruppy dizelya (How different diesel fuels and coolant temperatures affect the wear of the cylinder-piston assembly parts). Povysheniye iznosostoykosti detaley dvigateley vnutrennego sgoraniya In: Improving the durability of internal combustion engine parts. Collection of papers. Mashinostroyeniye, Moscow, pp 43–48 9. Prosolov BV (1965) Davleniye podachi smazki i vozmozhnosty uluchsheniya raboty podshipnikov skolzheniya (Lubrication supply pressure and possibilities for improving the performance of sliding bearings). Vestnik mashinostroyeniya 1:19–22 10. Snegovskiy FP (1974) Raschet i konstruirovanie podshipnikov skolzheniya (Calculation and design of sliding bearings). Kiev, Technika, p 86 11. Leonov OB, Shkarupilo AYa (1977) Nagruzki podshipnikov kolenchatogo vala na neustanovivshichsya rezhimach raboty dizelya (Load crankshaft bearing during unsteady modes of operation of the diesel engine). Mashinostroyeniye 8:15–18 12. Antipin VP, Durmanov MYa, Karshev GV (2017) Proizvoditelnost, energozatraty i resurs mashinno-traktornogo agregata (Performance, energy consumption, and service life of an agricultural aggregate). Polytech Publishing House, St. Petersburg, p 484 13. Antipin VP (1987) Kharakter vliyaniya rashoda topliva na iznashivaemost dvigatelya pri rabote v neustanovivshemsya rezhime (How the fuel consumption affects the engine wear in non-steady states). Dvigatelestroyeniye 3:48–50 14. Moore DF (1997) Principles and applications of tribology. Pergamon Press 15. Durmanov MY, Martynov BG, Spiridonov SV (2019) Energy and Fuel Consumption of Agricultural Aggregate. In: Radionov A., Kravchenko O., Guzeev V., Rozhdestvenskiy Y. (eds) Proceedings of the 4th International conference on industrial engineering (ICIE 2018). Lecture Notes in Mechanical Engineering. Springer, Cham, pp 1601–1612. https://doi.org/ 10.1007/978-3-319-95630-5_171 16. Prokhorov VB, Antipin VP (1980) Vliyaniye neustanovivshikhsya rezhimov raboty DVS na iznosostoykost ego detaley (How Non-Steady State of an Internal combustion engine Affects the Durability of Its Parts). Dvigatelestroyeniye 10:25–27 17. Grigoriev MA, Doletsky VA (1978) Obespecheniye nadyozhnosti dvigateley (Engine Reliability Enhancement). Standards, Moscow, p 165 18. Suranov GI (1976) Snizhenie iznosa detaley dvigateley lesotransportnych mashin (Reduction of wear of engine parts for forest transport vehicles). Lesnaya promyshlennost, Moscow, p 168

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19. Durmanov MYa, Martynov BG, Spiridonov SV (2020) How Parameters of Agricultural Machine and Tractor Unit Affects Effectively Used Mean Indicated Power. In: Radionov A, Kravchenko O, Guzeev V, Rozhdestvenskiy Y (eds) Proceedings of the 5th International conference on industrial engineering (ICIE 2019). Lecture Notes in Mechanical Engineering. Springer, Volume II, pp 299–312. https://doi.org/10.1007/978-3-030-22063-1_33 20. Antipin VP, Durmanov MYa, Mikhailov OA (2020) Method to reduce oil burningin diesel engine of agricultural machine and tractor unit. In: Radionov A, Kravchenko O, Guzeev V, Rozhdestvenskiy Y (eds) Proceedings of the 5th international conference on industrial engineering (ICIE 2019). Lecture Notes in Mechanical Engineering. Springer, Volume II, p 313–323. https://doi.org/10.1007/978-3-030-22063-1_34

Oil Consumption Through Burning in Heavy-Duty Operation of an Agricultural Machine and Tractor Unit M. Ya. Durmanov(B) , B. G. Martynov, and S. V. Spiridonov S.M. Kirov Saint Petersburg State Forest Technical University, 5U, Institutsky pereulok, St. Petersburg 194021, Russia [email protected]

Abstract. The paper dwells upon how the parameters of an agricultural machine and tractor unit (MTU) affect the oil consumption through burning when plowing heavy soils. The reason for the increased oil consumption through burning values is the discrepancy between the lubricating mode of the diesel friction pairs and the rapidly changing load and speed modes. Unsteady operating modes of the MTU associated with load fluctuations on the tractor’s driving wheels affect changes in the amplitude and lag phase of the oil pressure increment in the main oil-distributing passage (MODP) of the diesel engine and the magnitude of the mechanical-loss moment. To improve the performance of the lubrication system and friction modes and reduce the oil consumption through burning, a adjuster installed in the diesel engine’s MODP allows. The frequency response (FR) section method considered in the paper can be used to assess how these parameters will affect the operating and environmental parameters of an MTU while designing it. The FR section method allows estimating the oil consumption through burning by components, i.e., the burning due to changes in the amplitude and in the phase lag of the MODP oil pressure incrementation; due to MTU suspension vibrations in a longitudinal–vertical plane; due to mechanical losses in the engine; and the total dynamic component of oil consumption. When plowing heavy soils, oil consumption through burning greatly depends on the amplitude and phase of MODP oil pressure gain as a function of the variable load increase and longitudinal–vertical suspension vibrations. Keywords: Machine and tractor unit · Diesel engine · Oil consumption through burning · Adjuster · Frequency response

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_25

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1 Introduction In the real world, MTUs mainly function in non-steady states [1–8]. It has been found out [7, 9, 10] that the oil consumption through burning is proportional to the hourly fuel consumption and is the sum of the regular component Ccir0 (1) and the variable component Ccir (ω, υ0 ) (2) that are consumed when overcoming the regular and the variable MTU movement resistance forces. The lubrication system of a YaMZ-238ND5 engine can reach such a state, where the least amplitude of the moment of load corresponds to the maximum MODP oil pressure, and vice-a-versa. In this state, more oil will leak from the gaps of friction pairs; sprayed by the inertial forces, it will create thick oil mist in the crankcase pan. The pumping effect causes suspended oil to be injected into the combustion chamber through the locks of piston seals. At the same time, overregulated rotation speed and untimely injection cause excess fuel intake in the combustion chamber; mixed with the suspended oil, it inhibits the combustion process, as the oil flash point is 153 °C higher than that of the air/fuel mixture. As a result, the mixture will partly complete burning in the exhaust manifold, resulting in hotter exhaust gas, greater fuel and oil consumption through burning, lower attainable power, and worse environmental performance [7, 9, 10]. Increased fuel and oil consumption through burning in non-steady-state operation reduces the service life of the diesel engine cylinder–piston assembly (CPA) [11–17]. The goal hereof is to find how the design parameters of a diesel engine and an attached MTU might affect its operating and environmental performance. This predictive assessment must be available as early as designing the unit and will use the frequency response (FR) surface states of oil consumption through burning characteristic of a YaMZ-238ND5 diesel engine: standard-configuration unit vs. adjuster-equipped unit.

2 Method To determine the influence of tractor design parameters on the efficiency of MTU operation in dynamic (unsteady) loading modes, a theoretical and experimental model presented by transfer functions is developed. The transfer functions of the oscillations of the sprung MTU are obtained theoretically. Transfer functions of speed control systems, fuel supply, and engine lubrication are obtained experimentally. The results of calculations of MTU energy consumption, fuel, and oil consumption through burning, as well as the wear rate of diesel friction pairs obtained by the section method of frequency response have satisfactory accuracy and reliability and are confirmed by the results of bench studies of engines under dynamic loading modes and MTU operation in real conditions.

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2.1 Analytical Expressions to Find Oil Consumption Through Burning in Plowing p

When plowing, the oil consumption through burning Ccir of an MTU diesel engine can p be found by the following equations for the regular component Ccir0 and the variable p component Ccir (ω, υ0 ):   R ks2 p p [A1 + A2 + A3 n20 ] + D1 (a1 + b1 n0 ) − Min ; (1) Ccir0 = ks1 Pm0 + Min it ηm     R ks2  2  p Ccir (ω, υ0 ) = ks1 ω · |G61 (jω, υ0 )| + (2A3 ω · U11 (jω, υ0 ) Min it ηm p

+A4 ω2 · |U11 (jω, υ0 )| + frf ω|v (jω, υ0 )|)   a1 · |G61 (jω, υ0 )| + b1 ω · |U11 (jω, υ0 )| +D1 · Mna ; Pmn

(2)

πR 2 where A1 = mg sin α + frf mt g cos α; A2 = fpf mpl g cos α + kf ab; A3 = ( 30i ) ξ ab; t p

πR A4 = 30i m; D1 = Vπcτiee . t The parameters included in the expressions for the regular (1) and variable (2) components of the oil consumption through burning, and their values are given in [18–20]. The transfer function of the MTU power plant rotation speed in terms of disturbance is [7, 18–20]

U11 (jω, υ0 ) =

ke1 (T22 s2 + 2T2 ξ1 s + 1) (T1 s + 1)(T32 s2 + 2T3 ξ2 s + 1)(T4 s + 1)

,

(3)

where ke1 is the rotation speed transmission ratio; T1 , T2 , T3 , T4 are the constants of time; ξ1 , ξ2 are the attenuation coefficients. For a YaMZ-238ND5 engine, ke1 = 1.85; T 1 = 0.796 s; T 2 = 0.370 s; T 3 = 0.199 s; T4 = 0.183 s; ξ1 = 0.200; ξ2 = 0.150 [7, 18–20]. Note that for the MTU and its mass m, the applied-to-crankshaft moment of inertia Ia and the time constant T1 are written as Ia = Ie +

mR2 π n2n Ia , ; T1 = 2 30 Nn it

(4)

where Ie is the engine moment of inertia; Nn is the rated power of the engine. The transfer function of the MTU carcass vibrations in the longitudinal vertical plane when operating in the plowing mode s = jω is [7]   p c2 + β 2 ω 2 2 v (jω, υ0 ) = z0 k0 mtp ω , (5) (c − mtp ω2 )2 + β 2 ω2 where z0 is the amplitude of harmonic irregularity; mtp is the sprung weight of the tractor in plowing; c = 2c1 ; c1 is the front-axle and rear-axle tyre stiffness; β = 2β1 =

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√ 4ν c · mtp ; β1 is the front-axle and rear-axle tyre dissipation; ω is the irregularity rep

etition rate, ω = 2π υ lip ; υ is the MTU speed; lip is the

length of an irregularity of the plowed surface; τ is the lag of the second axle, τ = l υ; l is the interaxle distance; k0 is the axle factor which equalizes two tractor axles to a single generalized one: k0 = cos

ωl ωτ = cos . 2 2υ

(6)

For an MTU based on a Kirovets K-744R-05 tractor, assume that [7, 18–20] z0 = 0.03 m; mtp = 13,400 kg; k0 = 0.707; c1 = 1,500 kN/m; l = 3.20 m; ν = 0.1. Transfer function of oil pressure in the main oil-distributing passage (MODP) by disturbance is [7, 20] G61 (jω, υ0 ) =

km1 , 2 (T1 s + 1)(T3 s2 + 2T3 ξ2 s + 1)

(7)

where km1 is the MODP oil–pressure transmission ratio. The oil–pressure transfer function (7) adjusted for the presence of a MODP adjuster (two series-connected pneumatic hydraulic reservoirs, PHR, and a throttle) is written as [7, 20] ∗ G61 (jω, υ0 ) =

km1 (T2 s + 1)(T5 s + 1) , (T1 s + 1)(T32 s2 + 2T3 ξ2∗ s + 1)

(8)

where km1 = 1.35 MPa/N·m; T1 = 0.796 s; T2 = 0.37 s; T3 = 0.199 s; T5 = 0.131 s; ξ2 = 0.150; ξ2∗ = 0.2.  p  Substitute |U11 (jω, υ0 )| from (3), v (jω, υ0 ) from (5), and |G61 (jω, υ0 )| from (7) and (8) in (1) and (2) to find the frequency response (FR) surface states of oil consumption through burning as shown by the MTU diesel engine when plowing, see Fig. 1.

Fig. 1. K-744R-05-based MTU: FR state surfaces of oil consumption burning through as a function of travel speed at suspension stiffness c1 = 1,500 kN/m: a standard-configuration diesel engine; b adjuster-equipped MODP.

Numerical values of oil consumption through burning can be found by substituting the following source data in (1) and (2) [7, 20]: ks1 = 0.09 kg/MPa·h; ks2 = 0.45 kg/h; Vc

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= 1.875 l; ie = 8; τe = 4; a1 = 0.45; b1 = 0.97 × 10–3 ; Pmn = 0.6 MPa; Pm0 = 0, 9Pmn = 0.54 MPa; nn = 1,900 min–1 ; R = 0.8 m;Nen = 220 kW; Ie = 2.45 kg·m2 ; Men = 1,239 N·m; ηm = 0.8; Fca = 0.15 Men ; it = 63.4; a = 0.15 m; b = 3.2 m. For heavy-soil plowing, assume the following MTU operating conditions [7]: frf = 0.15; fpf = 0.60; kf = 6 × 104 N/m; ξ = 2,000 kg/m3 ; α = 3°. 2.2 MTU Diesel Engine: Oil Consumption Through Burning in Plowing The formula (2) has been used to find the oil consumption through burning for each constituent in a frequency spectrum 0 … 20 s–1 , as well as the total consumption for various suspension stiffness values c1 = 1,500; 1,200; 900 kN/m, see Figs. 2 and 3:

Fig. 2. K-744R-05-based MTU with a PUN-8–40 plow, FR of oil consumption through burning when plowing heavy soils at c1 = 1,500 kN/m and travel speed υ0 = 2.01 m/s, breakdown by constituents: a standard-configuration diesel engine, b adjuster-equipped MODP; (1) attributable to the amplitude and phase of MODP oil pressure rise lag; (4) attributable to the MTU suspension vibrations in the longitudinal vertical plane; (5) attributable to the mechanical losses in the engine; (6) total dynamic component of oil consumption.

Fig. 3. K-744R-05-based MTU with a PUN-8–40 plow, FR of oil consumption through burning when plowing heavy soils at c1 = 900 kN/m, υ0 = 2.01 m/s, breakdown by constituents: a standardconfiguration diesel engine; b adjuster-equipped MODP; other notation is as in Fig. 2.

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1. Attributable to changes in amplitude and phase lag of MODP oil pressure gain p Ccir1 (ω)

ks1 · Mna = · ωle

ω=20 

ω |G61 (jω)| d ω;

(9)

ω=0

2. Attributable to plow resistance dynamics (cutting and removal of soil layers) p Ccir2 (ω)

2ks2 RA3 · Mna = · Min it ηm ωle

ω=20 

   2  ω U11 (jω) d ω;

(10)

ω2 |U11 (jω)| d ω;

(11)

ω=0

3. Attributable to the inertial forces of the MTU p Ccir3 (ω)

ks2 RA4 · Mna = · Min it ηm ωle

ω=20  ω=0

4. attributable to the MTU suspension vibrations in the longitudinal vertical plane p Ccir4 (ω)

ks2 Rfrf Mna = · Min it ηm ωle

ω=20 

 p  ω · v (jω) d ω;

(12)

ω=0

5. Attributable to the mechanical losses in the engine friction pairs

p Ccir5 (ω)

ks2 D1 · Mna = · Min ωle

ω=20   ω=0

 a1 · |G61 (jω)| + b1 ω · |U11 (jω)| d ω . Pmn

(13)

Total oil consumption caused by dynamic loads p Ccir (ω)

Ma = n · ωle

ω=20 

  p G (jω) d ω, 41

(14)

ω=0 p

where ωle is the lowest eigenfrequency of load fluctuations; G41 (jω) is the transfer function of oil consumption through burning when plowing [7]. Table 1 summarizes the calculated integrals (9) to (14) for a plowing-mode MTU.

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Table 1. Results of calculating the oil consumption through burning of an MTU based on a K-744R-05 with a PUN-8–40 plow: heavy-soil plowing at υ0 = 2.01 m/s. p

Dynamic components Ccir (ω), g/h as a function of stiffness c1 , kN/m

Configuration of a Constituents of the dynamic YaMZ-238ND5 diesel component C p (ω), g/h at ciri engine stiffness c1 = 1,500 kN/m 1

3 4

70

1 43 27 141

133

125

With an adjuster in the 53 MODP

1 44 25 123

115

106

568

560

552

550

542

533

Standard

5

Regular component of the oil consumption through

1,500

1,200 900

427

p burning Ccir0 , g/h

Standard

Actual oil consumption through burning, g/h p

p

p

Ccira = Ccir0 + Ccir (ω) With an adjuster in the MODP

Note The second part of the dynamic component (the function of plow resistance) is not given in the table, as it is relatively small

3 Results and Discussion MTU travel speed affects the dynamic component of oil consumption through burning significantly, whether in plowing or in transport mode [7, 20]. Calculating the dynamic component of the heavy-duty oil consumption through burning shows that at constant speed, such consumption greatly depends on the amplitude and phase of MODP oil pressure gain as a function of the variable load increase and longitudinal–vertical suspension vibrations, see Table 1, within the eigenfrequency range of the diesel engine and its speed controls/fuel feeders, the oil pressure amplitude, and phase lag peak (–180°), and so does the oil consumption through burning [7, 20]. Acknowledgments. The authors hereof would like to thank Associate Professor Valery Antipin and Associate Professor Gennady Karshev for his invaluable assistance in writing the manuscript.

References 1. Zhdanovsky NS, Kovrigin AI, Shkrabak VS et al (1974) Neustanovivshiesya rezhimy porshnevykh i gazoturbinnykh dvigateley avtotraktornogo tipa (Unsteady modes of reciprocating and gas turbine engines of auto-tractor type). Mashinostroyeniye, Leningrad, p 224 2. Vernygor VA, Solonsky AS (1983) Perekhodnye rezhimy traktornykh agregatov (Transient modes of tractor units). Mashinostroyeniye, Moscow, p 183 3. Krutov VI (1978) Dvigatel vnutrennego sgoraniya kak reguliruemy obyekt (Internal combustion engine as a regulated object). Mashinostroyeniye, Moscow, p 472

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4. Antipin VP, Vlasov EN, Desyatov AN (2001) Issledovaniye energozatrat dizelnym dvigatelem lesopromyshlennogo traktora na neustanovivshichsya rezhimach (Study of energy consumption by a diesel engine of a timber tractor in unsteady modes). Dvigatelestroyeniye 2:30–33 5. Denisov AS, Nagorny VI (1980) Iznashivaniye detaley pri peremennykh rezhimach raboty (Wear of parts under variable operating conditions). Dvigatelestroyeniye 1:16–21 6. Antipin VP, Sluchenkov AM (1981) Opredeleniye chasovogo raskhoda topliva avtotraktornogo dizelya v neustanovivshemsya rezhime (Determining the hourly fuel consumption of a tractor diesel engine in an unsteady mode). Dvigatelestroyeniye 2:12–14 7. Antipin VP, Durmanov MYa, Karshev GV (2017) Proizvoditelnost, energozatraty i resurs mashinno-traktornogo agregata (Performance, energy consumption, and service life of an agricultural aggregate). Polytech Publishing House, St. Petersburg, p 484 8. Antipin VP, Shevtsov AA (1986) Kharakter vliyaniya moshnosty dvigatelya na raskhod topliva v neustanovivshemsya rezhime (The nature of the influence of engine power on fuel consumption in an unsteady mode). Dvigatelestroyeniye 10:45–46 9. Mokhnatkin EM, Besedina LT (1983) Metodicheskiye osnovy rascheta raskhoda masla na ugar (Methodological basis for calculating oil consumption through burning). Dvigatelestroyeniye 7:9–14 10. Pikman AR, Kobyakov SV (1986) O pokazatele raskhoda masla na ugar (About the indicator of oil consumption through burning). Dvigatelestroyeniye 1:5–14 11. Antipin VP, Durmanov MYa, Karshev GV, Michasenko VI (2006) Iznos dvigatelya na neustanovivshichsya nagruzochnom, skorostnom I smazochnom rezhimach (The wear of the engine during transient load, speed and lubrication regimes). Dvigatelestroyeniye 1(223):7–9 12. Deryabin AA (1974) Smazka i iznos dizeley (Lubrication and wear of diesel engines). Mashinostroyeniye, Moscow, p 184 13. Suranov GI (1982) Umensheniye iznosa avtotraktornych dvigateley pri puske (Reducing the wear of tractor engines during start-up). Kolos, Moscow, p 143 14. Denisov AS, Baskov VN (1986) Iznashevanie detaley dvigatelya na peremennych rezhimakh raboty (Wear of engine parts in variable operating modes). Dvigatelestroyeniye 1:33–38 15. Drozdov YuN, Pavlov VG, Puchkov VN (1986) Treniye i iznos v ekstremalnykh usloviyakh: Spravochnik (Friction and wear in extreme conditions). Mashinostroyeniye, Moscow, p 324 16. Anilovich VYa, Grinchenko AS, Litvinenko VL et al (1986) Prognozirovaniye nadezhnosti traktorov (Prediction of reliability of tractors). Mashinostroyeniye, Moscow, p 274 17. Moore D.F. (1997) Principles and Applications of Tribology. Pergamon Press 18. Durmanov MY, Martynov BG, Spiridonov SV (2019) Energy and Fuel Consumption of Agricultural Aggregate. In: Radionov A, Kravchenko O, Guzeev V, Rozhdestvenskiy Y (eds) Proceedings of the 4th International Conference on Industrial Engineering. ICIE 2018. Lecture Notes in Mechanical Engineering. Springer, Cham, pp 1601–1612. https://doi.org/10.1007/ 978-3-319-95630-5_171 19. Durmanov MYa, Martynov BG, Spiridonov SV (2020) How Parameters of Agricultural Machine and Tractor Unit Affects Effectively Used Mean Indicated Power. In: Radionov A, Kravchenko O, Guzeev V, Rozhdestvenskiy Y (eds) Proceedings of the 5th international conference on industrial engineering. ICIE 2019. Lecture Notes in Mechanical Engineering. Springer, vol II, pp 299–312. https://doi.org/10.1007/978-3-030-22063-1_33 20. Antipin VP, Durmanov MYa, Mikhailov OA (2020) Method to Reduce Oil Burningin Diesel Engine of Agricultural Machine and Tractor Unit. In: Radionov A, Kravchenko O, Guzeev V, Rozhdestvenskiy Y (eds) Proceedings of the 5th international conference on industrial engineering. ICIE 2019. Lecture Notes in Mechanical Engineering. Springer, vol II, pp 313– 323. https://doi.org/10.1007/978-3-030-22063-1_34

Modeling of Turbine Rotor Journal Machining with Location on Bearing and with Center Pregrinding A. V. Shchurova(B) South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, Russia [email protected]

Abstract. Restoration of worn turbine rotor journal without removing it from a power unit is carried out with location on cylindrical plain bearing bottom half. Thus, the workpiece is located on the machinable surface. Such location causes difficulties in the required cylindrical accuracy guaranteeing. Our earlier studies have shown that reduction of circularity deviations to zero cannot be obtained using this locating method. Since the rotor journal has a center hole on its face plane, it has been hypothesized that restoring machining can be improved using a preparatory machining with partial location on this hole. Preparatory machining can be performed with the aid of additional device. This device should be held up by the rotor journal on the center hole on the one side and on the cylindrical surface on the other side. It is clear that complete highly efficient machining is not realizable in consideration of sizes of locating device and location accuracy. Therefore, after the proposed preparatory machining, the finish machining with location on bearing bottom half has to be performed. The present study demonstrates that in cases of initial ellipse and three-lobed surface of primary part the accuracy of machined shaft journal has not been significantly increased, although there is some minimum of the resulting circularity deviation under certain machining parameters. Keywords: Turbine restoration · Rotor journal · Location on journal · Location on bearing · Centerless grinding · Circularity deviation · Voxel modeling · 3D modeling

1 Introduction As known, during normal operational life of a turbine, its rotor damage may arise due to several factors such as steam erosion, rotor rubbing, etc. [1, 2]. Wear of rotor journals seating surfaces is often the case that generates increased vibration and stops of the equipment. In this case, repair operations, including turning, milling, and grinding of such seating surfaces on the mounting bearing, are carried out.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_26

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In view of rotor large size and weight, one of the most economical ways of its journal restoration is to machine it without removing from the power unit [3, 4]. In this case, the upper half of the plain bearing is removed and the opened upper journal half is machined. Mobile machining device is installed on the half-plane of the unit, and the journal is machined due to the radial feed of a tool, rotating abrasive tool, for example [5]. At the same time, turbine rotor is rotated around its axis with location of its machinable journals on the bottom bearing half. Since the worn journal has irregularities, rotation with the location on its surface results in constant displacement of the rotor shaft axis along different directions. All this causes difficulties in ensuring the required circularity deviations [6–12]. Our previous studies have shown that using this machining method reduction of resulting circularity deviations to zero has not been obtained under any combination of cutting data or other conditions [13–16]. For that matter, it has been hypothesized that the accuracy of shaft journal machining with location on plane bearing can be increased by premachining of worn journal lobes. In this case, machining can be performed using hand scraping, which is quite frequently used in practice [17, 18]. It is for this reason that machining with location on center is the obvious way to obtain the required accuracy. A large number of turbine shafts have face planes with center holes close enough to their rotor journals. Thus, the following machining method can be used. It is necessary to prepare an additional device with movable cutting tool head. This device should be located on the center hole on one side. The other side of the device can be located on a cylindrical surface adjacent to the rotor journal, in case if such surface exists and is accessible for locating (Fig. 1). Shaft journal surfaces are used as locating surfaces in many cases [19, 20].

Fig. 1. a Turbine rotor; b model of a rotor in a bearing with preparatory machining device (1) and finish machining device (2).

It is clear that primary machining of locating cylindrical surface on centers during the same operation as journal surface grinding itself is the most appropriate solution. This method would minimize the run-out of these two surfaces relative to each other. However, such conditions are rather an exception to the rules. Therefore, the proposed method is likely an ideal solution. In reality, locating cylindrical surface has a run-out relative to the journal. In such a case, device location systematic error–displacement of device rotation center relative to the original shaft journal axis is generated. In addition, there is one more disadvantage. Longitudinal sizes of the proposed preparatory machining device should be great. Consequently, device lateral rigidity is low. Holding of non-rigid device in a vertical position without additional rigid supports on the turbine casing results

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in the absence of machining rigidity as a whole. Therefore, the proposed additional device cannot be used for final machining, since machining errors are unavoidable. So, this device should be used for preparatory machining. It is proposed to perform final machining using traditional stationary device rigidly fixed on the turbine casing with common location on its bearing [5]. Thus, the objective of this research stage is to test the advanced hypothesis that it is possible to increase rotor journal machining accuracy without its removal from the turbine casing by preparatory journal machining using a special device. This device should be located on the rotor center hole on one side, and on the other side on the cylindrical surface adjacent to the journal.

2 Modeling of Preparatory Machining of Rotor Journal with Location on the Center Hole and on the Adjacent Cylindrical Surface Modeling of preparatory machining of rotor journal with location on the center hole and on the adjacent cylindrical surface can be structured in two stages. At the first stage, it can be assumed that locating cylindrical surface has no run-out relative to the original journal axis. Mathematical relations to calculate a point cloud of rotor journal surface with various types of harmonic deviations were presented in the previous publication [16]. The resulting values of worn journal surface points radius vectors and point coordinates are determined as follows. The total cylindricity deviation R(ϕi , zi ) of the journal surface is calculated by the superposition [16]: R(ϕi , zi ) = R(ϕi ) + R(zi ),

(1)

where R(ϕi )– the deviations in the radial section (depending on polar angle ϕi ); R(zi ) –the deviations in the axial section and the helical shape of such deviations (depending on the applicate zi ). Then the coordinates of the journal surface points can be determined by the following formulas [16]: xi (±i ) = [Ri max (ϕi ) + R(ϕi , zi )] cos(ϕi );

(2)

yi (ϕi ) = [Ri max (ϕi ) + R(ϕi , zi )] sin(ϕi ),

(3)

where Ri max (ϕi )– the radius of the middle cylinder of the journal. If necessary, it is possible to represent it as a function of the polar angle, additionally. The following additional relations are used to model preparatory machining with location on the center. Workpiece radius Rmax in preparatory machining of journal surface lobes using the proposed locating device is calculated as Rmax = max{Ri max (ϕi ) + R(ϕi , zi )} − Rp ,

(4)

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where Rp – radial value of journal surface lobe cutting off in preparatory machining.  If (xi (ϕi ))2 + (yi (ϕi ))2 ≥ Rmax , than xi (ϕi ) = Rmax cos(ϕi ) and yi (ϕi ) = Rmax sin(ϕi ). (5) In case of additional displacement of tool-holding device for the reason of the runout of the locating cylindrical surface, the direction of such displacement should be specified. This direction can be determined by measuring the run-out of the stated cylindrical surface relative to the center hole. If the run-out vector direction is determined by φc – the angle to the X-axis and the run-out Dc , then the calculation is performed according to the following formulas: xi (ϕi ) = 0.5Dc cos(ϕc ) + Rmax cos(ϕi ) and yi (ϕi ) = 0.5Dc sin(ϕc ) + Rmax sin(ϕi ). (6) Apparently, the worst case should be expected if the worn journal surface is an elliptical cylinder, if ϕc = 0 and the major axis of the ellipse has the same angle. This situation will be further considered in the practical modeling. The other calculation formulas for the shaft journal resulting profile during machining with location on the machinable surface have been published by the author earlier [13– 16].

3 Computer Modeling of Preparatory Machining of the Shaft Journal with Location on the Center Hole and on the Adjacent Cylindrical Surface and of Following Machining with Location on the Machinable Surface For better understanding of the changes in the case of shaft journal premachining, the examples of calculated journal point clouds after premachining and without premachining are shown in Fig. 2. Shaft journal parameters are as follows: average journal radius R = 150 mm; journal length Lz = 400 mm. Surface circularity deviations are tenfold increased for greater visibility. In the present case, radius deviation from the circle in the radial section is rϕ = 3 mm. The number of journal profile peaks in radial section is ωϕ = 3. The deviation from the straight line—the element of the cylinder in its axial section—is rz = 2 mm. The number of peaks on the specified line within the journal length is ωz = 5. The deviation from the straight line—the element of the cylinder along its axis caused by rotation of the considered surface point along a helical line— is rzϕ = 1 mm. The number of peaks on the specified helical line within the journal length is ωzϕ = 5. The amount of metal removed along the radius beyond the maximum diametrical journal size is 3 mm. As can be seen in Fig. 2 (marked by ovals) after premachining, surface peaks are deleted. This enables us to state and, accordingly, to propose a hypothesis that the location of the shaft on this pre-machined surface is more stable and should result in better machining accuracy. Further, to test the hypothesis and to ensure results comparability, results of machining modeling with location on machinable surface in the absence of preparatory machining are presented. The results of machining modeling with premachining using location

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on the center hole if Rp = 0.3 mm and next the results of modeling with the same premachining if an offset with respect to offset from the center is equal to 0.2 mm are presented. Machining of the shaft journal with average radius R = 150 mm, amplitude of deviation from the average value rϕ = 0.3 mm, the number of peaks ωϕ = 2 for the first case and ωϕ = 3 for the second case was modeled as an example. Surface shape of the worn journal is considered to belong to the class of non-circular cylindrical surfaces. As presented in previous studies, the best installation angle of the tool—the angle between the vertical axis and the axis of the abrasive wheel— is ψ = 42◦ , and the number of workpiece revolutions is n = 10. The calculation results are shown in Fig. 3.

Fig. 2. a Shaft journal without preparatory machining; b pre-machined journal; c roundness chart.

The charts reflect the circularity deviation R in relation to the total displacement of abrasive tool along the workpiece radius Sm. In these charts, solid blue line corresponds to computer modeling results and dashed red line corresponds to the approximating second-order polynomial. Charts (a), (b), (c) correspond to rotor journals with two initial peaks and charts (d), (e), (f) to rotor journal with three initial peaks. Charts (a) and (d) correspond to machining without premachining; charts (b), (e)—to machining with premachining with location on the center hole for total tool displacement Sm = 0.3 mm; (c), (f) —to similar premachining with the axis run-out from the center hole equal to 0.2 mm. The roundness chart of the cross section of the surface pre-machined with location on the center hole and finally machined with location on the machined surface for Sm = 1 mm is shown in Fig. 2c. As can be seen in the charts, for the absence of preparatory machining total tool displacement to the workpiece axis increase from 0.5 to 1.0 mm results in circularity deviation decrease from the initial value of 0.6 mm to 0.3 mm—for the case of journal with two peaks (a) and to 0.5 mm—for the case of journal with three peaks (d). Further increased tool displacement results in deviation increase. In the case of preparatory machining with location on workpiece center hole, similar tool displacements merely increase the circularity deviation from the initial value of 0.3 mm to 0.7 mm. In the case of machining with surfaces run-out, the deviations from the initial value also increase. Thus, the calculations show that preparatory machining does not provide improvement of shaft journal accuracy. Hypothesis testing necessitated the calculation of R deviations depending on the number of workpiece revolutions n for optimal parameters: total tool displacement Sm = 1.0 mm and the tool installation angle ψ = 42◦ . Calculation results are shown

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Fig. 3. Machining accuracy depending on tool displacement: a, b, c—journal with two and d, e, f—with three peaks along its surface.

in Fig. 4. Modeling results depending on angle ψ for constant n = 10 and Sm = 1.0 are shown in Fig. 5. As can be seen in the charts of Fig. 4, for the absence of journal premachining circularity deviation R (a) and (d) is increased for both workpiece types during approximately ten revolutions and then increases again. Premachining on the center hole (b) and (e) practically does not change circularity deviation (within 0.1 mm). Premachining with the axis run-out from the center hole (c) and (f) results in circularity deviation increase with an increase in the number of revolutions. Thus, these calculations show that premachining increases inaccuracy of journal surface. As can be seen in the charts of Fig. 5, for the absence of premachining circularity deviation R is reduced up to tool installation angle equal to 40°, and then is increased again. Premachining on the center hole only increases the deviation for large tool installation angles. Thus, these calculations also show that premachining does not increase the accuracy of journal surface. Therefore, the hypothesis put forward has not been confirmed.

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Fig. 4. Machining accuracy depending on number of workpiece revolutions: a, b, c—journal with two and d, e, f—with three peaks along its surface.

Fig. 5. Machining accuracy depending on tool installation angle: a, b, c—journal with two and d, e, f—with three peaks along its surface.

4 Conclusions The results of modeling show that the hypothesis about reducing surface circularity deviation by preparatory machining of worn turbine rotor journal and finish grinding with location on turbine plant bearing bottom has not been confirmed. Neither the location of the preparatory machining device on the center hole or certain device run-out due to location on the cylindrical surface adjacent to the rotor journal has increased machining

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accuracy. Thus, it is necessary to search for other methods for increasing the accuracy of journal machining with location on its machinable surface on the bearing of the turbine plant.

References 1. Mobile Lathe Information Sheet (2008) Alstom, France, Saint-Queen: 3P 2. Bloch HP, Geitner FK (2005) Machinery component maintenance and repair: practical machinery management for process plants. Elsevier Inc., USA, p 630 3. Orbital Tool Technologies. Shaft and Journal Repair (2012) USA, p 2 4. Portable machine tools. Solutions for all in situ site machining applications (2011) Acteon, Derby, UK, p 13 5. Molochek V (1968) Remont parovyh turbin (Steam turbine repair). Energy, Moscow, p 376 6. Brian RW (2009) Principles of modern grinding technology. William Andrew, USA, p 416 7. Kang K (2003) Modelling of the centrless infeed (Plunge) grinding process. KSME Int J 17(7):1026–1035 8. Wu Y, Kondo T, Kato M (2005) A new centerless grinding technique using a surface grinder. J Mater Process Technol 162–163:709–717 9. Xu W, Wu Y, Sato T, Lin W (2010) Effects of process parameters on workpiece roundness in tangential-feed centerless grinding using a surface grinder. J Mater Process Technol 210:759– 766 10. Xu W, Wu Y (2011a) A new in-feed centerless grinding technique using a surface grinder. J Mater Process Technol 211:141–149 11. Xu W, Wu Y (2011b) A new through-feed centerless grinding technique using a surface grinder. J Mater Process Technol 211:1599–1605 12. Weixing X, Yongbo Wu (2012) Simulation investigation of through-feed centerless grinding process performed on a surface grinder. J Mater Process Technol 212:927–935 13. Shchurova AV (2017) Modeling the turbine rotor journal restoration located on cylindrical surface of the supporting bearer. Procedia Eng 206:1142–1147 14. Shchurova AV (2017) Izmenenie polozheniya osi vala pri ego shlifovanii s bazirovaniem v polucilindricheskoj opore (Axis relocation of a grinded shaft that is located on hemicylindrical bearing seat). Bulletin of Tula State University, Ser. Tech Sci 8(1):338–344 15. Shchurova AV (2018) Effect of the tool-operating mode on circularity deviation in multilobed turbine rotor journal restoration with location on a bearing bottom half. Lecture Notes in Mechanical Engineering, Proceedings of the 4th International Conference on Industrial Engineering -ICIE 2018, pp 1613–1620 16. Shchurova AV (2020) 3D modeling of turbine rotor journal machining with location on a bearing bottom half. In: Proceedings of the 5th international conference on industrial engineering (ICIE 2019). ICIE 2019. Lecture Notes in Mechanical Engineering. Springer, pp 191–198. https://doi.org/10.1007/978-3-030-22063-1_21 17. Electronic Scraper and accessories (2008) CH BIAX Maschinen GmbH.: Catalog, p 16 18. Grinders, files and deburring tools. Pneumatic tools for professionals (2013) Schmid & Wezel GmbH & Co. Maschinenfabrik: Catalog, p 17 19. Mobil’nye tekhnologii v energetike (Mobile technologies in the energy sector) (2019) Mobil’nye tekhnologii, Vladivostok, p 9 20. Portable On-Site Machining Solutions for Large Flange Machining. CM6200 milling machine (2013) Climax, p 10

Industrial Manipulating Robot Finite Element Mesh Generation Based on Robot Voxel Model E. I. Shchurova(B) South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, Russia [email protected]

Abstract. Industrial robots are increasingly being used as a substitute for multiaxis metal-cutting machines in complex workpiece machining. However, there is a problem with robots’ low rigidity compared to cutting machines. For this reason, robots machining accuracy is still insufficient. Many of the studies explore the estimation of robot links strains to make appropriate corrections of their control software. The finite element method is the most relevant method for strain calculation. However, detailed workpiece CAD models describing all the design features use extremely large number of finite elements. This is a fact that limits application of finite element method by manufacturing engineers. Thus, not only manufacturing engineers but also robot developers find it too difficult to calculate the rigidity using such models. Therefore, there is a problem to modify manufacturing robot control data considering robot strains. In the short and medium terms, this problem can be solved only by using an innovative approach. An application of the robot finite element model, based on its voxel model, is proposed as such an approach. In this case, the voxel model itself is developed using exact robot CAD models developed by manufacturing companies. These voxel and finite element models do not contain specific features of robot design. These models are opensource data and can be distributed from developers to engineers to be used in CAM systems when developing control data for workpiece processing. This approach is illustrated by modeling a four-link industrial manipulating robot. Generated mesh includes 480,000 finite elements and makes it possible to calculate displacements of the robot end effectors during machining process and to consider these displacements in control software developing using CAM system. Keywords: Manipulating industrial robot · Finite element model · Voxel model · Computer-aided manufacturing · Control software · Deviation calculation · Machining accuracy

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_27

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1 Introduction Most of the workpieces with complex surface shape are machined using computerized equipment, for example, metal-cutting CNC machines. The units of these machines are highly rigid and thus provide high machining accuracy. Sizes of the machines correspond to sizes of the workpieces. Large-sized machines are required to cut large workpieces. This fact results in high cost of equipment and production. Currently, industrial manipulating robots controlled by computers are increasingly used instead of machine tools [1–3]. Robots are lightweight and have lower price, and their working zone is rather large. However, robots have a disadvantage. Their rigidity is not high. This fact causes large strains of robot units and substantial end-effector displacements from the desired position [4, 5]. Therefore, manipulating robot machining accuracy is much less than metal-cutting machines accuracy. For this reason, extensive use of robots for multi-axis processing of large-sized workpieces is limited [6]. Many solutions are currently proposed to overcome this drawback. In particular, it is offered to use force sensors installed on robot units and to control electric current in engines [7]. However, robot drives accuracy characteristics and data processing speed does not guarantee to adjust robot positioning during the machining effectively. The ability to control robot end-effector positioning by installing spherical probes on it and by using laser interferometer is widely studied [8–10]. Using these probes true position of end effectors at each moment of machining can be determined. This information is used by the robot control system for additional impact on robot drives. Thus, robot end-effector actual position during machining can be corrected. Such correction system seems to be effective. However, low performance of signal processing and of modern computers still does not ensure the required location of robot end effector in the workpiece coordinate system. Another way to solve this problem is a preliminary calculation of robot strains for each moment during machining. This calculation results in control software modification considering robot possible strains before the machining is started. Thus, machining accuracy is guaranteed. Since the calculations are performed before the start of machining, considerable time can be consumed for them. Consequently, the necessary calculations accuracy is provided. In this regard, this approach also can be considered to apply. However, this method has significant drawbacks. Accurate data on robot rigidity and on displacements of its end-effector body cannot be obtained by calculation. In this regard, the empirical determination of displacements using laser interferometers is widely used [11–14]. Combined offline and online methods are often proposed to apply [11, 12]. Some attempts have been made to determine robot rigidity using various load tests [15, 16]. Several studies continue to use analytical calculations of robot rigidity [17]. However, rigidity calculation using the finite element method is considered as the most promising method [18–20]. It is necessary to get robot CAD model and then to develop CAE model on its basis for such calculation. Existing robots are quite complex devices and have thousands of parts of large and small sizes. Surface shape of these parts may be both simple and complex. Complex surface shape requires finite element mesh thickening in small areas. Thus, CAE models developed on the basis of CAD models include tens of millions of finite elements. An extremely large amount of finite elements makes it impossible to calculate robot rigidity either by robot developers themselves or,

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moreover, by manufacturing engineers who use CAM systems. Thus, this approach is not widely applied in practice. In connection with the above analysis, the problem of accuracy increasing of multiaxis workpiece machining using industrial manipulating robots is an urgent need. The aim of this research is to solve the problem by calculating robot strains before the machining is started and by modifying control software in advance. Robot strain calculation method suitable for modern CAM systems on the basis of finite element model including relatively small number of elements is proposed. This method is based on the voxel approach. Thus, the main purpose of this study is to increase the accuracy of machining with industrial manipulating robots based on preliminary calculation of robot strains by developing small-sized finite element models using the voxel approach.

2 Methodology of Developing Small-Sized Finite Element Model This study proposes to generate finite element mesh of robot using its voxel model. In that case, each voxel (e.g., shaped like a cube) is next converted into a finite element. Therefore, it is necessary to develop voxel mesh of the entire robot in its current position in specified coordinate system during workpiece machining. Voxel mesh spacing should be equal to expected finite element size. Mesh spacing should be sufficiently large; otherwise, the number of robot voxels and therefore finite elements number may exceed certain limit value. Thus, robot strain calculation using CAE system may be almost impossible. It is necessary to decrease mesh spacing and consequently finite element size to describe robot features adequately. This is the reason to use a large number of voxels. So there is a contradiction between limiting the number of voxels for the CAM system efficiency and necessity to use a large number of voxels to ensure the model adequacy. This contradiction cannot be solved without a reasonable compromise. A large number of parts in assemblies are another specific aspect of modeling mechanical systems such as robots. Some parts are fixed to each other, for example, using thread connections or rivets. The others have flexible joints, e.g., rolling-contact or sliding bearing joints, as well as serrated and spline joints. Ideally, all the joints in the finite element model should be described using contact pairs. However, it is clear that calculations of these pairs result in nonlinear problem formulation, and thus calculation time is increased. Therefore, firstly it can be stated that all assembly units with fixed joints have to be replaced by equivalent single parts. These parts will occupy the same space as parts of the substituted assembly. The second statement is that all assembly parts with flexible joints have to be replaced by their equivalent parts. This statement is reasonable since contact pairs of parts are rigidly connected by the forces acting on them during the machining process. Joint surfaces are in the close contact. Thus, it can be considered that flexible joints are almost the same as the fixed joints at this point. In view of this, the second assumption can be considered as correct, to some extent, as well as the first one. Hence, all flexible and fixed joints should be replaced by rigid ties. In this way, the robot as a whole can be replaced with one single part. Rigidity of this equivalent part is higher than the rigidity of a real robot. It is planned to compare the stiffness obtained from real robot experimental data with the stiffness of the equivalent part in further

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research. The appropriate correction factors should be used in CAM calculations. These correcting factors will represent both the number of flexible joints and their quality, e.g., actual clearance sizes, wear of flexible joints, and influence of grease. Mandatory regular robot calibrating procedure can be implemented once per month for this purpose, for example, procedure of stiffness determination in several typical positions of robot elements. The statements specified above are necessary but not sufficient. Voxel mesh regularity raises a problem. All the voxels should be located in space in a certain way. However, robot elements and parts are generally arranged in an arbitrary manner during machining. This results in mismatch of the voxel mesh node positions and the part surfaces. Voxel mesh nodes can be placed above or below part surfaces, unlike the finite element model nodes which are located on these surfaces using mesh generators. Similar results can be observed when using the finite difference method or the SPH method, for example. Voxel or finite difference geometric model approximations are improved by using smaller mesh spacing. Ideally, the misalignment between mesh nodes and part surfaces should not exceed surface roughness texture heights. However, such texture has sizes of sub-micrometers to sub-millimeters. If robot dimensions are equal to 500 by 500 by 500 mm and voxel size is equal to 1 mm then the mesh will contain 125 million nodes. Consequently, the finite element model will contain the same number of nodes. This model size is not realizable for existing CAM systems. Robot occupies only a part of the described cube with specified dimensions, but the number of robot model nodes is decreased by one or two orders of magnitude only. Therefore, CAD model approximation using voxel model is hardly possible if voxel size is less than 1 mm. Industrial robots consist of various elements, for example, large gears and shafts, and at the same time thin-walled elements such as casings or covers. The latter may have a thickness of about 1 mm. Approximation of these elements using voxel mesh with 1 mm spacing may be unrealizable. Moreover, elements with thinner walls can create gaps in voxel models with such spacing. Therefore, stiffness of some elements can be overestimated, and stiffness of other elements can be underestimated. The superposition of these estimates in general can provide rigidity evaluation adequate to the real construction. Adjustment of this model can be performed using correcting factors according to the same principles of comparison with a real robot. Thus, the third statement to introduce is the approximation of all equivalent robot parts using voxel and corresponding finite element mesh with spacing about 1 mm. This can result in both upward and downward differences of approximating model from approximated model. It is necessary to use robot CAD model in the current position during machining to generate voxel nodes of the equivalent robot part. It is obvious that the developer of the robot is the owner of this model. Therefore, robot model is not an open-source data. So, only developers can generate voxel mesh of equivalent robot part. The equations to determine voxel belonging to the body of equivalent part are xmin ≤ xi ≤ xmax ∪ ymin ≤ yi ≤ ymax ∪ zmin ≤ zi ≤ zmax ,

(1)

xmin = min{ x (yi , zi )}, xmax = max{ x (yi , zi )},

(2)

ymin = min{ y (xi , zi )}, ymax = max{ y (xi , zi )},

(3)

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zmin = min{ z (xi , yi )}, zmax = max{ z (xi , yi )},

(4)

where xi xi , yi yi , and zi zi are the coordinates of each ii voxel of the voxel mesh; x(yi , zi ) x(yi , zi ), y(xi , zi ) y(xi , zi ), and z(xi , yi ) z(xi , yi ) are CAD model surface point coordinates for corresponding voxel node coordinates. min i max means: for xx, respectively, at the left and at the right; for yy, respectively, at the front and at the back; for zz, respectively, at the bottom and at the top for each segment inside the robot. These segments should belong to the straight lines which are parallel to the coordinate axes and pass through the node of the concerned voxel with coordinates (xi xi , yi yi , zi zi ). The well-known relations are used to fill the entire robot body with voxels: xi = xmin + x, yi = ymin + y, zi ≤ zmin + z,

(5)

where xx, yy, and zz are the mesh spacings. Nodes and elements of robot finite element model are determined after calculation of the robot equivalent part voxel mesh coordinates. Considering the constancy of element sizes and the parallelism of element boundaries to the coordinate axes, less computationally expensive finite difference method can be used.

3 Development of Voxel and Finite Element Models of Industrial Manipulating Robot Equivalent Part CAD model of the industrial manipulating robot has been used as an example [21]. The voxel model has been developed on the basis of the method described above (Fig. 1). Model voxels have been further transformed into finite elements. In this way, the finite element mesh of the equivalent robot part has been generated. The model includes 480 thousand nodes. Strains caused by the force applied to robot end effector are calculated using this model in order to check the finite element model integrity and absence of mesh errors (Fig. 2). As shown in the figure, a number of robot links in the CAD model, for example, electric motors, are modeled as solid parts. Moreover, it can be seen that smooth surfaces of the CAD model are represented by stepped surfaces in the finite element model (Fig. 2, right). All of this will result in errors in rigidity calculations. These errors have to be adjusted by correcting factors obtained experimentally. In general, as the calculation results show, the proposed approach has proved to be realistic and can be used to correct the control software obtained by CAM system. The presented solution has its own disadvantages. In particular, robot links constantly change their relative position during the process of workpiece machining. Calculation for each link position in the equivalent CAD model and corresponding voxel and finite element meshes is problematic. This circumstance relates to the keeping secret of robot data detail problem. In this regard, there are two possible problem solutions. The first way is related to providing information about robots’ equivalent parts and their connection conditions by developers. Based on this, voxel and finite element meshes with conditions of robot links’ mobility relative to each other can be further generated. The second

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way is related to the fact that robot developers provide information about robot links’ voxel meshes and their joints’ meshes only. The latter case appears to be more realistic. Therefore, possible solutions for it are further considered.

Fig. 1. CAD model of the manipulating robot (some covers are removed) [21] and robot voxel model.

Fig. 2. Strain calculation based on CAE model of the manipulating robot, strains in the robot links sections on the right.

Voxel meshes in a Cartesian coordinate system include nodes located on the lines parallel to the coordinate axes. When one part of the mesh is rotated relative to the other, mesh nodes’ position excludes correct nodes merge. In this regard, it is proposed to use specific meshes for all joint types that are used in robotics. Representative volume elements’ structures within the voxel model can be used. Examples of such meshes are shown in Fig. 3. As seen in the figure, mesh nodes are merged upon the shaft rotation to every 10°. Spherical and retractable (prismatic) joints are modeled in a similar way. In the latter case, displacement step is equal to the mesh spacing. The shaft rotation angle also has to be discrete. The angular step of this rotation is approximately equal to the value of φ = x/Rφ = x/R rad. In order to reduce the angular step, it is necessary to reduce voxel mesh spacing, which is generally unacceptable. However, robot rigidity in the specified link position does not change significantly if link angles of rotation and displacements are limited. Therefore, it is useful to calculate rigidity in the intervals of rotation and displacement. Further, this data has to be used for the control software correction.

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Fig. 3. Finite element meshes changing upon rotation of the shaft to every 10° and at moving to the right.

4 Conclusions The proposed methodology to develop small-sized finite element models of industrial manipulating robots provides the opportunity to calculate robot strains caused by cutting forces during workpiece machining. Finite element mesh generation using voxel model of the robot equivalent part is the basis for both further obtaining adequate simulation results and for protection of robot developers’ technical secrets. Mesh spacing constancy is the basis for calculations using the finite difference method, which is more computationally efficient. It is necessary to use voxel domain structures corresponding to all types of joints used in robotics to perform calculations considering displacements of robot links. The present methodology does not provide accurate consideration of some strain calculations features; however, it can be improved by calibration finite element models using experimental data periodically.

References 1. Pandremenos J, Doukas C, Stavropoulos P, Chryssolouris G (2011) Machining with robots: a critical review. Proceedings of DET2011. 7th international conference on digital enterprise technology. Athens, Greece, pp 1–8 2. Aliev R, Guseynov R (2011) Milling robots—technical state view. Autom Modern Technol 11:11–18 3. Moler D-IC, Schmidt HS, Koch P (2017) Machining of large scaled CFRP-parts with mobile CNC-based robotic system in aerospace industry. Procedia Manuf 14:17–194 4. Kuka KR 3 R540. Technical data. 0000–270–971/V16.3/05.09.2018/en 5. Sirinterlikci A, Tiryakioglu M, Bird A, Harris A, Kweder K (2009) Repeatability and accuracy of an industrial robot: laboratory experience for a design of experiments course. Technol Interf J 9(2):1–10 6. Liu S, Liao W, Tian W et al (2017) The problem in accuracy compensation of industrial robot. Int Rob Auto J 3(2):282–283. https://doi.org/10.15406/iratj.2017.03.00050 7. Nemec B, Žlajpah L (1994) Force control of an industrial robot with adaptive compensation of the environment stiffness. Informatica (Ljubljana) 18(1):81–91 8. Morozov M et al (2016) Assessing the accuracy of industrial robots through metrology for the enhancement of automated non-destructive testing. IEEE international conference on multisensor fusion and integration for intelligent systems (MFI), Baden-Baden, pp 335–340. https://doi.org/10.1109/MFI.2016.7849510 9. Slamani M, Nubiola A, Bonev I (2012) Assessment of the positioning performance of an industrial robot. Ind Robot 39(1):57–68. https://doi.org/10.1108/01439911211192501

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10. Semyonov EN, Sidorova AV, Pashkov AE, Belomestnykh AS (2016) Accuracy assessment of KUKA KR210 R2700 extra industrial robot. Int J Eng Technol 16:19–25 11. Yuan L, Pan Z, Ding D, Sun S, Li W (2018) A review on chatter in robotic machining process regarding both regenerative and mode coupling mechanism. IEEE/ASME Trans Mechatron 23(5):2240–2251. https://doi.org/10.1109/TMECH.2018.2864652 12. Schneider U, Drust M, Ansaloni M et al (2016) Improving robotic machining accuracy through experimental error investigation and modular compensation. Int J Adv Manuf Technol 85:3– 15. https://doi.org/10.1007/s00170-014-6021-2 13. Kamali K, Joubair A, Bonev IA and Bigras P (2016) Elasto-geometrical calibration of an industrial robot under multidirectional external loads using a laser tracker. IEEE international conference on robotics and automation (ICRA), Stockholm, pp 4320–4327. https://doi.org/ 10.1109/ICRA.2016.7487630 14. Józwik J, Ostrowski D, Jarosz P, Mika D (2016) Industrial robot repeatability testing with high speed camera phantom V2511. Adv Sci Technol Res J 10(32):86–96. https://doi.org/10. 12913/22998624/65136 15. Olabi A, Damak M, Bearee R, Gibaru O and Leleu S (2012) Improving the accuracy of industrial robots by offline compensation of joints errors. 2012 IEEE international conference on industrial technology, Athens, pp 492–497. https://doi.org/10.1109/ICIT.2012.6209986 16. Zhang H, Pan Z (2009) Improving robotic machining accuracy by real-time compensation. ICCAS-SICE international joint conference, IEEE, USA, pp 4289–4294 17. Östring M, Gunnarsson S, Norrlof M (2003) Closed loop identification of an industrial robot containing flxibilitie. Contr Eng Pract 11(3):291–300. https://doi.org/10.1016/S09670661(02)00114-4 18. Prabhu N, Anand MD, Ruban LE (2014) Structural analysis of Scorbot-ER Vu plus industrial robot manipulator. Prod Manuf Res 2(1):309–325. https://doi.org/10.1080/21693277.2014. 907533 19. Zhang J, Cai J (2013) Error analysis and compensation method of 6-axis industrial robot. Int J Smart Sens Intell Syst 6(4):1383–1399. https://doi.org/10.21307/ijssis-2017-595 20. Pup˘az˘a C, Constantın G, Negrıl˘a S, (2014) Computer aided engineering of industrial robots. Proc MS 9(2):87–92 21. Cherchelanov E (2019) 5-axis industrial robot drawing. 3D model. https://www.izhaotuzhi. com/product/view157.html. Accessed 01 May 2019

Axis Determination Based on Regression for Calculation of Virtual Pitch Thread Diameter Using a Point Cloud from CMM I. A. Shchurov(B) South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, Russia [email protected]

Abstract. Thread gauges are widely used to obtain the values of complex parameters of thread surfaces. The virtual pitch thread diameter (VPTD) is the main standard complex thread accuracy figure. In practice, limit gauges are still applied to determine the value of this parameter. Despite the extensive use of coordinate measuring machines (CMMs), such machines have not replaced limit gauges for thread control still. One of the problems faced in thread control using CMM is the accurate determination of thread longitudinal axis. Earlier, the author has published studies aimed at determining thread axis based on the average values of the coordinates of point clouds for the starting and ending thread areas. The presented paper considers another approach to determine thread axis—the application of regression. The research results show that the case if the thread axis is the straightline regression provides better results for small angles of axis rotation relative to the CMM coordinate system. However, if axis angular deviations increase, the previous method of axis determination is preferable. The paper presents research results for the cases that thread axis is a circle arc or a sine wave. In addition, the case that thread axis is a curved line in three dimensions is considered. Both axis determination methods have certain advantages in specific cases. Keywords: Virtual pitch thread diameter · Coordinate measuring machine · Point cloud · Thread axis location · Regression

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_28

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1 Introduction Thread surfaces are widely used for the assembling of various components. The thread accuracy frequently has to be high. In drawing annotation, this condition is set up by the tolerance grade. According to the standards GOST 16093–2004 or ISO 965–1998 thread accuracy is determined by the tolerances of pitch diameters. According to the standard GOST 11708–82, tolerances of such diameter are determined by virtual pitch thread diameter (VPTD—p. 5.11 of ISO 5408:209), and simple pitch one simultaneously. Obviously, VPTD is more complex characteristic and is the limiting factor. Thus, in practice, thread accuracy estimation is usually executed by measuring its VPTD. In practice, limit gauges are still applied to control threads [1, 2]. In case of special thread control, special gauges have to be produced. This fact significantly increases the product cost, especially in the context of small-scale production [3]. This problem can be solved using coordinate measuring machines (CMM). However, the software of existing CMMs still does not include procedures to calculate VPTD [4– 6]. Thus, general methodology for the determination of VPTD using thread point cloud has not been developed by now. Most of the research is focused on the determination of simple pitch diameter. A number of studies have been devoted to determine this diameter using point sets of thread axial sections [7–14]. Obtaining sufficiently large number of thread surface points is one of the problems in thread measuring. A growing number of studies focus on optical measuring equipment [15–17]. However, these studies do not consider VPTD calculation either. The previously published method [18] makes it possible to determine VPTD for the case if the axis of the measured thread is precisely determined. However, the thread axis is an ideal concept. An arbitrary thread radial section has no fixed center point, as, for example, any circle has. A thread, as a helical surface, has the center of gravity of its radial section only. Determination of such an averaged thread characteristic along the length of starting and ending thread areas has been used in the previously published study [19]. This methodology, obviously, will make sense if the axis of the real thread is the straight line. However, for the case if thread axis is a 3D curve, this approach may result in significant deviations. It is necessary to develop a methodology to calculate VPTD in the case that the thread axis is curved. In this regard, the presented study attempts to determine the location of part thread axis using a more general approach. Method of regression analysis has been applied as an instrument for calculation [20]. Thus, the aim of this study is an assessment of the possibility of applying regression to determine the position of the straight thread axis for subsequent VPTD calculation using thread point cloud obtained from CMM.

2 The Methodology to Determine Regression Equation of Part Thread Surface Axis 2.1 Problem Statement It is known that regression analysis provides the opportunity to determine a straight line for both two variables and for three or more variables [20]. To meet the target, firstly, it is reasonable to explore the relationship between any two of three coordinates, and

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secondly, to explore the relationship between all three coordinates in 3D space at once. The second way is considered to be less adequate, but initially it seems to be more general and universal, since it may result in determination of the equation of thread axis located in space. However, this way does not have a practical advantage over the first one, since the axis equation is used for its further rotation together with the thread surface in the initial CMM coordinate system [18]. This rotation should ensure the location of the real thread axis along the coordinate axis, for example, Z-axis of the calculation coordinate system. For that purpose, three basic rotation matrices around three coordinate axes have to be used. In this regard, the first way to determine regression equations for coordinates X –Z and Y –Z is more practical. The coefficient of Z coordinate is related to the tangent of the angle of inclination of the line to the axis. This angle should be used in transformation matrixes of CMM coordinate system rotation to thread surface coordinate system for VPTD calculation. 2.2 Calculation of Regression Equations’ Coefficients As noted above, to determine the location of straight axis of the part, axis projections of the coordinate planes in the CMM coordinate system were considered. Accordingly, regression equations with two variables were considered: x = a0x + a1x z and y = a0y + a1y z.

(1)

Formulas for calculating coefficients of these equations are well known [18]. For the first Eq. (1): n a0x =

i=1 xi

n

n

n n    2 − ni=1 xi ni=1 zi + n ni=1 zi xi i=1 zi − i=1 zi i=1 zi xi and a = ,  2   1x  n z 2 2 n ni=1 zi2 − ni=1 zi i=1 zi − i=1 i

n

(2)

where xi and zi are thread surface point coordinates from the point cloud obtained using CMM. In this case, zi are coordinates measured along the thread axis, and xi are coordinates measured in the radial direction, parallel to CMM coordinate plane. For the second Eq. (1) in order to calculate a0y and a1y , it is necessary to replace xi by yi in formulas (2). In this case, τx and τy angles of basic rotation matrices are determined as τx = arctan(a1x ) and τy = arctan(a1y ).

(3)

2.3 Determination of Thread Surface Curved Axis Equation It is quite clear that real thread surface axis is generally a curved line in the space. To verify the approach advanced above, it is advisable to develop models of thread axes and of thread surfaces related to them. It is obvious that straight axis is the simplest kind of axis. Its location in space is characterized by two angles indicated above and by displacements along the same axes after axis rotation. Regression coefficients a0x and a0y provide a solution to the second question.

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A circle arc is a line of the second level of complexity following a straight line. Since the aim of this study is to determine thread axis location in general, the most complex kind of axis has to be explored. In the simplest case, circular arc start and end points are located on the axis. It is clear that the regression line is parallel to this axis. A case if the tangent to the arc at the start point coincides with Z-axis is more complex. In this case, arc end point is located below at a certain distance max . This distance is considered as the characteristic of thread axis deviation from the ideal location—the location of Z-axis. The equations of circle arc radius R, current deviation i from Z-axis, arc deflection R are determined as follows: R = ((zmax − zmin )2 + 2max )/2max , i  = − R2 − zi2 + R, R = ||m | − |min + max |/2|,

(4)

where    2 + R,  2 2 m = − R2 − (0.5(zmin + zmax ))2 + R, min = − R2 − zmin max = − R − zmax + R

(5)

A sine wave is the line type next in complexity for thread axis modeling. Displacements of point coordinates along radial axes xi and yi are xi = max sin(k1 zi /(zmax − zmin ) + ψ1 ) sin(k2 zi /(zmax − zmin ) + ψ2 ),

(6)

yi = max sin(k1 zi /(zmax − zmin ) + ψ1 ) cos(k2 zi /(zmax − zmin ) + ψ2 ),

(7)

where max is oscillation amplitude of sinusoidal thread axis in the radial plane and in the circumferential direction; k1 and k2 are numbers of periods of oscillation of the sinusoidal thread axis in the radial plane and in the circumferential direction; ψ1 and ψ2 are phase shifts of sinusoidal thread axis oscillation in the radial plane and in the circumferential direction. Thus, all the necessary dependencies for modeling thread axis and its location in space are obtained.

3 Computer Modeling of Threads with Various Axis Types, Determination of Thread Location and of VPTD Using dependencies presented above, computer modeling was carried out. Calculations were performed for thread M12 × 1.25–7 g—L (50) GOST 8724–2002. Point cloud was obtained by modeling based on previously published procedure [21]. Point cloud form is shown in Fig. 1. The first series of calculations was performed for thread straight axis rotated about X -axis in a vertical plane Y 0Z to angles μ = 0.1, 0.2, … 1.0°. The results of axis inclination calculations according to previously published method ξx [19] and τx — results of calculations according to method based on regression—are given in Table 1.

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Fig. 1. Point cloud of M12 × 1.25–7 g – L (50) GOST 8724–2002 thread with ideal axis location. Table 1. Initial axis inclination μ and calculated axis inclinations ξx and τx . μ, deg

0.1

ξx , deg

0.095 0.190 0.285 0.380 0.475 0.570 0.664 0.759 0.854 0.949

100(μ − ξx )/μ,% 4.93 τx , deg

0.2 5.14

0.3 5.00

0.4 5.12

0.5 5.08

0.6 5.05

0.7 5.11

0.8 5.12

0.9 5.11

1.0 5.10

0.099 0.192 0.285 0.378 0.471 0.564 0.657 0.750 0.843 0.935

100(μ − τx )/μ,% 0.67

3.89

4.96

5.50

5.82

6.03

6.19

6.30

6.39

6.46

As indicated in the table, regression produces better results for inclinations less than 0.3°. For higher inclinations, the previous approach using the first iteration provides better accuracy. Since these approaches imply the use of two or more iterations with clarification of inclination, ultimately, the regression approach is more accurate. At the next stage of the study, the case if thread axis is a circle arc was examined (4) and (5). Maximum axis vertical deviation is equal to 0.5 mm (Fig. 2). VPTD value calculated according to the previously published method [21] d2v = 12.40114 mm. After the thread axis is calculated, the previous method [19] results in inclination of the straight thread axis to Z-axis ξx = 0.544◦ . The regression approach yielded τx = 0.566◦ . After point clouds rotations to these angles and VPTD calculations according to the previously published method [19] d2v = 11.1986 mm, the regression approach results in d2v = 11.1966 mm. Thus, no significant advantages of the new approach are found. Finally, the case if thread axis is a sine wave was examined. Thread point clouds were generated using the same procedure [21] for the following conditions: oscillation amplitude is equal to 0.1 mm, total thread length is equal to one and to two periods of oscillation (Fig. 3). For the case if thread length is equal to one, period d2v = 11.08068 mm before rotations is performed. After the thread axis is calculated, the previous method [19] results in inclination of the straight thread axis to Z-axis ξx = 0.251◦ . The regression approach yielded τx = 0.225◦ , after point clouds rotations to these angles and VPTD calculations according to [19] d2v = 11.25223 mm. Therefore, the new approach does not show significant advantages also. For the case if thread length is equal to two oscillation periods, d2v = 11.0810 mm before rotations are performed. After the thread axis is calculated, the previous method [19] results in inclination of the straight thread axis to Z-axis ξx = 0.125◦ . The regression approach yielded τx = 0.116◦ , after point clouds rotations and VPTD calculations according to [19] d2v = 11.2070 mm. Consequently, the new approach does not show significant advantages too.

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Fig. 3. Point cloud of M12 × 1.25–7 g—L (50) GOST 8724–2002 thread with the sine wave as the axis, with one or two oscillation periods located along thread length.

Fig. 2. Point cloud of M12 × 1.25–7 g—L (50) GOST 8724–2002 thread with the circle arc as the axis.

4 Results and Discussion The present methodology to determine thread axis location in order to calculate VPTD is obviously a compromise one. The advantages of the previous calculation method based on the average values of the coordinates of point clouds for the starting and ending thread areas are predictable in the case of a straight thread axis rotated to a certain angle. Absence of visible advantages of the regression method in the case of curved axis is not an expected fact. This fact is especially unexpected in the case if thread axis is a sine wave with one period along thread total length: the thread has an asymmetric axis. Therefore, further problem studies are required.

5 Conclusion The accomplished researches have the following conclusion: the proposed method of using regression to determine the location of thread axis of a real part by coordinates of the point cloud obtained from CMM does not provide significant advantages compared

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to the previously proposed method for searching the thread axis based on the average values of the coordinates of point clouds for the starting and ending thread areas.

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19. Shchurov IA (2019) Improved Axis Determination Method for Calculation of Virtual Pitch Thread Diameter Using a Point Cloud from CMM. In: Proceedings of the 4th Int. Conf. on industrial engineering. ICIE 2018. Lecture Notes in Mechanical Engineering. Springer. https://doi.org/10.1007/978-3-319-95630-5_173 20. Korn GA, Korn TM (1961) Mathematical Handbook for Scientists and Engineers. New York. Toronto – London. McGraw W – Hill book Company, Inc. 21. Shchurov IA (2004) Raschet tochnosti obrabotki i parametrov instrumentov na osnove diskretnogo tverdotelnogo modelirovaniya: Monografiya (Calculation of machining accuracy and tool parameters on the basis of discrete solid modeling). Univ, Chelyabinsk, South Ural St

Improving Technology of Manufacturing Preparations for Brackets of Heavy Truck Cars A. V. Shaparev(B) and I. A. Savin Kazan National Research Technical University Named After A. N. Tupolev-KAI, K. Marx Street 10, Kazan 420111, Russia [email protected]

Abstract. The possibility of using laser cutting systems for the manufacture of blanks brackets for heavy trucks. The use of laser cutting tools eliminates the cutting of blanks in the form of cards, eliminates the cold perforation of a sheet 10 and 12 mm thick, and cuts metal along any complex contour with an accuracy of 0.1 mm and a high-quality cutting line without further processing. Rational technological schemes for the production of brackets for heavy trucks by laser cutting and welding of bracket parts have been developed. Test calculations of the strength of the brackets were carried out using the finite element method, and prototypes of the brackets were made for testing. The use of laser cutting and welding technologies increases production efficiency due to the high automation of manufacturing processes, optimization of cutting blanks, the complete absence of rejects due to the high precision of manufacturing and welding, and the absence of additional mechanical processing (milling of chamfers, drilling holes, etc.). Using the proposed technologies allows us to produce a wide range of brackets for any brands of trucks with a metal thickness of up to 12 mm, as well as to produce single brackets as spare parts by order of repair organizations and car service enterprises. The absence of high-temperature technological operations (hot stamping, casting) eliminates the change in the structure of the metal during cooling. Keywords: Bracket for heavy trucks · Laser cutting · Laser welding · Production technology · Strength calculation · Finite element method

1 Introduction At present, the procurement departments of machine-building workshops are equipped with longitudinal and transverse cutting units, various designs of shears for metal cutting. Sheet blanks for cold sheet stamping have simple rectilinear forms, usually in the form of sheets, cards, or rolls [1]. The use of laser cutting units makes it possible to cut the metal along any complex contour with an accuracy of 0.1 mm and a high-quality cutting line without subsequent mechanical processing [2]. Therefore, the use of laser cutting units in the procurement departments of machine-building production is an urgent and timely task. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_29

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2 Setting a Research Problem Consider the possibility of producing blanks for brackets of heavy trucks using laser technology. As an example, we use the detail “Suspension box suspension bracket” for KAMAZ vehicles. Structurally, the part consists of metal, flat blanks of different geometric shapes: (base, plate, and six holes), welded together and forming an assembly unit (Fig. 1). The “Plate” part is perpendicularly welded to the “Base” part, and then six stiffeners are welded to the base plate and base. Blanks have different thicknesses: Base, plate— 12 mm, ribs—10 mm. At the base, there are four holes with a diameter of 17 mm. The center distance must be strictly maintained with specified dimensions with an accuracy of 0.2 mm. Through these four holes, the bracket is attached to the frame side members [3, 4]. The bracket plate has two holes with a diameter of 31 mm. With these holes, the bracket assembly rigidly holds the transfer case. To ensure the required accuracy, these holes are machined on a drilling machine. The need to drill these holes at the end of the technological cycle arises due to residual deformations obtained during manual welding [5, 6]. In the case of laser processing of these holes in the early stages of the technological process, it is not possible to ensure the required dimensional accuracy due to thermal deformations during arc welding of bracket parts. In addition, the plate and six stiffeners are milled by two 4 × 45 mm chamfers. These six stiffeners have a triangular shape, of which two pairs are identical in design, and the rest have a different geometric shape. These stiffeners give the necessary rigidity and strength of the bracket design. The disadvantages of the existing technology are the need for multiple movements of workpieces of parts of the bracket in various production areas (blank and stamping department, areas of arc welding, machining, painting) [7, 8]. In order to improve the production technology of the brackets, it is proposed to exclude the production processes of blanks in the form of cards, cold sheet punching, and hole drilling operations. This goal is achieved by installing laser systems for cutting bracket parts directly in the blank compartment. The introduction of laser technology for cutting and subsequent welding allows brackets for trucks to be produced with a high accuracy of 0.1 mm. Laser welding of parts of the bracket allows to obtain welds of small width with deep penetration of the seam [9–11].

3 Development of a New Design for Transfer Case Suspension Bracket Parts Due to the fact that the current design of the suspension bracket for the transfer case has a great complexity of manufacturing and significant difficulties in ensuring the required dimensional accuracy, it became necessary to develop a new design of the part, in particular, in the tongue-and-groove system. Externally, the design of the suspension bracket for the transfer case does not change, and the change in design is associated only with the details of the bracket. Changing the

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Fig. 1. Design drawing and general view of the part “Bracket Transfer Case Suspension”.

design of the bracket parts will significantly increase the accuracy of assembly, simplify the technology of assembly and welding of the bracket, while the use of special devices for welding the bracket is completely excluded from the process [12, 13, 14]. The “tongue-and-groove” system eliminates any displacement of parts during assembly of the structure, since the workpiece accurately and tightly enters the square hole to a depth of the width of the inserted workpiece (12 mm) and length (23 mm). This eliminates the deformation of the bracket when welding parts, which significantly reduces the likelihood of marriage [15, 16]. The novelty of the design lies in the fact that in the parts of the bracket, square holes are additionally cut with high accuracy, and in other parts, spikes are cut with high precision in appropriate places (Fig. 2). High-precision manufacturing of parts with holes and spikes is achieved using a TruLaser 3030 CO2 laser with high accuracy of ±0.1 mm and a cut roughness of Ra = 10 µm. At the same time, the requirements of the design documentation for dimensional accuracy and roughness of the cut zone are fully satisfied, and high accuracy of assembly of the bracket is ensured. The big advantage of the new design of the bracket parts is the ability to cut all the holes of the workpieces on high-precision laser equipment, excluding additional mechanical refinement of the edges, the operation of drilling holes after welding. Edge milling is also eliminated due to the tight fixation of parts when assembling the bracket.

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Fig. 2. The design of the grooves of the part “Bracket Base”.

The assembled bracket after welding and painting meets all the requirements of the design documentation for dimensional accuracy and processing accuracy (see Fig. 1). The simplicity of assembly of parts using the tongue-and-groove system does not require the use of expensive equipment for welding bracket parts, while the assembly and welding time of the bracket by the tongue-and-groove system is reduced by 73% compared to the existing assembly method in welding equipment. The new design of the bracket using the “tongue-and-groove” system provides high accuracy of fixing the parts of the bracket before welding, while significantly reducing residual deformation of the bracket structure after welding and maintain dimensions within the tolerance. The use of laser technology also allowed the introduction of high-quality laser marking of the bracket [17–19].

4 The Method of Calculation To perform verification calculations, a solid-state model of the mounting brackets of the transfer box KAMAZ-6560, made in the CAD/CAM/CAE system NX Unigraphics [20, 21], was used. Fixing the computational model in space was carried out by limiting all degrees of freedom (rigid fastening) along the truncated frame points. All elements of the structure are bolted to each other [5]. To fasten the transfer case from the brackets, tight connections were made to the center of mass point, and the weight of the transfer case with attachments was set to m = 460 kg. From the point of the center of mass, a rigid connection is made to the middle of the 2 input shaft. The whole model is acted upon by gravity g = 9.81 m/s , directed in the

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opposite direction from the Z-axis [6]. To assess the strength of the mounting brackets of the transfer case, the three-dimensional model is simplified to the middle surfaces, and then a finite element model of the mounting is built (Fig. 3). On the brackets, there is a 2D finite element mesh of the QUAD type with an element size of 8 mm [22].

Fig. 3. RMS stresses in the right transfer case mounting bracket.

Bracket loading was simulated as follows. A diagonal frame hanging was simulated, and the values of gravitational acceleration of 9.81 m/s2 and torque of 25,000 Nm were set [7]. Figure 4 shows the rms stress in the right bracket for holding the transfer case. As follows from the calculations, the most loaded elements of the part are the junction of the ribs with the plate [6]. The safety factor is calculated by the following formula:  (1) Kz = Re Rm where Re is the yield strength, Rm is the maximum stresses arising. The strength condition for the bracket is performed (Table 1). With the application of the tilting moment to the center of the input shaft of the transfer case, the minimum factor of safety for yield strength was Kz = 1.27. Maximum stresses occur at the junctions of the ribs with the plate.

5 Conclusion • The use of laser cutting and welding technologies increases the production efficiency due to highly automated manufacturing processes, optimization of cutting blanks, a complete lack of rejection due to high-precision manufacturing and welding, and the absence of additional machining (milling chamfers, drilling holes, etc.).

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Fig. 4. Equivalent voltages of the transfer case bracket. Table 1. The values of the resulting stresses and the corresponding factors of safety. Type of loading

Maximum stress (MPa)

Yield strength (MPa)

Safety factor Kz

Diagonal hanging of the car frame with g = 9.81 m/s2 and torque 25,000 Nm

193

245

1.27

• The use of the proposed technologies makes it possible to manufacture a wide range of brackets for any brand of truck with metal thickness up to 12 mm, as well as to make single brackets as spare parts for repair organizations and car service enterprises. The absence of high-temperature technological operations (hot stamping, casting) excludes a change in the structure of the metal and the subsequent leash during cooling. • The disadvantage of the proposed method of manufacturing brackets for trucks using laser cutting and welding is the high initial cost of technological laser equipment, which tends to decrease recently. Therefore, to reduce the technological cost of production of the brackets, full loading of the laser equipment is necessary, while the payback period of the laser systems is reduced to 6–12 months.

References 1. Shaparev AV, Savin IA (2015) Improving the production technology of bimetallic tapes. University Book, Kursk 2. Shaparev AV, Savin IA, Ptichkin SN (2018) Production of truck brackets using laser technology. University Book, Kursk

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3. Shaparev AV, Savin IA (2018) Influence of the state of the contact surfaces on the formation of the joint of steel and brass during cold cladding. Cold State Phenomena 265:313–318 4. Shaparev AV, Savin IA (2016a) Calculating the bottles of the cold rolling of bimetals. Mater Sci Forum 870:328–333 5. Skhirtladze AG, Grechishnikov VA, Chemborisov NA, Grigoriev SN, Savin IA (2016) Cutting materials. Cutting tool, Yurayt, Moscow 6. Savin IA (2016) Determination of the system of mechanical engineering. European J Nat History 3-C:94–97 7. Shaparev AV, Savin IA (2016b) Calculation of joint plastic deformation, necessary for the formation of a metal compound in a cold state. Procuring Prod Mech Eng 10:32–36. https:// doi.org/10.4028/www.scientific.net/SSP.284.319 8. Gavariev RV, Savin IA (2018) Research of the mechanism of destruction of compression molds for casting under pressure of color alloys. Solid State Phenom 284:326–331. https:// doi.org/10.4028/www.scientific.net/SSP.284.326 9. Gavariev RV, Savin IA, Leushin IO (2019) To the question of casting alloys of non-ferrous metals in the metal mold. Mater Sci Forum 946:631–635. https://doi.org/10.4028/www.sci entific.net/MSF.946.631 10. Gavariev RV, Savin IA, Leushin IO (2017) Increasing the quality of the surface of zinc castings by applying multi-layer protective coatings. Tsvetnye Metally 5:84–88. https://doi. org/10.17580/tsm.2017.05.13 11. Leushina LI, Leushin IO, Plokhov SV, Deev VB (2018) Recycling cullet from quartz ceramic shells used in investment casting. Steel Transl 48(11):699–703 12. Safronov NN, Mingaleeva LV, Savin IA (2018) Optimization of charge material composition in shs process with ferrosilide fabrication from gaseous wastes of metallurgical production. Chernye Metally 2:53–59 13. Savin IA, Akhmedeev MV (2020) Connection of the steel pipes having a polymeric covering on internal and external surfaces. Solid State Phenom 299:766–771. https://doi.org/10.4028/ www.scientific.net/SSP.299.766 14. Balabanov IP, Simonova LA, Balabanova ON (2015) Systematization of accuracy indices variance when modelling the forming external cylindrical turning process. IOP Conference Series: Mater Sci Eng 86(1). https://doi.org/10.1088/1757-899X/86/1/012010 15. Gavariev RV, Savin IA, Soldatkina EN (2020) Choice of protective coating of metal molds for casting non-ferrous alloys. Solid State Phenom 299:867–871. https://doi.org/10.4028/www. scientific.net/SSP.299.867 16. Shaparev AV (2020) Investigation of the effect of oxygen content in the auxiliary process gas on the quality and speed of laser cutting of steel sheets. Solid State Phenom 299:457–461. https://doi.org/10.4028/www.scientific.net/SSP.299.457 17. Leushin IO, Subbotin AY, Geyko MA (2015) Recycling of galvanized steel scrap for use in cast iron melting in induction melting facilities. CIS Iron Steel Rev 10:19–22 18. Gilman VN, Balabanov IP, Faskhutdinov AI (2019) Improving the efficiency of shaving through the use of wear-resistant coatings, vol. 570, SCOPUS. https://doi.org/10.1088/1757899X/570/1/012024 19. Balabanov IP, Gilman VN, Timofeeva TS, Faskhutdinov AI (2018) Modeling of the cutting edge rounding influence on the tool life in processing a gear wheel by the Power Skiving method. Int J Eng Technol(UAE) 7(4):71–73. https://doi.org/10.14419/ijet.v7i4.7.20386 20. Gavariev RV, Savin IA (2017) Improvement of surface quality of casting produced by casting under pressure. Solid State Phenom 265:988–993. https://doi.org/10.4028/www.scientific. net/ssp.265.988

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21. Leushin IO, Chystyakov DG (2016) Technologies for use in the formation of a differentiated structure in iron billets used in glass molds. Met Sci Heat Treat 5–6(58):299–302 22. Thompson MK, Moroni G, Vaneker T, Fadel G, Campbell R, Gibson I, Bernard A, Martina F (2016) Design for additive manufacturing: trends, opportunities, considerations, and constraints. CIRP Annals Manuf Technol 65(2):737–760. https://doi.org/10.1016/j.cirp.2016. 05.004

Methodology and Tools for Computer-Aided Calculation of Characteristics of Electromechanical Clamping Drive Actuated by Induction Motor B. Prydalnyi1(B) , Y. Kuznetsov2 , and V. Lyshuk1 1 Lutsk National Technical University, 75, Lvivska St., Lutsk 43018, Volyn Region, Ukraine

[email protected] 2 National Technical University of Ukraine “Kyiv Polytechnic Institute”, 37, Prosp. Peremohy,

Kiev 03056, Ukraine

Abstract. The article is devoted to solving the problem of determining the parameters of electromechanical drives of clamping mechanism of lathes. The conducted research is directed at the creation of methodology for calculating the main characteristics of a mechanism for workpiece fixation, made on the basis of a new structure with an electromechanical drive. The obtained results were used to create a computer program, which presents the results of calculations in the form of characteristics to time dependency graphs. The use of the developed tools makes it possible to study the mechanism operation as a process consisting of separate strictly defined stages. The obtained model identifies the change in characteristics as they move from one stage of operation to another. The developed research tools also allow defining the optimal adjustment of this type of mechanism. Keywords: Clamping mechanism · Electromechanical actuator · Calculation of characteristics · Computer program

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_30

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1 Introduction Significant progress in the development of electrical systems, and electric drives, in particular, gives new opportunities for their use in place of their mechanical counterparts. This trend also applies to machine tool knots. For example, a traditional drive that provides the main movement in the machine tool and contains a gearbox is often replaced by a motor spindle when creating advanced machine tool models. This opens up new potential for improving the performance of metalworking machines and requires improvements to its other subsystems. The advantages of electrical systems related to the efficiency of energy conversion and transmission, as well as the efficiency of control, have led to active proliferation to create modern mechanisms. It is known that improving characteristics of fixation of a workpiece on machine tools makes it possible to increase the processing modes; therefore, the use of electrical subsystems in a structure of modern clamping mechanisms is predictably expedient. The process of developing new hightech machine components is often closely linked to the usage of mathematical modeling and automated calculation tools. The calculation of characteristics of mechanisms due to which dynamic loads occur is relatively complex, so it is especially important to use computer equipment. Work cycles of mechanisms for clamping workpieces occur in the process of clamping and unclamping a workpiece. Machine tools with automation in mass production lines are characterized by the rapid execution of a limited number of operations (often their number is reduced to one). This requires frequent movement (reinstallation) of workpieces when processing them on different machine tools. Therefore, each of these processing steps is associated with the need to clamp and unclamp workpieces in automatic mode with minimal time (this often lasts for a split second). Therefore, the main period of operating a mechanism of the workpiece clamp occurs under unsteady (unstable) modes. As a result of non-linearity loading of mechanism elements, transition processes emerge not only at the beginning and the end of each clamping or unclamping cycle, but also during the transition between the different stages of these processes (gaps elimination, generation of tension, etc.). This leads to accelerated movement of the elements of the mechanism and the emergence of additional dynamic loads. The effect of significant centrifugal inertia forces resulting from the rotation of the clamping mechanism together with the machine tool spindle also has an impact on the performance of the mechanism. To effectively design clamping mechanisms with optimal performance and the ability to determine the optimal settings according to processing conditions, it is necessary to consider the above-mentioned features of its operation. This greatly increases the complexity of calculations and requires automation of this process based on a specially developed methodology. Within the current tendency of active introduction of electrical subsystems into the structure of technological equipment, some constructions of clamping mechanisms with electromechanical actuators have been developed, which have several advantages in comparison with hydraulic, pneumatic, and mechanical ones. The developed constructions are based on a structure containing an induction motor and provide energy transfer to the input of the clamp mechanism through a magnetic field between the stator and the rotor of the motor. For further efficient design, manufacture, and operation of clamping

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mechanisms with an electromechanical actuator, there is a necessity for multiple calculations, which are related to the determination of parameters of optimal interaction of their subsystems at different stages of the operation cycle under different operating conditions and different structural features of machine tools in the structure they are integrated into.

2 The Purpose of the Research The purpose of the research is to develop a tool in the form of software for personal computers, which would allow simulating and calculating the basic characteristics of the electromechanical drive of the workpiece clamping mechanism with an induction motor taking into account the features of two main stages of operation, transients, and the possibility to simulate the load of the output link of the mechanism.

3 Research The design of the electromechanical actuator as part of the clamping mechanism is considered to identify the initial calculation data. Its schematic diagram (Fig. 1) is typical for mechanisms like this. The mechanism is powered by electrical energy sources ES with voltage U through a switching device SD, which regulates the stator current of an induction motor with stator and rotor. As a result, an electromagnetic torque Ma appears on the cage motor rotor and gives it a rotational motion with frequency n. The torque of the rotor is converted by a drive self-braking mechanism (DSBM), which is made in the form of a screw transmission, into the axial force Fa, which is transmitted to the collet clamping chuck (CC) and is converted by its conical connection into a radial force to fixate the object (OC). A feature of the clamping mechanism of this design is that the input force is brought in contactless—due to the electromagnetic interaction of the elements of the stator and rotor of the electromechanical actuator, and the value of force Fr for clamping OC can be effectively changed, according to the needs, switching device SD. Also, using electronic means to control the operation of the electromechanical actuator motor different modes of operating of the clamping mechanism can be effectively set, depending on the sphere of

Fig. 1. The conceptual sketch of the electromechanical actuator of the clamping mechanism according to the patent of Ukraine Nu. 95323

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usage: automatic and semi-automatic cycles and “push-button” control—for performing debugging operations. The structure of the process of determining the characteristics of the electromechanical clamp actuator is shown in the form of an outline flowchart (Fig. 2).

Fig. 2. Flowchart of the process of calculating the characteristics of the electromechanical clamping actuator

A mathematical model of the asynchronous cage induction motor used to create the computer program is designed to analyze the performance of an engine both

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autonomously and as an element of a complex system. It allows us to calculate the basic electromechanical time dependencies and then analyze them as a separate element or element of the system as a whole. For the basis of the equations, we take the differential equations of a three-phase asynchronous motor in the cosogonal coordinate system, written directly in the normal Cauchy form [1]: dIS = AS (US − rS IS ) + ASR (ψR − rR IR ); dt dIR = ARS (US − rS IS ) + AR (ψR − rR IR ) dt

(1)

where I S , I R —the columns of stator currents and converted rotor currents; U S —the column of the source voltage;  R —the column of full flux linkage rotor windings; r S , r R —resistive resistors of stator and rotor windings; V R —the column of rotor winding voltage; AS , ASR , ARS , AR —the matrix of coefficients. (2) It should be noted that the saturation of the magnetic circuit in asynchronous motors is rarely taken into account (positions in the matrix are marked with zeros). It appears in dynamic, capacitor, and valve braking process, overvoltages, etc. Therefore, for this variant, the matrix of the coefficients A of the motors is presented in the form (3).

(3)

The angular velocity matrix  according to [1] will have the form (4) where αS , αR , αm —inverted inductance of dissipation stator and rotor windings and main inverted inductance of the motor; ω—angular velocity of rotation of the rotor. The column of full flux-linkage is as follows: ΨRj =

ISj + IRj IRj + , αm αR

j = A, B.

(5)

The equation of the electromagnetic state should be supplemented by the equations of the mechanical state to calculate the angular velocity ω shown in (4): p0 dω = (ME − M (ω)); dt J

dγ = ω; dt

n=

30ω . π

(6)

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ME =

√

3p0 αm (IRA ISB − IRB ISA ),

261

(7)

where M(ω)—mechanical torque; p0 —the number of pairs of magnetic poles; J— moment of inertia of the rotor; M E —electromagnetic torque, γ—the angle of rotation of the rotor in electric radians. The differential Eqs. (1), (6) are a circular A-model of a three-phase induction motor. For practical use of this model, it is necessary to know the resistive resistances of the stator windings RS and the rotor RR , inverted inductance of dissipation αS , αR windings, the moment of inertia J, the number of pairs of magnetic poles p0 , the voltage of stator windings U S , and the mechanical torque on the rotor shaft M (ω). In case of absence of complete information about the EMF motor from the manufacturer, the values of its inductive and active resistances can be calculated. The magnitudes of the inductances of the stator and rotor of electromechanical CA are determined by calculation, based on the previously known passport data of a typical motor prototype and the parameters of the L-shaped or T-shaped scheme (Fig. 3) substitution in the following order [2]. In the presented calculation, the parameters of the L-shaped substitution scheme for series 4A electric motor in relative units were used to determine the required parameters.

Fig. 3. L-like alternate circuit of electric motor

After calculating the parameters of the electric motor, we proceed to the absolute values of the resistances: r = R ·

Uf .nom ; If .nom

x = X ·

Uf .nom , If .nom

(8)

or in expanded form xm = Xm · r

2

=R

2

Uf .nom Uf .nom Uφ·HOM  ; r = R1 · ; x1 = X1 · ; Iφ·HOM 1 If .nom If .nom . Uf .nom Uf .nom   · ; x2 = X2 · If .nom If .nom

(9)

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where the rated phase current of the motor is taken from the reference book [3] or calculated by the formula If .nom =

P2nom . 3 · Uf .nom ηnom cos ϕnom

(10)

According to [3], the value of the inductive resistance of dissipation of the stator winding phase is found xσ 1 ≈

2x xm 2x xm  1  1 .xσ 1 ≈ . 2 + 4x  · x 2 + 4x  · x xm + xm x + x m m m m 1 1

(11)

Further, based on [2], the stator phase resistances are determined r1 , x1 . r1 . mT

(12)

x1 − r1 ρ1 , 1 + τ1

(13)

r1 = x1 =

where mT — is the coefficient of reducing the active resistance to the calculated operating temperature [1–4], which is determined by the insulation class for heat resistance (for insulation classes F and H, mT = 1.38); τ1 , ρ1 respectively, the dissipation coefficients and the stator phase resistance. τ1 =

x1 , xm

ρ1 =

r1 m . x1 + xm

(14)

Having resolved jointly (12), (13), (14), the possibility of calculating the resistances of the rotor’s windings was obtained: r2 =

r2 mT (1 + τ1 )2 · (1 + ρ12 )

;

x2 =

x2 (1 + τ1 )2 · (1 + ρ12 )

.

(15)

It follows that the inverted motor inductances can be calculated by the formulas 1 ω 1 ω 1 ω = ; α2 = =  ; αm = = , L1 x1 L2 x2 Lm xm , 1 ω 1 ω 1 ω α1 = = ; α2 = =  ; αm = = , L1 x1 L2 x2 Lm xm

α1 =

(16)

where ω = 2π f = 2 · 3.14 · 50 Hz = 314 s−1 —the angular frequency of voltage in the electrical grid. Initial calculation data which characterizes a specific electromechanical clamping actuator should be entered into the corresponding cells of the main program window (Fig. 4). By changing these values, a selection of optimal characteristics can be performed. The input data for the calculation are

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• • • • • • • • • • • • • • • • •

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maximum voltage stator windings, V; the angular frequency of supply voltage, s−1 ; active resistance of the stator winding phase, Ohm; active resistance of the rotor winding phase, Ohm; inverted value of inductance of dissipation (leakage inductance) of the stator phase, Hn−1 ; inverted value of inductance of dissipation (leakage inductance) of the rotor, Hn−1 ; the main inverted value of the inductance of the magnetic circuit (magnetization branches), Hn−1 ; moment of inertia of the rotor, kg•m2 ; number of pole pairs of the electric motor; duration of the first stage of ACM operation, s; the resistance torque which counteracts rotor rotation during clearance adjustment (eliminating gaps on the first stage of motion), Nm; duration of electricity supply to the mechanism (can be less than the duration of the clamping process due to the work of inertia forces), s; the maximum axial workload on the output link, determined by the required amount of force to clamping the workpiece, N; the time constant; the thread diameter of the screw gear, m; the thread pitch of the screw, m; reduced angle of friction in the screw gear, °.

Fig. 4. The main window of the program

The presented program realizes the possibility of determining the characteristics of the DSBM as a two-stage process—elimination of gaps and creation of mechanical tension. The first stage is characterized by an increase in the velocity of the units of DSBM

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and, in particular, the angular velocity of the rotor of the motor. Therefore, energy is expended to provide the motion of the mechanism in the idle mode (equal to the electromechanical torque Mamin ) and to overcome the forces of inertia. The amount of torque on the motor rotor that is required for idling the mechanism (overcoming friction forces while moving units without creating mechanical tension) can be determined approximately experimentally. The load of the output link in the second stage of the DSBM operation can be set constant or in the form of an exponential time-dependent function with maximum value Fa, which is indicated in the corresponding cell of the program window and depends on the required amount of clamping force. This maximum load value corresponds to the electromagnetic torque on the motor rotor Mamax . Controlling the rate of the exponential growth of the load on the output link to the maximum (setpoint) is achieved by changing the time constant in the corresponding cell of the program window. The zero time constant corresponds to the absence of load on the output link of the DSBM in the second stage, which means the clamping process takes place in the idle (without the workpiece). The value of the time constant of one or higher means an increase in the rate of increase of the load until its maximum (preset) value. The minimum duration of the first step of clamping can be taken to be equal to the length of time tk1 during which the rotor of the motor is accelerated before the steadystate operation with a predetermined torque Mamin . The value tk1 can be determined from the graph of electromagnetic moment dependence on time (Fig. 5) as the point where Ma ≈ Mamin . That is, to detect the minimum value of that time interval, it is necessary to set a known longer duration of the first stage of the EMRP operation and to find the value of the start time of the condition Ma ≈ Mamin on the graph. The value tk1 can also be determined by estimating the nature of the changes in other characteristics, such as the rotor speed. According to the graph (Fig. 5), for Mamin = 5HM with stable execution of the condition Ma ≈ Mamin , the minimum required duration of the first stage of work is defined as tk1 = 0.3 s. Therefore, the second stage of operation of this DSBM begins at a time after tk1 = 0.3 s and related to emerging the load on output link by the force which corresponds to the electromagnetic moment Ma ≈ Mamin . In a real mechanism, the duration of the first stage can be adjusted by changing the free run (acceleration) of the rotor on the threaded surface without moving other elements of the DSBM. The results of the calculations are displayed in the form of graphs of time dependencies: rotor speed n, magnitude of the current of a stator winding I, electromagnetic torque Ma (Fig. 5) arising on the rotor, and displacement of the X T of the output link of the DSBM. The program can be adapted (by code settings) to build dependencies between the other specified values (not time).

4 Conclusions Automation of the calculation of the performance characteristics of the DSBM is one of the factors of successful solutions to the problems of their design, and increase of operational efficiency. The developed computer program helps to increase the efficiency of designing DSBM and the process of operation by automating the process of selection of more optimal parameters of work and settings. The obtained results also contribute to the development of automation tools for the search design of these mechanisms [5–9].

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Fig. 5. Dependence of electromagnetic moment on time

References 1. Gol’dberg OD, Gurin YaS, Sviridenko IS (2001) Proektirovanie elektricheskikh mashin: Ucheb. dlya vtuzov (Electrical Machine Design: A Textbook). Vyssh.shk. Moscow, p 430 2. Kravchik AE, Shlaf M, Afonin VI, Sobolenskaya EA (1982) Asinkhronnye dvigateli serii 4A: Spravochnik (Induction motors 4A series: Directory). Energoizdat, Moscow, p 504 3. Kuznptsov YuM, Pridal’nii BI (2015) Analiz protsesu zatisku-roztisku til obertannya v zatisknomu mekhanizmi z elektromekhanichnim privodom (The analysis of the process of clamping-rotation of bodies of rotation in the clamping mechanism with electromechanical drive). Inzhenerni nauki: visnik KhNTU 4(55):48–56 4. Kuznptsov YuM (2016) Privodi zatisknikh mekhanizmiv metaloobrobnikh verstativ: monografiya (Drives of clamping mechanisms of machine tools: monograph). Luts’k, Vezha-Druk, p 352 5. Kuznptsov YuM, Pridal’nii BI (2016) Peredumovi avtomatizatsi| poshukovogo proektuvannya privodiv zatisknikh mekhanizmiv (Prerequisites for automation of search design of clamping actuators). Naukovi notatki. LNTU 55:216–221 6. Kuznptsov YuM, Pridal’nii BI, Red’ko RG (2011) Pristrii dlya zatisku prutkovogo materialu (Device for clamping rod material) Pat. Ukrainy 95323, Bill. 14 7. Gerra Khamuiela ZhA, Kuznetsov YuN, Khamuiela TO (2017) Genetiko – morfologicheskii sintez zazhimnykh patronov: monografiya (Genetic - morphological synthesis of chucks: a monograph). Lutsk, Vezha-Druk, p 328

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8. Chaban V, Lishuk V (2011) Matematichna model’ vuzla zhivlennya asinkhronnikh mashin: monografiya (Mathematical model of the power node of asynchronous machines: a monograph). Luts’k, RVV LNTU, p 116 9. Shinkarenko VF (2002) Osnovi teori| evolyutsi| elektromekhanichnikh sistem: monografiya (Fundamentals of the theory of evolution of electromechanical systems: a monograph). Kiev, Naukova dumka, p 288

Road Fuel Consumption by Dump Truck in Mountain Conditions A. M. Umirzokov1 , K. T. Mambetalin2 , and S. S. Saidullozoda2(B) 1 Tajik Technical University Named After M.S. Osimi, 11, Academicians of the Radjabovs,

Dushanbe 734042, Tajikistan 2 South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, Russia

[email protected]

Abstract. The article presents the results of experimental studies on the estimation of road and transport fuel consumption in the construction of the Rogun Hydroelectric Power Plant (HPP) for heavy vehicles—dump trucks—an empirical formula for determining the road fuel consumption of vehicles is proposed. The factors affecting fuel consumption are analyzed, of which the elevation angle of individual sections of the road, which can often reach 6 degrees, dominates and higher. Another factor forming fuel consumption is elevation altitude. In the conditions of the Republic of Tajikistan, heavy-duty trucks are operated at altitudes of 1000–2000 m above sea level. Experimental studies were carried out in summer on different routes, with shoulder lengths from 4.5 to 6.0 km and at altitudes from 1100 to 1180 m. In determining the estimated value of the traveling and transport fuel consumption, a dynamic coefficient was introduced taking into account the complexity of the operating conditions in mountain quarry roads. Keywords: Vehicles · Fuel consumption · Mountain conditions · Road slope · Dynamic ratio · Efficiency

1 Introduction Under the conditions of the Republic of Tajikistan, heavy-duty trucks are operated mainly in the construction of hydraulic structures, mining, and ore-dressing enterprises. Due to the fact that 93% of the territory of the Republic of Tajikistan is occupied by mountains, a large number of these structures and enterprises are located in mountainous and highland regions of the republic [1]. Therefore, due to the complexity of the geometry of roads, their low reliability, the variability of environmental conditions, round-the-clock—threeshift operation—as well as due to the significant height above sea level, vehicles are operated in harsh, close to extreme conditions. The operating conditions for mining trucks in the Republic of Tajikistan, unequivocally, can be attributed to the most severe of all the conditions where such vehicles are used on the globe. The severity of the operating conditions for mining trucks determines the corresponding reliability of the DVRS system. In connection with the foregoing, the operating conditions of mining © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_31

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trucks in the mountainous and highland regions of the Republic of Tajikistan can be classified as extremely harsh. Despite the severity of the operating conditions, measures can be taken to prevent a decrease in the reliability of the DVRS system [2, 3]. Dump trucks Shacman-SX3256, BelAZ-7540B, and Howo-ZZ3257 have fully justified themselves as reliable vehicles in the Republic of Tajikistan. To assess the efficiency of operation of these dump trucks in the Republic of Tajikistan, it is necessary to study their technical and economic indicators. An important parameter that determines the efficiency of operation of quarry dump trucks in the Republic of Tajikistan is the travel fuel consumption, which in some cases may exceed 2 or more times of the nominal (base) value. For example, for the Shacman-SX3256 vehicle in operation in mountain quarries, this indicator can reach up to 200 l/(100 km) or higher in particularly difficult sections of the route when driving on the rise. Among the many factors that form the fuel consumption in the road, the prevailing factors are the complexity of the road conditions, the mass of the cargo transported, and the elevation altitude, the influence of which on fuel consumption can be reduced by organizational and technical measures [4, 5].

2 Experimental Study For a Shacman-SX3256 dump truck equipped with a row 6 cylindrical (R6) WEICHAI WP10.336E53 and MT 10 + 2 diesel engine developing a rated power of 247 kW (336 hp.) amounts to 81 l/(100 km) or 69.66 kg/(100 km) when running on summer diesel fuel with a density of 0.86 kg/l [6–8]. For dump trucks of the BelAZ-7540B and Howo-ZZ3257 brands, they were determined by calculation. In different quarries on the territory of the Republic of Tajikistan, as well as in the operation of dump trucks in the same quarries, but under different operating conditions, this indicator can vary within a wide range. For mining dump trucks, the following criteria can be attributed to the main criteria characterizing operating conditions: natural and climatic conditions (altitude, sea temperature, etc.); road conditions; shoulder of the transportation route; load and speed modes of movement; the technical condition of the vehicle associated with the timeliness and quality of maintenance and repair; quality of fuel used; etc. Heavy-duty mining trucks in the Republic of Tajikistan are operated in rather difficult environmental and climatic conditions (at altitudes from 1100 to 1400 m, where the ambient temperature during the year usually can vary from −15 to +30 °C). For the construction conditions of the Rogun HPP, the ambient temperature varies from −7 to +30 °C. In this case, the average annual air temperature is +8.2 °C. The wind speed in the construction area of the Rogun HPP varies during the year from 2.4 to 3.5 m/s. The average wind speed will be 2.9 m/s. The average monthly rainfall varies over a fairly wide range: from 150.4 mm in May to 2.8 mm in July. The average annual rainfall is 79.55 mm [7]. For the conditions of the Republic of Tajikistan, more precisely for the conditions of construction of the Rogun HPP, on the basis of timing studies, experimental data on the traveling fuel consumption are determined. According to experimental studies, graphs

Road Fuel Consumption by Dump Truck in Mountain Conditions

269

of the dependence of the traveling fuel consumption of a vehicle—Shacman-SX3256 dump truck on operating conditions at the construction of the Rogun HPP when the vehicle is moving with and without cargo are plotted (Fig. 1).

Fig. 1. Graphs of the dependence of the traveling fuel consumption of a vehicle—ShacmanSX3256 dump truck on operating conditions at the Rogun HPP construction site when the vehicle is moving with cargo (a) and without cargo (b): hasl —elevation altitude, m; QR —travel fuel consumption according to experimental studies; Qav —the average value of the direct fuel consumption.

For vehicles, dump trucks, it is customary to determine the travel fuel consumption per ride. For the conditions of construction of the Rogun HPP, the graph of the dependence of the traveling fuel consumption by a vehicle—Shacman-SX3256 dump truck on operating conditions for one trip—is shown in Fig. 2.

Fig. 2. The graph of the dependence of the traveling fuel consumption of a vehicle—ShacmanSX3256 dump truck on operating conditions at the Rogun HPP construction site per trip: hasl — elevation altitude, m; QR —road fuel consumption according to experimental studies; Qav —the average value of travel fuel consumption per ride.

3 Mathematical Model Based on the results of experimental studies, an empirical formula is proposed to determine the path fuel consumption of automobiles—dump trucks in mountain conditions 

QR = (1 + kd + k ± ki + kt + kb ) · QB + 1, 5 · mc ,

(1)

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where QB —is the basic road fuel consumption of a vehicle (for a vehicle ShacmanSX3256 dump truck QB = 81 l/(100 km), and for vehicles BelAZ-7540B and HowoZZ3257 dump trucks, the basic values of the road fuel consumption are determined by calculation); k d —is a dynamic coefficient that takes into account the complexity of operating conditions, the value of which depends on the condition of the roadway, the geometry of the road, traffic intensity, the ratio of steady and unsteady movements, etc. (for the construction conditions of the Rogun HPP, you can take k d = 0.12–0.13); k h —coefficient taking into account the road fuel consumption on the elevation altitude (for the construction conditions of the Rogun HPP k h = 9:10–5 :h); k i —coefficient taking into account the influence of the road slope on the road fuel consumption (accepted k i = 0.15:i); k t —coefficient, the influence of air temperature on road fuel consumption; k b — coefficient taking into account the effect of air resistance on the road fuel consumption; mc —mass of transported cargo, tons; h—elevation altitude, m; i—is the average slope of the road, %. For the operation of dump trucks in the construction of the Rogun HPP, we can neglect the influence of air temperature on the road fuel consumption (k t = 0) due to the average annual air temperature equal to +8.2 °C, and we can also neglect the influence of air resistance on the road fuel consumption (k b = 0) due to the low speeds of vehicles on routes. Therefore, Eq. (1) can be rewritten in the form  (2) QR = (1 + kd + k ± ki ) · QB + 1, 5 · mc . The proposed empirical formula is in good agreement with the results of an experimental study for the construction conditions of the Rogun HPP. The proposed empirical formula does not take into account the influence of temperature and air resistance on the fuel flow rate. The fact is that under the conditions of construction of the Rogun HPP, the average annual air temperature is +8.2 °C, and the average value of the speed of vehicles and dump trucks varies between 10 and 30 km/h. For heavy vehicles dump trucks in mountain operating conditions, the travel fuel consumption for one ride can be determined by the empirical formula  (3) QR = (1 + kd + k) · QB + 0, 75 · mc . To verify the theoretical assumptions outlined above, experimental studies of heavy vehicles—dump trucks in mining quarries—were carried out. As the objects of study, heavy trucks were selected—dump trucks of the ShacmanSX3256, BelAZ-7540B, and Howo-ZZ3257 brands, operated under the conditions of the Rogun HPP construction. Experimental studies were carried out with the aim of a comparative assessment of the fuel and economic performance of heavy vehicles—dump trucks of the Shacman-SX3256, BelAZ-7540B, and Howo-ZZ3257 brands.

4 Results Experimental studies were carried out in accordance with the regulatory and technical documentation installed on heavy vehicles—dump trucks Shacman-SX3256, BelAZ7540B, and Howo-ZZ3257 [8]. When conducting, experimental studies were guided by the requirements provided for in the standards GOST 20306–90 [9].

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The conditions of experimental studies (meteorological and road conditions, the characteristic of driving modes, road slope) were selected in accordance with the requirements of GOST R 58137–2018 [10]. For testing heavy trucks—dump trucks of the Shacman-SX3256, BelAZ-7540B, and Howo-ZZ3257 brands—routes with shoulder lengths of 4,500, 5,500, and 6,000 m, a maximum slope of 6%, at altitudes from 1000 to 1250 m and an adhesion coefficient were selected on individual sections of the route 0.5 … 0.6 (for dry unpaved roads) [11]. Each experience in determining the fuel and economic indicators of dump trucks of the Shacman-SX3256, BelAZ-7540B, and Howo-ZZ3257 brands was carried out in triplicate on each of the driving routes; the average values of the test results when driving vehicles with cargo, without cargo, as well as the results of calculating the travel fuel consumption determined by formulas (4), (2) are summarized in Tables 1 and 2. The average values of the test results for one ride of dump trucks of the Shacman-SX3256, BelAZ-7540B, and Howo-ZZ3257 brands, as well as the results of the calculation of the traveling fuel consumption determined by formula (3) are summarized in Tables 3, 4, and 5.

5 Conclusions 1. Empirical formulas for determining the road fuel consumption of trucks in mining quarries are proposed. 2. According to the proposed formulas, the values of the ride fuel consumption for dump trucks of the Shacman-SX3256, BelAZ-7540B, and Howo-ZZ3257 brands for various routes of their movement and in various road conditions are calculated. The research results show a good agreement between the experimental and theoretical data on the ride fuel consumption. The relative discrepancy between the actual and estimated values of the line fuel consumption varies from 0.1 to 2.9. 3. The efficiency of the use of various brands of heavy trucks dump trucks operating in the conditions of the construction of the Rogun HPP on the actual values of the transport fuel consumption is substantiated. The actual value of the transport fuel consumption during the construction of the Rogun HPP on average per ride for the ShacmanSX3256, BelAZ-7540B and Howo-ZZ3257 dump trucks is 4.8, 6.2 and 5.3 l/(100 t km), respectively. 4. According to the actual value of transport fuel consumption during the construction of the Rogun HPP along with a Shacman-SX3256 dump truck, BelAZ-7540B and HowoZZ3257 dump trucks can also be recommended for transport work in the conditions of mountain’s carrier.

14.1

14.1

14.1

22.9

22.9

22.9

15.2

15.2

15.2

Shacman-SX3256

Shacman-SX3256

Shacman-SX3256

BelAZ-7540B

BelAZ-7540B

BelAZ-7540B

Howo-ZZ3257

Howo-ZZ3257

Howo-ZZ3257

21.3

22.2

19.4

28.8

30.0

30.5

24.7

25.2

26.4

Mass of cargo, t

8.0

7.4

6.0

12.9

12.3

10.1

8.9

8.1

6.8

Actual fuel consumption, l

1120

1100

1180

1120

1100

1180

1120

1100

1180

Elevation altitude, m

* —the rate of road fuel consumption is determined by calculation

Curb weight vehicle, t

Mark dump truck

6.0

5.5

4.5

6.0

5.5

4.5

6.0

5.5

4.5

Leverage of transportation, km

20

18

13

32

30

26

23

22

19

Travel time with cargo, min

0.63

0.58

0.60

0.63

0.58

0.60

0.63

0.58

0.60

The average slope of the road, %

5.0

5.5

4.5

5.0

5.5

5.0

4.0

4.0

4.5

Loading time, min

18.0

18.3

20.8

11.2

11.0

10.4

15.6

15.0

14.2

Actual speed vehicle movement, km/h

75*

75*

75*

132.5

132.5

132.5

81*

81*

81*

Road rate fuel, l/(100 km)

133

134

133

215

223

224

148

147

151

Actual road fuel consumption, l/(100 km)

131.0

131.6

128.2

218.1

218.7

220.8

144.0

144.0

146.6

Estimated road value fuel consumption, l/(100 km)

1.8

2.2

3.2

1.4

2.2

1.6

3.0

2.3

3.1

δ, %

Table 1. The results of tests of vehicles dump trucks for fuel efficiency when driving with cargo in mountain conditions.

6.3

6.1

6.9

7.5

7.4

7.4

6.0

5.8

5.7

Actual transport fuel consumption, l/(100 t km)

272 A. M. Umirzokov et al.

5.2

5.6

6.7

Shacman-SX3256 14.1

Shacman-SX3256 14.1

22.9

22.9

22.9

15.2

15.2

15.2

BelAZ-7540B

BelAZ-7540B

BelAZ-7540B

Howo-ZZ3257

Howo-ZZ3257

Howo-ZZ3257

5.2

4.8

3.9

9.2

8.2

4.2

1120

1100

1180

1120

1100

1180

1120

1100

1180

6.0

5.5

4.5

6.0

5.5

4.5

6.0

5.5

4.5

12

10

7

18

16

14

12

11

10

Curb Actual fuel Elevation Leverage of Travel weight consumption, altitude, transportation, time vehicle, l m km with t cargo, min

Shacman-SX3256 14.1

Mark dump truck

30.0 30.0 19.3 20.6 20.0 25.9 30.3 30.0

−0.58 −0.63 −0.60 −0.58 −0.63 −0.60 −0.58 −0.63

75*

75*

75*

132.5

132.5

132.5

81*

81*

88.3

87.3

86.7

153.3

149.1

148.9

93.3

94.5

93.3

27.0

−0.60 81*

Actual Road rate Actual road speed fuel, fuel vehicle l/(100 km) consumption, movement, l/(100 km) km/h

The average slope of the road, %

84.8

85.3

85.6

149.9

150.6

151.2

91.6

92.1

92.4

4.1

2.3

1.3

2.3

1.0

1.5

1.8

2.6

1.0

Estimated δ, road value % fuel consumption, l/(100 km)

Table 2. Test results of vehicles dump trucks for fuel efficiency when driving without cargo in mountain conditions. Road Fuel Consumption by Dump Truck in Mountain Conditions 273

1120

1150

24.7

3

Av 25.4

1100

5.3

6.0

5.5 39

42

39 6.7

7.0

6.0

7.0

25.2

36

2

4.5

26.4

1

1180

Mass of Elevation Leverage of Driving Total cargo, t altitude, m transportation, time per loading and km ride, min unloading time, min

№

16.3

17.1

16.9

15.0

12.9

14.5

13.3

11.0

Average Actual fuel vehicle consumption speed per per ride, l ride, km/h

120.4

120.8

118.2

122.2

Actual road fuel consumption per ride, l/(100 km)

118.4

117.8

118.6

118.9

1.7

2.5

0.3

2.8

Estimated δ, % value of the road fuel consumption per ride, l/(100 km)

4.8

5.2

4.7

4.6

Actual transport fuel consumption per ride, l/(100 t km)

Table 3. Test results for the fuel economy of a Shacman-SX3256 vehicle for one ride in mountain conditions (basic rate of road fuel consumption of 81 l/(100 km) with a curb weight of 15.2 tons).

274 A. M. Umirzokov et al.

1120

1150

28.8

Av 29.8

5.3

6.0

5.5 57

68

55 8.3

8.0

9.0

8.0

3

1100

48

30.0

2

4.5

30.5

1

1180

Mass of Elevation Leverage of Driving Total cargo, t altitude, m transportation, time per loading and km ride, min unloading time, min

№

11.3

10.6

12.0

11.2

19.8

22.1

20.5

16.8

Average Actual fuel vehicle consumption speed per per ride, l ride, km/h

185.8

184.2

186.4

186.7

Actual road fuel consumption per ride, l/(100 km)

185.1

184.0

185.3

186.0

0.4

0.1

0.6

0.4

Estimated δ, % value of the road fuel consumption per ride, l/(100 km)

6.2

6.4

6.1

6.1

Actual transport fuel consumption per ride, l/(100 t km)

Table 4. The results of the fuel efficiency tests of the BelAZ-7540B vehicle for one ride in mountain conditions (the basic rate of road fuel consumption of 132.5 l/(100 km) with an equipped mass of 22.9 tons).

Road Fuel Consumption by Dump Truck in Mountain Conditions 275

1120

1150

21.3

3

Av 20.9

1100

5.3

6.0

5.5 33.3

39

35 6.7

7.0

7.0

6.0

22.2

26

2

4.5

19.4

1

1180

Mass of Elevation Leverage of Driving Total cargo, t altitude, m transportation, time per loading and km ride, min unloading time, min

№

19.4

18.5

18.8

20.8

11.8

13.2

12.2

9.9

Average Actual fuel vehicle consumption speed per per ride, l ride, km/h

110.3

110.0

110.9

110.0

Actual road fuel consumption per ride, l/(100 km)

107.7

107.9

108.4

106.9

2.4

1.9

2.3

2.9

Estimated δ, % value of the road fuel consumption per ride, l/(100 km)

5.3

5.2

5.0

5.7

Actual transport fuel consumption per ride, l/(100 t km)

Table 5. The results of the fuel efficiency tests of the Howo-ZZ3257 vehicle for one ride in mountain conditions (the basic rate of travel fuel consumption of 75 l/(100 km) with a curb weight of 14.1 tons).

276 A. M. Umirzokov et al.

Road Fuel Consumption by Dump Truck in Mountain Conditions

277

References 1. Tursunov AA (2003) Management of automobile performance in mountain conditions of operation: abstract of the dissertation of the doctor of technical sciences. Dushanbe 2. Umirzokov AM, Saibov AA, Mazhitov BZh, Berdiev AL, Tursunov FA (2016) Evaluation of the efficiency of car operation in the high mountains of the Republic of Tajikistan. Actual problems of operation of vehicles: Materials of the XVIII International Scientific and Practical, Conference of Nov, pp 110–117 3. Umirzokov AM, Mambetalin KT, Saydullozoda SS, Saibov AA, Abaev AKh, Berdiev AL (2019) Classification of the DCRE system. Polytech Bull, Series Eng Res 1(45):161–176 4. Konov M (2017) Improving the fuel economy of an internal combustion engine. Young Sci 24:155–159 5. Vakhlamov VK (2006) Cars. Operational properties. Publishing Center “Academy”, Moscow 6. Mining dump trucks BelAZ-7540A, BelAZ-7540V, BelAZ-7540C, BelAZ-7540D, BelAZ7540K, BelAZ-7547, BelAZ-75471, BelAZ-75473 and their modifications (2013) Repair manual 7547–3902080 RS. Republic of Belarus 7. Pagoda in Tajikistan (2019) Areas of republican subordination. https://tajikistan.pogoda 360.ru/. Accessed 19 Oct 2019 8. LLC TehKomplektServis (2019) Technical specifications HOWO-ZZ3257N3847N1 and SHACMAN-SX3256DR384 dump trucks. Areas of republican subordination. https://tehkom servis.ru/. Accessed 19 Dec 2019 9. GOST 20306-90 (1991) Motor vehicles. Fuel efficiency. Test methods. Publishing house of standards, Moscow 10. GOST R 58137-2018 (2018) General automobile roads. Life-cycle risk assessment guide. Publishing house of standards, Moscow 11. Filkin NM, Shaikhov RF, Buyanov IP (2016) Fundamentals of the theory of the study of the operational properties of a car. Perm s

Very Hard Titanium Carbosilicide Coatings to Protect Parts of Energy Machines S. R. Shekhtman(B) , N. A. Sukhova, and M. Sh. Migranov Ufa State Aviation Technical University, 12, Karl Marx Str., Ufa 450008, Russia [email protected]

Abstract. This paper discusses a method for synthesizing very hard vacuum carbon-based coatings applied by plasma ion-assisted deposition. It describes graphite-silicon cathodes used to create a solid titanium carbosilicide-based coating. Such cathodes are analyzed herein in terms of their phase composition. The research team has developed a new technology that uses a graphite cathode to apply very hard coatings; the steps are as follows: prepare the substrate, bombard the surface with an ion flux, preheat the surface after treating it with metal plasma, apply the titanium carbon-based coating using two electric-arc spraying guns, and then apply an ion flux to fix the obtained coating. The research team also tested the adhesion and the microhardness of the synthesized single-layer, multilayer, and nanostructured coatings. The paper presents microhardness values for a variety of coatings, as well as surface layer quality assessment results. Keywords: Coatings · Power engineering · Structure · Multilayer coatings · High hard coatings

1 Introduction Abrasion, friction, wear, corrosion, or sundry aggressive effects of whatever environment a part is exposed to often destroy the surface layer. Vacuum plasma spraying is the most common advanced hardening technology. Vacuum ion-plasma technologies (VIPT) can produce surface layers of special physical and mechanical properties; the processes are versatile and produce coatings at a high rate, while also being environmentally friendly and featuring stable parametric reproducibility [1–5]. Carbon-based coatings show promise when it comes to enhancing the durability. Carbon compounds can exist in amorphous and crystalline state alike. Many various carbon compounds can be produced by varying the layer application order, layer thickness, and numbers, as well as by using various elements for doping in film synthesis [5–9]. Carbon has small ion radius and is capable of producing surface layers with minimum excess energy against volume, thus adding barrier qualities to the surface, which is why carbon is the coating material of choice [10–12]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_32

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This paper dwells upon carbon coatings produced by depositing material from graphite-silicon cathodes of varying thickness, made under various conditions in inert argon environment [13–15]. To synthesize coatings of good operating qualities such as hardness, durability, etc., the research team devised a deposition process for an upgraded industrial NNV 6.6—l1 unit equipped with two arc spraying guns (cathodes), which functioned as sources for vacuum-arc discharge of metal plasma. A PINK plasma generator was used to activate plasma by high-current arc discharge [16–20] (Table 1). Table 1. The composition of the graphite-silicon cathode. Element C

Si

SiO2 SiC Fe Ca

Share, % 45.77 41.3 7.5

Al

Mg

5.2 0.2 0.05 0.01 0.01

Synthesis of very hard carbon coatings was staged as follows: • prepare the surface: clean in an ultrasonic cleaner, clean in ethanol, and then dry in a drying chamber; • clean the surface by an ion flux in a glow discharge; • apply coating from two carbon electric-arc spraying guns based on commercially pure titanium; • heat with an ion flux contained in a vacuum chamber.

2 Research Results Figures 1, 2 and 3 show current densities in correlation with the process parameters, as observed on a Jm target. By testing the capacities of integrated cold graphite-silicon cathodes, the researchers were able to optimize the parameters of applying vacuum ion-plasma coatings (i.e., applied by plasma ion-assisted deposition) based on carbon and carbon–metal formulation. Tests confirmed the thickness of applied coatings (5–7 µm), determined the deposition rate, and helped assess the adhesion. The thickness of such applied coatings was found by gravimetry as well as by a NEOFOT-2.1 metallographic microscope on microscopic sections made perpendicular to the original surface. Coating-to-base adhesion was tested by diamond pyramid impression when measuring the microhardness. Tests prove the coating adhesion excellent, as no exfoliation or chipping was observed when applying a diamond pyramid to the carbon-silicon coated surfaces. For microhardness measurements, the research team used a diamond pyramid with an angle of 136° between its faces and an indenter load of 1–10 g. To obtain comparable results in different measurement series, the loading time (15 s) and the load exposure time (15 s) were not altered.

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Fig. 1. Target current density as a function of argon pressure (Ub = 50 V; Jd = 50A).

Fig. 2. Target current density as a function of the arc current (Ub = 50A; P = 10–1 Pa).

Indenter-made impressions for these measurements were small; hence, the hardness values could have an error of 10–20%. Seven measurements were run to obtain a fairly reliable mean. Arithmetic microhardness means were equal at different points of the specimen. Graphite-silicon coatings had microhardness of 3.5–3.86 GPa with the baseline hardness varying from 2.34 to 2.51 GPa. Table 2 shows the microhardness of the synthesized Ti-C-Si coatings. Multiple studies show that the number and thickness of layers as well as their subsequent thermal treatment (annealing) do affect the mechanical properties of synthesized coatings. A multilayer VIP coating made up of nanometric layers (up to 100 to 150 nm) has better properties by redistributing the hardness enhancement of the surface material as compared to the volume. Further annealing increases the content of complex carbides

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Fig. 3. Target current density as a function of the focus current (Jev = 50A; P = 10–1 Pa). Table 2. Microhardness measurement results. Material

Type of coating

Microhardness, GPa

Titanium alloy

Single-layer coating

19.3

Multilayer coating Ti-(C-Si)-Ti

21.5

Nanostructured coating

25.5

Single-layer coating

16.1

Multilayer coating Ti-(C-Si)-Ti

17.7

Nanostructured coating

25.3

Heat-resistant steel

and carbosilicides in the coating provided that the coating layer structure and the particle size are preserved. Aside from corrosion, erosion, and fatigue resistance, the compressor blades in a power unit need heat-resistant sprayed coatings. Review of literature and experimental studies shows that metal carbide-based VIP coatings retain their operating properties and functionality up to the temperatures, exceeding which will compromise their quality. To test the effects of temperature on multilayer coatings, the research team focused on three core factors: duration of exposure, temperature, and temperature change rate. To find the thermal stability in terms of hardness, the coated specimens were heated in a drying chamber to T = 600 °C and kept for 4, 8, or 16 h. Figure 4 shows coating microhardness as a function of time. Specimens were kept at T = 600 °C. Heat resistance tests of Ti-C-Si coating on VT6, EP718 ID, and EI961-Sh materials (Heating = 400–800 °C, exposure time = 4, 8, or 16 h) show that an SMC coating offers better heat resistance than multilayered coatings. Thus, 16-h exposure at T = 600 °C

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Fig. 4. The dependence of the results of microhardness measurements on the heating time at T = 600 °C. Substrate EP718–ID: 1—three-layer coating, 2—a three-layer coating with t/r (200 °C), 3—coating with a QMS structure with t/r (600 °C) 4—coating with a QMS structure, 5—coating with a QMS structure with t/rev (200 °C).

reduces the microhardness of SMC coating by 10% and that of multilayered coatings by 25–30%. Annealing at 200 °C causes the surface microhardness to peak in SMC coatings, supposedly due to such heat treatment finishing the synthesis of titanium carbides and carbosilicides. In a real-world setting, starting a power plant is associated with continuously changing temperatures. Thermal fatigue may cause system failure. When applying metal carbide-based VIP coatings to the surface layers, there emerges high residual compressive stress; coated parts might be susceptible to thermal fatigue. Besides, there’s little on this problem; no problems regarding how the layer thickness affects heat resistance. Neither is there data on how subsequent heat treatment could affect heat resistance. Most tests utilize low-cycle loading with tmin being the maximum compressive stress and tmax being the minimum. The difference between mechanical fatigue and thermal fatigue lies in the stress level, which during the thermal cycling depends on the elastoplastic properties for the entire coating-substrate complex. Besides, numerous experiments have coating to first start breaking during thermocycling. In addition, there are practically no about this problem; there are no problems associated with the influence of layer thickness on heat resistance. And also there is no data on the effect of subsequent heat treatment on heat resistance. In most cases, studies are carried out under a low-cycle load at which the maximum compression stress is tmin and the minimum stress is tmax. The difference between mechanical fatigue and thermal fatigue lies in the level of arising stresses, which for the entire coating-substrate complex during thermal cycling is determined by elastoplastic properties. Moreover, as shown by numerous experiments, the coating first collapses during thermal cycling.

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3 Conclusions This research has produced a Ti-C-Si coating application technology based on bombarding the surface with a glow discharge to modify it, preheating the treated surface with metal ions, spraying the cathode material, and condensing the ions on the substrate to form a layer by secondary ion bombardment. Studies have shown that depositing very hard carbon–metal-based coatings to form a triple-layer Ti-C structure raises microhardness by 10–15%, while the microhardness of nanostructured coatings rises by 30–60%. Compared to a triple-layer coating based on a carbon–metal composition, nanostructured coatings have a 20–45% higher microhardness.

References 1. Barsoum W (2000) The MN+1AXN. A new class of solids; thermodynamically stable nanolaminates. Prog Solid St Chem 28:201–281 2. Sun ZM, Murugaiah A, Zhen T (2005) Microstructure and mechanical properties of porous Ti3 SiC2 Acta Materialia 53:4359–4366 3. Bazhin PM, Stolin AM, Titov NV (2016) Composite protective coatings based on TiC-W2 CCo, obtained by arc welding with SHS-electrodes on parts of agricultural machinery. Compos Nanostruct 8(1):58–64 4. Shekhtman SR, Suhova NA (2016a) Producing multilayer composites based on metal-carbon by vacuum ion-plasma method. J Phys: Conf Ser 729(1):012010 5. Barsoum MW, Yoo HI, Polushina IK (2000) Elerctrical conductivity, thermopower and hall’ effect of Ti3 AlC2 , Ti4 AlN3 and Ti3 SiC2 . Phys Rev B 62:10194–10198 6. Finkel P, Barsoum MW, El-Raghy T (1999) Dislocation, kink and room temperature plasticity of Ti3 SiC2 . J Appl Phys 86:71237126 7. Shekhtman SR, Suhova NA (2016b) Synthesis of multilayer vacuum ion-plasma coatings Ti-TiN during the surface modification. Mater Sci Forum 870:113–117 8. Bazhin PM, Stolin PA, Stolin AM et al (2018) Ceramic electrospark coatings obtained by SHS electrodes based on the MAX phase Ti-Al-C. Harden Technol Coat 8(164):359–362 9. Naruaki N, Munakata K, Kubo H et al (1987) Cotting performance of cooted carbide tools. Bull Lap Eng 4:205–206 10. Pazniak A, Bazhin P, Shchetininc I et al (2019) Dense Ti3 AlC2 based materials obtained by SHS-extrusion and compression methods. Ceram Int 45(2):2020–2027. https://doi.org/10. 1016/j.ceramint.2018.10.101 11. Zuev LB, Danilov VI, Konovalov SV et al (2009) Influence of contact potential difference and electric potential on the microhardness of metals. Phys Solid State 51(6):1137–1141 12. Konovalov SV, Kormyshev VE, Gromov VE et al (2016) Formation features of structure-phase states of Cr–Nb–C–V containing coatings on martensitic steel. J Surf Invest 10(5):1119–1124 13. Zhang HB, Zhou YC, Bao YW (2006) Oxidation behavior of bulk Ti3 SiC2 at intermediate temperatures in dry air. J Mater Res Soc 21:402 14. Gilbert CJ, Bloyer DR, Barsoum MW (2000) Fatigue-crack growth and fracture properties of coarse and fine grained Ti3 SiC2 . Scripta Mater 42:761–767 15. Shekhtman SR, Sukhova NA, Yansaitova MI (2017) Analysis of the quality indices of the technological process for depositing coatings obtained by deposition from a vacuum arc discharge. Qual Innov Educ 1:40–45 16. Shekhtman SR, Sukhova NA (2016) Properties of vacuum ion-plasma coatings with SMC structure based on titanium carbosilicides). Bull UGATU 3(73):44–48

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17. Tabakov VP (1998) The efficiency of cutting tools with wear-resistant coatings based on complex nitrides and carbonitrides of titanium. Ulyanovsk 18. Hussainova I (2003) Effect of microstructure on the erosive wear of titanium carbide-based cermets, pp 121–128 19. Golombek K, Dobrzanski LA (2007) Hard and wear resistance coatings for cutting tools. Journal of Achievements in Materials and Manufacturing Engineering, pp 107–110

Marking Metal Products by Anodic Etching by Means with Semiconductor Electrode Tools V. V. Glebov(B) Don State Technical University, 1, Gagarin Sq., Rostov-on-Don 344000, Russia [email protected]

Abstract. Industrial and theoretical aspects of the technological application of electrochemical marking in machine-building production are analyzed. Some results, received in the practical application of these methods, are discussed. It is shown that some of the disadvantages of these methods can be reduced or eliminated using semiconductor electrode tools. The features of receptions of conductive films on semiconductor electrodes-tools for electrochemical machining are investigated. The results of experimental research of electrochemical marking in machine-building production by this method have been considered. On engineering parts from steel AISI 304 (08X18H10) type, a clear, durable, and changeresistant marking is obtained. The applied marking is visually readable from a distance of 1 m in artificial and natural light conditions of at least 50 lx. In addition, recommendations on the selection of treatment modes are given, in particular, on the flow rate of the electrolyte, the voltage on the electrodes, the composition of the electrolyte, and the illumination of the electrode-tool, which allows you to effectively manage the process of electrochemical marking. Keywords: Electrochemical machining · Semiconductor wafer · Transparent film · Electrode-tool · Electrochemical marking · Digital printing

1 Introduction In a number of engineering industries at the stages of processing and assembly of parts, there is a need for their marking. Electrochemical marking (ECM) allows you to perform these operations in ways that do not reduce the strength of the product, especially in thinwalled parts with high-quality marks. ECM can be deep or shallow. With a deep ECM, depressions are formed on the surface of the part due to anode etching. The reaction products from the recesses are washed away by a stream of electrolyte. With small ECMs, color changes occur at the treatment sites due to precipitation of the reaction products in the recesses. Marking a part to a depth of 0.01 mm takes several seconds, to a depth of 1 mm or more-several minutes [1–7].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_33

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Electrochemical printing has also found application for engraving printing plates and special types of printed products, the manufacture of consumer goods and the application of a conductive pattern of printed circuit boards [8–10]. The amount of information applied as well as the possibilities of its rapid replacement (for example, numbering in mass production) is determined by the design of the electrode tool (EI), the composition of the electrolyte, the hydrodynamic parameters of the process, etc. Three electrochemical marking methods can be distinguished [4, 10–15]: • Marking can be done using stencils on which the necessary information is applied in the form of slits. EI has a continuous flat conductive surface. Stencil-based ECMs are used in both flowing and non-flowing electrolytes. The main disadvantages of this method are the need to make new stencils when changing information, shallow processing with a non-flowing electrolyte, and the need for a jumper when drawing signs that contain closed areas, for example, letters Q, D, numbers 0, 6, 8, etc. Thin stencils are obtained on plotters (vector or analog printing) or on dot-matrix printers (digital printing). With the digital stencil manufacturing method, the perforation density of the holes is 104 –106 cm−2 . • The working surface of the EI can be performed using signs with the desired profile. Conductive signs are obtained by a set of individual elements of a typographic font, by engraving, or by the photochemical method on the end surface of the EI case. Then the recesses are poured with dielectric material, and the surface of the EI is polished until the necessary electrically conductive pattern appears. This method achieves the best quality of the applied image however, the complexity of manufacturing EI and the need for its manufacture for each drawing limit the application of this method. • If it is necessary to identify each product and other cases of frequent changes in the applied information, raster (sectional) EI is used. The working surface of such EI is made of isolated from each other rods, plates, or tubes in the form of a raster lattice. Modern installations for raster ECM using programming devices that switch the necessary sections allow you to quickly change the applied information. The main disadvantage of this method is the discrete nature of processing, which in some cases significantly distorts the information. The reduction in the area of each section leads to an overall increase in the number of sections and the associated complication of switching and control of EI. It is possible to simplify the switching and control system of a raster type EI by using semiconductor materials for the manufacture of its sections [3, 4, 9]. Projection onto the non-working part of the EI through a stencil of light radiation onto a layer of photoconductive material allows you to commute the metal grid with the illuminated sections of EI. Nevertheless, it is impossible to completely get rid of the discreteness of processing by this method. Thus, the existing ECM methods do not allow the formation of arbitrary images of complex configuration with the ability to quickly replace the applied information. This method of electrochemical processing was carried out by us using a semiconductor wafer as the working surface of EI. This EI allows you to apply any information to the surface of the product due to the corresponding illumination of the back side of the semiconductor wafer.

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2 Theoretical Analysis Semiconductor wafers have a large resistivity, therefore, to obtain an equipotential surface, it is necessary to apply a transparent metal film to the back surface. The solution of many technological problems depends on the ability to form a certain type of nanoand microrelief on the surface of a semiconductor wafer. The technology of thermal vacuum deposition is widely used to form promising semiconductor heterostructures and nanoscale devices based on them [2, 5, 16, 17]. For the manufacture of semiconductor EI, it is important to correctly determine the thickness of the metal film and the semiconductor wafer itself. One of the factors affecting the accuracy of an ECM by a semiconductor EI is the transverse diffusion of nonequilibrium charges in a semiconductor with its local exposure. If the diffusion is excessively large, then the charge carriers generated by the light flux will be distributed over a significant surface of the electron beam, and a significant part of the anode will be etched instead of the desired dimensional processing, and image formation on the workpiece will be impossible. The diffusion of no equilibrium carriers in the transverse direction (along the x-axis, Fig. 1) is determined by the exponential law N x ~ exp (−x/L D ), where L D is the diffusion length of current carriers. It follows that the decrease in concentration with distance from the illuminated area by e ≈ 2.7 times occurs at a distance L D , which is determined by the equation

Fig. 1. Distribution of photogenerated charge carriers under local illumination of a semiconductor wafer surface: 1-photomask; 2-the direction of the light flux; 3 - semiconductor wafer.

 LD =

μτ kT e

(1)

where μ is the mobility of charges; τ is the average lifetime of diffusing charges; k is the Boltzmann constant; T is the temperature; and e is the elementary charge.

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For silicon at T = 300 K, we can take τ = 10–7 s, μ = 103 cm2 V−1 s−1 as estimated values; then for the “broadening” of the photoactive zone we get L D = 1.5 × 10–5 m (Fig. 1). Thus, when using single-crystal silicon as an EI, the transverse diffusion of charge carriers should not affect the accuracy of the ECM, especially since the width of the signs necessary for etching on a photographic template can always be reduced. In the longitudinal direction (along the y-axis, Fig. 1), the photon concentration at depth d is determined according to the Bouguer-Lambert law:   4π (2) Ny = No exp − nχ d λ where N 0 is the concentration of photons of the incident wave at the surface of the EI; p is the refractive index of the absorbing medium; χ is the main indicator of the absorption of the medium; and λ is the wavelength. The reciprocal of the absorption coefficient ξ = 4π nχ /λ is equal to the depth of absorption at which the radiation intensity decreases by e≈ 2.7 times. The BouguerLambert law through the value of the absorption coefficient has the form, N y = N 0 exp(−ξ d). Thus, the depth of absorption depends on the wavelength. For short-wave radiation with a wavelength of 0.5–0.7 µm in silicon, it is 1–5 µm. For infrared radiation, in the region of maximum spectral sensitivity with a wavelength of 0.8–0.95 µm, the penetration depth is 10–50 µm, for λ = 1.06 µm, respectively, 0.5–1.0 mm. For experiments, we used plates with a thickness of 380 µm, which is quite acceptable for effective photoabsorption. The generation of charges inside the semiconductor during the photoelectric effect leads to a disruption in the continuity of streamlines, since this continuity is performed only with a constant charge flowing through any section in the current tube. The rate of optical generation f at a depth d with normal incidence of light is determined by the formula f = βλ ξ λ(1 − a)exp( − ξ λd )

(3)

where a is the reflection coefficient of the flow from the surface; β λ is the quantum yield of the internal photoelectric effect, equal to the fraction of absorbed photons that led to the generation of charges. For the estimated calculation of the maximum photocurrent density in a photosensitive layer without internal amplification, it can be assumed that the current density along the light flux is constant. If monochromatic light with an energy power per unit surface P and wavelength λ is incident on the surface of a semiconductor, and this light is completely absorbed in the photoconductive layer with a quantum output β, then for the photocurrent density jf we obtain jf =

eλβP hc

(4)

where h = 6.63 × 10–34 J × c - Planck’s constant; c = 3 × 108 m/s is the speed of light in vacuum.

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Let the semiconductor be illuminated with normally incident solar radiation with a flux power of P = 1.37 kW/m2 . For evaluative calculations, we consider it to be monochromatic, with a wavelength of λ = 0.85 µm (this is the maximum spectral sensitivity for silicon). β = 0.85 [1, 6, 7] can be taken as a typical value of the quantum yield. The corresponding calculation according to formula (3) gives the value jf = 9.3 × 10−2 A/cm2 . The dark current is several orders of magnitude less than the photocurrent; therefore, the obtained value shows the limiting value of the current during ECM for photoactive EI, and this is the fundamental difference between semiconductor EI and metal EI.

3 Experimental Part Preliminary research results showed that it is possible to use p-type silicon wafers with a crystallographic substrate orientation of {100} and {111}, such as KDB, with a resistivity of 1–10  × cm as the basis for the manufacture of EI. The semiconductor wafers were rinsed in a 1:1 HF electrolyte (49%): C2 H5 OH before vacuum deposition of the aluminum film. To increase adhesion, the temperature of the substrate was 500 °C, and the pressure in the chamber was 10–3 Pa. Heating the substrate during sputtering improves the uniformity of the structure and reduces the resistivity of the film. The surface resistivity of the films was measured by the standard method of a four-point probe. Figure 2 shows typical current–voltage characteristics (I–V ) of semiconductor wafers that can be used as photoactive EI. Curve 1 shows the I–V characteristic under illumination, on curve 2 the I–V characteristic without lighting, on curve 3, the photocomponent component of the I–V characteristic obtained by subtracting curves 1 and 2. Analysis of the I–V characteristic 3 shows that the film-semiconductor interface has good ohmic contact and photosaturation occurs at low voltage-4 V. Probably, this is due to the fact that aluminum itself is an acceptor impurity. The low photocurrent value is due to the high reflectivity of aluminum. The refractive index for aluminum n = 1.44, for comparison, for copper n = 0.62, which also leads to a decrease in photocurrent. A p-type Si plate (doped with boron) with a diameter of 76 mm, a thickness of 0.38 µm, and a surface resistance of 263 /sq, was used as a substrate. For thermal spraying of a transparent film, aluminum was used on a tungsten spiral. The optical transmittance of the film in red light was 70%. The surface resistance of the film was 1.9–2.2 /sq, the transmittance of light in the optical range was 55–60%, and the film thickness was 15 nm. An additional copper layer for a current supply 0.5 cm wide along the perimeter of the film had a thickness of 0.3 µm. It can be seen from the graph that a p–n junction (Schottky barrier) has formed at the double-layer boundary, which, under ECM conditions, operates in the photodiode mode. The ECM process was studied on standard plane-parallel electrochemical cells [1, 4, 5, 14, 18]. The interelectrode gap thickness was of the order of 0.1 mm, and the electrolyte flow rate was 5 m/s. The performance, accuracy, and quality of ECM are to a large extent determined by the correct choice of electrolyte parameters. AISI 304 (08X18H10) type stainless steel parts were labeled in 10% aqueous NaCl electrolyte. The prints were black, durable and change-resistant. The surface morphology

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Fig. 2. Current–voltage characteristics of photoactive EI in an electrochemical cell: 1-under illumination with P = 0.1 W/cm2 ; 2-dark current; 3-photocurrent.

after ECM was studied using a Linnik MII-4 interferometer. The applied marking is visually readable from a distance of 1 m in artificial and natural light conditions of at least 50 lx. Based on the results of an experimental comparison of the results of ECMs of different electrolyte compositions, the electrolyte composition for deep ECM surfaces of parts made of structural steels is recommended: for one liter of a neutral aqueous electrolytesodium nitrite 150 g, potassium sodium tartrate 30 g. For shallow ECM, to obtain darker prints, the concentration of potassium sodium tartrate can be reduced to 2%. However, the processing time for deep marking was more than 10 min. This can be explained by the low current density of semiconductor EI. This time can probably be reduced by using semiconductors with internal amplification of the photocurrent [4, 6, 7].

4 Conclusion Peculiarities of manufacturing systems for ECMs using semiconductor EI are considered. To select the necessary materials, their current-voltage characteristics were studied under lighting and without lighting. Methods for applying alphanumeric and coding information to engineering products using photoactive semiconductor EI have been developed and practically confirmed. Recommendations are given on the choice of processing modes, the composition of the electrolyte for marking structural and tool steels. This composition does not change

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its properties during storage, is practically non-toxic, does not cause corrosion of the marked part, and does not require additional passivation or neutralization of the marked surface after marking, the electrolyte remains are removed with rags. On engineering parts from steel AISI 304 (08X18H10) type, a clear, durable, and change-resistant marking is obtained. The applied marking is visually readable from a distance of 1 m in artificial and natural light conditions of at least 50 lx.

References 1. Kukoz FI, Glebov VV, Kirsanov SV, Konovalenko VV (1996) A method for producing a photographic image with the use of a semiconductor electrode. Russ J Electrochem 32(9):1060–1061 2. Dikusar AI et al (2008) Photoelectric structures based on nanoporous p–InP. Surf Eng Appl Electrochem 44(1):1–5 3. Glebov VV (2017) Investigation of effect of parameters of electrochemical processing with scanning electrode tool on material removal rate and quality of engineering products processing. Procedia Eng 206:918–923 4. Kukoz PhI, Kirsanov SV, Glebov VV (2000) The possibility of amplifying the density of technological current in the photoactive electrode instrument. Elektronnaya Obrabotka Materialov 4:4–6 5. Glebov VV (2015) Thermal vacuum deposition of transparent conductive layers on semiconductor electrode tools for electrochemical machining of engineering products. Procedia Eng 129:510–517 6. Datta M, Landolt D (2000) Fundamental aspects and applications of electrochemical microfabrication. Electrochim Acta 45:2535–2558 7. Davydov AD, Volgin VM, Lyubimov VV (2004) Electrochemical machining of metals: fundamentals of electrochemical shaping. Russ J Electrochem 40(12):1230–1265 8. Glebov VV, Prisyazhnyuk JuV, Kaplin LA (2012) Features of electrochemical machining of details from magnetic alloys. Nauchno-Tehnicheskij Vestnik Povolzh’ja 5:140–142 9. Volgin VM et al (2016) Modeling of electrochemical machining through a monolayer colloidal crystal mask for metal surfaces nanostructuring. Procedia CIRP 42:350–355 10. Kirsanov SV, Glebov VV (2004) Using the methods of electrochemical labeling in machine building. Elektronnaya Obrabotka Materialov 5:4–6 11. Glebov VV, Prisyazhnyuk JuV, Kirsanov SV (2011) Roughness and accuracy at electrochemical machining of details from magnetic. Kazanskaya Nauka 2:31–33 12. Glebov VV, Danilenko IN, Ratushinsky RI (2018) Hole drilling and milling of magnetic alloys parts by shaped tube electrolytic machining. MATEC Web Conf 226:03017 13. Crespilho FN, Zucolotto V, Oliveira ON, Nart FC (2006) Electrochemistry of layer-by-layer films: a review. Int J of Electrochem Sci 1:194–214 14. Shippell RJ (1978) Electro-chemical marking of circular strain grids. Exp Tech 5:1–4 15. Kirsanov SV, Glebov VV, Prisyazhnyuk JuV (2004) Influence of doping additives in alloy YuND 4 on capacity of electrochemical processing and roughness processed of surfaces. Metallobrabotka(Metal Working) 20(2):26–28 16. Kavei G, Gheidari AM (2008) The effects of surface roughness and nanostructure on the properties of indium tin oxide (ITO) designated for novel optoelectronic devices fabrication. J Mater Process Technol 208:514–519 17. Lee ES, Park JW, Moon YH (2002) A study on electrochemical micromachining for fabrication of microgrooves in an air-lubricated hydrodynamic bearing. Int J Adv Manuf Technol 20:720–726 18. Kukoz FI, Glebov VV, Kirsanov SV, Konovalenko VV (1995) Method of electrochemical marking. Surf Eng Appl Electrochem 5:67–68

Features of Design and Practical Application of Digital Twin of Internal Grinding Operation with CNC A. V. Akintseva(B) , A. V. Prokhorov, and S. V. Omelchenko South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, Russia [email protected]

Abstract. The emergence of modern CNC machines, which allow performing processing on specified cycles, revealed the problem of lack of effective design tools for optimal cycles of mode parameters control. To solve the problem, a system for designing optimal control cycles of mode parameters is proposed. This system includes digital models of accuracy limitations, roughness, etc., mathematical optimization too—dynamic programming method, method of optimal cycle designing, digital twin internal grinding, including a model of allowance removal and force model of the process. A digital twin of internal grinding operation essentially describes the process of the treated surface forming during the whole hole length throughout the cycle, considering initial technological conditions, features of metal removal in reverse and non-reverse zones, and unsteadiness of the processing. The article presents the features of digital twin designing for internal grinding. In addition to the optimization system, DT of internal grinding can be used for predicting the processing accuracy, identifying possible processing problems, verifying reliability of the designed cycles for the CNC machine under unstable processing conditions of batch parts, etc. Keywords: Digital twin · Internal grinding · CNC machines

Nomenclature V soc S rad VW V GW P Rb b DPM

Speed of wheel axial speed, mm/min Program value of radial component of the cutting force, mm/double stroke Speed of part rotation, m/min Speed of wheel rotation, m/sec Allowance, mm B-th workpiece radius, mm Sequence number of a workpiece radius Dynamic programming method

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_34

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1 Introduction CNC machines, which are the basis of the modern automated production, are becoming more and more popular at the enterprises of the engineering industry. Modern CNC machines make it possible to control the operation productivity by means of automatic stage cycles. In Fig. 1a the cycle of mode parameters control (radial feed— S rad mm/double stroke, speed of axial feed—V soc mm/min, speed of part rotation— V W m/min, speed of wheel rotation V GW m/sec—is not considered, being unregulated parameter) is given on the basis of the internal grinding (Fig. 1b). During the grinding process, the program values of mode parameters are changed in steps by the active control commands in dependence of the remaining allowance part (P, mm). The number of stages is limited by the technical capabilities of the used active control device. For each stage, the program values of the cutting modes and value of the removed allowance are set. Combination of these parameters must be optimal for the specified processing conditions. In other words, the cycle must provide the maximum productivity or cost price of the operation when meeting the requirements of the drawing for accuracy and quality in the parts batch, considering the instability of processing.

Fig. 1. Two-stage cycle of mode parameters S rad , V soc , and V W1 control in dependence on the value of the removed allowance (a) and scheme of internal grinding (b).

Currently, in existing CAD/CAM systems the process of cycles designing is partially automated: only for the programming backing off and advance of the grinding wheel. Mode parameters in existing CAD/CAM systems are set manually by technologist on the basis of personal production experience and (or) according to the recommendations of normative reference literature for universal machines. As a result, full automation of all stages of the design cycle becomes impossible, and, consequently, introduction of smart manufacturing and the concept of industry 4.0 [1, 2] also becomes impossible.

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It should be noted that to ensure the requirements of the drawing for the accuracy and quality of the treated surface the cutting modes are taken understated and, accordingly, nonoptimal. Many of both domestic [3–7] and foreign scientists [8–14] were engaged in improving the productivity of cycles and stabilizing the accuracy and quality in the designing cycles. However, most of these works have a number of general comments: • mathematical optimization methods are not always used. As a result, the designed cycles are rational; • optimization of only one parameter (most often radial feed) is considered, and other mode parameters are set according to the normative reference literature, reflecting the level of productivity and fleet of machine tools of the 60 s; • missing one of the most important models of productivity limitations for processing accuracy; • influence of variable technological factors is not considered. The solution to the problem above is to develop an automatic design system of optimal control cycles of cutting modes for all types of mechanical operations with CNC (Fig. 2). The development of the optimal cycles design system should be carried out in a single virtual environment using technologies of digital modeling and designing, by creating a digital twin of the mechanical processing [15–17]. In open sources, the demonstration works, describing external DT functions without description of calculation models, are presented. There are no works dedicated to developing DT of any mechanical processing, including internal CNC grinding. Therefore, the development of the digital twin for mechanical processing operation is currently relevant. It should be noted that DT for mechanical processing operation must give the possibility to simulate the processing of the billet considering initial conditions and variable technological factors for the parts batch (fluctuation of allowance and initial radial runout) and technological process in general (fluctuation of blunting degree and wheel diameter).

Fig. 2. Automatic design system of optimal control cycles of cutting modes.

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2 Features of Design and Practical Application of the Digital Twin of the Internal Grinding Operation Realized on the CNC Machine Consider in more detail the features of DT design on the example of internal grinding. Firstly, operation DT must reliably simulate all physical phenomena occurring in the cutting zone (kinematics, elastic and plastic deformations, friction and destruction, thermal and chemical phenomena), and also consider functional components of the physical content of the technological process (TP): mutual position of the part and tool, chip formation, cutting force, heat and temperature, tool wear (Fig. 3a).

Fig. 3. TP Functional structure (a) and structure of internal grinding cycle (b).

On the one hand, the cycle has a control effect on TP, and on the other hand, unstable processing conditions (allowance fluctuation, etc.) have a disturbing effect on TP. It is possible to get a control effect on TP by means of a cycle through control parameters (control cycles of mode parameters, geometrical parameters, overrun value, etc.); the result will be the output variables required by the production conditions (accuracy, quality, cost price, etc.). However, the designed cycle is limited by a number of input variables—cycle limitations (accuracy, roughness, power absorption, etc.). Therefore, the operation DT must consider all structural components of the cycle (Fig. 3b), which will give a capability of more complete TP control through the cycle. It should be noted that not only control cycles of the mode parameters need complex optimization, but also other parameters of cycle control—geometrical parameters and wheel characteristics, extension of grinding mandrel and many others. Most scientific research is devoted to optimization of only one mode parameter, most often radial feed [18, 19], and complex optimization of more than two parameters is not considered. DT of internal grinding operation essentially should describe the changes of allowance removal value on each radius of the considered section during the whole length of the treated hole at all workpiece revolutions and on each stroke of the grinding wheel considering

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• initial processing conditions (input variables—Fig. 3b); • kinematics of the internal grinding process (Fig. 1b); • mutual position of the part and tool, as well as its changes during the processing under the influence of the radial cutting force (elastic deformation of the technological system); • features of metal removal typical for internal grinding, which include (a) grinding mandrel with the wheel has the greatest compliance in the process of internal grinding. As a result, under the impact of the radial component of the cutting force the wheel is squeezed from the contact zone with the workpiece, what leads to a change of the wheel active height in the middle section of the workpiece hole and has a significant impact on the removed allowance; (b) presence of overrun and variable wheel height in the input and output sections of the workpiece hole (reverse zones), leading to the instantaneous change of the area of the workpiece and wheel contact zone; (c) alternation of different grinding types in the reverse zones and presence of stages of the wheel plunge in the input section and dwelling, resulting from unnoticeable delays in the switching system of the machine feed. • variable technological factors which include fluctuations of the blunting degree and the wheel diameter, initial radial runout, and workpiece allowance. All of the above is considered in the developed model of the metal removal in the internal grinding process [20], which is a digital twin of the internal grinding operation, considering the initial processing conditions and their fluctuations in the process. The basis of the proposed model of metal removal is the developed force model [21], which essentially reflects all physical phenomena occurring in the cutting zone. In other words, the force model of the internal grinding process sets the interrelation between the cutting forces, physical and mechanical properties of the treated material, geometry of the contact zone of the tool and workpiece, tool characteristic, and other indexes that affect the processing. The necessity of developing the force model of the internal grinding is conditioned by the fact that the majority of works [22–25] is devoted to the cutting force modeling in the form of empirical dependences in a narrow range of variable factors. Often these models do not set a direct relation between the cutting forces and cutting modes and do not consider the process of the wheel grains blunting. Due to the fact that the model of metal removal allows calculating the value of removed allowance on each considered radius of the treated sections across the whole length, it becomes possible to calculate the current values, what lets to describe the forming process of the treated surface during the whole processing cycle. Knowing the current values of different section radii located along the whole workpiece, it becomes possible to impose cycle productivity on the processing accuracy [26]. In addition to the digital twin of internal grinding, digital models of limitations must also be developed for the full function of the designing system of the optimal cycles; these models are connected with

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• drawing requirements of the part (accuracy, absence of burnt place, roughness); • certificate data of the machine (ranges of mode parameters, compliance of the technological system, drives power); • tool parameters (wheel characteristic, wheel wear, blunting degree of the wheel grains); • setting operation parameters (wheel overrun, setting of cutting modes in the reverse zones), etc. The optimal cycle design system also requires a tool of mathematical optimization (Fig. 1). For example, in the developed methodology of optimal cycles designing on internal grinding operations [27], the dynamic programming method is used as a mathematical optimization method [28]. The main time was used as the target function in the developed method, but it would be more logical to use two criteria: optimal main time and cost price of the operation, performing two-criterion optimization [29]. This will allow to design cycles from single to mass production type, considering features of production release. For example, in single and short-run productions it is advisable to use two-stage cycles, because increasing the number of stages when processing a small number of parts will not give appreciable economic benefits. As for the mass and large-scale production, it is advisable to use three- and four-stage cycles, because the productivity increase of the operation even by 1% can give an appreciable economic benefit when processing a large batch of workpieces. The obtained optimal cycle is also a digital twin of the designed cycle. Similarly, it is possible to get a digital twin of the factory cycle for the technological operation. Therefore, in addition to system optimization DT of internal grinding operation is possible to use to prevent reject and identify the causes of its formation, prediction of processing quality, reliability proving of the designed cycles for CNC machine to a set of unstable processing conditions of the parts batch, etc.

3 Conclusions DT of internal grinding operation allows to do iterative calculations of the allowance removal and current radii value in the considered sections along the entire length of the hole throughout the whole grinding cycle, considering the initial processing conditions, features of metal removal, and variable technological factors. Therefore, the DT of internal grinding operation is a fundamental element of the design system for optimal control cycles of mode parameters. Also, in addition to optimization system of DT, internal grinding operation can be used for prediction of the processing quality, identification of possible processing problems, verifying the reliability of designed cycles for CNC machine under unstable processing conditions of the parts batch, etc. Acknowledgements. This research was funded by Ministry of Science and Higher Education of the Russian Federation (grant No. FENU-2020-0020).

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References 1. Vasja Roblek V, Meško M, Krapež A (2016) A complexity view of Industry 4.0. SAGE Open, 1–11. https://doi.org/10.1177/2158244016653987 2. Krishnamurthi R, Kumar A (2020) Modeling and simulation for industry 4.0. A roadmap to industry 4.0: smart production, sharp business and sustainable development, pp 127–141. https://doi.org/10.1007/978-3-030-14544-6_7 3. Lur’e GB (1979) Optimizing the grinding cycle by adaptive control. Mashinostroitel’, Moscow 4. Bratan SM (2006) Tekhnologicheskie osnovy obespecheniya kachestva i povysheniya stabil’nosti vysokoproizvoditel’nogo chistovogo tonkogo shlifovaniya (Technological basis for ensuring quality and improving the stability of high-performance fine grinding). Dissertation, University of Odessa 5. Novoselov YuK (2012) Dinamika formoobrazovaniya poverhnostej pri abrazivnoj obrabotke (The dynamics of the formation of surfaces during abrasive processing). Izd-vo SevNTU, Sevastopol’ 6. Guzeev V, Nurkenov A (2016) Researching the CNC-Machine stiffness impact on the grinding cycle design. Procedia Eng 150:815–820. https://doi.org/10.1016/j.proeng.2016.07.118 7. Shipulin LV, Ardashev DV (2019) Concept of dsigning high-speed processing operations based on complex process simulation. Procedia Manuf 1:1–18 8. Tung L, Hong T, Cuong N, Vu N (2019) A study on optimization of manufacturing time in external cylindrical grinding. In book: Advances in engineering research and application, Proceedings of the international conference on engineering research and applications, ICERA 2019. https://doi.org/10.1007/978-3-030-37497-6_14 9. Amitay G, Malkin S, Koren Y (1981) Adaptive control optimization of grinding. J Eng Ind 103(1):103–108. https://doi.org/10.1115/1.3184449 10. Gao S, Yang C, Xu J, Fu Y, Su H, Ding W (2017) Optimization for internal traverse grinding of valves based on wheel deflection. Int J Adv Manuf Technol 92:1105–1112. https://doi.org/ 10.1007/s00170-017-0210-8 11. Dong S, Danai K, Malkin S, Deshunukh A (2004) Continuous optimal in feed control for cylindrical plunge grinding. Part 1. Methodology. J Manuf Sci Eng 126(2):327–333. https:// doi.org/10.1115/1.1751423 12. Alagumurthi N, Panairadja K, Soundararajan V (2006) Optimization of grinding process through Design of Experiment (DOE)–A comparative study. Mater Manuf Process 21(1):19– 21 13. Phan AM, Summers MP, Parmigiani JP (2011) Optimization device for grinding media performance parameters. Int Mechan Eng Congr Expos (IMECE) 3:915–923 14. Barrenetxea D, Alvarez J, Marquinez JI, Gallego I, Perello IM, Krajnik P (2014) Stability analysis and optimization algorithms for the set-up of infeed centerless grinding. Int J Mach Tools Manuf 84:17–32. https://doi.org/10.1016/j.ijmachtools.2014.04.005 15. Uhlemann TH-J, Lehmann C, Steinhilper R (2017) The digital twin: realizing the cyberphysical production system for industry 4.0. Procedia CIRP 61:335–340. https://doi.org/10. 1016/j.procir.2016.11.152 16. Uhlemann TH-J, Schock C, Lehmann C, Freiberger S, Steinhilper R (2017) The digital twin: demonstrating the potential of real time data acquisition in production systems. Procedia Manuf 9:113–120. https://doi.org/10.1016/j.promfg.2017.04.043 17. Kannan K, Arunachalam N (2019) A digital twin for grinding wheel: an information sharing platform for sustainable grinding process. J Manuf Sci Eng 141(2):021015. https://doi.org/ 10.1115/1.4042076

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18. Pereverzev PP, Pimenov B (2015) Optimization of control programs for numerically controlled machine tools by dynamic programming. Russ Eng Res 35(2):135–142. https://doi.org/10. 3103/s1068798x15020197 19. Shipulin L, Nurkenov A, Mazein P (2018) Implementation of the design concept of a highspeed processing cycle for CNC machines in the form of a software module CAM-system. IOP Conf Series Mater Sci Eng 450(3):032028. https://doi.org/10.1088/1757-899x/450/3/ 032028 20. Akintseva AV, Prokhorov AV, Omelchenko SV (2020) Modelling of correlation of actual and program feeds in the automatic cycle. IOP Conf Series Mater Sci Eng 709:033003. https:// doi.org/10.1088/1757-899x/709/3/033003 21. Pereverzev PP, Akintseva AV (2016) Model of cutting force while managing two regime parameters in the process of internal grinding. Procedia Eng 150:1113–1117. https://doi.org/ 10.1016/j.proeng.2016.07.222 22. Ding H, Han Y-C, Zhou K (2020) Grinding force modeling and experimental verification of rail grinding. RCHIVE Proc Inst Mech Eng Part J J Eng Tribol 208:1994–1996. https://doi. org/10.1177/1350650119900738 23. Pereverzev PP, Pimenov DY (2016) A grinding force model allowing for dulling of abrasive wheel cutting grains in plunge cylindrical grinding. J Frict Wear 37(1):60–65 24. Brinksmeier E, Aurich J, Govekar E, Heinzel C, Hoffmeister H, Klocke F, Peters J, Rentsch R, Stephenson D, Uhlmann E, Weinert K, Wittmann M (2006) Advances in modeling and simulation of grinding processes. CIRP Annals - Manuf Technol 55(2):667–696. https://doi. org/10.1016/j.cirp.2006.10.003 25. Trung D, Man N, Son PX (2019) Determining cutting force after surfaceRoughness measurement in grinding. Springer Nature Switzerland AG 63:1–7. https://doi.org/10.1007/9783-030-04792-4_33 26. Pereverzev PP, Akintseva AV (2016) Model of formation of processing errors intragrinding. Russ Eng Res 36(12):1048–1053. https://doi.org/10.3103/s1068798x16120133 27. Akintseva AV, Prokhorov AV, Omelchenko SV (2020) Methodology for designing optimal internal grinding cycles resistant to varying processing conditions. IOP Conf Series Mater Sci Eng 709:033004. https://doi.org/10.1088/1757-899x/709/3/033004 28. Bellman R (1960) Dynamic programming. Foreign Literature Publishing House, Moscow 29. Pereverzev PP, Akintseva AV, Ardashev DV (2019) Two-criteria optimization of automatic grinding cycles for CNC machines. STIN 11:15–18

Assessing Cutting Force: A Study of Varying Internal Grinding Wheels A. V. Akintseva(B) , A. V. Prokhorov, and A. A. Kopyrkin South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, Russia [email protected]

Abstract. We developed a cutting force model which takes into account the kinematics and features of internal grinding. Our model also lays out the relationships between cutting force, cutting modes, and other technological factors which have a significant impact on its value, including the concept of “wheel dulling degree.” The degree of wheel dulling (η) is equal to the relation of the total area of the abrasive grain dulling to the geometric area of the entire working surface of the wheel. η determines the relative base surface of the wheel on the dulling areas of the wheel grains. Our proposed cutting force model will further serve as the foundation for a stock removal model for internal grinding, which in turn will allow for the optimization of internal grinding cycles. This will ensure the precise accuracy and quality of the treated surface under variable technological conditions. This article presents experimental confirmation of the mathematical model of interrelation between the cutting force and parameters of the wheel performance indicators through the complex parameter “degree of wheel dulling.” Keywords: Grinding · Wheel · Wheel performance indicators · Grains dulling

Nomenclature V soc S rad Sf VW V GW M 3, M 4 σi d D T η Py Q

Speed of wheel axial speed, mm/min Program value of the radial component of the cutting force, mm/double stroke Actual radial feed, mm/stroke Speed of part rotation, m/min Speed of wheel rotation, m/sec Coefficients determined by formulas (2) and (3) Intensity of the stress condition, N/mm2 Workpiece diameter, mm Wheel diameter, mm Height of the grinding wheel, mm Degree of wheel dulling Radial component of the cutting force, N Stock removal rate in one working stroke, mm3 /min

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_35

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1 Introduction The performance indicators of the abrasive wheel are the most important technological factors affecting the cutting force, and therefore the quality of the treated surface of the workpiece after internal grinding. However, the analytical interrelation between the wheel performance indicators, cutting modes, and quality of the treated surface has still not been determined entirely. Namely, it has not been determined in wideranging mathematical models for processing conditions in the normative space of all combinations of steel grades, wheel performance indicators, parameters of accuracy and quality of the treated surface, the diameters and geometry of the contact zone of the wheel and the workpiece, parameters of machine tools, cutting modes, engineering setup, etc. Therefore, in automated engineering, there are no methods for automatic designing of the optimal cycles of cutting modes considering the parameters of the wheel with different characteristics. To solve this problem, it is necessary to experimentally confirm the mathematical model of cutting force which contains a parameter that considers the wheel performance indicators as a whole.

2 Review of Existing Methods for Developing Models of the Cutting Force Occurring During Internal Grinding Radial cutting force Py is the main integral parameter which determines the elastic movements of metal-cutting machines and, accordingly, through the actual radial feed, stock removal rate, and current values of the radii of the treated surface [1–4]. It can be said that the radial component has the strongest influence on the accuracy parameters of the workpiece and the quality of the treated surface. Grinding is often the final stage of the technological process, after which the finished product is delivered to the consumer. Therefore, grinding operations are held to strict requirements for the quality and accuracy of the treated surface. For example, the requirements for internal grinding are as follows: diameter dimensions—5–6 accuracy grade; deviation from roundness and deviation of the longitudinal section profile by 5–7 accuracy grade; fine finish of the surface—Ra 0.06–2.5; there must be no burnt places, cracks, abrasive scratches, and other defects. The development of force models of the grinding process and experimental confirmation thereof has been the focus of papers by researchers from around the world [5–12]. Most of these are devoted to modeling cutting force in the form of empirical dependencies in a narrow range of variable factors (for one wheel performance indicator and several steel grades) without considering the dulling of the wheel grains. In addition, there are no power models of internal grinding that take into account fluctuations in technological conditions over a wide range as well as the kinematics of hole grinding. It is worth noting the work of Korchak [5], which describes a cutting force model, realized on the basis of equality of cutting forces and resistance force of the processed metal to plastic deformation during grinding with a single abrasive grain. Also of note is the work of Pereverzev [13], who determined the balance of power of cutting forces using a model with a single abrasive grain. At the same time, the functional correlation between the intensity of stock removal during surface grinding and the deformable volume of metal in the shear zone is used as the foundation of their research. The power balance

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of the cutting forces makes it possible to sum the cutting forces of single grains in the cutting zone of the wheel and the workpiece. As a result, the researchers obtained a force model of external grinding with radial feed [13]. The power balance of the cutting forces makes it possible to sum the cutting forces that occur on each abrasive grain in the zone of allowance. The model sets the interrelation between the cutting force, cutting modes, geometrical parameters, and the performance indicators of the grinding wheel.

3 Analytical Model of the Cutting Force that Occurs During Internal Grinding Using the model of the interaction between abrasive grains and the workpiece developed in work [5], and summing up the cutting forces from each abrasive grain [13], we obtained a mathematical model of the cutting force for internal grinding. This model was more thoroughly described in a previous publication [14]. In this article, we will only need the radial element of the cutting force:  (1) PY = M1 Sf + M2 Sf Coefficients M 1 and M 2 can be found by formulas: M1 = 

1.86σi π dVSoc

2 (VGW + VW )2 + VSoc  dD σi ηT M2 = 3 d −D

(2)

(3)

To account for cutting force fluctuations during processing, we must consider the dulling of the abrasive grains on the wheel during grinding. Therefore, we will take a parameter called the degree of wheel dulling as a measure of the dulling of the abrasive grains and denote it using the variable η. Degree of wheel dulling η is equal to the relation of the total area of grain dulling to the area of the wheel working surface, i.e., η determines the relative base surface of the wheel on areas of the wheel grains dulling. It should be noted that the obtained force model [14] considers the kinematics of grinding holes and the features of the process internal grinding and defines the relationship between all the main technological parameters affecting the process of stock removal (cutting modes, grinding wheel performance indicators, contact area of the wheel with the workpiece, properties of the processed material). Many parameters in the cutting force model of internal grinding (1) maintain the values of their constants: workpiece diameter and width, physical and mechanical properties of the processed material, circumferential speed of wheel rotation, etc. Three parameters are exceptions: the radial component of the cutting force, actual radial feed, and the degree of wheel dulling. Therefore, for our experimental tests of the cutting force model, it is sufficient to control only two parameters if the constant value of the third parameter is ensured.

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4 Experimental Studies of the Cutting Force in Internal Grinding with Wheels with Various Performance Indicators Through analysis of experimental methods, we have determined that if grinding is performed with a constant value of the radial element of the cutting force Py = const, then we can measure the experimental values of the actual radial feed S f and ratio of the wheel dulling η. With these data, it is possible to plot the graph S f = f (η) and complete an adequacy assessment of the force model. To obtain the analytical model S f = f (η), we solve Eq. (1) in relation to the actual radial feed S f and obtain an expression (4) showing the interrelation between the actual radial feed, the degree of wheel dulling, and the radial component of the cutting force:  ⎡ ⎤2 −(ηM2 ) + (ηM2 )2 + 4M1 PY ⎦ Sf = ⎣ (4) 2M1 Experimental studies were conducted to assess the adequacy of the cutting force model. The experiments were conducted on a special stand that ensures constant pressure at the wheel–workpiece interface. During the experiment, we measured actual radial feed S f and the degree of wheel dulling η. The change in actual radial feed S f was measured through the stock removal rate Q by periodically measuring the volume of stock removed from the sample at specified time intervals. The productivity of the stock removal rate Q can be calculated using the following formula (for internal grinding) [15]: Q = π dVSoc Sf .

(5)

Express the formula (4) through the parameter Q after the joint solution of the Eqs. (4) and (5):  ⎡ ⎤2 −(ηM2 ) + (ηM2 )2 + 4M1 PY ⎦ . (6) Q = π dVSoc ⎣ 2M1 Samples from different steel grades were ground during the experiment. The radial component of the cutting force (Py = const) was selected in a way that allows to carry on grinding in a guaranteed dulling mode with the formation of dulling areas on the back surface of cutting grains. Grinding was carried out from 0.5 to 2 min in dependence on the force Py = const and wheel characteristic. In the intervals between grinding the sample, the stock removal rate Q and the ratio of the wheel dulling η were measured. The experimental value of η was determined by measuring the dimensions of the grain dulling areas [16–18]. The value of the parameter η was calculated as the relation of the total area of the grain dulling areas on the measured working surface to the working surface of the wheel. The abrasive grain dulling areas were measured using a binocular microscope installed on the grinding tool above the grinding wheel. When installing the microscope, the axis of its lens is directed along the axis of the grinding wheel (Fig. 1) such that the working surface of the wheel and grain dulling areas

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are perpendicular to the axis of the microscope lens. A point light source was directed into one eyepiece of the microscope. The other eyepiece has a built-in grid, by which the grain dulling areas were measured at 105x magnification.

Fig. 1. Scheme of the measurement of dulling areas: 1—Microscope; 2—Point source of light; 3—Ray; 4—Measuring grid; 5—Section of the grinding wheel profile.

All grain dulling areas involved in the metal cutting and friction on the back surface are located perpendicular to the ray of light coming from the microscope lens; they are clearly visible (Fig. 2). Grinding was carried out using wheels 5 50x40x63 25AF60M7V35A1 (40 mm wheel diameter), at 35 m/sec wheel speed, with the revolution speeds of the wheel and the workpiece equal to 2600 min−1 and 180 min−1 , respectively. The diameter of the sample before processing was 60 mm. The width of the processed surface of the sample is equal to 100 mm. During the experiment, the diameter of the sample was measured using a micrometer. The wheel was dressed with a C-1 diamond dresser. An aqueous solution of soda (1%) and sodium nitrite (0.4%) was used as the coolant. Samples of the S600 steel grade were polished on the stand. The chemical composition of steel in % according to standard 19265-73 is as follows: carbon C 0.85–0.95%;

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Fig. 2. Dulling areas of grains in reflected light (250X).

magnesium Mg ≤ 0.5%; nickel Ni ≤ 0.4%; sulfur S ≤ 0.03%; phosphorus P ≤ 0.03%; chromium Cr 3.8– 4.4%; molybdenum Mo ≤ 1%; tungsten W 8.5–9.5%; vanadium V 2.3–2.7%; cobalt Co ≤ 0.5%; silicon Si ≤ 0.5%; the remainder is iron Fe. Stress intensity σ i = 3198 MPa [5]. Grinding time was 60 s. Figure 3 displays our obtained graphs of the experimental dependencies of changes in the stock removal rate Q and ratio of the wheel dulling η when grinding a sample of P9 steel with constant pressure at the wheel–workpiece interface.

Fig. 3. Experimental points and theoretical dependence between stock removal rate and degree of dulling.

Analysis of our experimental data shows that the stock removal rate decreases as the abrasive grains of the wheel dull during grinding with constant pressure at the wheel– workpiece interface. That is, our experiment confirmed the correctness of the theoretical model of cutting force.

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In Fig. 3, we show an approximation of the experimental data of the theoretical curve according to formula (14). Statistical manipulation of the results of the experiments showed that the calculation error does not exceed 15% with a confidence interval of 0.95. Therefore, our mathematical model (2) can be applied to the model of surface formation during grinding.

5 Conclusions The existing model of cutting force for internal grinding [14] takes into account the kinematics of hole grinding and the features of stock removal process. Our model also lays out the relationships between cutting force, cutting modes, and other technological factors which have a significant impact on its value, including the introduced concept of “degree of wheel dulling.” This article presents an experimental confirmation of the mathematical model proposed in [14] for the relationship of cutting force with the parameters of a wheel’s performance indicators. This relationship was found through a complex parameter of the degree of wheel dullness. Analysis of our obtained experimental data confirms the theoretical model of cutting force which posited that the stock removal rate decreases as the abrasive grains of the wheel become dull during grinding with constant pressure at the wheel–workpiece interface. In the future, the developed cutting force model will serve as the foundation for a stock removal model for internal grinding [19], which in turn will allow for the optimization of internal grinding cycles [20]. Doing so will support the precise accuracy and quality of processed surfaces under varying technological conditions.

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9. Leonesio M, Sarhangi M, Bianchi C, Parenti P, Cassinari A (2015) A Meta-model framework for grinding simulation. Procedia CIRP 31:357–362. https://doi.org/10.1016/j.procir.2015. 03.086 10. Barrenetxea D, Alvarez J, Marquinez JI, Gallego I, Perello IM, Krajnik P (2014) Stability analysis and optimization algorithms for the set-up of infeed centerless grinding. Int J Mach Tools Manuf 84:17–32. https://doi.org/10.1016/j.ijmachtools.2014.04.005 11. Xuekun L (2010) Modeling and simulation of grinding processes based on a virtual wheel model and microscopic interaction analysis. Dissertation, Tsinghua University 12. Shavva MA, Grubiy SV (2015) Cutting forces calculation at diamond grinding of brittle materials. J. Appl Mech Mater 770:163–168. https://doi.org/10.4028/www.scientific.net/AMM. 770.163 13. Pereverzev P, Pimenov B (2015) Optimization of control programs for numerically controlled machine tools by dynamic programming. Russ Eng Res 35(2):135–142. https://doi.org/10. 3103/S1068798X15020197 14. Pereverzev PP, Akintseva AV (2016) Model of cutting force while managing two regime parameters in the process of internal grinding. J. Procedia Eng 150:1113–1117. https://doi. org/10.1016/j.proeng.2016.07.222 15. Pereverzev PP, Popova AV, Pimenov DY (2015) Relation between the cutting force in internal grinding and the elastic deformation of the technological system. Russ Eng Res 35(3):215– 217. https://doi.org/10.3103/S1068798X15030156 16. Pereverzev PP (1993) Theory and calculation method of the optimal cycles of parts processing on the circular grinding machines with program control. Dissertation, University of Chelyabinsk 17. Pereverzev P, Akintseva A, Ardashev D (2019) Calculation of dulling ranges of grinding wheels of various characteristics between edits. STIN 11:37–40 18. Ardashev DV, Guzeev VI (2017) Calculation of dulling ranges of the grinding wheels with different characteristics between dressings. J. Russian Eng Res 37(2):164–166. https://doi. org/10.3103/S1068798X17020046 19. Akintseva AV, Prokhorov AV, Omelchenko SV (2020) Modelling of correlation of actual and program feeds in the automatic cycle. IOP Conference Series Materials Science and Engineering 709:033003. https://doi.org/10.1088/1757-899X/709/3/033003 20. Akintseva AV, Prokhorov AV, Omelchenko SV (2020) Methodology for designing optimal internal grinding cycles resistant to varying processing conditions. IOP Conference Series Materials Science and Engineering 709:033004. https://doi.org/10.1088/1757-899X/709/3/ 033004

Analysis of the Influence of Installation Deformations of Diesel Cylinder on Its Operating Indicators I. E. Agureev, R. N. Khmelev(B) , and K. Yu. Platonov Tula State University, 92 Lenin Ave, Tula 300012, Russia [email protected]

Abstract. The article presents the results of experimental studies of changes in the inner diameter of the cylinder of air-cooled multipurpose diesel engines from the action of mounting forces, as well as the patterns of the effect of mounting deformations of the diesel cylinder on its performance. The internal diameter of the investigated cylinders was measured on control and measuring machine after the application and removal of mounting forces. To simulate the application of mounting forces, a cassette device was made that simulated the upper part of the diesel crankcase and the cylinder head and made it possible to measure the internal diameter of the cylinder in a stressed state. It is established that cylinder deformations are elastic. To increase the stability of the cylinder geometry, the technology of honing cylinders in a stressed state (in cassette devices) was tested and an experimental assessment of its effectiveness was carried out. The test results of the 1H9,5/8,0 diesel engine with serial and experimental cylinders are presented. It is shown that a diesel engine with an experimental cylinder at an operating time of 13 h, has effective indicators that fully meet the requirements of TU and are practically not inferior to a diesel engine with serial cylinders at an operating time of 21 h. An analysis of the results allows us to recommend a running time of 13 h. Keywords: Diesel · Cylinder · Mounting deformations · Operational indicators

1 Introduction The cylinder is one of the most critical parts of internal combustion engines (ICE). All other things being equal, the level of deformation of the cylinder and the stability of its geometry significantly affect the duration of engine break-in, the value of mechanical losses [1–3], the probability of sticking (wedging) in the cylinder–piston group (CPG) at the stage of a break-in, and the possibility of the engine achieving the required output characteristics stick [4]. The noted, to a greater extent, is characteristic of single-cylinder high-speed diesel engines with air cooling [5].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_36

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The works by Ageev [5], Putintsev [6, 7], Chaynov [8], Pospelov [9], are devoted to the study of mounting deformations of the ICE cylinder, as well as their influence on engine performance Efros [4], Vagabov [10, 11], Chugunov [12] and other scientists [13, 14]. In the published works, questions of the nature of the occurrence of strains, their modeling [15, 16], methods of reduction are considered, however, due attention is not paid to a comprehensive analysis of the influence of mounting deformations of a diesel cylinder on its performance indicators, such as • • • • • •

effective power; effective torque; specific effective and hourly fuel; consumption of crankcase gases; moment of mechanical losses; the duration of diesel operating time before bearer and periodic tests.

In this work, for various designs of cylinders of high-speed diesel 1H9,5/8,0, experimental studies of the inner diameter of the cylinder at various stages of the life cycle are performed, namely: • after finishing machining • in assembly under the influence of installation efforts; • after operating time and tests.

2 Investigation of Elastic Properties and Level of Mounting Deformations of Cylinders An experimental assessment was made of the impact of the proposed technology for honing cylinders in cartridges (under the influence of mounting forces) on the operating time and operational performance of a 1H 9,5/8,0 diesel engine. At the first stage, an experimental assessment was made of the elastic properties and the level of mounting deformations of 1H8,5/8,0 and 1H9,5/8,0 diesel cylinders [17–19]. To conduct experimental studies, a cassette device was made that simulated the upper part of the diesel crankcase and the cylinder head and made it possible to measure the internal diameter of the cylinder in the assembled state. The device consists of two steel rings. The lower ring imitates the upper part of the diesel crankcase for cylinder fit and has four threaded holes for the studs. The upper ring (false head) with four holes and a groove imitates the cylinder head [20]. A general view of the cylinders in the cartridges is shown in Fig. 1. Measurements of the inner diameter of the cylinders were carried out on a coordinate measuring machine (CMM) with an accuracy class of 5 µm. The coordinates of the cylinder belts during measurements are given in Table. 1. The top of the cylinder is taken as the beginning of the report. The cylinder layout during measurements is shown in Fig. 2. When measuring the cylinders of diesel engines 1H8,5/8,0 and 1H9,5/8,0 with diameters of 85 mm and 95 mm, respectively, the fact of restoration of the original internal

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Fig. 1. Cylinders in cartridge.

Table 1. The coordinates of the cylinder belts when taking measurements on a coordinate measuring machine. № zone

1

2

3

4

5

6

7

8

Coordinate mm 5.0 15.0 22.0 50.0 80.0 100.0 115.0 140.0

Fig. 2. Diagram of the cylinder during measurements.

diameter after application and removal of mounting efforts was established. In this case, the maximum difference in cylinder diameters before installation and after was no more than 7 µm. For the considered cylinder designs, the level of mounting deformations largely depends on the size of their diameters. The graphs of changes in the inner diameter of

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the cylinders in four vertical planes are shown in Fig. 3a, b. The graphs show that changes in the cylinder diameter of the 1H9,5/8,0 diesel engine compared to the 1H8,5/8,0 diesel engine during installation are more significant and exceed 20 µm in some zones. At the same time, in a 1H8,5/8,0 diesel engine with a cylinder diameter of 85 mm, these deformations do not exceed 8 µm.

Fig. 3. Averaged results of measuring the diameter of the cylinders of diesel engines in a free state and in the assembly: a 1H 9,5/8,0; b 1H8,5/8,0.

In order to reduce the distortion of the shape of the cylinder of the 1H9,5/8,0 diesel engine that occurs during its installation, and to reduce the duration of the break-in cycles, as well as taking into account the revealed effect of restoring the shape of the inner surface of the cylinder from the action of mounting forces, the process of honing the cylinders in cartridges was tested. The existing tool for the honing machine has been upgraded so that it can be installed in the machined cylinder in the cassette. The diagram of the device for honing cylinders was chosen classic: rigid fastening of the workpiece and a tool movable on hinges.

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Studies have shown that the cylinder almost completely restores the original shape of the inner surface obtained by honing in the cartridge, after disassembly and subsequent assembly into the cartridge [17].

3 The Research of the Effect of Mounting Deformations of the Diesel Cylinder on Its Performance At the second stage, an experimental assessment was made of the influence of mounting deformations of the diesel cylinder on its operational performance, as well as checking the effectiveness of the technology of honing cylinders diesel 1H9,5/8,0 in cartridges [21]. The experiment was conducted at the bench for technological break-in and diesel testing. The test object is a diesel engine 1H9,5/8,0 with an operating time of 30 h. Cylinders for testing in the amount of six pieces were taken from the same heat. During the tests, the production program for diesel operating time before bearer tests in the amount of 21 h (seven cycles of 3 h each) was taken as the basis. The stand provided measurements in the operating range of speed and load modes of the following diesel engine performance indicators: • • • • • •

after finishing machining, n; load, M; instant fuel consumption, Ge; pressure and oil temperature, Poil and Toil ; exhaust gas temperature, Tgas . crankcase gas flow rate Gk .

The test results of the 1H9,5/8,0 diesel engine with serial and experimental cylinders are shown in Fig. 4 and Table 2.

Fig. 4. Test results of a diesel engine with serial a and experimental b cylinders for operating hours.

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Table 2. Test results of a diesel engine with serial and experimental cylinders. Characteristic cylinder

Ne, kw (at n = 3350 rpm)

ge „ (at n = 3350 rpm)

1 Gk , min

Conditional mechanical losses, kW

Required Operating Time, h

Serial

11.82

289

12.67

5.84

21

Experimental

11.75

288

11.0

5.65

13

Based on the results given in Table 2, we can conclude that the 1H9,5/8,0 diesel engine with an experimental cylinder and an operating time of 13 h have effective indicators that fully meet the requirements of technical conditions and practically are not inferior to a diesel engine with serial cylinders with an operating time of 21 h (Fig. 5).

Fig. 5. The results of measuring the diameters of the cylinders of diesel engines in the cartridge before and after the test run.

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After the graphs analyzing, we can conclude that, in the process of engine break-in, there is an increase in the diameter of its cylinder by 0.005–0.02 mm. In this case, the geometry of the cylinder wall changes slightly. This fact allows us to conclude that the entire surface of the cylinder is worked out equally.

4 Conclusion Thus, for the considered cylinders with the elastic nature of mounting deformations, honing in the stress state is uniform since it contributes to the stability of their geometry. An analysis of the results allows us to recommend a running time of 13 h for a 1H9,5/8,0 diesel engine with a test cylinder characterized by a lower level of mounting deformations. Studies have shown that after 13 h of running time, the crankcase gas consumption practically does not change, the specific effective consumption fuel and conventional power of mechanical losses.

References 1. Lukanin VN, Alekseev IV, Shatrov MG and others (2007) Internal combustion engines. Dynamics and Design: a textbook for high schools. Higher school, Moscow, p 40 2. Vyrubov DN et al (1983) In: Orlin A S, Kruglov M G (eds) Internal combustion engines: Theory of piston and combined engines., Engineering industry, Moscow, p 183 3. Pronin MD (2009) Reducing mechanical losses by improving the design of the piston of a high-speed diesel engine: abstract dissertation. BMSTU, Moscow 4. Efros VV et al (1976) Air-cooled diesels of the Vladimir Tractor Plant. Mechanical Engineering, Vladimir, p 267 5. Ageev AG (2017) Reducing mechanical losses in a high-speed air-cooled diesel engine by improving the design of CPG parts, dissertation. BMSTU, Moscow 6. Putintsev SV (2018) Introduction to the tribology of piston engines: a textbook. Publishing House MSTU, N.E. Bauman, Moscow, p 319 7. Putintsev SV (1998) The reduction of mechanical losses in automotive internal combustion engines: dissertation. BMSTU, Moscow 8. Chaynov ND, Ivashchenko NA, Krasnokutsky AN, Myagkov LL (2011) The design of internal combustion engines: a textbook for university students. Mechanical Engineering, Moscow, p 496 9. Pospelov DR (1961) Air-cooled internal combustion engines. Edition of literature on tractor and agricultural engineering, Moscow, p 556 10. Yakhyaev NI, Vagabov NM (2009) Complex method of analysis of geometrical accuracy of cylinders in the process of assembly of small-size marine diesel engines. AGT Messenger. Ser Mar Eng Technol 1:256–261 11. Vagabov NM (2010) A study of the assembly accuracy of a small ship diesel engine and the development of methods for reducing the deviations of macrogeometry of cylinders: Abstract. Dissertation. DSTU, Makhachkala 12. Chugunov GP (2003) Increasing the durability of the cylinder-piston group of the KamAZ engine by reducing mounting deformations, dissertation. Penza 13. Lan LP, Xiang JH, He LG (2015) Deformation characteristics of diesel engine cylinder liner under pretightening condition. Neiranji Xuebao/Trans CSICE (Chin Soc Intern Combust Eng) 33(6):555–561

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14. Ma Z, Henein NA (2002) Cylinder liner surface analysis during si engine break-in. Tribol Trans 45(3):397–403 15. Bulatov VP, Bochkarev VN, Yakhyaev NYa (1988) Evaluation of assembly deformations of cylinder liners for small diesel engines, Strength of Materials 20(6):826–831 16. Gutieva NA (2007) The calculation of the deformation of the supporting ribs of the cylinder liners and the block-crankcase of diesel engines, Vestnik DSTU. Tech Sci 13:62–63 17. Agureev IE, Platonov KYu, Khmelev RN (2018) Analysis of the laws of deformation of the diesel engine cylinder with air cooling from the actions of assembly efforts. In: Progress of vehicles and systems-2018: proceedings of the international scientific-practical conference. Volgograd State Technical University, pp 52–53 18. Agureev IE, Khmelev RN, Platonov KYu (2019) Computational and Experimental Studies of Deformation of Air-Cooled Diesel Cylinders at Its Assembling. In: Radionov AA, Kravchenko OA, Guzeev VI, Rozhdestvenskiy YuV (eds). Proceedings of the 5th International Conference on Industrial Engineering (ICIE 2019). Lecture Notes in Mechanical Engineering, vol 2. Springer, pp 261–270 19. Platonov KYu, Khmelev RN (2017) Modeling and analysis of deformations of the cylinder ofa diesel single-cylinder engine in the assembly stage. In: Design, use and reliability of agricultural machinery. Publisher, Bryansk State Agrarian University, pp 274–278 20. Birger IA, Iosilevich GB (1990) Threaded and flanged connections. Machine Building, Moscow, p 368 21. Khramtsov NV (1991) Run-in and test of tractor engines. Agropromizdat, Moscow, p 125

Studies on the Effect of Output Parameters on Productivity When Turning Titanium Alloys A. V. Savilov1(B) and A. G. Serebrennikova2 1 Irkutsk National Research Technical University, 83, Lermontov St., Irkutsk 664074, Russia

[email protected] 2 Komsomolsk-Na-Amure State University, 27, Lenin Av., Komsomolsk-na-Amure 681013,

Russia

Abstract. The article presents the results of studies on productive turning of titanium alloys which are widely used in different industries, including the aircraft one. Methods used to achieve maximum productivity of the manufacturing system were analyzed. The factors deteriorating cutting productivity were analyzed. The effect of output parameters on cutting productivity was studied. Cutting power was estimated under various cutting modes. Temperatures were analyzed under various cutting modes and their effect on the material and the cutting tool was studied. A decrease in cutting speeds was investigated. Turning cutters with replaceable carbide inserts with a protective coating were used. Cutting forces and temperatures were measured. Cutting power was calculated by measuring cutting forces. The effect of machining modes on temperatures and productivity was analyzed. The dependences of productivity on cutting power were determined. It was shown that VT20 and VT22 titanium alloys are cut in a different way. Effective methods for improving turning productivity were developed. The directions for further research on titanium alloy turning productivity were described. Keywords: Titanium alloys · Turning · Cutting power · Cutting temperature

1 Introduction For the aircraft industry, it is a crucial task to improve cutting productivity. Better productivity decreases technological costs. Expensive high-performance equipment is the most effective one for manufacturing complex parts made from hard-to-cut materials. Tough-to-machine materials include titanium, alloys of nickel, and some stainless and high alloy steels. Large cutting forces increase temperatures which can be high in the cutting area [1, 2]. Heating of the tool and the material have a negative effect on their properties and microstructure. Tool edge wear is a result of high cutting forces and temperatures which reduce permissible cutting speeds and efficiency [3]. These problems can be solved by optimizing the geometry of the tool by using a protective coating, cooling under high and ultrahigh pressure, etc. [4, 5]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_37

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The maximum effect can be achieved when simulating the cutting process [1, 2, 6, 7]. The simulation results depend on the adequacy of mathematical models. An analysis of publications shows that approaches based on the deformation cutting model are the most productive [8]. However, to obtain reliable results, it is necessary to conduct experiments [9, 10]. In machining titanium alloys applied in the aircraft industry, it is necessary to control maximum permissible temperatures. This limits cutting modes and optimization possibilities [1–3]. The cutting speed should be no more than 100 m/min. Any increase can change temperatures to the values at which structural phase changes affect the mechanical properties of alloys [3]. Changes in other cutting parameters can increase temperatures in the cutting zone. Therefore, to improve titanium alloy machining productivity, it is necessary to assess the output parameters. Machining equipment influences the cutting productivity. Metal-cutting machine tools have fixed technical parameters that determine productivity. These parameters include spindle power and torque. To avoid machine tools overloading, values of spindle parameters (power and torque) should exceed values of similar cutting parameters. However, in most studies dealing with output parameters, cutting power is not taken into account. Most researchers measure cutting forces. This approach can be justified from a scientific point of view, but it does not contribute to the effective implementation of research results in real machine-building production. Therefore, it is necessary to determine cutting power as an output parameter. It should also be taken into account that the unit volume of the material to be removed is determined by different variations of machining parameters and corresponds to different values of cutting forces, temperatures, power, and torque. The energy needed and cutting temperatures are important technological parameters. Legal, economic, and ecological drivers make manufacturers reduce energy consumption and negative impacts of manufacturing processes on the environment. Optimization of cutting modes by minimizing energy costs can improve the productivity of a manufacturing system [11]. The article aims to develop ways to improve turning productivity for titanium-based alloys in order to use capabilities of the machine and not to increase cutting temperatures to critical values.

2 Materials and Methods VT20 (Ti–6% Al–2% Zr) and VT22 (Ti–5% Al–5% Mo–5% V) titanium alloys were studied. These alloys are widely used in the aircraft production industry. The DMG NEF 400 CNC machining center was used for turning. The Sandvik Coromant DCLNL 2020 K 12 with CNMG 120408-MM 1115 carbide inserts was applied. The geometric parameters of the cutter were as follows: the reentrant angle is ϕ = 95°; the lip angle is ε = 80°; the rake angle is γ = 3°; the relief angle is α = 6°. The raw material bar was inserted into a three-jaw chuck. The Kistler 9129AA dynamometer was used to measure cutting forces. To measure the temperature on the surface, a thermal imaging camera and thermocouples were used [12]. Under stable conditions, cutting vibrations were not measured. It Is well known that they have a negative effect on tool life, surface quality and tools [13].

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The following parameters were selected as variable cutting parameters: feed per revolution fn (mm/rev), cutting speed Vc (m/min), depth of cut ap (mm). The cutting modes varied in the following ranges: cutting depths ap = 0.5 … 3.5 mm; cutting speeds Vc = 45 … 75 m/min; feed values fn = 0.1 … 0.3 mm/rev. Productivity was calculated by formula Q = ap × fn × Vc (cm3 /min). To calculate cutting power, the following formula was applied: Pc = (Fz × Vc ) / 60,000, where Fz is the cutting force determine using a dynamometer.

3 Results and Discussion Figures 1, 2 and 3 show depssendences of cutting power, temperatures, and productivity determined when varying cutting parameters. Figure 1 shows cutting power (Fig. 1a) and temperature (Fig. 1b) identified by changing cutting speeds Vc . The feed per revolution was fn = 0.2 mm/rev. The cutting depth was ap = 2.5 mm. The relationships between cutting parameters were determined for VT22 and VT20. In cutting VT20, the relationship between cutting power and productivity is linear. In turning VT22, the situation is different. At a cutting speed of Vc = 55 m/min, cutting power has a minimum value. Under this cutting mode, the cutting force decreases due to changing stress–strain properties of alloys caused by elevated temperatures in the deformation zone (Fig. 1b). The relationship between temperature and productivity is adversarial. If for VT20 alloy, at Vc = 55 m/min, the temperature is minimum, for VT22, it is maximum. The nature of the relationship helps determine cutting speeds at which the cutting process is efficient excluding both the equipment overload and critical high temperatures. All cutting speeds are in the range allowable for machining aircraft parts.

Fig. 1. The relationship between output parameters and productivity Q at variable cutting speeds Vc in machining VT20, VT22: a cutting power; b temperature.

Values of cutting power (Fig. 2a) and temperatures (Fig. 2b) determined by varying feed per revolution fn are shown in Fig. 2. The speed was Vc = 55 m/min, the depth was ap = 2.5 mm.

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In contrast to the graph shown in Fig. 1, the relationship between cutting power and productivity are similar for VT22 and VT20 (Fig. 2). At a feed of 0.2 mm/rev, power values for VT20 and VT22 are similar. Given that VT22 has a higher degree of hardness, this feed is not optimal for cutting VT20. With a further increase in feed, the power decreases monotonically, which confirms the classical theory of cutting. An increase in feed has a positive impact on the cutting process in terms of its temperature. Figure 2b shows that an increase in productivity increases the temperature. On the contrary, minimum temperatures correspond to maximum productivity. When cutting VT22, both temperature and power values are higher due to the fact that VT22 has a higher degree of hardness.

Fig. 2. The relationship between output parameters and productivity Q at variable feeds per revolution fn in machining VT20 and VT22: a cutting power; b temperature.

Values of cutting power (Fig. 3a) and temperatures (Fig. 3b) identified by changing cutting depths ap are shown in Fig. 3. Cutting speed was Vc = 55 m/min, feed per revolution was fn = 0.2 mm. In varying cutting speeds (see Fig. 1), the nature of relationships for various titanium alloys is different. For VT20, an increase in productivity is accompanied by a monotonous increase in cutting power to a cutting depth of ap = 2.5 mm, after which cutting power remains constant (Fig. 3a). The comparison of the graphs of cutting power and temperature (Fig. 3b) does not explain this phenomenon. The presence of extreme temperatures does not have a predicted influence on the cutting power. In machining VT22 at a depth of ap = 3.5 mm, the cutting power is lower which means that the combination of cutting parameters is not optimal for VT20. When cutting VT22, an increase in temperatures is monotonous and insignificant. The cutting depth increases from 2.5 to 3.5 mm. It can be assumed that this increase improves the machinability of alloys and decreases cutting forces. The results may indicate the impact of temperatures on the interaction in the cutting zone which softens alloys. This process is complex and ambiguous [10, 12]. It is necessary to investigate this more detailed in future. An increase in productivity values by increasing cutting depths and feeds is more preferable than an increase in cutting speeds.

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Fig. 3. The relationship between output parameters and productivity Q at variable cutting depths ap in machining VT20 and VT22: a cutting power; b temperature.

The study of dependences of productivity on temperatures at different values of machining parameters shows that it is more preferable to improve productivity by increasing feed. In this case, energy consumption per unit volume of material is minimal for high productivity that was reached. The relationship between temperature and productivity is more complex. It depends on titanium alloy type. Minimal temperature T = 150 °C for VT20 was measured when maximal productivity was reached with a depth of cut increasing. The opposite situation took place for titanium alloy VT22 machining. Maximal temperature T = 525 °C was measured when maximal productivity was reached with a depth of cut increasing and minimal temperature T = 420 °C occurred when feed increasing.

4 Conclusion The relationship between cutting power, temperatures, and productivity for VT20 and VT22 allowed us to evaluate specific energy consumption per unit volume of material and cutting temperatures. Most of the relationships are systemic, consistent with the theory of metal cutting and previous experimental studies. The impact of cutting depths on result parameters is an avenue for further research. Also, contact processes in the cutting zone must be studied when titanium turning. Cutting data that minimize specific energy consumption per unit of the material removed were determined. It is necessary to improve productivity by increasing feed. To improve productivity, temperatures in the cutting area should not be critical. The subject of further research may be an analysis of the tool life under various options for improving productivity. It is also important to control surface roughness [14, 15], which makes it possible to obtain high-quality surfaces when rough and semifinished turning titanium. Structural phase changes in the materials and cutting tools caused by high temperatures and cutting forces should be studied [16–19]. Geometrics parameters of cutting edges are important. All experiments were conducted for a turning tool with one insert type. It is important to investigate the influence of different geometrics on titanium alloys cutting dynamics.

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Chip formation is the subject of additional research too. It must be studied under different cutting parameters to get continues and segmented chips. An influence of chip type for cutting dynamics and energy consumption per unit of the material removed is important. All experiments were conducted with a sharp cutting edge of turning tool. Tool wear progression is inevitable in material cutting. It is evident that tool wear will influence on the cutting process. The influence of tool wear on power consumption at machining center, its spindle, and levels of process is yet to understand. Cutting forces will increase due to tool wear [20–22]. Cutting power and temperatures expected to increase too. The dependences of cutting productivity on power consumption per unit volume of material taking into account tool wear and cutting temperatures are an avenue for further research. The results can be used to optimize cutting modes for VT20 and VT22 titanium alloys when high productivity turning. Acknowledgments. The reported study was funded by the Engineering center “Innovational technologies and materials” of “Komsomolsk-na-Amure State University” Komsomolsk-na-Amure, Vice-rector for Research and Innovations Belykh S.V. All experiments were conducted in the research laboratory of “High productivity machining” of Irkutsk National Research Technical University. The authors express their gratitude to the senior researchers of the laboratory: Alexey Pyatykh, Sergey Timofeev, and Andrey Nikolaev

References 1. Karaguzel U, Bakkal M, Erhan Budak (2016) Modeling and measurement of cutting temperatures in milling. In: Procedia 7th CIRP conference on high performance cutting 2. Karaguzel U, Bakkal M, Budak E (2017) Mechanical and thermal modeling of orthogonal turn-milling operation. In: Procedia CIRP 58 3. Balaji JH, Krishnaraj V, Yogesvaraj S (2013) Investigation on high speed turning of titanium alloys. In: Procedia engineering of international conference on design and manufacturing 4. Jagadesh T, Samuel GL (2014) Investigation into cutting forces and surface roughness in micro turning of titanium alloy using coated carbide tool. In: Procedia materials science 5 5. Koca R, Budak E (2013) Optimization of serrated end mills for reduced cutting energy and higher stability. In: Procedia 14th CIRP conference on modeling of machining operation 6. Çelebi C, Özlü E, Budak E (2013) Modeling and experimental investigation of edge hone and flank contact effects in metal cutting. In: Procedia 14th CIRP conference on modeling of machining operation 7. Nikolaev AYu (2017) Simulation of the plain milling process. IOP conference series: Materials science and engineering, Vol 177. https://doi.org/10.1088/1757-899X/177/1/012080 8. Muhammad R, Roy A, Silberschmidt VV (2013) Finite element modelling of conventional and hybrid oblique turning processes of titanium alloy. In: Procedia 14th CIRP conference on modelling of machining operations 9. Chinesta F, Filice L, Micari F, Rizzuti S, Umbrello D (2008) Assessment of material models through simple machining tests. Int J Mater Form, Supplement 1:507–510 10. Belhadi S, Marouki T, Rigal JF, Bouanouar L (2005) Experimental and numerical study of chip formation during straight turning of hardened AISI 4340 steel. J Eng Manuf 219:515–524 11. Mavliutov AR, Zlotnikov EG (2018) Optimization of cutting parameters for machining time in turning process. IOP conference series: materials science and engineering, Vol 327. https:// doi.org/10.1088/1757-899X/327/4/042069

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12. Sergeev AS, Tikhonova ZS, Uvarova TV (2017) Method for measuring thermo-emf of a “toolworkpiece” natural thermocouple in chip forming machining. MATEC web of conferences 129. https://doi.org/10.1051/matecconf/201712901044 13. Eynian M, Altintas Y (2009) Chatter stability of general turning operations with process dumping. J Manuf Sci Eng 131(4). https://doi.org/10.1115/1.3159047 14. Ninthyanandam J, Lal Das S, Palanikumar K (2014) Surface roughness analyses in turning of titanium alloy by nanocoated carbide insert. In: Procedia materials science of international conference on advances in manufacturing and materials engineering 15. Singh D, Rao PV (2007) A surface roughness prediction model for hard turning process. Int J Adv Manuf Technol 32(11–12):1115–1124 16. Nikolaeva EP, Mashukov AN (2017) Evaluation of residual stresses in high-pressure valve seat surfacing. Chem Pet Eng 53(7–8):459–463 17. Hauk V (1997) Structural and residual stress analysis by nondestructive methods: evaluation, application, assessment. Elsevier, Amsterdam, Netherlands 18. Pan Z, Shih DS, Garmestani H, Liang SY (2019) Residual stress prediction for turning of Ti-6Al-4V considering the microstructure evolution. Proc IMechE Part B: J Eng Manuf 233(1):109–117. https://doi.org/10.1177/0954405417712551 19. Kara S, Li W (2011) Unit process energy consumption models for material removal processes. CIRP Ann. https://doi.org/10.1016/j.cirp.2011.03.018 20. Liu ZY, Guo YB, Sealy MP, Liu ZQ (2016) Energy consumption and process sustainability of hard milling with tool wear progression. J Mater Process Technol 229:305–312. https:// doi.org/10.1016/j.jmatprotec.2015.09.032 21. Garg A, Lam JSL, Gao L (2016) Power consumption and tool life models for the production process. J Clean Prod 131:754–764. https://doi.org/10.1016/j.jclepro.2016.04.099 22. Jawaida A, Che-Harona CH, Abdullah A (1999) Tool wear characteristics in turning of titanium alloy Ti-6246. J Mater Process Technol 92–93:329–334. https://doi.org/10.1016/S09240136(99)00246-0

The Study of Stress State Uniformity Along with the Thickness of the Constructive Element of Housing High-Pressure Vessels Deformed by Conjugated Elements of Physical Separation of Heating Elements Embedded in the Vessel Housing D. Elovenko1(B) and V. Kräusel2 1 Irkutsk National Research Technical University, 83, Lermontov street, 664074 Irkutsk, Russia

[email protected] 2 Technische Universität Chemnitz, 70, Reichenhainer Str., 09126 Chemnitz, Germany

Abstract. This study represents the research dependency of uniform stress distribution degree in an elastic isotropic deformable body (elastic half-plane and elastic monolithic thick cylinder) from the distance between the rectangular elements which have contact with the deformable body considered in the two-dimensional formulation. The nature of contact interaction with deformable rectangular elements presented as unidirectional exposure on the deformable body of rigid either elastic rectangular stamps, as well as exposure to uniform pressure simulating contact pressure in the line of contact interaction. The mathematical model is obtained for calculating stresses in an elastic half-plane loaded with uniform constant pressure in two sections of finite length in the two-dimensional formulation (development of an analytical solution to the Michel task). A method for assessing the relative uniformity of the stress distribution in an elastic isotropic deformable body is proposed. This method is based on discrete control of the absolute values of the target stress components on finite element models (FEM). The results of a numerical study of the stress state of objects emulating the inner casing of the insulating layer (Pimshtein et al. in Autoclave for the synthesis and growth of crystals in hydrothermal conditions, 1997; Elovenko in Future directions of the development of high-pressure autoclaves. Herald Irkutsk State Tech Univ: 41 277–279, 2010] or a constructive element on which multilayer components of the bearing part of the vessel housing are mounted in contact with the distance planks (Elovenko et al. in Experimental study of the autoclave model for hydrothermal synthesis of minerals. Baikal Lett DAAD 7:11–19, 2010) are presented by FEM. The effectiveness of the proposed numerical research method is confirmed by comparing the results of solving typical test problems with known analytical solutions. Keywords: Contact · Deformable body · Uniformity of stress distribution · Distance planks of heating elements · Pressure vessel © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_38

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1 Introduction Design features of some units of machines and equipment often have continued contact interaction of adjacent constructive elements during all the cycles of their work. One example of such technological equipment is pressure vessels. In such vessels, the heating elements are located inside the housing [1–3] and are separated by remote structural elements of a rectangular profile (distance planks). From the action of internal technological pressure in the vessel, [1–3] compressive deformations arise. Thus, the distance planks of the heating elements are located inside the vessel housing are in contact with the inner casing of the layer of thermal insulation material or constructive element on which the multilayer components of the vessel are installed (cylinder shells). The nature of this interaction in the radial plane is similar to the contact of rigid (if the elastic modulus of the planks is significantly greater than the inner casing) or elastic (if the elastic modulus of the planks approximately coincides with the inner casing) stamps with an elastic half-plane. It is also possible that contact pressure from distance planks is possibly represented as constant pressure on the contact piece which is emitting contact pressure. Contact tasks for rigid objects of the rectangular stamp type with an elastic half-plane in a two-dimensional setting and volumetric (3D) presentation have been extensively researched and described in scientific papers. The frictionless contact problem of a rigid stamp with an elastic body was researched in [4–9]. The study [4] is described as the frictionless contact problem between an elastic layer bonded to a rigid support and a rigid stamp. The plane contact problem for an elastic layer bonded to rigid support on its top surface is considered according to the theory of elasticity. The layer is subjected to a concentrated load at its bottom surface by means of a rigid stamp. The problem is formulated in terms of a singular integral equation. The much later paper [5] the surface elasticity in the form proposed by Steigmann and Ogden is applied to study a plane problem of frictionless contact of a rigid stamp with an elastic upper semi-plane. The results of this work generalize the results for contact problems with Gurtin–Murdoch elasticity by including additional dependency on the curvature of the surface. Also, frictionless contact problem considered in paper [6] where the stress distribution is along the contact boundary of half-plane with stamp investigated by the polarization optical method. The stress state was investigated at contact points for different ratios of elastic constants of the stamp and half-plane. A plane elastic problem for an orthotropic infinite strip with mixed boundary conditions is investigated in [8]. A model of the strip has been built by using the method of integral Fourier transforms. We obtain relationships which allow us to formulate singular integral equations for the various types of boundary conditions on one of the stamp edges. The authors’ study [9] has plotted lines of energy flow in the problems on the uniform vertical force applied at the boundary of an elastic half-plane and on the indentation of a smooth pressing stamp in a rigid plastic half-plane. The influence of stresses on displacement velocities was analyzed. Accounting for the weight of the material half-plane implemented in [7].

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The frictional contact problem of a rigid stamp with an elastic body was researched in [10–13]. The paper [11] considers the problem of contact with adhesion and sliding between a stamp with a rectilinear foundation and a strip one of whose sides is fixed. The Wiener– Hopf method was used to reduce the system of integral equations of the problem to an infinite system of algebraic equations. The sliding frictional contact problem in two-dimensional graded materials loaded by a flat stamp was considered in [12]. The sliding frictional contact problem for a halfplane which is graded in two dimensions was studied. The effect of medium properties gradient and coefficient of friction in contact mechanics of two-dimensional (2D) graded materials which are loaded by a flat stamp have been investigated by developing two FEMs, in macro- and microscales. The frictional sliding contact problem between a functionally graded magnetoelectroelastic material and a perfectly conducting rigid stamp subjected to magnetoelectromechanical loads under plane strain conditions was studied in [13]. The main objective of this paper is to study the effect of the non-homogeneity parameter, the friction coefficient, and the elastic, electric, and magnetic coeffic0ients on the surface contact pressure, electric displacement, and magnetic induction distributions for the case of flat stamp profiles. The contact problem of a pair stamp with an elastic body was researched in [14– 18]. The problem of the impression of two symmetrical rectangular stamps with narrow rectangular bases into an elastic isotropic half-space under the effect of vertical forces was considered in [16]. An integral transform solution was developed to reduce the solution of the problem into a Fredholm integral equation of the second kind. The contact problem of indentation of a pair of rigid stamps with plane bases connected by an elastic beam into the boundary of an elastic half-plane under the conditions of plane strain state was considered in [17]. The interior part of each of the contact regions and the tangential stresses obeying the Coulomb law act on their boundaries. The solution of the constitutive system together with three conditions of equilibrium of the system of punches connected by a beam is constructed by direct numerical integration by the method of mechanical quadratures. In [18], the problem of the contact interaction of a rigid cylindrical ring stamp and half-space with initial (residual) stresses is considered disregarding the friction forces in the case of unequal roots of the characteristic equation. The study was performed in common form for the theory of large (finite) initial deformations and two variants of the theory of small initial deformations within the framework of the linearized theory of elasticity for arbitrary elastic potential. The shape of the stamp and the elastic body with which contact occurs also may be different in 2D section. For the case where a stamp, whose horizontal cross sections are confocal ellipses, and whose vertical cross section by the plane y = 0 is an inverted trapezium, is pressed into an elastic half-space, analytic expressions are obtained for the distribution of the contact pressure under the base of the stamp and for the displacement of the surface of the elastic material outside the stamp [19]. Also known the study [20] investigates the contact interaction between a rectangular object (a compressible object) and two stressed half-planes taking into account friction.

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Also known the solution of a contact problem [21] for an elastic rectangle is reduced to a quasi-completely regular infinite system of linear algebraic equations with finite absolute terms. In this study, the stamps are located opposite each other on opposite sides of the elastic rectangle. Finally, there is an analysis approach for contact problem of a stamp and a half-plane in which the action of the stamp can be replaced by the action of distributed load in the contact zone [22–24]. The development of this method has been presented in studies [25–27]. Condition of infinitely large friction. The authors found out that under all other equal conditions the numerical values of stress in a half-plane depend on the magnitude of the soil lateral pressure coefficient (Poisson coefficient) [25]. The article [26] provides the analytical task solution for the tool which is under the influence of evenly distributed load under finite friction magnitude on contact “Stress state of elastic half-plane in case of inclined loading attached to the tool under condition of its full sticking to the rectilinear inclined basis—inclined basis with straight-line boundary.” And the article [27] provides the analytical task solution for the stamp which is under the influence of evenly distributed inclined loading under the condition of its full sticking to the inclined basis with rectilinear border. As already mentioned, the phenomenon of contact of the inner casing of the heat-insulating layer (either constructive element on which multilayer components are installed of the bearing part of the vessel housing) and distance planks, in our opinion, can be represented as the interaction of an elastically deformable half-plane and rectangular stamp type elements in two-dimensional staging or as the effect of uniform normal contact pressure to this half-plane.

2 Test Problems and Verification of the Simulation Method To assess the degree of achievement of a uniform distribution of radial stresses in the inner casing of thermal insulation material is possible only by a numerical method of calculation by FEM. Moreover, the adequacy of any FEM to solve specific application tasks should be determined by comparing the results of solving a typical problem obtained by FEM with a known result from an analytical solution. To verify our research method, three typical tasks were solved. Sadowski’s task, as well as Mitchell’s task and its development. Analytical solution of the Sadovsky problem [24, 28] (static contact of the elastic half-plane and absolutely rigid stamp) to determine normal to the contact line (radial stress in a cylindrical coordinate system) voltage has the form. p(x) =

√

P

π a2 − x2

,

(1)

where P = q0 ·2a. An example of a typical case was considered in which an elastic isotropic body is a half-plane y ≤ 0 have Young’s modulus—E = 200 GPa and Poisson’s Ratio—μ = 0.3. Stamp wide is 2a = 30 mm and weight P interacts with a half-plane without friction force. Outside the contact zone, the half-plane is free of load.

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Distribution curves of normal stress p(x) to the contact line in the half-plane section under the zone of contact with the stamp −a ≤ x ≤ a at q0 = 50 MPa analytically and FEM is obtained in Fig. 1a is shown.

Fig. 1. a the stresses in the elastic half-plane (y/a = 0) normal to the contact line with an absolutely rigid stamp; b the stresses in the elastic half-plane (y/a = 0.2) normal to the action line of distributed uniform pressure.

The second typical example of Michel task also has a well-known analytical solution [22–24]. For the taken calculation scheme according to [24], it has a view p(x) = −

p (2(β1 − β2 ) − (sin 2β1 − sin 2β2 )). 2π

(2)

Expressing angles β 1 and β 2 in this equation through the coordinates of the point Z [24] get the expression for determining the stress    |a| − x P π y ) p(x) = − 2 ( + arctg( ) − arctg( |a| + x 2π 2 y     (3) |a| − x π y ) . − sin 2 + arctg( ) − sin 2arctg( |a| + x 2 y As in the previous problem, the stress state of the half-plane is symmetric relative to the vertical axis y therefore, the curves of the results of the numerical and analytical method for calculating stresses is shown only for the positive value areas x > 0 (Fig. 1b). As a next step, let’s consider the case of periodic loading of a half-plane pressure uniform in magnitude and direction, for example, at two intervals with a length of 2a (Fig. 2a). The solution to this problem also can be obtained from known relations (2) and (3) by appropriate mathematical transformations for the calculation scheme presented

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in Fig. 2b. Thus, the expressions for calculating the normal stress to the contact line p(x) = σ y in the half-plane will have a general view.   P σy = − (2(β1 − β2 ) − (sin 2β1 − sin 2β2 )) 2π   (4) P + − (2(α1 − α2 ) − (sin 2α1 − sin 2α2 )) , 2π which for the case of a point Z(x,y) under load site is -2a ≤ x ≤ 0 (negative region of the horizontal axis of the half-plane) (Fig. 2b) is expressed as    ⎛  ⎞⎞ ⎛ |x| y π + arctg − arctg − 2 ⎟⎟ ⎜ P ⎜ 2 y 2|a| − |x| ⎜ ⎟   ⎟  σy = ⎜ ⎠⎠+ ⎝− 2π ⎝  |x| y π + arctg − sin 2 arctg − sin 2 2 y 2|a| − |x|     ⎛ ⎛ ⎞⎞ π π 2|a| + b + |x| b + |x| − − 2 + arctg + arctg ⎜ P ⎜ ⎟⎟ 2 y 2 y ⎜ ⎟.   ⎟  +⎜ ⎝− 2π ⎝  2|a| + b + |x| π b + |x| ⎠⎠ π + arctg − sin 2 + arctg − sin 2 2 y 2 y (5)

Fig. 2. a scheme of uniform pressure loading symmetrical relative to the y-axis elastic half-plane in two intervals; b calculation scheme for determining stress.

The case of Z(x,y) point locations in the half-plane under the free interval is 0 ≤ x ≤ b calculated expression for stresses into account the angle β 1 < 90° will have the view   

    

P y y y y σy = − 2 arctg − arctg − sin 2 arctg − sin 2 arctg 2π x 2|a| + x x 2|a| + x ⎛  ⎞⎞ ⎛    π π 2|a| + (b − x) b−x − − + arctg + arctg ⎟⎟ ⎜ P ⎜2 2 y 2 y ⎜ ⎟⎟ ⎜ +⎜− ⎜     ⎟⎟ ⎠⎠ ⎝ 2π ⎝ π 2|a| + (b − x) π b−x − sin 2 + arctg − sin 2 + arctg 2 y 2 y

(6)

Similarly, the expression can be obtained for the case of Z(x,y) point location in the half-plane under the load is 2a ≤ x ≤ 0 (positive area of the horizontal axis of the half-plane) (see. Fig. 2b).

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Fig. 3. a distribution the normal stress to contact line in elastic half-plane for parameter y/b = 0.25; b parameter y/b = 10; c parameter y/b = 50.

Comparison curves for the results of numerical and analytical calculation methods stress calculation for Z(x,y) point position in the sub-area of the half-plane under the site 0.5b ≤ x ≤ 2a for different y/b are presented in Fig. 3. Note that they also have a symmetrical location under the section from the edge of the left loaded interval to the middle of the free area is −2a ≤ x ≤ 0.5b (see Fig. 2a). A comparative analysis of test problems showed a good convergence of the results obtained by analytical solution and FEM. Based on them, we consider as possible to make a study of the degree of uniformity of the distribution of normal stress to the contact line (radial stress in a cylindrical coordinate system) by FEM. Then we analyze the degree of uniform stress distribution in an elastic body which emitting inner insulation casing, from contact interaction with rectangular elements emitting distance planks of heating elements of the pressure vessels and the distance between planks.

3 Numerical Research At the first stage, an FEM analysis of the contact of two rigid rectangular stamps with elastic half-plane (E = 200 GPa; μ = 0.3) was held according to the design scheme shown in Fig. 4a. Figure 4b shows normal stress distribution curves σ y in the half-plane for various parameter y/b. Stress curves have symmetry relative to the y-axis and are shown only for the positive sub-area. Then a similar analysis was carried out for cases of contact of two and four rectangular elements (stamps) with half-plane. All contacted elements had equivalent elastic deformation characteristics. The results are presented in Fig. 5a, b, respectively. Moreover, two-dimensional contact analysis of two elastic elements emitting distance planks with the inner surface of a thick-walled cylinder element was carried out under the same magnitude of the load as in previous tasks on the stamps. The analysis results are shown in Fig. 5c. The main influence on the uniformity of the distribution of stress–strain state in the radial direction of the inner casing of thermal insulation is having the size of the free zones between the distance planks b in which the heating elements are located.

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Fig. 4 a calculation scheme for constant pressure loading of two rigid stamps in contact with the elastic half-plane symmetrically located relative to the y-axis; b curves of normal stress σ y to the contact line in the half-plane

Fig. 5. a curves of normal stress σ y to the contact line in the half-plane for the design contact scheme with two stamps; b with four stamps; c normal stress σ r to the contact line in the thickwalled cylinder element with two elastic elements having the profile of the distance planks in a cylindrical coordinate system.

Dependence of the inner casing thickness of thermal insulation for pressure vessel bodies [1, 2] or thickness of the constructive element on which the multilayer components of the vessel are installed (cylinder shells) [3] from the distance between adjacent planks b. Ultimately, this is the main constructive parameter for determining the minimum design thickness of this element s. The minimum value of s must be such that the radial stresses have a sufficient degree of uniform distribution. This circumstance is important to ensure equivalent deformation of any point or segment of the circular arc of the outer radius of the constructive element with thickness s in the radial direction. In our opinion, this is the main condition for ensuring uniform elastic deformation of the heat insulation layer or multilayer structural elements of the pressure vessel body. The fulfillment of this condition should favorably affect its strength characteristics. Determination of the relative uniformity distribution of normal stress (radial stress for a cylindrical coordinate system) to the contact line εy (εr ) along with the thickness s of the elastic constructive element between the centers of adjacent spacer planks (width

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2a) vessel heating elements by distance 2a + b with y/b = const avg

εy =

σy

avg σy

· 100%.

(7)

In this formula, the Δσ y avg is the absolute non-uniformity of the average value of stresses σ y with y/b = const, determined by the formula

n

i avg − σ

σ y i=1 y avg , (8) σy = n and the average value of stresses σ y avg at a distance of 2a + b at with y/b = const has the form n i i=1 σy avg , (9) σy = n where n is the number of control points on the current radius with a constant step in which stress values σ y are fixed. Based on the results of research calculations the graphical dependence is obtained Fig. 6. The curves show the ratio y/b (s/b) which corresponds to a certain level of relative irregularity εy stress σ y (for radial stresses—σ y in a cylindrical coordinate system is εr ). Based on this graph, the minimum design thickness s can be determined for the inner casing of the heat-insulating material of the vessel [1, 2] or a constructive element on which the multilayer components of the vessel are installed (cylinder shells) [3].

4 Conclusions The results of the analysis of typical tasks used as evidence showed that all the necessary methods allow you to get corrective results with the required accuracy and can be used to solve the study of the phenomena of contact interaction of parts in the nodes of devices and equipment of a similar level of complexity. The study of the stress state of objects emitting the inner casing of the heat-insulating layer or the structural element on which the multilayer components of the bearing part of the vessel body are mounted in contact with the distance bars by means of FEM showed that a relative voltage non-uniformity of 5%, allowed when constructively choosing wall thickness parameters, can be reached even with the thickness of the contact part twice the distance between the planks (y/b = 2). We also note that in the cylinder a uniform stress state is achieved with a given accuracy with a slightly smaller thickness of the elastic isotropic cylindrical element s/b ≈ 1.625.

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Fig. 6. The relative unevenness graph stress distribution is σ y (σ r ) in an elastic body depending on the distance between the stamps. 1—stress σ y in the elastic half-plane in contact with two separate rigid stamps; 2—stress σ y in the elastic half-plane in contact with two separate elastic stamps; 3—stress σ y in the elastic half-plane in contact with four separate elastic stamps; 4—stress σ y in the elastic half-plane from exposure to constant pressure on the contact line size as in case 1 or 2; 5—stress σ r in a cylindrical object emitting an inner casing of the heat-insulating layer or a constructive element on which the multilayer components of the vessel are installed in contact with two distance planks.

References 1. Pimshtein PG, Murashev BG, Borsuk EG, Pogodin VK, Drevin AK, Trishkin SV, Oleinik VN (1997) Autoclave for the synthesis and growth of crystals in hydrothermal conditions. RF patent 2093481, Bull. 29 2. Elovenko DA (2010) Future directions of the development of high-pressure autoclaves. Herald Irkutsk State Tech Univ 41:277–279 3. Elovenko DA, Pimshtein PG, Repetsky OV, Tatarinov DV (2010) Experimental study of the autoclave model for hydrothermal synthesis of minerals. Baikal Lett DAAD 7:11–19 4. Kahya V, Birinci A, Erdöl R (2001) Frictionless contact problem between an elastic layer bonded to a rigid support and a rigid stamp. Math Comput Appl 6:13–22 5. Zemlyanova AY (2018) Frictionless contact of a rigid stamp with a semi-plane in the presence of surface elasticity in the Steigmann-Ogden form. Math Mech Solids 23:1140–1155. https:// doi.org/10.1177/1081286517710691 6. Konev SV, Mikhailets VF, Bazyleva AA (2013) The study of the elastic contact stamp with a half-plane. Model Dev Metal Form Process 19:67–72 7. Plotnikova AYu, Plotnikov YuG (2011) Tasks for a stamps on an elastic half-plane. Scientific, Technical and Economic Collaboration of the Countries of the Asian-Pacific Countries in the XXI Century 2:256–264

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Modeling Metal Removal in Automatic Circular Grinding Cycles Taking into Account Process Dynamics P. P. Pereverzev1 , A. D. AlMawash1,2(B) , and M. K. Alsigar3 1 South Ural State University, 76 Lenin Avenue, Chelyabinsk 454080, Russia

[email protected] 2 University of Kufa, 21 Kufa, Najaf 54003, Iraq 3 Thi-Qar University, 31, Dhi Qar, Nasiriyah 3629, Iraq

Abstract. The article discusses the solving of the issue of increasing the efficiency of a circular grinding with CNC by applying a model of processing accuracy prediction, which considers the dynamics of the process of the circular grinding process, taking into account the multi-stage and the instability of the process during designing and optimization stages of control cycles for the radial feeds, where the model for calculating the performance of metal removal during circular external grinding is presented taking into account the dynamics of the process on CNC machines for a given automatic the cycle step of grinding. The model performance allows calculating the current feed values, the actually taken stock over the steps of the cycle and the main time for stock removal. The model depends on the relationship between cutting forces and the operating parameters of the cycle, the elastic deformations of the technological system and the main technological factors. Keywords: Modeling · External grinding · Cutting force · Process dynamics · Actual feed

Nomenclature j d D B σi vk n Sp1 Sp2 εi η β

Flexibility, mm/kg Diameter of the workpiece, mm Diameter of the grinding wheel, mm Width of the grinding wheel, mm Stress intensity, kg/mm2 Circumferential speed of wheel, m/s Workpiece rotation, rpm Speed of programmed feed of the first stage, mm/min Speed of programmed feed of the second stage, mm/min Intensity of the deformation degree Degree of dullness Cutting angle

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_39

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1 Introduction Continuous improvement of the quality of the manufactured machines while ensuring high productivity of the technological processes of their manufacture is one of the main tasks of modern engineering. Grinding is the major technique of ensuring the manufacturing of machine parts with high accuracy. The ratio of grinding machines to the total of metal-cutting equipment is continually increased and reached, for example, 80% at automobile plants in Western countries [1, 2]. Among the grinding machines, nearly half are circular grinding machines [3, 4]. Lately, there has been the inclination in native and foreign engineering to increase the ratio of grinding machines equipped with active control devices. The productivity of processing on these machines is 1.5–2.5 times higher contrasted to manually controlled machines [5, 6]. The performance management of operations on programmed circular grinding machines is performed according to the control program, by stepwise changing the programmed feed rate according to the commands of the active control device depending on the remaining part of the stock [7]. The feature of the operation of these machines is the presence of vibrations caused by the action of different sources, lead to the reduction in the accuracy and purity of processing, as well as to other violations of technological processes [8–13]. The weakest link in the technological system is the wheel of grinding and which it has the greatest impact on the stability of the quality parameters of parts [14–18]. From the analysis of well-known scientific methods, the practice of processing cycles showed that two groups of research directions: • The first group studied the static process of external grinding without taking into account the dynamics of the process. • The second group studied the dynamics of the external grinding process without taking into account the technological features associated with ensuring the accuracy of processing. So, ensuring the maximum possible productivity of external grinding operations performed on CNC machines by selecting the optimal control cycles for radial feeds taking into account the dynamics of the process is currently an urgent and unsolved scientific and technical task. The aim of the article is to increase the productivity of external grinding operations performed on CNC machines by applying a dynamic model of the processing cutting process while optimizing the external grinding cycle taking into account unstable processing conditions for a batch of parts.

2 Dynamic Displacement Modeling The technological system (TS) of grinding is basically a mechanical system. Therefore, the major characteristics in the description are strength characteristics. The technological process of external grinding is impossible without the force interaction of the workpiece

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and tool. So, for its application, it is needful to guarantee mechanical coupling between the major elements of the TS [14]. The values of the interaction forces of the individual elements of the system are determined taking into account the mutual position of the workpiece and the tool, the characteristics of the dissipation of the supplied energy, the properties of the interacting bodies (masses, elasticity, specific heat, etc.) [17]. Formula (1) describes the dynamic behavior of the TC external grinding without taking into account the deviation of the tool shape: ..

.

m y +h y +cy = Py

(1)

where Py —the radial cutting force; characteristics of the TS (m—mass; c—stiffness TS; h—the linear damping coefficient characterizing the energy dissipation of the elements under consideration). Suppose that h˙y = 0, then (2) ..

m y +cy = Py

(2)

Pereverzev [1], calculated a given value of the radial cutting force, as given in the formula (3):   (3) Py = K 1 S f + K 2 S f = K 3 tf + K 4 tf where S f is the speed of actual radial feed, mm/min; Δt f is the actual radial feed, mm/rev.; K1 , K2 , K3 i K4 are the coefficients of analytical description, analyzing the interrelationship of technological parameters of the external grinding, which were already calculated [6]: σ ε tan β σ K1 = π d B i i ; K 2 = ηB i ; Vk 3



dD σ ε tan β σ ; K3 = π d B i i ; K4 B i n(d + D) Vk 3

 dD ; (d + D)

σ i is stress intensity, N/mm2 ; d and D are diameters of the workpiece and the grinding wheel respectively, mm; B is the width of the grinding wheel, mm; V k is the circumferential speed of the grinding wheel, m/s; n is the rotation of workpiece, rpm; εi is the intensity of the deformation degree; β is cutting angle; ï is the degree of dullness. The research [9] found the relationship between the programmed and actual radial feed speed, as in the formulas (4) and (5):   −τ (4) S f = Sp 1 − e T   K2 T = j  (5) 2 Sp where S p is the speed of programed radial feed, mm/min; j is compliance (j= 1/c), mm/N; T is time constant, min. Substituting Eqs. (3–5) into (2), the equation of the dynamic balance of the cutting force in the TS is obtained by formula (6):      m y¨ + cy = K 1 Sp 1 − e

−τ T

+ K 2 Sp 1 − e

−τ T

(6)

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To obtain the displacement equation y(τ ) , Eq. (6) was solved with the initial conditions y(0) = 0 and y(0) = S p at the first stage of the cycle, as shown in formula (7): v3 2 v2 v4 v1 v3 τ + 2τ − 2 e−aτ + 2 + 4 (7) 2w 3 w w + a2 w w √ √ √ K 1 S p +0.414K 2 S p 0.531K 2 S p 0.3K 2 S p ; v = ; v = ; where w = mc ; a = T1 ; v1 = 2 3 m mT mT 2 y(τ ) = Acos(wτ ) + Bsin(wτ ) −

p v3 v1 v2 av4 4 v4 = 1m p ; A = w2v+a 2 − w 4 − w 2 ; B = w − w 3 − w (w 2 +a 2 ) . After obtaining the displacement equation, the speed of elastic deformation can be given by Eq. (8)

K S

S

.

y = −Aw sin(wτ ) + Bw cos(wτ ) −

(τ )

v3 v2 av4 τ+ 2+ 2 e−aτ 3 w w w + a2

(8)

And also the formula for accelerating of elastic deformation in the following formula (9): ..

y = −Aw 2 cos(wτ ) − Bw 2 sin(wτ ) −

(τ )

v3 a 2 v4 −aτ − e w3 w2 + a 2

(9)

where y˙ (τ ) and u¨ (τ ) are the speed and acceleration of elastic deformation. After obtaining the equation of the accelerating of elastic deformation for the cutting process, the elastic deformation y can be calculated by formula (10). ..

y = j Py − jm y

(10)

The research [1], calculated the value of elastic deformation, as in the formula (11): yz,i − yz,i−1 = tpz,i − t f z,i

(11)

where z is the number of the step; i is the serial number of the revolution at the z-th step; Δt f z,i ; Δt p z,i are actual and programmed feed at the i-th revolution of the z-th stage, mm/rev. From the formulas (3, 10, and 11), it is possible to calculate the actual radial feed, as in the formula (12): ⎡ t f z,i

=⎣

− j K4 + 2(1 + j K 3 )



 ⎤2 

2 t pz,i + j Pyz,i−1 + jm yz,i − y¨z,i−1 j K4 ⎦ + 2(1 + j K 3 ) (1 + j K 3 )

(12)

Also, the research [1], calculated the value of the actual radial feed speed, as in the following formula (13): S f z,i =

t f z,i τz,i

(13)

where Δτ z,i is the time interval of the i-th revolution of the z-th step, min, it was already calculated [5], as in the formula (14): τz,i =

1 n

(14)

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After calculating the actual radial feed per revolution, the limited allowance of cutting and the allowance removal time can be calculated, as in the formula (15) tf =

i z   1

t f z,i ; τ =

i z  

1

1

τz,i ;

(15)

1

where t f —the limited value of the allowance on each side, mm; τ —allowance removal time, min.

3 Results and Discussions The results were obtained according to previously obtained formulas for 100 revolutions in two steps, the first step ends at 75 revolutions based on the input data shown in Table 1. Table 1. Input data. No. Input data

Value

1

Flexibility j, mm/kg

0.003

2

Diameter of the workpiece d, mm

50

3

Diameter of the wheel D, mm

300

4

Width of the wheel B, mm

30

5

Stress intensity σi , kg/mm2

180

6

Circumferential speed of wheel vk , m/s

30

7

Workpiece rotation n, rpm

180

8

Speed of programmed feed of the first stage Sp1 , mm/min

3

9

Speed of programmed feed of the second stage Sp2 , mm/min 0.1

10

Intensity of the deformation degree εi

2.732

11

Degree of dullness η

0.03

12

Tangent of cutting angle tan β

0.68

Figure 1 shows a graphical representation of the relationship between the speed of the programmed and the actual radial feed for different masses with the rotation of the workpiece. This figure shows that the addition of mass significantly effects on the speed of the actual radial feed since the difference between the speed without mass and the speed with mass is large. Figure 2 shows a graphical representation of the relationship between the programmed and actual cutting depth for different masses with the rotation of the workpiece. This figure showed that the increase in mass affects the amount of allowance removal. Figure 3 shows a graphical representation of the relationship between the radial cutting force for different masses with the rotation of the workpiece. This figure showed the effect of mass on the radial cutting force but with oscillator effect.

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Fig. 1. Graph of the speed of programmed and actual radial feeding.

Figure 4 shows a graphical representation of the relationship between elastic deformation for different masses with the rotation of the workpiece. In this figure, it is clear that an increase in mass reduces elastic deformation due to an increase in actual cutting depth. Figure 5 shows a graphical representation of the relationship between the acceleration of radial movement for different masses with the rotation of the workpiece. This figure showed that an increase in mass reduces acceleration because it is self-evident that the relationship between them is the opposite.

4 Conclusions • The relevance of modelling the process of metal removal in automatic cycles of circular external grinding, taking into account the dynamics of the process implemented on CNC machines, is due to the lack of automated design systems, reference books, and design techniques for cycles that satisfy the requirements of modern automated production. • The solution to the problem of designing and calculating automatic cycles of circular external grinding taking into account the dynamics of the process is presented in the methodology for calculating the actual feeds and cutting forces for a given cycle and grinding conditions. • The presented methodology for calculating automatic cycles was developed on the basis of establishing the relationship between the fundamental laws of the mechanics of plastic deformation of the metal in the cutting zone, the model of cutting forces actual feeds, elastic deformations of the technological system associated with the program, cutting conditions, and the kinematics of the processes of circular external grinding, taking into account the dynamics of the process, that allows you to calculate the parameters of the cycles in a wide range of variation of various technological factors.

Modeling Metal Removal in Automatic Circular Grinding Cycles

Fig. 2. Graph of programmed and actual cutting depth.

Fig. 3. Graph of radial cutting force.

Fig. 4. Graph of elastic deformation.

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Fig. 5. Graph of acceleration of movements.

References 1. Pereverzev PP, Akintseva AV (2016) Modeling of metal removal during an internal grinding in view of kinematics cutting feature. Russ Eng Res 36(10):888–893. https://doi.org/10.3103/ S1068798X1610015 2. Kumar S et al (2018) Multi-parametric optimization of Universal Cylindrical grinding using Grey Relational Analysis. IJEEE 5:12–18 3. Alsigar MK (2018) Mathematical model to predict material removal rate of reverse zones. J Adv Res Tech Sci. North Charleston USA 9–1:27–30 4. Velusamy K (2019) Design and analysis of internal and external grinding attachment for lathe. IRJET 6:1410–1414 5. Almawash AD et al (2020) Model of proces;sing accuracy prediction with consideration of multi-stage process of circular grinding with axial feed. In: IOP Conference Series: Materials Science and Engineering 709 (2020) 033006. https://doi.org/10.1088/1757-899x/709/3/ 033006 6. Akintseva AV, Pereverzev PP (2017) Modeling the influence of the circle over travel on the stability of internal grinding process. Proc Eng 206:1184–1188. https://doi.org/10.1016/j. proeng.2017.10.615 7. Patil MS et al (2017) Loading and unloading system design for external centerless grinding machine using automation. IJSRD 4:2321–0613 8. Bellman R (1960) Dynamic programming. Foreign Literature Publishing House, Moscow 9. Hassui A, Diniz AE (2003) Correlating surface roughness and vibration on plunge cylindrical grinding of steel. Int J Mach Tools Manuf 43:855–862 10. Novoselov YK (2012) Dynamics of surface formation during abrasive processing. SevNTU, Sevastopol 11. Tsiakoumis VI (2011) An investigation into vibration assisted machining—application to surface grinding processes. PhD thesis, Liverpool John Moores University 12. Kharchenko AO et al (2010) Improving the vibration resistance of machining equipment of floating repair shops. SevSTU 107:33–40 13. Vladetska EA (2014) Development of shaping filter, simulating dynamics of sea waves on floating repair shop. SevSTU 150:17–25

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14. Sidorov D et al (2016) Building a dynamic model of the internal cylindrical grinding process. In: International conference on industrial engineering, ICIE 2016, vol 150, pp 400–405 15. Bratan SM et al (2018) Modeling of dynamic links which characterize static properties of grinding wheel and workpiece during flat grinding process. In: International conference on modern trends and prospects for the development of processing technologies and equipment in mechanical engineering, vol 4, No 12, pp 13–19 16. Sharma R et al (2016) Optimization of surface roughness in cylindrical grinding. IJESRT 3(12):482–486 17. Karande RJ et al (2017) Modeling and optimization of cylindrical grinding parameters for MRR and surface roughness. IJESRT 6(4):498–503. https://doi.org/10.5281/zenodo.556376 18. Cherepashkov AA, Samoilov PA (2018) Modeling and analysis of the efficiency of dynamic models of integrated automated systems of machine-building manufacture. In: International conference on current trends and prospects for the development of processing technologies and equipment in mechanical engineering, vol 4, No 12, pp 38–43

Development of a Method for Verification of API Thread Measurement Results by Comparing Them with Measurement Results of Reference Measuring Instruments D. S. Lavrinov(B) Ural Federal University Named After the First President of Russia B.N.Yeltsin, 19 Mira St., Yekaterinburg 620002, Russia [email protected]

Abstract. Steps were determined to develop the verification method for the thread measuring system. Thread parameters measurement errors were calculated for reference tools. The method of verification of measurement results of geometrical parameters of the pipe thread was developed. The sequence of parameter verification was determined. The technical means and methods allowing to measure the verifiable parameters were proposed and tested. Their error is equal or less than half of the required tolerances. The values of absolute deviations from the average value of each thread parameter for each measurement were taken as a result. A coordinate-measuring machine and an optical microscope were selected from the proposed tools and methods. The optimum thickness of casts for microscope measurement was determined. According to the results of the experiment, the deviations were not exceeded the tolerances. According to results, the coordinatemeasuring machine can be used for reference measurements of taper and standoff and the optical microscope can be used for reference measurements of pitch, height, flank angle, root, and crest diameters. Keywords: Laser scanner · Triangulation · Error · Analysis · Pipe · Verification · Thread · CMM · Microscope · Thread

1 Introduction Modern optical measuring systems show errors comparable to contact measuring systems according to the ISO test [1]. However, this test only measures spheres and plane parallel gauge blocks, but not complex reliefs with different roughness and reflection. Nevertheless, optical measurement systems are usually designed for such complex problems. Therefore, the most representative test for the customer will be to inspect their products.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_40

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In this case, the problem arises to obtain for testing the parts with known geometrical dimensions. The error of measurement of these dimensions according to the common rule in metrology and to the Nyquist–Shannon sampling theorem [2] should be equal or less than half of their tolerances. Often metrological departments of plants don’t have parts measured with such precision. This is also typical for the manufacturers of threaded pipes and couplings. Therefore, there is a need to develop a method to verify the measurement results by comparing them with the results of reference measuring instruments. They can be considered as reference tools if they provide the required measurement error for each parameter. Reference parts should be measured to obtain high-precision parameters values using reference precise tools. A number of steps should be taken to develop the verification method: • To select technical means for reference measurement of parts • To determine the approach for measuring the elements of part for each technical mean (part installation location, part coordinate system, required number of points to measure each element of the part) • To determine the sequence of measurement of the part elements, as with different measuring approaches the parameters may have different mutual dependencies • To evaluate the deviation of the measurement results obtained with this technical tool In this study, coordinate measuring machine and automatic optical microscope are used as reference tools to verify API 5CT [3] standard triangle thread measuring system. This system is based on a coordinate measuring machine and 2D triangulation laser scanner. Pitch, height, flank angle, root and crest radiuses, taper, and standoff were chosen for the experiment as the most important thread parameters.

2 Standard System Accuracy and Production Requirements The thread measuring system was tested according to ISO 10360-2, 10360-5, 10360-8 [4–6] while observing the requirements for environmental parameters. The values of the main parameters were determined in Table 1. Calculation of these parameters is necessary for certification of the system in accordance with international standards, but for the customer is important to measure their parts. It is possible to calculate the errors required for reference measurement tools. The calculation should be based on the table of tolerances for each thread parameter and common recommendations of metrology Table 2. A required error level can be achieved with Gagemaker [7] manual contact measuring instruments. However, experience has shown that it is extremely difficult to maintain Gagemaker repeatability within the required tolerance. Repeatability will depend on the correctness of expert manipulations during measurement, i.e., the human factor.

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Table 1. Thread measurement system test results according to ISO 10360-2, 10360-5, 10360-8. Measured parameter

Value

Probing error (MPEP ). Test comparable to EN/ISO 10360-2 MPEP using 1 sigma sphere fit

0.003 mm

Ball bar length (MPEE ). Test comparable to EN/ISO 10360-2 MPEE 0.008 mm +L/300 mm Multi-stylus test (MPEAL ). Test comparable to EN/ISO 10360-5 MPEAL

0.012 mm

ISO Probing form error. PForm.Sph.1x25:Tr:ODS,MPE: Maximum probing form error using 25 representative points in translatory scanning mode

0.0105 mm

ISO Probing size error all. PSize.Sph.All:Tr:ODS,MPE: Maximum probing size error All using all measured points in translatory scanning mode

0.0094 mm

ISO Probing dispersion value. PForm.Sph.D95%:Tr:ODS,MPL: Maximum probing dispersion value using 95% of the measured points in translatory scanning mode

0.0219 mm

Table 2. Measured parameter tolerances and error requirements. # Measured parameter Parameter tolerances Error of measurement of the parameter with a reference device ±0.075 mm

±0.0375 mm

2 Height

±0.05 mm

±0.025 mm

3 Flank angle

±1°

±1°

4 Root radius

±0.0225 mm

±0.01125 mm

5 Crest radius

±0.0225 mm

±0.01125 mm

6 Taper

±0.22 mm

±0.011 mm

7 Standoff

±0.625 mm

±0.3125 mm

1 Pitch

3 Development of a Method to Verify the Thread Measurement To ensure repeatable data acquisition, automatic measuring means must be used. Such means are CMMs. An example of this is Hexagon Dea Global Performance [8], which in configuration with the Tesastar-m rotary head and Renishaw TP20 touch probe provides measurement accuracy of 1.8 µm + L/300 (L is the length between two measured points, for 73-mm diameter threads L is negligible and can be set as 0). The minimum diameter of the stylus for a CMM is 0.3 mm. Needle styli are also available, but practice shows that they are difficult to use and give a significant error, even with minimal deviation from the normal direction of movement during data collection.

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One of the bottlenecks of the thread is the root, the diameter of which is 0.6 mm for triangular threads and for some premium threads the diameter is 0.29 mm. Consequently, it is theoretically possible to measure the root diameter of a triangular thread. Due to their simplicity, the other parameters can be considered as available for CMM measurement in the configuration described above. It is possible that an optical microscope will be appreciated to measure them. It is necessary to determine the sequence of parameters measurement for this method. The taper is calculated from the angle of the cone, which is formed by the pitch line. Standoff can be calculated from the diameter of the cone cross section at a certain distance from the face. Thread needs to be measured in the central section of the thread cone, therefore it needs to be found. Pitch, height, diameters, and flank angle will be independent of each other as well as of the other parameters if they are measured in a plane passing through the central axis of the thread cone. To find it, the conical section next to the end of the thread is need to be measured, which is the chamfer. This cone will allow to set a coordinate system, one of whose axes will be the thread cone axis. According to API standard requirements, thread measurement should be carried out in at least four central sections of the thread cone, located at the same angles to each other. The thread measurement method was developed for CMM and optical microscope. It consists of several sequential steps: • Recognition of geometrical primitives on the image: lines corresponding to the sides of the flank angle; circles corresponding to the diameters of the roots and crests • Finding the intersection points of the lines • Calculation of the distance between the intersection points of the lines, which gives the value of the thread pitch • Calculation of the distance between the centers of root and crest circles with the addition of the radii lengths of these circles, which gives the value of the thread height An experiment was performed to measure the thread of the tubing 73 nipple on a CMM of the described configuration. The measurements were taken according to the required sequence. For the experiment, the nipple was measured ten times. Each time it was re-installed at the measuring area. In each measurement, eight thread profiles were scanned at locations corresponding to the four central thread cone sections, which are arranged at equal angles to each other, see Fig. 1. The thread geometry makes it difficult to move the stylus along the normal direction to the surface, especially given the roughness of the surface and the use of a small stylus diameter. Even in the automatic measurement trajectory search mode, some thread points are measured with a large error and visually fly out of the envelope curve of the thread, see Fig. 2. According to the picture, it is obvious that the thread roots are the worst measured. The result is the values of absolute deviations from the average value of each parameter for each measurement, see Fig. 3a–g. The figures show that only the repeatability of the taper and standoff satisfies to the tolerances. This is due to the fact that the cone is determined from the crests of a large number of thread teeth and by averaging a large number of points. Therefore, the cone is less susceptible to outliers. The standoff is calculated in the cross section of this cone.

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Fig. 1. CMM with 0.3 mm stylus measures thread.

Fig. 2. Outliers of the envelope curve of the thread using CMM for thread measurement.

The results of the experiment show that only two thread parameters can be measured with a CMM in this configuration. The others require a different tooling and approach. One of the ways to evaluate the quality of thread in production is to analyze thread casts on a magnifying projector [9]. This method does not allow to measure parameters values, but only to determine their approximate correspondence to the reference. On the other hand, casts can be measured with an automated optical microscope. For example, Optiv 321 [10] has a measurement error of 1.5 µm and allows automatic measurement of the part. The taper and standoff cannot be measured with this method because the casts give information about the thread segment in one section and they are independent of each other. The two-composite casting material Compare-C was chosen for the experiment. This material is intended for obtaining high-precision casts from the surface of metal products for subsequent measurement and visual inspection of geometric parameters. Volume shrinkage of this material is no more than 0.05%, the recovery of shape after deformation is 99.8% [11]. In order to be placed on the table of the microscope, the cast must have flat sides, for which flash must be cut off, see Fig. 4.

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Fig. 3. a deviations of the pitch (X-axis—number of tests, Y-axis—mm); b deviations of the height (X-axis—number of tests, Y-axis—mm); c deviations of the flank angle (X-axis—number of tests, Y-axis—degree); d deviations of the crest diameter (X-axis—number of tests, Y-axis— mm); e deviations of the root diameter (X-axis—number of tests, Y-axis—mm); f deviations of the taper (X-axis—number of tests, Y-axis—mm); g deviations of the standoff (X-axis—number of tests, Y-axis—mm).

Fig. 4 Pipe thread with cast.

In the course of the experiment, it is also necessary to determine which thickness of the cast is best suited for measuring with the microscope. Therefore, casts of 0.5, 1, 2, and 3 mm thicknesses were made.

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In the course of determining the optimum thickness of the cast, significant tooth width expanding was found when using casts with a thickness greater than 1 mm. This is due to the fact that the thread is cut as a helicoid with a pitch of 3.175 mm. Therefore, the tooth width for optical measurement method depends on the thickness of cast. If the cast thickness contains a significant segment of helicoid, then it will lead to measurement errors, see Fig. 5a. Using only top light does not allow to clearly recognize the top of the cast and make accurate measurements. If casts are thinner than 1 mm, then they can be easily deformed due to their thinness, see Fig. 5b. You can see on the picture that a thin cast has a large number of lints. Due to cast flexibility, it is difficult to clean it before measuring.

Fig. 5. a Significant tooth width expanding using casts with a thickness greater than 1 mm; b a large number of lints on the microscope picture using casts thinner than 1 mm.

Therefore, the optimum thickness of the cast for measurement with an optical microscope can be considered 1 mm. The visual tooth width doesn’t have a significant impact on the measurement results. The cast retains its shape well and can be cleaned before measurement, see Fig. 6.

Fig. 6. The microscope picture using casts of the optimum thickness.

An experiment was performed to measure casts from the thread of the tubing nipple 73 on the automatic optical microscope Optiv 321. One nipple was measured ten times. Eight casts were taken at each measurement at the places corresponding to four central thread cone cross sections, which are arranged at equal angles to each other. Visual analysis using the microscope of each cast helped to detect the places where were deformations,

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bubbles, and other distortions. These places were removed from the calculations. The figures show the values of absolute deviations from the average value of each parameter for each measurement, see Fig. 7a–e.

Fig. 7. a deviations of the pitch (X-axis—number of tests, Y-axis—mm); b deviations of the height (X-axis—number of tests, Y-axis—mm); c deviations of the flank angle (X-axis—number of test, Y-axis—degree); d deviations of the crest diameter (X-axis—number of tests, Y-axis—mm); e deviations of the root diameter (X-axis—number of tests, Y-axis—mm).

According to the results of the experiment, the deviations have not exceeded the tolerances. Therefore, the optical microscope can be used for reference measurements of pitch, height, flank angle, root, and crest diameters.

4 Conclusion The method of verification of measurement results of geometrical parameters of the pipe thread was developed. The technical means and methods allowing to measure the verifiable parameters were proposed and tested. Their error is equal or less than half of the required tolerances. The sequence of parameter verification was determined.

References 1. LC15Dx—Closing the gap with tactile probe accuracy (2018) Nikon Metrology NV. https:// www.nikonmetrology.com//images/brochures/lc15dx-en.pdf. Accessed 12 Sept 2018 2. Lyons R (2011) Understanding digital signal processing. Pearson Education Inc, Michigan

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3. American Petroleum Institute (1988) API 5B specification for threading, gaging, and thread inspection of casing, tubing, and line pipe threads. American Petroleum Institute, Dallas 4. European Committee for Standardization (2001) Geometrical Product Specifications— Acceptance and reverification tests for coordinate measuring machines. Part 2. CMMs used for measuring size (ISO 10360-2). European Standard, Brussels 5. European Committee for Standardization (2005) Geometrical Product Specifications— Acceptance and reverification tests for CMMs. Part 5. CMMs using single and multiple stylus contacting probing systems (ISO 10360-5). European Standard, Brussels 6. European Committee for Standardization (2013) Geometrical product specifications—Acceptance and reverification tests for coordinate measuring systems. Part 8. CMMs with optical distance sensors (ISO 10360-8). European Standard, Brussels 7. Dimensional measurement technology (2020) Gagemaker. http://gagemaker.com/products/. Accessed 21 Jan 2020 8. Hexagon Metrology (2012) Probes & Sensors for Coordinate Measuring Machines. Product Catalogue. Turin 9. Dimensional inspection (2020) Laboratory Testing Inc. https://www.labtesting.com/metrol ogy-calibration-services/dimensional-inspection/. Accessed 21 Jan 2020 10. Metrology Hexagon (2015) Optiv Classic 321 GL/tp. Product Catalogue, Turin 11. Silicone casting material Compar-C (2020) Impex Craft. https://ic-tec.ru/catalog/ottiskno-sle pochnyy-material-kompar/kompar-s1_8077/. Accessed 21 Jan 2020

Calculation of Contact Tensions in the Process of Thermofrictional Treatment N. Pokintelitsa and E. Levchenko(B) Sevastopol State University, 33, Universitetskaya St., Sevastopol 299053, Russia [email protected]

Abstract. It has been established that in the process of thermofrictional cutting, the layer being cut undergoes a significant shape formation, under which the conditions of simple loading, uniformity, and monotonicity of plastic deformation are not observed. An analysis of the calculated values of the stress state parameters of the deformable elementary volume near the cutting edge of the tool is presented, indicating that both on the front and rear surfaces they are slightly dependent on the cutting speed. It has been proved that, depending on the physicomechanical and thermophysical properties of the processed materials and the cutting conditions, and, consequently, the degree of deformation, not only the length of the plastic contact changes but also the outline of its contour. The nature of the change in normal stresses, confirming the hypothesis of the constancy of hydrostatic pressure in the cutting zone, is determined. The calculated dependencies are given for determining contact stresses during thermofrictional processing, which, taking into account the patterns of the deformed state of the cut layer, can be used to develop a scientifically based system for optimizing the thermofrictional cutting process. Keywords: Thermofrictional treatment · Dynamic appliances · Differential equations · Dynamic model · Operator view · Structural model · Parameters of oscillations

1 Introduction One of the effective ways of improving the machinability of metals by cutting includes the preheating of the cut layer, which leads to decreasing resistance to deformation of the processed material, determines the increase of cutting rates, tool life, and rise of labor productivity. Thermofriction cutting is a combined method that mixes thermal and mechanical effects on the machined metal by direct contact of the workpiece with rotating at high peripheral speed (up to 80 m/s) steel cutting disc (CD).

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_41

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This type of treatment is characterized by high-temperature heating of the contact area of the chip formation zone and inextricably connected thermal softening of the processed material, significant reduction of its mechanical properties and friction forces on the front surface of CD. Flow chips, formed under such conditions, have, as a rule, negative shrinkage and shearing angles greater than 45°, as determined by metallographic studies [1, 2]. Previous studies have made it possible to create the mathematical models of energy– power and thermal phenomena. Peculiarities of the process of chip formation and resistance were studied, as well as perspective designs of disks were proposed [3–5].

2 Main Text The method of thermal friction treatment (TFT) is specific, and the study of contact phenomena in the chip formation zone is connected with great difficulties. The nature of the processes taking place in the cutting zone can be determined primarily on the basis of the analysis of indirect indicators and dependencies (temperature and pressure in the cutting zone, deformation rate, type of chips, etc.). The aim of this work is to determine the deformed and stressed state of the TFT contact zone, which is an important and necessary stage for studying the features of the CD workpiece processing. In the process of thermofriction cutting, the shear layer undergoes a significant formation, in which the conditions of simple loading, uniform, and monotonicity of plastic deformation are not observed. However, for a considered material particle occupying a very small volume of deformable body, it is possible to guarantee the monotonicity of the deformation process when the directions of the principal axes of the stress state in that elementary particle are known, which, according to the monotonicity condition, must coincide with the principal axes of the deformation rate and the principal axes of the resultant deformation. At that, the type of stressed state will correspond to the type of final deformation [6–9]. In (Fig. 1), there is decomposition scheme of the equivalent force Rn , applied at the contact point A on the tool cutting edge into the normal force N and frictional force FN for forces PS and PN , acting, respectively, in the direction of the maximum shear stress Au and perpendicular to it, as well as the forces PZ0 and PN0 , which are a part of the main and normal components of the equivalent force corresponding to a given point of the cutting edge on the front surface of the tool. In accordance with this scheme, the angle ρ between the equivalent force Rn and the force PS , as well as the additional angle ψ2 , can be represented by the dependencies ρ = ω + χ = ηn − γ + χ ; ψ2 = 90◦ + γ − (ηn + χ ),

(1)

where ω is the angle of action for point A on the cutting edge of the tool; ηn —friction angle for the specified point; χ —the angle determining the direction of action of the maximum shear stresses. Taking into account the fact that ψ2 = 45◦ , the value χ can be written as follows: χ = 45◦ +

ηn + ω γ − . 2 2

(2)

Calculation of Contact Tensions in the Process

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Fig. 1. Decomposition scheme of the equivalent force at the point of contact on the tool cutting edge.

Correspondence (2) is similar to the well-known K.A. Zvorykin formula for the shear angle F, if in this formula, instead of using the internal friction angle, use the angle of action ω. On the basis of formula (1), it can be concluded that the angle ϕ1 between the direction of the main stress σ1 and the front surface of the tool is equal to the friction angle ηn , which in turn is the angle between the perpendicular lowered from given point of contact to the direction of the equal force Rn , and the front surface. It follows a very important consequence that the main stress σ3 = 0. Indeed, the normal stress σ and total tangential stress τn acting in an arbitrarily inclined area with guide cosines l, m and n are defined by the equations: σ = l 2 σ1 + m2 σ2 + n2 σ3 .

(3)

τn2 = l 2 σ12 + m2 σ22 + n2 σ32 − σ 2 .

(4)

In relation to the front surface of the tool, if accepted, it is obtained σ = σ1 cos2 ϕ1 . τn2 = σ12 cos ϕ1 − σ12 cos4 ϕ1 = σ12 cos2 ϕ1 sin ϕ1 .

(5)

τn = σ1 cos ϕ1 sin ϕ1 .

(6)

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ϕ1 sin ϕ1 where in tgηn = τσn = σ1 σcoscos = tgϕ1 and ηn = ϕ1 . 2ϕ 1 1 The hydrostatic pressure in this case (at σ3 = 0) is calculated by the formula:

  2 p = σ3 = − σi cos 60◦ − Φ 3

(7)

It can be also shown that p = σ  when σ = τ n . This takes place in the area located at an angle of 45° to the direction of the main stresses σ1 and σ3 , where there are maximum tangential stresses. For this area σχ = σ1 cos2 45◦ + σ3 cos2 45◦ = τ31 =

σ1 + σ2 . 2

σ1 − σ3 . 2

If σχ i τ31 is expressed through the deviatoric stresses σ1 , σ3 and hydrostatic pressure p there will be obtained σχ =

σ1 − p + σ3 − p σ  + σ3 σ = 1 − p = − 2 − p. 2 2 2 τ31 =

σ  − σ3 σ1 − p − σ3 + p = 1 . 2 2

At σχ = τ31 , σ  − σ3 σ1 + σ3 −p= 1 and p = σ3 . 2 2 The shown data indicate that, at point A on the cutting edge of the tool, there is plane stress at σ3 = 0. It can be affirmed that it also applies to other plastic contact points on the tool front surface. At the same time, negative ball tensor (hydrostatic tension pressure) is superimposed on the deviator. Taking into account expression (7), the formulas for main stresses calculating the will have the form √   ◦  2 3  2 2 σi cos Φ − 30◦ . σ1 = σi cos Φ + σi cos 60 − Φ = 3 3 3 √   2 3 2 2 ◦ ◦ σ2 = σi sin(Φ − 30 ) + σi cos 60 − Φ = σi sin Φ (8) 3 3 3 σ3 = 0. The maximum shear stress τ31 acting in the direction of Au at an angle χ to the cutting plane (Fig. 1), as well as the normal stress perpendicular to this direction, can be calculated by the formula: √   3 σi cos Φ − 30◦ . τ31 = σχ = 3

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In the direction AD at a shear angle F, the tangent and normal stresses are determined by the expressions √   3 τ= σi cos Φ − 30◦ sin 2(ξ − Φ). 3 √   2 3 σ = σi cos Φ − 30◦ cos2 (ξ − Φ). 3 According to formulas (5) and (6), at ϕ1 = ηn normal σn and tangential τn stresses at point A on the tool front surface are expressed by the dependencies: √   2 3 2 σi cos Φ − 30◦ cos2 ηn , σn = σ1 cos ηn = (9) 3 √   3 1 σi cos Φ − 30◦ sin 2ηn , τn = σ1 sin 2ηn = (10) 2 2 where ηn = 45 + γ − χ . From the formula (10) √ 3τn 2τn . = sin 2ηn = σ1 σi cos(Φ − 30◦ ) The analysis of this formula shows that the angle of friction ηn on the tool front surface at the cutting edge is always less than 45°. Within the limits of a possible change in the angle of shear 0 < Φ < 60◦ , the maximum value of the angle will be at F = 0 i F = 60°. Within the indicated limits sin 2ηn
30◦ , the size b0 on the front surface is always greater than the width of the cut b and ε2 > 0. In determining the law of distribution of deformation intensity εi along the length of plastic contact, it is assumed that in the process of moving chips along the disc surface, the value of the triangle of the deformation, constructed as an addition to the Mor diagram for the material point on the burning edge of the tool. According to this assumption, in the direction perpendicular to the cutting edge ε1 − ε3 does not change for all contact points. Using dependencies for the main components of the deformation ε1 = εi cos βε ; ε2 = εi sin(βε − 30◦ ); ε3 = −εi cos(60◦ − βε ), It is possible to write: √ 3ε2 [cos βε + cos(βε − 60◦ )]ε2 ε1 − ε3 = = . ◦ sin(βε − 30 ) tg(βε − 30◦ )

(11)

From the above formula (11), it is obtained the following expression for calculating the angle of the type of deformation at any contact point √ √ 3 ln bbx 3ε2x ◦ tg(βεx − 30 ) = = . ε1 − ε3 ε1 − ε3 If the value βεx is known, it is possible to determine the strain intensity at each point using one of the following formulas: εix =

ln bbx ; sin(βεx − 30◦ )

ε1 − ε3 . εix = √ 3 cos(βεx − 30◦ )

(12)

Calculations according to formulas (12) show that in the immediate vicinity of the cutting edge the intensity of deformation varies very slightly. At points more distant from it, the value εix increases and reaches a maximum at the end of the plastic contact. Thus, all the necessary data for calculating at any point of contact of the normal strain σnx are determined, the formula for which on the basis of dependence (9) can be represented as √   2 3 σix cos βεx − 30◦ cos2 ηnx . σnx = 3 The intensity of the stress state σix is determined by a certain value of the strain intensity εix , and the friction angle ηnx by the formula: √ 3τn . sin 2ηnx = σix cos(βεx − 30◦ )

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Analysis of the calculated values of parameters of the stress state of deformed elementary volume near tool cutting edge shows that both on the front and rear surfaces they depend to a small extent on the cutting speed. Strength and thermophysical characteristics of the processed material have a significant influence on the value of contact stresses. Thus, as the limit increases and the thermal conductivity decreases, the values of stress intensity, main and tangential stresses, as well as hydrostatic pressure increase. The calculations showed that on the front and rear surfaces there is a plane stress state with equal to zero principal stresses, σ1n and σ23 , respectively. Analyzing the calculation data, it can be concluded that the stress state of the elementary volume near the cutting edge can be considered as a result of hydrostatic pressure applying to the simple compression scheme.

3 Conclusion The nature of the change in normal stresses and hydrostatic pressure clearly confirms the hypothesis that the hydrostatic pressure in the cutting zone is constant. As a result of the conducted studies using the plasticity theory, the calculated dependencies for determining contact stresses and forces on the disc cutting surfaces are determined, which, taking into account the regularities of the deformed state of the cut layer, can be used for the development of a scientifically based system of optimizing the thermofriction cutting process.

References 1. Strutinskiy VB, Pokintelitsa NI (2014) The mechanism of formation of a wavy surface when handling parts thermofrictional. J Vestnik SevNTU, Seria: Mashinopriborostroenie i transport 161–169 2. Zarubitskiy EU (1986) The temperature of the allowable allowance during thermal friction cutting. J Optim Process Cutting Heat-resistant and High-strength Mater 106–110 3. Kozochkin MP (2005) Vibroacoustic diagnostics of technological processes. In: IKF “Catalog, Moscow 4. Sorokin GM (2000) Tribology of steels and alloys. Nedra, Moscow 5. Nasad TG, Ignatiev AA (2002) High-speed processing difficult materials with additional streams of energy in the cutting zone. STSU, Saratov 6. Strutinskiy VB (2001) Mathematical modeling of processes and systems of mechanics. ZETI, Zhitomir 7. Goryacheva IG (2001) Mechanics of frictional interaction. Nauka, Moscow 8. Shaduya VL (2008) Modern methods of processing materials in machine building. Technoprospect, Minsk 9. Gik LA (1990) Rotary cutting metals. Bk. Publishing House, Kaliningrad 10. Chichinadze AV (2001) The basics of tribology (friction, wear, lubrication). Mashinostroenie, Moscow 11. Penkin NS, Penkin AN, Serbin VM (2008) Fundamentals of tribology and tribotechnology. Mashinostroenie, Moscow 12. Mazur NP (2010) Basic theory of cutting materials. Novyj Svet, L’vov 13. Khomenko AV, Lyashenko JA (2010) Periodic intermittent boundary friction. J Sci Techn Phys 27–33

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14. Strutinskiy VB (2005) Tensor mathematical models of processes and systems. ZHGTU, Zhitomir 15. Strutinskiy VB, Drozdenko VM (2010) Dynamic processes in machine tools. Osnova-Print, Kiev 16. Terentyev VF (2001) Cyclic strength metallic materials. Mashinostroenie, Moscow 17. Bosheh SS, Mativenga PT (2006) White layer formation in hand turning of H13 tool steel at high cutting speeds using CBN tooling. Int J of Mach Tools Manuf 225–233 18. Gusanelli G, Hessler-Wyser A, Bobar F et al (2004) Microstructure at submicron scale of the white layer produced by EDM technique. J Mater Process Technol 289–295 19. Garbar I (2001) Microstructural changes in surface layers of metal during running-in friction processes. J Sci. Meccanica 631–639 20. Guo YB, Sahni JA (2004) Comparative study of turned and cylindrically around white layers. J Sci Mach Tools Manuf 135–145 21. Jachymek M, Gurey I et al (2012) Computer simulation of friction hardering of superficial layers of machine details. J Sci Manuf Process Some Probl. Basic Science Applications 49–62

Effect of Mode Amplitude on Power Consumption in Vibrating Mixer N. Dubkova1 , V. Kharkov1(B) , and B. Ziganshin2 1 Kazan National Research Technological University, 68, Karl Marx Street, Kazan 420015,

Russia [email protected] 2 Kazan State Agrarian University, 65, Karl Marx Street, Kazan 420015, Russia

Abstract. A paper deals with a study of the influence of dynamic parameters for a vibrating apparatus and physicomechanical properties of treated material on its power consumption. The most reliable expression for calculating the power consumption is presented, from which the value of the power is proportional to the amplitude in the first degree and the vibration frequency in the third degree. In order to verify this theoretical formula for different materials, a test setup was developed. A description of the design and operating principle of the experimental setup is reported. Bulk materials (cement and potassium chloride with 5% additives) and fusible material (80% potassium chloride and 20% epoxide resin) have been the subject of the investigation. The experiments of influence of the vibration amplitude on the power consumption during the mixing were performed at a constant vibration frequency of 60 Hz and amplitudes of 0.64; 1.03; 1.44; 1.83 mm. It was concluded that the theoretical formulation of the linear dependence of power consumption on vibration amplitude is matched to the results of experiments. The simple interrelationships of initial, maximum, and final power consumption on amplitude are obtained. It was found that under optimal vibration parameters specified by the mixing kinetics, the approximate time of the constant temperature setting can be determined at the point in time at which constant power is fixed. Keywords: Vibration · Mixing · Bulk material · Fusible material

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_42

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1 Introduction Vibrating mixers have a wide distribution in the chemical, petrochemical, and food industries [1–4]. An exposure of vibration on mixed material and end-effectors of the apparatus significantly reduces power consumption and increases the rate of productivity, as well as the quality of the mixture. Moreover, in some cases, vibration only intensifies the main process (e.g., screw vibrating in the screw mixer), in others, it induces specific vibration effects that are used for mixing (e.g., circulation motion of the mixture inside the cylindrical or toroidal vessel) [5–7]. Vibration pulses cause the following processes: chaotic collisions of material particles and their separation by shape, density, and size; destruction of the formed conglomerates; reduction of friction between particles. Although mixing occurs in almost any process where vibration is used, good homogeneity of the derived mixture is obtained only in certain apparatuses with directed vibration [8–10]. The circulation of the load as an auxiliary factor in vibration mixing contributes to the renewal of the diffusion surface by moving volumes of particles lengthwise and crosswise of the mixer body. This fact results in uniformity throughout the mixture. According to [11], the absence of load circulation significantly slows down the mixing process even with high-intensity vibrations. Therefore, in order to reach maximum mixing velocity, it is important to select the operating parameters of the mixer, providing intense vibration and load circulation [12–14]. Thus, the basis of technological calculations of vibration mixers is to determine the power consumption of the load circulation, depending on the physicomechanical properties of bulk and fusible materials, as well as design and dynamic parameters [15–18]. In addition, the value of power consumed by the vibrating apparatus is the initial data for designing the drive and strength analysis of the components. The purpose of this paper is to study the influence of the vibration amplitude of the apparatus on power consumption when mixing fusible and bulk materials.

2 Study Objects and Methods According to the report [19], the power consumption is substantially determined by the vibration of the mixer body with loading. Therefore, taking into account the dynamic parameters of the vibrating apparatus and physicomechanical properties of the treated material, the most reliable expression for calculating the shaft power N (kW) has the form: N=

mω3 (r − A)fmp d 4qr 2 mω5 sin 2γ  +  , 204 204 p2 − ω2

(1)

 where q = m (m + M ); m is the debalance weight, kg · s2 /m; M is the loaded mixer weight; r is the eccentricity of debalance, m; p is the natural frequency, 1/s; ω is the angular velocity of vibrating shaft rotation, 1/s; γ is the phase-shift angle between forced vibrations and driving force; A is the vibration amplitude of the apparatus body, m;fmp is the reduced coefficient of friction in a rolling bearing; d is the bore diameter of bearing cup, m.

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It can be seen from the formula (1) that the power is proportional to the amplitude in the first degree and the frequency in the third degree. For purposes of clarity, in the first term of Eq. (1), one can introduce the amplitude (m) for the case of forced vibrations as A=

qrω2 p2 − ω 2

(2)

For the practical application of the formula (1), it is necessary to verify it in terms of the constituent parameters using an experimental approach. So, to study the effect of the operating mode on the power consumption of the vibrating apparatus for different materials, a test setup was developed (Fig. 1).

Fig. 1. Scheme of experimental set-up. 1—mixer body; 2—central pipe; 3—vibrator shaft; 4—debalance; 5—flexible support; 6—bearing support; 7—flexible connector; 8—intermediate support; 9—V-belt transmission; 10—variator; 11—motor

The vibrating mixer has a horizontal body with an inner central pipe. The mixer installed on flexible supports, being an end-effector with mass M. A vibrator shaft is placed inside the central pipe on bearing supports. Plates with debalances (m) and eccentricity (r) are fixed at both ends of the shaft. Shaft rotation is driven by an electric motor (4.5 kW and 2880 rpm) through a system of a flexible connector, a V-belt transmission, and a speed variator. The vibration amplitude of the apparatus body depends on the number of the withdrawable debalances. The amplitude value is measured by the VR-1 vibrograph (Vibropribor, Russia). The study of the influence of the vibration amplitude on the power consumption during the process was performed at a constant vibration frequency ν = 60 Hz and amplitudes of 0.64; 1.03; 1.44; 1.83 mm. The frequency of vibrations is determined by the number of vibrator shaft turns and is recorded using the ST-5 stroboscopic tachometer (Analypribor, Georgia). It should be mentioned that the value of vibration amplitudes was specified in the experimental work [20] in accordance with the patterns of vibration mixing. To measure the power consumption, the laboratory setup is equipped with a CL8516 wattmeter (Mir, Russia). The body of the vibrating apparatus has a heating jacket with hot water, which comes from the boiler with a built-in thermostat (Ariston, Italy) using the circulation

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pump (WILO, Germany). The temperature mode is controlled by the IT-17-S digital thermometer (Eksis, Russia) with the TSP-100 thermocouple mounted inside the apparatus. Bulk materials, such as cement and potassium chloride with various additives, have been the subject of investigation. Additives (5%) in the dissolved state were applied to potassium chloride powder. Then the solvent was removed and the composition was sieved. As fusible material, a composition of 80% potassium chloride and 20% epoxide resin ED-5 was used. The physical properties of the test components are shown in Tables 1 and 2. Table 1. Properties of bulk materials Composition

Bulk density (kg/m3 )

Particle size distribution (μm)

Temperature (°C)

KCl (95%) + glycerin (5%)

980

125–360

18–20

KCl (95%) + paraffin (5%)

903

125–360

18–20

90 and less

18–20

Cement

1707

Table 2. Properties of fusible material Liquid phase

Temperature (°C)

Density (kg/m3 )

Dynamic viscosity (Pa•s)

Epoxide resin ED-5

20

1165

25

Epoxide resin ED-5

80

1135

0.2

3 Results and Discussion Figure 2 presents experimental data of change in the power from different amplitudes in case of the fusible material. It should be noted that there are no temperature curves of the composition during vibration mixing in this figure. Therefore, the power plot shows the characteristic temperature dots at the initiation and termination of the epoxide resin fusing, as well as the dot at which constant set temperature is reached. It has been found that with an increase in the amplitude of vibration, the heating time of the mass load to the fusing temperature drops (dot “a” is closer to the ordinate axis). Furthermore, there are the reductions in fusing time (the distance “ab” decreases) and time of reaching the constant set temperature under this condition. The reason for the temperature changes of the mass loading is the densification of the mass movement with increasing vibration amplitude. So, this fact leads to the improvement in the heat transfer between the apparatus body and the material, as well

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А = 0.64

a

А = 1.03

Power consumption N, kW

А = 1.44 А = 1.83 1

b

a a

b c a

0,5

0

c b

b

0

c c

50

100

150

Time, min

Fig. 2. The vibration amplitude A (mm) dependence of power consumption N (kW) for fusible material (80% potassium chloride + 20% epoxide resin) at a frequency of 50 Hz. Temperature dots: a—fusing initiation (80 °C); b—fusing termination; c—constant set temperature (~87 °C)

as greater heating of the mass due to friction. It is reasonable that intensification in the motion of the mass requires additional power consumption. So, under optimal vibration parameters specified by the mixing kinetics, the approximate time of the constant temperature setting can be determined at the point in time at which constant power is fixed. Based on the curves in Fig. 2, the interrelationships of initial, maximum and final power on amplitude are obtained (Fig. 3). 1,5 Ni

Power consumption N, kW

Nmax Nf 1

0,5

0 0

0,5

1 Amplitude A, mm

1,5

2

Fig. 3. Change in values of initial, maximum, and final power consumption from vibration amplitude at a frequency of 50 Hz

These graphics can be closely approximated by simple expressions: Ni = 0.159A + 0.243,

Effect of Mode Amplitude on Power Consumption in Vibrating Mixer

Nmax = 0.592A + 0.223, Nf = 0.356A + 0.185,

367

(3)

where Ni and Nf are initial and final power (kW), respectively; Nmax is maximum power (kW). The experimental value of power consumption in the loaded vibrating mixer may be considered under two parts. The first one is the power transmitted directly to the load to overcome the resistance caused by the material, and the second one is the power consumed to vibrate the empty mixer. The value of power transmitted to the load can be considered useful, going directly to the intensification of mixing, since this part of power goes to the circulating motion and vibrations of the load in the mixer. The power for vibrating the empty mixer at the different vibration modes is obtained by the experimental approach. The linear dependence of power consumption on vibration amplitude is confirmed by the results of the experiments carried out on different bulk materials (Fig. 4). The experimental results for materials with different physicomechanical properties verified the linear dependence of the function N = f (A) and hence are in full agreement with the theoretical expression (1). The power consumption when mixing the fusible composition (80% potassium chloride + 20% epoxide resin) is obtained by subtracting the values for unloaded mixer from the experimental values Ni , Nmax , Nf at the same vibration modes. The maximum power is transmitted the load at the optimum amplitude A = 1.44 mm so that the desired water content of the material is achieved in the shortest time. 1,5

1

Power consumption N, kW

2 3 4

1

0,5

0 0

0,5

1 Amplitude A, mm

1,5

2

Fig. 4. N = f (A) dependence for various bulk materials: 1—unloaded apparatus; 2—cement; 3—KCl (95%) + glycerin (5%); 4—KCl (95%) + paraffin (5%)

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4 Conclusion It has been stated that the theoretical formulation of the linear dependence of the power consumption on the vibration amplitude is matched to the results of the experiments carried out on fusible and bulk materials. The simple interrelationships of initial, maximum, and final power consumption on amplitude are obtained. Furthermore, it was found that with an increase in the amplitude of vibration, the heating time of the load to the fusing temperature drops, as well as the fusing time and time of reaching the constant set temperature. This fact leads to an improvement in the heat transfer between the apparatus body and the material, as well as greater heating of the mass due to friction. Thus, under optimal vibration parameters specified by the mixing kinetics, the approximate time of the constant temperature setting can be determined at the point in time at which constant power is fixed. The advantages of the vibrating mixers are considerable simple design, high weight load factor, providing a high rate of productivity, good homogeneity of the derived mixture, and high-level of industrial safety.

References 1. Borodulin D, Zorina T, Ivanets V et al (2019) Key operation parameters of the vibration mixer in the production of flour baking mixes. Food Process Tech Technol 49:77–83. https://doi. org/10.21603/2074-9414-2019-1-77-84 2. Sana T, Shiomori K, Kawano Y (2005) Extraction rate of nickel with 5dodecylsalicylaldoxime in a vibro-mixer. Sep Purif Technol 44:160–165. https://doi.org/10. 1016/J.SEPPUR.2005.01.005 3. Shamlou PA, Gierczycki AT, Titchener-Hooker NJ (1996) Breakage of flocs in liquid suspensions agitated by vibrating and rotating mixers. Chem Eng J Biochem Eng J 62:23–34. https://doi.org/10.1016/0923-0467(95)03054-9 4. Keppler S, Bakalis S, Leadley CE, Fryer PJ (2016) A systematic study of the residence time of flour in a vibrating apparatus used for thermal processing. Innov Food Sci Emerg Technol 33:462–471. https://doi.org/10.1016/J.IFSET.2015.12.003 5. Cai H, Miao G (2019) Horizontal flow in a vertically vibrated granular layer. Particuology 46:93–98. https://doi.org/10.1016/j.partic.2019.03.001 6. Li CX, Dong KJ, Shen YS, Yu AB (2019) Particle conveying under microgravity in a vibrating vessel. Adv Powder Technol 30:3163–3170. https://doi.org/10.1016/J.APT.2019.09.025 7. Chaudhury A, Barrasso D, Pohlman DA, et al (2017) Mechanistic modeling of high-shear and twin screw mixer granulation processes. Predict Model Pharm Unit Oper 99–135. https:// doi.org/10.1016/B978-0-08-100154-7.00005-3 8. Ivanets VN, Borodulin DM, Shushpannikov AB, Sukhorukov DV (2015) Intensification of bulk material mixing in new designs of drum, vibratory and centrifugal mixers. Foods Raw Mater 3:62–69. https://doi.org/10.12737/11239 9. Baragetti S (2015) Innovative structural solution for heavy loaded vibrating screens. Miner Eng 84:15–26. https://doi.org/10.1016/J.MINENG.2015.09.011 10. Golovanevskiy VA, Arsentyev VA, Blekhman II et al (2011) Vibration-induced phenomena in bulk granular materials. Int J Miner Process 100:79–85. https://doi.org/10.1016/J.MINPRO. 2011.05.001 11. Korf OY (1961) Issledovaniye protsessa tsirkulyatsii zagruzki v vibrosmesitele (Study of circulation of load in vibrating mixer). In: Issledovaniya po betonu i zhelezobetonu. Riga, p 43

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12. Mizonov V, Balagurov I, Berthiaux H, Gatumel C (2017) Intensification of vibration mixing of particulate solids by means of multi-layer loading of components. Adv Powder Technol 28:3049–3055. https://doi.org/10.1016/J.APT.2017.09.016 13. Kharkov VV (2018) Mathematical modelling of thermolabile solutions concentration in vortex chamber. J Phys: Conf Ser 980:012006. https://doi.org/10.1088/1742-6596/980/1/ 012006 14. Hashemnia K, Pourandi S (2018) Study the effect of vibration frequency and amplitude on the quality of fluidization of a vibrated granular flow using discrete element method. Powder Technol 327:335–345. https://doi.org/10.1016/J.POWTEC.2017.12.097 15. Menbari A, Hashemnia K (2019) Effect of vibration characteristics on the performance of mixing in a vertically vibrated bed of a binary mixture of spherical particles. Chem Eng Sci 207:942–957. https://doi.org/10.1016/J.CES.2019.07.026 16. André C, Demeyre JF, Gatumel C et al (2012) Dimensional analysis of a planetary mixer for homogenizing of free flowing powders: Mixing time and power consumption. Chem Eng J 198–199:371–378. https://doi.org/10.1016/J.CEJ.2012.05.069 17. Li Z, Cao G (2019) Rheological behaviors and model of fresh concrete in vibrated state. Cem Concr Res 120:217–226. https://doi.org/10.1016/J.CEMCONRES.2019.03.020 18. Yang SC (2006) Segregation of cohesive powders in a vibrated granular bed. Chem Eng Sci 61:6180–6188. https://doi.org/10.1016/J.CES.2006.05.048 19. Varsanofiev VD, Kolman-Ivanov EE (1985) Vibratsionnaya tekhnika v khimicheskoy promyshlennosti (Vibration technology in chemical industry). Himia, Moscow 20. Dubkova NZ (2001) Polucheniye pishchevykh poroshkoobraznykh produktov iz rastitelnogo syrya (Production of food powdered products from vegetable raw materials). Kazan state technological university

Multi-stages to Ensure Quality Control of Designing and Production at External Cylindrical Grinding Machines M. K. Alsigar1,2(B) , P. P. Pereverzev1 , and A. D. AlMawash1 1 South Ural State University, 76 Lenin Str., Chelyabinsk 454080, Russia

[email protected] 2 College of Engineering, Thi-Qar University, 31, Thi-Qar, Nasiriyah 64001, Republic of Iraq

Abstract. This article describes the solution of a problem of constructing a mathematical model for operation efficiency management during cylindrical external grinding with radial and axial in-feed at CNC. Basically, this model is used for five main purposes: to test the prediction accuracy (the diametrical error in dimensions, deviation of the shape as well as in the mutual arrangement of surfaces, treated surface taking into account the variables of process conditions, degree of blunting of the grinding wheel and initial radial run-out, etc.). As a result, in multistages, the quality parameters of the model processing differ significantly from the quality parameters with those of another surface being treated. This article describes a methodology for optimizing operational parameters at the stage of cutting during cylindrical external grinding with radial and axial in-feed process of a reversible stage. The model approach can be successfully applied to designing and optimization of different stages in grinding cycles with radial and axial in-feed at CNC. Keywords: Cycles · Cutting modes · External grinding · Axial feed · Optimization

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_43

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1 Introduction The distinctive feature during cylindrical external grinding with radial and axial in-feed process of a reversible stage is the alternation of the different methods of cylindrical external grinding with radial Rp and axial Soc in-feed at the stage of wheel grinding steps cutting into the workpiece and at the stage of wheel grinding stopping for reverse motion when the workpiece makes several revolutions and the process of grinding is carried through the tightness in the technological system. Therefore, the cutting modes in a non-reversible zone greatly differ from the modes in a reversible zone. The obtained generalized model of shaping a ground surface takes into consideration the peculiarities of processing in reversible and non-reversible zones allowing the calculation of the current radius data in different sections of processed surface throughout the full-cycle optimization in grinding selected conditions of Rp with Soc. Thus, it is possible to build a model of calculating radius values for the processed surface to estimate error and productivity of processing during Rp and Soc. Presented model for the process of surface shaping was designed based on the functional relationship between the Rp , Soc, and elastic deformations Y of a technological system, taking into consideration the peculiarities of machining in reversible (Sects. 1 and 3) and nonreversible (Sect. 2) zones. The model also established the relationship of productivity of grinding with cutting forces, mechanical properties of manufactured materials, dulling abrasive grains of grinding wheel, stiffness of the technological system, cutting modes, and the kinematic features of grinding in operation and idling in the reversible zones of the wheel with obtained precision of processing during simultaneous in-feeds and control of grinding cycles using the automatic step cycles of radial and axial feeds incorporated into CNC machines. Malkin [1] made a significant contribution to the theory of grinding and to the study of automatic grinding cycles; it was established that there is an interrelationship among forces of cutting, deformations of elastic, programmed, and actual in-feed, which affect depth of cutting and accuracy of processing. The effect forces of cutting, deformations of elastic, and actual in-feed on the accuracy of processing for various cutting sub-steps were confirmed cylindrical grinding with radial feed by [2]. Developed the theory of modeling of metal removal during grinding of cycles and modeling of cutting force and connection of grinding modes with productivity and accuracy of processing at different grinding stages [3–8, 5, 9–12]. An analytical model of cutting force during grinding was developed in [13–15]. An improvement in the quality of processing by using automatic grinding cycles was studied in [16–18]. The design of cylindrical grinding cycles was investigated in [19]. The aforementioned studies made it possible to perform a range of tasks aimed at improving the productivity of processing and surface quality [20]. However, most of the considered works provided methods for estimating precision and quality of processing based on empirical evidence without the use of a wide range of analytical models of shape formation which are necessary for computer-aided design systems for preparing the control programs of CNC machine tools. In particular, the existing literature provides no data on models for estimating the set grinding parameters of current values of feed, strength of cutting, or elastic deformations of the technological

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system along the ground surface (in reversible and non-reversible zones) under joint monitoring with radial and axial feed using CNC machine. The process during cylindrical external grinding with radial and axial in-feed where each stroke double begins with the cut-in step of grinding wheel in the reverse zone with a cut-in radial feed, while the axial feed is zero. Therefore, the cutting conditions at the reverse stage in the reverse zone which are fundamentally different from cutting modes are used of all cutting in the process when the axial feed is greater than zero. As a result, in the reverse zone, the quality parameters of the whole processing differ significantly from the quality parameters with those of another surface being treated. This article describes a methodology for optimizing operational parameters at the stage of cylindrical external grinding with radial and axial in-feed cut-in of reverse and non-reverse.

2 Model of Stages of a Relationship Between Stages at External Cylindrical Grinding A mathematical model in the article during radial and axial in-feed at CNC allows modeling in three sections: first section (reverse zone) by S1, S2, S3, S4, and S5; second section (non-reverse zone) by S1, S2; and third section (reverse zone) by S1, S2, and S3. Table 1 presents stages of grinding in numerical order with radial and axial feed using CNC machine. First section which cycle in the section is working with the stage of penetration S1, the stage is performed by radial infeed. Following a cycle, radial infeed finished in S2. The sections characteristic of the model is switchable by turning reverse S1, S2, and non-reverse S3, in other words, we can say the changing process from Rp feed to Soc feed. Although this S2 is short, it will look difficult because the stage includes a spark-out with radial feed only. Following termination of stages S1 and S2 with radial feed, model subject to two stages non-reverse, respectively, to start S3 and S4 with axial feed only (Table 1). After coming off stages S3 and S4 (non-reverse), stage S5 is working mathematically with radial feed, S5 is performed with programming spark-out feed. As it can be observed in models that had many stages on the grinding cycles, which is characterized by two types of grinding cycle: Rp and Soc feed. The most complicated processes of surface shaping consisting of five stages took place during each double stroke in first Sect. 1; they are marked S1–S5, accordingly (Table 1). Stage S1, (Table 1), is the first stage in the double stroke and begins from the moment the wheel cuts into a workpiece during cylindrical grinding with radial feed. During this stage, the control program of the CNC machine tools manages the movement of the grinding wheel with radial minute programmed feed Rp [mm/min]. The wheel grinds the workpiece until it performs the move Fpk,i,z [mm/stroke] of the programmed feed set in the control program. The graph of the radial actual feed Afk,i,z [mm/min] is shown in Fig. 1. The broken line was formed due to the initial radial run-out of the workpiece. The axial programmed feed Soc at this stage is equal to zero. Stage S2 occurred in the reverse mode when the programmed radial feed stopped, i.e., Rp = 0 and the connection of the programmed axial feed Soc was in preparation. However, though radial actual feed decreases, it is not equal to zero; the axial programmed feed at this stage is equal to zero (Fig. 1).

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Table 1. Grinding process in three zones Grinding process

Type of feed

First Sect. 1

Reverse zone

Processing zones Plunge

Reverse

Working stroke

Idling stroke

Spark-out

*

*

S5

S3

S4

*

*

*

*

*

*

*

S1

S3

*

Radial feed mm/min S1

S2

Axial feed mm/min *

*

Second Sect. 2

Non-reverse zone

Axial feed mm/min

Third Sect. 3

Reverse zone

Radial feed mm/min

S1 *

S2 S2

Axial feed mm/min *

*

Stage S3 is carried out in cylindrical grinding conditions with axial feed. During cylindrical external grinding with radial and axial in-feed, stage S3 in the third section (reverse zone) is typically carried out by the axial feed (Table 1). The wheel of grinding has already moved by the programmed feed Fpk,i,z , where, k—cycle’s radius changes of the workpiece; i—revolution of the workpiece; z—cycle of grinding through the stages. The actual feed has a different physical meaning being measured by millimeters to stroke or millimeters to revolution. In Fig. 2, the graph of feed at stage S3 joints with the graphs at stages S1 and S2. The axial programmed feed at this stage is above zero. In Sect. 3, the grinding consists of three stages—S1, S2, and S3 (Fig. 1). Stage S1 is carried out during cylindrical grinding with axial feed in working stroke (WS) mode (Fig. 2) and the switched-on axial feed Soc. Stage S2 is conducted in reverse mode. The cylindrical grinding is carried out through radial feed by means of tightness with programmed radial feed switched off, i.e., Rp = 0. The preparation for switching on the programmed axial feed in the idling stroke mode (IS) occurs during the reverse stoppage. The axial programmed feed Soc at this stage is equal to zero. Stage S3 is conducted but with a reverse idling stroke. The axial feed is switched on at this stage, and it is above zero. Soc feed is working with the S1, where Rp = 0. Stage S2 is conducted in reverse mode when there is no any other programmed feed, but grinding is performed by means of the tightness in the technological system in the form of cylindrical grinding with radial feed, i.e., Rp = 0. Figure 1 shows the graph of the grinding cycle in Sect. 1 workpiece based on the grinding cycle given for calculating the current radius values of the machined surface and obtaining the surface shaping model. Figure 2 shows the interconnection of the accumulated data for radial programmed Fpk,i,z and actual feed Afk,i,z of elastic deformation Yk,i,z of a technological system and current radius Rk,i,z in the section of machined

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Fig. 1. Multi-stages to ensure quality control of designing during cylindrical external grinding (Sect. 3)

Fig. 2. Reverse zone and non-reverse zone of designing during cylindrical external grinding (Sect. 3)

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⎤ Fpk,i,z in S1 ⎥ ⎢ ⎣ Fpk,i,z in S3⎦

(1)

Fpk,i,z in S3 ⎤ Afk,i,z in S1 i  z k   ⎥ ⎢ = ⎣ Afk,i,z in S3⎦

(2)

surface:

⎡ Fpk,i,z =

Afk,i,z

i  z k   1

1

1

1

1

1

⎡

Afk,i,z in S3

Yk,i,z = Vk,i,z · γ

(3)

Rk,i,z = Rworkpiece − Afk,i,z

(4)

Taking into account the cutting force Vk,i,z in grinding of cycle (third section), also depends on the actual feed, the interconnection is expressed as follows: (5) Vk,i,z = C1 .Afk,i,z + C2 . Afk,i,z The programmed and actual feed are connected to elastic deformations Yk,i,z . As the grinding of cycle in the third section is performed by the tightness in the technological system then, as can be seen in Fig. 1, the value of the tightness is composed of the Yk,i,z with Afk,i,z . According to the dimensional relationships in Fig. 1, it is seen that the current value of tightness could be found via the accumulated programmed feed, actual feed, and initial radial runout of a workpiece using the following expression: Rk,i,z = Rmax − Rworkpiece

(6)

To solve Eqs. (1)–(6) with respect to Afk,i,z gives the formula (7), allowing for the calculation of Afk,i,z for every revolution and stroke of the workpiece throughout the full grinding cycle: ⎡ ⎤

 2 − Af − R Fp −γ C2 γ C2 workpiece ⎦ k,i,z k,i,z 2 2 + Afk,i,z = ⎣ + 2(1 + C11 γ ) 2(1 + C11 γ ) 1 + C1 1γ (7) where Vk,i,z —cutting force, N; Afk,i,z —actual in-feed of the grinding, mm; Yk,i,z — elastic deformation of the cycle, mm; C1,C2—coefficients of analytical characterization of the cycle; γ —rigidity of the technological system of the grinding, mm; Fpk,i,z — programmed in the feed of stage in grinding cycle, mm/stroke. Thereby, the set of formulas (1)–(7) represent a model of surface shaping in a grinding cycle. The process of shaping a ground surface for Sects. 2 and 3 will be considered in more detail as well. In Sect. 2, the grinding process only involves a single mode of cylindrical grinding with axial feed. The working stroke and idling stroke are performed during the stroke. Experiments were conducted during cylindrical external grinding with at CNC on Paragon GU model GU-3250-CNC machine with an active control device BV-6067 at the Department of Engineering Technology of SUSU. Experiment presents a comparison of accuracy obtained at the UstKatav factory.

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3 Conclusion 1. A mathematical model has been created for controlling the performance of the round cylindrical external grinding on Paragon GU model GU-3250-CNC machine, allowing for the given control cycles of radial and axial feeds and various technological conditions of the operation to calculate the current values of the actual feeds and cutting forces in reversible (Sects. 1 and 3) and non-reversible (Sect. 2) zones. 2. A methodology has been developed for designing optimal control cycles for radial and axial feeds in reversible and non-reversible zones. 3. Formation model of the grinding surface in the operation of external cylindrical grinding with reverse zone and non-reverse zone on CNC machine allows to predict the actual Afk,i,z dimensions of the surface for a given cycle and technological conditions of machining as well as to construct a model of the machined surface. 4. Existing engineering techniques based on the recommendations of article and particular empirical data do take into account the changes in variable processing conditions in the operation of external cylindrical grinding with reverse zone and non-reverse zone.

References 1. Malkin S (1984) Optimal infeed control for accelerated spark-out in plunge grinding. ASME J Ind 106(1):70–74 2. Alsigar M et al (2020) Model of processing accuracy prediction with consideration of multistage process of circular grinding with axial feed. In: International Conference on Modern Trends in Manufacturing Technologies and Equipment (ICMTME 2019), vol 709, Springer, Sevastopol, p 157 3. Moerlein AW (2009) In-process force measurement for diameter control in presion cylindrical grinding. Int J Adv Manuf Technol 42(1):93–101 4. Brian Rowe W, Yan L, Malkin S (1994) Applications of artificial intelligence in grinding. Ann CIRP 43(2):521–531 5. Peters J (1974) The significance of chip thickness in grinding. Ann CIRP 23(2):227–237 6. Allanson D, Thomas A (1994) Simulation of feed cycles for grinding between centres. Int J Mach Tools Manuf 34(5):603–616 7. Dornfeld D, He GC (1984) An investigation of grinding and wheel loading using acoustic emission. ASME J Eng Ind 106:28–33 8. Pereverzev PP, Alsigar M et al (2019) Designing optimal automatic cycles of round grinding based on the synthesis of digital twin technologies and dynamic programming method. Mech Sci 10:331–341. https://doi.org/10.5194/ms-10-331 9. Razavi H, Kurfess T (2003) Detection of wheel and workpiece contact. J Manuf Sci Eng Trans ASME 125(2):394–395 10. Pereverzev P, Akintseva A (2017) Modelling of renting of metal in reverse zones in the course of internal grinding. STIN 9:29–33 11. Couey JA, Marsh ER, Knapp BR, Vallance RR (2005) Monitoring force in precision cylindrical grinding. Precis Eng 29(3):307–314 12. Snoeys R, Peters J, Decneut A (1974) The significance of chip thickness in grinding. Ann CIRP 23(2):227–237

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13. Murphy S (2011) The effect of wheel eccentricity and run-out on grinding forces, waviness, wheel wear and chatter. Int J Mach Tools Manuf 51(10–11):766–774 14. Singh V, Rao P (2010) A new model for grinding force prediction and analysis. Int J Mach Tools Manuf 50(3):231–240 15. Shin Y (2007) The study on chatter boundaries plunge of cylindrical grinding with process dynamics condition. Int J Mach Tools Manuf 47:1563–1572 16. Razavi H (2001) Control of a reciprocating surface grinder using unfalsification. Int J Adapt Control Signal Process 15(5):503–518 17. Maillot M (1997) Online prediction of surface finish in grinding using network-based sensor. Int J Mach Tools Manuf 37(9):1201–1217 18. Zhang C (2013) Experimental and numerical studies on the temperature field in precision grinding of SiCp/Al composites. Int J Adv Manuf Technol 67(5–8):1007–1014 19. Chen G, Li P (2010) Deformation simulation for an internal grinding cirque by finite element method. Mod Mach 43(5–6):455 20. Hahn R (1964) On the nature of the grinding process. In: Proceeding of the international machine tool design and research conference, p 129–154

Design of High-Efficiency Device for Gas Cleaning from Fine Solid Particles V. Zinurov1 , A. Dmitriev1 , and V. Kharkov2(B) 1 Kazan State Power Engineering University, 51, Krasnoselskaya Street, Kazan 420066, Russia 2 Kazan National Research Technological University, 68, Karl Marx Street, Kazan 420015,

Russia [email protected]

Abstract. This paper deals with an urgent issue to enhance the efficiency of removing fine particles of size less than 10 μm from dust-laden process gases. The developed device comprises several rows of the double-T-shaped elements inside the body. It is proposed to use this device as a preliminary stage before the fine-cleaning device, which extends the service life. A description of the design and operating principle are reported. A study of the preferred distance between the rows of the double-T-shaped elements was conducted to enhance the efficiency of the device. The study showed that the reduction of the distance between rows of the separation elements leads to an increase in efficiency, but there is a significant rise in the hydraulic resistance coefficient. However, under certain conditions, maximum efficiency is achieved with moderate hydraulic resistance. Specifically, the circle with the center of the web for the element must pass through the extreme points of the adjacent rows. The advantages of the developed device are the following: high efficiency in capturing particulate matter, simple design, relatively low capital, and operating costs. Keywords: Separation · Double-T-shaped elements · Hydraulic resistance

1 Introduction Pressing problems of many industrial enterprises are the need to clean gas from fine solid particles and to prepare processed gases in aspiration systems [1, 2]. The attention has been devoted to environmental problems and the recent trends toward the effective use of resources and materials [3, 4]. Many industries have been deeply involved in the development and implementation of technological schemes for the reusing of material collected in dust-cleaning equipment [5–8]. Coarse-cleaning devices (inertial, centrifugal, and gravitational) are the most commonly used equipment for the collection of dust, which are capable of separating gas from coarse particles up to 10–20 μm in size with high efficiency [9–11]. However, the complexity of the technology results in the increase in the dispersion of the fine-dispersed particle in the gases [12]. As a result, many modern enterprises utilize various gas systems, including coarse- and fine-cleaning devices (bag © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_44

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filters, electric filters, etc.), which are suited for high-efficient separation of the gas flow from fine particles [13, 14]. However, in order to maintain a high collection efficiency of the fine-cleaning devices, periodic maintenance is required to replace the consumable materials or remove collected dust. So, enterprises incur extra costs due to the slowdown or shutdown of production. Thus, the search for new engineering solutions to develop an economically and energy-efficient design of the device capable of extending the service life of fine filters and increasing the efficiency of dust capturing processes are urgent problems for many industrial enterprises [15–17].

2 Study Objects and Methods The authors of this work have developed a device to increase the separation efficiency of process gas emissions from fine solid particles with a size of 10–20 μm and under [18]. The device is proposed to be used as the first stage before the fine-cleaning device, which extends the service life of the filters due to a decrease in the clogging rate. One of the main advantages of the device is its simple design, consisting of a number of rows of the double-T-shaped elements 3 inside the body 2. It is worth noting that rows of the separation elements are formed by inserting several single plates into the cross plates with slots intended for the gas flow motion. Thus, the entire design of the device is assembled from rectangular plates with various sizes, see Fig. 1. The inlet 1 and device body 2 can change the geometric shape in accordance with the shape of the gas duct and operating requirements. Nevertheless, the collection efficiency does not fall, since the arrangement of the double-T-rows relative to one other inside the device remains unchanged.

Fig. 1. 3D device model (sectional view): 1—gas inlet; 2—device body; 3—double-T-shaped elements

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The operating principle of the device can be described as follows. The dust-laden gas entering from the duct through the inlet 1 flows around several rows of the doubleT-shaped elements 3, which leads to the initiation of set points of centrifugal forces that form the swirling flow. In consequence of this fact, the fine particles are beaten out of the structured flow and adhere to the surfaces of the elements under the electrostatic forces. The purified gas further exits the device and goes to the fine-cleaning device. Besides, it should be noted that this device design, in particular, the arrangement of rows of the double-T-shaped elements relative to each other, has a significant effect on the collection efficiency and its hydraulic resistance. Therefore, the purpose of this work is to determine the best distance of the arrangement of the double-T-rows relative to each other to achieve the maximum collection efficiency at moderate hydraulic resistance. During the study [19–21], the authors proposed a hypothesis that in order to achieve the maximum collection efficiency of the device, the mutual arrangement of the rows of double-T-shaped elements should satisfy the following condition: the circle with the center of the web for the element must pass through the extreme points of the adjacent rows. In other words, the distance between adjacent rows of double-T-shaped elements L can be determined by the formula: L = 0.625b

(1)

where b is the length of the double-T-shaped element, mm. Further, to test the hypothesis described above, three types of devices with different distances between adjacent rows of the double-T-shaped elements were investigated. The distance calculated by (1) was taken as a basis with a change of more and less 15%. Thus, in these three devices, the distances between the rows of the double-T-shaped elements are 0.75L, L i 1.25L. The study was performed by numerical simulation using the ANSYS Fluent software package. In view of CFD calculations require high computational resources, we simplify the task by replacing the three-dimensional model of the device with a two-dimensional one. This assumption can be justified by the fact that the shape of the separation elements does not change in height. The following assumptions have also been taken into account. The thicknesses of the double-T-shaped elements and body walls were given as infinitesimal. The gas flow is stationary. The dust concentration excludes the mutual interaction between particles. The influence of solid particles on the motion of the carrier medium is neglected. During numerical experiments, the gas flow velocity varied from 3 to 10 m/s at the inlet of the device, and the atmospheric pressure was 101 325 Pa at the outlet of the device. The following parameters were constant: the number of particles in the gas was n = 1000; dynamic viscosity of air was μ = 18.1·10−6 Pa·s; the number of elements rows was 4; a number of the elements in each row was 10. The size of particles was in the range from 1 to 10 μm. The sticking condition was set on surfaces of the double-T-shaped elements. The following formula evaluated the efficiency of collecting fine particles from the dust-laden gas flow: nk (2) E =1− , n

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where nk is the number of fine-dispersed particles in the gas flow after the cleaning process in the device. The hydraulic resistance coefficient of the device ξ is determined as follows: ξ=

2p ρWh2

(3)

where p is a pressure drop in the device, Pa; ρ is gas density, kg/m3 ; W h is the velocity in the contraction between the device elements, m/s. The velocity of the gas flow in the constriction between the separator elements was found from the inseparability equation as Wh =

FW , Fh nh

(4)

where F is the inlet cross-sectional area of the device, m2 ; F h is the cross-sectional area of the contraction between the device elements, m2 ; nh is a number of contractions in one row of elements.

3 Results and Discussion The results are presented graphically in Fig. 2, 3, 4 and 5. As a result of changing the distance between the rows of double-T-shaped elements, different flow patterns arise. So, the efficiency in capturing fine solid particles from the gas rises when the distance between the rows of elements decreases. Otherwise, the collection efficiency falls by increasing the distance. It should be noted that these factors are valid only for particles with a size from 1 to 5 μm. When particle size exceeds 5 μm, the efficiency of gas cleaning from them is above 99% for all distances between the rows of double-T-shaped elements (Fig. 2). The change in the inlet velocity of the gas flow does not affect the separation efficiency in the case of fine particles with a size of less than 3 μm (Fig. 3). However, when cleaning gases from particles larger than 3 μm, the change in the inlet velocity results in an increase in the efficiency, which reaches 100% at the velocity of 10 m/s (Fig. 4). Thus, the increase in efficiency of gas cleaning from fine particles with a size less than 3 μm is caused by increasing the probability of contact particles with surfaces of the elements and sticking to them under electrostatic forces due to the reduction of the distance between the rows. However, the hydraulic resistance of the device increases significantly when the row distance decreases. Reduction of the distance between the rows of the elements from L to 0.75L increases the hydraulic resistance coefficient of the device by 2 times. When the distance changes from L to 1.25L, the coefficient of hydraulic resistance decreases by 2% (Fig. 5), while the collection efficiency for particles 1–7 μm in size decreases by 7% on average (Fig. 2). It can thus be seen that the distance defined by the formula (1) allows providing the most efficient gas flow pattern, combining high separation efficiency with the moderate hydraulic resistance coefficient of the device. For the gas flow with fine particles from 1 to 7 μm in size, the collection efficiency of device averages 91.1, 67.2, and 60.3% at a distance between the rows of the double-Tshaped elements 0.75L, L and 1.25L, respectively. It is worth noting that a high-efficiency

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separation of gas from fine solid particles (more than 99%) occurs at various dispersity and distances between rows of the double-T-shaped elements in different ways. So, when the distance between the elements in the device equal to 0.75L, L, and 1.25L, the efficiency is more than 99% with their sizes of 3, 5, and 5 μm, respectively, as indicated in Fig. 2.

Fig. 2. Dependence of gas flow separation efficiency on fine particle size under the various distance of the rows of the double-T-shaped elements: 1–0.75L; 2–L; 3–1.25L. Inlet gas flow velocity W = 8 m/s

In the case of cleaning gas flow from fine solid particles 1 μm in diameter, the separation efficiency almost does not change as the inlet gas velocity goes up. It may account for the reduction in the effect of centrifugal forces on beating out these particles from the flow. The average separation efficiency of the device with gas inlet velocity changed in the range of 3–10 m/s is 64.9, 14.3, and 9.1% at a distance of the rows of the double-T-shaped elements 0.75L, L and 1.25L, respectively. As can be seen, the smallest distance between the rows of the separation elements provides a higher efficiency of the gas flow from fine particles with a size of 1 μm. This fact indicates that the cleaning of the gas from particles of 1 μm or less is carried out mainly by electrostatic and intermolecular forces, so with the closer dust-laden gas flow around the surfaces of the double-T-shape elements, the probability of sticking these particles to them increases (Fig. 3). When cleaning gases from fine solid particles with a size of 3 μm, the efficiency increases on an average by 9.2% with the rise in inlet gas velocity by each 1 m/s. As the particle size grows, the effect of centrifugal forces on their beating out from the flow increases too. On average, the separation efficiency of the gas flow from fine solid particles is 78.2, 52.6, and 42.4% at a distance of the rows of the double-T-shaped elements 0.75L, L and 1.25L, respectively, at inlet gas flow velocity lies in the range between 3 and 10 m/s (Fig. 4). The hydraulic resistance coefficient of the device, according to (3), is 30.5, 15.3, and 14.9 at a distance between the rows of the double-T-shaped elements 0.75L, L, and 1.25L, respectively (Fig. 5).

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Fig. 3. Dependence of gas flow separation efficiency on inlet gas flow velocity under the various distance of the rows of the double-T-shaped elements: 1–0.75L; 2–L; 3–1.25L. Size of fine particles a = 1 μm

Fig. 4. Dependence of gas flow separation efficiency on inlet gas flow velocity under the various distance of the rows of the double-T-shaped elements: 1–0.75L; 2–L; 3–1.25L. Size of fine solid particles a = 3 μm

4 Conclusion We can conclude from this investigation that the reduction of the distance between the rows of the double-T-shaped elements leads to the increase in the efficiency of capturing fine particles from gas, but there is a significant rise in the hydraulic resistance coefficient due to the formation of numerous vortices. The last ones cause reverse flows, which are energy intensive and uneconomic. The obtained formula (1) enables us to calculate the distance between the rows of the separation elements, which provides a preferred flow pattern with peak values of centrifugal forces. The hydraulic resistance coefficient of the device was demonstrated to be approximately equal both at the distance L and at 1.25L (the difference is about 2%). But the separation efficiency is higher on average by 7% at a distance equal to L relative to 1.25L.

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Fig. 5. Change in hydraulic resistance coefficient from inlet gas flow velocity at the following distance of the rows of the double-T-shaped elements: 1–0.75L; 2–L; 3–1.25L

Furthermore, it has been found that the gas cleaning from fine particles less than 3 μm in size is predominantly carried out only by contact with the surfaces of the separation elements (sticking condition) due to electrostatic and intermolecular forces. As for particle size exceeding 3 μm, centrifugal forces have a significant influence, and, therefore, when the inlet gas velocity goes higher, the efficiency of separating fine particles from dust-laden process gas increases. The advantages of the developed device are the following: high efficiency in capturing particulate matter, simple design, relatively low capital, and operating costs. Acknowledgments. The reported study was funded by the grant of the President of the Russian Federation, project number MK–616.2020.8.

References 1. Koshkarev SA, Azarov DV, Majd A (2016) Evaluation of the Degree of the Leak-Through of Fine Dust in a Wet Cleaning Abatement Decreasing Dust Systems of Aspiration Schemes in the Building Construction Industry. Procedia Eng 150:2087–2094. https://doi.org/10.1016/j. proeng.2016.07.243 2. Kumar D, Kumar D (2018) Dust Control. In: Sustainable Management of Coal Preparation. Elsevier, p 265–278 3. Quina MJ, Bontempi E, Bogush A et al (2018) Technologies for the management of MSW incineration ashes from gas cleaning: New perspectives on recovery of secondary raw materials and circular economy. Sci Total Environ 635:526–542. https://doi.org/10.1016/j.scitot env.2018.04.150 4. Zhang A, Li M, Lv P et al (2016) Disposal and Reuse of Drilling Solid Waste from a Massive Gas Field. Procedia Environ Sci 31:577–581. https://doi.org/10.1016/j.proenv.2016.02.089 5. Xia D, Zhang F-S (2018) A novel dry cleaning system for contaminated waste plastic purification in gas-solid media. J Clean Prod 171:1472–1480. https://doi.org/10.1016/j.jclepro.2017. 10.028

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6. Gao S, Zhang D, Fan Y, Lu C (2019) A novel gas-solids separator scheme of coupling cyclone with circulating granular bed filter (C-CGBF). J Hazard Mater 362:403–411. https://doi.org/ 10.1016/j.jhazmat.2018.07.065 7. Zatsarinnaya JN, Logacheva AG, Solovyova AA (2019) Analysis of thermodynamic efficiency of the fuel preparation systems with an intermediate hopper at thermal power plants. IOP Conf Ser Earth Environ Sci 288:012130. https://doi.org/10.1088/1755-1315/288/1/012130 8. Dmitriev A, Zinurov V, Vinh D, Dmitrieva O (2019) Removal of moisture from contaminated transformer oil in rectangular separators. E3S Web Conf., p 110:1026. https://doi.org/10. 1051/e3sconf/201911001026 9. Akhbarifar S, Shirvani M (2019) Improving cyclone efficiency for small particles. Chem Eng Res Des 147:483–492. https://doi.org/10.1016/j.cherd.2019.05.026 10. Fassani FL, Goldstein L (2000) A study of the effect of high inlet solids loading on a cyclone separator pressure drop and collection efficiency. Powder Technol 107:60–65. https://doi.org/ 10.1016/s0032-5910(99)00091-1 11. Sibanda V, Greenwood RW, Seville JPK (2001) Particle separation from gases using cross-flow filtration. Powder Technol 118:193–202. https://doi.org/10.1016/s0032-5910(01)00311-4 12. Kharkov VV (2018) Mathematical modelling of thermolabile solutions concentration in vortex chamber. J Phys: Conf Ser 980:012006. https://doi.org/10.1088/1742-6596/980/1/ 012006 13. Tsareva OV, Balyberdin AS, Vakhitov MR et al (2020) Investigation of filter materials for gas cleaning from sulfuric acid. IOP Conf Ser Earth Environ Sci 421:072014. https://doi.org/10. 1088/1755-1315/421/7/072014 14. Tronville P (2008) Developing standards: Global standards for air cleaning equipment. Filtr Sep 45:28–31. https://doi.org/10.1016/s0015-1882(08)70369-0 15. Baltr˙enas P, Chlebnikovas A (2019) Removal of fine solid particles in aggressive gas flows in a newly designed multi-channel cyclone. Powder Technol 356:480–492. https://doi.org/10. 1016/j.powtec.2019.08.018 16. Singh R, Shukla A (2014) A review on methods of flue gas cleaning from combustion of biomass. Renew Sustain Energy Rev 29:854–864. https://doi.org/10.1016/j.rser.2013.09.005 17. Risi F, Poggiani C (2015) Heat Exchange and Separation Efficiency in a Cluster of Gas-solid Separators in a Complex Cement Production Plant. Energy Procedia 82:886–892. https://doi. org/10.1016/j.egypro.2015.11.834 18. Dmitriev AV, Zinurov VE, Dmitrieva OS (2018) Influence of elements thickness of separation devices on the finely dispersed particles collection efficiency. MATEC Web Conf 224:02073. https://doi.org/10.1051/matecconf/201822402073 19. Dmitriev AV, Zinurov VE, Dmitrieva OS (2018) Intensification of gas flow purification from finely dispersed particles by means of rectangular separator. IOP Conf Ser Mater Sci Eng 451:012211. https://doi.org/10.1088/1757-899x/451/1/012211 20. Dmitriev AV, Zinurov VE, Dmitrieva OS (2019) Collecting of finely dispersed particles by means of a separator with the arc-shaped elements. E3S Web Conf 126:00007. https://doi. org/10.1051/e3sconf/201912600007 21. Zinurov VE, Popkova OS, Nguyen VL (2019) Separator design optimization for collecting the finely dispersed particles from the gas flows. E3S Web Conf 126:00043. https://doi.org/ 10.1051/e3sconf/201912600043

Geometry of Six-Dimensional Space for Engineering V. E. Lelyukhin, O. V. Kolesnikova(B) , and E. V. Ruzhitskaya Far Eastern Federal University, 8, Sukhanov St, Vladivostok 690091, Russia [email protected]

Abstract. In modern engineering practice, analytical and graphical representations of geometric objects are used in the design and manufacture of various mechanisms. From the industrial practice perspective, both forms are characterized by two problems. The first problem is that tools of modern geometry can’t operate with nonideal shapes and configurations of material objects. The second problem is the absence of methods and tools for describing generation circuits of geometric objects, from the manufacturing lines to the end structure, which is characterized by the relative location of the surfaces. The article describes the generalized geometry position of imperfect objects, which is the theoretical basis for the formal synthesis of mechanisms and their elements, and avoids the representation issues of the geometrical configurations in the practice of engineering and design manufacturing technology in shipbuilding and ship repair. The basis of this geometry lies in the structural and parametric representation of objects existing in the six-dimensional space defined by linear and angular vectors. An object is defined by a closed subspace bounded to one or a set of mating surface or overlapping surfaces. The considered tools for describing the composition and structure of the part configuration with a six-dimensional unit vector in the form of six-cell tables can be effective not only for creating design automation systems, but also for computer-free analysis of drawings and processes in order to optimize them. Keywords: Digital engineering · Real component · Surfaces · Geometric configuration · Formalization design · Processing technology

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_45

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1 Introduction In the design and manufacture of parts of robotic devices, various machinery and mechanisms, great importance is given to the geometric configuration of the constituent components, also known as parts. It is characteristic that the functionality and interchangeability of these parts are determined not only by the configuration, but also the accuracy of its manufacture [1]. Given the impossibility of manufacturing ideal geometrical configurations with completely absolutely accurate dimensional characteristics in the physical world, range essentially regulations are used globally to normalize the deviations and for interaction [2, 3]. The mathematical core of modern CAD (computer-aided design), which led to CAM (computer-aided manufacturing) systems, are based on the provisions of modern analytical geometry, which essentially formalizes the description of ideal geometric configurations their elements [4–8]. The state of modern geometry, due to the history of geometry, is based on the need to formally submit a variety of existing and possible configurations of planar and spatial figures [9]. Among the founders include Albrecht Dürer, Rene Descartes, Pierre de Fermat, Gaspard Monge, Gottfried Leibniz, Leonhard Euler, David Hilbert, Bernhard Riemann, Charles Hermite, Paul de Casteljau Pierre Bezier et al. In modern engineering practice, two forms of representation of geometric figures (images) are used: analytical and graphical. However, despite the fundamental differences between these forms, both can “work” (to display and convert) independently with ideal or idealized geometric objects. It can be said that the geometric shape and configuration of real objects in the physical environment have identified discrepancies with mathematical and graphical images [6, 10]. The existence of these differences leads to problems with the automation of object design processes and the development of technologies for their manufacture. The purpose of this article is to examine the proposed geometry imperfect objects, which is the theoretical basis for the formal synthesis of mechanisms and their elements, as well as avoid problems representation of geometric configuration in the designing and manufacturing practice of design technologies in shipbuilding and ship repair.

2 Modern Problems of Representation Geometric Configuration of Products and Their Components If you wonder why, despite advances in the development of mathematics and information technology engineering practice since Gaspard Monge uses drawings language rather than formulas? Graphic language is the basis of modern systems of modern systems of 3D modeling. A certain degree of abstraction from reality is a characteristic feature of mathematical representation of the geometrical configurations of the material objects. As the practice shows, in the use of mathematical abstractions to describe the technical objects there are two fundamental problems that are not solvable within the existing geometries [6, 10]. The first problem is that the toolkit of any modern geometry can’t operate with imperfect shapes and configurations of material objects. In reality, any object (part, assembly, or product) has a set of deviations (errors) from the originally simulated

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image. In addition, each surface is characterized by inaccuracies in shape and roughness inaccuracies, and errors of mutual position of surfaces that determine the functioning of the object [6, 11, 12]. So, the two parts are that look similar to each other, but having differences in the above-mentioned errors that significantly affect their functionality, are identical (indistinguishable) when described using conventional mathematical tools [7]. In local and foreign engineering uses a special set of rules, which defines the limits of permissible deviations from the ideal geometrical configurations [13, 14]. In fact, imaginary ideal dimensions in engineering practice are called nominal values, which are determined in relation to the maximum permissible values of deviations of actual dimensions. To demonstrate the fact that geometry does not have a tool for representing different configurations of imperfect (nonideal) objects, consider the following scenario. Examples of defining planes 1, 2, and 3 for the ideal image shown in Fig. 1a, and three different real images in Fig. 1b, c, and d, respectively. In this case, at first glance, all four objects in Fig. 2 might seem the same. Note that, the original coordinate system is used to uniquely determine the configuration, which is associated with the position of each surface. This helps to eliminate the ambiguity in defining the configurations. Figure 2a shows the arrangement of the planes relative to each other in three dimensions defined by l1 , l2 , and l3 . From the geometric perspective, such description is consistent, as well as the fact that l1 = l3 − l2 ; l2 = l3 − l1 ; and l3 = l1 + l1 .

Fig. 1. Position of planes: a for an ideal geometric configuration; b, c, and d the actual geometric configuration.

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Fig. 2. Two types of vectors: a linear; b angular.

However, the real picture of the obtaining (manufacturing) the planes under consideration, taking into account the above error, indicates that there are three differing results (options). As shown in Fig. 2b, while maintaining the dimensions l1 and l3 , dimension l2 is formed (is obtained) “itself”, as a result of the location of the planes 2 and 3, but the errorΔ2 of the “Closing” dimension l2 , equal to the sum of errors “components” l1 and l3 dimensions, i.e., Δ2 = Δ1 + Δ3 [2]. Similarly obtained errorΔ3 = Δ1 + Δ2 and Δ1 = Δ2 + Δ3 for dimensions l3 and l1 , for the configurations shown in Fig. 2c and d, respectively. That is why in the unified system of design documentation, dimensional chains are designed as non-closed cycles [15]. The example shown indicates that the result of forming geometrical configuration depends on the processing technology used in manufacturing the part, thus the generation circuit. The second problem of modern geometry hence becomes to review existing configurations regardless of how they are formed, which results in lack of tools for describing generation circuit configurations objects [7, 10]. For example, consider an analytic description of a general plane. The general equation of a plane in three-dimensional space [16] Ax + By + Cz + D = 0

(1)

To describe the horizontal planes 1, 2, and 3 of the part shown in Fig. 2a, Eq. (1) becomes Cz + D = 0

(2)

Then, for determining the first, second, and third planes in Fig. 2a, respectively, we obtain Cz1 = D;

(3)

Cz2 = D + l1 ;

(4)

Cz3 = D + l3 .

(5)

Note that for the second surface, the equation can be written as Cz2 = D + l3 − l2 ,

(6)

Cz3 = D + l1 + l2 ,

(7)

and for the third

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Thus, when describing the location of the second surface, it does not matter which dimensional relationships are given in the drawing, since Cz2 = D + l1 = D + l3 − l2 . Similarly for the third surface Cz3 = D + l3 = D + l1 + l2 . This example clearly shows that when representing the geometrical configuration of real objects using analytical geometry, the structure of dimensional relationships defined by the drawing is lost. This is confirmed by fundamental mathematical publications, “One and the same plane can be represented by the set of equations in which the coefficients and the free term are proportional” [17]. Based on theoretical research, practically proven in manufacturing plants, the authors propose a special tool for the formal representation of the geometric configuration of imperfect objects based on discrete mathematics.

3 The Fundamental Provisions Geometry of the Six-Dimensional Space Considering a particular finite-dimensional space as the point of origin and the existence of real geometric objects, whose properties match the properties of the surrounding material objects in the aggregate state of the rigid body with a metastable structure. To form objects, it is postulated that the geometric configuration of an object is formed by a finite number of complex conjugate or intersecting surfaces n (n ≥ 1) that form a closed space filled with “material” substance with the specified properties. This corresponds to the concept of part [18, 19]. In modern geometry, there is a well-known concept of the vector as a straight line with direction (Fig. 2a) indicating its starting points and the end point [17]. It is known as a linear vector. The concept of angular vector is shown in Fig. 2b. An angular vector is an angular value (angle) between the two linear vectors lying in one plane indicating of the direction of rotation. The presence of angular vector allows in many cases to simplify and reduce the perception of computation in the processes of geometric transformations. In the geometry of nonideal (real) objects, a six-dimensional space is used, wherein the position of any point on the object is defined by six coordinates, three of which are represented by linear vectors and three more are represented by angular vectors. The validity of this viewpoint is supported by the wide use of six degrees of freedom in the various fields of science and technology [20]. As a basis, an ordered set of six vectors, which consists of two orthonormal coordination systems at the origin point. One of the coordination systems consists of three non-coplanar ordered linear vector, and the other three angular vectors with similar properties. Figure 3 shows the process of forming the basis of the six-dimensional space the  x, ∝  y, ∝  z, three linear vector ex , ey , ez with the origin O’ and three angular vectors ∝ with the origin at a point O , by transferring of O and O about point O.  x, ∝  y, ∝  z known as basic vectors As shown in Fig. 3, base vectors ex , ey , ez and ∝  y, ∝  z are arranged in mutually perpendicular planes, which  x, ∝ and the angular vectors ∝ in turn are perpendicular to the respective linear vectors ex , ey , ez . In six-dimensional space given by the specified basis, well-known geometrical configurations exist. The elements that make up these configurations are the points, lines, and surfaces.

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Fig. 3. Forming the basis of a six-dimensional space: a three linear vectors; b three angular vectors; c six-dimensional space.

A point is the original “brick” to generate other more complex elements. This element has zero dimensions. The position in space of ith point is determined by only three linear coordinates (x i , yi , zi ). A more complex element is a line, which is regarded as an infinite one-dimensional space represented by an inseparable set of points. Characteristically, in the vicinity of any point belonging to the line, are not more than two adjacent points that are not in contact with each other. It may be noted that each line is continuous, smooth, and infinite. Among the set of lines, L can be identified as basic lines: straight ls and circle lc , which correspond to linear and angular basis vectors. By line is meant straight line, the first derivatives in all its points coincide (are constant). Circle is a line at which the first derivative of the increment between any two pairs of equally spaced dots are equal [19]. Surface represented as an endless, smooth two-dimensional space formed by an inseparable plurality of lines in the vicinity of each of which there are not more than two adjacent, but not contiguous lines. Full set of surface S is limited by any various forms acceptable for the existence in the above six-dimensional space. Among all surfaces allocated three elementary surfaces: plane sp , cylinder s,c and sphere ss . Plane, cylinder, sphere are elementary, since the fact that only the surface kinematically may be formed using two elementary lines producing the line and the circle. As you know, using the same set of surfaces can be produce quite diverse geometries changing structure relationships and dimensional characteristics [19].

4 The Configuration of the Actual Parts and Its Display The process of creating a geometric configuration of a part is represented as the formation of a suitable combination of a selection of the mutual arrangement of a finite number of surfaces. For an unambiguous description of the structure, the surfaces must specify the relationship between the surfaces in all six of the above measurements. We represent the geometric configuration of parts as a certain set of surfaces to specify their location relative to each other. Description of the relative position is determined by the presence of the necessary links for each of the six coordinates of the space  x, ∝  y, ∝  z [13]. ex , ey , ez , ∝

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In general, for an unambiguous determination of the location of the surface of complex shape in space required to orient it in each of the six measurements (three linear and three angular). However, elementary surface for unambiguous orientation indefinitely provided they require fewer restrictions. For example, for the orientation of the plane  y ez . To deter x, ∝ shown in Fig. 4a is necessary to define two rotation and one moving ∝ mine the position of the surface in space, you can use the representation in the form of a single six-dimensional vector, where the presence of a connection is designated—1, which characterizes the restriction of freedom, and 0—its absence.

Fig. 4. Presentation surfaces position in space: a plane; b cylinder; c sphere.

For example, for a plane, shown in Fig. 4a, can be written ex = 0, ey = 0, ez =  y = 1, ∝  z = 0 or {001110}. For visualization, the indicated unit vector is  x = 1, ∝ 1, ∝ conveniently depicted in the form of a six-cell table. Various combinations of freedom fixation relevant coordinate directions, which determine the position of the surface in six-dimensional space for elementary surfaces: a plane, a cylinder, and a sphere shown in Fig. 4. Using the consideration of the submission can uniquely specify the location of any surface si details on the other. And since the positional relationship determined by the necessary and sufficient set of linear and angular dimensional coordinate bonds appears mechanism job structure and geometric configurations for any particular items. Figure 5a shows an exemplary relative location of three planes (P1, P2, and P3) and the cylindrical surface (C1) of deviations with predetermined parameters, and Fig. 5b in the respective table’s units designated coordinates are six-dimensional space, for which it makes sense to the job links with other surfaces. As seen in Fig. 5a, surfaces interconnected dimensional constraints and requirements limiting deviation from perpendicularity. These communications and determine the spatial geometric configuration fragment under consideration. If we consider that in this space there are six independent coordinates, the overall geometric configuration of the structure can be represented as a plurality of projections of structures in all six dimensions of space [4, 13]. The most convenient means of presenting the structures are graphs. A graph is represented as a pair of sets (V, E). The set V = {v1 , v2 , …, vn } consists of a finite set of vertices and the set E = {e1 , e2 , …, em } includes a finite set of ribs which characterize the connection between the pairs of vertices.

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Fig. 5. Fragment of the geometrical configuration of: a positioning surfaces; b the map in the form of tables.

5 Discussion Modern forms of representation of geometric information and ways of its transformation from the point of view of engineering practice are characterized by the presence of two problems. The first of these is that modern geometry tools cannot operate with nonideal shapes and configurations of material objects. The second problem is the absence of the methods and tools for describing generation circuit’s geometric objects, from the manufacturing lines and the ending of the structure, which characterizes the relative location of the surfaces.

6 Conclusion The article describes the generalized geometry position imperfect objects provides a unique representation of the geometrical configuration of the real parts having deviations of form and position of surfaces. The basis of this geometry is a structurally parametric representation of objects having the right to exist in the six-dimensional space defined by linear and angular vectors. An object is defined as closed subspace limited to one or a set of mating surface or overlapping surfaces.

References 1. JM, Soh GS (2010) Geometric design of linkages, 2nd edn, Springer, New York, Dordrecht, Heidelberg, London. doi:10.1007/ 978-1-4419-7892-9 2. RD 50-635-87 (1987) Methodical instructions. Dimensional chain. Basic Concepts. Methods of calculating linear and angular chains. Publisher standards, Moscow, p 45 3. Tsitsiashvili GSh, Lelyukhin VE, Kolesnikova OV, Osipova MA (2016) Formal design of structure process in machining parts. In: Modeling and Analysis of Safety and Risk in Complex Systems Proceedings of the Thirteenth International Scientific School MA SR − 2016 SUAI, SPb, pp 76–79

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4. Goldman R (2019) An integrated introduction to computer graphics and geometric modeling. CRC Press. September 18, p 47 5. Lee K (2004) CAD Basics (CAD/CAM/CAE). Peter, SPb, p 560 6. Lelyuhin VE, Ignatiev FU, Drenin AS, Kolesnikova OV (2018) The formalization of the concepts of geometric configuration of machine parts. Nat Tech Sci 7:109–112 7. Drake PJ Jr (1999) Dimensioning and Tolerancing Handbook (McGraw-Hill). Printed in the United States of America, A Division of The McGraw-Hill Companies 8. Lelyukhin VE, Kolesnikova OV (2019) Digital information space of marine manufacturing equipment. Marine intellectual technologies. Sci J 2 (44):45–49 9. Thimm G, Lin J (2005) Redimensioning parts for manufacturability: a design rewriting system. Int J Adv Manuf Technol 26:399–404. https://doi.org/10.1007/s00170-003-2002-6 10. Lelyukhin VE, Ignatiev FYu, Drenin AS, Kolesnikova OV (2018) Geometry for description of real parts of machines. Modern High Technol 8:95–99. http://top-technologies.ru/ru/art icle/view?id=37126. Accessed 14 Dec 2019 11. Ayadi B, Anselmetti B, Bouaziz Z, Zghal A (2008) Three-dimensional modelling of manufacturing tolerancing using the ascendant approach. Int J Adv Manuf Technol 39:279. https:// doi.org/10.1007/s00170-007-1225-3 12. Louati J, Ayadi B, Bouaziz Z, Haddar M (2006) Three-dimensional modelling of geometric defaults to optimise a manufactured part setting. Int J Adv Manuf Technol 29(3–4):342–348 13. GOST 25347-2013 (2014) Basic norms of interchangeability. Geometrical characteristics of products. tolerances on linear dimensions of the system. Rows tolerances, the tolerances of holes and shafts. Standartinform, Moscow 14. ISO 286-1: 2010. Geometrical product specifications (GPS)—ISO code system for tolerances on linear sizes. Part 1: Basis of tolerances, deviations and fits. International Standard. Published in Switzerland 15. GOST 2.307-2011 (2012) ESKD. Dimensioning and tolerances. Standartinform, Moscow, p 31 16. Vinogradov IM (1982) Mathematical Encyclopedia. Volume 1, Science, Moscow, p 1140 17. Vygodsky MYa (2006) Handbook of higher mathematics. Astrel, Moscow, p 991 18. GOST 2.101-2016 (2019) ESKD. Types of products. Standartinform, Moscow 19. Lelyukhin VE, Kolesnikova OV, Antonenkova TV, Drenin AS, Kuzminova TA (2019) Geometry of nonideal objects in marine engineering design and manufacturing process. Marine Intell Technol 2(46):46–52 20. Pennestrı E, Cavacece M, Vita L (2005) On the computation of degrees-of-freedom: a didactic perspective. In: 2005 ASME International design engineering technical conferences and computers and information in engineering conference. California, USA. https://doi.org/10. 1115/detc2005-84109

Providing the Working Accuracy of CNC Metal-Cutting Machine O. Yu. Kazakova and L. B. Gasparova(B) Samara State Technical University, 244, Molodogvardeyskaya Str, Samara 443100, Russia [email protected]

Abstract. The article deals with the issues of working accuracy improvement with the evaluation of the impact degree of errors in toolholder geometric forms on the accuracy of the axial location and rigidity of toolholders when workholding in spindle. The article deals with the issues of working accuracy improvement with evaluation of the impact degree of errors in tool holder geometric forms on the accuracy of the axial location and rigidity of toolholders when workholding in spindle. We considered the most frequent cases of form errors, occurring when producing the toolholders; they are circular deviation (particularly occurrence of out-of-roundness in cross-sectional view), deviations of straightness of cone generatrix (bulge, incurvature), angular errors. To evaluate the accuracy of the in-line arrangement and rigidity of corners of the tool spindle intersystem we used Ansys, the software product of finite element analysis. Keywords: Toolholders · Automatic tool change · Machine tool · Working accuracy

1 Introduction Nowadays, improvement of working accuracy of CNC metal-cutting machine is one of the crucial tasks. Along with machine inaccuracy, workpiece fitting, elastic deflection, and thermal alteration of the technological system which influence the machining process, a significant role goes to the axial location and rigidity of toolholders when workholding in the spindle of the machine [1–5]. This component plays an important role during multiple tool changes on machines equipped with an automatic tool change system [6–9]. In this case, the errors of the axial location of the toolholder will be associated with the conjugation conditions of the conical surfaces of the spindle and the toolholder, which depend on the deviation of the conical surfaces from perfect ones. The modern capabilities of machine tools with CNC systems allow to take into account and compensate for the existing errors of the conical surface of the spindle. However, it is impossible to take into account the errors in the conical surface of the toolholders with respect to a significant number of tools [10–12]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_46

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In addition to the fact that the errors of the cones of the toolholders are formed during their production, in the process of their multiple use, there develop wear-out phenomena significantly affecting macrogeometry [13]. In connection with the foregoing, it becomes necessary to use numerical methods to solve problems associated with the consideration of the process of fixing the toolholder in the spindle of the machine.

2 The Formation of Defects in the Form of Toolholders The most common shape defects that occur in the manufacture of toolholders are deviation from roundness (in particular, ovality in the cross section, deviations of the straightness of the cone generators (convexity, concavity) (Fig. 1), angular errors (Fig. 2). The indicated errors, supplemented by changes in shape during operation, can reach significant values.

Fig. 1. Schemes of deviations from straightness in a longitudinal section along the generatrix of the cone: a, d concavity (convexity) of the conical part of the toolholder; b, e concavity (convexity) of the conical part of the spindle; c, f concavity (convexity) of the conical part of the toolholder and spindle

Fig. 2. Cone angle deviation: a figured on from small diameter; (b) figured on from large diameter; c figured on from the top of cone O

According to GOST 19860-93, cones 40 and 45 (the most frequently used) with a taper of 7:24 set the tolerance on angles and shapes of cones from 3 to 7 degrees of accuracy (Tables 1, 2).

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Table 1. Tolerance on cone angles Cone D designations

d

L0

Tolerance on cone angles, microns, ATD Degree of accuracy 3

4

5

6

7

40

44,450 25,492 65

3,0 5,0 8

12 20

45

57,150 32,942 83

3,0 5,0 8

12 20

Table 2. Tolerance on the shape Cone designations

Designation of tolerance

Tolerance on shape, microns, ATD Degree of accuracy

40; 45

Tolerance of cone forming straightness

3

4

5

6

7

0,8

1,2

2,0

3,0

5

3 Using Finite Element Analysis to Assess the Accuracy of the Axial Location of the Tool Holder and the Angular Stiffness of the Spindle-Tool Subsystem In order to evaluate the accuracy of the axial location of the toolholder and the angular stiffness of the spindle-tool subsystem, the Ansys finite element analysis software was used, which allows to model the spindle-tool subsystem in two processes: the fixing process and the operation process under the following conditions: fixing the tool holder without taking into account form errors; fixing the toolholder in the presence of an allowable maximum and minimum error on the angle of the cone (both in larger diameter and in small diameter) of the toolholder; fixing the toolholder in the presence of the minimum and maximum permissible deviations of the straightness of the generatrices of the cone (convexity, concavity) [14, 15]. In geometric modeling, the base part of the spindle was modeled in a simplified way to reduce the calculation time, in the form of a ring with a conical inner hole with a taper of 7:24. The toolholder is in the form of a truncated cone with a cylindrical girdle on a larger diameter, which corresponds to the conical part of toolholder 40 taper of 7:24 (Fig. 3) [16, 17]. At the same stage, the design features and errors of the conical surface of the toolholder were modeled. In the calculation model, a restriction in the form of a hard seal was imposed on the cylindrical part of the spindle, and on the contour of the small diameter of the toolholder, rotation limits. The tightening force was modeled as a distributed force applied to the upper end of the toolholder. The instrumental toolholder 40 of the taper of 7:24 was modeled, manufactured both in nominal dimensions and with deviations [18–20]:

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Fig. 3. Toolholder 40 tapers 7:24

• a toolholder with a deviation of the straightness of the generatrices of the cone (convexity, concavity) corresponding to the manufacture of the toolholder for 3 and 7 degrees of accuracy. • a toolholder having deviations of a larger diameter D and a smaller d according to the third and seventh degree of accuracy. In the simulation, the spindle bore was assumed as ideal. The magnitude of the tightening force in the calculation was calculated according to Ptightening = p · π · (D − l · tg2β) · l · tg(2β + ρ),

(1)

where p is the average pressure on the conical surfaces; β is the angle between the generatrix and the axis of the cone; ρ is the angle of friction; l is the contact length of the cones; D is the average diameter in length l (Fig. 4). From Fig. 5, it is obvious that the greatest influence on the accuracy of the axial location of the tool holder has the presence of concavity along the generatrix of the toolholder. In the presence of concavity with an increase in the tightening force from 1000 N to 5000 N, the axial displacements of the toolholder inside the spindle increase in comparison with a toolholder manufactured in nominal sizes by an average of 2 times when manufacturing a toolholder with concavity within the third degree of accuracy, however, when manufacturing the toolholder with concavity within the seventh degree of accuracy, the axial displacements increase in comparison with a toolholder manufactured

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Fig. 4. The finite element model of the subsystem spindle tool

by nominal dimensions on average 5–6 times. The presence of a convexity along the generatrix of the toolholder slightly affects the change in the axial movements of the toolholder, both in the manufacture of the third degree of accuracy and the seventh. In the presence of angular errors caused by a decrease in both large and small diameters, the axial displacements of the toolholder increase by 5–6 times (when manufacturing the toolholder according to the seventh degree of accuracy), relative to the toolholder manufactured by nominal dimensions. With the increasing accuracy of the manufacture of the toolholder with the presence of an angular error formed by the reduction of both large and small diameters (in the manufacture of the toolholder according to the third degree of accuracy), the influence of the angular errors of the toolholder cone on the axial displacements decreases and becomes insignificant. The unstable behavior of axial displacements is manifested in the manufacture of a toolholder with an angular error formed by a decrease in small diameter (third degree of accuracy). Angular errors in D and d, formed by an increase in both large and small diameters (within both the third and seventh degree of accuracy) do not affect the axial displacements relative to the toolholder manufactured by nominal dimensions. The greatest negative effect is exerted by angular errors, both in larger diameter and in smaller ones with negative tolerance (within the seventh degree of accuracy) and concavity within the seventh degree. In the presence of these errors, the maximum axial displacements of the toolholder are 22 µ with a tightening force of 5 kN. This change in the position of the toolholder can lead to the fact that the initially adjusted position of the tool will be changed, which will affect the accuracy of processing (in particular when performing boring operations on coordinate boring machines).

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The presence of concavity of the toolholder, made by the third degree of accuracy, leads to an increase in the axial displacements of the toolholder to 4.7 µ. In order to assess the influence of the radial component of the cutting force on the conditions of fixing the tool in the spindle, the effect on the fixed toolholder of the radial force at the end of the toolholder simulating the radial component of the cutting force was simulated.

Fig. 5 Axial movements of a toolholder a the presence of errors within the 7th degree of accuracy; b the presence of errors within the 3rd degree of accuracy

The maximum radial displacements (at Ptightening = 5000 N, Pcutting = 2000 N) were observed at the toolholder in the presence of an angular error in D “-” during manufacture according to the seventh degree of accuracy. The magnitude of these displacements was 9 µ, which exceeded the value of displacements of the toolholder made by nominal dimensions by 4.5 times.

4 Conclusion Using finite element modeling of the tool fixing process allowed to make the following conclusions:

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1. The greatest influence on the accuracy of the axial location when basing and fixing the toolholder is exerted by such shape errors as the concavity of the generatrix of the toolholder cone and angular errors obtained by reducing both large diameter and small (increase in axial displacement by 5–6 times). Preference should be given to toolholders with a positive tolerance to the angle of the toolholder cone, regardless of the parameter of its formation: deviation of a larger or smaller diameter (as confirmed by analytical calculation). If it is necessary to use toolholders with minus angular errors of the cone (reducing a larger or smaller diameter), the degree of manufacturing accuracy should be increased. 2. The angular stiffness of the conical connection has a nonlinear character of changes from the action of the radial component of the cutting force up to 1000 N. With a further increase in force to 2000 N, the angular stiffness of the spindle-tool subsystem increases and has a linear character. In the presence of angular errors obtained by reducing both the diameter D and d, the rigidity decreases by ~4 times.

References 1. Levina ZM (1971) Contact rigidity of machines. Mechanical Engineering, Moscow 2. Levina ZM (1970) Calculation of rigidity of cylindrical and conical joints. Mach Tool 3:3–7 3. Orlikov ML, Kuznetsov YuN (1977) Designing clamping mechanisms of automated machine tools. Mechanical Engineering, Moscow 4. Levina ZM, Kornienko AA, Boim AG (1973) Investigation of the rigidity of conical joints. Mach Tool 10:13–17 5. Petrunin VI (1982) The study of the accuracy of the positioning of the tool on machines of the “machining center” type. Dissertation, Moscow Machine Tool Institute 6. Pronikov AS (2000) Designing of metal-cutting machines and machine-tool complexes. Mechanical Engineering, Moscow 7. Lizogub VA (2003) Influence of the parameters of the spindle unit of the machine on the accuracy of processing parts. Mach Tool 3:16 8. Averyanov OI (1981) Systems of automatic tool change. Mach Tooling 2:4–8 9. Kuznetsov YuI, Maslov AR, Baikov AN (1990) Tooling for CNC machine tools. Mechanical Engineering, Moscow 10. Kazakova OY, Gasparova LB (2020) Dependence of automatic installation of tool carrier process on orientation errors and their effect on performance characteristics of spindle-tool subsystem. Lecture Notes in Mechanical Engineering, pp 1043–1051 11. Denisenko AF, Kazakova OYu (2007) Formation of operational characteristics of the mechanism of automatic tool change. Bull Volgograd State Tech Univ 2:26–30 12. Denisenko AF, Petrunin VI, Kazakova OYu (2011) Accounting of contact processes in assessing the accuracy of anchoring the toolholder in the machine spindle. Bull Samara Sci Center Russ Acad Sci 4(3):713–716 13. Denisenko AF, Abulhanov SR, Kazakova OYu (2011) Rod tool with conical shank. Russian Federation Patent 2009103387/02, 20 Aug 2011 14. Belyakovsky VP, Seligey AM, Goldhreich GM (1979) Investigation of instrumental conical joints with small gradient angles. Mach Tool 6:15–17 15. Vragov YuD, Evstigneev VN, Ustinov BV (1977) Analysis of directions of cutting force and calculation of rigidity of multi-operation machines. Mach Tool 8:12–14

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16. Maslov AR, Balkov VP (2004) The use of shanks with a 7:24 taper and possible alternatives. Shavings 1:30–32 17. Burkov VA (2002) Device for fixing tool holders with a ball grip. Mach Tool 2:38–39 18. Denisenko AF, Kazakova OYu (2013) Formation of the error of tool holder with automatic tool change. Bull Samara State Tech Univ 2(38):111–116 19. Kazakova OYu, Kazakov AA (2016) Increase of accuracy of processing on machine tools due to minimization of errors of tool systems. High Technol Eng 12(66):35–39 20. Kazakova OYu, Gasparova LB, Kazakov AA (2018) The effect of the radial component of the cutting force and the geometrical parameters of the tool toolholder on its position in the spindle. Bull Bryansk State Tech Univ, Bryansk 1(62):18–23

Performance Study of Mills with Amorphous Silicon-Carbon Coatings S. Vlasov1(B) , V. Vlasova2 , and A. Zentsov1 1 Federal State Autonomous Educational Institution of Higher Education National Research

Nuclear University MEPhI (Moscow Engineering Physics Institute), 31, Kashirskoe Shosse, Moscow 115409, Russia [email protected] 2 Federal State Budgetary Educational Institution of Higher Education KG Razumovsky, Moscow State University of Technologies and Management (FCU), 73, Zemlyanoy Val Street, Moscow 109004, Russia

Abstract. In this paper, the efficiency of mills with coatings based on silicon and carbon, applied using plasma, is investigated. A mathematical model of the ion implantation process is presented in the form of a diffusion equation for a piecewise homogeneous medium. An analytical solution of a global nature is obtained, which can be used to estimate the depth of the diffusion layer and select the parameters of technological modes that provide the necessary operational properties of the cutting plates. The analysis of the obtained results of the diffusion state of the tool composition allows us to theoretically estimate the parameters of hardening at the stage of production of the cutting tool. Thus, it is possible to obtain technological modes of combined hardening treatment that provide the necessary properties of cutting tools made of high-speed steel and hard alloy. The intensity of wear of cutting tools after hardening by various methods in comparison with ion implantation was studied. Keywords: Milling · Hardening · Coating · Silicon · Plasma · Ion implantation · Diffusion

1 Introduction Both the intensification and automation of metalworking processes as well as reducing their cost require the creation of new tool materials that can ensure long-term and reliable operation of the tool. Methods of increasing the tool operability by applying wear-resistant coatings with sufficient performance and versatility are increasingly used around the world. Such methods have the ability to control the conditions of formation of coatings and the properties of the composition “coating-tool material”.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_47

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2 Relevance and Setting of the Problem For hardening products, widely known methods of applying thin-film coatings by physical (PVD) and chemical (CVD) deposition from the gas phase, etc., are used. However, they have significant disadvantages: high integral heating of the base, energy intensity, and the presence of a vacuum [1–3]. Final plasma hardening is a vacuum-tubeless process of plasma jet deposition of coatings from the gas phase with simultaneous plasma activation of the gas stream and the sprayed surface of the part. The name of the technology is associated with the main purpose of this process—to increase the durability and performance properties of parts by applying wear-resistant coatings to work surfaces at the final stage of manufacture (without changing the geometric dimensions and roughness) when exposed to electric arc plasma [4]. The process of finishing plasma hardening allows you to compensate for the above disadvantages of vacuum hardening processes, when used both independently and as part of a combined hardening treatment. The essence of the final plasma hardening consists of applying a wear-resistant coating with the simultaneous implementation of the process of repeated plasma quenching of the surface layer (to a depth of several micrometers). The coating is the product of plasma chemical reactions of substances that passed through the arc plasma torch. Quenching occurs due to the local impact of a highly concentrated plasma jet [5]. The main advantages of finishing plasma hardening are the following: • • • • • • • • • • • •

high reproducibility and stability of hardening; conducting the process of hardening in the air; no changes in surface roughness parameters after the hardening process; minimal heating during processing (no more than 100–120 °C) does not cause deformations of parts and allows strengthening materials with low heat resistance; ability to harden local volumes of parts in places of wear while preserving the original properties of the material in the rest of the volume; high microhardness of the coating; compressive residual stresses on the part surface; high adhesion strength of the coating to the substrate; low coefficient of friction; high hardening performance; possibility of automation; ecological safety.

3 Determination of Temperatures on the Surface of Parts During Final Plasma Hardening The structure of the thermal impact zone as a result of plasma exposure to the surface can be studied by considering the treatment as the thermal effect of the plasma flow on the base. Using the symmetry of the problem with respect to the vertical axis of the energy distribution (the OZ axis), the temperature distribution will be determined in

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Fig. 1. The scheme of plasma effect on the composition “coating–basis”

the XOZ plane, and the real position of the isotherms will be obtained by rotating the corresponding curves around the OZ axis (Fig. 1). Let a body is exposed by an instantaneous distributed heat source at a moment of time t = 0, wherein a body has a convective heat transfer with the environment according to Newton’s law. Then it is necessary to solve a system of Eqs. (1)–(3):   2   ∂ T ∂ 2T ∂T (1) =λ + 2 ; −l 2 < x < l 2; 0 < z < h; 0 < t < +∞, cρ 2 ∂t ∂x ∂z λ

∂T (x, h − 0, t) ∂T (x, h + 0, t) −l l = λ2 ; 2 < x < 2; 0 < t < +∞, ∂t ∂t     q = q0 · exp −k(x − ξ )2 ; −l 2 < x < l 2; z = 0; 0 < t < τ,

(2) (3)

where ci , ρ i , λi —specific heat, density, and thermal conduction coefficient of i material; hL1 , hL2 , … hL(k − 1) —the width of the first and second … k − 1—layer; l1 and l 2 —body sizes by the axis OX i OZ respectively; α—thermal efficiency; q0 —power density; t— time; τ I —impulse duration; k—radiation concentration coefficient; ξ —source center coordinate; x, z—variables. The solution of the equation system is the expression: T (x, z, t) =

+∞ 

Am,n · exp(−βm,n · t) · Um,n (x, z)

(4)

m,n=1

where Am,n —coefficient, depending on the thermal physical properties of the material, the geometric dimensions of the body and the technological parameters of plasma:

Am,n

l1/  2 l2 √ μ(x, z) · q0 · exp(−k(x − ξ )2 ) · τπu Um,n (x, z)dxdz 2 0 −l1/ 2 =



Vm,n 2

(5)

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where U m,n (x, z)—coefficient, depending on the geometrical sizes of the body, thermal– physical properties of the material, and the heat transfer coefficient: ⎧   sin ωm,n,1 z nπ x ⎪ ⎪ sin ωm,n,1 hL1 sin l1 , −l 2 ≤ x ≤ l1 2; 0 ≤ z ≤ hL1 ⎪ ⎪ ⎪   sin ωm,n,2 (z−hL1 ) ⎪ nπ x ⎪ ⎪ ⎪ sin ωm,n,2 (z−hL1 ) sin l1 , −l 2 ≤ x ≤ l1 2; hL1 ≤ z ≤ hL1 + hL2 ⎪ ⎪   ⎪ ⎨ sin ωm,n,2 (z−hL1 −hL2 ) sin nπ x , −l 2 ≤ x ≤ l 2; h + h ≤ z ≤ h + h + h 1 L1 L2 L1 L2 L3 l1 Um,n (x, z) = sin ωm,n,2 (z−hL1 −hL2 ) ⎪ · · · ⎪ ⎪ ⎪ ⎪  k−1  ⎪  sin ωm,n,k (l2 −z) ⎪ ⎪   sin nπ x , −l 2 ≤ x ≤ l1 2; hL1 ≤ z ≤ l2 ⎪ l ⎪ k−1 1  ⎪ i=1 ⎪ sin ωm,n,k l2 − hLi ⎩ i=1

(6) Knowing the distribution of temperatures of the action of a single pulse, using the principle of superposition, the temperature distribution can be obtained from the action of M impulses. Then the solution of the system of Eqs. (1) will have the form:    +∞ M 2 (i − 1)   βm,n 2 T (x, z, t) = Ai,m,n · exp − Um,n (x, z) · exp(−βm,n · t) · ν m,n=1

i=1

(11) where M—number of impulses; ν—pulse repetition frequency.

4 Possibility of Using Ion Implantation To increase the surface hardness and tool life, you can use a combined treatment that includes ion implantation and finishing plasma hardening. Ion implantation is a powerful universal method of hardening treatment that allows you to achieve the necessary mechanical characteristics of the cutting tool. The physical processes that occur in this case are very complex and insufficiently studied. Therefore, the construction of a mathematical model is relevant, since it creates prerequisites for determining the technological modes of creating a surface layer by means of directional formation of its properties and predicting the performance of such compositions. Ion bombardment of the substrate surface occurs at a constant source of charged particles and assumes the presence of inhomogeneity in the original equation. However, it is acceptable to consider the equation homogeneous, but the boundary condition depends on time. Consider the boundary value problem for the diffusion equation, in which the desired function is the concentration of the diffusing substance C = C(x, t) with an impermeable surface: ∂ 2c ∂c = D1 2 , x ∈ (0, +∞), t ∈ (0, +∞) ∂t ∂x

(13)

c|t=0 = 0, x > l,

(14)

c|x=l = ϕ(t), t > 0.

(15)

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To solve problems (13)–(15), we use the concept of convolution of functions and the Leibniz rule for differentiating an integral from a function that depends on a parameter, provided that the integration limits are also functions of this parameter t d t d  ∫ ψ(t − τ )χ (τ )d τ = ψ(0)χ (t) + ∫ χ (τ )ψt (t − τ )d τ. ψ(t) ∗ χ (t) = dt dt 0 0

(16)

Find a solution in the form 2 t x−l ϕ(τ ) − 4D(x−l) 1 (t−τ ) · d τ . c(x, t) = √ ·∫ · e 2 π D1 0 (t − τ ) 23

(17)

5 Setting Up and Conducting an Experiment The technological process of finishing plasma hardening is carried out at atmospheric pressure and consists of pre-cleaning operations (by any known method) and directly hardening the treated surface by mutual movement of the product and the plasma torch. The speed of movement is 1–10 mm/s, the distance between the plasma torch and the product is 10–15 mm, the diameter of the hardening spot is 12–15 mm, the thickness of the coating is 0.5–3 µ. The heating temperature of the parts during the final plasma hardening does not exceed 100–150 °C. The surface roughness parameters do not change after the final plasma hardening. As a plasma-forming gas used argon, the starting material for the passage of plasma chemical reactions and formation of the coating is a special liquid two-component drug CETOL (Silicon carbide). Its consumption does not exceed 0.5 g/h [6]. High-speed steel R6M5 was used as the base material in the research. The process of vacuum nitriding was carried out at «Magneton 3-2000» installation, and the final plasma hardening was performed at the «UFPU-108» installation. Coating was applied on the «HHV 6-6-I1» installation [7–21]. Wear tests were carried out on the «SMC2» installation. Wear tests were performed at a rotational speed of the lower sample of 1000 min−1 with a load of 1650 N. During the tests, the values of the moment of friction, mass wear, and the intensity of wear of the roller were recorded. Contact conditions—rolling friction with 20% slippage with lubrication.

6 Calculation Results Studies of the wear resistance of cylindrical samples made of P6M5 steel were of a comparative nature and were performed on samples of five types: without additional hardening; TiN coating; vacuum nitriding; finishing plasma hardening; vacuum nitriding; and finishing plasma hardening. The results of wear resistance studies are presented in Table 1. The mill tests were carried out during longitudinal milling of ledges on a 45 steel billet at a cutting speed of V = 10–40 m/min, feed Sz = 0.025–0.1 mm/tooth, a milling width and depth of B = 10 mm and t = 0.5 mm. Mills without additional hardening, after vacuum nitriding, after finishing plasma hardening, and after combined processing

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Parameter

Without hardening

Vacuum nitriding

CIB

Finishing plasma hardening

Vacuum nitriding and final plasma hardening

Wear rate, J,10−13

8.21

6.96

5.3

4.42

3.81

Coefficient of friction, f

0.0145

0.0108

0.0843

0.0703

0.0604

were examined. The reduction of the cutting force components Pz, Py, and Px, as well as the chip shrinkage coefficient when processing workpieces with cutters after combined hardening treatment, which is explained by an increase in the hardness of the surface and adjacent layers of the wear-resistant complex and a decrease in the tendency of the coating to adhesive setting in comparison with the tool without hardening.

7 Conclusion When studying the effect of adhesive layers on the performance of a high-speed tool, soft layers consisting of elements of the coating materials and the tool base and hard layers based on a complex nitride of these elements, as well as a combination of soft and hard adhesive layers, were used as the latter. Studies have shown that the presence of adhesive layers increases the adhesion strength of the coating to the tool base, affects the amount of residual stresses and practically does not change the period of the crystal lattice, the width of the X-ray line and the microhardness of the wear-resistant coating. Applying a soft adhesive layer slightly reduces the amount of residual stresses, and the presence of a solid and a combination of soft and hard adhesive layers increases the amount of residual stresses. The optimal ratio of the thickness of the adhesive layers and the coating is established, which provides the maximum increase in the tool life. Tests of high-speed plates with developed coating compositions have shown that the presence of a solid adhesive layer and a combination of soft and hard adhesive layers increases the durability period of TiN-coated plates by 1.5–2.2 times, depending on the cutting conditions and properties of the material being processed. In this case, the greatest increase in the durability period occurs when the cutting speed is reduced and the feed is increased, especially when using coatings with a combination of soft and hard adhesive layers.

References 1. Tabakov V, Chihkranov A, Vlasov S, Smirnov M, Romanov A (2012) Method of receiving of multilayer coating for cutting tool. Russian Federation pat. 2464340, 20 Oct 2012 2. Tabakov V, Chihkranov A, Vlasov S, Smirnov M, Romanov A (2012) Method of receiving of multilayer coating for cutting tool. Russian Federation pat. 2464341, 20 Oct 2012

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3. Tabakov V, Chihkranov A, Vlasov S, Smirnov M, Romanov A (2012) Method of receiving of multilayer coating for cutting tool. Russian Federation pat. 2464342, 20 Oct 2012 4. Tabakov V, Vlasov S, Sizov S, Chikhranov A (2015) Performance cutting tool coatings during the machining of workpieces of hard materials. Strength Technol Coat 7:5–9 5. Volkhonskii A, Blinkov I, Vereshchaka A, Vereshchaka A, Batako A (2016) Filtered cathodic vacuum ARC deposition of nano-layered composite coatings for machining hard-to-cut materials. Int J Adv Manuf Technol 5–8 (84):1647–1660 6. Brandon D, Kaplan W (2008) Microstructural characterization of materials. Wiley, Chichester, England, p 536 7. Saravanan R, Rani M (2012) Metal and alloy bonding: an experimental analysis. In: Charge density in metals and alloys. Springer, London, p 151 8. Vlasov S, Sizov S, Tabakov V (2013) Modeling of the impact of pulsed laser radiation on a multilayer coating. Hard Technol Coat 12:15–19 9. Tercelli K, Disaro D (2010) Continuous bloom casting with mild dynamic compression at the Posco Plant (Korea). Metall Plant Technol 1:15–21 10. Tabakov V, Chihkranov A (2009) Multicomponent nitride coatings for improving tool performance. Russ Eng Res 29(10):1047–1053 11. Flewitt P, Wild R (2003) Physical methods for materials characterization. Taylor & Francis, p 602 12. Bogomolov A, Bykov P, Serzhanov R (2014) Shift cogging modeling of the continuously cast bars. Life Sci J 11(6 s):167–170 13. Kanaev A, Reshotkina E, Bogomolov A (2010) Defects and thermal hardening of reinforcement rolled from continuous cast billet. Steel Transl 40(8):586–589 14. Doege E, Bernd-Arno B (2007) Umformtechnik. Grundlagen, Technologien, Maschinen. Springer, Berlin Heidelberg, New York, p 913 15. Guo Z (2005) The deformation and processing of structural materials. Woodhead Publishing Limited; Boca Raton: CRC Press, Cambridge, p 331 16. Tabakov V, Vereschaka A (2014) Development of technological means for formation of multilayer composite coatings, providing increased wear resistance of carbide tools, for different machining condition. Key Eng Mater 581:55–61. Trans Tech Publications, Switzerland 17. Tabakov V (2012) The influence of machining condition forming multilayer coatings for cutting tools. Key Eng Mater 496:80–85. Trans Tech Publications, Switzerland 18. Tabakov V, Chihkranov A, Vlasov S, Sagitov D (2015) Method of receiving of multilayer coating for cutting tool. Russian Federation pat. RU2629131C2, 15 Dec 2015 19. Tabakov V, Chihkranov A, Vlasov S (2017) Method of receiving of multilayer coating for cutting tool. Russian Federation pat. RU2687615C1, 10 Nov 2017 20. Tabakov V, Vlasov S, (2002) Influence combined hardening treatment to contact, thermal and wear of the cutting tool. In: Fundamental and applied technological problems of machine building. In: “Technology—2002”: Transaction Collection International Scientific-technical Conference. Part I. OSTU, pp 241–244 21. Tabakov V, Vlasov S, (2000) Laser treatment of cutting tools from hard alloys with coatings.Fundamental and applied technological problems of machine building. In: “Technology—2000”: Transaction Collection International Scientific-technical Conference. Part I. OSTU, pp 137–140

Fatigue Test Optimization for the Aircraft Engine Based on the Life Cycle Information Support and Modeling N. Kondratyeva1(B) and S. Valeev2 1 Ufa State Aviation Technical University, 12, K. Marx Str, Ufa 450008, Russia

[email protected] 2 Sochi State University, 7, Politekhnicheskaya Str, Sochi 354008, Russia

Abstract. Boosting efficiency of fatigue test for the complex technical object (for instance, aircraft engine) is possible applying assessment based on the integral relationship between the economic effect from the object operation and test parameters. The issue of assessing the efficiency criterion of fatigue test in the framework of the complex technical object life cycle is introduced. To implement this approach, it is necessary to use the life cycle modeling technologies of the complex technical object. Engine condition is described by numerous parameters during testing and operating. The problem of data acquisition and processing should be solved to build a life cycle model. The methodology of fatigue test optimization for the complex technical object based on the life cycle modeling is proposed in the paper. An example of the fatigue test assessment for the gas-turbine engine is discussed. The aim of maximizing the test efficiency was achieved by selecting the test modes, test duration, and number of tested engines. Keywords: Aircraft engine · Fatigue test · Life cycle · Efficiency · Modeling · Economic factors · Data acquisition

1 Introduction The aircraft engines belong to the class of complex technical objects containing thousands of components and parts. Engine condition is described by regularly measured numerous parameters during production, testing, and operating. Traditionally, the equality of damage to the aircraft engine elements in operational and test cycles is a criterion for the effectiveness of the fatigue tests for the complex technical object. The selection of the parameters of fatigue tests is carried out taking into account one or more main operational cycles. These cycles are proposed and controlled by the customer [1–4]. To make the fatigue test more adequate to the future operation, it is urgent to consider testing in the framework of the object’s life cycle taking into account such stages as design, manufacturing, operation, and utilization. The reliability of the design of an © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_48

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aircraft engine is affected by uncertainties in the operating environment (inlet air temperature, free flow velocity, etc.), as well as in the technological properties of parts and assemblies (profile geometry, material properties, and boundary conditions) [5]. Thus, to take into account these uncertainties, it is advisable to use the method of statistical modeling of operating and production conditions. The complex technical objects generate a large amount of data during their life cycle. On the other hand, simulation of the life cycle makes it possible to take into account the final effect of the object being created or commercially available, i.e., more reasonably determine the test parameters and, as a result, more efficiently conduct resource tests in comparison with the currently existing assessment methods [6–11].

2 Problem Definition and Big Data Concept Applying The main idea of this research is that modeling of the life cycle of a complex technical object, i.e., aircraft engine, aiming for estimation of the integral efficiency criterion (minimum cost, profit, etc.) can be applied for the fatigue tests assessment. The integral economic efficiency of the life cycle of the complex technical object contains the part E FT that is also due to such parameters as reliability, durability, maintainability, etc (Fig. 1). The total efficiency E FT presented in Fig. 1 depends on the costs on all the stages of the life cycle, from the requirement analysis to the reclamation (Z’DES , Z’DEV , Z’DT , Z’PR , Z’PT1 , Z’PT2 , Z’OP , Z’REP , Z’REC ). Special costs related to risks of incorrect fatigue tests assessment should be also noted (ZR.DEV , ZR.PR , ZR.OP ). The life cycle model training and improving can decrease the risks and associated additional costs. The model training is possible due to implementing data collected through the lifecycle of the concerned technical object as well as the data from similar objects (as previous experience) [12–15]. Such a statement of the problem requires data acquisition at all stages of the lifecycle, preprocessing, and storing large volumes of heterogeneous data. The main data and knowledge bases and flows are shown in Fig. 1, where DB1 , DB2 are integrated databases containing data on the engine life cycle, i.e., life spending details, life hours left, repair, economic factors, etc.; KB2 is knowledge base containing knowledge on the main life cycle stages together with control flows; D1 is a formal description of the engine; D2 , D3 , D4 , D5 are data necessary for the engine requirement analysis, design, developmental and periodic testing, production, and operation; K 1 is the knowledge on the engine operation; K 2 is the control flow for test parameters; K 3 is the control of the repair parameters; K 4 is the control of reclamation. Having all this in mind, the best tool for solving the task is big data technology. For instance, MapReduce distributed computing model can be used for parallel computing over very large, up to several petabytes, datasets in computer clusters. The set of utilities, libraries, and Hadoop framework can optimally manage distributed resources based for streaming data access. NoSQL databases are designed to process huge amounts of data, characterized by linear scalability, clustering, and fault tolerance, non-relational. These technologies are suitable for preprocessing source model data as well as simulation results [16–21].

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Fig. 1. The generalized scheme of the aircraft lifecycle model for assessing fatigue test parameters.

3 The Life Cycle Model Building The complexity level of the developed simulation model may be different, for example, for a mass-produced engine; the model may be in the form of “production—testing— operation”. The flowchart of the process of the fatigue test parameters assessment in the framework of the engine life cycle is presented in Fig. 2. The production stage is designed to simulate the quality of engine manufacture, characterized by a set of parameters p01 (i = 1, v). The technology for the manufacture, assembly, and control of gas-turbine engines is one of the main factors that make it possible to ensure their quality with maximum productivity and lowest cost. Moreover,

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Fig. 2. The flowchart of the process of the fatigue test parameters assessment in the framework of the engine life cycle.

the quality is characterized by a certain vector of initial state parameters P0 = [p01 , …, p0υ ]T (strength, wear resistance, geometry, etc.). Since engine parts are manufactured with certain tolerances, the quality indicators are scattered, i.e.,. are random variables with corresponding distribution laws. This leads to the fact that the efficiency from the implementation (operation) of the product is also a random variable. Obviously, the higher the engine manufacturing quality, the higher its reliability and resource indicators, and the less damage to its elements, components, systems, and assemblies accumulated in operating conditions. At the test stage, as a rule, models have the number of tested engines N FT , as well as the RFTς (τFT ) modes and the duration of their loading τFTς (ζ = 1, NFT ). Other parameters that affect the effectiveness of the test system may be included, for example: • parameters of the system for selecting and preparing engines for testing C SP = [cSP1 , …, cSPυ ]T ; • parameters of the control system, acceptance and shipment of engines C CAS = [cCAS1 , …, cCASξ ]T ); • quality parameters of the used test equipment C E = [cE1 , …, cEμ ]T , and others.

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The simulation result at this stage is an assessment of the reliability and resource of the tested engine, which is the basis for making a decision, for example, on the shipment or rejection of a batch of engines for which tests were carried out. At the operation stage, environmental conditions are simulated, the number of operating engines N OP , as well as the ROPk (τOP ) modes and the duration τOP of their loading (k = 1, NOP ) in accordance with the chosen operation strategy (for a fixed resource, as per condition, according to the combined method). The input parameters at this stage are the quantity of N OP and the quality of engine manufacturing. The simulation result is the parameters characterizing the total efficiency E FT of the operation of the engines: the costs and income from the operation, the probability of the engine (in the aircraft system) performing its functions, etc. Thus, in general, the following factors can be taken into account while optimizing the total efficiency of engines operation:  SP , C  CAS , C  E ). EFT = f (NFT , RFT (τ ), C

(1)

4 An Example of the Assessment of the Fatigue Test Parameters A comparative assessment of the effectiveness of the above methods for assessing the operational damageability of an engine was carried out in terms of profit and duration of tests in simulation of the life cycle of an auxiliary gas-turbine engine TA-6A. At the same time, the following elements were considered as limiting the engine resource: the working blade of the first stage of the turbine; angular contact rotor bearing; gear drive gear; fan bearing; generators of direct and alternating current. The conditions and loading conditions of the engine were set: • • • • •

air temperature at the engine inlet t n , °C; relative rotor speed n, %; the amount of air taken after the compressor Gext , kg/s; cooling airflow through the fan Gfan , kg/s; loading alternating and direct current generators N G1 and N G2 , kw.

In the framework of the model, the operation of the engine for a fixed resource was considered. An operation modeling method was used, in which the vector of accumulation of damage to engine elements formed in the simulation model. A comparison was made of the effectiveness of the tests, the justification of which was carried out using simulation modeling, with the equivalent-cyclic engine tests developed earlier at the enterprise by an industry methodology. A series equivalent cycle test program is designed to confirm a resource of 2,000 h and 3,000 launches. In this case, two engines are tested (N FT = 2). The characteristics of the serial test program are given in Table 1, and engine loading cycles are shown in Fig. 3. A comparison of the effectiveness of test programs was carried out for two cases: • at the same value of the maximum permissible difference of accumulation of damage to engine elements (δP*ζi )exp = (δP*ζi )ser = 20%. Efficiency was assessed by the duration of the tests;

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Table 1. Characteristics of the serial test program. Performance

Value

Performance

Value

The number of cycles

7500

Operating hours for 1 stage, hour

5

Cycle time, min

21

Total operating time for 1 stage, hour

6.5

Operating hours for 1 cycle, min

10

Number of stages

120

Total operating time for 1 cycle, min

13

Operating hours per test, hour

606

30

Total running hours, hours

786

The total test time, hour

1266

The number of cycles per stage Stage duration, min

630

n, % 100 90 0

5

10

N G1 , kw

G ext , kg /s

10

0,5

0

15 τ, min

5

10

15 τ, min

0

tH , °C

N G2 , kw

G fan , kg /s

25

50

0,5

0

5

10

15 τ, min

0

5

10

15 τ, min

0

5

10

15 τ, min

5

10

15 τ, min

Fig. 3. Engine loading cycles in serial fatigue tests (N*FT = 2)

• with the same test duration (τFT.exp = τFT.ser ). Efficiency was assessed by the value of the difference in the accumulation of damage to engine elements. • Initial data are the following: • model of bearing failure: t ΠB = 0

dt   ,   τ ∗ n, Ta∗ , Pa∗ , e, CB , X

(2)

• where n is rotor speed, %; T *a is inlet air temperature, K; P*a is inlet air pressure, kg/cm2 ; e is radial clearance which is a function of bearing geometry and fitting parameters, m; C B is bearing dynamic strength which is the function of e and other parameters signed as X¯ ; • model of failure of turbine rotor blade: t Πrb = 0

10−a1 dt; a1 =

m − σrb − 20; m = f (Trb , , k)Iˆ Gm ; 7, 02 · 10−3 · Trb

σrb = a0 + a1 n2 + a2 Pa∗ + a3 nPa∗



 Ta∗ ; Trb =

(3)

 

    b0 + b1 n 288 Ta∗ Ta∗ 288 , (4)

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where a0 …a3 , b0 , b1 are constants; m is parameter of long-time strength depending on blade temperature T rb and material quantity k; historical data on e and m values and parameters of engine loading: n, T *a , P*a ; • models of failure of the drive gear; fan bearing; generators of direct and alternating current (they are not listed here due to the limited scope of the article); • area of allowable values of operation regime parameters: 80 ≤ n ≤ 102%; 240 ≤ Ta∗ ≤ 623 K; 0, 7 ≤ Pa∗ ≤ 10 kg/cm2 ; n = 94% (Ta∗ < 339 K); n = 102% (Ta∗ > 339 K)

(5)

• economic factors (engine cost, cost value of operation and test hour, repair cost, profit in operation, etc.); • number of testing engines (N FT ∈ 1…3). Logical scheme was the following. The set of engines is rejected if one of the N FT engines fails. In the event one of engine fails in operation, this engine is repaired and other engines are operated without any complementary reliability check. Benefit in engines operation is considered as efficiency criterion:   ∗ ∗ ∗ ∗ EFT = Φ NFT , TFT (τ ), PaFTi (τ ), nFTi (τ ); NOP , TaOji (τ ), PaOPj (τ ), nOPj (τ ) → max. (6) The operation of 200 engines for a fixed resource was simulated. The optimal engine loading cycles in experimental tests are shown in Fig. 4. n, %

N G1, kw

1 2

100

G ext , kg/s

2

10

90 0

5

tH , °C

10

15 τ, min

0

1 2

10

5

10

15 τ, min

0

15 τ, min 2

50 5

1 2

0,5

N G2, kw

25 0

1

1 5

10

15 τ, min

0

10

5

G fan , kg/s

1

15 τ, min

2

0,5 0

5

10

15 τ, min

Fig. 4. Optimal engine loading cycles in experimental fatigue tests (N*FT = 2): curves 1 are loading cycles at (δPζi )exp = (δPζi )ser ; curves 2 are loading cycles at τtest.exp = τtest.ser

5 Conclusion It is proposed to assess the efficiency criterion of fatigue test for the complex technical object in the relationship with the object life cycle. To provide this concept, the simulation model of the object life cycle is designed. The modern gas-turbine engines belongs to the

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class of the complex technical systems. One of the complex technical objects features is the great amount of data generated during its lifecycle. It is stated that required data acquisition, preprocessing, and storing technologies can be realized in the framework of big data concept. Such powerful tools as MapReduce, Hadoop, and NoSQL are discussed. The use of simulation in the considered example case allowed to increase the level of test equivalence compared to the serial method (all other things being equal) by 1.7 times and reduce the test duration by 1.2 times. Simulation of the life cycle at the same time showed a possible increase in economic efficiency by 5%.

References 1. Cruse T, Mahadevan S, Tryon R (1997) Fatigue Reliability of Gas Turbine Engine Structures. NASA/CR 2. Prokopenko A, Torgov V (1980) Method for fatigue testing gas-turbine engine compressor blades in a corrosive atmosphere. Strength Mater 12:520–523. https://doi.org/10.1007/bf0 0769414 3. Fábry S, Spodniak M, Gasparovic P, Koscak P (2019) Aircraft gas turbine engine testing. Acta Avion J. https://doi.org/10.35116/aa.2019.0016:39-44 4. Asquith G, Pickard A (1988) Fatigue testing of gas turbine components. High Temper Technol 6:131–143. https://doi.org/10.1080/02619180.1988.11753390 5. Zagitova A, Kondratyeva N, Valeev S (2020) Information support of gas-turbine engine life cycle based on agent-oriented technology. In: Proceedings of the 5th International Conference on Industrial Engineering (ICIE 2019), pp 469–476. https://doi.org/10.1007/978-3-03022063-1_50 6. Iu F, Zheng W, Huang J, Feng M (2016) Life cycle performance estimation and in-flight health monitoring for gas turbine engine. J Dyn Syst Measur Control. https://doi.org/10.1115/1.403 3556 7. Malhotra V, Lear W, Khan J, Sherif, SA (2005) Life cycle cost analysis of a novel cooling and power gas turbine engine. J Energy Resour Technol 132. https://doi.org/10.1115/imece2 005-82934 8. Panella R, Barga M, McNally R (2020) Role of advanced technology on turbine engine life cycle cost. In: AGARD conference proceedings, vol 26, pp 1–26 9. Meyer R, DeCarlo R, Pekarek S, Doktorcik C (2015) Gas turbine engine behavioral modeling. J Eng Gas Turb Power 137:122607. https://doi.org/10.1115/1.4030838 10. Kondratyeva N, Valeev S (2016) Fatigue test optimization for complex technical system on the basis of lifecycle modeling and big data concept. In: Proceedings of 2016 IEEE 10th international conference on application of information and communication technologies (AICT 2016), Baku, Azerbaijan. https://doi.org/10.1109/icaict.2016.7991656 11. Guichvarov A, Kondratieva N (2001) Technical and economic assessment of aircraft engines fatigue testing on base of simulation modeling. In: Proceedings of AIAA/ASME/SAE/ASEE Joint Propulsion Conf. & Exhibit. 37th, Salt Lake City, Utah, 8–11 July, 2001, AIAA-20013817. https://doi.org/10.2514/6.2001-3817 12. Marr B (2020) GE: Big Data and the industrial internet. https://www.bernardmarr.com/def ault.asp?contentID=685. Accessed 21 Jan 2020 13. Boeing AnalytX (2020) It’s not about the data—it’s what you do with it! https://www.boeing. com/company/key-orgs/analytx/index.page. Accessed 20 Jan 2020 14. EMC (2015) Data science and big data analytics: discovering, analyzing, visualizing and presenting data, EMC Education Services (eds). Wiley & Sons, Inc., Indianapolis

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15. EMC (2015) Information storage and management: storing, managing, and protecting digital information in classic, virtualized, and cloud environments. 2nd ed., EMC Education Services (eds). Wiley & Sons, Inc., Indianapolis 16. Wiktorski T (2019) Hadoop Architecture: Principles and Fundamentals using Hadoop and Spark. https://doi.org/10.1007/978-3-030-04603-3_6 17. Akhgarnush E, Broeckers L, Jakoby T (2019) Hadoop: A Standard Framework for Computer Cluster. https://doi.org/10.1007/978-3-030-23719-6_18 18. Sterling T, Anderson M, Brodowicz M (2018). MapReduce. https://doi.org/10.1016/b978-012-420158-3.00019-8 19. He Ch, Zhang W (2020) Implementation of NN algorithm based on the MapReduce framework. https://doi.org/10.1007/978-3-030-25128-4_87 20. Lemahieu W, vanden Broucke S, Baesens B (2019) NoSQL databases. In: Principles of Database management: the practical guide to storing, managing and analyzing big and small data, pp 300–348. https://doi.org/10.1017/9781316888773.013 21. Telnarová Z, Žáˇcek M, Smolka P (2019) NoSQL databases for large volumes of data. In: AIP conference proceedings, vol 2186, p 060009. https://doi.org/10.1063/1.5137963

Reduction of Static Elastic Displacements During Processing on Vertical Milling Machines R. M. Khusainov1(B) , A. R. Sabirov1 , and V. V. Lozinsky2 1 Naberezhnye Chelny Institute (Branch) of Kazan Federal University, 68/19, Mira Str,

Naberezhnye Chelny 423812, Russia [email protected] 2 KAMAZ PTC, 2, Avtozavodsky Prospekt, Naberezhnye Chelny 423827, Russia

Abstract. This article focuses on improving the accuracy of processing on milling machines of complex parts, such as dies and molds. One of the important factors affecting machining accuracy is static elastic displacement. This article discusses the reduction of static elastic displacements due to the use of a spatial geometric factor called the stiffness axis. Methods for determining the axes of rigidity in the working space of a vertical milling machine through the use of finite element modeling are considered. A mathematical model is proposed that relates static elastic displacements along the normal vector to the treated surface with the angle of the resultant cutting forces relative to the axis of stiffness. Using this mathematical model, we studied the change in static elastic displacements with a change in cutting conditions, and as a result, with a change in the values of the cutting forces and the location of the resultant cutting forces relative to the stiffness axes. By solving the problem of optimization of the proposed mathematical model, cutting modes were defined to allow the equal cutting force to approach the axis of maximum rigidity, and as a result, to reduce static elastic movements. The adequacy of the developed mathematical model was tested experimentally. Keywords: Rigidity · Machine-tools · Cutting parameters

1 Introduction When processing dies and foundry molds in the conditions of modern production, there is a need to use finishing milling, as well as machining with small diameter mills [1, 2]. Under these conditions, in the balance of processing errors, static elastic deformations have a strong influence [3–5], which requires an increase in the rigidity of the device— machine—tool—part system [6]. 1.1 State of the Art in Modern Mechanical Engineering The traditional ways to increase rigidity are to increase the intrinsic rigidity of the elements of the technological system [7] and the rigidity of the joints between them © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_49

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[8, 9]. Meanwhile, the rigidity of the entire machine, that is, the perception of cutting forces and deformation resistance from these forces, is affected not only by the intrinsic and contact rigidity of its elements, but also by the geometric characteristics of the layout of the technological system [10]. These characteristics can be estimated as axes of rigidity [11, 12]. Scientific research does not pay enough attention to this factor. Meanwhile, if you evaluate the layout characteristics of modern machines of leading companies, especially the milling group, it becomes obvious that the high rigidity and vibration resistance of such machines is largely due to successful design solutions that provide a rational perception of cutting forces [13]. 1.2 Relevance Traditional methods of increasing stiffness by increasing their intrinsic and contact stiffness have almost exhausted themselves. In addition to these components, previous studies attach little importance to such a factor as a change in static elastic deformations depending on the direction of the force action vector. This is due to the fact that in the working space of the machine there are directions along which the deformation has a different meaning. We can distinguish: the axis of maximum rigidity along which deformations are minimal; axis of minimum rigidity along which deformations are maximum. 1.3 Statement of Problem To ensure the reduction of elastic deformations in this way, you can solve the direct problem—the construction of a rational layout of the machine, and the solution of the inverse problem—the selection of such cutting modes [14–16] that would provide such a direction of the resultant cutting force, at which it would be close to the axis of maximum rigidity. In this paper, we consider the second problem.

2 Determination of the Rigidity Axes in the Working Space of a Vertical Milling Machine Currently, with the spread of digital production technologies, three-dimensional modeling has become widespread [17]. In this regard, it is rational to apply computational methods using three-dimensional models and finite element modeling [18, 19]. A threedimensional model of a vertical milling machine JMD 3CNC is constructed to implement the computational method for determining the axes of rigidity. The determination of the stiffness axes was initially performed using a computational experiment. The finite element model of the machine was loaded with resultant cutting force. The resultant cutting force was applied to both the workpiece and the tool. During the computational experiment, the cutting force was successively rotated from 0° to 180° and at each position of the force, the static elastic deformation of the tool and the workpiece was determined. As a result, the direction of the axis with the maximum and the direction of the axis with the minimum deformations were revealed. However, this method has a high complexity of carrying out, as a result of which an analytical method was developed for determining the rigidity axes. It is also based on

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the application of a finite element model, but in this case the components of the strain tensor of the conditional finite element corresponding to the contact between the tool and the workpiece during cutting have been determined. As a result of the analysis of the deformation tensor, the main deformation values and the angles of the main deformation axes relative to the machine axes were determined [20]. Thus, having determined the axes of stiffness, they can be used to solve the technological problem of minimizing elastic deformations by approximating the resultant cutting force to the axis of maximum rigidity.

3 Mathematical Model for Optimization of Cutting Modes Since on parts with complex-shaped surfaces, there are surfaces with different location of the normal vector relative to the axes of rigidity, as the main criterion of optimization is chosen the average quadratic elastic deformation on the treated surfaces:   n  yi2 /n (1) y= i

Each component in this equation is defined as the projection of the deformation along the axes of rigidity on the normal vector of the treated surface. ⎡ P(Sz ,t,B) cos(η1(Sz ,t,B)) ⎤T ⎡ ⎤ cos(θ n1) j1 ⎢ z ,t,B)) ⎥ yi = ⎣ P(Sz ,t,B) cos(η2(S ⎦ · ⎣ cos(θ n2) ⎦ j2 P(Sz ,t,B) cos(η3(Sz ,t,B)) cos(θ n3)

(2)

j3

cos(η1(Sz , t, B)) = ca(Sz , t, B) cos(α1) + cb(Sz , t, B) cos(β1) + cg(Sz , t, B)cos(γ 1) (3) cos(η2(Sz , t, B)) = ca(Sz , t, B) cos(α2) + cb(Sz , t, B) cos(β2) + cg(Sz , t, B)cos(γ 2) (4) cos(η3(Sz , t, B)) = ca(Sz , t, B) cos(α3) + cb(Sz , t, B) cos(β3) + cg(Sz , t, B)cos(γ 3) (5) where Sz—the feed per tooth; t—cutting depth; B—width of cut; P—cutting force; cos (η1 ), cos (η2 ), cos (η3 )—direction cosines for the projection of the cutting force on the axle rigidity; θ ni—the angle between the axes of rigidity and the surface normal the angle of rotation of the point of application of resultant vector; cos (α 1 ), cos (β 1 ), cos (γ 1 )—direction cosines for the projection of the components of the cutting forces on the axis of rigidity. The deformation is determined as a function of the angles of the resultant cutting force relative to the rigidity axes. These angles are also functions of cutting forces. ca(Sz , t, B) =

Ph(Sz , t, B) P(Sz , t, B)

(6)

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cb(Sz , t, B) =

Pϑ(Sz , t, B) P(Sz , t, B)

(7)

cg(Sz , t, B) =

Px(Sz , t, B) P(Sz , t, B)

(8)

where Ph, Pv, Px—projections of the components of the cutting force on the machine axis x, y, and z, respectively.   Ph(Sz , t, B) = Pz cos(ε) + Pysin(ε) (9) Pϑ(Sz , t, B) =



PxB = P(Sz , t, B) =

Pz sin(ε) +



Pysin(ε)

Pz sin(2ω0 ) 2

Ph(Sz , t, B)2 + Pϑ(Sz , t, B)2 + Px(Sz , t, B)2

(10) (11) (12)

where Pz—tangential cutting force, summed on all working edges of the cutter; Py— radial cutting force, summed on all working edges of the cutter; ε—the angle position of the cutting edge; ω0 —angle of inclination of the screw groove of the cutter [21, 22]. On the basis of the proposed model “(1–12)”, the static elastic deformations are calculated on the example of groove milling on the selected part (Fig. 1). The cutting forces (Fig. 2) and angles of the resultant cutting force (Fig. 3) relative to the axes of stiffness are also determined by calculation.

Fig. 1. The calculated strain values.

From the analysis of the graphs, it can be seen that in the general case, with an increase in cutting conditions, the cutting forces and static elastic deformations increase. However, with some combination of cutting conditions, the static elastic deformations decrease. This decrease is due to the fact that with this combination of cutting modes, the resultant cutting forces approach the rigidity axis. Thus, the relationship between the location of the resultant cutting forces and static elastic deformation is visible. When the resulting cutting forces approach the axis of maximum rigidity, the static elastic displacements decrease, despite the increase in cutting forces.

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Fig. 2. Resultant cutting force.

Fig. 3. Cosine of the angle between the resultant cutting force and the axis of maximum stiffness.

This mathematical model can be used not only to study the behavior of deformations when changing cutting modes. The main objective of this study is to determine the cutting conditions that ensure the approximation of the resultant cutting forces to the axis of maximum rigidity, and, consequently, the reduction of static elastic deformations. This task was solved by optimizing “(1)” on the condition of a minimum of deformations. The cutting modes were applied as optimization parameters. The solution to this problem was carried out in the program Mathcad Prime 3.1 according to the KNITRO method. The solution of this mathematical model was found optimal cutting conditions when milling this part element: t = 2.5 mm, B = 0.5 mm for roughing; t = 1 mm, B = 0.2 mm for finishing.

4 Testing the Adequacy of the Developed Mathematical Model The experiment was performed in the form of milling grooves corresponding to the element of the stamp being processed, with various combinations of width and depth of cut. The experiment was carried out on a vertical milling machine JMD 3CNC, end mill diameter 4 mm, material of the workpiece is steel 45, material of the mill is steel R6M5.

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After the experiment, a deviation from the machined surface and a measurement of the width of the machined grooves (Fig. 4) were measured directly on the machine. In addition, directly during cutting, the measurement of power consumption was carried out, as an indirect measurement of cutting forces.

Fig. 4. The deviation of wall groove.

An analysis of the experimental results shows that static elastic deformations affect the change in the size of the groove. The deviations of the walls of the grooves are not the same. Deviations of the wall, when milling which the cutting force is closer to the axis of maximum stiffness, more responsive to changes in cutting conditions. The deviations of this wall depending on the cutting modes are shown in Fig. 4. As can be seen, the experimental data are close to the calculated data. The difference averaged is 5.5%, which confirms the adequacy of the developed model. Thus, this model can be used to optimize cutting conditions to minimize static elastic deformations.

5 Conclusions Using the methodology described in this paper, it is possible to increase the accuracy and reliability of machining with end mills on a vertical milling machine. To do this, it is necessary to initially determine the direction of the axes of rigidity for a particular technological system. Using modern 3D modeling and analysis tools, this task is not particularly difficult. Further, solving the optimization problem using the proposed mathematical model, it is possible to find cutting modes that provide an approximation of the resultant cutting forces to the axis of maximum stiffness. These cutting modes will ensure the reduction of static elastic deformations.

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References 1. Gavariev RV, Savin IA (2018) Research of the Mechanism of Destruction of Compression Molds for Casting under Pressure of Color Alloys. Solid State Phenom 284:326–331 2. Govorkov AS, Fokin IV, Lavrentyeva MV et al (2019) Methodology of the formalized approach of the automated construction of the manufacturing route of a mechanical engineering product. IOP Conf Ser: Mater Sci Eng 632(1):012093 3. Balabanov IP, Davletshin FF (2018) Implementation of ISO 9001, ISO 14001, ISO 45001 requirements with the systems of electronic document turnover. Int J Eng Technol (UAE) 7(4.7):20388 4. Lavrentyieva M, Govorkov A (2017) Identifying the objects in the structure of an e–model by means of identified formal parameters in the design and engineering environment. MATEC Web of Conferences. https://doi.org/10.1051/matecconf/201712903002 5. Safarov DT, Kasyanov SV, Kondrashov AG (2018) Informative Value of Measurements for Quality Management of Auto Parts. In: Proceedings of the 4th international conference on industrial engineering. ICIE 2018. Lecture notes in mechanical engineering. Springer. https:// doi.org/10.1007/978-3-319-95630-5_177 6. Salgado M, López de Lacalle LN, Lamikiz A et al (2005) Evaluation of the stiffness chain on the deflection of end–mills under cutting forces. Int J Mach Tool Manuf 45:727–739 7. Bianchi G, Paolucci F, Van den Braembussche P et al (1996) Towards virtual engineering in machine tool design. CIRP Annals—Manuf Technol 45:381–384 8. Kono D, Inagaki T, Matsubara A et al (2013) Stiffness model of machine tool supports using contact stiffness. Precis Eng 37:650–657 9. Whalley R, Ebrahimi M (2000) Analysis, modeling and simulation of stiffness in machine tool drives. Comput Ind Eng 38:93–105 10. Law M, Altintas Y, Phani AS (2013) Rapid evaluation and optimization of machine tools with position–dependent stability. Int J Mach Tool Manuf 68:81–90 11. Kolesnikov KS, Aleksandrov DA, Astashev VK et al (1994) Dynamics and stability of machines. Theory of mechanisms and machines. Mashinostroenie, Moscow 12. Timoshenko SP, Goodier J (1975) Theory of elasticity. Nauka, Moscow 13. Kudinov VA (1967) Dynamics of machines. Mashinostroenie, Moscow 14. Ryabov EA, Khisamutdinov RM, Yurasova OI et al (2019) Selection of the tooth depth of the ball end mill based on the analysis of the working conditions of the tool. IOP Conf Ser: Mater Sci Eng 570(1):012078 15. Balabanov IP, Kondrashov AG (2014) Shaping of cutting part of angle milling cutters with nonzero geometry. World Appl Sci J 30:1731–1734 16. Ryabov EA, Yurasov SY, Yurasova OI (2016) Parametric modeling of ball end mills. Russ Eng Res 36:784–785 17. Goncharov PS, Goncharov S, Artamonov IA et al (2012) NX Advanced Simulation. Engineering analysis. DMK Press, Moscow 18. Chan SK, Tuba JS (1971) A Finite Element Method for Contact Problems of Solid Bodies. Int J Mech Sci 13:213–230 19. Garitaonandia I, Fernandes MH, Albizuri J (2008) Dynamic model of a centreless grinding machine based on an updated FE model. Int J Mach Tool Manuf 48:832–840 20. Khusainov RM, Sabirov AR (2020) Stiffness maximization on the basis of layout characteristics of the elastic machine system and milling process. In: Proceedings of the 5th international conference on industrial engineering. ICIE 2019. Lecture notes in mechanical engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-22063-1_12 21. Gurin VD (2011) Improvement of milling efficiency on CNC machines by comprehensive diagnostic of the state of the tool in real time. Dissertation, Moscow State Technological University “STANKIN”, Moscow 22. Starkov YK (2009) Physics and optimization of material cutting. Mashinostroenie, Moscow

Effect of Wire Arc Additive Manufacturing Process Parameters on Deposition Behavior of Steel A. A. Kulikov(B) , A. E. Balanovskii, and M. V. Grechneva Irkutsk National Research Technical University, 83, Lermontov Street, 664074 Irkutsk, Russia [email protected]

Abstract. Additive manufacturing has gained a profound interest from the scientific community due to its economic benefits and the possibility to fabricate functional parts with complex geometrical structures using particularly any kind of material. Wire arc additive manufacturing is the cutting-edge additive manufacturing technology, which has a huge potential for industrial applications such as the production of real parts and their prototypes, maintenance, and repair operations. This article presents a study of the influence of process parameters on the deposition behavior of low-carbon low-alloy steel during the additive manufacturing process. The primary objective of the study is to identify the challenges and issues attributed to the utilization of this novel technology. During the experiments, the optimal process parameters were selected for the deposition of beads. The relationships between the process parameters and the bead geometry were determined. Adjustments of the parameters were made during the deposition of the walls consisting of a different number of layers. Once adjustments had been completed, more complex samples of square and cylinder geometric structures were deposited. After deposition, the common defects and their possible causes were identified, and recommendations for their elimination were given. At the end of the experiments, the quality of the samples obtained under these conditions and the available equipment was evaluated. Recommendations for improvement of the process are given and directions for future research are defined. Keywords: Additive manufacturing · Wire arc additive manufacturing · Gas metal arc welding · Process parameters · Carbon steel · Deposition behavior

1 Introduction The increased popularity of wire arc additive manufacturing (WAAM) in the industrial manufacturing sector over the past few decades caused by its capability to produce large metal components with high performance, relatively low-cost off-the-shelf welding equipment, and high material utilization [1]. Today, WAAM has become a promising fabrication process for various engineering materials such as titanium [2, 3], aluminum [4], nickel alloy [5, 6], steel [7, 8], and copper [9]. Compared to traditional subtractive © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_50

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manufacturing, the WAAM system can reduce fabrication time by 40–60% and postmachining time by 15–20% depending on the component size [10]. WAAM is a pioneer additive technology that utilizes an electric arc as a heat source and metal wire, rather than powder, as a feedstock [11–14]. WAAM technology has many advantages such as the utilization of readily available welding equipment and the application of commercially available and relatively cheap welding wires instead of expensive powders and technically complex powder bed systems [15–18]. Along with the manufacturing of new components, WAAM can also be used for maintenance and repair operations [19]. Due to the highly complex nature of metallurgical and welding processes occurring during deposition, many different aspects of the process need to be studied, including process development, process parameters, material quality and performance, the influence of heat input on characteristics of a final part. This paper reviews the study of the effect of various process parameters on the deposition behavior of low-carbon low-alloy steel after deposition by using WAAM technology. Finally, a discussion is given on improving the quality of WAAM parts fabricated through optimization of process parameters, deposition techniques, including proposals for future research.

2 Materials and Experimental Techniques A commercially available Sv-08G2S wire (see Table 1) with a diameter of 0.8 mm was used in this study to investigate the effect of WAAM process parameters on the deposition behavior of steel components. A Fe37-3FN structural carbon steel plate of 16 mm thickness was used as the substrate on which the wire was deposited. Table 1. The chemical composition of Sv-08G2S wire used in the study (wt%). C

Si

Mn Ni S

P

Cr N

0.06 0.8 1.9 0.2 0.02 0.02 0.1 0.01

An experimental robotic WAAM complex installed in the Irkutsk National Research Technical University was used to produce samples for this study and shown in Fig. 1. The deposition of the wire was performed by the gas metal arc welding (GMAW) method using a KUKA KR 210 R2700 prime (KUKA robotics, Germany) with a KEMPPI Kempomat 1701 in the flat position. GMAW method, also referred to as metal inert gas (MIG) welding or metal active gas (MAG) welding, is a welding process in which an electric arc generates between a consumable wire electrode and the workpiece metal, which heats the workpiece metal, causing it to melt [20]. Along with the wire electrode, a shielding gas feeds through the welding gun protecting metal from the contaminants in the air. Welding grade carbon dioxide (CO2 ) was used for shielding with a 10 L/min gas flow rate.

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Fig. 1. An experimental robotic WAAM complex.

In order to determine the relationship between WAAM process parameters and behavior of metal during deposition, the following welding parameters have been specified for this study: welding current, welding voltage, wire feed rate, torch travel speed, stick out distance. Adjustment of optimal parameters was performed by deposition of five 100 mm long beads. Once adjustment and selection of optimal parameters have been completed, 100 mm long and 20 mm high thin-walled structures were deposited to investigate the behavior of metal during the deposition in a layer-by-layer fashion.

3 Results The parameters that have a major effect on the formation of the layer are found to be the torch travel speed, wire feed rate, and welding current. The selection of welding current was based on a wire diameter which was 0.8 mm. The most suitable and optimal welding current for such diameter lies in the range of 100–120 A. Adjustment of these parameters allows achieving the desired quality of a deposited bead, its geometry, and the performance of the process. In particular, a linear relationship between the deposition

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speed (torch travel speed) and the width of the deposited bead was determined during the experiment. Figure 2 shows five different beads produced at various deposition speeds.

Fig. 2. Deposited beads using different process parameters.

As can be seen from Table 3, the width of the bead varies depending on the torch travel speed. Bead №1 was deposited at a speed of 0.005 m/s, which resulted in a too narrow bead with uneven melting of the metal. If this speed is used for the deposition of a real part, the accuracy of the geometric dimensions will be low, and the process of layering as such will be unstable and difficult to control. Increasing the welding current while maintaining the same deposition speed did not give a positive result since it was necessary to increase the wire feed speed as well which led to the intensive scattering of the molten metal and the formation of an uneven geometry of the bead. When depositing bead №2, the deposition speed was reduced to 0.004 m/s at a welding current of 120 A. Reducing the speed of deposition contributed to the formation of a bead of high quality since the metal was melted evenly with small distortions along the central axis. However, applying such deposition parameters, the height of the bead along the central line is significantly bigger than the height of the bead on the sides. It will negatively affect the formation of the next layers since the metal will not be able to evenly overlap the uneven surface of the previous layer. As a result, the metal will flow along the sides of the layer, leaving the center line unfilled. In this case, it will be quite difficult to control the process and achieve the desired accuracy of the dimensions of real parts. Further reduction of the speed to 0.003 m/s during the deposition of the bead №3 showed the best results. The formation of the bead is more than satisfactory, the layer itself is straight having the least distortion. The height of the bead is optimal and will contribute to the qualitative deposition of subsequent layers. Utilizing these parameters, it will be possible to predict the behavior of the metal during the deposition process and achieve dimensional accuracy. The subsequent reduction of the speed to 0.002 and 0.001 m/s during the deposition of samples №4 and №5 resulted in the production of the widest beads. Excessive heat input at these speeds leads to overheating of the metal and the formation of an inhomogeneous structure, which will inevitably contribute to the formation of defects. Additionally,

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Table 3. Relationship between process parameters and the geometry of the deposited beads. Weld bead, №

Width, mm

Height, mm

Welding current, A

Welding voltage, V

Wire feed Torch rate, m/min travel speed, m/s

Stick out distance, mm

1

4

2

100

26

4

0.005

14

2

6

3

120

28

5

0.004

13

3

8

3

120

28

4.5

0.003

11

4

10

2

120

28

4.5

0.002

11

5

12

2

120

28

4.5

0.001

11

applying such parameters, it will be quite difficult to achieve the dimension accuracy and quality of the deposited surface. Thus, the most optimal parameters for the deposition during this experiment are the following: welding current—100 A, welding voltage—26 V, wire feed rate—4,5 m/min, torch travel speed—0,003 m/s, stick out distance—11 mm). For the deposition of multilayer samples, a more precise parameter setting will be required during the layering process, depending on the geometry of the resulting part. Figure 3 shows multilayer walls deposited using the above-mentioned parameters. Table 4 shows the obtained geometry of the walls.

Fig. 3. Deposited walls.

As can be seen from Table 4, the average thickness of one layer was 2 mm. The deposition speed of 0.003 m/s is truly applicable for the deposition of even and fairly accurate layers, but the defects are still present. The most noticeable defects are the

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Table 4. Characteristics of the deposited walls. Wall, Number Height, Length, Wall Welding Welding Wire № of mm mm thickness, current, voltage, feed layers mm A V rate, m/min

Torch Stick out travel distance, speed, mm m/s

1

13

27

100

8

100

26

4.5

0.003

11

2

10

20

100

9

100

26

4.5

0.003

11

3

10

20

100

9

100

26

4.5

0.003

11

spreading of the metal and the slope of the wall at the end of the layer, which was the result of constant and severe heat input during the deposition process (see Fig. 4).

Fig. 4. Slope at the end of the wall.

Furthermore, there are elements of non-molten wire and splashes of metal. Some layers are deposited with a slight offset relative to the central axis of the wall, which leads to uneven overall wall thickness. To obtain a more accurate geometry and reduce defects, it is necessary to control the heat input and constantly adjust the parameters during the deposition process. During the course of the further experiment, a box with dimensions of 60 × 60 mm was deposited, the number of layers is 15, and the total height is 30 mm (see Fig. 5). The average value of the layer thickness of 2 mm, determined in previous experiments, is also preserved during the deposition of a sample with a more complex geometric shape. Layers’ deposition in a square-shaped sample differs from that in the wall due to the presence of angles and the constant change of the movement trajectory of the welding torch. Since the torch was moving along a trajectory consisting of 4 linear movements, there were minor stoppages of the torch in the corners of the square. This has led to a slight widening of the beads at the corners, but this is not an issue since post-process machining will help to correct the situation. Essentially, the formation of a square-shaped part is quite successful, the deviation from the specified dimensions are within the allowance for machining, which indicates the potential of WAAM technology for production parts of the complex angular shape. Then, the cylindrical samples were deposited (see Fig. 6). Cylinder №1 has a diameter of 80 mm and consists of 11 layers with an overall height of 22 mm. Cylinder №2 has a diameter of 50 mm and consists of 24 layers with an overall height of 48 mm. The previously defined layer height of 2 mm remains unchanged during the deposition of cylindrical shaped samples. A cylinder with a larger diameter has a more even bead shape and has less distortion over the entire length of the layer in comparison with a

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Fig. 5. Deposited box.

cylinder with a smaller diameter. A special effect on the process of forming the cylinder has the choice of the point, where the deposition of the next layer should starts. Since the deposition of each subsequent layer began at one point, a small roll was formed at this very place, which led to an uneven height of the cylinder and a broadening of the wall at this point. In order to eliminate this defect, it is necessary to change the start point of the deposition of each subsequent layer or to reduce the dwell time of the welding torch right before the deposition of the next layer.

4 Discussion In order to improve the stability of the process, eliminate or reduce the number of defects in the deposition process, as well as to achieve the accuracy of the deposited parts, it is necessary to choose the optimal process parameters. Since a one-time parameter setting is inadequate for obtaining a high-quality part, monitoring and controlling of all parameters is required during the actual deposition process. To do this, appropriate sensors and a video camera with special light filters are needed to be integrated into the existing WAAM system for remote monitoring and controlling of the process. Moreover, to improve the quality of deposited beads, it is imperative to utilize shielding gases of higher quality. Carbon dioxide alone is not able to provide the necessary quality, so it is preferable to use a mixture of argon and carbon dioxide. To increase the metal deposit factor and hence the WAAM process performance, the wire diameter should be

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Fig. 6. Deposited cylinders.

increased from 0.8 to 1–1.2 mm. For the production of real functional parts, it is vital to implement modern closed-loop welding machines that allow adjusting the process parameters directly from the robot control interface.

5 Conclusions This article presents the results of the study of the influence of process parameters on the formation of steel parts. During the course of the experiment, the relationship between the deposition speed and the geometry of the resulting bead was obtained. The most optimal torch travel speed for the deposition of steel parts using a 0.8 mm wire is 0.003 m/s at a welding current of 100A. This speed allows achieving the best bead formation with the least distortion. The deposition process itself is quite stable and allows produce beads with approximately the same geometry. At this speed, all layers of the walls, box, and cylinders have a thickness of 2 mm. The most common defects were detected during the deposition of walls, square and cylindrical samples. Due to the constant and repeated heat input, the geometry of the bead at the beginning and end of the layer is different, which leads to the formation of a slope at the end of the wall. Additionally, there are elements of non-molten wire and splashes of metal. During the deposition of square and cylindrical samples, noticeable defects are unevenness and widening at the transition points of the layers, which is caused by the peculiarity of the torch movement. In order to eliminate these defects, it is necessary to develop a path-planning program for more effective planning of the torch movement trajectory. In

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general, the parameters determined during the experiments can be used for the deposition of real parts prototypes. Further adjustment of the parameters will be required during the actual deposition process to achieve better results. The directions of future research are to study the parameters of forming real parts made from steel, titanium, and nickel, as well as to investigate the influence of process parameters on the microstructure and mechanical properties of the final parts. Acknowledgements. The authors would like to acknowledge the Department of Mechanical Engineering Production Technologies and Equipment for the given opportunity to use the KUKA robot for conducting the research.

Author Contributions. Anton A. Kulikov operated and programmed the KUKA robot and wrote the paper. Andrei E. Balanovskii and Maria V. Grechneva carried out the overall project management and participated in the discussion of the results.

References 1. Wu B, Pan Z, Ding D, Cuiuri D, Li H, Xu J, Norrish J (2018) A review of the wire arc additive manufacturing of metals: properties, defects and quality improvement. J Manuf Process 35:127–139. https://doi.org/10.1016/j.jmapro.2018.08.001 2. Wu B, Ding D, Pan Z, Cuiuri D, Li H, Han J, Fei Z (2017) Effects of heat accumulation on the arc characteristics and metal transfer behavior in Wire Arc Additive Manufacturing of Ti6Al4V. J Mater Process Technol 250:304–312. https://doi.org/10.1016/j.jmatprotec.2017. 07.037 3. Wang F, Williams S, Rush M (2011) Morphology investigation on direct current pulsed gas tungsten arc welded additive layer manufactured Ti6Al4V alloy. Int J Adv Manuf Technol 57(5–8):597–603. https://doi.org/10.1007/s00170-011-3299-1 4. Cong B, Ding J, Williams S (2014) Effect of arc mode in cold metal transfer process on porosity of additively manufactured Al-6.3%Cu alloy. Int J Adv Manuf Technol 76(9–12):1593–1606. https://doi.org/10.1007/s00170-014-6346-x 5. Xu F, Lv Y, Xu B, Liu Y, Shu F, He P (2013) Effect of deposition strategy on the microstructure and mechanical properties of Inconel 625 superalloy fabricated by pulsed plasma arc deposition. Mater Des 45:446–455. https://doi.org/10.1016/j.matdes.2012.07.013 6. Baufeld B (2011) Mechanical Properties of INCONEL 718 Parts Manufactured by Shaped Metal Deposition (SMD). J Mater Eng Perform 21(7):1416–1421. https://doi.org/10.1007/ s11665-011-0009-y 7. Ding D, Pan Z, Cuiuri D, Li H (2015) Wire-feed additive manufacturing of metal components: technologies, developments and future interests. Int J Adv Manuf Technol 81(1–4):465–481. https://doi.org/10.1007/s00170-015-7077-3 8. Haden C, Zeng G, Carter F, Ruhl C, Krick B, Harlow D (2017) Wire and arc additive manufactured steel: tensile and wear properties. Addit Manuf 16:115–123. https://doi.org/10.1016/ j.addma.2017.05.010 9. Ding D, Pan Z, Duin SV, Li H, Shen C (2016) Fabricating superior NiAl Bronze components through wire arc additive manufacturing. Materials 9(8):652. https://doi.org/10.3390/ma9 080652 10. Williams SW, Martina F, Addison AC, Ding J, Pardal G, Colegrove P (2016) Wire arc additive manufacturing. Mater Sci Technol 32(7):641–647. https://doi.org/10.1179/1743284715y.000 0000073

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11. Dickens P, Pridham M, Cobb R, Gibson I, Dixon G. Rapid prototyping using 3-D welding. In: DTIC Document 1992 12. Spencer J, Dickens P, Wykes C (1998) Rapid prototyping of metal parts by three-di-mensional welding. Proc Inst Mech Eng Part B J Eng Manuf 212:175–82 13. Kovacevic R, Beardsley H (1998) Process control of 3D welding as a droplet-based Rapid prototyping technique. In: Proceedings of the SFF Symposium, University of Texas at Austin, p 57–64 14. Dwivedi R, Kovacevic R (2004) Automated torch path planning using polygon subdivisionfor solid freeform fabrication based on welding. J Manuf Syst 23:278–91 15. Song YA, Park S, Choi D, Jee H (2005) 3D welding and milling: part I–a direct approach for freeform fabrication of metallic prototypes. Int J Mach Tools Manuf 45:1057–62 16. Song YA, Park S, Chae S-W (2005) 3D welding and milling: part II—optimization of the 3D welding process using an experimental design approach. Int J Mach Tools Manuf 45:1063–9 17. Zhang Y, Chen Y, Li P, Male AT (2003) Weld deposition-based rapid prototyping: a preliminary study. J Mater Process Technol 135:347–57 18. Zhang YM, Li P, Chen Y, Male AT (2002) Automated system for welding-based rapid prototyping. Mechatronics 12:37–53 19. Marenych O, Kostryzhev A, Shen C, Pan Z, Li H, Duin SV (2019) Precipitation strengthening in Ni–Cu Alloys fabricated using wire arc additive manufacturing technology. Metals 9(1):105. https://doi.org/10.3390/met9010105 20. Jacobs PF (1992) Rapid prototyping & manufacturing fundamentals of stereolithography, First edition edn. Society of Manufacturing Engineers, Dearborn, US

Study of the Axial Contact Points Method Applied When End-Milling Titanium Alloys A. V. Nikitenko1 , A. V. Savilov2(B) , and A. S. Pyatykh2 1 Pacific National University, 136 Tihookeanskaya St, Khabarovsk 680035, Russia 2 Irkutsk National Research Technical University, 83 Lermontov St, Irkutsk 664074, Russia

[email protected]

Abstract. Vibration reduction methods were described. A comparative analysis of constructive and software methods was given, their advantages and disadvantages were identified. The results of the study of vibration reduction methods based on optimal axial cutting depths were presented. The axial cutting depth which corresponds to a certain pitch of the cutter spiral and a certain number of contact points was determined. The titanium alloy used in the aircraft construction industry was milled. Vibrations were measured in the frequency and time domains. Possibilities of stable cutting without reducing productivity were studied for a specific technological system. The nature of vibrations was analyzed at various ACP values. The hypothesis on the effect of the ACP on vibrations was confirmed. Cutting forces were measured. The ACP effect on the tangential, radial, and axial cutting forces was studied. The practical significance of the results for designing machining processes was shown. The monolithic carbide mill was used in the experiments. Its geometry was optimized for high-productivity titanium machining. When end-milling titanium alloys, productivity can be improved by stabilizing the cutting process. Directions for further research on high-productivity titanium milling were described. Keywords: Titanium · Alloys · Milling · Vibration · Cutting forces

1 Introduction The urgent tasks of modern engineering require improvement of the performance of machining centers, implementation of high-performance machining technologies, improvement of quality of products. There are factors which prevent these tasks from being solved. One of them is vibrations occurring when cutting metals. They have a negative effect on the quality of machined surfaces, the resistance of cutting tools and the resource of expensive processing equipment. Milling refers to the machining processes for which the vibration damage is crucial. Moreover, the use of advanced elements of the technological system does not reduce vibrations and even increase them due to a higher spindle speed [1–4]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_51

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Various methods are used to reduce vibrations. These methods can be divided into software and constructive ones. Software methods include mathematical modeling [5– 11] and cutting speed modulation [12]. They do not require structural changes in tool setups, machining and clamping equipment. But the software methods require time and human resources for developing mathematical models, updating control programs for CNC machines, conducting experiments to verify the adequacy of machining models, etc. Constructive methods require either changes in the design of any element of the technological system, or the use of additional structural elements reducing vibrations [13–15]. Currently, mills, toolholders for turning tools and other types of toolholders with built-in dampers, as well as mills with a variable tooth pitch and an angle of the helix are used [13]. A variable tooth pitch is more characteristic of end mills. These tools are expensive but can reduce vibrations without additional costs. However, it should be noted that the maximum effect of these tools is achieved when calculating cutting conditions and planning the trajectory of their movement in the material [16–20]. There are combined vibration reduction methods (e.g., milling at an optimal ACP (Axial Contact Points) value). The ACP parameter shows the number of tool/material contact points. This parameter is equal to the ratio of the axial depth of cut ap to the pitch of the end mill helix. The ACP parameter determines a probability of vibrations. This method is typical for end milling at a large axial depth of cut ap. Some CAM systems provide recommendations for optimal ACP values which can prevent vibrations. In a favorable zone, you can choose more “aggressive” cutting modes without increasing the level of vibrations. However, CAM systems take into account only geometric aspects of this method and ignore the features of a specific technological system and materials being machined. Thus, it is necessary to evaluate the effectiveness of vibration reduction methods in specific technological situations. An analysis of studies on end-milling modeling and vibration reduction shows that insufficient attention is paid to the method of milling at optimal ACP values [9, 21]. Thus, this article aims to study the influence of axial cutting depths on the end-milling dynamics at various machining parameters [22]. The results can expand the application of this model and change the specific cutting force depending on the thickness of chips. This can contribute to the maximum productivity at low cutting forces and vibrations when machining nonrigid workpieces (thin walls, nonoptimal fastening patterns) or using long cutters. This is crucial when machining titanium alloys and other difficult-to-machine materials, as along with vibrations and high cutting forces, there are high temperatures in the cutting zone [21]. The warming up causes negative changes in the microstructure and properties of the tool and the material. High cutting forces and temperatures cause an accelerated tool wear.

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2 Equipment and Methods The experiments were carried out using the DMG DMU 80P duoBlock (Fig. 1). The VT20 titanium alloy (Ti-6% Al-2% Zr) workpiece 400 × 200 × 40 mm in size was machined. An end mill made from a hard material was used. The parameters of the cutting tool are as follows: the diameter Dc = 16 mm, the number of teeth z = 4, the maximum axial cutting depth apmax = 32 mm, the tool length l = 115 mm, the helix angle ω = 48°. This milling cutter was fixed in a hydroplastic chuck. The cutting forces were measured with the Kistler 9253B23. To measure vibrations, the Polytec OFV-505 was used.

Fig. 1. The working area of the DMU 80P duoBlock.

Milling was carried out under the following cutting conditions: radial cutting depth ae = 1 mm, feed per tooth fz = 0.1 mm/tooth, cutting speed Vc = 40 m/min, rotation speed n = 796 rpm. The axial cutting depth ap varied from 6 to 30 mm in increments of 2 mm. One more experiment was carried out at a cutting depth of ap = 11.3 mm, since it corresponds to ACP = 1. Figure 2 shows the graphical explanation of the ACP method. When setting the axial cutting depth, the pitch of the end mill spiral is taken into account. The spiral pitch is πD calculated by formula P = tan ω , where Dc is the cutter diameter, ω is the spiral angle. zap ACP = P , where z is the number of teeth, ap is the axial cutting depth. Thus, ACP = 1 corresponds to ap = 11.3 mm; ACP = 2 corresponds to ap = 22.6 mm, and so on. When the ACP is an integer, vibrations are minimal. However, it is not always possible to implement this condition (when milling edges of aircraft parts that have a certain height or in case of limited power and spindle torque values). Therefore, it is necessary to determine the dependence of vibrations on cutting depths within the entire length of

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the cutting edge. Of particular interest is the cutting depth which corresponds to a certain neighborhood of the integer ACP value.

Fig. 2. ACP values for the end mill used in the experiments.

The authors suggest estimating the cutting depth which differs from the step of the cutter spiral by 10%, i.e., when ACP = 0.9 and ap = 10 mm. The second important task is to study the dependence of the specific cutting force on the cutting depth. In this case, both the tangential Fy and radial Fx cutting forces and the axial cutting force Fz are analyzed. The tangential cutting force determines the cutting power. The radial cutting force affects the cutter deflection and machining accuracy. The axial cutting force initiates the pulling of the cutter from the chuck or the detachment of the part from this table when machining on the vacuum table.

3 Results and Discussion Figures 3 and 4 show vibration graphs in the frequency and time domains for ap = 6, 10, 11.3, and 30 mm. The minimum amplitude values were recorded for a cutting depth of 11.3 mm, which corresponds to ACP = 1. The nature of time-varying behavior of the vibration amplitude indicates a stable machining process. The vibration amplitude for this value is lower than that for ap = 10 mm. it is also lower than that for the minimum cutting depth ap = 6 mm. At a cutting depth of ap = 6 mm, pronounced self-oscillations were recorded. Although the vibration amplitude for the cutting depth ap = 30 mm exceeds the vibration amplitude for ap = 11.3 mm by 50%, in the time domain, the vibration graph demonstrates the absence of self-oscillations under these cutting modes. At a cutting depth of ap = 10 mm, self-oscillations were also recorded, their amplitude exceeds the vibration amplitude at ap = 11.3 five times, which is unexpected. This fact can be explained by steep boundaries of the regions of stable cutting of the technological system under study [1, 4]. Figure 5 shows the cutting force graphs. They show tangential Fy , radial Fx, and axial Fz cutting forces for cutting depths ap = 6, 10, 11.3, and 30 mm. When processing the measurement results, the minimum filtering mode was used. The nature of time-varying

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Fig. 3. Vibrations in the temporary domain measured at different axial cutting depths: a − ap = 6 mm, b − ap = 10 mm, c – ap = 11.3 mm, d – ap = 30 mm.

behavior of all projections of the main cutting force confirms the vibrational pattern recorded in Fig. 3. Figure 6a shows a dependence of the vibration amplitude on the cutting depth. It is possible to determine the most favorable values of ap ensuring stability of the cutting process. Obviously, the best results are achieved when working at axial cutting depths ap = 11.3 and 22.6 mm, which correspond to ACP = 1 and ACP = 2. This graph confirms the original hypothesis on stable cutting at integer ACP values. Figure 6b shows a dependence on the cutting forces on the axial cutting depth. Despite the fact that all the graphs show an increase in the cutting forces close to linear, it is possible to determine values of the axial cutting depth, where a relative decrease in the cutting forces is noticeable in comparison with neighboring points. These values also correspond to ACP = 1 and ACP = 2. This effect can be achieved by processing the data using preliminary filtering. When filtering values of the cutting forces measured at high vibrations, the calculation error increases.

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Fig. 4. Vibrations in the frequency domain measured at different axial cutting depths: a − ap = 6 mm, b − ap = 10 mm, c – ap = 11.3 mm, d – ap = 30 mm.

4 Conclusion When end milling the VT20 titanium alloy, dependences of the vibration amplitude and the cutting forces on the ACP parameter allowed us to identify cutting parameters that ensure the stability of the machining process and improve productivity. The hypothesis on vibration-free machining at integer ACP values was confirmed. It is necessary to study the ACP effect on the end-milling dynamics at various radial cutting depths and feeds. The subject of further research may be an analysis of surface roughness and accuracy of the dimensions [20]. The results can be used for optimizing cutting conditions and process productivity when milling the VT20 titanium alloy.

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Fig. 5. Tangential Fy , radial Fx and axial Fz cutting forces at different axial cutting depths: a − ap = 6 mm, b - ap = 10 mm, c – ap = 11.3 mm, d – ap = 30 mm

Fig. 6. Dependences of the output milling parameters on the axial cutting depth: a—vibration amplitude; b—cutting forces.

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Acknowledgements. All studies were conducted in the research laboratory of “High productivity machining” Irkutsk National Research Technical University. The authors express their gratitude to the staff of the laboratory.

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21. Krishnaraj V, Samsudeensadham S, Sindhumathi R, Kuppan P (2014) A study on high speed end milling of titanium alloy. In: Proced Eng 22. Engin S, Altintas Y (2001) Mechanics and dynamics of general milling cutters. Part 1: helical end mills. Int J Mach Tools Manufact 41:2195–2212 23. Mann BP, Young KA, Schmitz TL, Dilley DN (2005) Simultaneous stability and surface location error predictions in milling. ASME J Manuf Sci Eng 127:446–453

Investigation of the Effect on the Efficiency of Hot Die Forging Operations Cutting Off and Heating Blanks from Rolled Round Bar I. V. Telegin(B) Lipetsk State Technical University, d.30, st. Moscow, Lipetsk 398055, Russia [email protected]

Abstract. Hot die forging is one of the main technological processes for the forgings production with high performance properties for subsequent, as a rule, machining. One of the most important hot forming process efficiency indicator is its metal consumption, which is determined by the utilization of the metal (the ratio of the finished part mass to the mass of the blank from which this part is made). The value of the metal utilization coefficient depends on a number of interrelated indicators that determine the metal loss during the technological manufacturing operations of the finished part: manufacturing a bar of a given diameter with a certain accuracy, cutting of blank of a given length, heating the blank, stamping of the forging and its mechanical processing. The article proposes a methodology that establishes the influence of the accuracy rolled bar parameters, the blank cutting method, and the heating method on metal losses during hot stamping operations of round forgings on crank presses. The proposed mathematical model and computer program, developed on its basis, allows us to evaluate the effect of metal losses associated with the accuracy of the manufacture of the bar, the operations of cutting and heating the blank, on the metal loss in the manufacture of forgings. Keywords: Hot die forging · Forging · Metal consumption · Cutting off a blank · Heating a blank

1 Introduction For the manufacture of round forgings, measured cylindrical blanks are used. Hot Die Forging (HDF) on Crank Hot Die Forging Presses (CHDFP) is one of the most common methods for producing such forgings [1–3]. The most important indicators of its effectiveness are metal losses and time-varying forces values of the plastic deformation during stamping operations on crank presses [4–6], which lead to an increase in dynamic loads in forging equipment [7–11].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_52

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Metal losses in the manufacture of measured cylindrical blanks are related to the accuracy of the rolled bar diameter, the way the blank is cutting off, the burning of metal when it is heated. The value of these indicators are interrelated and vary within certain limits. Metal losses during the implementation of the HDF process on CHDFP depend on the applied technological process of stamping [2, 4, 6, 12] and the mass of the cylindrical blank. The values of the plastic deformation forces and the nature of their changes depend on the HDF technological scheme, and as a rule, grow with increasing mass of the billet. These indicators may in some cases be decisive when choosing the type (and cost) of CHDFP. In this study, the following tasks are solved: • Development of the mathematical model that determines the relationship between the blank’s accuracy parameters, depending on its method of manufacturing and heating. • Software solution development that allows you to perform an influence analysis of the rolled bar accuracy, methods of cutting off, and heating workpieces on its mass. • Evaluate the effectiveness of the standard hot die forging process on crank press of the round forging, depending on the weight of the blank.

2 Calculation of the Metal Consumption During the Manufacturing Process and Heating Blank When performing research, we will use the following definitions: • The minimum volume (mass) of the blank is the volume of the blank, which allows forging to be produced by the HDF method without forming defects due to not filling the die impression of the final stamp step. • The minimum permissible volume (mass) of forgings is the volume of forgings obtained from a minimum volume blank. The minimum volumes (masses) of forgings and blanks differ by the amount of metal waste due to heating of the blank. The formation of forgings at the final step most often occurs simultaneously with flow of metal in the flash (open die) or compensator (closed die). Accordingly, it is possible to determine the minimum forging volume based on its 3D models [13–15]. Accordingly, it is possible to determine the minimum forging volume by numerical simulation methods, for example, in the QForm program [16–18], or experimentally. In the manufacture of the blank, a significant increase in metal consumption can  Dmax occur due to inaccuracies in the diameter DDmin of the rolled bar, the inaccuracy of   max cutting B L min and rised metal waste when it is heated. The latter is determined by the method of cutting: on scissors, in a die, hacksaw and other machines, and by the heating method, in which part of the mass of the blank (U min , U max – in percent) is converted to scale.

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The diameter (D) and the minimum volume of forgings (F V min ) are the initial data for calculating its length (B L). The mass and volume of the workpiece are related by the relation: B M min = B V min · ρ, where ρ is the material density of the blank (forgings). The volume of the blank (B V ), its diameter (D) and length (B L) must satisfy the relations “(1)” 1.25 ≤

BL

D

≤ 2.5,

BV

=

π · D2 B L, 4

(1)

where the volume and length of the blank can take values from B V min , B L min to B V max , B L max , respectively. The diameter of the blank (D) will be considered equal to the nominal

diameter of the rolled bar corresponding size. Minimum and maximum blank heights “(2)”: B Lmin B Lmax

= B L + min , = B L + max .

(2)

Nominal length of the blank including waste of metal (3) BL

=

4 · V · (1 + 0.01 · Umax ) − min , 2 π · Dmin

(3)

where V is the minimum volume of the workpiece after heating and descaling. The mathematical model that allows us to study the loss of metal in the manufacture of the blank depending on the diameter and accuracy of the rolled bar, the heating method and the cutting off, is a set of dependencies “(4–10)”. Minimum and maximum volumes of the blanks before heating = V · (1 + 0.01 · Umax ),   4 · V · (1 + 0.01 · Umax ) 2 + max − min . B Vmax = 0.25π · Dmax · 2 π · Dmin B Vmin

(4)

Maximum metal loss  2 δV = 0.25π · Dmax ·

4 · V · (1 + 0.01 · Umax ) 2 π · Dmin

 + max − min − V · (1 + 0.01 · Umax ).

(5)

Metal loss due to heating (%) δVU =

V · Umax V · (0.01 · Umax − 1

+ D1−2

· D22 ) + 0.25 · π · (max − min ) · D2

.

(6)

.

(7)

Loss of metal due to inaccuracies in the cutting off (%) δVL =

250 · π · D2 · (max − min ) V · (0.01 · Umax − 1 + D1−2 · D22 ) + 0.25 · π · (max − min ) · D2

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I. V. Telegin

Loss of metal due to deviations in the diameter of the blank (%) δVD =

100 · V · (D1−2 · D22 − 1)

V · (0.01 · Umax − 1 + D1−2 · D22 ) + 0.25 · π · (max − min ) · D2

.

(8)

Limit values of blanks lengths (L min and L max ) for diameter D Lmin = Lmax =

4 · V · (1 + 0.01 · Umax ) , π · D2

2 · D2 2 + π · Dmin 4 · V · (1 + 0.01 · Umax ) · Dmax max · (max − min ) 2 D2 · π · Dmin

(9) .

(10)

The values L min , L max corresponding to the nominal diameter D in the expressions “(9)” and “(10)”, will be called conditional. These are the parameters of the blank that are used in the process of modeling HDF by the finite element method (FEM) [12, 16], in this case, the QForm program. The actual value of the nominal length of the cold blank (11) L=

4 · V · (1 + 0.01 · Umax ) − min 2 π · Dmin

(11)

3 Influence Analysis of the Rolled bar Precision, Cutting Methods, and Heating Blank on Its Mass For the formation of forgings by the HDF method at CHDFP, blanks with different values of diameter, length and accuracy of their execution can be used. The result is a different metal intensity of the technological process, various plastic deformation forces. To analyze various options for the values of the blank parameters, a special computer program [19, 20], was developed, the main window of which is presented in Fig. 1. Key features of the program: • the presence of built-in databases of standard parameters for the rolled bar products of circular cross section; • the presence of the databases of metal loss values for various heating methods; • the presence of databases of recommended accuracy values for the lengths of cut blanks when applying various methods of cutting; • preservation of up to five options for the production of blanks for further analysis and informed decision-making in the design of processes for HDF.

Investigation of the Effect on the Efficiency of Hot Die Forging Operations

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Fig. 1. Automation of the blank parameters calculating.

4 Effectiveness Evaluation of the Standard HDF Process on CHDFP for Round Forging Depending on the Mass of Blank Figure 2 shows the “Gear” part (the mass of the part is 1.83 kg) used to test the mathematical model “(1–11)”, software (Fig. 1), and the methodology for studying the impact on the metal consumption of HDF processes on CHDFP round forgings for cutting operations and heating blanks of the rolled bar.

Fig. 2. Drawing of part “Gear”.

Figure 3 presents the results of a metal consumption study for the HDF technological process depending on the nominal diameter of the blank (mm): 60, 63, 67, 70, 73. Analysis of the results of the study shows that there is a tendency to reduce losses associated with the manufacture of the blank with a decrease in its diameter. Specifically,

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I. V. Telegin

Fig. 3. Analysis results of the blank’s parameters.

reducing the diameter of the billet used from 73 to 60 mm leads to a reduction in losses of 0.01 kg without increasing the cost of the metal. Obviously, the reduction of metal losses can be achieved by using more expensive long products of increased accuracy, using more accurate, but expensive methods of cutting, heating, in this case, the proposed method allows us to generate data for calculating the economic efficiency of these solutions. Figure 4 shows the technological steps of open die stamping of the considered forging. For its manufacture, a rolled bar is used in accordance with GOST 2590–2006 with a nominal diameter of 70 mm, accuracy class B1. The cutting off the blanks on highquality scissors is ensuring accuracy ± 1.5 mm. Heating—flame using natural gas to a temperature of 1200 °C. The minimum estimated (conditional) length of the blank– 101.5 mm was obtained by numerically simulating the HDF technological process in the QForm 8 program, the maximum length –109.73 mm, calculated according to the proposed method, in accordance with dependencies “(1–10)” (Fig. 1).

Fig. 4. Technological steps of open die forging of the “Gear” part.

Investigation of the Effect on the Efficiency of Hot Die Forging Operations

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Figure 5 presents the results of modeling the HDF process on CHDFP K8544 with nominal force 25 MN. B L min = 101.5–technological force 14.4 MN; F L max > 109.73– technological force ≈22 MN; F L max > B L max . The connection between the technological effort and the mass of the blank is changed within the tolerance for its manufacture.

Fig. 5. Stamping at the final step with the conditional height of the blank: a –101.5 mm, b – 109.73 mm.

5 Summary The research results considered in the article allow: • To calculate the minimum and maximum lengths of the blank needed to simulate the technological process of hot stamping (for example, in the QForm program). • To calculate the utilization of metal depending on the method of manufacturing the blank. • To assess the effect of the mass of the workpiece within the accuracy of its manufacture on the technological efforts of stamping. The proposed methodology for assessing the influence of the manufacturing blank method on its mass can be useful to engineers and technologists involved in the design of high performance technological processes of HDF on CHDFP.

References 1. Konstantinov I (2014) Forging and die stamping: Tutotial. SFU, INFRA-M, Krasnoyarsk 2. Volodin IM (2006) Simulation of hot die forging: Monograph. Mechanical Engineering, Moscow 3. Semenov EI (2011) Forging and hot die forging. MSIU, Moscow 4. Semenov EI et al (2010) Forging and die stamping: book of reference. In: Semenov EI (ed) Materials and heating. Equipment. Forging, vol 1. Mashinostroine, Moscow 5. Lavrinenko SA, Evsyukov SA, Lavrinenko VYu (2014) Die forging on machines: Tutorial. BMSTU, Moscow 6. Volodin IM, Romashov AA (2008) The system of basic principles for designing processes of hot die forging and technologies created on its basis. Forging and stamping production. Process Mater Pressure 9:19–29

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7. Svistunov EV (2008) Forging and stamping equipment. Crank presses: textbook. MGIU, Moscow 8. Telegin I (2018) Shumilova T (2018) Comparing the efficiency of flowsheets for hot die forging on crank presses. MATEC Web Conf ICMTMTE 224:01092. https://doi.org/10.1051/matecc onf/201822401092 9. Telegin V, Kozlov A (2016) Computer realization of research into the dynamics of mechanical systems. IOP Conf Ser Mater Sci Eng 124. https://doi.org/10.1088/1757-899X/124/1/012101 10. Telegin IV, Kozlov AM, Sakalo VI (2019) The analysis of the impact of technological processes of hot forging on the dynamics of the crank press. IOP Conf Ser Mater Sci Eng 483. https://doi.org/10.1088/1757-899X/483/1/012006 11. Telegin IV, Kozlov AM (2017) Sakalo VI (2017) Solid modeling and dynamic analysis of mechanisms of pressforging machines. Int Conf Ind Eng ICIE 206:1258–1263. https://doi. org/10.1016/j.proeng.2017.10.628 12. Bukarev IM, Babin DM (2016) Modeling of the process of die forging in DEFORM 3D and QFORM 3D. https://studvesna.ru/db_files/articles/179/article.pdf. Accessed 02 Oct 2016 13. Telegin V, Telegin I (2019) Solid modeling in professional training of specialists for machine-building enterprises. Int J Innovat Technol Exploring Eng 8(9S3), Retrieval Number: I30020789S319/19. https://doi.org/10.35940/ijitee.I3002.0789S319 14. Telegin VV, Telegin IV, Kirichek AV (2019) Solid-state modeling and basic training of specialists in the field of mechanical engineering. IOP Conf Ser Mater Sci Eng 483:012004. https://doi.org/10.1088/1757-899X/483/1/012004 15. Telegin VV, Kozlov AM, Kirichek AV (2019) Solid modeling in Autodesk Inventor at initial stage of training of specialists in field mechanical engineering. In: Radionov A, Kravchenko O, Guzeev V, Rozhdestvenskiy Y (eds) Proceedings of the 4th international conference on industrial engineering. ICIE 2018. Lecture notes in mechanical engineering. Springer, Cham, pp 1241–1247. https://doi.org/10.1007/978-3-319-95630-5_130 16. Biba NV (2001) Development and application of QForm2D/3D three-dimensional punching simulation software. CAD and Graphics 9:18–19 17. Filippova MV, Temlyants MV, Pertyatko VN, Smetanin SV (2016) Modeling in QForm-3d stamping of a gear from a ball processing. Preparatory Production in Engineering 8:14–18 18. Vakalov AA (2016) Application of computer simulation programs in the development of processes of hot stamping of blade blanks. https://www.qform3d.ru/files_ru/2011_0002.pdf. Accessed 01 Oct 2016 19. Telegin IV, Volodin IM (2014) Forgings are round in plan (axisymmetric). Metal analysis. RU Patent: Certificate of state registration of a computer program 2014661697. 20. Telegin IV (2016) Hot Die Forging. Calculation of tool parameters. RU Patent: Certificate of state registration of a computer program 2016660707

The Express-Method for Determining the Workability of Structural Steels Using the Indicator of Specific Cutting Work A. V. Karpov(B) The Murom Institute (branch) of the Federal State Budgetary Educational Institution of Higher Professional Education, The Vladimir State University Named After Alexander and Nikolay Stoletovs, 23, Orlovskaya street, Murom 602264, Russia [email protected]

Abstract. The article is devoted to the problem of understanding and determination of one of the most important technological properties of structural engineering materials—their workability by cutting and rational technological conditions for cutting based on energy criteria of specific cutting work. Classical methods for determining workability are based on long-term and expensive resistance tests aimed at establishing the maximum cutting speed under reference conditions. In practice, the true values of the material workability coefficients may differ significantly from the tabular ones due to the spread of properties between nominally similar billets within the batch or between batches of billets, and often the values of these properties are not guaranteed or are not known at all. In this regard, reliable express-methods for determining the true workability are relevant for the mechanical engineering, allowing to establish rational processing modes and geometric parameters of the cutting tools. On the example of ISO-P structural steel cutting, the article shows that such express-methods can be based on the energy regularities of the chip formation process. The workability coefficients of widely used materials obtained in the standard test conditions differ from the corresponding reference values by no more than 6–8%, which allows us to conclude that the correct express-method for determining the true workability of structural steels in production conditions is obtained. Keywords: Structural steels · Workability · Material cutting · Power efficiency · Cutting work · Cutting power · Resistance tests

1 Introduction An important characteristic of modern structural materials is their workability by cutting, the qualitative and quantitative determination of which in mechanical engineering technology is associated with certain difficulties and allows for invariance of approaches [1–4]. Workability, in the most general sense, characterizes the ability of a material to undergo cutting, i.e., deep plastic deformation and destruction of continuity due to the © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_53

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introduction of a cutting wedge, chip separation, and the formation of a new surface of certain shapes, sizes, accuracy, and quality. In the first approximation, the workability is judged by the type, shape, fragmentation, and transportability of the chips formed during material cutting, or the presence or absence of tumors, notch wear, chipping, and other defects of the blade reference tool, as well as on the achievable surface quality in reference conditions [2]. It is impossible to quantitatively characterize the workability of any one or more indicators of material properties (tensile and shear strength, true yield strength, hardness, relative elongation, relative transverse contraction, impact strength, specific heat capacity, thermal conductivity, etc.), since they manifest themselves in a complex, complex and not fully elucidated mechanism of mutual influence during cutting [5–7]. Cited in reference literature values of workability coefficients (K C ) of different materials (let’s call them reference or tabular values) derived by the so-called classical method—as a result of long resistance tests aimed at establishing the values of cutting speed vC60 , m/min, a given material at which the reference tool in a reference condition has a durability T = 60 min, and relating this speed to the speed of cutting vCref 60 , m/min, reference material (steel 1045, CMC 01.2, σ = 650 MPa, HB 179) under the same conditions [3, 8, 9]. The classical method of resistance testing is regulated by the ISO 3685:1993 standard and is used mainly for new structural materials. Tabular values of K C are used in the technological practice of machine-building enterprises to calculate the optimal cutting speed of blanks from the corresponding material. The true values of workability differ from the reference values in one way or another due to the spread of physical, mechanical, and thermophysical properties of the material among different workpieces within a batch, or between batches of workpieces. In individual and repair production, often the values of material properties are not guaranteed or are not known at all. This variation is caused, for example, by any deviations from the nominal technological conditions of the previous forming and heat treatment of workpieces (casting, forging, hot stamping, welding, cutting, annealing, normalization, tempering, aging, cementation), the actual conditions of their storage and other random factors [5, 10, 11]. Therefore, the use of tabular values of K C coefficients inevitably leads to an error in optimal cutting speed setting, and as a result, leads to a decrease in the actual tool life, or to underutilization of its resource and an unjustified decrease in productivity. Carrying out long-term resistance tests to establish the workability of the material from each batch of blanks in the conditions of the enterprise is difficult to implement and economically impractical. In machine-building practice, it is important to have reliable express-methods for rapid determination of workability, allowing for each workpiece or each batch of workpieces to assign or adjust technological modes from the standpoint of full use of the cutting tool, ensuring maximum productivity and quality of cutting.

2 Purpose of Research On the basis of geometric, kinematic, and energy laws of the cutting process, we are going to develop and test an express-method for determining the workability of structural materials, which, due to its reliability and simplicity, would be implemented in

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455

production and used for a reasonable purpose (correction) of technological modes for processing workpieces in conditions of instability or uncertainty of the true values of their physical, mechanical, and thermophysical properties.

3 Results and Discussion The key issue is the interpretation of the concept of workability of structural material, or rather—the most correct understanding of this term from the standpoint of the laws of the cutting process. Tabular workability coefficients values K C of various structural materials, which are available in the reference literature [1, 2, 12], were obtained experimentally using reference turning tools. It is indicated that K C values can be used to calculate the optimal cutting speed not only for turning, but also for other types of material processing [13]. The latter statement is doubtful, since each type of processing is based on a particular method of shaping with its inherent geometric, kinematic, and energy patterns. When performing classical resistance tests on the workability of a material, the cutting speed was set corresponding to the 60 min resistance of the reference tool, while the standard period of economic resistance of real blade tools can differ significantly from 60 min and depends on the type of production, the purpose of the technological transition (roughing, semi-finishing, finishing), the presence or absence of coolant, technical characteristics, and equipment capabilities. Thus, the concept of workability cannot be interpreted solely as a permanent property of the structural material in isolation from the specific type and conditions of processing. Workability should be understood in a complex way: both as a characteristic of the material, depending on its properties, and as a characteristic of the technological impact on the material. However, this does not mean that the K C values must be determined individually for each type of cutting, which would require creating and standardizing not only reference turning tools, but also reference drills, milling cutters, broaches, taps, etc., and the tests themselves for workability would turn into a meaningless series of expensive experiments of the same type. It is more expedient to formulate a qualitative classification feature, according to which the variety of existing types of processing materials with blade tools could be divided into a number of groups depending on the kinematics of cutting and geometric features of the contact of the cutting blade with the workpiece. The role of such a classification feature can be a pattern of changes in the cutting power P during the working stroke of the tool τ [14]. It is possible to formulate at least four typical schemes of power change over time P = P(τ ) for known types of cutting (Table 1). If, when determining the workability of different materials, the quantitative factors of the cutting process (cutting depth, cutting speed, feed rate, tool material grade, geometric parameters of the cutting part of the tool, etc.) are made the same (reference), then the proposed schemes for changing the power over time will act as a characteristic of the type of processing that affects the workability due to its geometric, kinematic, and energy patterns. These schemes were used by us when creating express-methods for determining the workability of structural carbon and alloy ISO-P steels. The known express-methods for determining workability include the A.S. Kondratov method, the equivalent wear intensity method, and the face turning or conical turning

Cutting power increases intensively up to the maximum value and then the one decreases monotonically

Cutting power increases monotonically up to the maximum value and then the one decreases rapidly

Steady mode (cutting power is constant)

Regularity of changes in cutting power over time of cutting

P

Pmax

P

P max

P

P

τc

τc

τc

τ

τ

τ

Typical scheme for measuring cutting power over time

Face turning to the center of the workpiece; cross-section with a cutter; feed milling

Face turning from the center of the workpiece; axial processing of holes; milling against feed; gear milling with a disk cutter

Longitudinal cylindrical turning; drilling; planing and slotting on machines with hydraulic or rack-and-pinion drive; threading with cutters

Types of blade processing

Table 1. Typical schemes for changing the cutting power over time.

(continued)

1 · Pmax · τc = 2 = Pm · τc W0 =

1 · Pmax · τc = 2 = Pm · τc W0 =

W0 = P · τc

Cutting work W 0 during one cycle τ c of changing the cutting power

456 A. V. Karpov

Cutting power changes according to parabolic law

Regularity of changes in cutting power over time of cutting

P Pmax

τc τ

Typical scheme for measuring cutting power over time

Table 1. (continued) Cutting work W 0 during one cycle τ c of changing the cutting power

2 Planing and slotting on W0 = · Pmax · τc = machines with a rocker drive; 3 stretching and sewing; milling 4 mechanical symmetrical and = 3 · Pm · τc asymmetrical bilateral; substrobe; the finger gear milling and hobbing cutter

Types of blade processing

The Express-Method for Determining the Workability of Structural Steels 457

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A. V. Karpov

method, but all of them, like the classical method, are based on the construction of the diagram “resistance of the reference cutter—cutting speed”. Some researchers suggest limiting the quantitative evaluation of workability to a simple measurement of the tangential cutting force F t , N, or cutting power P, W. However, the F t and P values themselves do not fully characterize the cutting process, since they do not take into account the regularities of their change in time and the result of processing—the mass, volume of removed chips or the treated surfaces area. For the most complete assessment of workability, we propose an indicator of the specific cutting work e, J/mm3 , which includes a greater number of technological parameters and is equal to the ratio of the cutting work W c , J, performed by the reference cutting tool, to the result of this work—the volume of chips V, mm3 , during the working stroke [15, 16]. e=

60 · P Wc = V Q

(1)

where Q—chip production rate (minute chip removing), mm3 /min. Equation 1 allows you to calculate the specific cutting work e at a constant cutting power P over time (Table 1, diagram 1). If we take into account the factor of instability of the cutting power and its natural change P = P(τ ) according to one of the proposed typical schemes (Table 1, schemes 2–4), the calculated expression of the specific cutting work e takes the form [17] nc · W0 = e= V

60 · nc ·

τc 0

V

P(τ ) d τ =

60 · nc · kP · Pmax · τc 60 · kP · Pmax = V Q

(2)

where nc —the number of cycles of cutting power change P(τ ) during the working stroke; W 0 —the work performed by the reference tool during the time τ c , min, of one cycle of complete power change P(τ ); kP —the approximation coefficient that allows you to calculate the value of the W 0 as the area under the graph P = P(τ ) for the corresponding typical power change scheme (Table 1); Pmax —the maximum value of the cutting power for one cycle of its change. The specific cutting work e, J/mm3 , is the amount of energy spent by the cutting wedge on plastic deformation of the cut layer and separation as a chip of the material unit volume [18]. In the case of stabilizing processing modes (standard test conditions), specific cutting work can be considered as energy workability index that takes into account the mechanical and thermophysical material properties (in complex they are characterized by the value of cutting power P) and the processing result (minute chip removing Q) and also the characteristics of the cutting process (corresponding typical power change scheme and the approximation coefficient k P ) [18–20]. The smaller the value of the specific cutting work in the reference conditions means the better workability of the material. As in the case of classical resistance tests, it seems appropriate to correlate the value of the specific cutting work e, J/mm3 , of the material under test to the specific cutting work eref , J/mm3 , of the material taken as the reference one (steel 1045, CMC

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459

01.2, σ = 650 MPa, HB 179) KC =

eref e

(3)

Studies of the workability of materials K C using the index of specific cutting work e were carried out in relation to the semi-final turning of workpieces from six grades of carbon and alloy structural ISO-P group steels (Table 2). The reference tool was a turning cutter with an alloy plate NC3220, the front angle γ = + 5°, the rear angle α = 10°, the angles in the plan k r = k r1 = 45°, the angle of the cutting edge slope λ = 0°, the pick radius r ε = 0.8 mm. The value of the cutting power P, W, was fixed by the power consumption analyzer AR.5 M and the industrial power meter. The test procedure is described in more detail in [18–20]. Table 2. Workability coefficients of ISO-P group structural steels using the index of specific cutting work. Steel grade

CMC

Hardness HB

Tensile strength σ, MPa

Value of specific cutting work e, J/mm3

Value of workability coefficient K C , obtained as a result of classic resistance tests [1, 2]

Value of workability coefficient K C , obtained using the index of specific cutting work (Eq. 3)

1045 (G10450)

01.2

170–179

650

1.87

1.00

1.00

1060 (G10600)

01.3

235–241

690

2.53

0.70

0.74

1A (Gr.WCA, J02002)

06.1

120–126

420

1.13

1.50

1.65

5135 (G51350)

02.1

163

620

1.46

1.20

1.28

30ChGSA (30HGSA, 14,331)

02.1

225–229

720

2.92

0.70

0.64

4135 (G41350)

02.1

245

810

2.15

0.80

0.87

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The values of the workability coefficients of the ISO-P group steels specified in Table 2, obtained by the express-method using the specific cutting work index, differ from the values given in the reference literature [1, 2], and obtained as a result of other experimental studies [19, 20], by no more than 6–8%.

4 Conclusion The use of the indicator and a refined method for determining the specific cutting work (Eq. 2), allowed us to develop an express-method for determining the workability, which gives a stable convergence with reference values for structural steels of the ISO-P group. In conditions of dispersion or uncertainty of the actual values of the physical and mechanical properties of the processed materials, the proposed method avoids time-consuming resistance tests, which makes it suitable for production conditions at machine-building plants. Setting the actual value of the material workability coefficient makes it possible to assign or reasonably adjust the processing modes (first of all, the cutting speed) for each workpiece, or each batch of similar workpieces (forgings, castings, rolled products), ensuring the most complete use of the cutting tool resource. It is possible to determine the value of the specific work of cutting through the power indicators and minute chip removing on modern CNC machines or processing centers directly during the operation—during the working stroke of the tool. This makes it possible to monitor the current state of the workpiece, taking into account the variability of its physical and mechanical properties, and to implement adaptive control of technological processing modes via feedback channels in order to maintain rational cutting conditions corresponding to the current value of workability. The possibility of using an express-method for determining workability based on the index of specific cutting work for other groups of structural materials (corrosionresistant steels ISO-M, cast iron ISO-K, non-ferrous alloys ISO-N, heat-resistant alloys ISO-S, high-hardness materials ISO-H, composite materials ISO-O) requires additional verification.

References 1. Ordinartsev IA, Philippov GV, Shevchenko AN (1987) Spravochnik instrumentalschika (The toolmaker’s guide). Mashinostroenie, Leningrad 2. Kozhevnikov DV, Kirsanov SV (2012) Rezanie materialov (Metal cutting). Mashinostroenie, Moscow 3. Pikalov YY, Usov DA (2012) Obrabatyvaemost constructsionnykh materialov i sravnitelny analiz frezernogo instrumenta (Workability of structural materials and comparative analysis of milling tools). Vestnik mashinostroeniya, Moscow 4. Danilenko BD, Tiviriev EG (2015) Otsenka obrabatyvaemosti rezaniem constructsionnykh materialov (Evaluation of the workability of structural materials). Inzhenerny vestnik, Moscow 5. Ivanova VS (1979) Razrushenie metallov (The Destruction Of Metals). Metallurgia, Moscow 6. Turkovich BF, Calvos, (1968) Some applocations of physical metallurgy in metal cutting. Adv Mach Toll Des Resist 2:1051–1071

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7. Ramalingam S, Thomann B, Basu K, Hazra J (1975) The role of sulphide type and of refractory unclusions in the machinability of free cutting steels. Influence Metall Mach Am Soc Metals 1:111–129 8. Iwata K, Murotsu Y, Iwatsubo T, Fujii S (1972) A probabilistic approach to the determination of the optimum cutting conditions. J Transection ASME 4:137–146 9. Iwata K, Murotsu Y, Oba F (1977) Optimization of cutting condition for multipass operations considering probabilistic natur in machining processes. J Transection ASME 1:152–159 10. Black JT (1970) On the fundamental mechanism of large strain plastic deformation. Electron Microscopy Of Metal Cutting Chips, ASME, NY 11. Kunio U, Yuichi K (1984) Identification of chip formation mechanism through acoustic emission measurement. Ann CIRP 1:71–74 12. Trent EM, Wright PK (2000) Metal Cutting. Butterworth-Heinemann, Boston 13. Yashkov VA, Silin LV (2012) Internal grinding without thermal effects. Russ Eng Res 32:601– 603 14. Karpov AV (2019) K voprosu povyshenija energeticheskoi effectivnosti technologicheskih processov obrabotki rezaniem (To the issue of increase energy efficiency of technological processes of materials cutting). Sovremennye naukoemkie technologii, Moscow 15. Karpov AV (2012) Pokazateli energeticheskoi effectivnosti processa rezanija (Indicators of energy efficiency of the cutting process). Ser. Mashinostroenie, materialovedenie, Perm, Vestnik PNIPU 16. Karpov AV (2015a) Determining the effective conditions for machining fabrication procedures based on the cutting process energy patterns. Procedia Eng 129:116–120 17. Karpov AV (2015b) Towards energy intensity reduction of machining fabrication procedures. J Appl Mech Mater 756:111–115 18. Starkov VK (2009) Phisica i optimizaciya rezaniya materialov (Material cutting physics and optimization). Mashinostroenie, Moscow 19. Malashenko VM (2000) Snizhenie energeticheskikh zatrat pri naruzhnom prodolnom tochenii zagotovok na tokarnykh stankah (Reduction of energy costs for external longitudinal turning of workpieces on lathes). Dissertation. Bryansk State Technical University 20. Malashenko NA (2002) Snizhenie energeticheskikh zatrat pri obrabotke otverstiy rezcami i osevymi instrumentami (Reduction of energy costs when processing holes with cutters and axial tools). Dissertation. Bryansk State Technical University

Digital Space of Small Enterprises in Engineering V. F. Bulavin(B) , T. G. Bulavina, and A. S. Stepanov Vologda State University, 15, st. Lenin, Vologda 160000, Russia [email protected]

Abstract. One of the conditions for the transition of small enterprises to the digital design is the development of their information space. The said parameter is decisive for flexible production and responsible for increasing competitive advantages and accelerated access to the services market. The presence of digital imagery associated with PLM systems allows for the transition to a virtual type of production in conditions of the new economic framework. As a basis for teamwork, the PLM platform uses uniform rules to combine into a common information space a complete set of technical documentation: 3D models and 2D drawings, technical processes, as well as auxiliary attributes for project components. The electronic version of the documents acts as the main tool in the organization of parallel engineering, product modifications, as well as a means of coordinating all the chain links, from developer to consume. Keywords: Small enterprises · Digital technologies · PLM platforms · 3D model

1 Introduction New challenges of technological development are considered as driving factors for production and management spheres, and also determine all aspects of social and economic activities. Digitalization aims to boost the competitive level of goods and services, the quality of life, and ensure economic growth.

2 The Information Environment of the Enterprise Digital design reflects the technical section of the problem of small businesses production transition to virtual production based on innovative solutions and the producer’s information environment development. An integrated approach to the transition of production into the digital dimension involves the integration of research both technical and organizational, as well as economic, social, and psychological aspects [1–3].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_54

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Among foreign publications on the aspects of digital transformation in the fourth industrial period, one should note an academic study [2], which offers a six-level model of achievements in transforming the company and all business units into a new type of enterprise. A special place belongs to a report by Huawei and Oxford Economics [3], which outlines a new approach to measuring the real impact of the digital economy that, according to the authors, “reflects the value of the accompanying effects of digitalisation” and “the direct and indirect value arising from them” [3]. The principles of digital production are predominantly developed at large enterprises that have the required resources and capabilities. This process is also projected on growing small business in the engineering sector. Software and information support for automated preparation of production is an integral part of a common intellectual space within the network-based interaction of individual units. In the information field of the enterprise, the management of the production process is purposefully determined by the conditions of collective engineering and the level of access to individual parts of the project. This process results in the rising level of technological support in the field of organizational and managerial principles of production preparation. The complexity of design decisions in mechanical engineering, on the one hand, and the desire to improve the quality of design, on the other, determine the introduction of digital technologies in the field of design and technological support of production, ensuring flexibility of the company’s development strategy. These factors determine competitive advantages and meet the requirement of fast-track market entry. Electronic document flow in combination with innovative technologies in the organization of labor satisfies these conditions to the fullest. CAD, CAM, CAPP, CAE platforms based on 3D design protocols, with the support of reference data banks, expert and forecast-corrective analysis, serve as the basis for the implementation of Industrie 4.0 calls [1–3]. Directly in the field of design and production, the core of the information space is a set of software tools based on PLM ideology. The joint use of all format-compatible applications from this field allows for direct interaction in the chain: project manager– designer-developer–technologist–engineering calculations group–customer [4, 5].

3 Design Preparation of Production At the stage of design preparation of production, 3D model of the part becomes the pinnacle of digital design, as it forms the means of navigating the entire technological process (Fig. 1). Parameterisation allows, using a single design of a prototype to obtain configurations for similar parts. Mold-forming elements act as a means of filling the design and technological databases for subsequent projects [4–7]. Electronic models of assembly units and the whole product provide for the elimination of collisions and design errors, inspection of dimensional chains, and establishing tolerances using the principle of interchangeability of parts in a structure. An example of the implementation of CAD-technologies in the projects “Water disinfection module” and “Low-floor Trolleybus” is presented in Figs. 2 and 3. The source code provides for displaying the future product in 3D plane and in various projections, giving it a photorealistic image in accordance with the given material for a preliminary assessment of engineering, ergonomic and design solutions.

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Fig. 1. Solid-state digital model of the “Housing” part, a component of the optoelectronic device.

Fig. 2. Digitalised model of the product “Water disinfection module”.

4 Engineering of Parts and Assemblies The design phase of production preparation includes the study of product elements and assemblies in CAE applications for operability testing. Analysis of the stress–strain state of the part (assembly) under the static nature of the load enables detection of dangerous areas, cross-sections, and maximum deformations of the investigated construct, as well as the determination of the safety factor. A color legend visualizes simulation results [6–10]. Using the digital model, the developer can run experiments such as studies on stability, thermal deformations, cyclic loads. Figure 4 shows the result of modeling the stress–strain state of the part “Base plate”, a component of the optoelectronic device, when it is cooled to t = −50 °C. The deformation field indicates the achievement of critical values in the location zone (cutout A) of the block of coherent radiation generators. A flaw discovered at the

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Fig. 3. Digital layout of a low-floor trolleybus.

Fig. 4. a detail “Base plate” (alloy-AMg6); b detail “Base plate” when cooled to −50 °C.

design preparation stage required refinement of the part configuration and replacement of the material with the one having a lower coefficient of linear expansion.

5 Technological Preparation of Production The integrated use of digital technology involves the automation of technological support for production, which requires inclusion of CAM and CAPP platforms into the

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information flow. Functionality of CAM application ensures the design of the G-code for CNC equipment and machining centers when performing turning and milling operations for the designed product, in parallel simulating the metal processing of a part from a workpiece. Visual control of the technical process involves modeling the trajectory of the cutting tool, taking into account the movements of all executive and auxiliary pieces, identifying errors and collisions (Fig. 5). Criteria-based approach ensures identification of the optimal tool path.

Fig. 5. Visualization of the CNC processing of the “Frame” part.

During the technological preparation of production on the basis of the CAPP platform includes the design of technological processes for the operations of mechanical and heat treatment of parts, assembly of units and the structure as a whole. The functions of technological preparation include ensuring the manufacturability of parts and product design [4–6]. In the process of parallel engineering, interaction is carried out with group-based, standard, and unit-based technological processes. This serves as a basis for modernization of technologies for parts manufacturing and development of new technologies to meet the capabilities of existing equipment, for assignment of tools, specifications for the material and shape of the workpieces, and calculation of labor standards. CAPP complex provides for the formation of the entire package of technological documentation in automatic mode.

6 PLM Strategy The interconnection of digital models is reflected in the PLM platform, where the composition of the product tree is formed. Structured databases contain models, drawings,

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technology descriptions, supporting documents, and metadata. In the created databank, the designed product is stored as a virtual prototype, linked with the details and components present in the project. The digital set of documents formed in the PLM platform serves as the basis for the start of production, also acting as a logical link for the organization of collective work on the project. This concept presupposes organizational innovations regarding the enterprise’s functionality principles: quick and rational consideration of all changes, as well as the exchange of data of all participants, depending on the level of access [4, 5]. Integration of CAD, CAPP, PDM, ERP tools ensures implementation of end to end integrated software and information environment for better efficiency and flexibility of production preparation, which should be considered as factors of increasing labor productivity in the small business of the engineering industry [4–7]. The implementation of digital technologies in the legal field is based on international (national) standards, and in the technological field—on the segment of integrated computerized production.

7 Conclusions The formation of new competencies and accumulated experience allow us to proceed to the implementation of projects of a higher level, which acts as a growth driver for hightech industries. These factors tend to expand the scope of activities within the framework of compliance with international standards of the quality management system. The concept of a virtual enterprise is built in compliance to the strategy of ERP, MES, and PLM ideologies. The degree of implementation of innovative technologies in small businesses determines their level of competitive advantage and growth prospects in the transition to digital production. Strengthening the role of digital technology is necessary not only for the development of production, but also for marketing policy to increase the efficiency and growth of companies.

References 1. Sharonov A, Atnashev M et al (2017) Digital production. Methods, ecosystems, technologies. In: Working report of the corporate training department of the Moscow School of management SKOLKOVO. https://assets.fea.ru/uploads/fea/news/2017/11_november/17/tsifrovoe_ proizvodstvo_112017.pdf. Accessed Nov 2017 2. Schuh G, Anderl R et al (2018) Industrie 4.0 maturity index—managing the digital transformation of companies. In: The National academy of science and engineering of Germany. https://www.acatech.de/wp-content/uploads/2018/03/acatech_STUDIE_ Maturity_Index_eng_WEB.pdf. Accessed Mar 2018 3. Xu W, Cooper A et al (2017) Concomitant digitalization effect. Measuring the real impact of the digital economy. In: Presentation by Huawei and Oxford Economics. https://www.hua wei.com/minisite/gci/en/digital-spillover/index.html. Accessed 5 Sep 2017 4. Bulavin V, Yahrichev V, Stepanov A (2019) Politics of digital technologies in small machinebuilding enterprises. News High Edu Instit 9:35–45. Digital Technologies in Small Business of Machine-Building Industry CAD and Graphichttps://doi.org/10.18698/0536-1044-20199-35-45

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5. Bulavin V, Yahrichev V, Glazkov B (2018) PLM-strategy in small-scale production of machine-building industry. News High Edu Instit 8:37–49. Mashinostroeniehttps://doi.org/ 10.18698/0536-1044-2018-8-37-49 6. Bulavin V, Bulavina T, Yahrichev V (2017) Validation of CAD products in small enterprises of engineering sector. Fundam Appl Problems Eng Technol 5:64–72 7. Bulavin V, Yahrichev V (2018) Digital Technol Small Bus Mach-Build Ind CAD Graph 6:52–55 8. Bulavin V, Bulavina T, Yakhrichev V (2018) Engineering analysis and new technologies in the finite element method. Fundam Appl Problems Eng Technol 2(328):109–120 9. Alyamovskiy A (2010) Engineering calculations in solid works simulation. DMK-Press publ, Moscow 10. Zamriy A (2007) Practical training course. CAD/CAE ARM WinMachine System. DMK– Press publ., Moscow

Some Features of the Pisarenko–Lebedev Generalized Strength Criterion Application for Long-Term Strength Calculations A. V. Belov, A. A. Polivanov(B) , and N. G. Neumoina The Volgograd State Technical University, Kamishin Technological Institute (Branch), 6A, Lenin St., Kamishin 403874, Russia [email protected]

Abstract. The paper presents a method of describing the Pisarenko–Lebedev generalized long-term strength criterion. This method is used in determining the equivalent stress in the Yu. Rabotnov’s kinetic equation of damageability. To verify the accuracy of the calculation results obtained by the Pisarenko–Lebedev generalized long-term strength criterion and the offered method of its concretization, the calculations of destruction time of the rotating disk at a high-temperature are carried out. The simulation results obtained by this method differ from the experimental ones by 5%. These results are fairly reliable. Therefore, the proposed method determining the equivalent stress enables more accurate damage and time-to-rupture predictions, compared with other similar methods. Keywords: Destruction · Creep rupture strength · Rheology · Degradation of the mechanical properties

1 Introduction Ensuring the efficiency, durability, and reliability of various machines, devices, and structures operating under unsteady loading processes and under the influence of hightemperatures and an aggressive environment is an important engineering problem. As a rule, the reduction of the working life of such structures and its sudden failure is due to the degradation of the mechanical properties of materials during their operation. The geometric shape of these structures is quite complex, in most cases. It is in a complex and heterogeneous stress state and it is exposed to an aggressive environment of various types during an operation. As a result, the degradation of the material’s mechanical properties occurs, which is often latent until the moment of the structure destruction. Thus, the probability of an accident of such a structure due to its sudden destruction before the end of the design life is very high. As shown in [1], to solve this type of problem as accurately as possible, it is advisable to use an approach that is based on the continuum destruction mechanics. This approach has been used in solving many similar problems, for example [2]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_55

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As part of this approach, a numerical (scalar) damage parameter is introduced into the equations which determine the values of stresses and deformations in the structure. Its value changes from zero (the material is not damaged) to a value close to one (the material at this point is destroyed). For calculation of this parameter, the Yu. N. Rabotnov kinetic equation of damage [3], is used  Q σeq d ωC =C (1) dt 1 − ωC where: ωC —is the scalar damage parameter; C and Q—special parameters determined from long-term strength curves obtained from uniaxial tension tests of standard circular specimens at fixed temperatures; σ eq —equivalent stress, which is one of the long-term strength criteria. As a long-term strength criterion in (1) can be used [4, 5]. • maximum principal stress (the Johnson’s criterion): σeq = σ1

(2)

σeq = σi

(3)

σeq = 0, 5 · (σ1 + σi )

(4)

• stress intensity (the Katz’s criterion): • the Sdobyrev’s criterion: • the Trunin’s criterion: σeq = 0, 5 · (σ1 + σi ) · a

6σ0 1− σ +σ 1 i

(5)

• the Lebedev-Pisarenko criterion: σeq = χ (σi − σ1 ) + σ1

(6)

• the Lebedev-Pisarenko modified criterion: σeq = χ (τoct − σ1 ) + σ1

(7)

where: 0 —average stress; oct —octahedral shear stress; σ i —tangential  stress intensity, which, in a planar stressed state, is defined by the expression σi = σ12 − σ1 σ2 − σ22 ; σ 1 —main normal stress. When evaluating the long-term strength of a structure, the respective parameters a and can be found by testing the long-term strength of standard specimens subjected to uniaxial tension and compression, or by torsional testing of thin-walled tubular specimens. Finding the long-term strength criterion which most adequately describes the process of damage accumulation in a given structural element and at a given time is one of the important yet difficult to solve problems. There are many long-term strength criteria, but no accurate recommendations on its application, which is what makes this problem so difficult to solve. The authors suggest using the Pisarenko–Lebedev generalized strength criterion with a method for concretizing which was proposed in the [6, 7].

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2 Research Goal • The goal hereof is to: • selecting a method for determining the long-term strength criterion, which is used in calculating the equivalent stress in the Yu. N. Rabotnov kinetic equation of damageability; • realize the validation calculations of the destruction time of rotating flat disk for which there are corresponding experimental results; • based on these results, we can conclude about the accuracy of the offered method for selecting the long-term strength criterion.

3 Materials and Methods Determination of the stress–strain state of structures taking into account the material damageability in the creep is a problem covered in numerous papers. A more detailed review of these works is given in [7, 8]. Thus, it is established that under conditions of high-temperature creep of many structural materials, the following types of destruction are possible: • intragrain fracture, associated with shear deformations in grains (crystallites); • intragranular fracture, associated with the emergence and development of wedge shaped cracks on the grain joints; • intergranular fracture, associated with the formation and development of pores on grain boundaries. The first type of destruction prevails at high levels of stress and high strain rates. The level of stress intensity is significantly larger than the yield strength of the material. The second and third types of destruction prevail under the long-term effects of small loads that are less than the material elastic limit. It is related to the concentration of stresses along the grain boundaries, and the intensity of their flow depends on the level of the actual normal stresses. It was established experimentally that when the viscous destruction of decisive importance is the intensity of shear stresses, while brittle destruction is the level of active normal stress. Then the long-term strength criteria (2–7), are having a particular physical sense [9–11]. So, applying the Johnson criterion reflects the minimum calculated time to fracture (brittle destruction), but the Katz criterion reflects the maximum calculated time to fracture (plastic or viscous destruction) [9]. The Sdobyrev criterion is a halfsum of these two that these types of destruction develop simultaneously and are equally probable. So, these contributions to the overall process of destruction are the same. The generalized criteria (5–7), allow us to specify the share of particular types of destruction in the overall process of destruction, depending on the mechanical characteristics of the materials in each case. But, the parameters for these criteria are not available in the reference literature for most construction materials. Therefore, the usage of these criteria is difficult or impossible in calculations for long-term strength.

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Criteria (2–4), do not require additional data for its calculations, but it was built for a specific group of materials and particular deformation conditions. Therefore, different criteria for the same material and the same deformation conditions can produce different results, and there is no consensus on the reliability of these results. In this sense, when the use of such criteria, it is necessary to follow the recommendations of its authors in the first place. Thus, for a reliable description of the damage accumulation process in the material at creep in a complex stress state, the selected long-term strength criterion must correspond to the destruction type prevailing at the moment. The ranges of the transition between the destruction types should be determined by the results of metallographic studies, as presented in [12], or formed by the results of the statistical processing of experimental data. But currently, such information is not available for all materials and loading conditions. In [4, 5] and other works were shown that the ranges of the transition from plastic to brittle destruction can be determined from the value of the material yield strength, at a rough guess. To apply the long-term strength criteria in practical calculations, it is necessary to create a special algorithm. It should automatically select the most reliable long-term strength criterion, depending on the change in the material plastic properties at the creep. That algorithm is described in detail in [4, 5], and previous publications of the authors, such as [13], and can be presented as the following scheme: ⎧ a · σi , if σ0 < 0; ⎪ ⎪ ⎪ ⎨ σ , if σ > c · σ ; i i Y (8) σeq = ⎪ σ , if σ , < b · σ 1 i Y; ⎪ ⎪ ⎩ 0, 5 × (σ1 + σi ), if b · σY ≤ si ≤ c · σY . where σ Y —material yield strength. The first parameter (“a”) determined the change of σ eq under the action of compressive stresses, and the second and third parameters (“b” and “c”) are the ranges of transition between the brittle, mixed and plastic types of destruction. So, 0 ≤ a ≤ 1; 0,5 ≤ b < 1; 1 < c ≤ 1,5. Since at the time of development of this algorithm, the authors did not have the data to specify the generalized long-term strength criteria, it was not included in this algorithm. But the possibility of its use is provided. That method of determining the equivalent stress really allows increasing the reliability of the results and automating the transition between brittle and plastic types of destruction. But, the yield strength for many materials is a conditional value and cannot be considered a plasticity measure. Consequently, the results of calculations for long-term strength, obtained by this algorithm, cannot always be reliable. Therefore, the authors offered a simple and convenient to apply method to determine the equivalent stress, detailed in [7, 14]. Its essence lies in using the Pisarenko-Lebedev generalized long-term strength criterion in the following form: σeq = χ σi + (1 − χ ) · σ1 here χ is the material plasticity parameter [7].

(9)

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The parameter is the relative residual narrowing of a circular standard specimen, obtained by testing for creep and long-term strength at a fixed stress and temperature T. The possibility of this approach is due to the innumerable results of practical tests for creep and long-term strength, some of which were considered in this paper. Additionally, the authors conducted a study [7], which showed that the proposed option to concretize the Pisarenko–Lebedev generalized long-term strength criterion allows accounting for the altered plastic properties of the material (the embrittlement), which occurs in the development process of creep deformation.

4 Experimental Results The following step of research is to check the validity of the calculation results obtained by the Pisarenko–Lebedev generalized long-term strength criterion and the proposed method of its concretization. To carry out such a test, the experimental results of the creep and destruction of slim structures that represent shells of rotation are needed. In [6, 7], the calculations of time to failure a cylindrical shell under the action of internal pressure and a thin lamina with a round hole stretched by external radial forces are carried out. As an example, the creep and destruction of a rotating disk at a high-temperature will be analyzed in that work. Information about the destruction time and strain values at certain time moments are accessible for this experiment. The Steel R3 disk had the following dimensions: external diameter D = 280 mm; internal diameter d = 70 mm; wall thickness 22 mm. Calculations were made at a temperature T = 575 °C and a constant speed of 15,000 rpm. This natural experiment, the results of which are given in [15], by V. Rabinovich in the 1960s, was performed. The experiment’s goal was to study the strength of turbine disks operating at a creep and constant temperature. The geometric dimensions of the disk are shown in Fig. 1.

D = 280 mm Т = 575° С d = 70 mm

n = 1,5⋅104 min-1

Fig. 1. The geometric dimensions of the disk.

The goal of this task is to verify the validity of the proposed option for concretizing the Pisarenko–Lebedev generalized long-term strength criterion and the method for

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determining the stress–strain state shells under conditions of unsteady creep, taking into account the plastic deformations. For this purpose, the calculation results were compared with the data obtained at the tests for real disks. Mechanical characteristics of R3 steel are given in [15, 16]. So, in this work, the reliability of determining the time of the destruction of a rotating flat disk is estimated by comparing the experiment and calculations results. Analysis of the deformation development process and damage buildup of the disk will be studied by the authors in other papers in the future. The time to failure of the disk was obtained by the Johnson (2), Katz (3), Sdobyrev (4) long—term strength criteria, generalized Pisarenko–Lebedev criterion (9), and the algorithm for automatic criterion selection (8). Table 1 (column 2) shows the experimental values of the disk destruction time. It was obtained as a result of the two most successful experiments [15]. Columns 3–5 show the calculated results obtained by the long-term strength criteria (2–4) and algorithm (8); it was given in [4]. Column 6 shows the results obtained in this study by the criterion (9). Table 1. Results of V. Rabinovich experiment.

The time to failure (hours)

Experimental results

Calculation results σeq = σ1

σeq = 0, 5 · (σ1 + σi )

σ1 ≥ σeq ≥ σi

σeq = ψC σi + (1 − ψC ) · σ1

2878 2453

2010

5420

2286

2514

When comparing the experimental and calculated values of the disk destruction time shown in Table 1, the following conclusions were drawn: 1. The best coincidence of the calculated and experimental values of the failure time (an error of 5%) is provided by the Pisarenko–Lebedev generalized long-term strength criterion (9), and proposed method for its concretizing, given in this article and discussed in detail in [7]. 2. Using the automatically selected long-term strength criterion (which depends on the prevailing type of failure at this moment) according to the algorithm (8), allowed getting the result that differs from the experimental one by 14%. 3. Using the largest principal stress (Johnson criterion) as equivalent stress produces an underestimation of 25%, the estimated time to rupture, in comparison with the experiment. While the Sdobyrev criterion is overestimated the estimated time to rupture by more than two times. 4. The results of calculations were obtained by the Katz criterion are not shown in this study, as it returns a significantly inflated time to rupture of the disk.

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5 Conclusions Thus, in the course of the conducted scientific research, the reliability of the offered method for concretizing the Pisarenko–Lebedev generalized long-term strength criterion was affirmed. The obtained calculation results are good agreement with analogical experimental results. Consequently, that criterion provides the most accurate results of time to rupture predictions, compared with other long-term strength criteria, including a custom criterion which allows determining the equivalent stress automatically. However, this article considers only one characteristic of an experimental problem and one material. Thus, it is impossible to assert the universality of the considered long-term strength criterion only by these results. The research group behind this paper intends to continue out such research and will be grateful to all specialists who perform similar strength calculations of structures.

References 1. Khokhlov AV (2017) Criterion of destruction and long-term strength curves, generated by the defining relation of the nonlinear theory of heredity Yu. N. Rabotnov. Herald Mech Eng 6:39–46 2. Aliev MM, Shafieva SV, Gilyazova SR (2015) Criterion of long-term strength for materials of different resistance. Mater Sci Session Sci Almetyevsk State Oil Instit 1(1):254–257 3. Rabotnov YuN (1966) The creep of structural elements. Science, Moscow 4. Belov AV (1989) Axially symmetric elasto—plastic stressed—strained state of shells of rotation with an account of material damage at a creep. Dissertation, Kiev 5. Polivanov AA (2004) Axially symmetric elasto—plastic deformation of multilayered shells of rotation with an account of material damage at a creep. Dissertation, Volgograd 6. Belov AV, Neumoina NG, Polivanov AA (2019) About the choice of strength criterion in calculations for long-term strength in non-isothermal loading processes. Modern High Technol 1:20–25 7. Belov AV, Neumoina NG, Polivanov AA (2020) Selecting criterion of long-term strength in assessing durability of constructions operating under non-isothermal loading processes. Springer Nature Switzerland AG, p 209–216 8. Belov AV, Neumoina NG, Polivanov AA (2020) About the election strength criteria in calculations for long-term strength for non-isothermal processes of loading. J Phys: Conf Ser 1441 9. Shevchenko YuN, Terekhov RG, Braikovskaya NS, Zakharov SM (1994) Investigation of the processes of destruction of body elements as a result of material damage during creep. Appl Mech 30(4):21–30 10. Arutyunyan RA (2015) High-temperature embrittlement and long-term durability of metallic materials. Proc Russian Acad Sci. Solid Mech 2:96–105 11. Lebedev AA (2010) The development of theories of strength in the mechanics of materials. Strength Problems 5:127–146 12. Volegov PS, Gribov DS, Trusov PV (2015) Damage and destruction: an overview of experimental work. Phys Mesomech 18(3):11–24 13. Belov AV, Polivanov AA, Neumoina NG, Morozova EV (2018) Technique of engineering structures strength analysis taking into account damageability of materials during creep. In: Proceedings of the international conference actual issues of mechanical engineering (AIME 2018), p 406–411

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14. Belov AV, Neumoina NG (2014) On the use of Pisarenko-Lebedev generalized strength criterion in strength calculations for non-isothermal loading processes. International Journal of Applied and Basic Research 9:8–10 15. Rabinovich VP (1966) Creep of turbine disks. Engineering, Moscow 16. Pisarenko GS, Yakovlev AP, Matveev VV (2008) Materials Resistance Handbook. Delta, Kiev, p 816

Evaluation of the Impact of the Actual Geometry of the Planetary Gearing on Its Capabilities in the KISSSYS Program A. V. Plyasov(B) and N. N. Trushin Tula State University, 92, Lenin Avenue, Tula 300012, Russia [email protected]

Abstract. The main disadvantage of power transmission based on single and multiline planetary gears with an output to the carrier is a narrow range of reproducible transfer function in a single step, which is limiting their application area and requires the use of other technical solutions to the multiline transmission. The above drawback is completely eliminated in the new two-stepped indivisible multiline transmission 3 k-2 g-h with an input to the carrier via high-speed gear and output to a large central wheel. In article the main aspects affecting the efficiency and quality of links of multi-turn actuator on the basis of the indivisible two-stage planetary gear type 3 k-2 g-h and discrepancies in traditional and modern automatic design of the program complex of the company KissSoft AG, such as kinematic error, load distribution between rolling elements of bearings and satellites of the broadcast in question, as well as the formation of the contour of a tool constructed according to the profile of the wheel. Keywords: Quality indicators · Planetary gear · Initial contour · Gear tool · Reference dimensions · Center distance · Geometric synthesis

1 Introduction In the practice of computer-aided design of planetary gears using the 2 k-h, 3 k, and 3 k2 g-h schemes [1–3], the variety of existing and developing gear cutting tools that are applicable when cutting the gears of these gears is of great importance. For example, the design according to standards and technical regulations can be implemented in Compass 3D, KisssoftAG, APM Winmachine, etc. In some of them, it is also possible to model the operation of parts using the finite element method to refine the results. You do not need to pre-prepare models of parts for modeling in ANSYS, Comsol in Solidworks, or NASTRAN. However, the question arises as to how often the designer will be able to compare the results of research and database standards manually tabulated.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_56

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1.1 Problem Statement It is proposed to consider the main aspects of the influence of the tool parameters and deviations of the real geometry of wheels on the criteria of operability and quality of design calculations of the planetary transmission according to the 3k-2g-h scheme with two external and internal gears in the Kisssoft AG software package. The reason for this choice is due to a full set of tools of the software complex of this company, but the problem of modeling the engagement of wheels in the transmission is considered in a system with a drive body, a driver, coaxial shafts, axes for satellites, rolling bearings on which they are supported in the process of transmission, and conversion of motion. For example, the parameters of the wheels are taken from the approved parametric series developed at the Department “Design of machinery and machine parts” of Tulsu Doct. Techn. Professor Peter G. Sidorov [4–9], for multi-turn electric drives (Fig. 1), a valve with a retractable spindle of the pipeline [10–12].

Fig. 1. Electric drive with planetary gear 3 k-2 g-h in the section.

When creating parametric series, we took as a basis our own long-term experience in designing [3, 11] and studying planetary gears of employees of the Department of PMDM [3, 4, 6]: Kornyukhin I. F., Polosatov L. P., Krukov V. A., Plyasov A. V. and others. However, information about the available modern methods of design and toolmetrological support was limited, which did not allow us the advantages of Russian

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developments of drives with foreign analogues. For Fig. 1, the main type of multi-turn electric drive with two-stage planetary transmission 3k-2g-h is presented in the section that allows competent specialists in this field of machine science to immediately assess the quality of the drive’s superiority over many of the existing ones. When creating a drive model, we will rely on known regularities between the geometric parameters of the gearing, and very new ones, namely the gear ratio of the planetary transmission   zb2 · za1 zb1 b1 b1 1 = u · u = 1 + (1) uab12 b2 a1 h hb2 za1 zb2 · za1 − zb1 · za2 where za1 , za2 —the number of teeth of the small central wheel 8 i 18 (see Fig. 1), respectively, zb1 , zb2 —the number of teeth of the large Central wheels is 40 and 34 (see Fig. 1), respectively. 1.2 The Source Data of the Design Stage In the main window (source data) of the geometric calculation of one of the stages of the 3k-2g-h planetary transmission, shown in Fig. 2, specify only the basic parameters of the original contour of the cutting tool, and this module is 1 mm, profile angle is 20°, the coefficients of the bias source circuit for the Central wheel and the satellites and the degree of accuracy ISO 1328:1995—analogue of the standard GOST 1643–81. They are sufficient for carrying out a simplified calculation if you take a toothed rail in accordance with GOST 13,755–81 or an equivalent wheel as a cutting tool.

Fig. 2. Window for calculating the gearing geometry of the planetary gear stage.

However, in some cases, both in General mechanical engineering in the production of gearboxes, and in industrial machinery, especially in the automotive industry, machine

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tools, aircraft, oil and gas industry, etc., this simplification is undesirable, since the responsibility of the product with gears increases, and it is necessary to take into account the features of the real profile of the cutting tool. Therefore, in the source contour window, you can choose from four types of tools [13, 14], listed above—a worm cutter and a chisel. The result of forming the teeth of the Central wheels and the satellite in a hundred-night engagement can be viewed selectively in the visualization window or brought together in adjacent Windows to assess the quality, see Fig. 3.

Fig. 3. Envelope sections of an arbitrary tool using the envelope method for cutting 3 K-2 g-h planetary gear wheels: a Hob; b Cutter; c Cutter.

The database in the KISSsoft program for the tool is still limited, but can be supplemented through The KISSedit butt program on the basis of data from GOST 9323–79 and GOST 9324–80, etc., while DIN tools are presented. At the same time, in order to solve this problem quickly, there are four modes in this window: coefficients, diameter, etc., the following standards are presented for the initial contour: AGMA, JIS, DIN, and GOST [14–16].

2 Instrumental and Metrological Support The technological drawing of each Central wheel and satellites in Fig. 4, contains elements that provide information on tolerances and basic drawings of gears for forming working drawings and assembly for planetary transmission, see Fig. 5. These visualizations allow the designer, technologist, and metrologist to evaluate the quality of the future process according to standards at the design stage of the planetary transmission and preparation. But the real cutting tool is different or imposes a restriction, because to improve the quality of gear wheels it is necessary to change not only the height of the tooth profile angle and the radii of the transition, but the type of lateral profile as in the design stage of the wheels and turning tools. These include gear splitting of the inner teeth of the Central wheels and milling of the outer teeth of the 3 K-2 g-h planetary gear wheels. The formation of the side profile of the tool teeth can be carried out according to the drawing [13], uploaded in dxf format, to obtain a drawing (contour) of the edge of a special tool.

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Fig. 4. Diagram of the tooth lateral surface line drawing of the wheel.

Fig. 5. Drawing of one stage of planetary transmission 3 k-2 g-h.

At the finishing stage [13–15], grinding with an abrasive tool is carried out to reduce roughness, edit the profile after heat treatment hardening, but also offset the contact spot

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in the engagement of the wheels when working in the transmission in each of the 28 pairs of engagements. The reference dimensions are determined in accordance with standards with a lower and upper deviation [16–19], from the nominal value, which can be controlled in the drawing by setting the position of the tangent planes and surfaces of the measuring tool and rollers to the surfaces of the side profile of the teeth of the 3 K-2 g-h planetary gear wheels (see Fig. 5). All these parameters are presented in the Protocol for calculating the planetary transmission, a number of which can be prepared in a separate table in the process drawing (see Fig. 4), next to the other elements.

3 Simulation of Planetary Gear Operation When modeling the operation of a planetary transmission as part of a universal drive [20], an analysis of contact bending stresses was performed to determine the coefficients of load distribution between the teeth, along the tooth, and satellites, taking into account the deviation of the axes (see Fig. 6), from the nominal (parallel) position and the error of the axis pitch on the driver from the drawing and its deformations under load. It is also necessary to take into account the dynamics of the planar transmission operation in the universal drive [21–23], according to its loading diagram. To confirm the successful simulation of the involute gearing of the 3K-2g-h planetary transmission, we can note an increase in efficiency, determined by modeling the operation of a mechanical drive system based on the 3K-2g-h planetary transmission in the KISSsys program, as a result of improving the quality of its gears with a modified involute profile. When computer modeling, you can take into account the deviation of the side gap according to the standard [16–19]: GOST1643-81, DIN3967, ISO1328 (UNI 7880), DIN 58,405, ISO 23,509 and the center distance (see Fig. 4), which will allow us to consider the actual gearing of all the Central wheels with satellites simultaneously, taking into account the skew. In this case, the angular misalignment of the single-ring satellites relative to the wheels is allowed by the design (see Fig. 1) to reduce excess connections due to self-aligning spherical bearings. In most cases, the monitoring of the state of the wheel interface is considered in a stationary mode, which is unusual for some modern automatically regulated mechanical devices when taking into account the changes in the external load. There are variants of perspective hydro-mechanical devices [24], in which the kinematic and power parameters of the planar transmission are changed regularly, for example, after the reverse, the idling of the Executive body and the hydraulic shock in the pipeline lines.

4 Conclusion Therefore, we can conclude that there is a system approach that allows us to cover a variety of possible conditions for the formation of engagement to assess the actual quality of engagement in the design, manufacture, control of the surface condition, and operation of the planetary transmission 3 k-2 g-h drive and its operation in the appropriate climatic conditions.

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Fig. 6. Taking into account the position of the wheel axes and satellites for load distribution.

References 1. Kudryavcev VN et al (1977) Planetary gearings: handbook. Mashinostroenie, Leningrad (in Russian) 2. Bolotovsky IA, Bezrukov VI, Vasilieva OF et al (1986) Handbook of geometric calculation of involute gears and worm gears. Mashinostroenie, Moscow (in Russian) 3. Sidorov PG, Kozlov SV, Krukov VA et al (1995) Power gear transmissions of coal combines. Theory and design mechanical engineering, Mashinostroenie, Moscow (in Russian) 4. Krukov VA, Preis VV (2004) Construction of the drive of the Executive organs of a rotary technological machine taking into account the power balancing. In: Machinostronie and technosphere of the XXI century. Collection of MNTC DSTU, Donetsk, Ukraine, p 121–124 (in Russian) 5. Timofeev GA, Musatov AK, Popov SA et al (2016) Theory of mechanisms and machines. Bauman MSTU, Moscow (in Russian) 6. Sidorov PG, Plyasov AV et al (2004) Substantiation of the pair-meters of internal gearing of plus planetary drives of shut-off valves of pipeline transport. Mach Sci Syst Drives Mach Parts. Bul TSU 1:41–51 ((in Russian))

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7. Sidorov PG, Krukov VA, Plyasov AV (2006) New system for calculating the geometry of an internal involute gear en-gagement. Bul TSU. Ser: Mach Sci Drive Syst Mach Parts 3:23–35 (in Russian) 8. Sidorov PG, Krukov VA, Plyasov AV, at al, (2009) Synthesis of internal involute couplings of planetary transmissions. Russ Eng Res 29–6:531–537 (in Russian) 9. Krukov VA, Nguyen DT, Plyasov AV (2019) Geometrical synthesis of four-bar gear train with related gears. J Phys: Conf Ser 1260:112017. https://doi.org/10.1088/1742-6596/1260/ 11/112017 10. Sidorov PG, Pashin AA, Plyasov AV et al (2010) Two-stage planetary transmission. PCT Patent 2402707, 27 Octob 2010 (in Russian) 11. Sidorov PG, Pashin AA, Plyasov AV (2011) Multithreaded gear transmissions: theory and design methodology. Mashinostroenie, Moscow (in Russian) 12. Sidorov PG, Raspopov VYa, Plyasov AV et al (2011) Universal high-torque multi-turn electric actuator for shut-off valves of pipeline transport. PCT Patent 2457385, 30 May 2011 (in Russian) 13. Boriskin OI, Khludov SYa, Stakhanov NG, Yakushenkov AV, (2012) Features of forming a profile of a part outlined by arcs of a circle with rack and worm tools. Fundam Appl Problems Eng Technol 2–6(292):17–23 (in Russian) 14. Boriskin OI, Stakhanov NG, Khludov SYa, Yakushenkov AV, (2012) Obkatochny tool: processing of separate sections of the profile. Bul TulSU. Techn Sci 8:30–33 (in Russian) 15. Boriskin OI, Khludov SYa, Boriskina MO, Khludov AS, (2012) Experimental determination of the error of forming internal involute teeth of a part with centering on the surface of depressions. Bul TSU. Techn Sci 8:48–54 (in Russian) 16. Timofeev BP, Abramchuk MV (2013) To a new level of accuracy of domestic gears, gears and redactors. Eng Technol 1:64–68 (in Russian) 17. Timofeev BP, Novikov DV (2013) Improving the quality of gears and gears by developing new standards. Devices 9(159):37–40 (in Russian) 18. Timofeev BP, Abramchuk MV (2007) Problems of compliance of standards of accuracy of the lateral gap of gears and gears in GOST 1643–81 to ISO recommendations. In: Fundamental and applied problems of reliability and diagnostics of machines and mechanisms Eighth session of the international scientific school, Russia, p 262–264 (in Russian) 19. Timofeev BP, Abramchuk MV (2007) Comparison of table values of precision parameters of gears and gears in standards: ISO 1328 and GOST 1643–81. Theory of Mechanisms and Machines 5–1(9):60–70 (in Russian) 20. Alaluev RV, Plyasov AV, Raspopov VYa, et al (2012) Test results of a multi-turn electric drive for controlling shut-off valves of pipe-line transport. Fundam Appl Problems Eng Technol 5(295):125–135 (in Russian) 21. Kryukov VA, Plyasov AV (2019) Reducing the level of vibration in two-stream spur gear. Lecture Notes in Mechanical Engineering 9783319956299:499–507. https://doi.org/10.1007/ 978-3-319-95630-5_52 22. Kryukov VA, Saveljeva LV (2015) The choice of law of variation mesh stiffness in gear trains dynamic simulation. Bul TSU Tech Sci 11–1:65–70 (in Russian) 23. Kryukov VA, Saveljeva LV (2016) Reduction of dynamic loads in multiple-stream mechanisms. In: Yacun SF (ed) Vibration-2016: XII international scientific and technical conference on vibration technologies, mechatronics and control machines. Kursk, Russia (in Russian) 24. Antsev VYu, Trushin NN (2018) Hydro-mechanical transmission. PCT patent 2695477, 23.07.2019 (in Russian)

Predictive Simulation Tool for Control Over Precision of Geometrically Complex Mould Making at Preproduction Engineering Stage S. Lukina1(B) , S. Ivannikov2 , and M. Krutyakova2 1 Moscow State University of Tehnology STANKIN, 3a Vadkovsky, Moscow 127055, Russia

[email protected] 2 Moscow Polytechnic University, 38 B, Semyonovskaya St, Moscow 107023, Russia

Abstract. The article suggests a new method of controlling the precision of geometrically complex mould making, improving the quality of machine tool systems at the preproduction engineering stage. The method is based upon a developed set of predictive simulation tools, consisting of a total of mathematical, virtual, and simulation models, describing the process of geometrically complex mould making. A conceptual solution for the problem of control on geometrically complex mould making combines two methods. The first is the analytical generation of various structural & geometrical combinations of the elements of industrial process systems providing geometrically complex mould making. The second method implies the geometrical realization of a spatial virtual simulation model for geometrically complex mould making. The mathematical simulation of geometrically complex mould making is implemented for a free spatial camming surface represented by a total of a set of guideways and a set of generatrices. The error of metal treatment of an arbitrary surface point is defined by the difference of the radius vectors of the actual and set positions of the tool contact point and the workpiece treated surface. The control over the precision of geometrically complex mould making is implemented by means of the conditions, providing the location of a resulting error vector inside a computational region of the machine operation area by searching for an optimal combination of industrial, structural and operation parameters at the stage of project design of the elements of the industrial process metal treatment system. Keywords: Predictive simulation · Geometrically complex moulding making · Precision control

1 Introduction Modern state and trends of production development are characterized by increased requirements towards the metal treatment precision and quality, conditioned by the development and research of new materials, production machines and units [1–3]. Improving © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_57

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the service life, velocities and production efficiency, reducing weight and dimensions, as well as increasing the measurement precision are the main areas in the upgrade of industrial processing machines, treatment and measurement tools. That is why one of the advanced areas for developing applied research is making up and researching precision industrial process systems with various intended uses [3–10]. Machining is applied for treating various kinematic pairs, which make up a core of modern machines and mechanisms with such parameters that cannot be achieved by no methods but machining. Now the theoretical ultimate precision of the machined surfaces is determined by the dimension allowances by IT2-IT4 at the deviation from flatness 0.2 ÷ 2 um, deviation from circularity 0.2 ÷ 1 um, and roughness deviation to Ra 0.0075 ÷ 0.1 um. Today most research and development in the area of industrial process systems are developing toward its element upgrade: equipment and tools [1, 11–13]. Thus, for example, to improve treatment precision, metal treatment equipment was changed from precision to high-precision one, equipped with software control and regulated by the means of active control over treatment precision and quality. The structures of cutting and abrasive tools are developed in compliance with the principle of using the high-precision control elements of the positions of cutting edge points and new tooling materials. Alongside with a large number of research in the area of generating and developing precision industrial process systems, one can observe a vast scatter of the results, obtained by various applied sciences, which frequently halts using such results in allied scientific areas, significantly complicating or even making impossible their application. The increased interest of scientists towards precise industrial process systems is connected with the fact that the precision range requires new engineering technologies and corresponding specialized production equipment and tools. Today the key trend in the development of technology of design and making the machines and mechanisms with various intended uses is the development of algorithms and tools of predictive simulation [8, 12–14]. This trend in its turn causes the necessity of generating and improving the methods and software complexes, based upon optimal algorithms of information structuring, searching and treatment [2, 4, 7–9, 12, 14–18]. Predictive simulation is the tool providing the competitiveness of modern society and state. The key reason is the increasing performance and economic efficiency of a mathematical simulation comparing with natural tests. On the basis of the conducted review and analysis of available references, the authors draw a conclusion that the conceptual way of resolving the problem of control over the precision of generated machine systems can be the development of predictive simulation tools for defining mould making error. Such approach of simulating the mechanism of occurring errors in the elements of the industrial process system allows developing the algorithm of controlling the precision by changing structural, geometrical, physical and technical operation, and other parameters of elements. The purpose of the paper is developing the method for control of the precision of geometrically complex mould making at the stage of preproduction engineering by means of developing a set of predictive simulation tools. To that end, the research team sets forth the following research objectives in the paper:

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• Develop a set of predictive simulation tools, necessary for resolving the set research objective. • Appraise a developed set by the design basis justification of real structures of multiaxial machines.

2 Key Method Provisions The paper suggests a new approach to the control of geometrically complex mould making on the basis of the development of a set of predictive simulation tools, improving the quality of designed machine systems at the stage of preproduction engineering. The paper considers a tool of predictive simulation tools as a set of mathematical, virtual, and imitation models, describing the process of geometrically complex mould making. A conceptual solution of the problem of the control over geometrically complex mould making is presented in the form of two combined directions: • Analytical generation of the options of structural and geometrical combinations of industrial process systems, providing geometrically complex mould making • Geometric realization of a spatial virtual simulation model for geometrically complex mould making, which allows developing a set of ways and methods of its research and using control to reach a set precision level. In this paper, mathematical simulation of geometrically complex mould making is implemented for free spatial camming surface, presented as a combination of a total of guideways F(x, y, z) and a set of generatrices G(x, y, z). S(x, y, z) = F(x, y, z) ∪ G(x, y, z)

(1)

here F(x, y, z) = 0; G(x, y, z) = 0. The number of possible combinations F and G is defined by a direct product of sets. MF · MG = MS

(2)

where MF → ∞; MG → ∞; ⇒ MS → ∞. The position of an arbitrary point M o (x o , yo , zo ) of a regular curve or the surface of a machined part is set with the help of a system of mutually transverse unit vectors: no —unit vector of a normal of the curve L in M o ; bo —unit vector of a bi-normal of the curve L in M o ; to —unit vector of the tangential curve L in M o (Fig. 1). To describe the current movement between anchor points for any surface, expressed by the expressions (1–2), it is required to introduce the matrix Mt (t) [4 × 4], defining the current position of the system of mutually transverse unit vectors in the part coordinate system. The elements of the matrix Mt (t) are time functions.    Lt (t) Rt (t)    (3) Mt (t) =  0 1 

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Fig. 1. Position of the arbitrary point M o of a regular curve L.

where Lt (t)—matrix [3 × 3] of guiding cosines of transforming the system of coordinates of the surface tnbp into the coordinates of the tool system tnbc ; Rt (t) = [t t , nt , bt ]—vector, defining the position of the center of the system of transverse unit vectors tnbp in the tool coordinate system tnbc . In this case, the error of metal treatment of an arbitrary surface point can be defined by the difference of radius vectors of the actual ra and set positions rs of the tool contact point and the machined workpiece surface: δ = |ra − rs |

(4)

The influence of secondary instrument errors on the final mould making precision, normalized by the allowance G, is formalized. It is established that the error vector of mould making r is connected to the standard allowance G by the dependences of the type.

G≥δ=

r · N   = r · e N 

(5)

where e—unit normal vector; δ—treatment error, defined by the error vector projection r on the normal vector N. In compliance with the developed method, the control of the precision of geometrically complex mould making consists of forming such conditions (3–4), providing for the location of the resulting error vector r inside the computational region of the operating area (5), by searching for an optimal combination of interconnected industrial, structural, and operation parameters at the stage of the project design of a machine system [10].

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3 Method Implementation The developed method is practically implemented by the example of controlling the precision of geometrically complex mould making at the stage of preproduction engineering of multiaxial machines. An early design stage is the most responsible one as the correct selection of mould making systems of multiaxial machines defines the precision of geometrically complex surface treatment at other early conditions. At the construction of machine equipment, as a rule, one is guided by the expertise, existing structures of similar machines, and one’s own intuition. The problem of selecting an optimal option of mould making systems of multiaxial machines is complex and intricate, requiring to take into account multiple structural and technological constraints, the resolving of which involves predictive simulation tools and formal support of engineering designs acceptance. The machine synthesis sequence at the preproduction engineering was represented by the following stages: • Forming a set of options of structural machine layouts • Making up initial 3D–geometrical image for each variant of the machine structural layout • Forming a computational region of the machine operation space • Forming a computational region of the permitted, in compliance to (5), provisions of the resulting error vector inside a computational region of the operating space • Comparative computational analysis and parametric synthesis of the machine layout options. The graphic representation of numerical evaluations of the designed machine in a spatial geometrical form, built in the CAD environment of geometric simulation, and their visualization at the computer display allows developing the best design solutions in terms of their precision. This is implemented by means of comparison of the options of locating the resulting vector of the error r inside a computational region of the machine operation space (Fig. 2). The validity of the developed methods and models is confirmed by simulation experiments and the data of natural tests of serial samples of multiaxial machines. The example of implementing the method of control of the precision of geometrically complex mould making on the basis of 3D simulation with the directed forming of an optimal trajectory of tool movement, calculated with the account of mathematical models (1–5) and implemented as software with API macros, is given in Fig. 3. The authors manage to resolve the problem of selecting the elements of the industrial process system for metal treatment, providing for machining a part made of silumin with the precision within the allowed limits. The motion kinematics was simulated in the environment MashSim_adapt, which provides a full visualization of machining and allows tracking the correctness of the control programme being formed for achieving the set precision of mould making.

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Fig. 2. a draft 3D project of the option of a structural layout of a 5-axial machine; b the options of locating the resulting vector of the error inside a computational region of the machine operation space.

Fig. 3. a 3D geometrical model of the option of the layout of a 4-axial machine for machining the silumin part (b).

4 Conclusions The research has produced the following findings: 1. The control of the precision of mould making of geometrically complex surfaces at making precision machines should be conducted by the evaluation of the comparison of arrangement options of the resulting error vector inside a computational region of the machine operation space 2. A developed set of tools for the predictive simulation and control of the spatial precision of geometrically complex mould making, built in the CAD geometric simulation environment, can visualize the set and project results of the generated structural metric machine layout; thus, it can be applied to estimate the characteristics of the elements of industrial metal treatment systems during their design at preproduction engineering

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3. The efficiency of the developed set is defined by a high degree of its correspondence with the results of natural and lab experiments and the possibility of predicting the errors of free structure elements and configuration. Further research development is supposed to be the adaptation of a proposed new method for controlling the precision of geometrically complex mould making in hightech areas of engineering while manufacturing structurally complex parts with various intended uses.

References 1. Inasaki I, Tönshoff H, Howes T (1993) Abrasive machining in the future. CIRP Ann 42:723– 732 2. Hoda A (1993) Evolution and future perspectives of CAPP. CIRP Ann 42:739–751 3. Manaenkov I et al (2019) Forming and selection technique for optimal configuration of formshaping system for multiple-axis machining. In: Radionov A, Kravchenko O, Guzeev V, Rozhdestvenskiy Y (eds) ICIE’2018. 4th international conference on industrial engineering, Moscow, May 2018. Lecture notes in mechanical engineering. Springer, Cham, p 1919 4. Dimitriou V, Antoniadis A (2012) CAD-Based calculation of cutting force components in gear hobbing. J Manuf Sci Eng 134(3):031009. https://doi.org/10.1115/1.4006553 5. Lukina S et al (2019) Predictive modeling of design innovative solutions on tooling configurations at high-tech manufacturing companies. In: Radionov A, Kravchenko O, Guzeev V, Rozhdestvenskiy Y. (eds) ICIE’2018. 4th international conference on industrial engineering, Moscow, May 2018. Lecture notes in mechanical engineering. Springer, Cham, p 1885 6. Lukina S, Manaenkov I (2017) Methodology of multiaxial machines formats volumetric accuracy comparative evaluation. MATEC Web Conf 129:01046. https://doi.org/10.1051/ matecconf/201712901046 7. Mello CHP, Turrioni JB, Xavier AF et al (2012) Action research in industrial engineering: design organization proposal for its application. Prod J 1:1–13. https://doi.org/10.1590/S010365132011005000056 8. Rogalewicz M, Sika R (2016) Methodologies of knowledge discovery from data and data mining methods in mechanical engineering. Manag Prod Eng Rev 7:97–108. https://doi.org/ 10.1515/mper-2016-0040 9. Starzy´nska B, Hamrol A (2013) Excellence toolbox: Decision support system for quality tools and techniques selection and application. Total Quality Manag Bus Excellence 24:577–595. https://doi.org/10.1080/14783363.2012.669557 10. Trojanowska J et al (2018) A Methodology of improvement of manufacturing productivity through increasing operational efficiency of the production process. In: Hamrol A, Ciszak O, Legutko S, Jurczyk M (eds) Advances in manufacturing. Lecture notes in mechanical engineering, Springer, Cham, p 23 11. Argyris J, Litvin FL, Lian Q et al (1999) Determination of envelope to family of planar parametric curves and envelope singularities. Comput Methods Appl Mech Eng 75:175–187. https://doi.org/10.1016/S0045-7825(98)00367-3 12. Dimitriou V, Vidakis N, Antoniadis A (2006) Advanced computer aided design simulation of gear hobbing by means of three-dimensional kinematics modeling. J Manuf Sci Eng 129:911– 918. https://doi.org/10.1115/1.2738947 13. Lyashkov AA (2012) Shaping of harts with a helical surface by means of a disk mill. Russ Eng Res 32(4):404–406. https://doi.org/10.1016/j.proeng.2015.07.314

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14. Lukina S, Korshunova E, Dorozhkin I (2018) Methods of automated control over composition and structure of metalworking equipment. MATEC Web Conf 224:01095. https://doi.org/10. 1051/matecconf/201822401095 15. Lukina S, Korshunova E, Dobrolyubova M (2020) Planning methods of modernization of industrial enterprises using graph models. IOP Conf Ser Mater Sci Eng 709:044020. https:// doi.org/10.1088/1757-899X/709/4/044020 16. Wheaton J (1999) The non predictive part of predictive modeling. Catalog Age 12:128 17. Gonçalves R et al (2019) Model proposal to evaluate the quality of a production planning and control software in an industrial context. In: Trojanowska J, Ciszak O, Machado J, Pavlenko I (eds) MANUFACTURING’2019. Advances in manufacturing II. Lecture notes in mechanical engineering, Springer, Cham, p 38 18. Lyashkov A, Panchuk K (2015) Computer modeling of the pump screw and disc tool cross shaping process. Procedia Eng 113:174–180. https://doi.org/10.1016/j.proeng.2015.07.314

A Tool Management System Design Using Object-Oriented and Functional Modeling E. Krylov(B) , N. Kozlovtseva, and V. Barabanov Volgograd State Technical University, 28, Lenin avenue, Volgograd 400005, Russia [email protected]

Abstract. The article deals with the application of the methods of functional and object-oriented modeling with a focus on studying the effectiveness of tool management systems of intelligent production machines under high-variety machinery production conditions. The production processes functional models in the form of hierarchical structure and context diagrams, which formalize the sequence of technical equipment choice, are developed. The tool management system design begins with the analysis of its requirements and the construction of static structure diagrams—class diagrams. The authors consider the development of the rational selection and cutting tool control subsystem as an example of object-oriented programming task. The scientific research relevance of this topic has been substantiated and suitable monographs, articles, and regulations have been analyzed. The presented models make it possible to qualitatively evaluate the parameters of the developed or studied tool management system from various sides. In addition to the qualitative evaluation, a quantitative assessment of the information processing efficiency in the analyzed subsystems is being developed. Keywords: CNC machine · Tool management · IDEF0 · UML · Optimization

1 Introduction Most modern machinery industries produce small-lot products, and therefore, the readiness requirement for quick process equipment retooling is crucial for them when a new order is received. Under a market economy condition and dynamic pricing, enterprises need not only respond quickly to customer requirements, but also to produce quality products in the shortest possible time with a minimum prime cost. This is impeded by the notable time expenditures associated with the development of the flow process charts and operating technologies in small-lot and individual production. For complex shape products using new, as a rule tough to machine structural materials, the most laborious and nontrivial are the tasks of selecting and designing tooling (machine accessories, cutting and auxiliary tools) [1–6].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_58

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The implementation of the optimal procurement organization, supply, interworkshop transportation, installation, and active control of cutting tools (CT) is complicated by the fact that a considerable range of tooling from various domestic and foreign companies is used to fulfill the production order [7, 8]. To reduce the impact of these factors on the trouble free operation of the automated machinery’s tool management systems (TMS), it is necessary to conduct a complex cutting tool’s life cycle analysis due to various modeling methods with the aim to assess the quality of present TMS and search for ways to improve them. Issues of tool management systems rationalization for computer-integrated manufacturing were considered in the works of Lobanov [9], Kapitanov [10, 11], Simonov [12]. To achieve these objectives should be studied both the TMS connections with other units of a machinery production enterprise (warehouse systems, transportation services, etc.), and the internal structure and its subsystems interaction (tool diagnostics, failure accounting, processing parameters control, and correction).

2 Functional and Object-Oriented Modeling For research, we will use the following types of modeling: functional and object-oriented. The functional approach can be boiled down to the decomposition of the system into specific functions, for example, the system is divided into subsystems, which are divided into subfunctions, divided in into tasks, etc. As a functional analysis and design tool, the SADT (Structured Analysis and Design Technique) notation is the most common. Whils new systems development, SADT (IDEF0) is used to accurately determine the requirements for its functionality. In addition, IDEF0 can be used to analyze the functions performed by an already existing system. Model performed using IDEF0 contains a plurality of hierarchically arranged and interconnected diagrams [13]. Such models reflect most clearly the system functional structure: the actions performed and the relations between these actions. This allows tracing the interaction, logic, and structure of processes clearly. The main advantage of the functional approach is the ability to get, through its strictly regulated structure, the most complete information about each system. It can be used to identify all the shortcomings related to both the process as external factors: the duplication of functions, the absence of process regulating mechanisms, and the lack of conditional breakpoints. The advantages of functional modeling, as a rule, include: • Accurate and consistent results. • In-depth business processes analysis, possible problems identifying, discrepancies, and inaccuracies. • Universality of IDEF graphic languages, providing a description consistency and completeness. At the same time, there are certain disadvantages: • Analysis and model modification becomes difficult with the increase in the presentation levels number. • Rigid hierarchical structure does not always allow to fully reflect the internal interconnectedness of the system.

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Functional methods are most effective in the initial stages of research and design of automated systems, as they allow setting the most accurate and complete requirements for them. The main difference between functional and object-oriented design (OOD) is the way the system is decomposed. OOD uses object decomposition, in which the static structure of the system is described in terms of objects and relations between them, and the system behavior is described as the exchange of messages between objects. OOD is a methodology that combines the object decomposition process and the presentation of logical and physical, as well as static and dynamic models of the designed system [14]. UML (Unified Modeling Language) is not only a tool for creating visual models that should be uniformly understood by all developers involved in the project, but also a project communication tool. UML diagrams are created for system visualization from different points of view. For visual modeling on UML, eight kinds of diagrams are used, each of which contains specific elements. The main UML diagram is the Class diagram. This is the basis for code generation and the design main purpose. A great virtue is the ease of a design solution correcting in accordance with changing requirements, since in the dynamic construction of the model, there is no need for a complete restructuring inherent in the functional approach notation. In particular, the change of individual classes and the connections between them will not affect the general concept of the model. Also, the advantage of OOD can be considered the ability to automatically generate code based on UML models. OOD is notable for comparative ease of perception, visibility, and efficiency of models. The approach disadvantages include the possibility of certain types of diagrams misinterpretation and the inability to carry out a deep analysis of the processes. In sum, object-oriented modeling is best used for systems, the design of which does not require a detailed business processes analysis. We apply the described methods to research the TMS and its values for the enterprise. We begin with the production simulation by and large, and then we will consider decomposition levels containing the TMS. The functional model has a hierarchical structure presented in Fig. 1. Figures 2 and 3 shows the developed IDEF0 diagrams for the machining center TMS for computerintegrated manufacturing. The diagrams are made using ERwin Process Modeler software from Computer Associates BPWIN. In order to increase the information content in the complex of developed functional diagrams, different colors are used to designate arrows (links): green—for informational flows; blue—for material flows; red—to indicate regulations and standards; black—for technical documentation. The functional model has a hierarchical structure characterized by the alternation of documents and work. Sheet A-0 is a statement of the enterprise’s purpose. The initial data are design, technological and regulatory documentation for products. It is necessary to ensure the enterprise’s production competitiveness and get the maximum profit eventually [15, 16]. The next level of modeling (Fig. 2), itemizes the enterprise functions and is associated with the task structuring for the production design engineering, production, and realization of output. In the subsequent diagrams for each function of the enterprise structural unit (department, shop, area), new particular tasks are defined. Any material result is recorded by the relevant information presentation (reports, protocols). Thuswise, functional modeling covers all processes in the system under consideration and

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Fig. 1. Levels of decomposition in the functional model.

Fig. 2. First level of decomposition (A0).

allows revealing its functioning general patterns [17]. The set of tasks obtained as a result of modeling at various hierarchical levels with well-known connections between them makes it possible to significantly refine the understanding of an enterprise’s individual services work and form their optimization directions.

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Fig. 3. Cutting tool selection diagram (A313) [14].

We use a class diagram to simulate a static view of a system in a design sense. It is the most convenient way to describe the functional requirements for the system—the services it provides to the end user. The class diagram consists of the following set: • • • • • • • • • • •

List of CNC machines CNC machine Cutting tool remaining in stock Request for cutting tool delivery Cutting tool List of transducers List of tools-candidates Performance log Cutting tool performance statistics Workpiece Product.

Figure 4 shows the UML class diagram, which was developed by studying the TMS. The class name is given at the top compartment of the class rectangle. Class attributes or properties are recorded in the middle compartment of the class rectangle; for example, attributes for a product class will be Material, Product ID, Surface Geometry, Surface Quality, and Sizes. There is only one key attribute—the product ID. The operations or methods of the class are written in the bottom compartment of the rectangle. An operation is some kind of service provided by each instance of a class upon a specific requirement. The functional aspect of class behavior is characterized by the whole set of operations. For example, the class “Transducers” has four operations “Search by type of transducer()”, “Delete records()”, etc. Links that connect entities in the ER diagram are represented by associations between classes and reflect structural relationships between objects. Multiplicity of an association

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Fig. 4. Tool management system class diagram.

role is a number or expression whose value is a range of values indicating how many objects at one end of the association should correspond to each object at the opposite end of the association. These diagrams allow us to evaluate qualitatively the parameters of the tool management system being developed or studied from various angles.

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3 Evaluation of Information Processing Efficiency In addition to a qualitative assessment, it is necessary to develop mathematical relations that allow one to obtain an efficiency quantitative estimation of information processing performing in the analyzed subsystem [18]. Consider the machining center tool management system as one of the organizational and technological systems of a machine-building plant, which has a set of heterogeneous functions used at various stages of the product life cycle [19, 20]. To evaluate the functionality of the machining center TMS, let us present the set of functions performed by it in the form of directed graph (Fig. 5). The vertices of the graph are the TMS functions, and the directed edges determine the sequence of these functions execution.

Fig. 5. Directed graph of machining center TMS’s functions.

Figure 5 identifies the following TMS functions: tool input control (1), assembly (2), tool setting (3), coding (4), storage (5), palletizing (6), automatic transportation (7), manual transportation (8), workpiece storage loading (9), tool magazine loading (10), field adjustment (11), workpiece processing (12), continuous condition monitoring (13), workpiece processing time control (14), discrete condition monitoring (15), removal to the storage (16), loading into the pallet (17), disassembly (18), recycling (19). For any function performed by the TMS, we introduce the concepts of argument and result. The argument of the i-th function will be called the number of information material flow units received at the i-th function input for conversion for a known period of time. The result of the i-th function will be the number of information material flow units at the i-th function output for the same period of time. For a quantitative assessment of the actions (result) efficiency performed by the information and materials flow analysis system, we introduce the following relation:  Kij μij , (1) Rij = where I—functions quantity in the functional model (i = 1 … I); J—objects quantity in the functional model (j = 1 … J); μij = 1, if jth object is used by the ith function; μij = 0, if jth object is not used by the i-th function; K ij —the quantity of information

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and material flow units at each function output in the considered organizational and technological system; Rij —function result. For a comparative analysis of the certain objects functionality in the organizational and technological system, we introduce the ratio αij =

Rij Rij max

,

(2)

where αij —the degree of jth object functionality; Rij max —the maximum number of information and material flow units that can be processed by the jth object. To assess the subsystems functionality in the organizational and technological system, we will use the efficiency coefficient Aij Aij =



αij μij .

(3)

We introduce the following gradations of the efficiency coefficient Aij values and assign the corresponding linguistic variables: • • • • •

0 ≤ Aij < 0,40 —subsystem is used in rare conditions (insufficient) 0,40 ≤ Aij < 0,70 —subsystem is used irregularly (acceptable) 0,70 ≤ Aij < 0,90 —subsystem is used regularly (good) 0,9 ≤ Aij ≤ 1,0 —subsystem is used steadily (perfect) Aij > 1,0—subsystem is overload (faulty).

Introduced set  of quantitative characteristics ( = { Rij , αij , Aij }) will allow analyzing the activities of the company’s divisions, finding “weak” places and making changes to the functional model in accordance with the goals like to cut down economic costs, reduce the duration of the production cycle, decrease the amount of work in progress.

4 Results and Discussion As a result of the studies performed, a functional and object models complex of the multi-nomenclatural machine-building production activity was developed, which made it possible to establish the nature and content of relations between the organizational and technical systems that ensure the operation of the TMS. The production process decomposition models have been developed, which formalize the sequence of technical equipment selection that can be used to optimize the TMS composition. Mathematical relations, that have been proposed, allow the experts to evaluate the efficiency of information processing functions in the TMS of machining center. Acknowledgements. Authors would like to acknowledge the support and funding provided by The Volgograd State Technical University.

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References 1. Serdobintsev YP, Krylov EG (2015) Problem-oriented approach to improving tool operation at machining centers. Russ Eng Res 9:693–695 2. Krylov EG, Serdobintsev YP (2018) Povysheniye effektivnosti funktsionirovaniya instrumental’nykh sistem avtomatizirovannogo stanochnogo oborudovaniya (Improving the efficiency of the instrumental systems functioning in automated machine-tool equipment). VolgGTU, Volgograd 3. Krylov EG (2014) Multiblade cutting tools. LAP LAMBERT Academic Publishing, Saarbruecken (in Russian) 4. Grigor’ev SN, Grechishchnikov VA, Chemborisov NA, Skhirtladze AG, Savin I A (2018) Cutting of materials. Cutting tool in 2 p. Part 1. Yurajt Publ., Moscow (in Russian) 5. Baranchikov VI et al (2006) Tool designer reference guide. Mashinostroenie Publ, Moscow (in Russian) 6. Panov AA et al (2004) Metal processing by cutting: technologist reference guide. Mashinostroenie Publ, Moscow (in Russian) 7. Krylov EG, Makarov AM, Kozlovtseva NV (2015) Cutting tools organizational and technological preparation automation 1(156):59–61 (in Russian) 8. Grigor’ev SN (2017) Prospects for the development of the national machine-tool industry in the interests of ensuring the technological independence of Russian engineering industry. Stankoinstrument 1(6):18–23 (in Russian) 9. Lobanov DV, Yanyushkin AS (2013) Tool’s organizational preparation automation for processing composite materials. Autom Modern Technol 3:3–9 (in Russian) 10. Kapitanov AV (2014) Technological design of automated machine tools for diversified production. Autom Modern Technol 3:34–38 (in Russian) 11. Yakovlev AA, Krylov EG, Kozlovtseva NV, Kapitanov AV (2017) Search for optimal technological solutions in flexible manufacturing systems under uncertain information conditions. Izvestiya VolgGTU, 14(209: 64–68 (in Russian) 12. Simonova LA, Egorov BE (2014) Analysis of knowledge representation models in the intellectual information system of tool management. STIN 6:19–22 (in Russian) 13. Systems Engineering Fundamentals. Defense Acquisition University Press, 2001 14. Larman C (2004) Applying UML and patterns: an introduction to object-oriented analysis and design and iterative development, Prentice Hall 15. Krylov EG, Serdobintsev YP (2015a) Selecting the cutting tool for numerically controlled machine tools. Russ Eng Res 2:132–134 16. Solomentsev YM, Pavlov VV (2010) Modelirovaniye proizvoditel’nykh sistem v mashinostroyenii (Modeling of productive systems in mechanical engineering). Yanus-K, Moscow 17. Krylov EG, Serdobintsev YP, Makarov AM, Kozlovtseva NV (2014) Functional modeling of a cutting tool selecting process. Izvestiya VolgGTU 8(135):64–67 ((in Russian)) 18. Krylov EG, Fedorova NV, Kozlovtseva NV (2018) Development of multicriteria approach to cutting tools selection for automated manufacturing systems. In: 2018 International Russian automation conference, p 4. https://doi.org/10.1109/RUSAUTOCON.2018.8501835 19. Krylov EG (2018) Automation of the instrumental equipment preparation on CNC processing equipment. VolgGTU, Volgograd (in Russian) 20. Krylov EG, Serdobintsev YP (2015b) Multicriterial tool selection in automated systems. Russ Eng Res 9:689–692

Classification of Technologies for Obtaining Geometric Configuration of Parts V. E. Lelyukhin and O. V. Kolesnikova(B) Far Eastern Federal University, 8, Sukhanov St, Vladivostok 690091, Russia [email protected]

Abstract. The authors propose an original classification, which allows dividing all known methods of manufacturing parts into three categories of technologies: molding, additive, and subtractive technologies. The technologies for obtaining a geometric shape of the part by casting or plastic deformation of a workpiece belong to the first category. Technologies for obtaining a geometric shape of the part by building up (adding) a material belong to the second category. The third category includes technologies for obtaining the part shape by separating (subtracting) the material from the workpiece. Each category includes two classes. The classes combine the technologies with similar characteristics. There are two classes in the casting category: liquid casting and plastic casting. The set of additive technologies consists of two classes: macroadditive and microadditive. The category of subtractive technologies includes two classes: destructive technologies and splitter technologies. The use of this classification provides an unambiguous understanding and interpretation of methods and technologies for processing machine parts. This will have a significant impact on the developing of systems for the automatic formation of technological processes for the manufacture of parts. Keywords: Processing technology · Molding technology · Additive technology · Subtractive technologies · Features technology

1 Introduction Modern machine building has in its scope quite a wide range of technologies for manufacturing machine parts, which include technologies for obtaining mechanical, tribotechnical, chemical, electrophysical, optical, and other characteristics. A significant share of these technologies is the technology of forming the geometric configuration of a part [1–3]. In the article, the authors present an attempt to systematize a set of technologies that provide geometric parameters of individual elements and details in general.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_59

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According to the Russian standards, the part is a product made from a homogeneous material, without the use of assembly operations [4]. For example, a roller of one piece of metal; cast housing; a plate made of bimetallic sheet; printed circuit board; handwheel made of plastic (without fittings); length of cable or wire of specified length. The same products coated (protective or decorative), regardless of the type, thickness and purpose of the coating, or made using local welding, soldering, gluing, stitching, etc., for example, a screw chrome plated; a tube welded or welded from a single piece of sheet material; box glued together from one. Systematization of the existing variety of technological processes is the basis for building the theory and automation design of technology [5–8].

2 Classification of Manufacturing Techniques for Parts The above formulation shows that a part represents a single indivisible and monolithic unit of the product. We cannot separate a part without destroying it. When designing the technology for manufacturing parts, we solve two different tasks: • ensuring the geometric configuration of the part (within the tolerance range); • provision of specified properties (physical–mechanical, chemical, magneto electric, etc.) of the material of the part. Within the framework of the article, the authors confine themselves to the technologies used for achieving the geometric configuration of a part. Let us consider some part. The part has a strictly defined geometric configuration. We can regard it as a closed subspace, bounded by a set of intersecting and defined surfaces. These surfaces also constitute the boundary of the separation of the environment of the material of the part. Basic parameters defining the geometric configuration of a part are: (1) parameters defining the shape of each surface; (2) parameters that determine the relative position of these surfaces. Thus, in order to obtain a given geometric configuration of the part, it is necessary to ensure the shape and relative position of the individual elementary surfaces within the specified accuracy [9, 10]. In engineering, there are many different manufacturing techniques for parts [11–16]. Despite the differences in labor intensity, equipment, accuracy of geometric parameters, stability of material properties, etc., all existing technologies for obtaining the geometric shape of parts can be divided into three categories [9, 13]. Figure 1 is a diagram of the classification of manufacturing techniques for parts, in which each category includes two classes.

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Fig. 1. Classification of manufacturing techniques for parts.

3 The Results of Grouping of Technologies According to the Proposed Classification The first category includes molding technologies. The part is made by placing (pouring or pressing) the original molten or material in the state of plastic deformation of a certain mass into a preformed mold (chill, die, matrix, etc.). In the composition of this category, it is expedient to distinguish two classes: liquid molding and plastic molding. To the class of liquid molding, it is possible to classify technologies in which the raw material of the part is “transferred” to the liquid state, either by heating to melting, or by means of solvents, and poured into a pre-prepared form. This includes all types of casting, including liquid stamping. The class of plastic molding includes technologies that use natural plastic properties of the material. Typical of this class are bending, volume stamping, extract, etc. Figure 2 shows an example of a part obtained by pulling a sheet material.

Fig. 2. The part obtained by plastic molding.

Heating the material at a temperature below it’s melting point makes it possible to increase the material plasticity. Examples are free forging, rolling, hot volumetric stamping, extrusion, vacuum molding, etc.

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The second category consists of additive technologies that produce a part by adding the volume and mass of the initial billet through gluing, soldering, surfacing, etc., to the material [1, 17]. In the technical literature, additive technologies are often referred to as “rapid prototyping” or “3D printing” technologies. However, for rapid prototyping or production, not only additive but also subtractive technologies are used [18–20]. Note that the volume and mass of the material of the part is also added in the manufacture of welded glued and soldered parts. The authors propose dividing the category of additive technologies into two classes: macro additive and micro additive. It is advisable to classify macro additive technologies as technologies for the production of permanent structures (parts) by combining certain macro elements having a strictly defined shape (Fig. 3a) into a more complex configuration (Fig. 3b). Various types of welding and soldering, as well as gluing carry out mutual fixation of elements.

Fig. 3. a Part obtained by welding (macro additive technology): the initial set of macro elements; b ready configuration.

A characteristic feature of macro additive technologies is that the geometric shape of each element is part of the geometric configuration of the part. For example, in Fig. 3, the cylindrical shape of the boss, as well as the triangular prismatic shape of the rib, determine the final shape of the part. Thus, many types of macro additive technologies include all types of welding, soldering and gluing technology. Micro additive technologies involve the production of permanent structures (parts) by combining some trace elements that have a shape that does not determine the configuration of a part or its macro elements. For example, in one of the methods of 3D printing, the printer head forms a small drop of molten material (Fig. 4b), which is layered one upon another, thereby creating the body of the part (Fig. 4a). In this case, the shape of the material does not determine the geometric macro configuration of the part or any of its elements. There is a significant number of fundamentally different technologies of 3D printing (extrusion, laser sintering, gluing, stereo lithography, lamination, etc.), which refers to micro additive thus the geometric configuration (macro geometry) of the part does not depend on the shape of the original material element.

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Fig. 4. Part obtained by 3D printing (micro additive technologies): a the shape of the part; b form of microelement.

The third category consists of subtractive technologies. In contrast to additive technologies, here to obtain the part one needs to remove from the workpiece excess material. To date, these technologies are most common in mechanical engineering, since for the time being, they are the ones that ensure the production of parts with maximum geometric accuracy and minimum surface roughness. Subtractive technologies include all types of mechanical cutting; gas cutting; plasma and laser cutting; water jet cutting; ultrasonic and spark erosion processing; etching. The category of subtractive technologies includes two classes: destructive technologies and splitter technologies. To the class of destructive technologies, the use of which in the manufacture of a part is accompanied by the transformation into a chip of all excess material of the billet [21]. As a rule, such technologies are all types of cutting (turning, drilling, milling, grinding, etc.); etching; ultrasonic treatment and electro-erosion treatment. Figure 5 shows an example of a visualization of the ratio of the material used and the material of the part, which is cut on the lathe. The figure shows that most of the billet material is converted to chips. The other class consists of splitter technologies, the use of which makes it possible to separate considerable pieces of material from the billet without converting them into chips. This group, as a rule, includes technologies used for working with sheet materials, for example, laser, plasma and gas flame cutting, hydro abrasive processing and wire erosion treatment. In all these cases, the material becomes chips only in the separating layer.

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Fig. 5. Cross-section of the material used and transformed into chips during turning the workpiece.

4 Discussion The presented materials allow more accurately systematizing the terms and concepts used in engineering, making it possible to determine the belonging of existing technologies in accordance with their characteristic properties and features.

5 Conclusion Given the characteristics of obtaining the geometric shape of the parts, as well as the properties and characteristics of the materials used, a technology classification system is formed according to one of three categories. Within each category, a particular technology belongs to one of two classes. The use of the proposed systematization will allow to introduce an unambiguous understanding and interpretation of the system of methods and technologies for processing details, which will have a significant impact on the creation of systems for the automatic formation of technological processes for manufacturing parts.

References 1. Pirogova EV (2005) Design and technology of printed circuit boards: a Textbook. INFRA-M, Moscow, FORUM, p 560 2. Gorokhov VA (2011) Fundamentals of engineering technology and formalized synthesis of technological processes: in 2 hours: a textbook for universities in the direction of “Design and technological support for engineering industries”, Part 2. Stary Oskol, TNT, p 575 3. Matalin AA (1985) Engineering Technology: a textbook for engineering universities, specializing in engineering technology. Mechanical engineering, Leningrad, Metal-Cutting Machines and Tools, p 496

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4. GOST 2.101-68, (2007) Unified system of design documentation. Types of products, Standartinform, Moscow 5. Lelyukhin VE, Kolesnikova OV, Kuzminova TA (2019) Classification of methods for forming surfaces when machining parts on machine tools, In: 2019 International science and technology conference “EastConf”, Vladivostok, p 1–5. https://doi.org/10.1109/EastConf.2019.872 5366 6. Lelyukhin VE, Ignatiev FYu, Drenin AS, Kolesnikova OV (2018) Geometry for description of real parts of machines. Modern High Technol 8:95–99. https://top-technologies.ru/ru/art icle/view?id=37126. Accessed 14 Dec 2019 7. Halevi G (2014) Industrial Management—Control and Profit. G. Halevi. Lecture Notes in Management and Industrial Engineering 1, Springer International Publishing, Switzerland, p 284 8. Guo Y, Mileham A, Owen G, Li W (2006) Operation sequencing optimization using a particle swarm optimization approach. Proc Inst Mech Eng, Part B: J Eng Manuf 220(12):1945–1958 9. Lelyukhin VE, Kolesnikova OV (2016) Technologies of formation of geometrical configuration of details. International scientifically - practical conference innovative technologies in the contemporaneity. FECIT, Vladivostok, pp 3–12 10. Kolesnikova OV, Lelyukhin VE (2016) To the question about the problems of formalization of the design and technological information in mechanical engineering. International scientifically - practical conference Innovations in science and technology. FECIT, Vladivostok, pp 3–12 11. John R Walker, Bob Dixon Machining Fundamentals 9th Edition. Goodheart-Willcox; 9 edn., 19 August 2013, p 656 12. Outeiro JC (2003) Application of recent metal cutting approaches to the study of the machining residual stresses. Disertation, Department of Mechanical Engineering, University of Coimbra, Coimbra, p 340 13. Merchant ME (2003) An Interpretive Review of 20th Century US Machining and Grinding Research. Tech-Solve Inc., Cincinnati (OH) USA 14. Niku-Lari A (2013) Advances in surface treatments: technology—applications-effects. Elsevier 15. Kumaraguru S, Rachuri S, Lechevalier D (2014) Faceted classification of manufacturing processes for sustainability performance evaluation. Int J Adv Manuf Technol 75:1309. https:// doi.org/10.1007/s00170-014-6184-x 16. Nee YCA (2015) Handbook of manufacturing engineering and technology. Springer, London. https://doi.org/10.1007/978-1-4471-4670-4 17. Bilibin KI, Vlasov AI, Zhuravleva LV et al (2005) Design and technological design of electronic equipment: Design and technological design of electronic equipment. Publishing house MGTU im, NË Baumana, Moscow, p 568 18. Petrzelka JE, Frank MC (2010) Advanced process planning for subtractive rapid prototyping. Rapid Prototyping J 16(3):216–224 19. Matthew C Frank, Christopher V Hunt, Donald D Anderson, Todd O McKinley, Thomas D Brown (2008) Rapid manufacturing in biomedical materials: using subtractive rapid prototyping for bone replacement. In: Proceedings of the solid freeform fabrication symposium. 20. Pratik E Nikam, John L Frater (2005) Application of Subtractive Rapid Prototyping (SRP). For RSP Tooling, Mechanical Engineering Department, Cleveland State University, pp 33–34 21. Black JT, Kohser RA (2012) DeGarmo’s Materials and Processes in Manufacturing Copyright 2012. Wiley, Allrightsreserved

Methods of Designing Technological Trajectories of Single Layer of Laser Powder Cladding on Flat Surfaces of Part Model in CAM D. Rodionov(B) , A. Lyukhter, and V. Prokoshev Vladimir State University Named After Alexander and Nikolay Stoletovs, 87 Gorky St., Vladimir 600000, Russia [email protected]

Abstract. The article deals with the design of technological trajectories of laser robotic powder cladding on flat surfaces of the part model in the CAM system. A method for determining a given flat surface of processing and its boundaries on a three-dimensional polygonal model of a part is proposed. The methods of coating the surface of the processing in a given direction and a given step, considering the location and rotation of the part in the positioner of the laser robotic cladding complex are described. The developed methods were successfully implemented in the authors software development and tested at the industrial complex of laser robotic powder cladding. Keywords: Laser cladding · CAD/CAM · Offline programming · Additive technologies · Industrial robotic systems · Technological preparation

1 Introduction Currently, the process of laser cladding in the metalworking industry is accompanied by the use of robotic systems. The research of coatings, obtained through the use of various kinds of laser robotic cladding complexes (LRC-C), are carried out [1, 2]. The creation of modern LRC-C allowed one to realize the possibilities of laser cladding in a wide range, to automate the technological process and include it in the integrated system of high-efficiency production [3]. The question of solving the problem of computer-aided design of technological trajectories1 for industrial complexes of LRC-C remains open. The programming of the robotic arm movement is in most cases performed in specialized software systems known as CAD/CAM and CAPP [4–6]. Existing systems (ABB RobotWare, Machining FC, FANUC Roboguide, KUKA CAMRob, Motoman MotoSim EG, Robotmaster KMT CamPro, SprutCAM, RoboDK, DELCAM PowerMILL Robot 1 The trajectory of the LRC-C tool with the specified technological parameters at each point.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_60

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Interface [7], and others) do not fully meet the requirements for the design of technological trajectories of laser robotic powder cladding (next—LRPC). In this regard, the authors produced their own software development (Fig. 1), designed to solve the problems associated with the lack of ability to design the technological trajectories of LRPC in CAM.

Fig. 1. Author’s CAM system of laser robotic complex.

To date, research in the design of technological trajectories of laser robotic powder cladding on polygonal 3D models are relevant [8–12]. This article is part of the author‘s research aimed at developing methods for designing technological processes of laser robotic processing of metal products in the CAM system [13–16].

2 Problem Statement The aim of the research is to develop methods that allow to implement the process of computer-aided design of technological trajectories of LRPC on a flat surface of a three-dimensional polygonal model of a part for the LRC-C complex in CAM. The points of the technological trajectory are represented on the local basis of the model (next—LBM) [13, 15] (Fig. 2). The LBM is a standard Cartesian basis constructed

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Fig. 2. A local basis of a cube model designed with respect to one of its vertices (point O).

relative to the model. As a rule, its axes in the CAM graphic space have directions OX— to the left, OY —up, OZ—to the right, and the reference point coincides with the zero value of the model coordinates. In this case, each point trajectory of the LRPC will be set by   of the technological a set of coordinates p = px , py , pz , the orientation of the executive node (next tool) of the LRC-C, represented as Euler angles γ = {w, p, r} [17], as well as additional coordinates J = {J1 , J2 } of the positioning device (next—positioner), if the part is fixed to it. An example of a positioner is a two-axis device from the LRC-C (Fig. 3). In the CAM system, the technologist2 loads the product model and by means of the controls selects3 a flat surface on which he would like to carry out the cladding process with the LRC-C complex. The CAM user selects the processing parameters (or processing mode) from the database. On the basis of the selected processing mode, the CAM system should carry out the computer-aided design of technological trajectories of the processing surface. The process of computer-aided design should be a surface hatching, and its parameters (direction, step, line shape and connectivity) are laid down in the processing mode. In this case, to achieve aim of current research, it is necessary to solve the following tasks: • Determine the processing plane and its external boundaries on a three-dimensional polygonal model of the part; • Develop methods for designing technological trajectories covering a flat processing area with a given direction and step; • Develop methods of design of technological trajectories covering the flat area of processing in case of rotation of a detail in the positioner.

2 The user CAM. 3 The selection process is a hover and mouse click of the surface of interest.

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Fig. 3. The positioner and the tool LRC-C.

3 Preparation of a Three-Dimensional Polygon Model 3D polygon model of a part is a union of plane geometric primitives4 (next—polygons) defined in space by a set of vertices and a normal vector [18] (Fig. 4a). Moreover, the flat surface of the model can be a union of many polygons. The process of designing technological trajectories on the plane LRPC a process of hatching [19, 20] of the processing surface, determined by the direction, step, shape, and connectivity of the hatch lines. To implement the hatching process, it is necessary to determine the outer boundaries of the processing surface, but from the point of view of the three-dimensional polygonal structure of the model, the processing surface can consist of many polygons. This specificity requires their definition. As a sign of the definition of polygons of a single flat surface, the researchers used the condition of parallelism of adjacent polygons. If the feature condition is satisfied, the polygons will represent a single processing surface (Fig. 4b). Calculations of flat surfaces of the model occur at the stage of its loading into the CAM. Thus, when designing the technological trajectories of LRPC, the CAM user works with already prepared planes.

4 As a rule, triangles act as polygons.

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Fig. 4. a Model parts, represented in the form of flat triangles and b with the applied method based on the feature of determination of flat surfaces.

4 Design of Technological Trajectories of LRPC on a Flat Surface The design of technological trajectories LRPC a flat U surface is a process of hatching a polygon with lines. The main input parameters of the hatching process are the direction d and the distance between the lines (next—step) h. Let the outer boundary of the processing surface be represented by an ordered set  i=N y=N of segments B = vi , vi+1 i=1 , then {vi }i=1 are the vertices of the outer faces of adjacent polygons of which the surface consists in the number of N pieces. An example y=8 of a flat processing surface from the outer boundary {vi }i=1 is illustrated in Fig. 5.

Fig. 5. An example of a flat processing surface U represented by a polygonal structure with an outer boundary {vi }.

In this case, the hatching algorithm can be represented by the following sequence of actions:

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1. Hatching start. The process of hatching a polygon is convenient to start with the j=N  boundaries vj , vj+1 j=1 1 parallel to the given direction d . If there are no such boundaries, then there is a search for those vertices that will lie outside of the processing surface when the vector d is transferred to them. Mathematically it is representable as follows: j=N      • Definition vj , vj+1 j=1 1 : vj , vj+1 ∈ B i vj , vj+1 ||d ; j=N  2 • If vj , vj+1 j=1 1 = ∅, then start vertices are represented {vk }k=N :         k=1 y−vk x−vk z−vk L vk , d ∩ B = ∅, where L vk , d ≡ dx − dy − dz = 0 the spatial line passing through the point vk along the direction d ; j=N   • Choice of the boundaries of start ls = max  vj , vj+1  j=1 1 ; 2 • The choice of the start vertex vs ∈ {vk }k=N k=1 is arbitrary.

2. Design of hatch lines. Hatch lines are a set of segments parallel to d and covering the processing area with a step h, starting from ls or vs . The construction process is as follows: • Designing the first line segment s0 . If ls = ∅, to s0 = ls . Else s0 = [a 0 , b0 ] is     based on vs so that a0 , b0 ∈ vs , vs−1 , vs , vs+1 ∩ L vs + d ⊥  · h, d , where d ⊥ 

d ⊥ = d × n and n —is the vector normal to the machining plane (× —cross). With d¯ ⊥ : ∃r ∈⇒ d¯ ⊥ · h ∩ B = ∅. ends of the n-th line • Designing sn line segment. Let sn = [an , bn ], then the

segment are defined by an , bn ∈ B ∩ L an−1 +

d ⊥    d ⊥ 

• The end of the design occurs when B ∩ L an−1 +

· h, d .

d ⊥    d ⊥ 

· h, d

= ∅.

3 In this case, the set of parallel segments S = {sn }n=N n=1 will represent the hatching of a given LRPC processing area in the direction d with a step h (Fig. 6), and each element sn technological trajectory of the complex LRC-C. It is also worth noting that the B boundaries of the flat hatch area can be set manually by the CAM user. The solution of this problem can be relevant in cases when it is necessary to carry out the process of LRPC not on the whole flat surface, but on its part. The example illustrated in Fig. 7, displays the LRPC result designed in CAM, where the flat surface area was bounded by a rectangle. In order to ensure the continuous execution of the LRPC process, it is required that the technological trajectories from S have alternating directions of motion. In this case, we introduce a notation, where S↑↑ will be denoted as a co-directional hatching d , and

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Fig. 6. The result of hatching the selected part surface for the LRPC process.

Fig. 7. a The technological trajectory designed in CAM with the given boundaries of the processing area in the form of a square and b its result on the LRC-C.

S↓↑ alternating hatching. Then these sets can be defined as follows:  S↑↑ = [an , bn ] : an bn ↑↑ d ∪[bn , an ] : an bn ↓↑ d S↓↑ = {[an , bn ] : n ∈ 1, 3, 5 . . . N3 ∪ [bn , an ] : n ∈ 2, 4, 6 . . . N3 , where an , bn : [an , bn ] ∈ S↑↑ }

A necessary condition for the execution of the LRPC process in a continuous mode is alternation, that is, S = S↓↑ , but sufficiency is provided by the connectedness of adjacent segments sn ∈ S. For this, it is necessary to modify S and present as follows:        S = [a0 , b0 ], [b0 , a1 ], [a1 , b1 ], . . . aN3 −1 , bN3 −1 , bN3 −1 , aN3 , aN3 , bN3

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The methods described above are well applicable in the case where the processing surface U is a convex  set. Otherwise, there

 may be difficulties when the number of     elements in the set B ∩ L an + d ⊥  · h, d  > 2.   d ⊥  In this case, the line segment can be divided into several.  To do this, represent [an , bn ]   as sub-sections pi , qi : pi , qi ∈ B ∩ L an + d ⊥  · h, d . Among them, we choose d ⊥ 

only those that are on the U . Then we get that the line segment [an , bn ] will be   surface represented by pieces pi , qi on the surface U (Fig. 8). It is worth noting that such a technique, on the one hand, allows you to build a hatch in a given direction d and a given step h on non-convex surfaces, but on the other hand, puts a ban on the possibility of continuous execution of the LRPC process.

Fig. 8. The hatching scheme is not a convex flat surface.

One fact that is not considered when designing hatching is the determination of the orientation of the tool. It should be noted here that in the process of designing technological trajectories of LRPC in CAM, the technologist from the database of processing modes makes a choice of the surfacing angle, which determines the orientation of the tool. From a technological point of view, during the entire process of LRPC, the orientation of the tool retains its value and, in most cases, coincides with the direction of the normal to the processing plane.

5 Design of Technological Trajectories LRPC on a Flat Surface with the Rotation of the Part in the Positioner For the performance of the technological process of LRPC, there are cases when lines of a hatch it is convenient to represent not segments, and the circles inscribed in each other. An example is the product in Fig. 6, in the case where it is necessary to carry out LRPC on the entire surface. Such problems belong to the category of designing bodies of rotation. From a technical point of view, the processes in which the methods of designing bodies of rotation are used are realized through the use of movable rigs that allow for rotational movements.

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In this case, the task of designing the technological trajectories of LRPC can be reduced to the design of inscribed circles with a step h and covering a given processing surface. The algorithm for designing the technological trajectories of LRPC, in this case, will be similar to the algorithm from Chap. 4, but there will be the following modifications: • The start of the hatching occurs from the vertex vs , where it will be the center of the circle;   • The hatch lines are circles (arcs of circles), that is, instead of the function L vk , d , 2  2  the function (vs , r) = x − vs,x + y − vs,y − r 2 = 0 is used; • At each iteration step, the radius is represented by rn = rn−1 − n · h; • The completion of the hatch lines occurs when r < h. This algorithm, schematically shown in Fig. 9, is a shrinking circle method where the initial radius r0 represents the largest radius and is defined as r0 = max({|vs − vi |}). To implement the expanding circle method, it is necessary to represent the sequence of generating radiuses as rn = rn−1 + n · h, where r0 = 23 h.

Fig. 9. Hatching scheme of a non-convex plane surface by circles, relative to the vertex vs .

It should be noted that the design of technological trajectories of LRPC lines of circles is best done when the processing area has the shape of a circle. But the modified algorithm described above will be poorly adapted in this case, since the center of the circles will not be in the geometric center O of the processing surface. In this case, vs should not be an arbitrary point of the outer boundary of B, but should coincide with O. The point O for an arbitrary planar polygon formed by vertices r i,1 , r i,2 and r i,3 can be defined as the center of mass of a homogeneous surface. Since the surface area is initially represented as triangles of the polygonal model, the center of mass will take the following form:  i ci · Si O=  i Si   here ci = 13 r i,1 + r i,2 + r i,3 —is the centroid of the ith triangle, and Si is its area.

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Design of continuous process execution LRPC, in the case of rotation of the part positioner was made by linking adjacent circles cut, so that the difference of angles between adjacent segments of the connection was 90°. The technological process of LRPC, where the inscribed circles act as hatch lines, implies the implementation of the movement of the part in space by means of moving the positioner, and as a rule, the tool LRC-C, during the surfacing process remains fixed in one position. Thus, each point of the technological trajectory will represent the same position of the tool in each hatch line in space, but a different position of the positioner, creating a rotation of the part. This method of LRPC, something may resemble a playback system on record players.

6 Conclusion In this paper, the authors researched the issues of designing technological trajectories on flat surfaces of a three-dimensional polygonal model of a part for the LRPC process in CAM. Methods for determining the processing surface and its outer boundary on a 3D model were proposed. Methods and algorithms were developed for designing technological trajectories on the flat surface LRPC the part model in the form of hatching covering it. Methods of design of technological trajectories in cases of execution of LRPC process by means ofrotation of a detail in a positioner were offered. The obtained results can be applied in the design of technological trajectories of multilayer surfacing on flat surfaces of products by the industrial complex LRC-C. Acknowledgements. This work was supported by the Ministry of science and higher education of the Russian Federation. Grant agreement No. 075-15-2019-1833 dated December 04, 2019. the Unique identifier of the applied scientific research is RFMEFI60419X0245.

References 1. Tatarinov E (2015) Laser surfacing of shut-off valve elements. News of Tula state University. Technical Science 15:101–107 2. Morunov I, Krylova S, Oplesnin S (2017) The principle of laser purification by powder materials in the environment of protective gases corrosive-steel steel. In: VIII International scientific and technical Ural school-seminar of metallurgists-young scientists “Ural school of young metallurgists”, p 27–31 3. Grigoryanc A, SHiganov I, Misyurov A, (2006) Technological processes of laser treatment. Bauman Moscow state technical University, Moscow, p 664 4. Mourtzis D, Makris S, Chryssolouris G (2018) Computer-Aided Manufacturing. Int Acad Prod Eng, CIRP Encycl Prod Eng. https://doi.org/10.1007/978-3-642-35950-7_6550-4 5. Lin W, Luo H (2014) Robotic welding. Handbook of Manufacturing Engineering and Technology, p 1–36. https://doi.org/10.1007/978-1-4471-4976-7_106-1 6. Pan Z, Polden J, Larkin N, Duin S, Norrish J (2011) Automated offline programming for robotic welding system with high degree of freedoms. Adv Comput Commun Control Autom 685–692. https://doi.org/10.1007/978-3-642-25541-0_86

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7. Iglesiasa I, Sebastiána MA, Aresc JE (2015) Overview of the state of robotic machining: Current situation and future potential. Manuf Eng Soc Int Conf, MESIC, Procedia Eng 132:911–917. https://doi.org/10.1016/j.proeng.2015.12.577 8. Zheng HD, Cong M, Dong H, Liu Y, Liu D (2019) CAD-based automatic path generation and optimization for laser cladding robot in additive manufacturing. Int J Adv Manuf Technol 101:2873–2887. https://doi.org/10.1007/s00170-018-3107-2 9. Zheng HD, Dong H, Liu Y (2019) Optimization of STL model and layer shape for laser cladding forming. Int J Adv Manuf Technol 100:599–608. https://doi.org/10.1007/s00170018-2714-2 10. Urbanic RJ, Hedrick RW, Burford CG (2017) A process planning framework and virtual representation for bead-based additive manufacturing processes. Int J Adv Manuf Technol 90:361–376. https://doi.org/10.1007/s00170-016-9392-8 11. Wang X, Sun W, Chen Y, Zhang J, Huang Y, Huang H (2018) Research on trajectory planning of complex curved surface parts by laser cladding remanufacturing. Int J Adv Manuf Technol 96:2397–2406. https://doi.org/10.1007/s00170-018-1737-z 12. Chen L, He Y, Yang Y, Niu S, Ren H (2016) The research status and development trend of additive manufacturing technology. Int J Adv Manuf Technol, 1338–1343. doi:https://doi. org/10.1007/s00170-016-9335-4 13. Rodionov D, Lyukhter A, Prokoshev V (2018) The mechanisms of constructing trajectories of a laser robotic complex for 3d polygonal models. J Phys Conf Ser. https://doi.org/10.1088/ 1742-6596/1109/1/012007 14. Lyukhter A, Rodionov D, Lokhanov A (2017) Methods of processing information obtained by scanning a part of a distance sensor to optimize a trajectory. Proc Int Conf Perspect Technol Inf Transm Media 2:138–141 15. Lyukhter A, Zvyagin M, Golubev A, Rodionov D (2017) Transfer of coordinates of 3D CAD-models to the space of machined parts in robotic machine complexes. Dyn Complex Syst—XXI Century 1:40–46 16. Rodionov D (2019) Control of the laser robotic complex in the edge areas of the treatment zone. Dyn Complex Syst—XXI Century 3:5–13. https://doi.org/10.18127/j19997493-201903-01 17. Flores P (2015) Euler angles, bryant angles and euler parameters. concepts and formulations for spatial multibody dynamics, p 15–22. https://doi.org/10.1007/978-3-319-16190-7_4 18. Milewski J (2017) Computers, Solid Models, and Robots. Addit Manuf Metals, Springer Ser Mater Sci 258:99–117. https://doi.org/10.1007/978-3-319-58205-4_6 19. Sovertkov P, Hohlov D (2003) Hatching a closed polygon. Comput Tools Edu 1:73–79 20. Suarez J, Belhadj F, Boyer V (2017) Real-time 3D rendering with hatching. Vis Comput 33(10):1319–1334

Aeroacoustic Cartography as Method of Non-destructive Testing of Turbine Blades Based on Fiber Optic Sensor Systems V. Yu. Vinogradov1(B) , O. G. Morozov1 , and R. Z. Gibadullin2 1 Kazan National Research Technical University Named After A.N. Tupolev–KAI, 10, K. Marx

Street, Kazan 420111, Russia [email protected] 2 Kazan State Agrarian University, 65, K. Marx Street, Kazan 420015, Russia

Abstract. The article is devoted to the development of a method for aeroacoustic mapping of the state of the working blades of the flow part of turbomachines with the possibility of detecting a defect in a spatial format based on the results of fiber optic measurements in a distributed set of control points. It discusses the modeling of the gas flow cross-section nozzle for a turbomachine stationary and non-stationary operation modes, a mathematical model describing acoustic processes in the flow part of turbomachines and ways to improve them. The principles of creating complex systems of aeroacoustic cartography, which are accompanied by methods and means of measuring the parameters of gas dynamic flow in the flow part and in the cross-section of the turbomachine nozzle, are defined. The described principles make the control more informative and facilitate the development of an algorithm for a non-destructive method to monitor the state of the rotor blades. In general, it provides reliable data under conditions of parametric and structural uncertainty of the gas-air flow both on the controlled internal section of the flow path and on the output section of the turbomachine section. The problems of placement of control points and reconstruction of the spatial distribution of the field by dimensions in a discrete set of points are considered separately. The reconstruction of the acoustic field of the turbomachine is carried out based on measurements of the output of the fiber optic sensor only using a statistical approach. Keywords: Aerospace cartography · 3D localization · Control sensors · Mathematical modeling · Fiber optic sensor systems

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_61

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1 Introduction To control the state of the working blades of the flow part of turbomachines, it is advisable to use methods that have the maximum information content, complementing and clarifying each other. The variety of methods is explained by the fact that none of them can take into account all the requirements for forming a diagnosis with 100% accuracy and detail, since they carry specific information of different values. Currently, defects in the working blades of the flow part of turbomachines are detected in the operation only during periodic endoscope inspections, although the development of the defect from the origin to almost complete burnout of one or more blades occurs in a very short period of time from a few minutes to several hours [1–5]. The development and improvement of methods and tools for monitoring the condition of turbomachines in order to detect faults as early as possible and prevent catastrophic failures is an urgent task to improve safety. Environmental and economic factors are also important factors that influence the development of new methods and controls for turbomachine blades. Tests of turbomachines in operating modes require significant fuel consumption and resource development, as a result, the development of methods and means for monitoring the working blades during cold start is relevant. 1.1 Locational Sensing Equipment For a more complete understanding of the processes occurring in the flow part of the turbomachine, information and measurement systems for monitoring parameters and visualization of the processes of mapping parameters of physical fields on the turbomachine nozzle section during tests presented in Fig. 1, in the form of 1D and 2D format of fault localization [6–9]. For these purposes a single section and three-section aeroacoustic fiber-optic monitoring systems with the ability to diagnose turbomachines flow part rotor blades in the plane of the nozzle exit were designed. Both system have the ability to present measured parameters of the studied device as cartographic portret: first system with the possibility of defects localization at an early stage of their development and visualization as points in 1D format; second one - with possibility to localize the defect points in 2D format (area of nozzle exit) and in 3D format (volume of turbomachine). The operation of the turbomachine during cold scrolling is a mixed process, both unsteady and steady. Let the state of the turbomachine at each moment of time be uniquely described as m + 1 state variable X0 , X1 , X2 ,…,Xm . When performing an experiment on a turbomachine, the initial values of the state variables are set at time t0 and the current values of the state variables are measured in N + 1 point, belonging to a time period [t0 , tN ]. Let’s define a system of continuous lines on a segment [t0 , tN ] as k functions. The mathematical model is described by a system of ordinary differential equations, the coefficients in each equation are found from the minimum standard approximation condition “Eq. 1”. dX0 dXm = a00 f0 (t) + a01 f1 (t) + · · · + a0k fk (t), ... = am0 f0 (t) + am1 f1 (t) + · · · + amk fk (t) dt dt

(1)

Using a linear reference mathematical model of undisturbed flow, we can implement it by solving a particular problem of a mathematical model for determining faults in

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Fig. 1. Illustrative diagram of the turbomachine control system with the possibility of 1D and 2 D localization of the defect.

the flow part of a turbomachine by analyzing the measured and calculated parameters f (rpm). Therefore, you can use a linear mathematical model f (rpm) as a criterion for failure when monitoring the parameters of the turbomachine, since the change in the calculated parameters of the mathematical model will differ from the reference values in the initial section of the calculated derivatives. A linear mathematical model for describing the probing gas-air flow of a reference process for an unsteady FOB/min (LDB) mode is based on measurements over an initial period of time from 10 to 30 s. Using this model for the steady-state FOB/min mode leads to large values of the mean square error, i.e., to a large difference between the experimental values and the calculated ones. Therefore, a general mathematical model is constructed for unsteady and steady-state modes, which allows us to determine the beginning of the steady-state test mode of the turbomachine. The resulting control features can be solved by developing a mathematical model that describes the transition process from the point of view of changing the geometry of the flow part of turbomachines to the response of the mathematical model in the diagnostic process [10–12].

2 Acoustoelectric Method Some approaches have been developed which confirm either turbine suitability or a developing defect in a turbine in the process of control of rotor blade geometry. The approaches were developed in the form of creation of aeroacoustic cartography systems on the basis of acoustic and electric methods and creation of practical recommendations concerning probing gas aero stream formation with the required flow and speed characteristics. The researches were conducted both on models and on real gas turbine engines. What way do the stream noise spectrum change when a defect appears in a turbine flow path? Defects create ledges and cavities, where pressure and speed pulsation of the ambient gas emerge. Pulsation frequency and amplitude depends on defect size and is

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in the range of 10–20 kHz. Studies were conducted, which examined rotor blade defect influence on the stream noise level. Diagnostic researches were performed at different times: in the technical diagnostics laboratory under the guidance of Vinogradov Yu. V., PhD, then under the guidance of Corresponding Member of the Russian Academy of Science Professor Doctor of Science Tunakov A. P. A model of combustion chamber unit was used for the research, which is a segment (1/8) of an annular NK 8 combustion chamber. Seven stator blades (the first stage of NK8 engine) were chosen for the trial, one of the blades, which has no defect was marked “E”, the other 6 have burnouts of different degrees on the leading edge, trailing edge and back, the defected blades are marked as D1, D2, D3, D4, D5, D6 according to the defect scale from 0,005 mm to 0,84 mm ((0,005; 0,03; 0,25; 0,32; 0,7; 0,84). Defect scale: SD/SE, where SE = 425 mm. When measured defect values are input in the mathematical model and calculated coefficients are calculated, the results of numeric mathematical modeling of turbomachine flow path processes are the evidence of standard deviation change, which suggests that a measurement error can be a criterion for early stage defect detection, 5, 25, and 50% barrier distinguishes defects from the reference error.

3 Gas Dynamics Method as an Addition to the Acoustic Method The chapter is about non-destructive turbine control method applied on the basis of the study of gas dynamic characteristics with the help of a control device as a component of acoustic control method at a cold start. It is known that a gas stream contains all information about the engine flow path. An undulant pattern of a ring structure is created, and it depends on the rotational speed of the dynamic system and on the number of blades. Waves, created by dynamic systems are in the mid frequency range for high speeds and in the low frequency range for low speeds. Geometry change of the flexible system (ruptures, burnouts, notches) entails the ring structure changes and introduce high frequency components due to pressure and speed pulsations in defect cavities. Besides, beading and coke formation on the walls of the engine flow path also change the ring structure pattern and cause a gas dynamic parameters change and non-uniformity/inequity/imbalance of the parameter fields. The tests on a full-size NK8 engine allowed to prove all the above mentioned theoretical assumptions. The emphasis in this chapter is put on the cartography of the nozzle cross section parameters at hot and cold start in a low gas mode, in order to minimize the influence of harmful emissions during testing at different operating modes including a cruise mode. The gas dynamic control mode was used at study of different types of turbomachines it was also used during the control of stream acoustic features both on models and on 3 turbomachines: GTD, NK-8 with an oblique cut, NK-8 with a straight cut. The study proved its efficiency and control suitability both in the conditions of a closed chamber and on an actual unit during testing. Gas dynamic parameter processing, measured by «Pilon», shown in the picture 6, and calculation of gas stream features at the nozzle cross section are made in the following sequence on the basis of calculation by Ladogov. The regularity of parameters is revealed in the cut plane of the nozzle along the radius, from the center to the edge, the regularity persists at all modes from low gas to nominal for each turbine [13–15].

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It is established that introducing the defect “the last turbine stage blade edge burningout 2%” into a turbomachine causes a significant decrease of PCT , T, W and an increase of K PCT , K T , K W parameters. At that, a value of decrease of these parameters is enough to detect a defect even at the condition of 0.1 N. Unevenness of PCT parameter increases at all engine operating modes. An unevenness increase is observed closely to an engine nozzle cut edge. In comparison with reference unit, PCT unevenness change on a plane of a nozzle cut in a defective unit changes the next way: from 5 to 6% at the centre and from 2 to 4.2% at the edge of the nozzle cut. Treating unevenness changes at different operating engine modes it is possible to notice that PCT unevenness change increases in: 2% for 0.1 of nominal engine mode; 4% for 0.4 of nominal engine mode and 6% for 1.0 of nominal engine mode. This causes a conclusion that a defect could be determined according to changes of K PCT , K T , K W unevenness at the 0.1 of nominal engine mode. To improve air-acoustic cartography as a non-destructive control method, it is necessary to supplement it by a perfect measuring foundation based on optical fibre technology which will be discussed in the next chapter.

4 Fiber Optic Systems of Aeroacoustic Cartography Here the main emphasis is put on development and investigation of distributed fiber systems on the basis of control methods, which use multiplexed fiber optic control sensors to check the gas air stream parameters at the turbine nozzle cross section, when advantages of optic methods of information transmission are used and there is a device. Processes of outer physical field influence signal reception are studied, the reception is provided by long fiber measuring lines with amplitude modulation radiation, which require additional. At the measuring lines output photoelectronic recievers are put with function of logarithmic and rating operations. Acoustically disturbed diaphragm causes a move of fiber Bragg gratings placed on the nozzle cross section, this is shown in, for example, see Fig. 2. This causes a modulation of the light coming through a nozzle. Spectral selection range depends a lot on both the interval of the grating and the tilt angle to the radiation axis [16–19]. The system provides parallel separation of carrier frequencies, it means that the optic losses do not increase together with the channel number growth. It is important to use fiber optic sensory distributed detectors, which are easy to control, and do not require special calibration and do not cost much. The detectors are used for measuring line manufacturing, for example, see Fig. 3, for stream feature control at the turbine nozzle cross section. The system of distributed fiber optic detectors allows to control and detect lengthwise or local changes of the physical fields, that is important for local malfunction detection at the early stage. The levels of sound pressure are measured both at separate local points of a jet stream and throughout the nozzle cross section area. A closed system is used, the detectors can give signals about a dynamic change of their configuration under the influence of the engine jet stream noise. The grid step of a fiber optic detector increases towards the engine nozzle edge to give more information about the measured parameters. Spatial dynamic field (on the screen) changes in the defected points (blade burnout or other) to the direction different from the direction of the engine jet stream, creating a vacuum

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Fig. 2. Measurement at the nozzle cross section by the fiber-optic detector system.

Fig. 3. Selection of laying scheme of measuring lines.

effect. In the research, the aeroacoustic control method has been developed on the basis of fiberoptic technologies, the method allows to make a new step to solve the problem of exploitation safety of a turbomachine. It is necessary to place the minimum number of detectors in the acoustic field so that to get the maximum of useful information in order to get data of the acoustic field at the nozzle cross-section in an optimum way. The criterion of information maximum or entropy minimum is used. It is important to have

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statistic information about the field being investigated, if statistics are not available the more detectors we place the better. Here we use a probabilistic approach. There is a certain acoustic field S(x). The first sensor is placed in the point where the energy in proportion to amplitude square is maximum, the next point is the point where the orthogonal residue is the biggest in comparison to the first point, this way we place a number of sensors. Then we can process the sensor data and reconstruct the acoustic field as a continuous function. The field is spread out in a system of basic functions, Si(x)– it is supposed that the statistics are available. The task is to evaluate them. The evaluation is based on measurements, the measurements are made in a set of points, functions are set, when the measurements performed the reconstruction task can be completed taking into account the statistics. In our situation the reconstruction is adequate; the error is epsilon 0,001%. Spatial placement of the control points and acoustic field reconstruction according to discrete sensor readouts are based on a priori statistics information about the fields to be reconstructed. As soon as each aeroacoustic turbine control system is developed for all types of turbines, in real situations which are not subject to analytical calculation, an experiment can be organized reconstructing operating modes of acoustic field stimulation, measurement of a complex of acoustic field T(x) realizations can be performed with the help of universal measuring system with a large number of sensors. After that, the necessary statistic features are calculated: expected value m and correlation matrix R. The number of detectors provides the permissible value of reconstruction e = 0,01. The results of the research reveal that correlation presence of coefficients of decomposition of the radiation field according to functions cos2p leads to a decrease in the number of sensors required for reconstruction accuracy given. Values of the coefficient dispersion of the radiation field decomposition change insignificantly when a is changed. Based on the research, the following conclusions were obtained: turbo machine malfunctions can lead, already at the initial time interval, to a change in the experimental and measured values of parameters from the calculated ones, which signals the need to turn off the turbomachine; the developed control tools allowed us to solve the problem of localization of acoustic sources of defects in 1D, 2D, and 3D data measurement formats to improve the efficiency of early diagnostics of turbomachine blades. In this study, the theory of acoustic analogy and sound generation in a stream is developed from the point of view of its applicability to the blade geometry control in a gas turbine engine flow path. Some mathematic models are developed including a generalizing model which is represented as a different combination of parameters of a gas turbine engine flow path for a steady and unsteady operating mode at a hot and cold start. On the basis of the received solutions, the theoretical questions of the acoustic analogy and the sound generation theory have been discussed from the point of view of their change in the process of geometry deviation in an engine flow path. The method which allows to increase the informational value of the received solution also reveals opportunities for a superstructure for the further creation of an updated model of an aircraft gas turbine engine including dozens of interdependent parameters, that finally reduces a period of a gas turbine engine control and diagnostics, especially at a cold run mode.

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The principles of creation of complex systems of aeroacoustic cartography are developed, the systems are followed by methods and means of gas dynamic stream feature measurement in a gas turbine engine flow path and on a nozzle cross section, they increase the information value and algorithmization level of non-destructive rotor blade control, they provide data from the controlled inside sections of the flow path in the conditions of parametric and structural uncertainty of a gas air stream [20, 21]. Acknowledgements. The authors are grateful to employees of KNITU-KAI of the department of RFMT, MSandPB and the TDAD group (Republic of Tatarstan) for technical support. The work was carried out with the financial support of the Ministry of science and higher education of the Russian Federation for the design and basic parts of the state task “Asymmetry” in 2019 (V.Yu.V. and O.G.M.) and agreement № 075-03-2020-051 (fzsu-2020-0020) (O.G.M.).

References 1. Gcttlich EH (1988) A method for overall condition monitoring by controlling the efficiency and vibration level of rotating machinery. In: Proceedings of the institution of mechanical engineers - vibrations in rotating machinery, pp 445–447 2. Hill JW, Baines NC (1988) Application of an expert system to rotating machinery health monitoring. In: Proceedings of the Institution of mechanical engineers—vibrations in rotating machinery, p 449–454 3. A Van Dan Bos (1971) Alternative interpretation of maximum entropy stectral analysis. IEEE Trans. Luform. Theory IT-17:493–494 4. Il’in GI, Morozov OG, Pol’skii YuE (1996) Twofrequency oscillator for interferometers with dived channels. In: Proceedings of Europian symposium on lasers, optics and vision for productivity in manufacturing I, Bezanson, France, pp 132–138 5. Vinogradov VY (2000) Diagnosis of the state of gas turbine engines in the conditions of airfield-based. In: Russian Aeronautics, pp 32–35 6. Kasimov VA, Minullin RG (2019) Radar detection of ice and rime deposits on cables of overhead power transmission lines. Power Technol Eng 52(6):736–745 7. Kasimov VA, Minullin RG, Piskovatskiy YuV, Basharova EM (2019) Imitation and physical modeling of the influence of ice coating on the propagation of location signals on the wires of overhead transmission lines. Int J Innovat Technol Exploring Eng 8(8):2836–2840 8. Kasimov VA (2019) Ultimate capacities of location detection of damages and ice coatings on overhead transmission lines. Int J Innovat Technol Exploring Eng 8(8):3235–3240 9. Vinogradov VYu (2013) Control of technical condition of aviation gas turbine engines according to acoustic parameters measured by n a cut of the engine nozzle. Control. Diagnostics 3:53–57 10. Munier JD, JY, (1987) Spatial analysis in passive location systems using adaptive methods. TIIER 75(11):21–38 11. Anfinogentov VI, Mansurov SR (2017) Mathematical model and algorithms of reconstruction of physical fields from discrete samples. Appl Math Mech 36–42 12. Chryssis AN et al (2005) Detecting hybridization of DNA by higly sensitive evanescent field etched core fiber bragg grating sensor. IEEE J Sel Top QE 11(4):864–872 13. Vitrik OB (2001) The Problem of “sensitive skin” and fiber-optic measuring systems. Soros Edu J 7(1):108–115

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14. Anfinogentov VI, Daragan MA, Dorofeeva SF (2016) The role of applied problems and mathematical modeling in teaching mathematics at a technical University. I. In: Mathematical methods and models: theory, applications and role in education international scientific and technical conference: collection of scientific papers, p 176–180 15. Petrov VN, Malyshev SL, Anfinogentov VI, Makhotkin IA (2016) Method for calculating the ring mode of gas-liquid flow flow for effective management of the process of hydrocarbon production. Bull Technol Univ 19(8):54–57 16. Anfinogentov VI, Vinogradov VYu (2019) Restoration of parameters of acoustic fields measured by a fiber multi-sensor system on the turbomachine nozzle section. Phys Wave Process Radio Eng Syst 22(4–2):145–150 17. Belousov MG, Mashoshin OF (2018) Experimental studies of the spectrum of natural forms and vibration frequencies of compressor blades of auxiliary aircraft engine. Sci Bull Moscow State Tech Univ Civil Aviation 21(4):60–72 18. Mashoshin OF (2015) Assessment of the diagnostic value of information in solving problems in the field of aviation equipment operation. Sci Bull Moscow State Tech Univ Civil Aviation 219(9):53–56 19. Mashoshin OF (2007) Mechanism of failure formation and reasons for failure of bearing units of aircraft mechanization elements. Sci Bull Moscow State Tech Univ Civil Aviation 123:33–40 20. Vinogradov VYu., Morozov OG, Nureev II, and Kuznetzov AA (2015) Fiber-optic system for checking the acoustical parameters of gas-turbine engine flow-through passages. In: Optical technologies for telecommunications, pp 9633–95330K. https://doi.org/10.1117/12.2181434 21. Nureev II, Morozov O G, Agliyullin AF, Purtov VV, Ovchinnikov DL, Anfinogentov VI, Vinogradov VYu (2018) Microwave photonic polyharmonic probing for fiber optical telecommunication structures and measuring systems sensors monitoring. In: Optical technologies in telecommunications, pp 10774–107741J. https://doi.org/10.1117/12.2318738

Exploratory Design of Technical Systems with Fluid and Gas Working Body Based on Heuristic Modeling of Physical Operating Principles A. A. Yakovlev(B) , S. G. Postupaeva, and N. V. Fedorova Volgograd State Technical University, 28, Lenin Ave, Volgograd 400005, Russia [email protected]

Abstract. The paper describes the method of searching the design of cooling systems, which is based on a graph model of the physical operating principle, based on the thermodynamic description of physical processes. A logical-mathematical model has been developed to represent the physical principles of the operation of technical systems with a fluid and gas working body. The examples of modeling a gas turbine twin-shaft installation and a flow-through gas-discharge laser are presented. A new classification of functional units of a technical system is described, which allows the encapsulation of the basic properties of the elements and presenting them as environmental objects. Heuristic modification methods for developing the improved models of the physical operating principles are proposed. These models allow you to determine the functions of the elements of the designed system; get a number of options for the constructive implementation of the future product; choose the best options with the help of a computer according to specified quality indicators. Keywords: Physical operating principles · Model of the physical principle of action · Working body · Technical system · Element function · Heuristic technique · Technology development technical system

1 Introduction A feature of scientific and technological progress in the field of creating new technical systems (TS) in the industry is the advancing measure of complexity of the created products in comparison with the methods and technologies of their designing. The issue is most acute at the initial stages of design—the stages of technical proposal and preliminary draft, when fundamental decisions are made on the principle of operation, structure, and component composition of the designed product, a comprehensive assessment of all possible options for its creation is carried out, as well as a comprehensive development of the entire product is carried out in general and its most important features. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_62

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In many areas of industry at these stages, traditional, «manual» approaches, using «trial and error» methods, dominate. This type of work is difficult to formalize and automate, therefore, considerable time is allocated for it according to standards. For this reason, it is possible to significantly reduce the time of design developments by increasing the productivity of the designer by formalizing this type of design work. This issue fully concerns the initial stages of designing of TS with a fluid and gas working body. These include internal and external combustion engines, heat and refrigeration machines, magnetohydrodynamic generators (MHD generator), laser systems, gas turbine, steam power and gas–vapor installations, rifle and artillery systems, and many other TS. Such systems operate on the basis of various physical operating principles (POP) and incorporate many different structural units and elements. The process of developing a new technical solution with a reliable design and, at the same time, a set of necessary characteristics is a solution to many non-trivial tasks. Thereby, the formalization of the development of TS with a fluid and gas working body using the new methods of engineering analysis and design technologies that allow us to further develop appropriate software for computer support of the stages of the technical proposal and outline design is an urgent task. Its solution will increase labor productivity in the initial stages of design and by that reduce the development time and improve the quality of design decisions.

2 Modeling of Physical Principles of Action Most of the modern design methods are based on the use of the models of physical operating principles that reflect physical processes in the designed system [1–9]. The analysis showed that existing methods are highly specialized and are aimed at private subject areas. They take into account the specificity and features characteristic of each field of technology and allow engineers to obtain advanced technical solutions. However, their theoretical provisions cannot be used to obtain general guidelines for the design of TS, which is required for the development of universal automated decision support systems at the initial stages of design. As part of the study, an analysis was made of the prototype model of the POP of the engineering physical method, based on the conceptual apparatus of the theory of complex thermodynamic systems. This model is described in detail in [10–17], and as analysis has shown, to the greatest extent corresponds to the mathematical description of the processes carried out in most TS. It reflects the movement of the working body inside the device, it is possible to indicate the sequence of interactions and movements of the working body, as well as the features of the constructive organization of the designed product. In addition, the following symptoms are taken into account: the state of aggregation of the working body (fluid, gas, a combination of liquid and gas), the presence of a phase transition for the working body in two-phase states; closure or openness of the working body route; stationarity of physical processes. The performance of the function is achieved through the implementation of the physical process in TS. The German technical standard DIN 66,201 defines a physical process as «combinations of related events in a system that change, move, or store matter, energy, or information». If a process occurs in an artificially created device, it is called

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a technical process. The latter is defined in the above standard as «a process whose physical variables can be measured and changed by technical means". A generalized model of the physical/technical process is given in [18]. The relevance of the model under consideration is confirmed, for example, by the heat balance equation for a thermodynamic system. The terms of the equation describe interactions with various environmental objects represented on the POP graph. The heat balance equation for a thermodynamic system is presented as follows [19–21]. S2

S4 T dS −

U = S1

k2 T dS +

S3

l2 Wt dl −

Wp dk+ k1

y2

l1

Qx dy

(1)

y1

S S where U—is the change in the internal energy of the working body; S12 T dS S12 Tds— S interaction of the working body with heat transmitters; S34 TdS—interaction of the working body of the TS with heat receivers; T —is the absolute temperature; S—is entropy. In addition, the equation includes an expression that takes into account the interaction of the working body with external objects (the environment) to change the parameters of the working body. • interaction of the TS working body with objects for transporting the working body; W p —factor of the intensity of interaction (generalized strength); k—factor of the extensiveness of the interaction (generalized coordinate). • interaction of the working body of the TS with objects for transporting the working body; W t —factor of the intensity of interaction; l—factor of the extensiveness of the interaction. • energy loss during the operation of the TS; Qx —is the intensity factor of the interaction leading to the loss of energy of the working body; y—factor of the extensiveness of this interaction. It is convenient to represent the interaction data by the vertices and arcs of the directed graph. For example, fragments of graphs illustrating chemical transformations are shown on Fig. 1. The first peak v represents a subsystem of substances that enter into a reaction. Arcs incident to it i1 , i2 , …, in —are flows of substances that enter into a reaction. The peak v*—is the subsystem of reacted substances. Arc il is a stream of reacted substance. Arc, which is a flow of a chemical extensor echem (mass), is a loop. Arcs with symbols eex and eent —streams of the second extensor. The first graph (Fig. 1a) illustrates the conversion of the chemical form of motion into a given one, the second (Fig. 1b) illustrates the conversion of this form of motion into a chemical one. Thus, the interactions of the working body of the TS are represented on the POP graph by arcs with the designation of extensors associated with these interactions. These arcs are incident peaks—characteristic points. In the process of functioning, the substance of the working body of the TS can move inside the device, which necessitates the introduction of arcs of the second type—«route», connecting characteristic points.

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Fig. 1. a the conversion of the chemical form of motion into a given one; b the conversion of this form of motion into a chemical one.

For Fig. 2 shows a diagram of a gas turbine twin-shaft installation, and Fig. 3 shows a model of the physical principle of operation for this scheme. In this model, characteristic points and interactions between them are identified.

Fig. 2. Scheme of a gas turbine twin-shaft installation: 1—low pressure compressor; 2—air cooler; 3—high pressure compressor; 4—high pressure turbine; 5—high pressure combustion chamber; 6—low pressure combustion chamber; 7—low pressure turbine; 8—regenerator; 9—generator; 10—reducer; 11—starting motor.

The vertices of the POP graph are marked with the Latin letter v, with superscripts and lower indices. The indices indicate the state of the working body and the serial number of the characteristic point, respectively: v1 1 —air in the low pressure compressor; v2 2 —air in the air cooler; v3 3 —air in the high pressure compressor; v4 4 —air in the regenerator; v5 5 ,v5 6 —fuel–air mixture and combustion products in the high pressure combustion chamber; v6 7 —working body in a high pressure turbine; v7 8 ,v7 9 —fuel–air mixture and combustion products in the low pressure combustion chamber; v8 10 —working body in a low pressure turbine; v9 11 —exhaust gas in the regenerator; v10 12 , v11 13 —fuel in fuel pumps.

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Fig. 3. Graph of the POP model of a gas turbine twin-shaft installation.

Arcs denoting interactions are marked with the Latin letter e which also has upper and lower indices. The superscript indicates the type of interaction, the subscript indicates the sequence number of the interaction. Route arcs show the flows (movements) of the working body and are marked with the letter i. The superscript indicates the various phase states or chemical composition of the components of the working body, the subscript indicates the serial number of the flow of the working body. The equipment also uses units consisting of unitary converters operating in parallel. According to this scheme, for example, piston engines consisting of two, four, six or more cylinders are structurally realized. In the general case, a TS is part of a larger TS—a supersystem. Its working body interacts with other devices that are part of the supersystem and with the objects of the external environment. According to thermodynamic concepts, all these interactions are realized through the exchange of transfer substrates - extensors (generalized coordinates). Objects interacting with TS can be classified according to a hierarchical principle. 1. Technical and natural objects that are not part of the supersystem to which the TS belongs. For example, a car engine is part of a supersystem, which is a car. In this case, atmospheric air is an example of an object that interacts with the engine and is not part of the supersystem. 2. Technical objects that are part of the same TS, to which the EC belongs, and are at the same hierarchy level with it. Examples are transmission, braking system, car body. The same environmental objects at different points in time can perform different functions. For example, a mechanical drive of an internal combustion engine during a stroke performs the function of an energy consumer, during a compression stroke it is an environmental object of the second kind, and during cycles of absorption of a working mixture and expulsion of combustion products an object of the third kind.

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3 Heuristic Modification of PPA Models The purpose of constructing POP models is to obtain new, more efficient technical solutions for TS. In this regard, an important task is to develop mechanisms for modifying these models, that is, formulate rational operations on them. On the one hand, POP models are formal mathematical objects—graphs—and therefore, corresponding mathematical operations can be applied to them. Such an approach, although it has a purely formal character, but the impression of some completeness, since mathematical operations on graphs in themselves exhaust all possible manipulations on such objects. On the other hand, POP graphs are a reflection of some objectively proceeding physical processes in a technical device. Their peaks and arcs carry a specific content and many of the formal actions on such objects do not have practical meaning. From the point of view of the constructive approach, it may seem more appropriate to use heuristic techniques funds, which is a prescription or an indication of how to transform an existing technical solution or in which direction to look for a solution to a problem. Most heuristic tricks have two parts. The first is a description of the space of certain variable categories that should be changed. The second part is methods of changing these variables, i.e. some informal operations. Some techniques contain indications of several variables and/or several ways to change them. Such techniques are a combination of similar search operations and/or variable categories. An analysis of the heuristic techniques funds [22], shows that for modifications of the POP models, the techniques contained in them should be classified in accordance with the space of variables and the set of operations that characterize this model. For this, it is necessary to compare heuristic techniques with mathematical operations on graphs and classify heuristic techniques in accordance with these operations. In addition, it seems advisable to change the wording of some heuristic techniques in order to more conveniently use them for transforming the topology of POP graphs. Modification of the model by adding edges. The graph structure can be changed by using the operation of adding edges on it. Adding the edge e to the graph G1(V 1 , E 1 ) (the notation is—G1 (V 1 , E 1 ) + e, provided e∈ / E1 ) gives the graph G2(V 2 , E 2 ), where V2 := V1 &E2 := E1 ∪ {e}

(2)

This operation may make practical sense. The number of vertices remains unchanged, and therefore the semantics of adding an edge between already existing characteristic points can be reduced to introducing additional interaction or an additional channel for moving the working body between already existing characteristic points. The following heuristic methods are examples of such operations on a graph of the POP model: to separate harmful or undesirable impurities from a substance; split a moving stream into two or more; to connect objects homogeneous or intended for related operations, etc. Modification of the model by removing edges. Removing the edge e from the graph G1(V 1 , E 1 ) (the notation is – G1 (V 1 , E 1 ) – e, provided e ∈ E1 ) gives the graph G2(V 2 ,

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E 2 ), where V2 := V1 &E2 := E1 /{e}

(3)

The edges of the POP graph correspond to interactions of the working body and displacements of the working body. As a result of the physical process between the working body and its environment there are interactions that are not required for the functioning of the device, but often reduce the efficiency of the process. Such an operation on the POP graph is carried out using the following heuristic techniques: to exclude interaction while maintaining the object all the previous functions; to exclude the channel for moving the working body while maintaining the object of all previous functions; derive elements exposed to harmful factors beyond their scope, etc. Modification of the model by adding vertices. Adding the vertex v to the graph / V1 ) gives the graph G2(V 2 , G1(V 1 , E 1 ) (the notation is – G1 (V 1 , E 1 ) + v, provided v ∈ E 2 ), where V2 := V1 ∪ {v}&E2 := E1

(4)

As a result of the operation, a new isolated vertex is added to the graph. This operation is possible in combination with the operation of adding edges. It differs from simply adding an edge in that the goal is to add interaction with a new characteristic point or a new environment object. Such an operation on a graph is carried out using the following heuristic techniques: attach to the object a new element located in the working environment or in contact with it; add mechanical, electrical, thermal, electromagnetic, chemical interactions, as well as other heuristic techniques. Modification of the model by removing vertices. Removing the vertex v from the graph G1(V 1 , E 1 ) (the notation is – G1 (V 1 , E 1 ) – v, provided v ∈ V1 ) gives the graph G2(V 2 , E 2 ), where V2 := V1 /{v}&E2 := E1 /{e = (v1 , v2 )|v1 = v ∨ v2 = v }

(5)

Removing vertices, in most cases, it makes sense to simplify the device. Deletion is possible for vertices of both types, both characteristic points and environmental objects. Together with them, the edges are removed, i.e., all interactions with them. Such operation is performed using the following heuristic techniques: Exclude the most stressed (loaded) element. Exclude an element when the object retains all previous functions. Remove «unnecessary details» so that one element performs several functions, which eliminates the need for other elements, etc. The technique of heuristic modification of POP models has been successfully used to obtain new methods and technical solutions for tool cooling systems on various metalcutting machines [23–26] and can be recommended for other classes of TS with a fluid and gas working body.

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4 Conclusions As a result of the study, a new logical and mathematical model was developed to represent the physical principles of the operation of technical systems with a fluid and gas working body. These include internal and external combustion engines, heat and refrigeration machines, MHD generators, laser installations, gas turbine, steam power and gas–vapor installations, rifle and artillery systems, and many others. This model is intended for use at the initial stages of designing such systems – a technical proposal and a preliminary design. It allows you to: 1. significantly facilitate the task of finding design options for a new device, which, in this case, comes down to a formalized sequence of actions. This allows you to significantly expand the search for options for the design of the designed device in comparison with the traditional approach and create a technical solution with a level of novelty inherent in inventions and utility models; 2. to solve the problem of finding a new technical solution in stages, by using the encapsulation mechanism of the functions of individual nodes of the TS and sequentially considering them as objects of the environment, which can significantly reduce the complexity of this task; 3. use formal methods of heuristic modification to obtain improved POP models, for which a connection has been established between the majority of heuristic techniques from the intersectoral fund and mathematical operations that can be performed with the model as a formal object. This confirms not only the adequacy of the model, but also allows you to more effectively apply heuristic techniques in relation to it, since each method is associated with mathematical operations on the model; The developed POP model allows you to: determine the functions of the elements of the designed system; get a number of options for the constructive implementation of the future product; choose the best options with the help of a computer according to specified quality indicators.

References 1. Nam G et al (2015) Conceptual design of passive containment cooling system for APR-1400 using multipod heat pipe. Nucl Technol 189(3):278–293 2. Voinov B (2001) Information technologies and systems. Book I. Methodology of synthesis of new solutions. UNN Publishing house of N.I. Lobachevsky, Nizhny Novgorod 3. Norenkov I (2009) Essentials of automated design. MSTU Publishing house of N.E, Bauman, Moscow 4. Jiang J-G et al (2015) Application of TRIZ theory in problem based learning. In: ICCSE. proceedings of 10th international conference on computer science and education, Cambridge, United Kingdom, p 905–909 5. Belaziz M et al (2000) Morphological analysis for product design. CAD Comput Aided Des 32(5):377–388 6. Franke H (1976) Untersuchungen zur Algoritmisierbarkeit des Konstruktionsprozesses. Fortschrittsberichte VDI-Z 1(46):48–56

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7. Koller R (1976) Konstruktionsmethode fur den Maschinen, – Gerate – und Apparateban. Heidelberg, New York, Berlin 8. Bobrow D (1984) Qualitative reasoning about physical systems: an introduction. Art Intell 1–5 9. Forbus K (1984) Qualitative process theory. Art Intell 85–168 10. Buede D (2008) The Engineering Design of Systems Models and Methods. Innovative Decisions Inc., Reston, VA, United States 11. Yakovlev A (2007) Development of sets of technical solutions for energy transforming installations. In: Mechanical engineering-1, Moscow 12. Kamayev V et al (2005) Training in conceptual design of energy converters on the basis of the system approach. Otkrytoye Obrazovanie 5:62–69 13. Yakovlev A (2005) Metod to synthesize technical solutions for internal combustion engines at the initial design stages. Dvigatelestroyenie 3:26–31 14. Yakovlev A (2007) Development of a matrix of technical solutions for energy converters and an algorithm to form lists of function-compatible structural elements. Eng Mag Appendix 10:34–39 15. Yakovlev A et al (2010) Automated synthesis and choice of technical solutions for energy converters. Inf Technol 11:71–78 16. Yakovlev A et al (2016) Search design of cooling systems based on an engineering physical approach. Inf Technol 22(11):819–826 17. Yakovlev A et al (2017) A new method of search design of cooling systems and refrigerating systems containing a liquid and gaseous working medium based on the engineering physical approach. In: Creativity in Intelligent Technologies and Data Science. 2nd Conference, CIT&DS 2017, Volgograd, 12–14 September 2017, p 528–550 18. Olsson G et al (2001) Digital control automation systems. Nevsky dialect, SPb 19. Guchman A (2010) About the essentials of thermodynamics. LKI Publishing house, Moscow 20. Veynik A (1973) A thermodynamic couple. Nauka i tekhnika, Minsk 21. Alekseev G (1980) General heat engineering. High School, Moscow 22. Polovinkin A (1981) Automation of search design (artificial intelligence in machine design). Radio and communications, Moscow 23. Yakovlev A et al (2018) Development of the technical solution of the device for cooling the cutting zone of the milling machine by the method of search design. News High Edu instit Eng 3(696) 24. Yakovlev A et al (2009) Method of supply of lubricating and cooling technological means. Patent 2367556 of the Russian Federation, the IPC 23 Q 11/10 25. Yakovlev A et al (2015) Device for feeding of lubricating and cooling technological means. P. m. 154326 of the Russian Federation, IPC B23Q11/10 26. Yakovlev A et al (2009) A method to supply technological refrigerants. Patent 2367556 of the Russian Federation, the IPC B23Q 11/10

Computer-Aided Design of Precast End Mills Based on the Parametric Model A. V. Bogoyavlensky(B) and A. V. Shatilo The Ural Federal University, 19, Mira, Ekaterinburg 620002, Russia [email protected]

Abstract. Modern tools with interchangeable cutting inserts currently have a significant impact on the cost of production. A wide variety of tools from the world’s leading manufacturers and the binding of the tool casing to the manufacturer of the cutting inserts leads to large stock storage of the same type tools from different manufacturers at the enterprise. There is a division at the enterprise capable to make independently the case of the tool for any cutting inserts, but it is necessary to design the case of the tool for this purpose. This article discusses the design of end mill casings based on the parametric model in the SOLIDWORKS system. The parametric technology allows for a quick design of the end mill case based on the created prototype. As a result, it is possible in a short time to develop and manufacture the end mill case for various types of processing, which will lead to a positive economic effect for the enterprise. Keywords: Cutting tool · End mill · 3D model · Parametric model · Cutting inserts · 3D design

1 Introduction The twenty-first century is a century of technology and innovation development, where enterprises are constantly in a competitive environment, where it is necessary to respond to changing market conditions. Machine-building enterprises are forced to constantly update the range of products, which entails the purchase of new equipment and related tools, which in turn is one of the factors of the pricing of finished products. Metalworking companies are offered a wide range of tools from various leading manufacturers such as Seco, Sandvik Coromant, KORLOY, ZCC, Walter, KZTC and many others [1–6]. Tool manufacturers are trying to develop a specific solution for a specific type of processing of cutter bodies and cutting inserts. From a huge list of catalog tables, it remains to choose a ready-made solution. As a result, a large range of unused cutting bodies and inserts accumulate at machine-building enterprises when changing products. Often, businesses become tied to certain manufacturers of cutting bodies that are suitable for certain inserts. All of the above pushes machine-building enterprises with their tool shops to manufacture their own cutting bodies. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_63

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Due to the fact that the design and manufacture of end mills for a certain type of processing is a time-consuming process, it is advisable to develop a parametric 3D model of the assembled end mill using automatic design systems, for example, in SOLIDWORKS. The most difficult part of the cutter is its working part, equipped with replaceable cutting inserts. The parametric program of designing a working part of the end mill for processing planes, ledges, grooves, wells is considered in this article. It is assumed that a single parametric model of the assembled end mill should provide the design of cutter bodies for different types of processing with cutting inserts of different manufacturers in the diameter range 10–63 mm.

2 Materials and Methods Currently, milling is a fairly common type of Metalworking. End mills are often used in CNC machines as tools with wide technological capabilities. Cutters are used for processing planes, vertical projections, various grooves, wells and shaped surfaces both on vertical milling and horizontal milling machines [7]. The cutter can work as a lateral cylindrical part, and with the end part of the teeth. There are many publications on the design of end mills, which are mainly aimed at facilitating the work of the designer. Specific solutions are described that eliminate certain disadvantages of certain end mills, or that allow a particular cutter case to become more versatile [8–10]. It is also offered to do the universal case without addressing more to its designing and to change sockets under cutting inserts, or to design the new case under a new cutting mode constantly. As shown in [11–14], parametric technology allows you to quickly build models of typical products on the basis of a once designed prototype. In this article, we will show how you can design a special end mill case for a certain type of processing in one program with a parametric 3D model, or design a universal end mill case with minimal time. Let’s consider the main parameters that need to be taken into account in the parametric model of the precast end mill during the design process. The main parameters of the end mill that do not change are the material of the cutter case and the geometry of the base surfaces of the shank for fixing to the machine. The main variable parameters of the cutter, determined based on the processing conditions, are given in Table 1: • • • • • •

cutter diameter; number of teeth; tooth pitch (uniform/uneven); the angles of the cutting edges of the cutter; the back angle of the cutting edge; the geometry of the insert mounting hole (impression for the type and configuration of cutting inserts or cartridges).

The main changes in the design process will affect only the working part of the cutter case. Consider the basic principles of choosing the main parameters of the end mill.

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A. V. Bogoyavlensky and A. V. Shatilo Table 1. Adjustable parameters of the 3D model of the end mill.

Name of the parameter

Valid value

Cutter diameter

From 10 to 63 mm

Number of inserts or cartridges for insert

1–15 (Selected from the list)

Number of teeth depending on the diameter of the cutter

10(2), 12(2), 14(2), 16(2), 20(2), 22(2, 3), 25(2, 3), 32(3, 4), 40(4, 5), 50(5, 6) 63(6)

The pitch of the teeth uniform/uneven

Yes/no

Main angle in plan ϕ

From 10 to 90°

Radial front angle γp

From −11 to + 5°

Axial front angle γo

From −8 to + 20 to degrees

The diameter of the cutter is determined by the processing requirements and is set by the technologist. When choosing the diameter of the cutter, you need to consider the processing strategy and the end result. The number of cutter teeth is determined by the strength of the cutter tooth and the size of the replaceable cutting insert. Each cutter diameter can be selected in a limited set (the program specifies the possible range for selection). The cutter teeth pitch is traditionally uniform, but studies [15] have shown that the uneven pitch of the teeth has a positive effect on the processing by reducing the fluctuations of the machine. The effect of the cutter teeth pitch on the dynamics of the cutting process is shown in Fig. 1.

Fig. 1. The influence of pitch on amplitude of vibrations. A—with uniform step, B—with variable step.

Most important for the milling process are the angles of the cutting teeth. In a parametric model, you can specify them, but you should limit the possible limits for selection.

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The main angle in the plan ϕ is the angle between the main cutting edge of the cutting insert and the processed workpiece surface. The main angle in the plan affects chip thickness, cutting forces and tool life. The small main angle in the plan provides a smoother entry into the cutting, limits the radial cutting forces and protects the cutting edge from damage. However, higher axial cutting forces increase the load on the workpiece. Cutters with an angle ϕ = 45° provide a good balance of radial and axial cutting forces, which reduces the power requirements of the machine. Cutters of this type are suitable, first of all, for milling materials that give short chips and are prone to chipping in the event of excessive radial cutting forces on the gradually decreasing allowance at the end of cutting. Smooth entry into the cutting reduces the tendency to vibration when using a tool with a long overhang or short/nonrigid tool holders. Mills with the main angle of 60–75° allow you to work with increased depth of cut compared to cutters with an angle ϕ = 45°. Cutters with the main angle of 10° are designed for high feed milling and plunger milling. In this case, a thin chip is formed, allowing you to work with a very high feed on the tooth at a small depth of cut and, accordingly, at the maximum minute feed [16]. It should be noted that the cutting insert of the cutter can be rotated in radial and axial direction, respectively, the angle of rotation would be radial γp and axial angle of γo, which in turn can be positive, neutral or negative. The ratio of γp and γo angles can be different, as shown in Fig. 2.

Fig. 2. Types of geometry of milling cutters with inserts: 1—positive-positive, 2—zero-zero, 3—negative-negative.

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Positive-positive geometry is useful in the processing of nonferrous metals. In this case, the cutting process is facilitated, but the disadvantage is the weakened geometry of the cutter case. Negative-negative—here, the cutting edge is strong, withstands heavy loads and is used for processing high strength materials such as hardened steel, cast iron. Positive–negative here is the best contact with the workpiece. It is used for processing steel. The geometric parameters of the end mill can vary in a sufficiently large range; the parameters adopted for the design with the range of their changes are given in Table 1. End mills allow applying a wide variety of ways of fastening of cutting inserts. Therefore, a huge number of different types of such cutters are currently produced. In order to obtain the minimum radial and end runout of the cutting edges, the most complex methods of fastening allow adjusting the position of the plates in the socket [17]. In our model, we accept a variant with the fastening of cutting inserts by the screws pressing insert to a socket in the case. The above parameters determine the basic geometric and cutting parameters of the cutter, but they can be obtained by using cutting inserts of different shapes and different manufacturers. For this purpose, the program introduced 3D models of cutting inserts from different manufacturers. An example of a cutting insert is shown in Fig. 3.

Fig. 3. Example of 3D insert model in SOLIDWORKS.

3 Results The design process using the program begins with the selection of the main parameters of the cutter, described in Table 1. First, it is proposed to choose the diameter of the cutter from 10 to 50 mm in increments of 2 mm. Next, select the number of teeth and set the angles of the cutting edges. When selecting the number of teeth and assigning the angles of the cutting edges, the program does not allow you to go beyond the set range. It is also proposed to spread the teeth in diameter evenly or not evenly. Once the angles of the cutting insert are determined, the cutting insert to be applied is selected, taking into account the constraints.

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In the 3D model, each parameter received a number and was presented in a table for interactive input of values. An example of a screen with a model parameter number is shown in Fig. 4.

Fig. 4. Screen view when working with a model in SOLIDWORKS.

Further, the socket is formed for mounting the insert in the cutter case, according to the existing shape of the support surfaces of the cutting insert. This process is shown in Fig. 5. Next, the rounding in the corners of the socket under the insert is designed to ensure tight contact between the support surfaces of the cutting insert and the surfaces in the socket on the case. To press the cutting insert to the side surfaces of the socket, the axis of the threaded hole in the case is shifted relative to the axis of the hole in the cutting insert by 0.05 mm. The designed socket is copied as many times as the specified teeth of the cutter. The result is a model of the working part of the end mill. The result of the design is shown in Figs. 6 and 7. At the end of the work, the designer can use SOLIDWORKS to edit the cutter model. The modifications can include the addition of one of the variants of the cutter shank in accordance with the standard, channels for supplying the coolant depending on the manufacturing technology and other improvements. An example of a finally designed cutter is shown in Fig. 8.

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Fig. 5. Forming a socket for mounting the cutting insert.

Fig. 6. Working part of the cutter.

Even more advantageous from an economic point of view is the option of developing a universal cutter case for installing the cartridge in which the cutting inserts will be mounted. Switching from one manufacturer’s inserts to another manufacturer’s inserts will not change the cutter case. This technology will allow designing a lot of cartridges with different inserts, without changing the cutter case. It is proposed to make the seat in the cutter universal, so that

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Fig. 7. The working part of the cutter assembly with cutting inserts.

Fig. 8. An example of end mill with cutter inserts in SOLIDWORKS.

using cartridges with different angles to install the cutting plate at any angle without changing the cutter body itself. It should be noted that cartridges can be quickly manufactured by using additive technologies [18] with minimal mechanical processing of the base surfaces of the cartridge. Due to the fact that the cartridge has a small size, the manufacture of the cartridge is economically justified. An example of a universal cartridge for mounting a cutting insert is shown in Fig. 9.

4 Conclusion As a result of this work, we have obtained a convenient universal parametric 3d model with a user-friendly interface that allows you to quickly design the end mill with the required parameters. Using this parametric 3D model, machine-building enterprises have the opportunity to reduce their costs and time for the development and manufacture of the desired end mill using any cutting insert. The enterprises manufacturing own cases of cutters as much as possible minimizes the expenses on this type of the tool as the range of cases of cutters and inserts considerably decreases.

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Fig. 9. Variant of a universal cartridge for a cutting insert.

It is proposed to introduce universal cartridges with different geometries and angles for cutting inserts. Reducing the cost of manufacturing the cartridges is possible using additive technology.

References 1. Metal-cutting tools with replaceable carbide inserts: catalog (2013) Plant JSC “Spetsinstrument” . Russia, Georgievsk 2. Cutting tool (2019) https://www.spinstrument.ru. Accessed 12 Nov 2019 3. Metal cutting tools (2019) https://www.sandvik.coromant.com. Accessed 12 Nov 2019 4. Full catalog of the tool – 2014–2015 (2019) https//www.korloy-tools.ru. Accessed 12 Nov 2019 5. End mills (2019) https://www.korloy.com. Accessed 12 Nov 2019 6. ZCC-ST Main catalogue (2019) https://www.zcc-st-tools.ru. Accessed 12 Nov 2019 7. Filippov GV (1981) Cutting tool. Mashinostroenie, Leningrad, p 392 8. Volokh V, Sharivker L, Zeidner W, Bulakhov S, Gflipko V (2007) Method of manufacturing a vibration- resistant end mill. RU patent 2462336, 06.08.2007 9. Robert N. Mitchell (US) (1999) Mortise and end mill with universal slots for cutting plates. RU patent 212/2124970, 20.01.1999 10. KORLOY metal cutting tools (2019–2020) https://www.korloy.com/en/ebook/2019. Accessed 20 Nov 2019 11. Lukinskikh SV, Kugaevskii SS (2011) Product design in SolidWorks: studies. Handbook for students, Urfu, Ekaterinburg 12. Kugaevskii SS, Vlasov VV, Oreshkin AA (2017) 3D face mill model creation method using feature-based modelling. J Adv Res Tech Sci 11–17 13. Pritykin FN, Shmulenkova EE (2012) Basic elements of CAD of metal-cutting tools using parametric 3D modeling. Omsk Sci Bull 1(107):277–282 14. Yurasov SY, Yurasova OI, Ryabov EA (2016) Design and technological approaches to parametric modeling of cutting tools on the example of end radius cutters. STEEN 3:18–19 15. Milling cutters with SMP (2019) https://secotools.csod.com. Accessed 21 Sept 2019 16. Main angle in plan and chip thickness during milling (2019) https://www.sandvik.coromant. com. Accessed 21 Sept 2019

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17. Features of designs of milling cutters equipped with hard metal (2019) https://texinfo.inf.ua/ razdeli/reg_instr. Accessed 21 Sept 2019 18. Additivnye-tekhnologii-v-deystvii (2019) https://rostec.ru/news/. Accessed 20 Nov 2019

Modeling Cutting Force During Internal Grinding with Different Wheel Characteristics A. V. Akintseva(B) and P. P. Pereverzev South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, Russia [email protected]

Abstract. In modern engineering, a wide range of grinding wheels with different characteristics in hardness, grain, structure and other parameters is used. In the same grinding conditions by the wheels of different characteristics, the cutting force, temperature in the contact zone of the wheel and the workpiece, elastic movement of the technological system and the quality parameters of the treated surface will be different. Moreover, the parameters of the grinding process change significantly during the wheel durability between dressings due to the blunting of the wheel cutting grains. Therefore, considering the parameters of the wheel characteristic is mandatory when designing high-performance cutting modes, which ensure the stable quality in processing the parts batch. However, there are still no models and methods considering the parameters of the grinding wheel characteristic when calculating the cutting force, thermal indicators in the cutting zone, optimal cutting modes and quality indexes of the treated surface. The article proposes an approach for considering the wheel characteristic through the index of the wheel grain blunting in the cutting force model for the internal grinding. A method for calculating the range of blunting of the wheel grains between dressings in dependence on the parameters of the wheel characteristic is developed. Keywords: Grinding wheel · Wheel characteristic · Grain blunting · Dressing

Nomenclature Vsoc Srad VW VGW M3 , M4 σi SX d D T

axial feed rate, mm/min program value of the radial component of the cutting force, mm/double stroke speed of part rotation, m/min speed of wheel rotation, m/s coefficients determined by formulas (2) and (3) average value of stress intensity, N/mm2 contact area of wheel and workpiece in the plane of axial cutting force action, mm2 workpiece diameter, mm wheel diameter, mm total height of grinding wheel, mm

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_64

Modeling Cutting Force During Internal Grinding

η μ NN NN PZN , PZH ηNCP CP ηH ηmin H fN / NH fsk γc Es dz DM KS

549

ratio of wheel blunting coefficient of friction of the abrasive grain on the treated material cutting power according to standards for grinding by the abrasive wheel of any hardness different from H, kW cutting power for grinding by the abrasive wheel of hardness H, kW tangential components of the cutting forces corresponding to cutting powers NN and NN , N average value of the blunting ratio of wheels with different hardness, for which the coefficient KN is given average value of the blunting ratio of the wheel with hardness H minimum blunting ratio after the dressing wheel with hardness H critical self-sharpening force of the wheel with hardness H (N) critical value of the cutting force per grain of the wheel surface energy of a bundle material, J/m2 elastic modulus of a bundle material, Pa average diameter of the main grain fraction, mm diameter of bundle gap, mm coefficient determining a length of the initial crack in the bundle gapnnn

1 Introduction When grinding the accurate surfaces of the parts, the processing is carried out in the mode of wheel grain blunting, in which the tops of the grains are worn increasing the blunting areas on the back surface of the cutting grains (grains are not destroyed or torn out of the bundle under the cutting force action). Grain blunting leads to an increase in the cutting force on each subsequent part. The result is an amplification of various negative phenomena: processing accuracy diminution, appearance of cut and thermal defects, roughness increase, loss of the geometric shape by the wheel, etc. In the production to reduce negative phenomena, the grinding wheel is dressed. After dressing, the outer grains of the wheel are sharpened and the wheel surface takes the form of a regular geometric shape. Wheel dressing is a mandatory element for any grinding operation [1–3]. Considering all of the above, when developing the cutting force model, the issue of considering the value of the grain blunting between dressings at grinding parts batch becomes acute. The force model of the grinding process, considering the wheel blunting, allows calculating the cutting force fluctuation and evaluating the changes in the quality parameters of the treated surface between dressings. In the future, the force model can be used as the basis for the model of metal removal [4] in the method of optimizing the grinding process [5]. The solution to the problem of considering the wheel blunting in the force model is complicated by the fact that the blunting is directly dependent of the characteristics of

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the grinding wheel (hardness, grain grade, structure, etc.)—Figs. 1 and 2. For example, the harder the wheel, the more firmly the grains are held by the bundle, which leads to a greater blunting of the wheel grains after dressing and an increase of the initial cutting force after dressing [6–8]. This fact is confirmed statistically in the general machinebuilding standards of the cutting modes [9, 10], which are based on the statistics of the cutting modes at machine-building enterprises.

Fig. 1. Changes of radial a PY and tangential PZ b components of the cutting force in dependence on the wheel hardness (H, I, J, K, L, M, N) at grain grade F30.

Fig. 2. Changes of radial a PY and tangential PZ b components of the cutting force in dependence on the wheel grain grades (F80, F60, F40, F30) at wheel hardness H.

Analysis of known sources [11–16] has shown that most of the works are devoted to modeling the cutting force in the form of empirical dependencies in a narrow range of variable factors (for one wheel characteristic and several steel grades) and without considering the blunting of wheel grains. Therefore, the issue of developing the cutting force model, considering the changes of grain blunting between dressings in dependence on wheel characteristic, is currently actual.

2 Modeling the Cutting Force During Internal Grinding by the Wheels of Different Characteristics As the cutting force depends on the wheel grain blunting, it is possible to estimate the range of fluctuations of the wheel blunting from the fluctuations of the cutting force between dressings. From the practice of the grinding in mass production at measuring

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the maximum active power of the wheel drive in the circular grinding operations, it is experimentally determined [10] that the wheel dressing in the different grinding operations is held when the wheel cutting power increases by 1, 3…1, 5 during allowance removal. Considering that in mass production, the operation productivity is brought to the highest possible level, we take a range 1, 3…1, 5 of the cutting power fluctuation as the basis. As a measure of the wheel grain blunting, we will take a parameter called «ratio of the wheel blunting» and denote it using the variable η. The ratio of the wheel blunting η characterizes the value of the relative base surface of the wheel on the areas of grain blunting. To consider fluctuations of the cutting force during processing, it is necessary to take into consideration the ratio of the wheel blunting in the model of the cutting force. As the model of the cutting force, which considers parameter η, we will take the following analytical model of the cutting force in the example of internal grinding with a longitudinal feed of the tool, presented in work [17]. In this article, we present only the tangential cutting force:  (1) PZ = M3 Srad + M4 Srad Coefficients M 3 and M 4 are obtained by formulas: 2, 732σi VW π dVSoc 2 (VWG + VW )2 + VSoc  d ·D σi ημVW M4 =  d −D 3 (V + V )2 + V 2 M3 =

WG

W

(2)

(3)

Soc

Using reference [10], we find a correction factor on the grinding power, which depends on the wheel hardness (denoted as KN ). So for hardness H, I i J—KN = 1, for hardness K and L—KN = 1, 12, and for hardness M and N—KN = 1, 3. As a result, it can be assumed that the initial ratio of the wheel blunting increases as the wheel hardness increases, and, consequently, its strength which is characterized by an index of the critical force of self-sharpening [18]. Also, it should be noted that wheels of different hardness have a different blunting ratio in the first minutes after dressing: the greater the wheel hardness, the greater the critical force of self-sharpening and the initial blunting ratio of the wheel [10]. Correction factor KN sets the effect of the wheel hardness on the cutting power which increases due to a different initial blunting ratio of the wheel: KN =

NN N

(4)

To calculate the cutting power, we will express the coefficient KN through tangential cutting forces (6), put in the formula (4) expression (5) [18]: Nkp =

PZz,i VWG 1000

(5)

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PZN · VWG PZN = PZH · VWG PZ

KN =

(6)

Putting in the formula (6) expression (1), we get the average values of the blunting ratio of the wheel of different hardness and height:  M3 Srad + M4 Srad ηNCP  KN = (7) CP M3 Srad + M4 Srad ηH Analysis of the relation of two summands in numerator and denominator of the right side of Eq. (7) showed that in the real variability interval of technological parameters, the second summand is greater than the first one in 4…10 times. Therefore, the first summand M 3 S rad in the right side of the formula (7) is neglected, and we get the following equation by simplifying: CP ηNCP = KN · ηH

(8)

On the basis of production experience, the cutting power changes by 30…50% during the time of the wheel durability [18]. As a result, it can be assumed that the cutting force increases by 1,5 times during the time of the wheel durability. In accordance with formula (1), this increase of the cutting force for different ranges of the cutting conditions corresponds to an increase of the wheel blunting ratio in 1,8…2,2 times (or 2 times on average). Then the average value of the wheel blunting ratio is found by the formula: ηNCP = 1, 5ηmin

(9)

The maximum value of the blunting ratio ηmax at the end of the wheel durability is ηmax = 2ηmin

(10)

Putting formula (8) in (9), we get ηmin = ηmin H · KN

(11)

The value of the blunting ratio of the wheels run-in after dressing with hardness H on average is ηmin H ≈ 0, 015 [18]. ηmin = 0, 015 · KN

(12)

In the source [10], coefficient KN is given only for a certain grain grade and structure number. Therefore, to extend the range of the formula (12), we establish the interrelation of the coefficient K N with the critical self-sharpening force f ck , which considers parameters of the wheel characteristic in a complex way [18]. To obtain interrelation of the coefficient KN with the critical self-sharpening force, we approximate the normative points K N . It should be considered that the normative values of K N are close to a linear

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dependence and they are given for the range of the wheel hardness. So we will approximate the points with a straight-line dependence that passes through the extreme values of the entire range. As a result, we get KN = 0, 58

fcr − f +1 fN − f

(13)

The critical value of the cutting force per grain of the wheel, above which the grain is pulled out of the bundle or destroyed, is found by the formula [18–22]: ⎤⎤ ⎡ ⎡   3 K γ E 3 DM C C C d γE⎣ ⎦⎦ (14) fcr = π 1 − exp⎣−  8 2d 3 γ E Z

Let us list the ranges of some components of the formula (14) for different processing conditions. Elastic module of the bundle material for electrocorundum E z = 3,64 10 N/m2 , γ z = 72,9 J/m2 and for ceramic bundle E c = 0,735 10 N/m2 , γ c = 33,8 J/mm2 [20]. Average diameter of the main grain fraction d Z = 0,19 mm F80, d Z = 0,28 mm F60, d Z = 0,45 mm F40, and d Z = 0,5 mm F30 [19]. The diameter of the bundle gap is shown in Table 1; data is taken from the source [19]. The coefficient determining the length of the initial crack in the bundle gap KC = 1,71 [19]. Table 1. Diameter of the bundle gap in dependence on the grain grade and hardness of the wheel [19]. Wheel hardness

Grain grade of the wheel F80

F60

F40

F30

H

0,0,000,504

0,0,000,735

0,0,001,185

0,0,001,572

I

0,0,000,626

0,0,000,920

0,0,001,473

0,0,001,964

J

0,0,000,727

0,0,001,068

0,0,001,716

0,0,002,287

K

0,0,000,814

0,0,001,196

0,0,001,923

0,0,002,563

L

0,0,000,893

0,0,001,311

0,0,002,108

0,0,002,809

M

0,0,000,964

0,0,001,419

0,0,002,276

0,0,003,038

N

0,0,001,030

0,0,001,516

0,0,002,432

0,0,003,245

Solving Eqs. (13) and (14) conjointly, we get ηmin = 0, 009

fcr − f + 0, 015 fN − f

(15)

ηmax = 0, 018

fcr − fH + 0, 03 fN − fH

(16)

As a result, using formulas (15)–(16), the calculated ranges of changes in the blunting ratio of the wheel for different characteristics during their durability between dressings

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are determined. It will allow calculating changes in the processing quality during the optimization of the internal grinding cycle using the method described in the article [5]. In Fig. 3, the ranges of changes in the minimum and maximum blunting ratio for the wheel on a ceramic bundle of the 6th structure are presented; the grain material is electrocorundum.

Fig. 3. Changing the minimum and maximum blunting ratios of the wheel in dependence on its hardness and grain grade.

3 Conclusions 1. Parameters of the grinding wheel characteristic must be considered in calculating the cutting force, processing modes and in predicting the quality of the parts batch processing. 2. Generalized index of all parameters of the wheel characteristic can be used to measure the blunting ratio of the wheel which is a relative base surface of the wheel working surface, which is built on the areas of the wheel grain blunting. 3. On the basis of the model durability of the wheel matrix, consisting of the wheel and bundle grains, a method for calculating the ranges of wheel blunting with different characteristics (hardness, grain grade, structure, etc.) is developed; it is the basis for estimating the fluctuation of the cutting force between dressings. 4. The proposed approach for calculating the cutting force by the wheels of different characteristics of the range of the wheel blunting between dressings makes it possible to predict the stability of the accuracy and quality indicators in the process of optimizing the internal grinding cycle according to the method described in the article [5].

Modeling Cutting Force During Internal Grinding

555

References 1. Rowe WB (2013) Principles of modern grinding technology, 2nd edn. Elsevier, Liverpool 2. Tawakoli1 T, Daneshi A (2012) T-Dress, A Novel Approach in Dressing and Structuring of Grinding Wheels. J Adv Mater Res 565:217–221. https://doi.org/10.4028/www.scientific.net/ AMR.565.217 3. Feng Z, Chen X (2007) Image processing of the grinding wheel surface. J Adv Manuf Technol 32:452–458. https://doi.org/10.1007/s00170-005-0357-6 4. Sivarajan S, Dhiwedi SD (2015) Design and analysis of online grinding wheel dressing mechanism. J Rev Adv Mater Sci 1:13–15 5. Akintseva AV, Prokhorov AV, Omelchenko SV (2020a) Modelling of correlation of actual and program feeds in the automatic cycle. IOP Conf Ser Mater Sci Eng 709:033003. https:// doi.org/10.1088/1757-899X/709/3/033003 6. Akintseva AV, Prokhorov AV, Omelchenko SV (2020b) Methodology for designing optimal internal grinding cycles resistant to varying processing conditions. IOP Conf Ser Mater Sci Eng 709:033004. https://doi.org/10.1088/1757-899X/709/3/033004 7. Jackson MJ, Davim JP (2011) Machining with abrasives. Springer, London 8. Marinescu ID, Hitchiner M, Uhlmann E, Inasaki I (2207) Handbook of Machining with grinding wheels. CRC Press, London 9. Malkin S, Guo C (2008) Grinding technology: theory and applications of machining with abrasives. Industrial Press, New York 10. Inasaki I (1991) Monitoring and optimization of internal grinding process. J Ann CIRP 40:359–362 11. Oliveira JFG, Silva EJ, Guo C, Hashimoto F (2009) Industrial challenges in grinding. CIRP Ann Technol 58:663–680 12. Kim SH, Ahn JH (1999) Decision of dressing interval and depth by the direct measurement of the grinding wheel surface. J Mater Process Technol 88:190–194 13. Cutting modes for works performed on grinding and finishing machines with manual and semi-automatic control: reference (2007) ATKOSO publishing house, Chelyabinsk 14. Shavva MA, Grubiy SV (2015) Cutting Forces Calculation At Diamond Grinding Of Brittle Materials. J Appl Mech Mater 770:163–168. https://doi.org/10.4028/www.scientific.net/ AMM.770.163 15. Liu YM, Yang TY, He Z, Li JY (2018) Analytical modeling of grinding process in rail profile correction considering grinding pattern. J. Arch Civil Mech Eng 18:17–32. https://doi.org/ 10.1016/j.acme.2017.10.009 16. Rowe WB, Ebbrell S (2004) Morgan MN. Process requirements for cost-effective precision grinding. CIRP Ann 53(1):255–258. doi:https://doi.org/10.1016/S0007-8506(07)60692-1 17. Gao S, Yang C, Xu J, Fu Y, Su H, Ding W (2017) Optimization for internal traverse grinding of valves based on wheel deflection. Int J Adv Manuf Technol 92:1105–1112. https://doi.org/ 10.1007/s00170-017-0210-8 18. Leonesio M, Sarhangi M, Bianchi C, Parenti P, Cassinari A (2015) A Meta-model framework for Grinding Simulation. Procedia CIRP 31:357–362. https://doi.org/10.1016/j.procir.2015. 03.086 19. Pereverzev PP, Akintseva AV (2016) Model of Cutting Force While Managing Two Regime Parameters in the Process of Internal Grinding. J Procedia Eng 150:1113–1117. https://doi. org/10.1016/j.proeng.2016.07.222 20. Pereverzev PP, Pimenov DY (2016) A grinding force model allowing for dulling of abrasive wheel cutting grains in plunge cylindrical grinding. J Friction Wear 37:66–65. https://doi.org/ 10.3103/S106836661601013X

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21. Fadyushin OS (1992) Development of a calculation method for assigning the grinding wheel characteristic according to the thermal limit for computer-aided design of grinding operation. Publishing house of the SUSU, Chelyabinsk 22. Umino K (1997) Critical pressure at wear of grinding wheels (translation NA-54285). AllUnion center for translation scientific and technical literature and documentation, Moscow

Fuzzy Formalization of Individual Quality Criteria for Quality Level Evaluation by Using Two-Level Optimization Model G. Pipiay(B) , L. Chernenkaya, and V. Mager Peter the Great St.Petersburg Polytechnic University, 29, Polytechnic St, St. Petersburg 194021, Russia [email protected]

Abstract. The use of a multilevel model for evaluating the quality of instrumentmaking products assumes that the individual quality criteria are defined and quantified, since this overestimates the accuracy of obtaining the output result in the form of a numerical expression of the quality of the products produced; if we don’t determine individual quality criteria, our decision support system will give us incomplete information. The system in fact needs to contain information about a manufacturer, a supplier, and other quality information. The objective is to develop a method for the quantitative identification of individual quality criteria for instrument-making products for a two-level model of the product quality assessment. Results: the problem of assessing the quality level from the point of view of the decentralization is considered, the target quality functions and areas of definition for each level of optimization are proposed, a method for quantitative identification of individual quality criteria is developed, and the ways to improve the developed method are proposed. Keywords: Fuzzy sets · Decision-making · Quality assessment · Quality functions

1 Introduction To meet the current needs of the consumer and manufacturer, a multilevel hierarchy of product quality indicators at the production stage requires identification of the nature of quality indicators. At the same time, the multilevel hierarchy of quality indicators in accordance with the concept of the product quality monitoring model [1] must meet the following requirements:

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_65

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• The behavior of the lower level should be limited to the requirements of the upper level. • The quality function (main level) should not include indicators aimed at ensuring quality (sublevels), but these indicators should characterize the level of output quality (should act as restrictions). • The hierarchy of quality indicators should include both qualitative and quantitative indicators. • Quality indicators must meet the requirements of standardization, comparability, representativeness, sensitivity at threshold values, and the absence of duplication of quality indicators at each level. Indicators of the developed product quality along with the supporting information will allow regulating the quality of product flexibly. In particular, it will allow managing (in frames of Quality management) the enterprise resource planning (ERP) system and the production process management system. Meeting the Industry 4.0 requirements will allow optimizing production chain processes, such as logistics, design, production, operation, and after-sales service, in terms of time, resources, and quality loss [2–4].

2 A Mathematical Model for Assessing of the Product Quality Prior to identifying product quality indicators, it is necessary to describe a mathematical model for evaluating the product quality level. The mathematical model for evaluating the quality level will be based on a two-level linear optimization model, in which the first level is the leader, and the second level is the follower. The assessment of the quality level is determined from the following set-theoretic definition of the model: Q, X , Fi , Yi  where Q is the quality function (main level); X is the area for determining the numerical values of the quality function; Fi is the target functions (sublevels); and Yi is the area for determining the values of the target function. The finding of an optimal solution of the function (1) is carried out bottom-up: first, the optimal value of the sublevels Fi (Y i ) are found, then these values are substituted in (1), and values for the master level are found. The optimization problem for the top level, taking into account the restrictions imposed under the levels, looks like this [5, 6]:   (1) min Q[y(x), x] : G[y(x), x] ≤ 0, H [y(x), x] = 0, y(x) ∈ ψ(x) x

where y(x) = Fi ,Fi : y(x) ∈ ψ(x),ψ(x)—polyhedron, domain of constraints such that (Q : Rn × Rm → R, G : Rn × Rm → Rk , H : Rn × Rm → Rl for k indexes, there are restrictions with the sign “≤”, and for l th indexes, there are restrictions with the sign “ = ”). The target functions for the decentralization task, based on the requirements for

Fuzzy Formalization of Individual Quality Criteria for Quality Level Evaluation

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the quality indicators monitoring model, are as follows. Q(x, y1,2 ) is the effectiveness of the monitoring model, F1 (x, y1,2 ) is the cost function for the quality, and F2 (x, y1,2 ) is a supplier management function. Variables x are such that x ∈ X ⊂ Rn . The quality function is such that Q : X × Y1 × Y2 → R, where y is quality criteria, so yi ∈ Yi ⊂ Rmi , and Fi : X × Yi → R. min Q(x, y1 = y, y2 = z) = cx − d1 y + d2 z x∈X

Ax + B1 y1 + B2 y2 ≤ b1 min F1 (x, y) = cx + d1 y

yi ∈Y

(2)

Ax + B1 y ≤ b/ min F2 (x, z) = cx + d2 z zi ∈Z

Ax + B2 z ≤ b// . The state of operation of the upper level is determined by the following output parameters (see Table 1). Table 1. Output parameters of the status of the functioning of the top level. Level Name of the main indicator 1

Name of the private criterion

The effectiveness of the monitoring model Level of the output of suitable products The degree of effectiveness of the developed warning measures The degree of effectiveness of newly implemented technologies and techniques

1.1

The cost function for the quality

The cost of quality assessment The cost of prevention of discrepancies The cost of removal of internal inconsistencies

1.2

Quality criteria such that

Timely delivery The timeliness of addressing complaints about the quality of products

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3 Formalization of Unique Criteria for a Model for Assessing of Quality of Instrument-Making Products To obtain an updated value of the proposed indicator, it is necessary to take into account the specifics of the production of instrumentation products, namely. • structural complexity of the product after performing a certain technological operation is X1 ; • the shareof components with deviations by deviation is X2 ; • the shareof components with marriage certificates is X3 ; • the shareof components with acts of noncompliance is X4 ; • the shareof purchased items included in components (component parts of products) is X5 . Structural complexity of the product x1 is defined as the ratio of the complexity of the product at a certain operation (assigned index p) to the structural complexity of the product at the output (on the final operation, assigned index f ): x1 =

nf (n − 1) Cp mp × = . Cf np (n − 1) mf

(3)

where Cp is the complexity of products for a particular operation; Cf is the complexity of the product output; m is the number of elements in the product, and n is the number of connections in the product. Information on X2 , X3 , and X4 will be recorded by counting cases of registration of permits for rejection, acts of marriage, and acts of noncompliance. The share of purchased items X5 will be defined as the ratio of purchased items to the total number of used items in the product (design). In the indicator “the degree of effectiveness of the developed preventive measures (for the previous period)”, the following criteria should be taken into account: • • • • • •

the share of corrected (simple) technological operations is Y1 ; the share of corrected (specially responsible) technological operations is Y2 ; the share of the revised documents of the quality management system is Y3 ; the percentage of corrected critical blocks in the product is Y4 ; the percentage of corrected (noncritical) blocks in the product is Y5 ; the percentage of corrected (not visible to the consumer) functions of the product is Y5 .

The indicator “degree of efficiency from newly introduced technologies” determines how successful the investment was, and should be determined by the following criteria: • the share of the cost of developing a technological operation is Z1 ; • the share of expenses for the development of quality management system documentation is Z2 ; • the share of the cost of change of supplier is Z3 ;

Fuzzy Formalization of Individual Quality Criteria for Quality Level Evaluation

561

• the share of expenditure on adjustment of the design is Z4 ; • the share of costs for changing the functioning of the product is Z5 . These elements of a cost must be taken into account when evaluating the single criterion “degree of efficiency from newly technologies introduced”. Let’s set a linguistic variable to determine the level of output of suitable products. A linguistic variable is defined as follows: Xi , T (Xi ), U , G, M , where Xi is a name of the variable, T (Xi ) is a term-set of the variable Xi , U is the universal set, G is a syntactic rule, and M is a semantic rule. The term set T (Xi ) for the linguistic variables “level of output of suitable products”, “degree of effectiveness of developed warning measures (for the previous period)”, and “degree of efficiency from newly introduced technologies” will be low value, average value, and high value. The universal set U = [0, 1], and G : M = [1 − ut (u), (ut (u))2 ]. The following scale will be used in the rule database for the place of output value names: • • • • • •

low value x ≤ 0, 25; not the average value 0, 25 < x < 0, 45; average 0, 45 ≤ x ≺ 0, 6; low value 0, 6 ≤ x < 0, 75; high value 0, 75 ≤ x < 0, 85; very high value 0, 85 ≤ x. The following rating scale will be used for the place of names of input values:

• low value x < 0, 4; • average 0, 4 ≤ x < 0, 8; • high value 0, 7 ≤ x. The following functions will be used for input information: • Z-shaped accessory function for x < 0, 4; • Triangular accessory function for 0, 4 ≤ x < 0, 8; • S-shaped accessory function for 0, 7 ≤ x. To get a numerical expression of the quality indicator, the relative importance coefficients for each criterion must be determined. A mathematical model for determining relative importance coefficients is described as   f , K(X , Y , Z)n11 , ..., K(X , Y , Z)1m , ..., K(X , Y , Z)nmm , RN where f is the area of determining of the output values of relative importance coeffi 1,...,nm 1,...,nm 1,...,nm m cients, K(X , Y , Z)1,...,m = K(X )1,...,m , K(Y )1,...,n 1,...,m , K(Z)1,...,m , criteria Ki is such

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that each corresponds to a set ni (number of responses) of equally important criteria Ki1 , ..., Kini and the non-strict preference ratio RN . The quantitative importance information ϑ included in y(x) contains information about the degree of superiority of i, the criterion over other j criteria i h j, where h answers the question “how many times one criterion is more important than the other” [7, 8]. The implication operation is performed as μABC (x, y, z) = min {μA (x), μB (y), μC (z)}. The Z-shaped function will be found for a = 0 and b = 1. The S-shaped function will be found for a = 0 and b = 1. The triangular function will be found for a = 0, b = 0, 5, and c = 1. After finding the fuzzy value, the truth of the statement will be found by the Zane function, where a is an upper bound of i th scale interval for output values, presented in the previous sections. For numerical formalization of the above criteria, it is necessary to determine the cost management model and its mathematical form. There are many models of cost management; the main models given in [9, 10] are the following: the system “standard-cost”, target-costing method, the method of direct costing. The most appropriate model for cost management is the model given in [11]. n

n   Pi Qi − vci Qi + FC (4) PR = i=1

i=1

where n is the number of types of products, P is the price of products of ith type, Qi is a number of products of ith type, and vci are variable costs per unit of production of products of ith type, variable costs are vc = UVC PuVC , where UVC is the specific consumption of the resource, and PuVC is the price per unit. To apply the model (4), the individual criteria for each particular criterion of the quality cost function must be defined. The costs of quality assessment are characterized by the following single criteria [12, 13]: • The share of expenditure on critical functions that are visible to the consumer and the total costs is X1 ; • The share of costs for noncritical functions visible to the consumer to total costs is X2 ; • The share of costs for noncritical functions that are not visible to the consumer is X3 . The costs of preventing nonconformities are characterized by the following single criteria: • The share of expenditure on critical functions that are visible to the consumer and the total costs is Y1 ; • The share of costs for noncritical functions visible to the consumer to total costs is Y2 ; • The share of costs for noncritical functions that are not visible to the consumer is Y3 . The costs of eliminating internal inconsistencies are characterized by the following single criteria:

Fuzzy Formalization of Individual Quality Criteria for Quality Level Evaluation

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• The share of costs eliminated by working with the supplier to the total cost of resolving internal inconsistencies is Z1 ; • The share of costs included in the manufacturing technology to the total cost of eliminating internal inconsistencies is Z2 . In the case of the listed criteria in the model (4), it is necessary to substitute the argument from X ,Y ,Z in the specific resource consumption and in the variable costs vci , as follows:vci (X ),vci (Y ),vci (Z ), UVC (X ), UVC (Y ), and UVC (Z ). A cost-ratio model approach will be used to calculate single criteria for the supplier management function. An analysis of this approach is presented in [14, 15]. The private criteria for the supplier management function are based on the following unique criteria [16–18]: • the share of suppliers with a critical component of the total number of suppliers is X1

, Y1

, Z1

; • the proportion of outsourcing on the total number of suppliers is X2

, Y2

, Z2

; • the share of suppliers with imported products from the total number of suppliers is X3

, Y3

, Z3

; • the share of suppliers that make up 15% of the total cost of purchasing components to the total number of suppliers (products with high cost) is X4

, Y4

, Z4

. The timeliness of delivery is based on the formula [19, 20]:  n

1 i=1 z1 (t)i

bi1 z1 = × 11−d1 , × m z(t)b

(5)

where z1 (t)i is the time needed to eliminate defects for customer satisfaction, m is a number of reference points, z1 (t)b is the time needed to eliminate defects for customer satisfaction under the contract, and d1 is the ratio of the amount of the cost of components and the cost of applying them to their destination to the cost of the flaw detector. Criterion d2 z2 will be found by the formula: ⎡ n

z2 (t)i

⎢ i=1 b

i2 z2 = ⎢ ⎣ n

⎤ ⎥ ⎥ × 1 × 11−d2 , ⎦ z2 (t)b

(6)

where z2 (t)i is time points for delivering components, n is the number of reference points, z2 (t)b is the time to deliver components under the contract, and d2 is the ratio of the amount of the cost of components and the cost of applying them to their destination to the cost of the flaw detector. Criterion d3 z3 will found by the formula: b

i3 z3 = z3 where z3 is the relation of closed questions to the total number of questions.

(7)

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G. Pipiay et al.

The term set T (Xi ) for the linguistic variables “level of output of suitable products”, “degree of effectiveness of developed warning measures (for the previous period)” and “degree of efficiency from newly introduced technologies” will be low value, average value, and high value. The universal set is U = [0, 1], and G : M = [1−ut (u), (ut (u))2 ]. The following scale will be used in the rule database for the place of output value names: • • • • • •

low value x ≤ 0, 25; not the average value 0, 25 < x < 0, 45; average 0, 45 ≤ x < 0, 6; low value 0, 6 ≤ x < 0, 75; high value 0, 75 ≤ x < 0, 85; very high value 0, 85 ≤ x. The following rating scale will be used for the place of names of input values:

• low value x < 0, 4; • average 0, 4 ≤ x < 0, 8; • high value 0, 7 ≤ x. The following functions will be used for input information: • Z-shaped accessory function for x < 0, 4; • Triangular accessory function for 0, 4 ≤ x < 0, 8; • S-shaped accessory function for 0, 7 ≤ x.

4 Calculating the Quality Level Using a Two-Level Optimization Model The example of a task is listed in Table 2. Table 2. The example of a task. № Q

x1

x2 (y2 ) z2

y3

z3

b

№ Q

x1

x2 (y2 ) z2

y3

z3

b

–

≤ 1,0

–

≤ 1,0

1

E1 0,8 0.3

0,1 0,8 0,8 ≥ 0,68 1

E3

2

E2 0,3 0,1

0,6 0,9 1

≥ 0,63 2

E4

3

E3 0.7 0.9

1

0,7 1

≥ 0,84 3

4

E4 0,1 0.9

1

1

0,5 ≥ 0,68 4

5

E5 1

1

1

1

1

≤ 1,00 5

F2 x1

6

F1 x1

x2 (y2 ) z2

y3

z3

b/

6

E1 0.3 –

0,5 –

0,8 ≥ 0,53

7

E1 0,1

–

–

≤ 0,1

7

E2 1

1

1

8

E2

–

–

≤ 0,5

8

0,5

1

– –

1

E5

–

0,9 –

≤ 0,9

E6 0,9 0,7

–

–

≥ 0,8

z3

b//

x2 (y2 ) z2 –

y3 –

≤1

Fuzzy Formalization of Individual Quality Criteria for Quality Level Evaluation

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More detailed information about two-level programming could be found in [8]. Based on the results of the implementation of the simplex method, the quality level of the flaw detector at the production stage was determined as Q(x, y, z) = 0, 67.

References 1. Pipiay GT (2018) The method for multi-criteria evaluation as the planning instrument to quality assurance activity. Radio Ind (Russia) 2:115–120 2. Stock T, Seliger G (2016) Opportunities of sustainable manufacturing in industry 4.0. Procedia Cirp 40:536–541 3. Lee J, Bagheri B, Kao HA (2015) A cyber-physical systems architecture for industry 4.0-based manufacturing systems. Manuf Lett 3:18–23 4. Gilchrist A (2016) Industry 4.0: the industrial internet of things. Apress 5. Zhang G, Lu J, Gao Y (2015) Multi-level decision-making. Springer, Berlin 6. Nguyen KA, Do P, Grall A (2015) Multi-level predictive maintenance for multi-component systems. Reliab Eng Syst Saf 144:83–94 7. Podinovsky VV (2013) Quantitative importance of criteria and additive value functions. J Comput Math Math Phys 53(1):133 8. de Almeida AT, de Almeida JA, Costa APCS, de Almeida-Filho AT (2016) A new method for elicitation of criteria weights in additive models: Flexible and interactive tradeoff. Eur J Oper Res 250(1):179–191 9. Rehacek P (2017) Quality costs as an instrument of verifying the effectiveness of quality management system. Calitatea 18(161):109–112 10. Titov S, Nikulchev E, Bubnov G (2015) Learning practices as a tool for quality costs reduction in construction projects. Calitatea 16(149):68 11. Dykman ES (2015) Modern methods to control the quality costs at industrial enterprises. Actual Problems Econ Manag 3(7):20–26 12. Hribar P, Kravet T, Wilson R (2014) A new measure of accounting quality. Rev Acc Stud 19(1):506–538 13. Aksoylu S, Aykan E (2013) Effects of strategic management accounting techniques on perceived performance of businesses. J US-China Public Adm 10(10):1004–1017 14. Otley D (2016) The contingency theory of management accounting and control: 1980–2014. Manag Account Res 31:45–62 15. Klimova GV (2013) General principles of creation of evaluation supplier model. Bulletin of Udmurt University. Ser Econ Law 3:45–50 16. Liou JJ, Chuang YC, Tzeng GH (2014) A fuzzy integral-based model for supplier evaluation and improvement. Inf Sci 266:199–217 17. Wang M, Li Y (2014) Supplier evaluation based on Nash bargaining game model. Exp Syst Appl 41(9):4181–4185 18. Galankashi MR, Helmi SA, Hashemzahi P (2016) Supplier selection in automobile industry: A mixed balanced scorecard–fuzzy AHP approach. Alexandria Eng J 55(1):93–100 19. Wang X, Sun X, Dong J, Wang M, Ruan (2017) Optimizing terminal delivery of perishable products considering customer satisfaction. Math Problems Eng 20. Franz B, Leicht R, Molenaar K, Messner J (2017) Impact of team integration and group cohesion on project delivery performance. J Constr Eng Manag 143(1):04016088

Programming Industrial Robots for Wire Arc Additive Manufacturing A. A. Kulikov(B) , A. V. Sidorova, and A. E. Balanovskii Irkutsk National Research Technical University, 83, Lermontov Street, Irkutsk 664074, Russia [email protected]

Abstract. Additive manufacturing is an alternative method to traditional subtractive manufacturing, where the material is added layer by layer instead of being sequentially removed from the workpiece. 3D printing enables the manufacturing of parts with complex geometric shapes made from expensive metals with higher productivity and economic efficiency. However, there is currently no specialized software that would provide the utilization of additive technologies in the industrial scale. This article describes a case study of programming industrial robots for 3D printing of metal products. Once the desired objects were made in the CAD system, they were uploaded into the slicer where they were split into the layer structures. Special software for offline programming of industrial robots was used to translate the program into the robot language and perform 3D printing using the experimental robotic complex. As a result, the objects of cylindrical and square geometric shapes made of steel were printed using a welding machine and metal wire. Keywords: Additive manufacturing · Wire arc additive manufacturing · Gas metal arc welding · Industrial robots · Offline programming

1 Introduction Currently, the majority of metal products are manufactured using subtractive manufacturing methods. In subtractive manufacturing processes, such as milling, the solid metal bar is formed to the desired shape by sequentially removing pieces of the material. As a result, most of the material is wasted on metal shavings, which makes this process economically unprofitable and time-consuming, especially when producing parts from highly expensive metals such as titanium and nickel [1–3]. In additive manufacturing, on the contrary, the required part shape is achieved by adding material layer by layer. This helps to significantly increase the material utilization rate and increase the performance of the process. Moreover, additive technologies are capable of manufacturing parts with complex geometric shapes that are impossible or impractical to produce using traditional methods [4–6].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_66

Programming Industrial Robots for Wire Arc Additive Manufacturing

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Commonly used feedstock materials for additive manufacturing of metals are metal powders and metal wires. Powder methods are more prevailed because of their ability to provide a high accuracy of geometric dimensions. However, these technologies have a number of disadvantages, which are mainly the use of both expensive equipment and metal powders, the complex nature of the metallurgical processes of sintering powders, and low productivity (about 10 g/min) [7]. In the last few decades, wire and arc additive manufacturing (WAAM) technology has been developed that enables manufacturers to utilize off-the-shelf welding equipment and industrial robots. Since the capabilities of modern 3D printers are limited by the small work area and the number of materials suitable for printing, WAAM offers an alternative solution for industrial 3D printing of metal products. Metal wires that are used as raw materials are much cheaper than metal powders. The performance of the process is also higher and ranges up to 330 g/min, which is about 30 times more than that of powder technologies. The deposition of layers is implemented by melting the wire with an electric or plasma arc. The precise movement of the welding torch through the layers is provided by a manipulator, which can be a readily available industrial robot [8, 9]. Because WAAM is a relatively novel technology, many aspects of this process require detailed research. In particular, one of the main problems is the lack of specialized software that would enable manufacturers to fully automate this process. Even though industrial robots are easily programmed for common manufacturing processes such as machining, welding, packaging, and painting, adjusting a robot for 3D printing is still a challenge [10–13]. This article provides a case study of one of the methods for programming an industrial robot for WAAM technology.

2 Materials and Equipment The Autodesk Fusion 360 CAD/CAM system was used to create 3D models of objects for 3D printing. The Ultimaker Cura 3D printing software was used for slicing the models to layers and setting printing parameters. Simulating the printing process and generating of the final program was performed in the RoboDK program. Sv-08G2S welding steel wire with a diameter of 0.8 mm was used for printing. The deposition of the wire was performed on a steel plate with a thickness of 16 mm. The gas metal arc welding method was used for melting a wire in a protective CO2 gas environment. The industrial robot KUKA KR 210 R2700 prime was applied as a welding torch manipulator. The welding machine Lorch mobile SpeedPulse S3 was used as a power supply.

3 Case Study Preparing a part for 3D printing comprises the following stages: 1. 3D modeling, 2. Slicing and setting the printing parameters,

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3. Path planning and generating movement trajectory of a welding torch, 4. Transferring the program to the robot. Once the 3D models of the objects for 3D printing have been created in the CAD system (see Fig. 1), the file is saved in STL format for further loading into the slicer program.

Fig. 1. 3D models of the objects to be printed.

After that, the STL file is loaded into the slicer, where the object can be seen relative to the printing bed. Additionally, geometric dimensions can be adjusted. Dimensions can be set individually for each of the axes of the object, or adjusted proportionally as a percentage of the size of the loaded model. It is also possible to set the location of the part on the printing bed, rotate it, and set it to the optimal position for printing. When the geometric dimensions and location of the part are finally set, the adjustment of the printing settings should follow. First of all, it is necessary to specify the diameter of feedstock material. In the case of this study, a steel wire with a diameter of 0.8 mm is used. The parameters to be set are layer thickness and bed width. As a result of preliminary experiments, the following values were identified: the average height of the deposited bead is 2 mm and the average width of the bead is 10 mm. These values were obtained during deposition of wall structures at a printing speed of 3 mm/sec, which was found to be optimal for the deposition of a steel wire. Next, it is required to set the infill parameters of the object when printing. Since in this study printing of hollow objects is performed, 0% infill density needs to be specified. In this case, the program will automatically make the object hollow, and only the outer wall will be printed. The next step is to choose the path planning algorithm for the welding torch. This setting enables the choice of a point where the seam of each contour is placed. The seam is where the contour starts and ends printing. Several options are available that give great control over where the seam gets placed to minimize its impact or provide better conditions to remove the seam more easily in post-processing. Even if the path of the torch is a closed circle, a seam is still left where the deposition starts and ends because the printing process is never completely accurate. When printing layer by layer,

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the torch normally needs to move from one layer to the next. This movement causes the torch to stand almost still for a fraction of a second, which leaves a seam on the surface. By choosing the seam location properly, the visibility of the seam can be minimized by hiding it somewhere or spreading it around. The software provides several options for optimizing the movement of the torch during printing: • User specified. This option enables setting of a seam location manually. The seam will be placed in the corner that is closest to the chosen location. This will usually line up the corners very closely together, which provides better conditions to cut away the seam easily. It also allows fine-grained control over where the seam should be. But this option has the main disadvantage that is a presence of beadings at the start/stop places which can result in the formation of a small roll that eventually would lead to an uneven height of the outer walls and a broadening of the wall at this point. • Shortest. This option simply minimizes the length of travel moves leading toward the seam, making no effort to place it anywhere in particular. Because the travel path is shorter, a significant amount of time will be saved on travel moves. The seam will also be slightly smaller, because less material will be placed in the location where the torch lands on the contour. The desired corner of the preferences is still held by picking a corner close to where the torch is. Not the very closest corner is chosen, but a weighted preference is used to minimize travel moves somewhat but also use an appropriate corner. • Random. A random location around the perimeter is chosen for the seam. This random location is changed in every layer, so the seam will get spread out almost evenly around the model. Because the seams of the different layers don’t line up, the seam will hardly be visible. However, the surface will look slightly messier altogether. But the main advantage of this setting is that the future part will have an even surface with accurate dimensions throughout all axes. This will help to avoid beading and other potential defects. • Sharpest corner. The seam will be placed in the very sharpest corner of the whole contour, according to the corner preference. This may incur longer travel moves, but ensures that the seam is hidden or exposed maximally according to the preference set for the corners. • Spiral contour. Since the spiral mode causes only walls to be printed for most of the layers with a single contour, this single contour will take the form of a spiral. Because the torch is gradually moved up to the next layer, there will no longer be any seam where the torch moves to the next one. This method enables complete elimination of beadings and any defects that occur during the stop of the torch when moving to each next layer. In the case of this study, hollow objects of cylindrical and square shapes are printed. The most optimal torch trajectory for printing such objects is spiral contour. When spiralizing the model, the model will not get any infill and tops/bottoms. The height of the torch will gradually be increased over the thickness of a layer. This way a spiral is created following the contour of the model. There will be no torch movement from one layer to another, because the torch has already gradually moved toward the next layer.

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The next step is to select the print speed. As already mentioned earlier, it was found experimentally that the most optimal speed of the torch during the deposition of steel wire is 3 mm/sec. It is also possible to set the speed of the torch during the transition between layers, but this should be specified for printing more complex objects that cannot be printed using the spiral method. The travel speed is generally much higher than any other speed setting. Higher travel speed can slightly reduce the print time. However, increasing the speed also tends to make the torch vibrate more, which increases oscillations. Additionally, it is possible to choose printing additional test layers before printing the part itself, in order to adjust the wire deposition process and print a certain amount of wire to avoid defects at the beginning of the printing process. This test layer is called a skirt which is a single line encircling future print. It will not directly contribute anything to the characteristics of the future part. It causes the torch to prime before starting the printing of the actual model, to make sure that a wire is properly melting. Once all the necessary printing parameters are set, slicing itself can be performed. After slicing, the program will output the slicing models (see Fig. 2) and specify the print time. In this case, the objects will be printed for 40 min.

Fig. 2. Models after slicing.

The next stage is to save the finished object in a g-code format. G-code is a formal name for the programming language for computer numerical control (CNC) machines. This language is also supported by the majority of modern 3D printers. The program in the g-code format is necessary for generating the torch trajectory for the deposition of metal wire. G-code imports to a program for simulation and programming of industrial robots, where a robotic complex workplace has been previously created with an industrial robot and a working tool having been selected. In the case of this study, the KUKA KR 210 R2700 prime robot is used. Then process modeling continues in the software for offline programming and simulation. Offline programming enables testing and simulation of robot programs in a computer environment eliminating production break downs that occur during programming with robot teach pendant. Simulation and offline programming enable the analysis of several robot cell scenarios before creating the production cell. Offline programming is the best way to optimize robot systems and take maximum advantage of them. New technologies can be adopted in a single day allowing short-run output robotization.

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In order to use industrial robots as 3-axis or 5-axis 3D printers, advanced offline programming tools are required for translating printing programs into robot programs. Such software enables achieving the same results as 3D printers. The component dimensions are specified using CAD software and then translated by offline programming software into production programs. Then, production programs can be converted into programs written in robot language. To extend a working environment of the robot, various external axes can be synchronized with the robot. The external reference frame and the working tool need to be defined for a 3D printing project to be executed. The reference frame of the object for printing needs to be compatible with the printing reference in order to define the reference frame in a real work environment. Moreover, for the starting and ending movements of the robot, the approach and retract program should be adjusted. To minimize robot joint movements and keep the orientation of the working tool as constant as possible, it is necessary to use a tool orientation algorithm that provides a minimum change of tool orientation. Robot positioning requires defining a robot tool center point by using targets identified in the Cartesian space. The robot tool center point can be properly defined or configured using more than 3 or 4 configurations. This allows a more precise result to be obtained and helps to eliminate adjustments errors. Generally, 8 or more points are necessary for the most precise adjustment and 3 points if precision is not significant. Locating the object for printing with respect to a robot is performed by defining an external reference frame. This adjustment requires probing several points using a working tool. Before defining the reference frame, it is necessary to properly calibrate the robot tool center point. Otherwise, points measured from an external measuring system can be used. It is of high importance because the robot kinematics is used to define the reference points. This is also important if the robot operator receives points from the robot teach pendant. Then a printing program can be visualized, and all the reachable (colored in green) and unreachable points if any (colored in red) can be seen. With respect to the desired toolpath, the achievable points could be rotated to make the targets reachable by the robot. If certain points of the route cannot be reached, it is advised to shift the reference frame or set fewer restrictions to the tool rotation settings. Then updating the software is needed to get the program according to the settings given. If the software can be successfully created, a green checkmark is shown. A new program can then be seen in the station with the measured toolpath being displayed in green. The part should be located in a printable location where the robot can easily execute the downloaded program. According to the loaded model, the program automatically generates the torch path (see Fig. 3). The downloaded g-code is checked for errors and the possibility for the robot to execute this program. The program software also enables the specification of additional functions, such as turning the weld gun on and off, and additionally set the speed of movement, approach, and retract of the torch. More importantly, it is necessary to calibrate the welding torch properly so that its central point exactly matches the point at which printing begins.

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Fig. 3. Generated torch path.

The software automatically optimizes the robot’s trajectory, avoiding singularities, axis constraints, and collisions. Next, the coordinates of the location of the printing base and the working tool from the real work environment need to be set, after which the software checks one more time whether this program can be executed. The calculation of the contours and torch path which follows a set of instructions for the robot is provided. After all calculations and checks are completed, the simulation of the printing process can be executed where the programmer would see how the 3D printing process will proceed (see Fig. 4).

Fig. 4. Simulation of the printing process.

Once the simulation is completed, a programmer can see what the objects will look like when the printing process is complete (see Fig. 5). If the virtual program was simulated successfully, the final program written in the robot language is generated. A post-processor performs the conversion of simulation to an appropriate robot program. The peculiarities of each particular robot are taken into consideration by a post-processor.

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By default, every robot has a specific/default post-processor determined in the simulation software. In this case, the KUKA robot uses the KRL language.

Fig. 5. Objects at the end of printing simulation.

Postprocessors have full versatility to produce the robot programs for specific needs. There are post-processors for the majority of modern industrial robots. A programmer can easily create or modify post-processors. As a robot controller has restrictions for the file size or the number of lines of codes, long programs cannot be transferred to the robot. In particular, programs for 3D printing may contain a million of lines of code. To overcome this obstacle, it is preferable to subdivide a long program into subprograms that will be running in order by one main program. Once the program has been generated, it can be either sent to the robot directly from the simulator interface or downloaded to a flash drive and loaded into the robot control cabinet. A program can be transferred directly from the computer into the robot by means of the file transfer protocol or other special protocols. To start transferring, it is necessary to define the IP address of the robot and adjust the file transfer protocol settings in the menu of the robot connection. Additionally, programs can be downloaded on a USB disk. When the program is loaded into the robot, the code is checked on the robot teach pendant for safety reasons in order to identify issues and violations. The operator also has the capability of in-situ adding or removing of missing commands using the teach pendant. If the test ss carried out successfully and the trajectory is correct, the process will start together with the welding machine. The objects after printing using an experimental robotic complex can be seen in Fig. 6. During the course of the experiments, a box with dimensions of 60 × 60 mm was deposited, the number of layers is 15, and the total height is 30 mm. The printed cylinder has a diameter of 50 mm and consists of 24 layers with an overall height of 50 mm.

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Fig. 6. Printed objects.

4 Discussion The utilization of special software for offline programming of industrial robots has helped to reduce the preparation time for 3D printing by about 3 times compared to manual programming on the robot teach pendant. The combination CAD system + slicing software + industrial robots offline programming software enables automation and significant simplification of the 3D printing process compared to manual programming. However, for industrial applications, this combination requires improvement and the integration of additional software tools of narrow specialization. For example, it is highly preferable to implement a robot vision system to remotely monitor the printing process. This is necessary first of all to avoid possible defects and deviations of the geometric dimensions of the part from those set during CAD designing. Furthermore, welding signals, such as current, voltage, and wire feed rate need to be controlled and measured during the printing process. To do this, the welding machines should have feedback to be capable of adjusting welding parameters during the deposition process. And still, a highly specialized software system specifically for wire arc additive manufacturing should be developed. Standard software for 3D printing does not take into account all the peculiarities and features of complex metallurgical and welding processes, which is of high importance for 3D printing of metal products because heat input and the microstructure evolution directly affect the quality and mechanical properties of the deposited parts. Also in this project, the deposition of hollow objects was performed, which is not a particularly difficult task. Printing of more complex parts was not performed because it requires more detailed programming and a longer printing process. More thorough research is required to develop the process for printing solid objects. It is necessary to optimize the torch path and study in detail the behavior of the metal in the process of deposition of solid objects. Future research will focus on these areas, as the industry is in dire need of alternative methods for manufacturing parts from expensive metals such as nickel and titanium.

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5 Conclusion In recent years, additive manufacturing has become increasingly popular, and robotics in this area is a promising method for manufacturing geometrically complex functional parts made from expensive materials that suffer low buy-to-fly ratios. The flexibility and adaptability of robotics are consistent with the trends and features of small-, medium-, and large-scale manufacturing. This article describes the approach for programming an industrial robot for WAAM technology. Since there is currently no specialized software for 3D printing of metal products, one option is to optimize the available software for 3D printers. The slicer enables slicing of a CAD model into layers and setting printing parameters. Software for offline programming of industrial robots enables the utilization of industrial robots as 3D printers. The generated in the slicer g-code is easily recognized in the program and then translated into the robot language. The available software settings allow making programs for 3D printing of both simple hollow shapes such as a cylinder or a square and solid objects of complex geometric shapes. The program created for printing a cylinder and a square was successful and proved that this software combination can be used for 3D printing of metal objects.

References 1. Wu B, Pan Z, Ding D, Cuiuri D, Li H, Xu J, Norrish J (2018) A review of the wire arc additive manufacturing of metals: properties, defects and quality improvement. J Manuf Process 35:127–139. https://doi.org/10.1016/j.jmapro.2018.08.001 2. Wu B, Ding D, Pan Z, Cuiuri D, Li H, Han J, Fei Z (2017) Effects of heat accumulation on the arc characteristics and metal transfer behavior in wire arc additive manufacturing of Ti6Al4V. J Mater Process Technol 250:304–312. https://doi.org/10.1016/j.jmatprotec.2017.07.037 3. Wang F, Williams S, Rush M (2011) Morphology investigation on direct current pulsed gas tungsten arc welded additive layer manufactured Ti6Al4V alloy. Int J Adv Manuf Technol 57(5–8):597–603. https://doi.org/10.1007/s00170-011-3299-1 4. Cong B, Ding J, Williams S (2014) Effect of arc mode in cold metal transfer process on porosity of additively manufactured Al-6.3%Cu alloy. Int J Adv Manuf Technol 76(9–12):1593–1606. https://doi.org/10.1007/s00170-014-6346-x 5. Xu F, Lv Y, Xu B, Liu Y, Shu F, He P (2013) Effect of deposition strategy on the microstructure and mechanical properties of Inconel 625 superalloy fabricated by pulsed plasma arc deposition. Mater Des 45:446–455. https://doi.org/10.1016/j.matdes.2012.07.013 6. Baufeld B (2011) Mechanical Properties of INCONEL 718 Parts Manufactured by Shaped Metal Deposition (SMD). J Mater Eng Perform 21(7):1416–1421. https://doi.org/10.1007/ s11665-011-0009-y 7. Ding D, Pan Z, Cuiuri D, Li H (2015) Wire-feed additive manufacturing of metal components: technologies, developments and future interests. Int J Adv Manuf Technol 81(1–4):465–481. https://doi.org/10.1007/s00170-015-7077-3 8. Haden C, Zeng G, Carter F, Ruhl C, Krick B, Harlow D (2017) Wire and arc additive manufactured steel: Tensile and wear properties. Addit Manuf 16:115–123. https://doi.org/10.1016/j. addma.2017.05.010 9. Ding D, Pan Z, Duin SV, Li H, Shen C (2016) Fabricating superior NiAl bronze components through wire arc additive manufacturing. Materials 9(8):652. https://doi.org/10.3390/ma9 080652

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10. Sidorova AV (2019) Determination of optimal combination of industrial robot control parameters in a part edge processing robotic complex. Proc ISTU 23(4):723–730 11. Ivanova AV, Belomestnyh A, Semenov E, Ponomarev B (2015) Manufacturing capability of the robotic complex machining edge details. Int J Eng Technol 7(5):1774–1780 12. Semyonov EN, Sidorova AV, Pashkov AE, Belomestnykh AS (2016) Accuracy assessment of Kuka KR210 R2700 extra industrial robot. Int J Eng Technol 16(1):19–25 13. Sidorova AV, Semyonov EN, Belomestnykh AS (2018) Robotic edge machining using elastic abrasive tool. In: IOP conference series: materials science and engineering 11. international conference on mechanical engineering, automation and control systems 2017—simulation and automation of production engeenering, p 022097

Metrology Assurance of Assembling DESY’s XFEL Free-Electron Laser Accelerator of Elementary Particles Hristo Radev(B) , Dimitar Diakov, and Hristiana Nikolova Precision Engineering and Measurement Instruments, Technical University of Sofia, 8, Kliment Ohridski Blvd., 1000 Sofia, Bulgaria [email protected]

Abstract. Metrological assurance is considered an integral part of the machinebuilding industry technological support. It aims is to provide accurate information necessary to achieve and evaluate the quality of the manufactured products. Metrological assurance exists at all stages of production, while the article considers the performance measurements of the part quality geometric parameters inside the production process. A special place is occupied by the measurements related to the processes of alignment and adjustment of the mutual positioning during installation and repair. The stress is placed on the specificity of measurements in large-scaled parts and systems, related to their large dimensions and own mass. A methodology for measuring and adjusting the waveguide distribution system of the DESY’S XFEL free electron laser accelerator is offered. The description of the dual-channel laser measuring system, developed at Research and Development Lab. “CMME” of TU-Sofia, as a basic element of the metrological provision of installation is presented. Keywords: Metrology assurance · Large-scaled objects · Laser system · Measurement system

1 Introduction Metrological assurance is part of the technological process of mechanical engineering production. It aims to provide objective information necessary to achieve and evaluate the quality of production. Metrological assurance is present at all stages of production, but in this case it will talk about the realization of the geometric parameters of the quality of the equipment, directly in the production process. These are the linear and angular dimensions and the deviations of the form and orientation of the surfaces and axes of the parts and systems [1–5].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_67

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The quality of production can be ensured in two ways: • Separation of failed production by controlling compliance with the prescribed requirements; • Quality assurance through the technological process, by maintaining accurate and stable technological process. Group I: Measurement of details as representatives of the finished product in order to assess the conformity of their geometric parameters with the prescribed ones (tolerance control). Group II: Measurement of details as representatives of the technological process in order to assess its (of the process) accuracy and stability. Group III: Measurement of the precision parameters of the processing equipment in order to assess compliance with the prescribed requirements (e.g. verification of the geometric accuracy of machine tools). Group IV: Measurements related to the processes of alignment and adjustment of the relative positioning of objects during installation or repair. In large-scaled objects, the measurement has its own specificity, due to the huge mass and dimensions of the parts and the associated significant influence of temperature and elastic deformations on the measurement accuracy. This is particularly pronounced in Group IV measurements. The adjustment and alignment of the mutual orientation of the large-scaled objects is an essential stage of the manufacturing technology of a number of products from the transport and heavy engineering, energy, aircraft and other industries. Ensuring the deviations of the relative position within the prescribed limits in many cases is a serious metrological and technological problem, caused by the specifics of the regulated objects and the conditions of measurement. In many cases, difficulties arise in setting the details in a measuring position, securing the adjustments and alignment itself, and maintaining the position already achieved over time. The alignment and adjustment process consists of two basic operations: measuring and positioning until the prescribed displacement of the relative position is achieved. These operations can be performed simultaneously or sequentially. The methodology for this is determined by the measuring instruments used, the adjusting and centering devices, the schematic solutions and the conditions for performing the operations. The choice of measurement methods and systems for the adjustment and alignment of large-scaled objects is determined by the three basic requirements for each measurement process—accuracy, productivity and economy. Measurement accuracy is evaluated by the error characteristics or by the uncertainty measures. The productivity of the adjustment and alignment process should be evaluated not only in terms of limiting the impact of change over time of the influencing factors, but also in terms of the overall economic performance of the product and operation of the product concerned. When evaluating the economic feasibility of using one or other alignment or adjustment method, respectively, one or the other measuring instrument, attention should be

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taken not only of the repair and installation costs, but also of the significant losses that accompany the failure of these units and complex vehicles. This makes it justifiable to use sophisticated and expensive measurement systems with the use of laser and computing equipment. The subject of this report is the metrological provision for the installation of the DESY’s XFEL (X-ray free electron laser) waveguide distribution systems [6, 7].

2 Measurements During Installation of the Waveguide Distribution System 2.1 Object of Measurement The waveguide has a fixed rectangular cross section with dimensions of 82.5 ± 0.2 × 165.1 ± 0.2 mm and length 3400 m. Along the waveguide, as part of it (Fig. 1) there are 12 distribution modules with a length of 12 m. Each distribution module contains 8 shunttees through which a flange connection with the corresponding cryogenic accelerator modules is made.

Fig. 1. Waveguide distributor; 1—waveguide; 2—distributing module; I-VIII—shunt tee’s flanges, for assembling the cryogenic modules of the accelerator.

The top surfaces of the flanges of the shunt tees must lie in one plane and their axes, symmetrically to one straight line [8–14]. The deviation from flatness of the faces of the flanges with respect to their common associated median plane is 0.25 mm and to the axes of symmetry with respect to their total associated mean straight line is 0.2 mm. The target uncertainty UT of the measurement result of these deviations is, respectively, 50 μm and 40 μm. 2.2 Methodology for Measurement and Adjustment The distribution modules are mounted on a switchgear equipped with appropriate supporting and positioning devices. The diameters and the mutual orientation of the holes of the flanges’ faces are controlled beforehand by means of a complex caliber, and the flatness and parallelism of their faces are measured by a coordinate-measuring arm.

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The mutual orientation of the faces of the horizontal flanges of the shunt tees and their axes of symmetry are determined by measuring the x, y and z coordinates at three points on the flange according to some reference base (datum plane). The datum plane is equidistant to the XY plane of the taken XYZ coordinate system [15–21]. This datum plane is realized using a dual-channel laser measuring system (DCLMS). The datum plane is defined (reproduced) by the plane of two parallel rays of the system. With subsequent movement, the prescribed positioning deviations are achieved by means of the positioning devices of the support. The measurement and adjustment scheme is shown in Fig. 2.

Fig. 2. Distribution module measurement and control scheme: 1-5 positioning devices; 6—support; 7—distribution module; 8—shunt tee flange; 9—supporting module; 10—retro-reflector; 11—DCLMS; 12—positioning tripod.

By means of the positioning tripod 12, the datum plane realized by DCLMS 9 is oriented nominally parallel to the common plane of all flanges, and the plane of symmetry of the two rays coincides nominally with the common line of the centers of the flanges or with the line joining the centers of the two end flanges. By means of the base module 9, a plane equidistant to the face of the respective flange is realized. The coordinates of the three points of this equidistant plane are determined by a retro-reflector (triple prism) 10 of the laser beam placed in subsequently three fixed positions A, B and D. After the reflector, the laser beam falls on the PSD embedded in the DCLMS. By means of the positioning devices (positions 1 to 5) of the support 6, rotations about the X, Y and Z axes and translations on the Y and Z axes are reached. The flanges are positioned in accordance with the prescribed position tolerances. The supporting module (Fig. 3) comprises a base plate 1 and a retro-reflection module 2. When positioning, the measuring plate bearing the retro-reflection module is positioned on the measured surface of the respective flange and oriented identically to the

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centers and axes of each of the flanges, by means of pins 3, one of which has two cylindrical segments removed. The retro-reflection module 2 is positioned on the base plate in three spheres and fixed to it by magnets. At the base of the retro-reflective module are formed by 120° V-shaped channels, on which it is based on spheres 4. This ensures a unique positioning of the retro-reflector characteristic points in positions A, B and D when repositioning the module.

Fig. 3. Positioning module: 1—base plate; 2—retro-reflector; 3—pins; 4—spheres.

3 Introduction The dual-channel LMS developed by the R&D Lab “CMME” of TU-Sofia is a basic element of the metrology assurance of the installation of the distribution modules of the accelerator’s waveguide distribution system. The schematic diagram of the system is shown in Fig. 4. The beam emitted from the laser unit 1 is separated from the polarizing beam splitter (cube prism) into two orthogonal polarized beams, one of which is positioned parallel to the other beam by means of the reflecting prism 4. The parallelism of the two measuring channels (the two beams) is adjusted by the wedge compensator 3. The beams are reflected by retro-reflectors 7 (triple prisms) and after reflection, respectively, they are refracted by prism-cube 2 (beam I) and prism 4 (beam II) going over the surface of position sensing detector (PSD) 8. The polarization compensators 5 and 6 (plates λ/4) are introduced at the input of the beams to rotate the polarization plane. The switching of the two measuring channels is carried out by means of the polarization filter 9. During approbating LMS in laboratory conditions, the influence of the main factors determining the accuracy of the measurement was investigated. They relate to the main characteristics of the photodetector and the photodetector block, the structure and stability of the laser blocks, the stability of the base modules and positioning mechanisms. (These studies will be subject of a future publication). It was found that the uncertainty of measuring the deviation of the flange arrangement of the distribution module does not exceed the target.

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Fig. 4. Positioning module: 1—base plate; 2—retro-reflector; 3—pins; 4—spheres.

4 Conclusion The metrological assurance of the installation of the XFEL accelerator waveguide distribution system is a serious and responsible task, determined by the specifics of the objects. The proposed methodology for measuring and positioning the mutual orientation of the flanges of the waveguide distribution modules, based on the dual-channel LMS developed at R&D Lab. “CMME” of TU-Sofia, allows successful completion of this task.

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8. Kalimanova I, Diakov D, Nikolova H, Miteva R (2014) Measurement of geometrical parameters of waveguide components by menas of portative coordinate measuring machine. Metrol Dev, Sci J 1(II):86–90 9. Nikolova HN, Diakov DI, Vassilev VA (2018) Form Deviations Measurement of Planar Surfaces by Overlapping Measuring Positions Using Reference Plane Method. XXVIII International Scientific Symposium “Metrology and Metrology Assurance 2018”, 10–14th September 2018, Sozopol, Bulgaria, pp 65–69 10. James K (2016) PC interfacing and data acquisition: techniques for measurement, instrumentation and control. Elsevier, 2000 11. Sladek J (2016) Coordinate metrology. Spinger-Verlag GmbH, Berlin, Accuracy of Systems and Measurements 12. Slocum A (2002) Precision machine design. Siciety of Manufacturing Engineers 13. Whitehouse DJ (2002) Surfaces and their measurement. Hermes Penton Ltd., London 14. Radev H et al (2010) Metrology and measurement techniques. Sofia, vol, Softtrade, p 2 15. Smith ST, Chetwynd DG (1998) Foundations of ultra-precision mechanism design (developments in nanotechnology). Overseas Publishers Association, Vol 2 16. ISO 1101:2017 Geometrical Produce Specification (GPS) Geometrical Tolerancing Tolerances of Form, Orientation, Location and Run-out 17. ISO 10360 - 1, 2, 3, 4, 5: 2000 Geometrical Product Specifications (GPS), Acceptance and reverification tests for coordinate measuring machines (CMM). Part 1: Vocabulary; Part 2: CMMs used for measuring linear dimensions; Part 3: CMMs with the axis of a rotary table as the fourth axis; Part 4: CMMs used in scanning measuring mode; Part 5: CMMs using multiple stylus probing systems 18. Zhelezarov I (2010) Analysis of measuring devices and measurement systems. Mechanical Engineering in XXI Century. Nis, Serbia, pp 199–200 19. Dichev D, Koev H, Bakalova T, Louda P (2014) A model of the dynamic error as a measurement result of instruments defining the parameters of moving objects. Measur Sci Rev 14(4):183–189 20. Vassilev V (2019) System for measurement geometric parameters of large-scaled. Softtrade 21. Vassilev V (2019 Procedure for calibrating devices for linear measurements. Youth science conference machines, innovations, technologies “MIT - 2019”, 7–8 November Sofia, pp 111– 116

Modeling Geometric Obstacles in the Assembly of Complex Products A. Bozhko(B) Bauman Moscow State Technical University, 5/1, Ul. 2-Ya Baumanskaya, Moscow 105005, Russia [email protected]

Abstract. Geometric properties of products have a great influence on the process of assembly. The problem of modeling geometric obstacles in CAD systems is considered. A review of modern methods for modeling geometric obstacles is performed. It is shown that these methods do not allow minimizing the number of geometric tests. Therefore, they require high computational costs. A concept of g-situation is introduced. G-situation is a mathematical description of assembled product fragments for which a test for geometric obstacles is correct and necessary. Two assertions about geometric inheritance during assembly are formulated. A mathematical model of geometric solvability in the assembly of complex products is proposed. It is a game of the decision maker and nature by coloring the vertices of an ordered set. A rational game strategy allows you to minimize the number of necessary geometric tests that are performed using motion planning or collision detection algorithms. To minimize the number of tests, various a priori and a posteriori algorithms of coloring ordered sets can be applied. A theorem on the properties of colored ordered sets is proved. Keywords: Assembly · CAAP · Geometric obstacles · Geometric inheritance · Collision detection · Game with nature · Ordered set

1 Methods of Geometric Solvability Automated synthesis of the assembly process of complex products is an actual problem of computer science and design theory. It is actively discussed in modern publications on computer-aided assembly planning (CAAP) [1]. Assembly sequences and the contents of assembly operations depend on the geometric properties of the product. For each part, there must be a movement that transfers it from the storage position to the assembled position. In CAAP papers, this necessary condition for the existence of any assembly process is commonly called geometric solvability [2].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_68

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1.1 Separability of Geometric Sets Geometric solvability in the assembly can be considered as a special case of the well-known problem of combinatorial geometry—the separability of geometric sets (separability problem) [3]. We give its formal statement for the general case. Given a set of geometric bodies (sets) IP = {P1 , P2 , . . . , Pk } in n-dimensional space E n . Let int(Pi )—the set of internal points, and let bound(Pi ) = Pi \int(Pi )—the set of boundary points of a body Pi . It is assumed that for any pair of bodies belonging to IP, relation int(Pi ) ∩ int(Pj ) = ∅ is valid. It is said that there is a motion separating the body Pi from the body Pj if there is a trajectory t : [0, 1] → E n such that int(Pi , t) ∩ int(Pj ) = ∅. A body Pi is separated with IP, if Pi is separated with each Pj ∈ IP. Set IP is separable if there is a permutation of bodies (Pi1 , Pi2 , . . . , Pik ) such that Pil is separated from (Pil+1 , . . . , Pik ) for l = 1, 2, . . . , k − 1. In [3, 4], the separability problem of simple geometric figures (spheres, intervals, convex figures on the plane, etc.) is discussed. Technical system parts often have complex three-dimensional shapes. Therefore, the analysis of geometric obstacles in the assembly of complex products cannot be performed by combinatorial geometry methods only. 1.2 Combinatorial Methods of Geometric Solvability The most severe restrictions on movement during assembly are given by the parts in contact. It was shown in [5] that the set of directions of possible movements of a part is represented as a convex polyhedral cone (PCC) in three-dimensional Euclidean space. A method for the synthesis of PCC is proposed. If PCC = ∅, then the part does not have the freedom of local movement. This method takes into account only local geometric obstacles and linear trajectories of movement of parts. A method for automated computation of a geometric precedence relation (GPR) is proposed in [6]. GPR is a binary order relation that the structure of geometric obstacles defines on the set of parts of a product. A minimal constraint assembly state of a part x (MCAS(x)) is introduced. MCAS(x) is a minimum set of parts that prohibits the dismantling of part x. Obviously, any part must be installed before the MCAS of this part. To obtain MCAS(x), it is necessary to find the minimum DNF of a Boolean function, which describes geometric obstacles in different directions. A method for analyzing geometric solvability in three-dimensional space is discussed in [7]. The process of disassembling a product is considered, and it is assumed that each part can be dismantled by moving along a straight path. It is assumed that parts contact only on fragments of flat surfaces. Cylindrical, spherical, and other matings of a complex profile are represented in the form of polyhedral approximations. It is shown that all possible linear paths for disassembling a part make up a solid angle in space. By the value of the solid angle, one can judge the possibility or impossibility of dismantling the part. 1.3 Collision Detection Methods In the methods of this group, a geometric model of a part moves in a given direction in three-dimensional space. During the movement, intersections of the mobile body with

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the static part of the scene is checked. Fixed elements of the scene are the assembled parts of the product. To approximate part simple geometric shapes are used: cubes„ spheres, polyhedra, convex hulls, polytops, etc. [8]. This method requires very high computational costs, since a computational experiment must be performed for each assembly operation and its design alternatives. In the general case, this number equals n!, where n is the number of parts of a product. To reduce the number of geometric tests, two heuristic rules are proposed in [9]. A part is excluded from the inspection if (1) all its surfaces are in contact; (2) it does not have degrees of freedom in the direction of disassembly. In [10], a method of modeling geometric obstacles in the assembly of products is proposed. This method uses, as in any collision detection algorithm, analysis of the intersection of mobile and static objects. Parts are presented in the form of rectangular shells. From the vertices of shells, rays are launched in the direction of disassembling the product. The intersection of the rays with static fragments of the product is checked (ray casting interference test). In [11], the geometric solver of the BRAEN system (B-rep Assembly Engine) is described. The parts of a product are presented by the B-rep model consisting of pieces of B-spline surfaces. A disassembly direction is given. All the pieces that make up the geometric model of a part are moved in this direction. The intersection of moving and static pieces is checked. In [12, 13], methods for analyzing geometric obstacles by the location of projections of parts on a selected projection plane are suggested. If the projections of the two parts do not intersect, then these parts can be assembled independently of each other. If the intersection is not empty, then the projections of these parts onto the plane perpendicular to the first are considered. A more advanced procedure of this type is described in [13]. The product geometry information is extracted from a STEP-file. On the basis of this information, the interference-free matrix is formed. This is a square matrix A = ||aij ||n×n of order n, where n is the number of parts of a product, in which aij = 1 if and only if part j does not create obstacles for part i. The interference-free matrices formed for six assembly (disassembly) directions (+x, −x, +y, −y, +z, −z) provide all the necessary information about the geometric relationships of the parts. 1.4 Graph Methods of Geometric Solvability The most stringent geometric constraints on the movement of parts are imposed by its surroundings. The most popular method of modeling of local geometric obstacles is described in [14]. Let us consider it in more detail, since this method is widely used in modern CAAP systems, for example, STAAT [1]. Let X be the set of parts of a product. Let a certain direction d be given. We define a graph G(d) = (X, R, d) in which the vertices describe parts and two vertices a, b ∈ X are connected by an arc (a, b) ∈ R if and only if part b prevents an infinitesimal linear movement of part a in the direction d. This graph G(d) is called a directional blocking graph or db-graph. In Fig. 1a, a simple product is shown, and Fig. 1b, c show two db-graphs in the directions d 1 and d 2 .

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Fig. 1. A simple product (a); db-graph in the direction d 1 (b); db-graph in the direction d 2 (c).

Directional blocking graphs allow formulating the condition of disassembly of products. If no arc comes from a vertex x ∈ X of db-graph G(d), then the corresponding part has local freedom in the direction d and it is a candidate for disassembly. If there are no such vertices, the graph G(d) can be divided into several strongly connected components (bicomponents) [15]. Among them, there is a component from which no arc emerges. In this case, the candidate for disassembly will be part of the product that corresponds to the component. Finally, if G(d) is strongly connected, it is not possible to dismantle the product in this direction. If one direction of motion is given by a unit vector, then the set of all directions in three-dimensional space is represented by a unit sphere. The unit sphere can be divided into spatial cones (solid angles), in each of which a db-graph of the product remains unchanged. In some cases, solid angles are rays or half-spaces. Partitioning the unit sphere into cones, within which the db-graph does not change its topology, together with the graph itself, is called a nondirectional blocking graph (ndb-graph) [14]. Ndb-graph is a very informative model. It gives a lot of information about disassembly directions and the possible sequences of disassembly of the product. Figure 2 shows the ndb-graph of the product shown in Fig. 1a. Since db- and ndb-graphs describe only local geometric obstacles and do not take into account the global geometry of products, these models allow us to formulate only necessary conditions for disassembly, but are not sufficient. In [16], db- and ndb-graphs are considered for any movement of parts. In addition, an iterative computational procedure for constructing db- and ndb-graphs with polynomial complexity was proposed in this paper. The task of selective disassembly of products is formulated in [17]. Let us give its mathematical description. Given a product X = {xi}ni=1 and it defines a set of parts A ⊆ X . Find the sequence of disassembly ρ(X , A) = xi1 , xi2 , . . . , xik , . . . , xin , in which / A; xik ∈ A and k = arg max R, where R—the set of all sequences of xi1 , xi2 , . . . , xik−1 ∈ ρ∈R

disassembly of the product without collisions with geometric obstacles. In other words, you need to find the minimum set of parts whose removal from X makes it possible to dismantle the set of parts A. Geometric obstacles are represented as a RI-graph (Removal influence graph). The RI-graph describes the nesting depth of parts in a product. This parameter is calculated according to the disassembly direction specified by an expert. In the graph RI = (X, D), X is the set of parts, two vertices a, b ∈ X are connected by a weighted arc d = (a, b, r) ∈

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Fig. 2. The ndb-graph of the product shown in Fig. 1a.

D if and only if the vertex a can be dismantled in the direction r after removal of the vertex b. It is shown that any topological sorting of the vertices of the RI-graph gives a description of a sequence of disassembly of the product without collision with obstacles. The described method is implemented in the system A3D (Assembly and Disassembly in Three Dimensions). 1.5 Motion Planning Methods Works [18, 19] are devoted to computer-aided design of assembly sequences using motion planning methods. Only geometric constraints on the movement of parts are taken into account. The synthesis of an assembly plan is formulated as a problem of holonomic motion planning. Each assembled part is represented by a point in the configuration space of the assembled product. The probabilistic roadmap method (PRM) is used to search for collision-free trajectories of parts. The considered approaches to modeling geometric obstacles in CAAP-systems have two main disadvantages. • Structural constraints (connections and mates between parts) on the assembly sequence are ignored. This means that the geometric constraints must be tested for all parts except the first part and all possible assembly plans. That is, the number of geometric tests is equal to (n − 1)n!, where n is the number of parts of the product. • The important problem of minimizing the number of tests for geometric solvability is not considered.

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2 Game-Theoretic Model of Geometric Solvability Consider a mathematical model that allows you to limit the search in the combinatorial space of geometric configurations. 2.1 Geometric Situations We introduce the necessary symbols and definitions. Let X = {xi }ni=1 be the set of parts of a product. Definition 1 S-set is a set of parts Y ⊆ X that can be assembled independently. A method for generating s-sets using the hypergraph model of products is described in [20–24]. Definition 2 G-situation (geometric situation) is a pair (Y, x), Y ⊆ X , x ∈ X , in which Y and Y ∪ {x} age s-sets. A g-situation is a mathematical description of such a fragment of a product for which testing for geometric obstacles is meaningful and necessary. The G-situations are divided into two types: resolved and unresolved. Definition 3 We call a g-situation (Y, x) resolved if the part x can be mounted on the assembled fragment Y without collisions with obstacles. The situation is called unresolved otherwise. Figure 3 shows a product (a) and two g-situations: resolved (b) and unresolved (c).

Fig. 3. A product (a); resolved (b) and unresolved (c) g-situations.

Let’s consider all g-situations of a product related to the mounting of a part x. We denote this set as GS(x). It is obvious that the set GS(x) is divided into two disjoint subsets: subsets of all resolved and unresolved g-situations. We order set GS(x) by including the first coordinates of g-situations, (A, x) ≤(B, x) if A ⊆ B. It makes GS(x) an ordered set (GS(x), ≤). The situations of one set GS(x) will be denoted by the names of their first coordinates. The ordered set (GS(x), ≤) is represented as a Hasse diagram. In this graph, the vertices describe g-situation, and a vertex A is located below a vertex B if A ≤ B (A ⊆ B). These vertices are connected by an edge if there is no vertex C such that A ≤ B ≤ C. Figure 4 shows a transmission (a) and Fig. 5—the ordered set of all g-situations GS(7) related to the mounting of bearing 7.

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Fig. 4. The drawing of a transmission.

2.2 Geometric Inheritance We introduce two assertions about inheritance of geometric relations in the assembly of products. Assertion 1 Let a situation A ∈ GS(x) be resolved. Then any situation B ∈ GS(x) such that B ⊆ A is also resolved. Indeed, if the s-set A does not contain geometric obstacles to the mounting of the part x, then there cannot be any geometric obstacles in the simpler s-set B. Assertion 2 Let a situation A ∈ GS(x) be unresolved. Then any situation B ∈ GS(x) such that A ⊆ B is unresolved. If the s-set A contains geometric obstacles for the part x, then adding new parts to A cannot remove these obstacles. On the Hasse diagram of the ordered set GS(x), we will represent resolved g-situations in white, unresolved g-situations in black, g-situations of undetermined status in gray. If the situation A ∈ GS(x) is resolved, then, according to assertion 1, all vertices of the ordinal ideal I (A) = {B ∈ GS(x)|B ≤ A} are colored white. If the situation A ∈ GS(x) is unresolved, then, according to assertion 2, all vertices of the ordinal filter F(A) = {B ∈ GS(x)|B ≥ A} will be black.

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Fig. 5. The ordered set of all g-situations GS(7), related to the assembling of bearing 7.

Synthesis of an optimal program of tests for geometric solvability can be represented in the form of a game of a decision maker (DM) and nature. This game is played according to the following rules. Given an ordered set all vertices of which have an undetermined status and are colored gray. A move of DM is to choose a vertex from this set. Nature’s answer is to determine a color of the given vertex. If the vertex is black, all vertices of the ordinal filter are colored black. If the vertex is white, then all vertices of the ordinal ideal are colored white. The next move of DM is to select a vertex in the uncolored part of the ordered set, etc. required to paint the ordered set (GS(x), ≤) with the least number of moves. Choosing a color of a vertex means implementing some geometric test that will determine the status of the situation. The optimal coloring strategy will provide a program with a minimum number of geometric tests using collision analysis or motion planning methods. We denote G(R) the games of this type, where R is an ordered set. Figure 6 shows an example of coloring an ordered set R1 . The vertices selected by the decision maker are marked with circles. 2.3 Correct Colorings of Ordered Sets Definition 4 Coloring of an ordered set generated by main filters and main ideals is called correct. In any coloring of this type, the black and white vertices occupy divided positions and cannot mix with each other. Figure 7a shows all variants of correct coloring of an ordered set. Figure 7b shows an example of wrong coloring, in which white and black vertices alternate.

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Fig. 6. Coloring an ordered set R1 : the initial state (a), R1 after the first move of DM (b), R1 after the second move of DM.

Fig. 7. The colorings of an ordered set: correct (a), wrong (b).

In the definition of the game model, the correct coloring of an ordered set was generated algorithmically by specifying a sequence of unpainted vertices and selecting a color for each of them. The exact characterization of correct colorings of ordered sets is of interest. Let be (GS(x), ≤) a colored ordered set, all vertices of which are assigned one of the colors (white or black). Let W be the subset of the white vertices and B be the subset of the black vertices of the given set, that is W ∪ B = GS, W ∩ B = ∅. Theorem A coloring of the ordered set (GS(x), ≤) is correct if and only if ∀b ∈ B and ∀w ∈ W it is true w ≤ b or w||b (vertices w and b are incomparable). Proof We begin with necessity and assume that in some correct coloring there exist two vertices w and b, w ∈ W , b ∈ B, such that w ≥ b. Since these vertices are comparable, then, by definition the correct coloring is either b ∈ I (w) and then vertex b is white, or w ∈ F(b) and then vertex w is black. We show sufficiency. The vertex set (GS(x), ≤) is divided into two disjoint subsets of the white W and the black B vertices such that W ∪ B = GS, W ∩ B = ∅. We denote M = {mi}ki=1 a set of all minimal elements of B. The set M is not empty, since any finite ordered set has at least one minimal element [25]. One of the possible coloring of the set B is obtained by combining the filters of all elements of the set M = {mi}ki=1 , that is B = ∪ki=1 F(mi).

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Let P = {pi }ri=1 be a set of maximal elements in W. The set P = ∅, since any finite ordered set has at least one maximal element [26]. A correct coloring of the set W can r

be obtained by combining the ideals of all its maximal elements W = ∪ I (pi). i=1

According to the initial assumption, the filters (ideals) of the set B (W ) inherit this k

r

i=1

j=1

property in the set GS. Therefore, the coloring generated by the set ∪ F(mi) ∪ I (pj) is correct. The theorem is proved.

3 Conclusion The problem of modeling geometric obstacles in CAD systems during the assembly of complex products is considered. In most papers, only local geometric obstacles are taken into account. Modeling local obstacles allows formulating only necessary conditions for disassembling. First of all, these are methods for analyzing degrees of freedom of parts and methods using db- and ndb-graphs. The exact sufficient conditions for assembling or disassembling can be obtained using collision detection or motion planning algorithms. Such an analysis requires very high computing resources, if you do not take into account the structural properties of the product. In the general case, it will be necessary to perform (n − 1)n! geometric tests, where n is the number of parts of a product. Therefore, the problem of finding a rational strategy for analyzing geometric obstacles is very important and relevant. Two assertions about geometric heredity in the product assembly are introduced in the paper. These assertions allow you to extend the results of testing one configuration to others. A game-theoretic model of geometric solvability in the assembly of complex products is proposed. It is the game of the decision maker and nature by coloring an ordered set in two colors. In this game, the DM chooses an uncolored vertex of the ordered set. Nature specifies a color for the selected vertex. In meaningful terms, an uncolored vertex corresponds to a fragment of the product that requires a test for geometric solvability, the color of the vertex is a result of the test. A rational coloring strategy minimizes the number of time-consuming geometric tests that are performed using motion planning or collision detection algorithms. The theorem on the properties of correct colorings of ordered sets is proved.

References 1. Ghandi S, El Masehian (2015) Review and taxonomies of assembly and disassembly path planning problems and approaches. Comput Aided Des 67–68:58–86. https://doi.org/10.1016/ j.cad.2015.05.001 2. Homem de Mello LS, Lee S (1991) Computer-aided mechanical assembly planning. Springer, Boston 3. Toussaint G (1985) Movable separability of sets. Mach Intell Pattern Recogn 2:335–375. https://doi.org/10.1016/B978-0-444-87806-9.50018-9 4. Dehne F, Sack J-R (1987) Translation separability of sets of polygons. Visual Comput 3:227– 235. https://doi.org/10.1007/BF01952829

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Information Model of the Automated System of Assembling Plant Identification and Traceability V. Nosenko1(B) , A. Silaev1 , and S. Grednikov2 1 Volzhsky Polytechnic Institute, Volgograd State Technical University, 42a Engelsa Str.,

Volzhsky 404121, Russia [email protected] 2 LLC VPA, 53b, Mira Str. Volzhsky 404131, Russia

Abstract. The introduction of an automated identification and tracking system in the existing production processes is a promising and important direction in the development of the industry. Such technologies are especially effective for largescale assembling plants, where accounting for more materials and components in all technological and controlled operations is the key factor for improving the efficiency of organization and scheduling of production. Two technologies are considered as means of identification: QR coding and RFID technology. In the framework of mass production, where products are produced in large volumes, it is advisable to combine identification technologies. As an example of the implementation of the information model of the automated system of identification and traceability of products, an abstract production process of multi-operation assembling production is presented. The proposed information model of ASITP is sufficient to track the entire production chain by the product ID, the time and date of manufacture. To understand the application of the proposed information model of ASITP, the algorithm of product tracking for the final stage of production, quality control department and finished product warehouse is considered. The implementation of the production traceability system will allow solving the following problems: achieve “transparency” of the production process management system and traceability of the production cycle; increase productivity; provide operational control of production facilities; reduce defects due to early detection of non-conforming products. This model has the ability to expand and integrate with other enterprise information systems. Keywords: Traceability plant product · Production identification · Industry 4.0 · RFID · QR code

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_69

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1 Introduction Recently, increasing attention is being paid to the digitalization of the economy. One of the directions of digitalization advancement is the development of “end-to-end” technologies at plants [1]. These technical solutions were made possible by the new concept of the fourth industrial revolution or Industry 4.0. Industry 4.0 is based on the following technologies: Big Data, Internet of Things, blockchain, augmented and virtual reality. Big Data technology provides tools for storing and processing large amounts of information received from industrial facilities. Cloud technologies are the preferred solution for implementing “Big Data”. The Internet of Things technology is a concept of interaction between machines and people. Various smart sensors are used to get information about the surrounding world by “things”. To exchange information in real time, mainly wireless data transmission technologies are used. Blockchain technology is designed to process information generated by blocks on various devices or systems. Blockchain allows ensuring cybersecurity of processed data received and is used by various participants of the information process. The basis of the blockchain is the idea of storing a control hash sum in each block of information, which is formed taking into account the information stored in the previous blocks. Therefore, information in general is extremely difficult to change by unauthorized persons. Augmented and virtual reality technologies provide tools for creating a visual interface for people to interact with information systems. The technologies are based on a system of labels with the binding of real objects to their augmented digital counterparts. Thus, the concept of Industry 4.0 allows implementing “end-to-end” technologies in that real objects interact with each other through information systems. These technologies include the implementation of full traceability of products at all stages of their life cycle. The implantation of an automated identification and tracking system (ASITP) in existing production processes is a promising and important direction in the development of the industry. This allows having full information about the product, its movement, that allows excluding falsification and reducing the cost of re-release of products in case of detection of product defects [2]. Such technologies are especially effective for large-scale assembling plants, where accounting for more materials and components in all technological and controlled operations is the key factor to improve the efficiency of organization and scheduling production [3]. At the same time, at the moment of industry development, the problem of product traceability is relevant. Many factories have implemented an imperfect system for tracking raw materials, parts or assembling units, that consist in checking only the finished product that entails the assumption of flaws at an intermediate stage, an increase in the consumption of components, insufficient efficiency in obtaining information and other flaws when performing operations. Thus, the solution to the problem of implementing an automated system of identification and traceability of products is important for assembling plants. This paper is proposed to consider an information model of the automated system for identification and traceability of production assembling plants and algorithm traceability to the final stage of production, quality control department and warehouse of finished inventories.

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2 The Theoretical Studies According to GOST [4], traceability of products at production allows using identification tools to trace: the origin of components; the background of the production; and distribution and location of products in the warehouse. Product identification and traceability system is an automated system that allows collecting, controlling and analyzing information about technological operations, personnel and resources involved in the production process [5]. Identification is carried out by setting special tags on the product in accordance with the design and technological documentation, indicating all the necessary characteristics of the product that affect its quality and necessarily unique identification number [6, 7]. Traceability of products is the process of preparation of technical documentation, which is a process of recording technological and control operations, indicating the detected defects and measures taken to eliminate them. Currently, two technologies have proven themselves as identification means [8]: QR coding and RFID. QR coding is the application of graphic information to the surface of the product for further reading by technical means. The QR code is based on the arrangement of dark square elements inside the matrix. A QR code is defined as a two-dimensional black-andwhite image that is translated into a binary code with a checksum check. Each element has a specific size, and its position encodes the data. The main advantages: independence from electromagnetic fields; low tag cost; and small overall dimensions [8]. The main disadvantages: the need for direct visibility of the tag to read the information; limited memory for recording information (up to 3072 bytes); low resistance to harmful environmental influences; the inability to record additional information and changes in the existing physical labeling; and short reading distance [9]. RFID is a way to automatically identifying objects using an electronic tag that stores unique information about the object [10]. The RFID system consists of a reading device (reader) and a transponder (tag). The reader generates a radio frequency tag interrogation signal. If the label is located in the area of propagation of the signal from the reader, it generates a response signal with a unique identifier. The RFID tag consists of two parts. The first part is an integrated circuit (IC) for storing and processing information, modulating and demodulating the radio frequency (RF) signal. The second is the antenna for receiving and transmitting the signal [10–13]. The main advantages of RFID: not necessary to have direct visibility of the tag to read it; high speed reading of information from the tag; ability to record additional information; and a large amount of code information [10]. The main disadvantages: inability to place under metal and electrically conductive surfaces; mutual collisions when reading information from multiple tags; and exposure to interference in the form of electromagnetic fields [10]. The analysis of works devoted to the application of identification technologies in various industries allows concluding that in the framework of mass production, where products are produced in large volumes, it is advisable to combine identification technologies.

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Traceability of products is the technical documentation formation process, in those records about the conducted technological and control operations are made [5, 6, 14]. The main features of product traceability are control of the movement of materials, components and products inside the production [15, 16]; construction of the technological route and control over its keeping [12, 17, 18]; identification of all specified operations with binding to executors [19]; taking into account the actual time for each operation of the entire process [5, 20]; and integration with ERP and MES systems in the enterprise [20, 21]. There are two types of traceability: internal traceability (within the shop-floor or enterprise); chain traceability (complete product tracking at the stages of its life cycle) [22]. This article will focus on the traceability of products within the enterprise. Analysis of literature sources [23, 24] showed that the system of identification and traceability of products have to support at least two complementary types of traceability: traceability of marked products and documentary traceability of products. For the significance of the relevance of research, we present Fig. 1 showing the effectiveness of solutions as a result of the introduction of ASIP as part of MES systems in Russia [25]: return on investment ROI—from 200%; payback time of the system—from 6 months; increasing the output of finished products through the use of the implemented system—from 25 to 45%; reduction of work in progress by increasing the speed of passing orders when using MES—from 20 to 60%; and increase the load factor of the equipment—from 30 to 60%. These criteria allow doing conclusions about the effectiveness of the implementation of such systems in assembly production. This article involves the development of an information model of the identification and traceability system, so the following paragraphs of the article is devoted to the implementation of documentary traceability of products. It should be noted that many papers provide general information about identification and traceability tools. The problems of justification and practical use of such systems are solved [26, 27]. Examples of practical implementation of systems are not considered.

3 Practical Implementation As an example for the implementation of the information model of the automated system of identification and traceability of products, an abstract production process of multioperation assembling production is presented. Presumably, the technological process consists of N production operations, technical control operations and warehousing operations. To implement traceability at the first operation, the following information has to provide: (1) The name of the operation; (2) ID of the operation; (3) ID of the equipment used; (4) ID of the executor; (5) Materials (the required number of materials for the manufacture of a unit of production); (6) ID of the received production (semi-finished production); (7) Technological parameters (values of technological parameters in the manufacture of products); (8) Start and end time of the operation.

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Fig. 1. The block diagram of product traceability.

To implement traceability on the following operations, information about previous operations and information about the current operation has to provide: (1) The name of the operation; (2) ID of the operation; (3) ID of the equipment used; (4) ID of the executor; (5) Materials (the required number of materials for the manufacture of a unit of

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production); (6) ID of the received production (semi-finished production); (7) Technological parameters (values of technological parameters in the manufacture of products); (8) Start and end time of the operation. For a technical control operation, the following information is required: (1) Name of the control operation; (2) ID of the operation control; (3) ID of the equipment used; (4) ID of the executor of the quality control department (QCD); (5) Product ID; (6) Control parameters (values of controlled parameters); (7) Product quality status (suitable, for revision, flaw); (8) Start and end time of the control operation. For the operation of warehousing, the following information is required: (1) Product ID; (2) Storage location ID. The proposed information model of ASITP is sufficient to track the entire production chain by the product ID and the time and date of production. The block diagram of product traceability is shown in Fig. 1. To understand the application of the proposed information model of ASITP, the algorithm of product tracking for the final stage of production, quality control department and warehousing operations is considered. At the same time it is noted that traceability at these areas is implemented on a fairly large territory and between different structures of the enterprise and with different document flow. In addition, these are the most important operations for the end customer of the product. For identification of production facilities, the following solutions are proposed: to identify the performers of operations, use RFID tags with the ID of the executor; to identify the equipment that can use RFID tags with the ability to record information about the equipment; to use QR tag to identify the finished products; to use an RFID tag to identify pallets in the warehouse. Operation rules of the operator of the final operation: 1. Upon arrival at the workplace, the operator is registered at his workplace in the ASITP using his pass with a built-in RFID tag. 2. The operator’s workplace has its own unique identifier. 3. When the next unit of production is released, the operator creates the record in the ASITP and prints the tag that include QR code with the following information: Equipment number; Full name of the executor; Time of production of this unit production; ID of the unit of production. 4. The operator pastes the tag and sends production to the quality control department. Operation rules of the operator of the quality control department: 1. Upon arrival at the workplace, the executor of the QCD is registered at his workplace in the ASITP using his pass with a built-in RFID tag. 2. The workplace of a QCD executor has its own unique identifier. 3. Each product unit is checked for compliance with quality requirements. 4. When a unit of production is controlled, there are three possible options: If the inconsistencies are not subject to revision the tag code is read and marked as “flaw” in the ASITP. If the discrepancies are subject to revision, the tag code is read and marked as “requiring revision” in the ASITP.

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If there are no discrepancies, the tag code is read and marked as “good” in the ASITP. 5. When checking the next good unit of production, a tag is printed, which has all the necessary information for the customer: Number of the workplace of the QCD executor; Executor’s full name; Date and time of certification of this unit of production; and Product quality status. 6. The QCD executor pastes the tag and sends the certified products to the finished product warehouse. Operation rules of the operator of the warehouse: 1. Upon arrival at the workplace, the warehouse employee is registered at his workplace in ASITP using his pass with a built-in RFID tag. 2. The employee gets the received batch of finished products and places it in the required place. The warehouse is pre-marked by zones. 3. When the party units of finished products is placed operator fixes location each of them. By the number of the pallet the storage location of the batch of finished products can be determined. 4. Each product unit is received at the warehouse, and the warehouse employee identifies by reading the QR-tag. 5. During product identification, data is transmitted to the integrated system of the enterprise. 6. When the product is shipping, the employee receives a storage location, takes the product and records that the space is vacated. In that way, product traceability between the final production operation, quality control operation and warehousing is ensured. The algorithm proposed by the authors is a sequence of actions and operations that must be performed by employees of the enterprise in the implementation of product traceability. At the same time, access rights of operators and employees of the QCD and warehouse are controlled which allows ensuring correct work with the traceability system. With the help of automatic identification and code reading system, information is automatically entered into the enterprise database. It eliminates the human factor when entering product information into the traceability system. In addition, automatic entry of information into the system allows reducing the time of entering information. At the same time, it is worth noting that most operations and actions of employees are sequential, and the algorithm does not involve branching and choosing actions. Only the employee of QCD is given the opportunity to choose actions depending on the quality of the finished product. Therefore, it is advisable to automate product quality control operations as much as possible to ensure maximum production efficiency.

4 Conclusion The obtained information model of ASITP can be used at serial multi-operation productions. Combining types of object identification can reduce the cost of implementation and operation of the traceability system.

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Traceability of production significantly improves the production management system by implementing a single integrated ASITP. Implementation of the production traceability system allows solving the tasks: (1) “Transparency” of the production process management system and traceability of the production cycle; (2) Increase productivity; (3) Operational control of production facilities; (4) Reduction of defects due to early detection of non-conforming products. Main business fields included in the traceability system: (1) Management of raw material flows; (2) Management of production process; (3) Management of the inspection process of finished products; (4) Management of finished products; (5) Management of information flows. The considered system is installed in workplaces in the divisions of an enterprise. System operation is assumed only where automated workstations will be installed that are a hardware and software complex. This model has the ability to expand and integrate with other enterprise information systems. For example, the equipment traceability model can be integrated with the maintenance and repair system (MRS) and the history of maintenance and repair of equipment can be viewed. By using the employee number, we can interact with the HR accounting system. So we will have information: had done or not advanced training of operator after the replacement of technological equipment to new. And the fact is empowering the traceability system requires virtually no capital costs. Thus, we can talk about “end-to-end” technologies and digitalization of production.

References 1. Presidium of the Council under the President of the Russian Federation for strategic development and national projects (December 24, 2018). The passport of the national program “Digital economy of the Russian Federation”. http://static.government.ru/media/files/urKHm0gTP PnzJlaKw3M5cNLo6gczMkPF.pdf. Accessed 15 Mar 2020 2. Vasil’eva S, Krayneva K (2016) Metodika mnogourovnevogo tekhnologicheskogo audita kachestva na mashinostroitel’nom predpriyatii (Methodology of multi-level technological quality audit at a machine-building enterprise). Econ Manage, ASR 3. Nosenko VA, Silaev AA, Efremkin SI, Grednikov SB (2019) Study of the assembly manufacturing automated traceability system identification tools. X Int. Sci. Practical Conf. KSTU. https://doi.org/10.1051/matecconf/201929701005 4. Fundamentals and vocabulary, International standard ISO 9000 (2005) Geneva, Switzerland. https://www.iso.org/iso-9001-quality-management.html. Accessed 15 Mar 2020 5. Engineering company “Sovtest ATA” (2019) Identification and traceability system. https:// sovtest-ate.com/news/company-news/ooo-_sovtest-ate_-o-rezultatakh-vnedreniya-sistemyidentifikatsii-i-proslezhivaemosti/. Accessed 15 Mar 2020 6. Fernández-Caramés TM, Blanco-Novoa O, Froiz-Míguez I, Fraga-Lamas P (2019) Towards an autonomous industry 4.0 Warehouse: A UAV and blockchain-based system for inventory and traceability applications in big data-driven supply chain management. Sensors. https:// doi.org/10.3390/s19102394 7. Al-Turjman F, Mostarda L (2019) A hash-based RFID authentication mechanism for contextaware management in IoT-based multimedia systems. Sensors. https://doi.org/10.3390/s19 183821

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Modeling of Production Process Energy Characteristics in Mechanical Engineering V. Salnikov(B) and Yu. Frantsuzova Tula State University, 92, Lenin Ave, Tula 300012, Russia [email protected]

Abstract. An approach to modeling the energy characteristics of production processes in mechanical engineering is proposed. The proposed approach is to estimate the energy consumption and efficiency since the receipt of a billet in the stocks of the company. This allows estimating the energy costs of maintaining buildings and premises during the entire production process. To assess the energy characteristics of the transformation of labor items at each hierarchical level and at each stage of the production process, it is proposed to allocate useful work performed during this transformation as a function of the parameters of the performed operations—energy efficiency directly depends on the parameters of the transformation of labor items. It is assumed that all the information needed to evaluate energy efficiency is available both at the preproduction stage and directly at the production stage. The production process is modeled on the basis of the proposed mathematical model. The analysis of parameters that affect energy efficiency at some hierarchical levels of an industrial enterprise is made, and some ways to improve it are proposed. Keywords: Energy efficiency · Energy consumption · Industrial production · Mechanical engineering

1 Introduction The energy intensity of Russia’s GDP is 2–2.5 times higher than the global average. In 2008, a decree of the President of the Russian Federation [1] set a goal to reduce the energy intensity of GDP by 40% by 2020 from the level of 2007. To achieve these goals, the state program “Energy conservation and energy efficiency” was adopted [2], which is part of the state program “Energy efficiency and energy development” [3]. The energy intensity of the Russian Federation’s GDP is one of its main target indexes. One of the objectives of the program is to reduce the value of this indicator by 13.5% from the 2007 level due to the implementation of the program’s activities, which together with other factors will ensure the achievement of the goal set by the President of the Russian Federation [1].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_70

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As of 2018 [4], it was possible to reduce the energy intensity of GDP from the 2007 level by 8.3%, while according to the reports of the Ministry of Energy of the Russian Federation, this figure in 2017 [5] was also 8.3%. This indicates a slow pace and significant difficulties in implementing programs to reduce the energy intensity of GDP. According to energy balance data, industrial production is most energy-intensive, since it consumes more than half of the total energy resources [6]. Specific energy costs in the cost of products produced by Russian enterprises are 1.5–2 times higher than those in developed countries [7]. The trend for a constant increase in resource intensity is inextricably linked to the growth of energy and information saturation of production [8]. Manufacturing has historically been one of the largest sources of carbon dioxide emissions in the world. It accounts for about 38% of global CO2 emissions [9, 10]. Increasing demand for energy resources, combined with limited supply in world markets, leads to a constant increase in energy prices. Together with the dynamics in pricing, they create uncertainties for market organizational schemes based on precisely calculated energy costs [11]. Therefore, increasing energy efficiency becomes a driving force for manufacturing enterprises in terms of reducing energy intensity and cost of production and, as a result, reducing carbon dioxide emissions into the atmosphere. Summarizing the above, we can conclude that domestic production does not spend energy resources efficiently, which significantly reduces the competitiveness of their products in the world and domestic markets [12]. Therefore, increasing the energy efficiency of industrial production is extremely important. An important role in solving this problem is played by modeling production and technological processes in order to obtain the energy characteristics of their implementation. This will allow not only to evaluate and plan energy efficiency, but also to identify ways and measures to improve it.

2 Mathematical Modeling According to State Standart 14.004-83 [13], the production process is the totality of all actions of people and tools required at a given enterprise for the manufacture and repair of products. According to State Standart 3.1109-82 [14], a technological process is a part of the production process that contains purposeful actions to change and (or) determine the state of the object of labor. Here, the object of labor is understood as a thing or a set of things that a person affects in the process of production with the help of tools for the purpose of producing material goods. Together with the means of labor, they form the means of production. The means of labor include tools, industrial buildings and structures, means of moving goods, and land. To assess the energy efficiency of production processes and analyze possible ways to improve it, it is necessary to know the places where energy is used and converted by elements of the production system. The time required to produce a product consists of the time that items of labor are in production stocks and the production cycle, which covers the working period and the

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duration of breaks in production [15] tp = ts_i + tpc + ts_o ,

(1)

where t p —time of production; t s_i —time of storage of labor items before the start of the production cycle; t pc —time of the production cycle; and t s_o —storage time for finished products. Energy resources are involved in each of these stages and are subject to transformation in one way or another. The energy representation of the production process is shown in Fig. 1.

Fig. 1. Energy representation of the production process in time.

The structural construction of modern production systems is subordinated to the hierarchical principle [8, 16, 17]. Each level contributes to the conversion of labor items into finished products, is characterized by a certain proportion of nonproductive energy losses, and performs background work necessary to maintain the conversion process. Therefore, to assess the energy characteristics of the transformation of labor items at each hierarchical level and at each stage of the production process, it is necessary to identify the useful work performed during this transformation. Energy at the stages of storage of labor items and finished products is spent exclusively to maintain the functioning of the main production assets of the enterprise heating, air conditioning, ventilation, lighting, etc., of buildings and structures of the enterprise. At the stage of the direct production process associated with the transformation of labor items into finished products, it is necessary to allocate the energy of useful work performed at each hierarchical level of the production system, and the energy of the work

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of maintaining the transformation process. In this case, the entered components must be expressed as a function of the parameters of the performed operations—the energy efficiency directly depends on the parameters of the conversion of labor items. The current degree of production informatization as well as the constant trend of its growth show that most of the technological parameters at different levels of the production system can be identified both at the stage of production preparation and at the stage of operational control [18–21]. In this regard, the parameters of the item, operations, and equipment must be taken into account (Fig. 2).

Fig. 2. Parameters for evaluating energy efficiency.

At this stage, it can be concluded that reducing the time spent on labor items and finished parts in inventory reduces the energy intensity of the production process. A technological process implemented in a specific production system (PS) can be represented as a sequence of operations O ={o1, o2, …, oNo } for changing a finite number P = {p1, p2, …, pNp } of geometric and physical-mechanical properties from the workpiece to the finished part where N o —number of operations in the technological process structure; N p —the number of workpiece properties. The production system can be represented as a linked oriented graph (tree) of the following type: GPS = (V , E)

(2)

where V = {vki }, i = 1, 2, …, N SE is set of the structural elements of the SS (the nodes in the tree); N SE —number of structural elements; k—hierarchical level number from K = {k i }, i = 0, I, II, …, N k —set of ordinal numbers of hierarchy levels; N k —number of levels (height of the tree); E—representation of the set V in V, which can be expressed

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through the following rule:     Γ (vi ) = vj : ∃ vi , vj ∫ A

(3)

where A—is a set of links of elements with each other (tree branches GPS). This parameter determines whether the system can implement a set of operations TO = {to1 , to2 , …, toNto }, where toi is a certain type of operation, and N to —the number of operations implemented in the PS. It is determined by the useful work that the system is able to implement and the set of restrictions imposed on these operations. For example, useful work in machining operations should be considered the formation of a given surface on the workpiece, a set of restrictions may be the size of the equipment, etc.; and during heat treatment—changing the physical properties of the surface layer of the workpiece—increasing the strength. Each type of operation being implemented is divided into types KO = {ko1 , ko2 , …, koNko }, where koi is a specific type of operation, and N ko is their number. It is mainly determined by the equipment. For example, machines allow one to implement two types of machining operations: milling and turning. In turn, the configuration of the equipment imposes restrictions on the parameters of the performed operations: restrictions on the size of the processed workpieces, on the feed and cutting speeds, etc. Then the technological process can be represented as a sequence of operations O of specific type toi and kind koi, implemented in a production system GPS and regulating the mode of its structural element of vki for each hierarchical level k. In addition, the type and kind of operations performed, and their parameters, determine the energy consumption of the production process, as well as energy efficiency. The proposed approach is graphically presented in Figs. 3 and 4.

Fig. 3. The energy performance of the production process, which is implemented in the system GPS.

The hierarchical structure can be divided into the following k levels, as shown in Fig. 5. The share of energy spent on maintaining the production process is significantly higher at levels with a lower order number k. For example, a significant amount of energy is spent on the maintenance of buildings and structures—working and emergency lighting of premises and territory, ventilation, conditioning, heating, etc. Sometimes the share of these costs is much higher compared to the one that goes to the implementation of the directly produced process by elements of lower levels, i.e., to perform useful work—the impact on blanks and converting them into finished products. The situation is the same at lower levels. For example, according to various experts, even when turning

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Fig. 4. Energy graph of the production process.

Fig. 5. Energy hierarchy of an industrial enterprise.

only 10 … 15% of the energy injected into the processing zone is spent on the formation of new surfaces on the workpiece and the rest of the energy is spent on chip formation and heating [8].

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3 Simulation Modeling Let us consider an example of modeling the energy characteristics of the following production process: • the blank is delivered to the company’s warehouse; • after storage time tsw, it is transported to one of the divisions; • the o1 operation is performed by turning the outer cylindrical surface, the result of which is shown in Fig. 6 (type of operation to1—machining; type of operation ko1);

Fig. 6. The result of its processing.

• after the operation is completed, the finished part is sent to the finished product warehouse for tws time. Operations for transporting blanks and finished parts will be considered o0 and o2, respectively. Their main task is to change the spatial position of objects of labor in order to deliver them to the elements of transformation or storage. The material of the workpiece is made of structural steel. A batch of 10 blanks is processed on the HAAS UMC 750SS machine. To model the energy characteristics of machining operations, we will use the previously proposed model [14, 16, 22, 23]. It is based on the representation of the energy characteristics of the technological impact, i.e., in this case, the mechanical removal of the material by turning, as a function of the formed surfaces. This allows us not only to estimate the energy cost of implementing this operation, but also to evaluate its energy efficiency.

4 The Performance of the Experiment At the preproduction stage, there are 3D models of the product and the workpiece, which represent a set of surfaces, a control program that sets the routes and processing modes for converting the workpiece into the finished product, and parameters of the equipment on which it is proposed to process the workpiece [19]. The contour of the workpiece was obtained using the developed module for energy analysis of control programs for multipurpose CNC machines [16]. Modeling of energy characteristics of the production process was carried out using the MATLAB/Simulink mathematical package. The cutting mode according to the control program has the following characteristics: cutting depth t = 5 mm, feed per revolution S = 0.78 mm, cutting speed V = 0.0792 m/min, and cutting length l = 0.65 m.

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In accordance with the energy consumption model of machining processes [22], the cutting power during turning can be represented as follows: N (b, V , S) = AtS + BtV + ESV

(4)

where Si [m/s]—the amount of feed carried out due to the operation of the drive of i-axis; V [m/s]—cutting speed; t [m]—removable allowance; tS i [m2 /s]—the cross-sectional area of chip formed in the processing; tV [m2 /s]—the rate of formation of the side surface of the chip; SV [m2 /s2 ]—directly formed surface; A [J/m2 ], B [J/m2 ], E [J·s/m2 ]—energy coefficients of the energy consumption model. For processing the workpiece material used in this production process, the values of the coefficients A, B, and E are 398698036.4 [J/m2 ], 199387.7753 [J/m2 ], and 4790140.746 [J·s/m2 ], respectively. Let us introduce the following characteristics that affect the energy consumption of the production process: time t s_i of waiting for the release of equipment to inventory is 120 min; standby time t s_o of sending finished products to the end user in inventory is 180 min; power lighting and heating warehouse space with blanks (inventory), warehouse with finished products, and production units are 500 and 3000 W, 800 and 5000 W, and 600 W and 3000 W, respectively; the processing time of the workpiece at the spindle speed of 315 min−1 will be t pc = l/S = 2.64 min. Let’s plot the formation of tS, tV, and SV surfaces during the production process (Fig. 7).

Fig. 7. Surface formation during the production process.

The graph of surface formation on the workpiece characterizes the useful work performed during the turning operation. Figure 8 shows graphs of the energy characteristics of the operation being performed.

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Fig. 8. Surface creation power.

As can be seen from Fig. 9a, the cost of energy resources for the maintenance of fixed assets is almost 3 times higher than the energy consumed for performing a technological operation. At the same time, if you allocate the energy costs of creating a new surface for the part (Fig. 9b), the background costs exceed them by almost 18 times.

Fig. 9. The ratio of energy consumption for the maintenance of fixed assets Wf, energy for the implementation of the turning operation Wm (a), and energy of useful work Wu (b). 5.

It can be concluded that one of the main ways to increase energy efficiency and, as a result, reduce the energy intensity of the production process, is the rational organization of the structures of the production system, the technological process, and their management systems.

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5 Results and Discussion We will highlight the following ways to increase the efficiency of energy consumption during the production processes at some hierarchical levels of industrial enterprises of machine building profile: Enterprise level: • reduction of the time spent for blanks and finished products in warehouse stocks and in the enterprise as a whole; • use of an effective logistics system within the company to reduce the time of transport operations. Division level: • selection of the optimal route for processing the workpiece, taking into account the multivariant size of the equipment and its level of wear. Equipment level: • selection of the optimal route for processing the workpiece surfaces (elimination of “irrational idling”, reduction of the share of auxiliary time in the preparatory-final and auxiliary time in the machine’s operating time Fund) [18]. Level of impact: • selection of optimal impact parameters (taking into account the actual state of the equipment) in terms of energy efficiency (entering the minimum required amount of energy into the impact zone for conversion) [18]. At the highest hierarchical level, one of the main barriers to improving energy efficiency and, as a result, improving the competitiveness of products is also the conservatism of management in this area. Business leaders often underestimate the high degree of savings from energy efficiency programs. They believe there is a certain degree of technical and financial risk in their implementation. These programs have a lower priority than traditional commercial offers. In addition, with relatively low energy costs, it is difficult to convince management of the need to implement complex energy efficiency projects, although it is known that energy efficiency programs are also needed in enterprises where the cost of energy is about 5% of the cost of production [24–27]. The proposed approach to modeling production processes has a sufficiently good visibility and accuracy to convince the management of the enterprise in carrying out energy saving measures and implementing programs to improve energy efficiency.

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References 1. Decree of the President of the Russian Federation of 04.06.2008 N 889 “On certain measures to improve the energy and environmental efficiency of the Russian economy” (2008), Moscow 2. State program of the Russian Federation “ Energy saving and energy efficiency improvement for the period up to 2020”, Moscow 3. State program of the Russian Federation “Energy efficiency and energy development”, Moscow 4. Report on the implementation of the state program “Energy efficiency and energy development” for 2018 (2018), Moscow 5. Report on the implementation of the state program “Energy efficiency and energy development” for 2017 (2017), Moscow 6. The industry of Russia (2012) Rosstat, Moscow 7. Ivanov VA (2015) Analysis of energy consumption in various industries. https://doi.org/10. 15862/144TVN115 8. Salnikov VS (2003) Technological basis for energy efficiency of production systems, Tula 9. EIA (2010) “Annual Energy Review 2010” 10. Int. Energy Agency (IEA) (2008) Worldwide Trends in Energy Use and Efficiency, Key Insights from IEA Indicator Analysis (online) 11. Jucker B, Leupp P, Sjökvist T (2008) Electrical energy – The challenge of the next decades. Abb Review, pp 8–13 12. Salnikov VV, Frantsuzova YuV (2018) Energy representation of some objects of industrial enterprises. Izvestiya, Tula State University. Technical Sci 10:108–113 13. State Standart 14.004-83 (1983) Technological preparation of production. Terms and definitions of basic concepts (with Amendments N 1, 2), Moscow 14. State Standart 3.1109-82 Unified system of technological documentation (ESTD). Terms and definitions of basic concepts (with Amendment N 1), Moscow 15. Smilyansky GL et al (1983) Reference Book of the ACS TP Designer. Publishing House “Engineering”, Moscow 16. Salnikov VV, Frantsuzova YuV (2019) Energy analysis of control programs for multi-purpose machines. Modeling, optimization and information technologies. The Scientific J 7(2):275– 286 17. Erzin OA, Salnikov VV (2014) One aspect efficiency evaluation of technological systems. Izvestia Tula State University. Technical Sci 11–2:594–603 18. Salnikov VV, Ivutin AN (2017) The role of technological information in ensuring efficient energy consumption of an enterprise. Izvestiya Tula State University. Technical Sci 8–1:165– 170 19. Salnikov VV, Ivutin AN, Frantsuzova YV (2018) Computer support use of energy resources in the production system. Izvestiya Tula State University. Technical Sci 6:106–114 20. Salnikov VV, Ivutin AN (2017) One of the aspects of collecting technological information for assessing the efficiency of production energy consumption In: Collection of theses of the congress of young scientists. Electronic edition, Saint-Petersburg, ITMO University 21. Salnikov VV (2018) Computer based support for efficient use of energy in manufacturing. In: 7th mediterranean conference on embedded computing (MECO). https://doi.org/10.1109/ meco.2018.8405994 22. Salnikov V, Frantsuzova Y (2020) Energy Consumption Modeling of Machining Processes. In: Radionov A, Kravchenko O, Guzeev V, Rozhdestvenskiy Y (eds), Proceedings of the 5th international conference on industrial engineering (ICIE 2019). ICIE 2019. Lecture Notes in Mechanical Engineering. Springer, Cham, p 1285–1294. https://doi.org/10.1007/978-3-03022063-1_136

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23. Salnikov VV (2016) Method of rationing energy resources costs of a technological operation In: Intellectual and information systems: materials. Tula 24. Salnikov VV (2017) Mathematical model of energy consumption of industrial equipment In: Intellectual and information systems: Materials of the International scientific and technical conference, Tula 25. Prokopenko I (2001) Efficiency and Quality Management: a Modular program. Translated from English, Moscow 26. Kezai Koho Centre (1981) How Japan is curtailing energy consumption. Case studies of 50 companies, Tokyo 27. Zackrison HB (1984) Energy conservation techniques for engineers. New York

Control Algorithm for Compensated Tripod-Based Manipulators V. Zhoga1,2(B) , V. Dyashkin-Titov3 , and N. Vorob’eva3 1 Volgograd State Technical University, 28, Lenin Avenue, Volgograd 400005, Russia

[email protected] 2 Innopolis University, 1, Universitetskaya Str., Innopolis 420500, Russia 3 Volgograd State Agrarian University, 26, University Avenue, Volgograd 400002, Russia

Abstract. The paper presents an algorithm for synthesizing the control forces of a tripod-based manipulator, for which it uses a mathematical dynamics model where control-element masses are taken into account. There have been obtained dependences of the programmed forces of drive motors when moving the grabber on a spatial straight line. The algorithm for the formation of control voltages is formed on the basis of complete equations of dynamics of the manipulator, taking into account the kinematic parameters of the manipulator in all degrees of freedom. The parameters of the equations characterizing the character of dynamic errors change allow varying the characteristics of manipulator controlled movements. Actuator control loops are synthesized while algorithmizing the trajectory control. The algorithm to stabilize the programmed gripper motions as set in a parametric form is synthesized by the assigned trajectory using feedback sensor signals. The algorithm for calculating the control forces is one of the compensating type algorithms. Keywords: Manipulator · Parallel structure · Tripod · Dynamics · Control forces

1 Introduction Parallel manipulators are used in such processes that require high speed and acceleration of the end-of-arm [1–4]. Tripod-based manipulators are used in chip assembly, product sorting, and packaging. They spend less than a second per operation [5–7]. The drives must provide end-of-arm acceleration that is several times as large as the free-fall acceleration. Dynamic analysis of manipulators solves two problems: direct and inverse [8]. The inverse problem is to determine the control signals that provide a given movement of the working unit [9, 10]. The results of the solution are used to form a block diagram of the control system [11]. In this case, simplified manipulator-dynamics models cannot be used to synthesize the programmed end-of-arm movements or accurate control-force values [12–15]. The control system ensures the accuracy of the program movements if it is based on a complete dynamic model of the mechanism [16, 17]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_71

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2 Mathematical Manipulator-Dynamics Model Design of the manipulator, whose kinematic diagram is shown in Fig. 1a [18].

Fig. 1. a Kinematic diagram of the tripod-based manipulator; b moving coordinate system rotation angles.

Actuators are attached to the base by two-DoF hinged joints in order to enable omnidirectional movement of the end-of-arm. The actuator drive consists of a DC motor, an irreversible gearbox, and a ballscrew pair. All actuators are equipped with analog movement sensors. Assume that the manipulator consists of six masses: three electriccylinder housings and three pins. Electric-cylinder housings move spherically, while the pin of each actuator performs translational spherical and relative straightforward progressive motion. Electric-cylinder housings and their pins have the same angularvelocity vectors. The manipulator configuration is entirely defined by three independent generalized coordinates. In order to find the spatial position of the actuator housing, four coordinate systems are introduced, see Fig. 1b: the absolute system Oxyz linked to the fixed base, and the moving coordinate systems Ox i yi zi , (i = 1–3), linked to the housing of each actuator. The orientation of each moving coordinate system Ox i yi zi in relation to the absolute system Oxyz is specified by two angles: ϕi (t) when rotating around the fixed axis Ox, and δi (t) when rotating around the moving axis Oyi . The generalized manipulator coordinates are the control-element lengths li (t) and the angles δi (t), ϕi (t), (i = 1–3) of electric-cylinder rotation in relation to the absolute coordinate system. Three coordinates are independent.

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The directional cosines of the moving coordinate axes are found by the expressions α11i = cos δi , α12i = sin ϕi sin δi , α13i = − sin δi cos ϕi , α22i = cos ϕi , α23i = sin ϕi , α21i = 0, α31i = sin δi , α32i = − cos δi sin ϕi , α33i = cos δi cos ϕi .

(1)

The directional cosines expressed in terms of actuator lengths and actuator-to-base attachment coordinates are written as • for Actuator One

α311 =

xM l1

, α321 =

yM −OA , l1

α331 =

zM l1

,

(2)

• for Actuator Two

α312 =

xM − OB yM zM , α322 = , α332 = , l2 l2 l2

(3)

xM + OB yM zM , α323 = , α333 = , l3 l3 l3

(4)

• for Actuator Three

α313 =

Six holonomic constraints are imposed on all the coordinates; the constraints are formed from the expressions (1–4) f1 = ϕ2 − ϕ3 = 0, f2 = l3 cos δ3 − l2 cos δ2 = 0, f3 = l1 cos δ1 cos ϕ1 − l2 cos δ2 cos ϕ2 = 0, f4 = l3 sin δ3 − l2 sin δ2 − 2OB = 0, f5 = l1 sin δ1 − l2 sin δ2 − OB = 0, f6 = l1 cos δ1 sin ϕ1 − l2 cos δ2 sin ϕ2 − OA = 0.

(5)

Manipulator-system dynamics equations are derived by reference Lagrange’s second-kind equations [19–22] with holonomic constraints (5)   6 d ∂T ∂  ∂fi ∂T = Qs − + λi , s = 1 ÷ 9, − dt ∂ q˙ s ∂qs ∂qs ∂qs i=1

(6)

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where qs are the generalized manipulator-configuration coordinates, the number of which equals the n degrees of freedom of the manipulator plus the number of constraint equations; T is the kinetic energy of the manipulator; Qs is the generalized force corresponding to the s coordinate; λi are Lagrange multipliers; −∂/∂qs is the generalized force potential corresponding to the s coordinate. In order to compile the Eqs. (6), find the kinetic and potential energy of the manipulator expressed in terms of nine coordinates qs , q˙ s . The use the specified forces that the manipulator control elements are exposed to in order to compute the generalized forces Qs . Implementing the formalism (6) produces a mathematical model of the manipulator (Fig. 1a) that can be written as nine ordinary second-order differential equations. Now there is a system of eighteen Eqs. (5), (6) for finding the same number of variables qs (s = 1–9), λi (i = 1–6), and ui (i = 1–3). This system can be used for dynamic studies into manipulators [23–26].

3 Synthesizing the Programmed Control Forces The first six (6) equations of the mathematical manipulator-dynamics model are linear algebraic equations concerning the six unknown Lagrange multipliers λi ,i = 1–6. The coefficients of Lagrange multipliers form a 6 × 6 matrix. The determinant of this matrix is non-zero, as it is transposed in relation to the matrix composed of the coefficients of the Jacobian independent-equation matrix (5). Using Cramer’s formulas [27], solve the system (6) as  (7) λi (qs , q˙ s , q¨ s ) = Di D, where D is the main determinant of the system (6); Di is the auxiliary determinant derived from the main determinant D of the system by substituting its ith column with a column of absolute terms (left side of the equations). After substituting the obtained expressions λi in the three remaining expressions, find expressions for the control forces as a function of the set laws of programmed manipulator grabber movements. The programmed manipulator grabber movement trajectory is set in a parametric pr pr pr form xM (t), yM (t), zM (t). These functions are twice-differentiable over time and meet specified initial conditions. Programmed laws of control-element length alteration (Fig. 1a) and from (1–4) the programmed laws of altering the rotation angles of these control elements. The actual grabber trajectory x M (t), yM (t), zM (t) may differ from the configured pr pr pr trajectory xM (t), yM (t), zM (t) due to the inertia in the gear mechanisms and in the ballscrew pair. In order to compensate such deviations from the programmed trajectory, synthesize a control algorithm by the following method [28]. The algorithm for generating the control voltages ui (t) received by the manipulator drive inputs shall be based on a requirement pr that the deviations δi (t) = li − li , match the solution of the second-order differential equation δ¨i (t) + α1i δ˙i (t) + α2i δi (t) = 0, (i = 1−3),

(8)

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where α1i , α2i are the constant positive coefficients that define the nature of the transient. The process (8) will take place in the case the acceleration of altering ¨li the length of control elements can be found from (8) ¨li (t) = ¨l pr + α1i δ˙i (t) + α2i δi (t) = 0. i

(9)

The form of this equation enables altering the dynamic characteristics of the controlled manipulator movements. Find the desired laws of control-force alteration   pr  F1 = m1 ¨l1 + α11 δ˙1 + α21 δ1 + 0.5m1 ϕ˙12 cos2 δ1 + δ˙12 (l10 − 2l1 )−    (10) −D3 D cos ϕ1 cos δ1 − D5 D sin δ1 − D6 D cos δ1 sin ϕ1 ,   pr   F2 =m2 ¨l2 + α12 δ˙2 + α22 δ2 + 0.5m2 ϕ˙22 cos2 δ2 + δ˙22 (l20 − 2l2 ) + D2 D cos δ2     + D3 D cos ϕ2 cos δ2 + D4 D sin δ2 + D5 D sin δ2 + D6 D cos δ2 sin ϕ2 , (11)   pr  F3 =m3 ¨l3 + α13 δ˙3 + α23 δ3 + 0.5m3 ϕ˙32 cos2 δ3 + δ˙32 (l30 − 2l3 )   (12) − D2 D cos δ3 − D4 D sin δ3 . In order to generate a control-voltage algorithm, substitute the Eqs. (10)–(12) in equation the dynamic characteristic of a separately-excited DC drive and neglect the value τ of the electromagnetic constant of time for the motor so as to finally solve the problem of synthesizing the programmed movements of the manipulator grabber. The stability of this algorithm is ensured by selecting such coefficients α1i , α2i (8) so that the roots of its characteristic equations had negative real parts. Indeed, after substituting the control forces (10)–(12), we obtain a differential equation of the kinematic trajectory of the closed-loop system mi ¨li + α1i ˙li + α2i li = mi ¨li + α1i ˙li + α2i li . pr

pr

pr

(13)

Solutions such a (13) are functions li (t) = li (t) + Ci1 expβ1 t +Ci2 expβ2 t , (i = 1 − 3) pr

where C i1 , C i2 are the constants found from the initial conditions; β1 , β2 are the roots of the characteristic equation for (8). Since α1i > 0, α2i > 0, the real part of the roots β1 , β2 is always negative, thus pr li (t) → li (t) at t → ∞. Recommendations on how to select coefficient values are given in [28, 29]. Figure 2 shows the structural diagram of a system to control the ith control element. In Fig. 2, Qi (qs , q˙ s ) denotes the components of (10)–(12) that depend on δi (t), ϕi (t) as well as their time derivatives. They are calculated for the current values li (t), ˙li (t).

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Fig. 2. Structural diagram of the automatic control system (1—motor, 2—ball screw).

4 Programmed Control Force: A Calculation Example Technological operations analysis show that end-of-arm movement along a spatial straight line is one of the most common movement types. Equation for a straight line passing through the points with coordinates x M (0) = x M0 , yM (0) = yM0 , zM (0) = zM0 , and coordinates x M (T ) = x Mk , yM (T ) = yMk , zM (T ) = zMk will canonically [9, 30] be written as yM (t) − yM 0 zM (t) − zM 0 xM (t) − xM 0 = = ,

x

y

z where x = xMk − xM 0 , y = yMk − yM 0 , z = zMk − zM 0 . Denoting through





2 x + 2 y + 2 z

2 x + 2 y + 2 z

2 x + 2 y + 2 z , Ky = , Kz = , Kx =

x

y

z the laws of altering the Cartesian coordinates x M (t), yM (t), zM (t) of the point M are obtained as xM (t) =

S(t) + xM 0 KX S(t) + yM 0 KY S(t) + zM 0 KZ , yM (t) = , zM (t) = , (14) KX KY KZ

where S(t) is the law of altering the arc coordinate as the point moves along the straight line. Setting such movement law S(t) of the point M along a straight line, find the lengthpr pr pr alteration laws for the control segments li (t), angles δi (t) and ϕi (t). The law of altering the arc coordinate is adopted as [30]     S(t) = 10 − 15t T + 6t 2 T 2 t 3 T 3 Se , T ≥ t ≥ 0, (15) where S e is the trajectory length equal to Se = (xE (T ) − xE (0))2 + (yE (T ) − yE (0))2 + (zE (T ) − zE (0))2 . The law ensures the equality to speed and acceleration zero point at the trajectory starting and ending points.

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Fig. 3. Control-force alteration laws.

Then find the control forces in the linear actuator drives Fi (t), i = 1 − 3 from (10)–(12). Figure 3 shows the laws of altering the control forces of the linear control segments of a tripod-based manipulator. The calculations were done for the following manipulator and trajectory parameters:mi = 2.7 kg, mi2 = 6.3 kg, J i = 0.683 kgm2 , J ir = 1.027 kgm2 , (i = 1–3), x M0 = −162.2 mm, yM0 = 154.1 mm, zM0 = 778.6 mm, x Mk = 300 mm, yMk = 50 mm, zMk = 950 mm, α1 = 50, α2 = 525.

5 Conclusion The control-voltage generation algorithm is based on the kinematic parameters of the manipulator for all of its degrees of freedom; it has also been derived from the complete manipulator motion dynamics equations. The way the equations are written to characterize changes in deviations enables altering the dynamic characteristics of the controlled manipulator movements. The above algorithm is a compensating algorithm. In order to improve the accuracy of finding the control forces, the mathematical manipulator model must be complemented with a dynamic model of gearbox and ballscrew-pair dynamics. The proposed algorithm has been implemented as a control-voltage calculation app for Mathcad, a symbolic-math package. Acknowledgements. The reported study was funded by RFBR and the Volgograd region according to the research project № 19-48-340013 and the grant of the President RF № MK-210.2020.8

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References 1. Bushuev VV, Hol’shev IG (2001) The mechanisms of parallel structure in mechanical engineering. STIN 1:3–8 2. Afonin VL, Podzorov PV, Slepcov VV (2006) Processing equipment on the basis of mechanisms of parallel kinematics. Mashinostroenie, Moscow 3. Glazunov VA, Koliskor AW, Krainev AF (1991) Spatial mechanisms of parallel structure. Moscow 4. Rybak LA, Grinenko GP (2013) “Innovative processing equipment on the basis of parallel structures: prospects and directions of commercialization. Eng Technol Mech Eng 7(25):32– 39 5. The handling robot FlexPicker IRB 360 company AAB (2014) http://www.roboticturnkeys olutions.com/robots/abb/datasheet/IRB_360.pdf. Accessed 21 Sept 2014 6. Robots with parallel kinematics EXPT, tripods (2014) http://festo.promsis.biz/pdf/EXPT_R U.PDF. Accessed 21 Sept 2014 7. The robots of the Delta (2014). http://omron.nt-rt.ru/images/manuals/Delta.pdf. Accessed 21 Sept 2014 8. Zhoga V et al (2014) Walking Mobile Robot with Manipulator-Tripod. Proc. of Romansy 2014 XX CISM-IFToMM Symposium on Theory and Practice of Robots and Manipulators. Mech Mac Sci 22:463–471 9. Dyashkin-Titov VV, Vorob’eva NS, Terehov SE (2016) The algorithm of positioning the gripper of a manipulator-tripod. Sci Edu, Modern Machinery p 634–644 10. Zhoga VV, Dyashkin-Titov VV, Nesmiyanov IA, Vorob’eva NS (2016) Manipulator of parallel- serial structure with a controlled gripper positioning task. Mechatronics, Autom, Control 8(17):525–530 11. Nesmiyanov I, Zhoga V, Skakunov V, Terekhov S (2015) Synthesis of control algorithm and computer simulation of robotic manipulator-tripod. Commun Comput Inform Sci 392–404 12. Staicu S (2015) Dynamics modelling of a stewart-based hybrid parallel robot. Adv Robot 29(14):929–938 13. Li Y, Staicu S (2012) Inverse dynamics of a 3-PRC parallel kinematic machine. Nonlinear Dyn 67(2):1031–1041 14. Ibrahim O, Khalil W (2010) Inverse and direct dynamic models of hybrid robots. Mech Mach Theory 45(4):627–640 15. Liu N, Wu J (2014) Kinematics and application of a hybrid industrial robot Delta-RST. Sens Transduc 169(4):186–192 16. Zhoga VV, Gerasun VM, Nesmiyanov IA, Vorob’eva NS (2015) Dynamic Creation of the Optimum Program Motion of a Manipulator-Tripod. J Machinery Manuf Reability 44(2):181– 186 17. Dyashkin-Titov VV, Zhoga VV, Nesmiyanov IA, Vorob’eva NS (2017) Dynamics of the manipulator parallel-serial structure. Sci Edu, Modern Machinery, pp 439–449 18. Zhoga VV, Dyashkin-Titov VV, Dyashkin AV, Vorob’eva NS (2017) RU Patent 2616493, 17 Apr 2017 19. Lur’e AI (1961) Analytical mechanics. Moscow 20. Kolovskii MZ, Sloushch AV (1998) Foundations of industrial robot dynamics. Moscow 21. Korendesev AI, Salamandra BL, Tyves LI (2006) Theoretical basis of robotics. In 2 books. Institute of machines science named after A.A. Blagonravov of the Russian Academy of Sciences. Moscow 22. Kobrinskij AA, Kobrinskij AE (1985) Manipulation systems of robots. Moscow 23. Nesmiyanov IA, Zhoga VV, Vorobieva NS, Dyashkin-Titov VV (2016) Dynamics of tripod drive with elastic self-sustaining transmission. VP Vibroengineering Procedia 8:512–516

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Modeling and Assessment of Production Cycle Information Entropy Under Joint Activities R. Fatkieva1(B) , E. Evnevich1 , and A. Vasiliev2 1 Russian Academy of Sciences, St. Petersburg Institute for Informatics and Automation, 39, 14

Line, St., Petersburg 199178, Russia [email protected] 2 Sinara Group, PJSC Zvezda, 123, Babushkina ul., St. Petersburg 192012, Russia

Abstract. Development of optimal interaction scenario of industrial facilities under joint activities is a problem requiring taking into account strategic planning and tactical coordination of goals and scenarios of participants of production cycle. The collaborative scenario is proposed to be presented as an interrelated set of scenarios of participants resulting in a common strategy by eliminating contradictions and fixing common goals. Objective functions of joint activities and criteria for achieving them are formulated. Balanced scorecard of an enterprise is created and used for joint activities monitoring and control as well as dynamic assessment of goal achievement, harmonization and correction of operational plans at all stages of production cycle. A model and a method of assessing the degree of trust in operational processes of participants are developed along with subsequent control measures in case of deviation from the interaction scenario. The model and the method are illustrated by numerical modeling example of optimization of inventory nomenclature to be purchased. The space of states of the process under investigation is formed and transition probabilities are determined as a solution of corresponding Kolmogorov’s system of differential equations. Information entropy is calculated and compliance of the parties of joint activities is estimated according to the method of Nikolayev-Temnov. Modeling results confirm the correlation between entropy growth and compliance decrease and, as a result, performance sustainability degradation. Monitoring entropy can serve a tool of joint production cycle maintenance. Keywords: Industrial facility · Balanced scorecard · Production modeling · Joint activities · Processes compliance · Information entropy

1 Introduction Efficient control of operational processes (OpPs) under joint activities (JA) of operational cycle parties in a competitive environment requires the use of new technologies. Imposing stronger requirements on product quality under resource saving in the production cycle leads to a need of searching for new approaches to production cycle control. The main © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_72

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problem of monitoring the achievement of target indicators consists in the dynamic change of information concerning production and technologic processes as well as in the uncertainty being contributed to the process by the participants. Production cycle control in the industrial facility (IF) is a complex process for the following reasons: • rather long duration and high labor intensity of processing cycle inherent to existing technological solutions; • inconsistency of operational plans of different services due to the lack of information and analytical technologies; • insufficient data relevance on the accomplishment of ongoing works resulting in inaccuracy of production time limits; • high variety of nomenclature of tools used in production leading to considerable costs of inventory accounting. Besides, manufacturing process being knowledge-consuming and technologically complex, it imposes additional constraints on changes in the production chains since inconsistent design and manufacturing changes could lead to security losses during finished products exploitation. All the above said put forward a task of production sustainability assessment. Modeling and assessment of the dynamism of production processes based on the changes of information entropy is presented in the studies [1–3]. The work [4] proposes a method of detecting irregularities by means of operational analysis of spectral and spatial features. Models based on forecasting and situation control are presented in [5–19]. The above mentioned models and methods aim at assessing uncertainty as regards the outside environment and do not consider adaptation mechanisms concerning incompliance of actions inside the system [9–14]. The task arises of assessing the level of trust in operational processes and their compliance under JA in order to form a control action in case of deviation from the scenario of interaction having been specified during strategic planning.

2 Collaborative Strategy Development In general the solution of the optimization task of strategic planning could be reduced to the selection of development trajectory meeting the requirement of either minimal integral expense in time interval (T0 , T ) T Wtoll (T0 , T ) → min

Z(t)dt

(1)

T0

where Z is the cost of production and expenses for IF maintenance; or of maximal net profit T Wprofit (T0 , T ) = max( T0

T TR(q, t)dt −

TC(q, t)dt) T0

(2)

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where TR(q, t)—profit gained during production; TC(q, t)—expenses for IF and OpP maintenance. In the context of dynamic system approach to the description of the performance of the industrial facilities (IF) and that of the operational process (OpP) under JA the problem statement is formulated as follows: W (t) = opt{S (t), Opp(t), C(t), X(t), A(t)} where W is target function; S(t)—is a number of elements included in the IF; Opp(t)—set of OpPs between the elements; C(t)—set of events generated by the OpPs; X (t)—set of indicators of target function implementation according to (1) or (2); A(t)—work amount in the specified time interval. Then an aggregate model consisting of a set of performance indicators of the structural elements providing dynamic determination of a number of participating OpPs at any moment of time and of a set of states of each OpP could be matched to each indicator group X (t) at each level. The above model enables to determine the set of OpPs and the corresponding sets of states arising under each OpP realization in the dynamic mode at any moment of time. It is necessary to use multi-criteria optimization approach in order to determine the target function of structural and parametric synthesis for the parties of the JA depending on the achievement of N target functions of the parties: W1 (Xrl ), . . . , WN (Xrl ) and on the JF functioning indicators vector Xrl on a set of admissible values: ⎧ W1 = opt W1 (Xrl ) ⎪ ⎪ ⎪ r,l ⎪ ⎨ ... Wint = (3) ⎪ ⎪ ⎪ l ⎪ WN = opt WN (Xr ) ⎩ r,l

where r = 1, …, R—indicator number, l = 1, …, L—number of level of target function detalization. It should be noted that in practical applications the target function use to be influenced and formed by criteria that may be inconsistent and/or in uncertainty with respect to each other. Hence, the problem of searching for optimal solution taking into account the above circumstances is reduced to the task of finding a compromise between optimal solutions for each of the parties. In case of many optimal solutions and taking into account spatialtemporal and technological constraints it is possible to form target functions Wint for each of the elements and to meet the requirement of the achievement of the strategic goal in the form: W L = f (W L (W1l , W2l , . . . , WNl )), where WNl is a set of integration strategies at the level l. In order to achieve optimal strategy as a whole or for each of the parties it is necessary to determine the current spatial-temporal structure of the integration of IFs and OpPs, the vector of admissible optimal solutions, the algorithm of goal achievement, and to develop criteria for their achievement and to form a sequence of spatial-temporal structure reconfigurations in order to estimate the structural dynamics of IFs and OpPs. The goal could not be achieved without control of the states of the processes taking place in the system. Therefore, in order to elaborate control actions it is necessary to form sets of indicators and criteria for monitoring the current state of IFs and OpPs. A

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special feature to be paid attention to while solving this problem is the possibility of arising of incompleteness of information on changes in current indicators resulting in a problem of choice and in a need to take into account the risk factor during structural dynamics control [11]. In this case the particular task of control consists in the assurance of required performance quality indicators at predetermined time intervals and in generation of control actions for changing the spatial and temporal structure according to changing of the indicators within predetermined upper and lower threshold values. Note that the problem could be aggravated if one of the parties of the JA provides not only incomplete but contradictory information on the indicators of achievement of the target function. Optimization problem formulation (3) requires the search for optimal JA strategies capable of analysis of production cycle technological links and of determination of a number of levels l necessary for the goal achievement. Those strategies should also be capable of forming the set of interaction scenarios for each of the participants  Ki (t) = K1 (t), K2 (t), . . . , KMi , where i = 1, M are interaction participants as well as of making selection of optimal scenario at each production stage. In general terms, the development strategy under JA could be presented as an interconnected complex of scenarios where each party seeks for realization of its target function depending on the need for tactical agreeing in the goal achievement. Achieving the goal under counteraction of participants is a rather common aspect of strategic planning of the JA. JA process is represented as a consistent goal-oriented development of a common strategy to achieve prescribed target function by eliminating revealed contradictions and by searching for common goals and tasks.

3 Creation of a Model of Trust in Operational Processes Creation of a model of trust in OpPs is an extension of strategic planning task. It has an impact on the decision-making process as regards control actions intended for the adjustment of the development course. Errors made at this stage lead to a breach at the agreeing stage, and in general they result in asymmetries in the information of one of the parties and in a decrease of trust from the other ones [12]. The reasons for information asymmetry could be the following: – information incompleteness (information insufficiency for decision-making, information discrepancy, information distortion including unintentional one); – information redundancy (resulting in problems in decision-making); – incompleteness of a set of solution means (lack of decision-making algorithm in the conditions of uncertainty); – information transfer delay (both intentional and for objective reasons); – deliberate counteraction to obtaining information. The asymmetry of information leads to a growth of information entropy in the system and to an increase in the potential of one of the parties as well as to the risk events such as unfavorable economic choices and increased transaction costs.

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Therefore, there is an urgent need to form a set of scenarios of interaction between the parties of the JA taking into account possible reactions to the set of scenarios obtained and searching for an optimal response to the situation. Model implementation includes the following steps: Step 1. Selection of the set of n roles for each of M participants of

JA. The set of interM action scenarios are determined for each role as follows: K = K1Mi , K2Mi , . . . KPMi , where pi is the number of scenarios for each role i. Step 2. For each scenario KpMi a set of m states is generated in which the object can find itself under single operations. Step 3. For each state a set of transition rules to the other states is established. Step 4. Set of state transition events is generated and probabilities pij of transition from the state i to the state j are determined. Step 5. Information entropy is estimated according to the formula [15–18]: H (Xevent ) = −

m m  

pij logm pij

(4)

j=o i=1

Space of threshold values of entropy deviations from the predetermined level being obtained under normal functioning mode is formed. Step 6. Strategic planning control is implemented by means of forecasting mechanisms and estimation of likelihood of event manifestation. In this case the control action could be considered as a subset of measures to ensure functional security.

4 Modeling Results In order to achieve the cost minimization strategy (1) a balanced scorecard of enterprises is developed [13] enabling operational control and being accompanied by online assessment monitoring of a goal achievement under JA with the possibility of reducing production time by virtue of agreeing at all production stages, of operational plans adjustment and by introducing analytical technologies of planning and inventory accounting systems. However, the use of a balanced scorecard could fail in the identification of production processes not being included in the main processing cycle but actually slowing down the production of finished goods. Scorecard is also problematic to be used in case of indicators “delay” or unreliability. In order to do with the above problem it became necessary to simulate OpPs taking into account the uncertainty of information about the IF functioning. Modeling is carried out using an example of optimization of the task “Reduction of losses by virtue of optimization of purchased tools nomenclature”. For this purpose the departments involved in the optimization process are selected as follows: Warehouse, Supply Department and Production Complex. To evaluate the operation of the tool procurement process the normal mode operation scenario (scenario 1), the ones with the partial violations in operation (scenarios 2–6) and that of completely violated cycle (scenario 7) are developed.

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Scenario 1:1—generation of the nomenclature list of tools required; 2—approval of the list; 3—transfer of the list to supply department; 4—transfer of tools to the warehouse; 5—delivery of tools to production complex. Scenario 2:6—incomplete list of required tools; 7—mismatch of quality of the required tools; 8—mismatch of tools quantity to the needs of production; Scenario 3: 9—no agreement between services involved in the process; Scenario 4:10—purchase of non-appropriate tools; 13—purchase of sub-standard tools; 14—long procurement terms; Scenario 5:11—incorrect inventory registration; Scenario 6: 12—delivery of a tool to non-appropriate service; 13—purchase of sub-standard tools; 14—long procurement terms; 15—delivery of incomplete kit; 16—delivery of inappropriate tools. Scenario 7: Complete set of violations. See Fig. 1.

Fig. 1. Model of disruption of the process of optimization of purchased tools nomenclature.

For each scenario, a set of all involved states is established thus making it possible to determine transition intensities and to calculate probabilities pij of transition from state i to state j. Transition probabilities are determined as a solution of a system of differential equations for different sets of transitions intensity values [19]. Having calculated transition probabilities the entropy of the system could be determined (4) as well as the compliance of the parties under JA. Compliance can be calculated according to the methods of M. Kendall and of Nikolaev-Temnov [15, 16] by formula: WH = 1 −

H n ln n

(5)

where n is the number of states. If the value of WH ≥ 0, 55 then the JA participants are in compliance. Simulation of the information entropy of the process “Reduction of losses by virtue of optimization of the purchased instrument nomenclature” at the moment of time t shows that in case of failure of functioning the entropy increases (Table 1, column H for each scenario number); at the same time for each scenario including cycle violations various quantitative estimates are calculated. On the basis of obtained estimates of entropy growth the threshold values characteristics of certain violations of the operational cycle could be determined thus making possible to identify the type of violation by corresponding entropy value.

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Table 1. Assessment of JA participants compliance. № Probability p1

H

p2

p3

1

0.01 0.2

0.5

0.16 0.15 … 0

1.29 0.58

2

0.03 0.18 0.3

0.15 0.06 … 0

1.86 0.4

3

0.05 0.2

0.1

0.11 … 0

1.63 0.47

4

0.01 0.35 0.2

0.07 0.07 … 0

1.79 0.42

5

0.01 0.35 0.18 0.13 0.2

6

0.09 0.22 0.4

7

0.04 0.08 0.03 0.02 0.04 … 0.007 9.56 0

0.2

p4

p5

W

… p16

… 0

0.14 0.06 … 0.04

1.57 0.49 1.67 0.46

The compliance values, calculated according to (5) and presented in column W of Table 1, show that compliance estimates are satisfactory (not less than 0.55) while operating in normal mode. However, compliance values decrease in the case of process disruption. Disruption takes place if the strategy of one of the participants of the JA changes because the operational cycle was originally developed taking into account the achievement of joint goals. The formation and analysis of the obtained estimates is an auxiliary tool and enables preventing the occurrence of violations in case of incomplete or unreliable information on the performance indicators of one of the parties.

5 Conclusion Application of the developed method of obtaining quantitative entropy estimates makes it possible assessing performance sustainability in an automated mode as well as forming subsets of measures to ensure secure functioning. It should be noted, however, that the proposed method had limitations on the number of processes under consideration due to the “curse of dimension” since the number of possible variants to be analyzed leads to the need of taking into account all the states of each process at all levels and so on, and so forth [1]. For the solution of the dimension problem the methods and algorithms of structural and functional decomposition of the production process seem to be promising.

References 1. Dulesov AS, Kondrat NN (2015) Opredelenie dlya prostejshej struktury‘ tekhnicheskoj sistemy‘ kolichestva informacionnoj entropii posredstvom eyo normirovki (Determination for the simplest structure of the technical system of the amount of information entropy through its normalization). Fundamental‘ny‘eissledovaniya (Fundamental Research) 2–20:4408–4412 2. Ma RG, Xu H, Liu WY, Wang X, Cheng CA (2019) Dynamic Yardstick Evaluation Approach for Assessing Development and Production Management Status of Grass-roots. Distrib Util IOP Conf Ser: Earth Environ Sci 223(1):012045

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3. Bychkova SM, Makarova NN, Zhidkova EA (2018) Measurement of information in the subsystem of internal control of the controlling system of organizations of the agro-industrial complex. Entrepreneurship Sustainability 6(1):35–43 4. Kim S (2015) Unsupervised spectral-spatial feature selection-based camouflaged object detection using VNIR hyperspectral camera. Scientific World Journal, 834635 5. Kozulia T, Bilova M, Kozulia M (2015) Environmental assessment development of anthropogenic objects using comparator identification method Eastern-European. J Enterp Technol 5(10):27–33 6. Chen C-B, Wang L-Y (2006) Rough set-based clustering with refinement using shannon’s entropy theory. Comput Math Appl 52(10–11):1563–1576 7. Yudin SV (2018) Metodika rascheta informacionnykh planov statisticheskogo priemochnogo kontrolya na osnove bajesovskogo podkhoda (Methodology of calculation of information plans of statistical acceptance control on the basis of Bayesian approach). Sovremenny‘enaukoemkie tekhnologii (Modern knowledge-intensive technologies) 11-1:90–94 8. Loginovskiy OV, Dranko OI, Hollay AV (2018) Mathematical Models for Assessment of Activity of Industrial Enterprises under the Conditions of Instability.Bulletin of the South Ural State University. Ser. Comput Technol, Autom Control, Radio Electron 18(4):88–102 9. Novikov DA (2008) Matematicheskie Modeli Formirovaniya i Funkcionirovaniya Komand (Mathematical models of formation and functioning of commands). Publishing House of Physical and Mathematical Literature, Moscow 10. Vinogradov GP, Burdo GB, Isaev AA (2015) A decision-making in high-tech products production systems. Softw Syst 2(110):75–82 11. Kulagovskiy EV (2016) Metodological tools for risk assessment industrial enterprises. Scientif-Technical J “Bull Civil Eng” 5(58):181–185 12. Gushchina EG, Vitalyeva EM, Volkov SK (2017) Influence of Asymmetry of information on the economic growth. Vestnik of Astrakhan State Technical University. Ser: Econ 4:7–14 13. Kaplan Robert S, Norton David P (2003) Sbalansirovannaya sistema pokazateley. (Balanced Scorecard). ZAO “Olimp –biznes”, Moscow 14. Podvalny SL (2016) Creation of Indirect control models in Information Computer Systems. Vestnik Voronezhskogogo sudarstvennogo tekhnicheskogo universiteta (Bulletin of Voronezh State Technical University) 12(6):44–51 15. Nikolayev VI, Brooke VM (1985) Systemotekhnika: Metody I Prilozhenia (Systems Engineering: Methods and Applications). Otdelenie, Leningrad, Mashinostroenie, Leningr 16. Nikolayev VI, Temnov VN (1972) On one method for determining objective and subjective value of data in control. Autom Remote Control 33(9):1521–1526 17. Dulesov AS, Khrustalev VI (2012) Entropy Definition as Information Measure by Comparison of Look-ahead and Actual Indicators of the Enterprise. Sovremennye Problemy Nauki I Obrazovaniya (Modern Problems of Science and Education) 1:151 18. Greyz GM, Kuzmenko YuG, Okolnishnikova IYu (2018) Entropy as a Status Indicator of the Industrial Enterprise Logistic System. Bulletin of Udmurt University. Ser Econ Law 28(1):7–14 (In Russian) 19. Kolmogorov AN (1938) Ob Analiticheskikh Metodakh v Teorii Veroyatnostei (On Analytical Methods in Probability Theory). Uspekhi Matematicheskikh Nauk (Successes of Mathematical Sciences) 5:5–41

Ensuring Stability of Wheeled Vehicles When Driving on Slopes I. N. Starunova1 , A. V. Starunov1 , and S. Yu. Popova1,2(B) 1 South Ural State Agrarian University, 48, Sonya Krivaya St., Chelyabinsk 454080, Russia

[email protected] 2 South Ural University of Technology, 9a, Komarovskogo St., Chelyabinsk 454052, Russia

Abstract. Ensuring the stability during performing technological operations by wheeled vehicles is one of the most urgent problems of the day. This is due both to the concern for the safety of wheeled vehicles operators and to the problem of ensuring equipment safety that is becoming more expensive from year to year. In addition, when tipping over, the vehicle takes significant damage, it is out of service for an indefinite period, and consequently this results in crop losses due to the failure to perform work on time. Existing methods for ensuring the stability of wheeled vehicles cannot always be applied for a number of reasons: design features of vehicles, reduced geometric cross-country ability, soil compaction, reduced efficiency, etc. The article considers the issues of longitudinal stability when a wheeled vehicle moves up and down. A mathematical analysis of the conditions under which a vehicle tips over is presented. It was revealed that, when a wheeled vehicle moves on a downhill or uphill, the position vector of the center of gravity is shifted toward tipping due to tire deformation. To ensure the stability of a wheeled vehicle when driving on a slope, an automatic tracking system for adjusting air pressure in tires is proposed; it helps to change the position vector of the center of gravity. The proposed mechanism can significantly reduce the probability of vehicle tipping over and ensure safe working conditions for operators. Keywords: Wheeled vehicle · Stability · Tire deflection · Wheel radius · Tipping over · Slope angle

1 Introduction A large number of agricultural lands in the Russian Federation is located in the areas with a complex land surface. Straightness error during technological operations on slopes and hillsides leads to a decrease in the quality of the technological process, the loss of speed and productivity, an increase in fuel consumption, deterioration of driving conditions and vehicle tipping over. Under such conditions when driving high traction class tractors such as K-701, T-150 K and grain combine the instability leads to their overturning and, as a result, to injury and death of operators due to the very heavy weight of vehicles and insecure cabin supporting structures [1–3]. The vehicles mentioned above, in comparison © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_73

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with other wheeled vehicles, have a highly located center of gravity, which is the cause of tipping over under special conditions of driving [4–8].

2 Theoretical Justification Let us consider the conditions of a wheeled vehicle movement on a horizontal surface and on the ascent (descent). During horizontal rectilinear movement of a wheeled vehicle on a smooth hard road, the translational speed of the front and rear wheels (all things being equal) is the same (Eq. 1), i.e., Vfront = Vrear .

(1)

In this case, the weight of the vehicle is distributed over the axles and the wheels in accordance with its design. For the cars and tractors with a 4 × 2 wheel arrangement, the weight of the car is distributed approximately like this: on the front axle is 1/3G; on the rear is 2/3 G. For the vehicles with a wheel arrangement of 4 × 4 it is distributed in the following way: 1/2 G on the front and rear axles each [9, 10]. We assume that weight redistribution on the wheels does not occur on a smooth horizontal road, crushing (deflection) of the tires corresponds to certain standards depending on the tires design and the pressure in them [9–11]. Under these conditions, the translational speed of any wheels is determined by the expression (Eq. 2): Vwheel =

S , t

(2)

where S is the path traveled by the vehicle, m; t is the time, s. Classically the path traveled by a vehicle is defined as S = 2 · π · r0 · n,

(3)

where n is the number of wheel revolutions; r 0 is the free radius of the wheel, m. We assume that during horizontal movement of the vehicle, the static radius r st of the wheel determines the amount of tire deflection and depends on the tire model and the pressure in it. Then the translational speed of the wheel is determined as follows: Vwheel =

2 · π · rst · n . t

(4)

When the vehicle is moving up or down, the decisive factor in tipping over is the redistribution of loads (weight) between the axles of a wheeled vehicle. When driving uphill, the tires deflection of the wheels of the front axle will be less than that of the rear axle due to its unloading (Fig. 1a). Taking this into account, the static radii of the wheels will be as follows:

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Fig. 1. a Scheme of forces acting on a wheeled vehicle during moving up the slope; b Scheme of forces acting on a wheeled vehicle during moving down the slope.

• rear (more loaded) axle (Eq. 5):

rstr = rst − rst ;

(5)

• front (unloaded) axle (Eq. 6):

f

rst = rst + rst ,

(6)

where ±r st is the value of tire deformation (deflection) during axles loading or unloading in a wheeled vehicle located on a slope, mm. When driving downhill, the radii of the wheels for the front and rear axles are determined from the expression (Fig. 1b): • rear (more unloaded) axle

rstr = rst + rst ;

(7)

• front (loaded) axle:

f

rst = rst − rst .

(8)

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It should be noted that the value ±r st is the function of quantity value for the slope angle α 0 , the tire pressure of the wheels ρ and the wheel load G (r st = f (α, ρ, G)). For the fixed values of the angle α 0 , r st will take the corresponding values: r stα1 , r stα2. … r stαn (with equal wheels radii of the axles in a wheeled vehicle). If the radii of the rear and front wheels are not equal, their static radii will be: during moving up: • rear (more loaded) axle:

up

(9)

rst front = rst front + rst(f ) ;

up

(10)

rstdown rear = rst rear + rst(r) ;

(11)

rstdown front = rst front − rst(f ) ;

(12)

rst rear = rst rear − rst(r) ; • front (unloaded) axle:

during moving down: • rear (unloaded) axle:

• front (more loaded) axle:

The analysis of the conditions (Eqs. 9–12) shows that when the wheeled vehicle moves uphill or downhill, the position vector of the center of gravity is shifted toward the tipping side due to tire deformation (Fig. 1). In view of the foregoing, it can be concluded that adjusting the static radii of the wheels along the axles (ascent, descent) can result in more stable and safe position. It should be noted that the movement of a wheeled vehicle is provided through the interaction of the pneumatic tire with the rolling surface. The quality of this interaction is greatly influenced by such key factors as tire pressure, wheel geometric parameters (radius, running track, percentage of wheel circumference, tread pattern, speed, air pressure in tires, etc.) [3, 12–14]. The equilibrium condition under which a wheeled vehicle can tip over if it is located on a slope (ascent, descent) in a static state (Fig. 1) relative to the tipping over point O1 (O2 ) is determined by the equation [9, 10, 15]. So relative to point O2 : G · cos α · a − G · sin α · hcg = 0,

(13)

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where G is the weight of a wheeled vehicle, kN; α is a slope angle (static), deg.; a is a longitudinal coordinate of the vehicle center of gravity, m; hcg is a vertical coordinate of the vehicle center of gravity, m. Thus a tgα = . (14) hcg Relative to point O1 , the equilibrium condition is determined from the expression: G · cos α · (L − a) − G · sin α · hcg = 0,

(15)

where L is the longitudinal base of the vehicle. Then tgα =

L−a . hcg

(16)

In the case when the reaction Rfront = 0 on the ascent (Fig. 1a), there is a moment when the front wheels are completely unloaded and all weight transfers to the rear wheels. In this case, the position vector of the center of gravity passes through the point O2 . The opposite situation occurs on the descent, when Rrear = 0 (Fig. 1b), the weight of the wheeled vehicle is redistributed to the front axle. In this case, the position vector of the center of gravity passes through point O1 . In the situations mentioned a wheeled vehicle tips over. Existing methods for ensuring longitudinal stability and controllability of wheeled vehicles (hanging loads, increasing the longitudinal base of a tractor, safety devices, etc.) cannot always be applied for a number of reasons: design features of vehicles, reduction in geometric cross-country ability, soil compaction, decrease in efficiency, etc. [2–4, 6, 16–18]. In this regard, the issue related to the need for justification and the development of systems that can automatically ensure the longitudinal stability of wheeled vehicles can be solved by automatically adjusting the air pressure in tires of a wheeled vehicle.

3 Research Results For this purpose, the authors of the article propose a schematic diagram of an automatic system for adjusting air pressure in tires when a wheeled vehicle moves along (up and down) and across a slope (Fig. 2) [1, 19, 20]. The system for adjusting air pressure in tires (Fig. 2) is automatically activated during wheeled vehicle movement without operator assistance. The proposed automatic system for adjusting air pressure in tires includes the following main elements [2, 3]: a pendulum-type clinometer with a movable scale, an electronic control unit (ECU) of automatic system, automatic reducers for adjusting air pressure in tires, high-pressure cylinders.

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Fig. 2. Schematic diagram of mechanism and control connections of automatic system for adjusting air pressure in tires: 1—clinometer; 2—electronic control unit (ECU); 3—automatic gearboxes for pumping (lowering) air pressure in the tires of wheels; 4—high pressure cylinders.

The clinometer is designed to measure the inclination angle of a wheeled vehicle when moving across a slope, up or down a slope and to transmit the information to an electronic control unit (ECU). The automatic system for adjusting air pressure in tires (Fig. 2) operates according to the pointer position of the clinometer connected to the systems for increasing and decreasing air pressure (ECU) by an electronic circuit. The increase and decrease in air pressure in tires (to the required values) will occur not instantly but over relatively short periods of time. This is due, to some extent, to the constancy of loading (unloading) the wheels, the value of slope angle, the inertia force when turning the vehicle, the path length, the air resistance in the channels of the system, the vehicle speed, the air (gas) pressure in a high-pressure cylinder of the system [1, 17, 19].

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4 Conclusion The proposed system helps to automatically control the center of gravity in a wheeled vehicle when moving on the sloped surfaces. This, in turn, ensures the secure work of operators when carrying out transport and technological processes.

References 1. Boykov VP, Belkovskiy VN (1988) Shiny dlya traktorov i sel’skohozyajstvennyh mashin (Tires for tractors and agricultural machines). Agropromizdat, Moscow 2. Gorshkov YuG, Starunova IN, Kalugin AA (2014) Avtomaticheskoe regulirovanie davleniya vozduha v shinah – faktor bezopasnogo dvizheniya kolesnyh mashin na sklonah (Automatic regulation of air pressure in tires is a factor of safe movement of wheeled vehicles on slopes). Tekhnika v sel’skom hozyajstve (Technique in Agriculture) 1:13–15 3. Gorshkov YuG, Starunova IN, Kalugin AA, Bobrov SV (2014) Avtomatizaciya processa ustojchivosti kolesnoj mashiny pri dvizhenii po poperechnomu i prodol’nomu sklonam (Automation of wheeled vehicle stability process when moving along transverse and longitudinal slopes). Nauchnoe obozrenie (Scientific Review) 12:59–65 4. Zhileikin MM, Yagubova EV (2014) Obosnovanie principov povysheniya ustojchivosti i upravlyaemosti kolesnyh traktorov pri dvizhenii na sklone v rezhime vspashki (Justification of the principles for increasing the stability and controllability of wheeled tractors when driving on a slope in the plowing mode). Izvestiya vysshih uchebnyh zavedenij. Mashinostroenie (News of Higher Educational Institutions. Mechanical engineering) 9(654):67–76 5. Kushlyaev VF, Yablokova AV (2014) K voprosu ocenki prodol’noj i poperechnoj ustojchivosti special’nyh mashin povyshennoj prohodimosti (The issue of evaluating the longitudinal and transverse stability of special off-road vehicles). Nauchnye i obrazovatel’nye problemy grazhdanskoj zashchity (Scientific and Educational Problems of Civil Protection) 4:103–108 6. Mamiti GI, Pliev SH, Tedeev VB (2014) Ustojchivost’ avtomobilya i nizkoklirensnogo kolesnogo traktora (The stability of a car and a low-clearance wheeled tractor). Traktory i sel’hozmashiny (Tractors and Agricultural Machinery) 12:20–23 7. Mamiti GI, Pliev SH (2009) Formirovanie optimal’noj ustojchivosti kolesnoj mashiny na stadii proektirovaniya (The formation of optimal stability of a wheeled machine at the design stage). Vestnik mashinostroeniya (Mechanical Engineering Bulletin) 2:84–85 8. Mihailovskiy EV, Tsimbalin VB (1960) Teoriya traktora i avtomobilya (Tractor and car theory). Sel’hozgiz, Moscow 9. Mushkudiani MI (2002) Snizhenie travmatizma operatorov mobil’nyh sel’skohozyajstvennyh agregatov za schet protivooprokidyvayushchih ustrojstv (primenitel’no k usloviyam gornogo zemledeliya) (Reducing injuries of mobile agricultural aggregate operators due to anti-tipping devices (in relation to mining conditions). Dissertation, Saint Petersburg-Pushkin 10. Korchan NS, Podrigalo MA, Polyanskiy AS et al (2010) Osobennosti issledovaniya poperechnoj ustojchivosti kolesnyh mashin s sharnirno-sochlenennoj ramoj pri oprokidyvanii (The features of studying the transverse stability of wheeled vehicles with articulated frame during tipping). Teoriya ta praktika sudovo|ekspertizi i kriminalistiki (Theory and Practice Of Shipboard Expertise and Criminalistics) 10:449–455 11. Starunova IN, Gorshkov YuG, Kalugin AA, Larionova GA, Bobrov SV, Baryshnikov SA (2015) Automatic system for adjusting air pressure in pneumatic tires of wheeled vehicles. The Russian Federation, No. 2589764. South Ural State Agrarian University. 6 October 2016

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12. Pliev SH (2012) Razrabotka nauchno obosnovannyh rekomendacij po obespecheniyu ustojchivosti kolesnyh traktorov (Development of scientifically justified recommendations for ensuring the stability of wheeled tractors). Izvestiya Gorskogo gosudarstvennogo agrarnogo universiteta (Bulletin of Gorskiy State Agrarian University) 49(3):262–275 13. Rejmer VV (2012) Obosnovanie metodiki povysheniya effektivnosti ekspluatacii kolesnyh traktorov klassa 1,4 pri rabote na naklonnoj opornoj poverhnosti (Justification of the methodology for increasing the efficiency of wheeled tractors operation for class 1.4 when working on sloping supporting surface) Dissertation, Orenburg 14. Starunova IN (2014) Kratkij obzor sposobov povysheniya poperechnoj ustojchivosti kolesnyh mashin (A brief overview of the ways to increase the lateral stability of wheeled vehicles). Sbornik nauch. trudov. Tekhnicheskie nauki (Collection of scientific papers. Technical science). Chernomor’e, Odessa 6:72–75 15. Starunova IN (2015) Teoreticheskoe obosnovanie i issledovanie momenta ustojchivosti kolesnyh mashin pri dvizhenii po sklonu (Theoretical substantiation and the study of stability moment of wheeled vehicles when driving on a slope). Izvestiya Orenburgskogo gosudarstvennogo agrarnogo universiteta (Bulletin of Orenburg State Agrarian University) 3(53):95–98 16. Chudakov DA (1972) Osnovy teorii i rascheta traktora i avtomobilya (Fundamentals of the theory and calculation of a tractor and an automobile). Kolos, Moscow 17. Ahmadi I (2013) Development of a tractor dynamic stability index calculator utilizing some tractor specifications. In: Turkish Journal of Agriculture and Forestry. http://journals.tubitak. gov.tr/agriculture/issues/tar-13-37-2/tar-37-2-10-1103-19.pdf. Accessed 21 Sept 2019 18. Pape D, Arant M, Hall D et al Heavy Truck Rollover Characterization (Phase-A). In: Final Report. https://www.academia.edu/33149170/U02_Heavy_Truck_Rollover_Character ization_Phase-A_Final_Report. Accessed 29 Sept 2019 19. Gorshkov YuG, Starunova IN et al (2019) Investigation of the slope angle influence on the loading imbalance of the wheeled vehicle sides and the change in the center of gravity vector direction. Journal of Physics 20. Winkler CB (2000) Rollover of Heavy Commercial Vehicles. http://www.umtri.umich.edu/ content/rr31_4.pdf. Accessed 10 Oct 2019

Conceptual Design Methodics of Hybrid Car Traction Drive A. Ch. Khatagov1(B) , S. B. Adzhimanbetov2 , and Z. A. Khatagov1 1 The North Caucasian Institute of Mining and Metallurgy (State Technological University), 44,

Nikolaev Street, Vladikavkaz 362021, Russia [email protected] 2 Gorsky State Agrarian University, 37, Kirov Street, Vladikavkaz 362040, Russia

Abstract. The article describes a parametric method of controlling the speed (due to a wide-range stepless change in the gear ratio of the transmission) and substantiates the choice of electric motor and internal combustion engine of hybrid cars. Based on this approach, a typical functional diagram of the drive structure and a two-stage technique for its automated conceptual design using common tools for computing (MS Excel) and modeling (MatLab/Simulink) are proposed. The paper shows an example application of this approach to determine the energy and kinematic parameters of a hybrid car drive on “Granta” chassis (stage 1 of the methodology) and the calculation of operational indicators and characteristics of the concept on the drive simulation model (stage 2 of the methodology) in four characteristic modes. Among them: acceleration-braking—to assess the dynamics of the machine; driving “on the highway” with various constant speeds—to develop recommendations for optimal driving; runs in the “urban” driving cycle, taking into account “traffic jams”—to assess fuel consumption and energy of the traction battery in the main mode of machine operation; the system operation in the “parking” self-charging mode of the traction battery—to assess the autonomy of the developed hybrid car. The developed computer tools of the proposed methodology allow one to make informed decisions even at the stage of conceptual design of hybrid cars very quickly. Keywords: Hybrid car · Traction drive · Parametric transmission · Concept designing · Simulation

1 Introduction The world-leading companies produce hybrid cars in series but the issues of the reasonable choice of drive motor capacities (and their ratios) have not been solved yet. The question of choosing the type of transmission remains open. This situation has developed due to the excessive variety of structural schemes of traction drives in the well-known developments [1–9]. Let’s consider these issues and try to justify their solution.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_74

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Transmission. In almost all modern vehicles, the longitudinal speed is controlled at a constant (or piecewise constant) gear ratio of the transmission by changing the engine speed. The alternative option: at a constant speed of the output shaft of the propulsion system, controlling the speed by changing the gear ratio of the transmission (parametric control) is not used, although it has obvious advantages. Let’s demonstrate this option. In the diagrams Fig. 1 on the abscissa axis we point the time in the relative units (p.u.) from the acceleration time; on the left axis of the ordinates (in p.u.)—the speed 1 of machine, the resistance to movement 2 on wheels and the moment of the propulsion system 3 with parametric control of the speed of movement; along the right axis of the ordinates is the gear ratio of the transmission inversely proportional to the speed of movement.

Fig. 1. a Acceleration; b vehicle braking. 1—longitudal machine speed; 2—resistance force to its movement; 3—torque required from the engine for parametric speed control; 4—transmission ratio.

Let the vehicle acceleration and deceleration take place that its speed increases (Fig. 1a) or decreases (Fig. 1b) linearly. In this case, the resistance to movement is the sum of the constant friction force of 0.33 p.u., the aerodynamic drag force is equal to 0.66 squares of the relative speed (since at the steady-state basic speed the aerodynamic component is approximately twice the friction force and their sum is 1 p.u.) and constant in magnitude but changing in sign with linear acceleration-braking of the inertia force (we assume it is equal to ±2.8 p.u.). If the gear ratio of the transmission is unchanged, then the propulsion system on its output shaft should provide a linear increase (decrease) in speed and overcome the torque directly proportional to the force 2 of the resistance to movement on wheels. In the case of parametric control, the constant speed of the output shaft of the propulsion system is divided and the moment is multiplied by the current gear ratio of the transmission, inversely proportional to the speed of movement. This time is much smaller than in a traditional drive, moment 3 fights off the same resistance force 2 on the wheels (the difference is tinted in gray). As a result:

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• During acceleration and driving at any reduced speeds (Fig. 1a)—fuel economy and, accordingly, reduction of toxic emissions from internal combustion engines (ICE), reduction of drive energy consumption and increase in range for hybrids and electric vehicles [10] are fixed. • The diagram Fig. 1b clearly shows that the required moment of braking 3 is significantly less than on curve 2. The load on the elements of the brake system is approximately halved, and if they are moved from the wheel disks to the output shaft of the propulsion system (transmission brake) it is almost an order of magnitude (with considering recovery). • On the other hand, this seems to indicate a decrease in recovery during braking. But the area of the tinted curved triangle in Fig. 1a is about 25-30% more than in Fig. 1b: winnings on over clocking cover this loss. For the electric-battery hybrids and electric vehicles the disposal of excessively powerful charging currents of the battery (Fig. 1b, curve 2) is possible only due to the buildup of the additional equipment and represents a separate difficult technical problem, which is solved with much less effort when working on curve 3. • Transmission efficiency significantly affects the energy and fuel savings with transmission ratios less than 1.2 (i.e., at high speeds). The efficiency of the known variators just on these gear ratios is close to maximum. In addition, the highest speed of movement is almost always limited by the control electronics to a level lower than what is technically achievable for the machine and therefore the drive energy (due to the support of several times smaller required moments) is consumed more slowly than in the traditional scheme even with the ideal transmission. Let us estimate approximately the value of the required control range from the following considerations. Driving away from the place of the modern cars is carried out as follows: the engine is turned on in the parking or neutral control joystick, after it is heated, the brake pedal is depressed, then the joystick is put in the drive position, the brake is released and the accelerator pedal sets the acceleration rate. If you do not touch the accelerator, then the car with an almost imperceptible jerk begins to “creep” at a speed of about 5 km/h. Assuming that the gear ratio of a parametrically controlled transmission at the maximum speed of ordinary passenger cars (140–180 km/h) is 1, at the “creeping” speed we get the gear ratio (140 ÷ 180)/5 = 28 ÷ 36. This is the main problem of such a transmission as the variators used in the automotive industry [11–14] provide a maximum range of up to 13. Drive structure. If the economic criterion of the cost of ownership is taken as an indicator of the effectiveness of a hybrid vehicle then for the given technical (mass and dimensions, acceleration dynamics, maximum speed) and service requirements (degree of autonomy, various usability) it is necessary to minimize the cost of drive elements and operating costs for energy, fuel and maintenance. This is achieved not only by selecting the minimum power (and therefore cost) of drive elements but also by the ideology of the system. Considering that at present the cost of 1 kWh of energy consumed on the shaft of the electric motor is about 3 times lower than on the shaft of the gasoline ICE and the efficiency of the electric motor is almost 3 times higher, it is obvious that the movement

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should be carried out mainly on the electric traction. ICE should be connected in two cases: • When for a given pace or current driving conditions, the power of one electric motor is insufficient or its unacceptable heating is possible. • When the traction battery is below a critical level. To increase the machine autonomy, it is rational not only to use the braking energy (recuperation) but also to tie the excess intensity of the internal combustion engine (throttle position) due to the traction battery charge lack. It is also reasonable to provide two options for stationary battery recharging: from an external network and from its own internal combustion engine (“self-charging during parking”). Consequence: each hybrid car engine must be connected to the transmission through its clutch. The choice of the electric motor type is determined not only by its power but also by the overload capacity k m by torque, i.e., a DC motor with k m = 5 ÷ 7 in the case of parametric control of the speed of movement can do the same job but it can be easier and more compact than an AC motor with a higher rated power with k m = 2.5 ÷ 3.

2 Scheme of the Proposed Drive Based on the foregoing, a typical structural and functional diagram of the hybrid drive should be as follows: The dashed lines show the sensors signals: joystick position ➀, accelerator pedals ➁, brake pedals ➂; variator output speed sensor ➃; battery voltage sensor ➄. Thin arrows show the signals controlling: I - the injection system controller and clutch 8; II—power converter; III—gear ratio of the variator; IV —brake 14. Joystick 3 modes of operation of the drive—four-position with the provisions: “neutral”, “forward”, “back”, “parking” and “self-charging”. Controller 7 contains a throttle position controller (output I), a signal driver of the desired speed (output II) and a gear ratio regulator of the variator (output III). Two-position clutch 8 and 13 are switched by built-in pulse amplifiers; in statics they don’t consume energy. The traction motor 10 may be AC or DC; what kind of converter it depends on what type of converter 11 is: either an unregulated (or partially regulated) inverter or a set of semiconductor proximity keys with control logic. The variator 15 should have the largest possible range of a smooth change in the gear ratio, but if blocks are added to the converter 11 to form the start of acceleration and the end of braking of the machine, the range can be narrowed to 12 ÷ 13.

3 Justification of the Conceptual Design Methodology The proposed standard scheme (Fig. 2) allows one to streamline the selection of its elements and automate the conceptual design of hydraulic structures based on a two-stage model-oriented approach using modern computer mathematics. At the first stage (pre-design calculation), a preliminary determination of the energy elements power of the drive (ICE, electric motor, battery) and the gear ratios of the

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Fig. 2. Hybrid car with parametric transmission. 1—fuel tank; 2—the controller of the engine injection system; 3—joystick of vehicle operating modes; 4—accelerator pedal; 5—a brake pedal; 6—ICE; 7—controller; 8 and 13—clutch with pulse switching; 9—matching gear (optional); 10—electric motor; 11—power converter (or switch) with a built-in control unit; 12—battery; 14—transmission brake; 15—variator with a wide range of variation of the gear ratio; 16—main gear.

main transmission elements is carried out. At the second stage (simulation modeling, verification calculation), the results of the first stage are checked and, if necessary, specified, and the design operational characteristics of the machine are determined in the typical test modes. In the calculations of the first stage, the following should be taken into account: (a) the resistance moment on the wheels to horizontal movement is calculated as the sum of the components of the rolling resistance, aerodynamic drag and inertia. Wind pressure and the route slope are not considered, since they will be countered by the automation (by connecting the internal combustion engine and adjusting the position of its throttle when an additional load occurs). Their influence can be specified at the second—“model”,—design stage; (b) for a reasonable choice of the catalog rated power of the hybrid vehicle engines, a solution of at least two equations is required that reflects the balance of the energy of the driving forces and the forces of resistance to movement in the most important modes for each engine. There are two such modes: • Long steady-state movement at the vehicle’s maximum (technically achievable) speed: maximum torque is required from the internal combustion engine, and the electric motor, in order not to overheat, should work in the nominal mode.

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• The end of a short (linear) acceleration to a given speed (for example, 100 km/h) when all its overload capacity is required from the electric motor and the internal combustion engine operates at that point of its external characteristic which is determined by the current speed of its crankshaft. (c) in the preliminary assessment of the battery capacity, we have in mind the following: • To maintain the battery life cycle, the state of charge in it must be maintained in the range from SOC = 80% to SOC = 30%, i.e., the nominal value of its capacity must be doubled relative to the energy consumed per day in the main (city) mode of the machine operation. • At the stage of pre-project calculation, a simplified formula for calculating the battery capacity is used [15, 16], with the subsequent refinement at the second (“model”) design stage.

4 Calculation Example According to the Proposed Methodology The first stage of design is implemented in the MS Excel spreadsheet (Fig. 3) and for clarity it is accompanied with graphs of the process coordinates.

Fig. 3. Excel form for preliminary calculation of the drive.

For the convenient use and errors elimination, the sheet of the Excel form is protected from changing the cells contents with formulas: only input cells of set values highlighted with a double border are available. In the tabulated calculation data, two lines are highlighted in gray: the middle one corresponds to the end of the vehicle acceleration by 100 km/h, the lower one to the steady-state movement at maximum speed. The result of the “sketch” calculation is displayed in the range of cells located in the red rectangle at the bottom left of the form sheet. These results are the initial ones for the subsequent “model” stage of drive designing. In the example form on Fig. 3, parameters

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of the dynamics and running platform of the car, which are close to the best-sold Russian “Granta” car are laid down. In accordance with the calculated design powers, we select from the catalogs: ICE from a VAZ-1111 car with a capacity of 21.5 kW (29.3 hp) and a general industrial independent direct current electric motor 2PN160M with nominal data of 18 kW, 220 V, 3150 rpm, as well as a traction lithium-ion battery with a capacity of 28 kWh. By weight and dimensions, such a hybrid propulsion system (with the exception of the battery) may well be inscribed in the Granta’s engine compartment instead of the standard engine and gearbox. At the second stage of designing, a detailed computer model (Fig. 4) of the proposed scheme of the traction drive of the hybrid car in the Simulink/Matlab package [17, 18] is used and its behavior in four characteristic modes of movement of the machine is analyzed.

Fig. 4. Simulink Hybrid Vehicle Drive Model.

Mode 1: acceleration from standstill to normalized speed (for example, 100 km/h), then additional acceleration to maximum speed, braking to normalized speed and complete stop due to recovery (with the accelerator pedal released)—to assess the dynamic characteristics of the machine. Mode 2: mileage on a highway with various constant speeds and initial battery charges—for evaluating performance with uniform movement. Mode 3: mileage in the ARDC urban driving cycle [19, 20] —to assess performance in conditions of maximum traffic intensity (taking into account traffic jams). Mode 4: checking the self-loading system of the traction battery, when the electric motor works as a generator rotated with the engine, clutch 8 (Fig. 2) is turned on, clutch 13 is turned off. The final results of the “model” design phase are as follows. Mode 1: acceleration to a speed of 100 km/h is linear, for 12 s, as specified in the Excel form; at the same time, the peak moment of the electric motor is 360 Nm, the maximum instantaneous overload coefficient is 6.6 (even less than the k m = 7 specified in the form).

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Mode 2: simulation shows: if you move on the highway at a speed of 80–100 km/h, then the range of the car is limited only by the capacity of its fuel tank, and the operating flow rate is 3.2 ÷ 5.1 l/100 km, depending on the charge traction battery state. Longterm movement at a constant speed of 110 ÷ 140 km/h is possible, but it is advisable to periodically alternate it with movement at a speed of “fast” travel recharging of 80 km/h (to exclude a decrease in battery charge below 30%). Mode 3: (1) in the first 4 cycles of the urban mode, 91.5 km were covered (80% battery charge at the beginning of the first cycle and 43.77% at the end of the fourth), in terms of: 1.78 l/100 km gasoline consumption, energy consumption batteries 9.96 kWh/100 km; (2) starting from the 5th cycle, they are identical, the battery charge (due to the operation of the 2nd throttle position control loop) is set at a constant level of 40.5%, that is, with this state of the battery, you can drive in the urban mode for as long as you like, but gas consumption increases to 4.3 l/100 km. In other words, if you want an economical ride—after every 90 km in the city, recharge the battery to 80%. Recharging can be carried out both from an external source of electric energy (cheaply), and from an internal combustion engine in the mode of parking self-charging (somewhat more expensive). Mode 4: Modeling for a battery discharged to 30% shows that a charge of up to 80% is achieved in exactly 1 h of internal combustion engine operation, with gasoline consumption of 3.82 l and 13.98 kWh of energy pumped into the battery.

5 Conclusion 1. A parametric method for controlling the hybrid vehicle speed through a mechanical channel (without controlling the engine speed) is proposed and justified. 2. A typical scheme of a hybrid car is developed based on the proposed parametric method of controlling the speed of movement by a direct change in the gear ratio of the transmission. 3. The calculation of the main parameters of the power unit in the proposed typical scheme of a hybrid car is analytically justified by jointly solving a system of two equations reflecting the balance of driving forces and resistance forces in two modes: the first one is the end of normalized acceleration (full use of the overload capacity of an electric motor with support from ICE); the second one is the steady motion of the machine at maximum speed (the electric motor operates at rated load, the internal combustion engine—at maximum torque). 4. A methodology for two-stage conceptual design of hybrid vehicles based on the preproject calculation of parameters using Excel forms with the subsequent verification of operational characteristics on a computer model has been developed.

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References 1. Gordeev SN (2009) Toyota Prius - going ahead! https://autodata.ru/article/all/prius_idushc hiy_vperedi/?sphrase_id=1517. Accessed 3 Sept 2019 2. Doe J (2019) How does a hybrid transmission? Why is everything wrong with the Toyota Prius ZVW50?: UNLOCK. autoblog. https://zen.yandex.ru/media/unlock_autoblog/kakustroena-gibridnaia-transmissiia-pochemu-v-toyota-prius-zvw-50-vse-ne-tak-5c87df4dc650 eb00b32815a4. Accessed 3 Sept 2019 3. Doe J (2017) Honda clarity plug-in hybrid review. https://plugincars.com/honda-clarity-plughybrid. Accessed 3 Sept 2019 4. Doe J (2019) Rating of the best hybrid cars. Top 10 hybrid cars 2018–2019. https://automo nth.ru/rejting-gibridnyh-avtomobilej/. Accessed 10 Now 2019 5. Doe J (2011) Hybrid transmission. Za rulem.RF http://wiki.zr.ru/%D0%93%D0%B8% D0%B1%D1%80%D0%B8%D0%B4%D0%BD%D0%B0%D1%8F_%D1%82%D1%80% D0%B0%D0%BD%D1%81%D0%BC%D0%B8%D1%81%D1%81%D0%B8%D1%8F. Accessed 3 Sept 2019 6. Vyacheslav_911 (2013) Kinematics of hybrid transmissions. https://engineering-ru.livejo urnal.com/98020.html. Accessed 10 Nov 2019 7. Doe J (2019) Presented hybrid crossovers Mercedes-Benz GLC and GLE. Accessed 23 Sept 2019. https://www.kolesa.ru/news/pervyy-seriynyy-gibrid-lamborghini-voplotil-idei-emobilya 8. Yezhov A (2019) The first production hybrid Lamborghini embodied the ideas of the E-mobile. https://www.kolesa.ru/news/pervyy-seriynyy-gibrid-lamborghini-voplotil-idei-emobilya. Accessed 23 Sept 2019 9. Ulzibat B (2011) We are testing new products from Honda on the track Twin Ring Motegi. https://www.drive.ru/test-drive/honda/4efb32db00f11713001e281f.html. Accessed 3 Sept 2019 10. Khatagov ACh, Adzhimanbetov SB, Khatagov ZA (2019) Two concepts of urban electric vehicle drive (conference paper). Int Russian Autom Conf, RusAutoCon 2019:8867798 11. Gulia N, Yurkov S New multi-disc variator with “soft” performance. In: N-T.ru, electronic library “Science and technology”. http://n-t.ru/tp/ts/mv.htm. Accessed 15 Dec 2019 12. Doe J (2014) The device of the variator. http://autoleek.ru/korobka-peredach/variator/ustroj stvo-variatora.html. Accessed 9 Sept 2019 13. Doe J (2019) CVT for small FWD vehicles. https://www.jatco.co.jp/products/cvt7.html. Accessed 10 Now 2019 14. Pronin BA, Revkov GA (1980) Besstupenchatye klinoremennye i frikzionnye peredachi (variatory) (Stepless V-belt and friction gears (variators)). Mechanical Engineering, Moscow 15. Doe J (2016) Electric car with your own hands. https://goldenmotor.ru/electromobil-svoimirukami/. Accessed 13 Now 2019 16. Raskin V, Samokhin S (2011) Dayosh “YO-mobilizaciyu” (Give “E-mobilization”) N Engl J Car Serv 1:18–20 17. MatLab Documentation Center>SimDriveline>Engines>Simscape Blocks>Generic Engine 18. Chernykh IV (2008) Modeling of electrical devices in MATLAB. DMK Press, Moscow, SimPowerSystems and Simulink 19. Vetrov J (2012) We represent ARDC - a drive cycle of the Autorevue for a fuel efficiency estimate. https://autoreview.ru/articles/proverka-na-dorogah/nauka-i-zhizn-1. Accessed 23 Sept 2019 20. Vetrov J (2014) The WLTC measuring driving cycle has been approved for all continents: what does it mean? https://autoreview.ru/articles/kak-eto-rabotaet/vsemirnyy-cikl-1. Accessed 23 Sept 2019

Results of Computer Simulation of a Braking Vehicle Energy Recovery System V. I. Posmetev, V. O. Nikonov(B) , and V. V. Posmetev Voronezh State University of Forestry and Technologies Named After G. F. Morozov, 8, Timiryazeva Street, Voronezh 394087, Russia [email protected]

Abstract. The relevance of increasing the efficiency of the operation of a timber truck by using the hydraulic drive of a wheel hydromotor for accumulating hydraulic energy during braking in a pneumohydraulic accumulator and its further use for accelerating a timber truck and loading unloading assortments is substantiated. A mathematical model of the braking energy recovery system of a timber truck is presented, supplemented by a model of an uneven supporting surface, in which the accumulation and release of hydraulic energy of the working fluid are calculated. A computer program has been developed to study the performance indicators of the energy recovery system during braking of a forest car with energy storage in wheel motors. A series of computer experiments on the movement of a forest car on a given surface was carried out in order to study the influence of the volume of a pneumohydraulic accumulator, the efficiency of the recovery system in charging and discharging modes, the average length of obstacles on average values of charging time, discharge of a pneumohydraulic accumulator, and also on fuel economy. The time dependences of the accumulated hydraulic energy in the pneumohydraulic accumulator are obtained for various values of its volumes and the efficiency of the recovery system. Keywords: Forest car · Recovery · Braking energy · Pneumohydraulic accumulator · Efficiency · Fuel efficiency

1 Introduction The operation of timber trucks is fraught with many problems, the most important of which are the depletion of natural resources and environmental degradation. Given the fact that in the Russian Federation the majority of timber trucks currently have low environmental performance, it can be concluded that studies aimed at reducing harmful substances from exhaust gases are relevant. In the process of moving a forest car during the removal of forest materials in off-road conditions, it almost constantly has to accelerate and slow down. This leads to the fact that the kinetic energy of a massive forest car, when it is braked, transforms into potential and dissipates unproductively in the form of heat into the environment. For the purpose of the beneficial use of this energy, © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_75

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and, therefore, to increase the ecological performance of the forest car by reducing fuel consumption and reducing the total amount of harmful emissions into the environment, various systems of braking energy recovery are used, the development and research of which are carried out in all over the world for many years [1]. The work of Ricardo Chicurel [2] provides a regenerative braking system of a city bus, which includes a hydraulic pump-motor with the possibility of switching on using a pneumohydraulic accumulator. Studies show that the proposed regenerative system will allow to accumulate during braking and it is useful to use up to 45% of the hydraulic energy of the working fluid. The article by Wei Yu and Rouchen Wang [3] describes the technologies used for regenerative braking of automobiles. A braking energy recovery model has been developed that takes into account the different driving conditions of the car. It was revealed that the accumulation potential during energy braking significantly depends on the frequency and braking force. A study by Boyi Xiao and Huazhong Lu [4] provides three new strategies for controlling regenerative braking in an electric vehicle, based on fuzzy logic with multiple inputs, taking into account the effects of engine power, braking force and battery charge. The results showed that new strategies will allow 12, 21.1, and 22.7% of the braking energy of an electric vehicle to be returned back to the system, respectively. In their work, Di Zhao and Liang Chu [5] present an electric vehicle regenerative braking system with a joint hydraulic braking system. The results of simulation showed the high efficiency of the proposed regenerative system. An article by Ryszard Dinford and Piotr Wos [6] provides an overview of methods for recovering and storing braking energy in hybrid vehicles. It has been revealed that at present, the hydrostatic systems used in serial hybrid drives of machines, especially in electro-hydraulic control systems for reversible drives, have been little studied. L. Pugi and M. Pagliali [7] propose an innovative technical solution based on the introduction of a system designed to restore the braking energy of a truck and use this energy for the operation of an onboard hydraulic drive system. Simulation results show that the proposed system is capable of producing more energy than is required by a hydroelectric station. Er. Amitesh Kumar [8] in his research proposes a new configuration of a parallel hydraulic recuperative hydraulic drive of a vehicle to increase the recovery potential of braking energy and engine efficiency. The results of simulation show that the proposed hydraulic drive effectively improve vehicle fuel economy. Wei Wu and Hui Liu [9] offer a hydraulic hybrid vehicle drive with braking energy recovery. The results of a study of the dynamic characteristics of the system in regenerative braking mode show that the pressure in the pneumatic-hydraulic accumulator positively correlates with the controlled angle of the hydraulic transformer. The analysis of existing works revealed that currently recuperative hydraulic drives of timber trucks with hydraulic braking energy recovery systems have not yet been developed, there are also no mathematical models and computer programs describing the operation of these systems. The aim of the study is to develop a mathematical model of the functioning of the system for recovering hydraulic energy of braking of a timber truck, as well as a computer program that allows you to study the influence of the main road parameters and parameters of the proposed system on its performance indicators when a timber truck moves along insufficiently equipped timber roads.

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2 Materials and Methods As a result of the studies carried out by the authors of the recovery of hydraulic and pneumatic energy in the recuperative hydraulic drives of a timber truck, containing the recuperative mechanisms of the boom, stick, slewing ring, suspension, traction coupling and fifth wheel coupling, a promising diagram of a regenerative braking system for a timber truck was proposed (Fig. 1) [10–14].

Fig. 1. Diagram of a recuperative system of braking energy of a forest car (authors’ own development [15]): 1—recuperative mechanism of wheels, 2–4—control valves, 5—pump-accumulator unit, 6, 7—hydraulic cylinders of the handle and boom of the manipulator, 8—rotary support device.

To study the effectiveness of its work, the authors developed a mathematical model and, on its basis, a computer program. Modeling is based on the methods of classical mechanics [16–19]. In the developed mathematical model, the forest car moves along the X axis. The current position of the forest car is determined by the x coordinate, and the instantaneous horizontal speed of the forest car is v. In order to be able to create an uneven supporting surface in a one-dimensional model, the speed of the logging truck, gravity, and coordinates are adjusted depending on the angle of inclination of the supporting surface α(x) at the considered point x. Taking into account Newton’s second law, the equation of motion of a logging car is written as follows: m

d 2x = Fforc − Fres.mov − mg sin α(x), dt 2

(1)

where m—weight of a timber truck; t—time; F forc —traction force; F res.mov —resistance to movement; g—acceleration of gravity; mgsinα(x)—the projection of gravity at the considered point x, on the tangent line to the supporting surface, placed relative to the horizontal direction at an angle α(x). The drag force of the undercarriage of a timber truck is determined by the following formula: Frec.mov = a + b

Ffors + cv2 , mfors g

(2)

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where a, b, and c—coefficients taken on the basis of experimental data on the operation of timber trucks. To solve the equation of motion of a forest car, which is a second-order differential equation, we use the second-order Runge-Kutta numerical method, which has a high model adequacy and solution accuracy, which is implemented step by step with the following formulas: xτ +1 = xτ + vτ · t +

aτ · (t)2 ; 2

vτ +1 = vτ + aτ · t,

(3) (4)

where τ —integration step over time; Δt—integration step value; aτ , x τ , and vτ — acceleration, coordinate, and speed of the forest car at the current integration step τ. In the developed mathematical model, the calculation of charging and discharging hydraulic energy of a pneumohydraulic accumulator is performed. Due to the difficulty of reproducing the braking energy when modeling a regenerative system, mathematical modeling is performed at the level of work and energy, without reference to a specific regenerative system. The accumulation of hydraulic energy during the charging of the pneumohydraulic accumulator is determined conditionally, in the absolute value of the accumulated hydraulic energy E PGA . The determination of the position of the piston x p of the pneumohydraulic accumulator is carried out according to the following formula:     EPGA xp = νRT ln xmax − ln xp , (5) where ν—amount of substance in the gas cavity of the pneumohydraulic accumulator; R—gas constant; T —absolute gas temperature; x max —the initial position of the piston in the discharged pneumohydraulic accumulator. The description of the equation in the finite differences of the processes of charging and discharging the pneumohydraulic accumulator will take the following form:  ⎧ ηch.dv. , ΣF ≥ 0; ⎪ V hyd .mot. τ ⎪ ⎪ EPGA + ΣF · k · t · 2π 1 ⎪ Rwh. · ⎪ ⎪ ηdich.dv. , ΣF < 0; ⎪ τ ⎨ τ +1 EPGA = EPGAm ; = E EPGA (6) PGAm , ΣF > 0; ⎪ ⎪ ⎪ ⎪ τ ⎪ ⎪ = 0; EPGA ⎪ ⎩ 0, ΣF < 0, +1 —hydraulic energy accumulated in the pneumohydraulic accuwhere E τPGA and E τPGA mulator at the current τ and the next τ + 1 integration steps; F = F rec.mov. + mg sin α—sum of forces counteracting traction; k—proportionality coefficient; Δt—integration step over time; V hyd.mot. —total displacement of hydraulic motors for the wheels of a forest truck; Rwh —wheel radius; ηch.dv , and ηdich.dv —the efficiency of the braking energy recovery system in the charging and discharging modes of a pneumohydraulic accumulator; E PGAm —maximum volume of pneumohydraulic accumulator.

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In this mathematical model, the position of the forest car is given by one x coordinate. To describe the irregularities of the supporting surface, it is not necessary to introduce an additional coordinate y, it is more rational to take into account two corrections when describing the movement of a timber truck in a vertical plane. The first correction introduced to the inclination of the supporting surface makes it possible to calculate the projection of gravity Gτ on the current direction of movement of the forest truck. This direction is tangent to the relief function of the supporting surface y(x) at the current location of the logging truck. Therefore, the force Gτ is added to the sum of the forces affecting the timber truck in the x direction: Gτ = m · g · sin α(x),

(7)

where m—weight of a timber truck; g—acceleration of gravity; α—angle of inclination of the surface at a given point x. The second correction is used to adjust the speed and acceleration from the tangent direction τ to the horizontal x. Correction is based on projection with the coefficient cos α(x): vx = vm cos α(x); ax = am cos α(x),

(8)

where vx and ax —the speed of the logging vehicle and its horizontal acceleration x; vτ and aτ —the speed of the forest car and its acceleration in the instantaneous direction of travel τ, inclined at an angle α at a given point x. Knowing the relief function of the supporting surface y(x), the angle of inclination α of the supporting surface at point x is found by the formula: α(x) = arctg

dy(x) . dx

(9)

The analytical representation of real supporting surfaces is described by the following formula:  Nb

(x − xi )2 y(x) = Hi exp − , (10) 2σi2 i=1 where N b —the total number of gaussian shape irregularities in the control section of a given length L c ; H i —the value of the height of the i-th roughness; x i —the coordinate of the center of the i-th roughness; σ i —length of i-th roughness. Distribution functions of random geometric parameters of irregularities and their linear density λ = N b /L c are set for the investigated support surfaces based on statistical data. The main indicators of the effectiveness of the braking energy recovery system, including the average charging time t ch.av and discharge t dich.av of a pneumohydraulic accumulator, and the fuel economy coefficient k f.eff of a timber truck are determined as follows: tch.av =

1

N

ch.av

Nch.av

i=1

 tiEPGA =EPGAm − tiEPGA =0 ;

(11)

Results of Computer Simulation

tdich.av =

1

N

dich.av

Ndich.av

i=1

kf .eff

 tiEPGA =0 − tiEPGA =EPGAm ;

⎧  τ F < 0; ⎪ ⎪ τM ⎨ 1, E τ  > 0;  PGAτ ⎪ > 0; F τ =1 ⎪ ⎩ 0, τ < 0; EPGA = τ  τ , M  1, F < 0 τ τ =1 0, F ≥ 0;

657

(12)

(13)

where N ch.av and N dich.av —the number of complete cycles of charging and discharging a pneumohydraulic accumulator during a computer experiment; i—number for fully charging or discharging the pneumohydraulic accumulator; τ —integration step number; τ m —total number of integration steps. To implement the presented mathematical model, a computer program was developed in Object Pascal language in the Delphi 7 programming environment that allows one to study the influence of the main parameters of the braking energy recovery system and the supporting surface on its performance indicators [20]. In order to study the effectiveness of the functioning of the system of recovery of braking energy in the hydraulic motors of the wheels of a forest car while it is moving along a sinusoidal and randomly uneven surface, four series of experiments were performed using the developed computer program. When performing a basic computer experiment, the period of the sinusoid of the sinusoidal supporting surface was 100 m, the amplitude of variation in the height of the roughness of the supporting surface was 10 m, the length of the supporting surface section along which the timber truck moved was 2.5 m. In order to establish the dependences of the effect of the volume of the V PGA pneumohydraulic accumulator on the performance indicators of the braking energy recovery system, a series of experiments was carried out in which the volume of the V PGA pneumohydraulic accumulator was changed with a step of 20 from 20 to 300 l. To study the influence of the efficiency η on the performance indicators of the braking energy recovery system, a series of experiments was performed in which, with a step of 10 from 50 to 100%, the efficiency η was changed in the process of charging and discharging a pneumohydraulic accumulator. During computer experiments, the movement of a forest car along a support surface with a random topography, the length of the control section of a randomly uneven surface was taken 2.5 km, the traction force of the truck required to maintain the same speed of 10 m/s changed randomly depending on the topography of the support surface. In order to study the effect of the total volume of the pneumatic-hydraulic accumulator V PGA on the average values of the charging time t ch.av , discharge t dich.av and the fuel economy coefficient k f.eff during the movement of the logging truck during timber removal along a random terrain, we conducted a series of computer experiments in which 20 changed from 20 to 300 l the volume of the V PGA pneumohydraulic accumulator. To establish the dependences of the influence of the average obstacle length bav on the average values of the charging time t ch.av , discharge t dich.av and the fuel economy coefficient k f.eff we

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performed a series of computer experiments in which the average obstacle length bav was changed from 15 to 120 m in steps of 15.

3 Results The dependences of the influence of the total volume of the V PGA pneumohydraulic accumulator on the average charging time t ch.av , discharge t dich.av , and fuel economy coefficient k f.eff during the movement of a timber truck during the removal of timber over a sigmoidal topography (Fig. 2a) are obtained. It was revealed that the charging time t ch.av and discharge t dich.av of the pneumohydraulic accumulator linearly increases with an increase in its V PGA volume. It was determined that when the volume of the V PGA pneumohydraulic accumulator changes from 120 l or more, it does not have time to fully charge and discharge, while t ch.av and t dich.av discharge to infinity during charging. The fuel economy coefficient k f.eff increases with increasing volume of the V PGA pneumohydraulic accumulator according to the exponential law. It was found that with a V PGA volume of a pneumohydraulic accumulator of 150 l or more, the fuel economy coefficient k f.eff does not change and amounts to 55%. The dependences of the accumulated hydraulic energy of the E PGA in the pneumatichydraulic accumulator on the time t were revealed for the volumes of the V PGA of the pneumatic-hydraulic accumulator 20 l (Fig. 2b, curve 1) and 200 l (Fig. 2b, curve 2). The dependencies show that with an increase in the volume of the V PGA pneumohydraulic accumulator from 20 l to 200 l, the amount of accumulated hydraulic energy of the E PGA decreases from 100 to 70%. It was found that for a given relief surface shape of the supporting surface, the efficiency η of the braking energy recovery system is lower than 70% (Fig. 2c), which leads to incomplete charging of the pneumohydraulic accumulator. This can be seen from the vertical shapes of the plots in the obtained dependences of the influence of the efficiency coefficient η on the charging time t ch.av and discharge t dich.av of the pneumohydraulic accumulator. Increasing the efficiency η from 70% to 100%, a significant decrease in the charging time t ch.av of the pneumohydraulic accumulator and an increase in the discharge time t dich.av are observed. The achievement of the same values of the charging time t ch.av and the discharge t dich.av of the pneumohydraulic accumulator is observed at a coefficient of efficiency η of the braking energy recovery system equal to 100%. An increase in the fuel economy coefficient k f.eff of a timber truck was also found with an increase in the efficiency η of the braking energy recovery system. The dependences of the influence of time t on the amount of stored energy of E PGA in a pneumatic-hydraulic accumulator are established for values of the efficiency η equal to 50% (Fig. 2d, curve 1) and 100% (Fig. 2d, curve 2), which show that the coefficient decreases efficiency η helps to reduce the amount of stored energy of the E PGA in the pneumatic-hydraulic accumulator. It was found that the charging time t ch.av of the pneumatic-hydraulic accumulator increases linearly, with an increase in the volume of the V PGA of the pneumatic-hydraulic accumulator to 200 l, t ch.av increases to 7 s, then decreases (Fig. 2e). The discharge time t dich.av of the pneumohydraulic accumulator significantly increases with a volume of

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Fig. 2. Dependences of the influence of the main parameters of the braking energy recovery system on its performance indicators.

V PGA of 250 l or more. Also, with an increase in the volume of the V PGA pneumohydraulic accumulator, an increase occurs according to a law close to the decreasingexponential coefficient of fuel economy k f.eff . It was found that the smaller the values of the irregularity lengths bav of the supporting surface, the higher the fuel economy coefficient k f.eff (Fig. 2f), the shorter the charging time t ch.av and discharge t dich.av of the pneumohydraulic accumulator.

4 Conclusion Thus, the developed mathematical model of the functioning of the regenerative braking energy of the forest car, and on its basis a computer program, allows us to conclude that: the optimal volume of the V PGA pneumohydraulic accumulator when the forest car moves along periodic irregularities, as well as along a random topography, is 120 l;

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to increase the fuel economy coefficient k f.eff , the efficiency η of the braking energy recovery system should not be lower than 70% when charging and discharging a pneumohydraulic accumulator; the described braking energy recovery system allows saving from 30 to 50% of fuel depending on the topography of the supporting surface.

References 1. Nikonov VO, Posmetev VI, Latisheva MA (2018) Problem status and overview of vehicle structures with braking energy recovery systems. Voronezh Scientific Technical Bull 2(24):4– 19 2. Chicurel R (1999) A compromise solution for energy recovery in vehicle braking. Energy 24(12):1029–1034. https://doi.org/10.1016/s0360-5442(99)00054-7 3. Yu W, Wang R, Zhou R (2019) A comparative research on the energy recovery potential of different vehicle energy regeneration technologies. Energy Procedia 158:2543–2548. https:// doi.org/10.1016/j.egypro.2019.02.001 4. Xiao B, Lu H, Wang H, Ruan J, Zhang N (2017) Enhanced regenerative braking strategies for electric vehicles: dynamic performance and potential analysis. Energies 10(1875):19. https:// doi.org/10.3390/en10111875 5. Zhao D, Chu L, Xu N, Sun C, Xu Y (2018) Development of a cooperative braking system for front-wheel drive electric vehicles. Energies 11(378):24. https://doi.org/10.3390/en1102 0378 6. Dindorf R, Wos P (2017) Development of energy efficient hydrostatic drives with energy recovery. Mechanik NR 8–9:8. https://doi.org/10.17814/mechanic.2017.8-9.114 7. Pugi L, Pagliali M, Nocentini A, Lutzemberger G, Pretto A (2017) Design of a hydraulic servo-actuation fed by a regenerative braking system. Appl Energy 187:96–115. https://doi. org/10.1016/j.apenergy.2016.11.047 8. Kumar ERA (2012) Hydraulic regenerative braking system. Int J Scientific Eng Res 3(4):12 9. Wu W, HLiu H, Zhou J, Hu J and Yuan S (2019) Energy efficiency of hydraulic regenerative braking for an automobile hydraulic hybrid propulsion method. Int J Green Energy 16(13):1946–1953. https://doi.org/10.1080/15435075.2019.1653875 10. Posmetev V I, Nikonov V O and Posmetev V V (2018) Investigation of the energy-saving hydraulic drive of a multifunctional automobile with a subsystem of accumulation of compressed air energy. IOP Conf Ser: Mater Sci Eng, ISPCIET’2018 441 012041:1–7. https:// doi.org/10.1088/1757-899x/441/1/012041 11. Posmetev VI, Nikonov VO and Posmetev VV (2019) Imitating modeling results of a recuperative hydraulic subsystem of the timber truck manipulator. IOP Conf Ser: Earth Environ Sci 392:1–8. https://doi.org/10.1088/1755-1315/392/1/012038 12. Nikonov VO, Posmetev VI and Posmetev VV (2019) Mathematical model of hydromanipulator of forest vehicle with recuperative hydraulic drive. IOP Conf Ser: Earth Environ Sci 392:1–8. https://doi.org/10.1088/1755-1315/392/1/012039 13. Nikonov VO, Posmetev VI, Posmetev VV (2019) The results of simulation modeling of the operation of the regenerative fifth wheel hitch of a timber trailer. IOP Conf Ser: Mater Sci Eng 656:1–8. https://doi.org/10.1088/1757-899x/656/1/012039 14. Posmetev VI, Nikonov VO, Posmetev VV (2019) The results of computer simulation of a regenerative towing device of a forest car with a trailer. Forestry J 4:108–123. https://doi.org/ 10.17238/issn0536-1036.2019.4.108 15. Nikonov VO (2018) Evaluation of the effectiveness of the hydraulic system for recovering the braking energy of a forest road train. Energy Efficiency Energy Sav Mod Prod Soc: Mater Int Sci Practical Conf 1:210–215

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16. Adler YuP, Markova EV, Granovskii YuV (1976) Planning an experiment when searching for optimal conditions. Science, Moscow, p 279 17. Granovskii VA, Siraya TN (1990) Methods for processing experimental data in measurements. Energoatomizdat, Leningr. Otd-tion, Leningrad, p 288 18. Troickii VA, Ivanova IM, Starostin IA and Shelest VD (1979) Engineering calculations on a computer. Mechanical Engineering, Leningrad, p 288 19. Kuzmichev DA, Radkevich IA, Smirnov AD (1983) Automation of experimental studies. Science. Main ed. Physical Mat. Letters, Moscow, p 392 20. Posmetev VI, Nikonov VO, Posmetev VV (2019) The program for simulating the movement of a forest car with energy storage in wheel motors. Certificate of state registration of a computer program 2019611251, declared 10.01.19 registered in the register of computer programs 23.01.2019

Investigation into Operational Reliability of Vehicle Electronic Systems Y. V. Bazhenov1(B) , V. P. Kalyonov2 , and M. Y. Bazhenov1 1 Vladimir State University Named After Alexander and Nikolay Stoletovs, 87, Gorky St.,

Vladimir 600000, Russia [email protected] 2 Dealer Center Peugeot, 24A, Kuibyshev St., Vladimir 600035, Russia

Abstract. The paper presents the results of research on operational reliability of the vehicle electronic systems are presented. The research was carried out on the basis of Peugeot dealer center (Vladimir) during maintenance and repair of vehicle electronic systems of cars of Peugeot brand. It has been shown that almost half of all failures arising during the operation of vehicles are in electronic and electrical systems. Statistical estimates of the average operating time of electronic systems of the car before their loss of operable condition have been determined. Statistical estimates of probabilities of failure-free operation and intensity of vehicle electronic systems failures by vehicle operating time intervals are given. The impact of failures of structural elements of the electronic engine control system on the main parameters of its operation was investigated: reduction of power, increase of fuel consumption, and emissions of harmful substances into the atmosphere with exhaust gases. The engines researched were those of Peugeot 3008 cars (1.6 THP Turbo Tiptronic) studied in the mode of active experiment with simulation of failures of each electronic engine control systems element. The main causes of operational failures of structural elements of electronic systems of cars and their impact on technical characteristics of car operation are identified. The results of the studies allow optimizing the system of maintenance and repair of vehicle electronic systems at the enterprises of the car service. The test of the results of the research is shown in the example of electronic systems of cars of Peugeot brand. Keywords: Reliability · Car · Electronic system · Failure · Operating time

1 Introduction A modern motor vehicle is a complex technical system in which a large number of different units operate simultaneously and in an interconnected manner, the operation of which is increasingly controlled by electronics and computer technologies. The use of electronics integrated into car control systems ensures the high consumer properties of cars in their operating conditions and improves road safety [1–4]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_76

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Depending on the functional purpose, the vehicle electronic systems (VES) can be divided into four groups [5–8]: • Electronic engine control systems (EECS), the use of which allows to achieve high technical and economic performance of internal combustion engine with simultaneous reduction of fuel consumption and compliance with strict environmental requirements • Electronic vehicle control systems ensuring safety during its movement (anti-lock braking system—ABS, active front steering—AFS, systems improving control and ergonomics of the vehicle, etc.) • Specialized on-board vehicle systems, including various systems of displaying information necessary for the driver to drive the vehicle, systems that increase comfort of the vehicle, navigation systems, electronic antitheft devices • Local area networks, which are multiplex information transmission systems based on CAN technology, the use of which allows to significantly reduce the number of wires, electrical contacts and increase the speed of information exchange.

2 Methods In the course of operation, various types of damages and faults inevitably occur in the structural elements of the VES (violation of adjustments, change of electrical characteristics, corrosion destruction of contacts, damage to insulation, etc.). At the same time, with saturation of cars with electronic systems, the number of operational failures of their elements increases significantly compared to other systems of the car [9–11]. Manufacturers of VES do not always have reliable information about faults occurring during operation, reasons for failure of their operability, operating time up to the limit state and other indicators characterizing operational reliability of their products. As a result, in real operating conditions, structural failures associated with imperfections in their design are often found among the causes of the VES failures [12–14]. The source of the most reliable information on the VES reliability, as well as other car systems, is operational tests. The information obtained during such tests is useful not only for manufacturers of electronic systems, but also for the sphere of operation, as it allows to scientifically justify the standards for ensuring their operable condition [15, 16].

3 Results and Discussion In this work, research was carried out on the basis of Peugeot dealer center (Vladimir) during maintenance and repair of Peugeot cars. According to the studies, almost half of all failures of these vehicles arising during operation are caused by failures of electronic and electrical systems (Fig. 1). These include failures of vehicle structural elements in which electric current flows (electronic control units, sensors, actuators, lighting and alarm system parts, generator, starter, etc.). As can be seen from the diagram, the electronic systems of Peugeot 3008 cars account for 30.5% of failures. The high probability of operational failures of electronic systems of the car is confirmed by the research of the British insurance company Warranty Direct,

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Fig. 1. Peugeot 3008 car failure distribution diagram.

according to which the most common failures of passenger cars are electrical failures arising during operation (22.34% of the total number of failures). The results of the VES operational reliability studies processed by the computer program Statistica are presented in Table 1 and in part in the form of histograms wi and their smoothing theoretical curves of the distribution of operating time to failure f (t) in Fig. 2. Table 1. Statistical estimates of the reliability characteristics of the electronic system of the car Peugeot 3008. Electronic system

Percentage of total VES failures

Mean operating time to failure, thousand km

Average standard deviation of operating time σ , thousand km

Coefficient of variation v

EECS

35

136.7

28.7

0.21

ABS–AFU*

17

138.3

24.9

0.18

Air-bag

13

162.4

47.1

0.29

Climate control system

11

157.1

48.7

0.31

9

147.2

22.1

0.15

–

–

–

Automatic transmission Others

15

*The AFU (Assistance Au Freinage d’Urgence, Emergency Braking Assistance System), developed by French engineers PSA (Peugeot Société Anonyme), works in conjunction with ABS and significantly expands its functional capabilities. The use of this system allows reducing the braking distance during emergency braking by an average of 15–20%

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Fig. 2. Histograms 1 and theoretical curves 2 of the distribution of operating time to failure t of VES: a EECS; b ABS–AFU; c Air-bag; d Automatic transmission.

The kind of curves, as well as the calculated values of the coefficients of variation v, show that the distribution of operation time to failure of the VES is well described by normal distribution. Testing the hypothesis that the experimental data belonged to a normal distribution using Pearson’s chi-squared test confirmed its validity [17, 18]. In addition to the average operating time to failure, it is advisable to use as indicators assessing the reliability of structural elements of VES: failure rate λ(t), which clearly shows the dependence of failures on mileage of the vehicle, and change of probability of failure-free operation P(t) in operating time intervals from the beginning of operation to the onset of the limit state [1, 19]. Failure rate is the number of failures per one serviceable article per unit of operating time, according to results of operational tests is as follows: λ¯ (t) =

N (t) − N (t + t) , N (t)t

(1)

where N (t), N (t + t) is quantity of operable items at operating time of t and t + t; t - operating time interval. Probability of failure-free operation P(t) is determined by ratio of number of serviceable items to total number of items under observation during operating time t: N− ¯ P(t) =

k  j=1

N

mj ,

(2)

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where N—number of serviceable items at the beginning of observations; mj —number of items that failed in j-th operating time interval; k = t/ t—number of operating time intervals. Statistical estimates of these indicators based on the results of tests and processing of the data array on reliability of the tested VES are given in Table 2. Table 2. Change of reliability indicators of electronic systems of cars Peugeot 3008 by operating time. Indicator

Operating time interval, thousand km 0–20 20–40 40–60 60–80 80–100 100–120 120–140 140–160 160–180 180–200

ABS-AFU P(t)

0.98

0.98

0.95

0.90

0.83

0.74

0.55

0.39

0.25

0.13

λ(t)·10−4

1.32

1.12

2.87

4.76

6.34

9.52

17.47

21.46

38.91

65.74

EECS P(t)

0.99

0.98

0.94

0.91

0.88

λ(t)·10−4 2.42

1.94

3.21

5.75

8.97

0.71 11.4

0.52

0.26

0.20

0.08

23.17

30.52

44.29

86.16

Air-bag P(t)

0.98

0.98

0.98

0.96

0.89

0.83

0.71

0.63

0.49

0.21

λ(t)·10−4 2.23

1.11

1.49

4.55

7.24

9.92

18.34

23.76

30.77

67.53

Climate control system P(t)

0.99

0.99

0.97

0.94

0.87

0.86

0.74

0.53

0.39

0.17

λ(t)·10−4

1.12

1.26

2.18

3.21

6.21

7.81

16.82

21.72

27.19

61.72

Automatic transmission P(t)

0.99

0.98

0.97

0.92

0.88

0.76

0.65

0.49

0.29

0.11

λ(t)·10−4 1.65

0.99

1.68

2.51

5.77

8.12

15.23

19.86

26.11

55.32

By analyzing the data in the table, some conclusions can be drawn on the operating reliability of the VES. For initial operating intervals from 0 to 100 thousand km, the probability of failure-free operation of electronic systems is quite high. During this period of operation, EECS and ABS-AFU structural elements, which are subjected to high mechanical and thermal loads, may be likely to lose their operability. By the operating time interval of 140-160 thousand km the probability of failure-free operation of all electronic systems is significantly reduced and by operating time of 260 thousand km practically all VES fully realize their resource. Studies have shown that the main causes of operational failures of components of electronic systems of cars are: wear of movable parts, aging of materials, application of operational materials of low quality, corrosion destruction, non-compliance with maintenance regulations, violation of operation rules. Damages occurring during operation in electronic systems lead to significant deterioration of vehicle operation and in case of their untimely detection and elimination to partial or complete loss of its operability [6, 20]. Table 3 shows the results of experimental

Investigation into Operational Reliability

667

studies on evaluation of the impact of failures of EECS elements, the most complex electronic system of the vehicle, on the main parameters of engine operation. The research was carried out on the engines of Peugeot 3008 cars (1.6 THP Turbo Tiptronic) in the mode of active experiment. On the tested engine the failure of each of EECS elements was simulated by its disconnection and the parameters selected for internal combustion engine (ICE) operation characteristics were measured using the appropriate equipment. Table 3. Impact of failures of EECS components on main engine parameters. The refused element

Change of parameter Power drop, %

Increase in fuel consumption, %

Increase in emissions of harmful substances, % CO

CH

Fuel pressure sensor

30

15

10

12

Solenoid valve of pressurizing pressure control

30

20

12

8

Electronic throttle valve

90

–

–

–

Forced aspiration pressure sensor

20

10

12

8

Electric motor of valve lifting change system of gas-distribution mechanism

85

–

–

–

Camshaft position sensor

15

5

5

5

Crankshaft position sensor

100

–

–

–

Oxygen sensor

15

20

20

18

Electronic thermostat (with coolant temperature sensor)

15

13

16

17

100

–

–

–

Electronic engine control unit (EECU)

Analysis of the results given in the table shows that in case of crankshaft position sensor and EECU failures engine starting is impossible, as fuel supply to engine cylinders is blocked. At emergence of malfunctions of an electric motor of valve lifting change system or the electronic throttle valve start of ICE is possible, however, the maximum frequency of rotation of a bent shaft is limited to n ≈ 1000 rpm; therefore, engine capacity decreases by 85–90% and the vehicle cannot move. The effect of failures occurring in other electronic systems on the performance of the vehicle is shown in Table 4.

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Y. V. Bazhenov et al. Table 4. Impact of VES failures on vehicle operation characteristics.

Vehicle electronic system Consequences of refusals of VES ABS-AFU

Reduction of braking system operation efficiency, increase of braking path, deterioration of vehicle controllability during braking

Air-bag

Increased risk of injury to occupants in traffic accidents

Climate control system

Reduced comfort of driving, increased fatigue of the driver

Automatic transmission

Total or partial loss of automatic transmission operability, malfunctioning gear mechanism

4 Conclusion The results of the performed tests of the VES operational reliability are the basis for optimization of their maintenance and repair, make it possible to justify the complex of diagnostic parameters for assessment of the state of structural elements of the systems, to develop algorithms of fault analysis and rectification. For example, before the operation time of 80 thousand km during routine maintenance of Peugeot 3008 cars, it is not necessary to control the technical condition of the structural elements of electronic systems, as the probability of their failure-free operation is at a sufficiently high level. It is advisable to perform in-depth diagnostics of these systems with operation time of 100 thousand km (planned maintenance PM-5), when there is a marked increase in failure rate λ(t) and probability of their failure-free operation P(t).

References 1. Bazhenov YV (2017) Foundations of machine reliability theory. Forum, Moscow 2. Tweg R (2003) Diagnostics of the electronic control system of the car engine. Astrel, Moscow 3. Tunin AA (2007) Diagnostics of electronic control systems of passenger car engines: tutorial. Solon-Press, Moscow 4. Sosnin DA (2005) The latest automotive electronic systems. Solon-Press, Moscow 5. Bazhenov YV, Kalyonov VP (2015) Ensuring the working condition of electronic engine control systems in operation. Automobile Ind 12:23–27 6. Bazhenov YV, Kalyonov VP (2016) Maintenance of reliability of electronic engine control systems in operation. Electron Elect Equip Trans 2:2–5 7. Hedicks E, Chevalier A, Jensen M, Event based engine control: practical problems and solutions. SAE paper No 950008 8. Khodasevich TI (2005) Devices and meters for inspection and control of electric equipment of cars: tutorial. NT Press, Moscow 9. Bazhenov YV, Kalyonov VP (2014) Diagnostics of electronic engine control systems. Fundamental Res 8–1:18–23 10. Rendall M (2012) Electrical and electronic equipment of automobiles. Alfamer Publishing, Moscow 11. Danov BA (2004) Electronic control systems of foreign cars. Telekom hotline, Moscow 12. Diagnostics of electronic systems of cars with NTS devices (2007) 9th edn. NPP “NTS”, Samara

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13. Nabokih VA (2013) Diagnostics of electric equipment of cars and tractors: tutorial. Forum, Moscow 14. Kuznetsov AS (2011) Maintenance and diagnostics of internal combustion engine: tutorial. Academy, Moscow 15. Erokhov VI (2011) Gasoline engine injection systems: tutorial. Hotline – Telecom, Moscow 16. Electronic portal of car manufacturer PEUGEOT. SERVICE BOX (2019). https://servicebox. peugeot.com. Accessed 02 March 2019 17. Boldin AP, Maksimov VA (2012) Basics of scientific research: textbook. Academy, Moscow 18. Danilov IK, Sychev AM, Marusin AV (2016) Mathematical modeling of processes of built-in system of technical diagnostics of diesel engines. Truck 11:16–19 19. Robert Bosch GmbH, Foerstner Dirk, Weber Reinhard. Fehlerdiagnoseverfahren und vorrichtung: DE-Aktenzeichen 10326557. B* 60 R 16/02. Anmeldedatum 12.06.2003, Veroffentlichungstag im Patentblatt 05.01.2005 20. Sarkisov AA (2004) Intelligent diagnostics of failures of automobile sensors. Electronics and electrical equipment of transport 3–4:46–52

Numerical Modeling of a Railway Wheel Profile in a Fillet Radius Space Using the Uniform Search Method L. B. Tsvik1 and E. V. Zenkov2(B) 1 Irkutsk State Transport University, 15, Chernishevskogo, Irkutsk 664074, Russia 2 Irkutsk National Research Technical University, 83, Lermontov str., Irkutsk 664074, Russia

[email protected]

Abstract. The article describes an approach used for improving the structural design of a solid-rolled railway wheel profile using the stress-strain state (SSS) uniformity criterion based on the finite element method (FEM). The uniform search method is described. The approach is implemented for an axial section of the wheel according to FS 9038-88. The first block of the uniform search determines rational values of wheel profile radii at constant values of one of the radii. The stress intensity, which determines the wheel strength under cyclic loading, is considered the main SSS characteristic. For each of the considered structural variants of the wheels, the convergence of the results of a numerical simulation of the stress intensity and the desired solution to the considered problem of elasticity theory is analyzed. The article presents the results of the FEM method application for the calculation of the stress intensity values depending on structural wheel profile parameters. Keywords: Railway wheel · Uniform search · Stress state · Stress intensity · Algorithm

1 Introduction In order to increase the working life of wheels and reduce crack formation at the junction of disks with hubs and rims, it is necessary to analyze the stress-strain state (SSS) of axial wheel sections. It helps identify the most promising and rational design solutions. When studying solid-rolled railway wheel profiles [1] by the finite element method (FEM), wheels with a technologically developed axial section profile having a piecewise constant contour curvature were analyzed [2]. The types of wheels that are promising for further improvement by the SSS uniformity criterion were identified. The uniform search method was used to find rational design solutions [3]. The method involves the search for values of functions by any comparison criteria (maximum, minimum, constant values). The method is an example of a direct one-dimensional optimization method used in each cycle [4–6]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_77

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2 Algorithm of Uniform Search Method The uniform search method algorithm for a minimum of the function of several variables is as follows. Let the function be f (x) : [a, b] → R,

(1)

and the task of its optimization is determined by f (x) → min . x∈[a,b]

(2)

Let n be a number of experimental observations of the function value in a calculation experiment. Then interval [a, b] is divided into (n + 1) equal parts by division points xi = a + i

(b − a) , i = 1, . . . , n. (n + 1)

(3)

Calculating F(x) at points x i , i = 1, …, n, let us determine point xm (m is a number from 1 to n) so that F(xm ) = minF(xi ),

(4)

among all i from 1 to n. The uncertainty interval is 2

(b − a) . (n + 1)

(5)

The error ε at the point of minimum x m of function F(x) is ε=

(b − a) . n+1

(6)

Let us describe a uniform search scheme on the example of wheels whose profile (see Fig. 1) is in compliance with FS 9038-88 [7]. Similar results can be obtained for profiles that correspond to FS 10791-2011 and have a more complex shape (a greater number of transition radii). When searching for a rational profile of the axial section, the wheel profile corresponding to [7] is considered nominal. According to [7], the nominal wheel was 378 kg. The first uniform search block was aimed at determining rational values of radii R1 , R2 , R3 , R4 in the R2 zone (at the junction of the rim and the wheel disk) where the maximum value of stress intensity is minimal compared to the nominal design option corresponding to [7]. The values are considered rational. The rational values of radii Ri , i = 1, …,6, were calculated at constant values of other five radii Ri . Stress intensity σi which determines the wheel strength under cyclic loading was considered the main characteristic of the stress-strain state of the wheels [8–11].

3 Results of Variant Computational Experiments The FEM [1, 12, 13] helped calculate maximum values of stress intensity σi depending on wheel profile radius values. The results are presented in Tables 1, 2, 3, 4 and Fig. 1, 2, 3, 4, 5. The radius values corresponding to [4] are marked with a vertical line.

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Fig. 1. The main radii of curvature of the axial solid-rolled wheel section profile corresponding to [4]. Table 1. The influence of R1 on the value of maximum stress intensity in the wheel rim zone. Value of radius R1 (mm)

52

50

Stress change (%)

0

−1.28 −0.80 −3.26 −5.91 −3.01

Wheel weight deviation from the nominal value (kg)

0

−0.87 −2.96 −4.97 −6.85 −8.73

Value of radius R1 (mm)

52

50

Maximum values of stress intensity σi on the 150.5 148.6 radius R2 surface (MPa)

45

40

35

31

45

40

35

31

149.3

145.6

141.6

146.0

Table 2. The influence of R2 on the value of maximum stress intensity in the wheel rim zone. Value of R2 (mm) Stress change (%)

50 4.32

45

40 3.24 0

Wheel weight deviation from the nominal value (kg) −1.56 −0.85 0 Maximum values of stress intensity σi on the radius 157.0 R2 surface (MPa)

155.4

35

30

−4.44 −5.96 0.96

150.5 143.9

2.05 141.6

Numerical Modeling of a Railway Wheel Profile

673

Table 3. The influence of R3 on the value of maximum stress intensity in the wheel rim zone. Value of R3 (mm)

50

Stress change (%)

−4.99 −3.42

Wheel weight deviation from the nominal value (kg)

45 5.19

40 0.00

145.4

30

0.78

6.65

0.00 −2.47 −4.79

2.57

Maximum values of stress intensity σi on the radius 143.0 R2 surface (MPa)

35

150.5

151.7

160.6

Table 4. The influence of R4 on the value of maximum stress intensity in the wheel rim zone. Value of R4 (mm)

60

55

3.70

−2.60

−1.51

0.00

0.77

1.68

4.01

Wheel weight deviation from the nominal value (kg)

−2.33

−1.46

−0.56

0.00

0.36

1.31

2.29

Maximum values of stress intensity σi on the radius R2 surface (MPa)

156.1

146.6

148.3

Stress change (%)

65

52

150.5

50

151.7

45

153.1

40

156.6

Fig. 2. Graphic dependence of maximum stress in R2 zone on the change in R1 .

For a numerical analysis of the stress state by the FEM, the MSC/NASTRAN [14–16] software was used. Discrete FE models of wheels were built in accordance

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Fig. 3. Graphic dependence of maximum stress in R2 zone on the change in R2 .

Fig. 4. Graphic dependence of maximum stress in R2 zone on the change in R3 .

with [1, 2]. For each constructive wheel option, the convergence of results of numerical modeling of stresses σi to the target elasticity solution was analyzed [17]. In case of uniform FE-decomposition of the wheel volume, the minimum number of FE (at which the relative error of stress intensity did not exceed 5% [18]) was 150,000 [19, 20]. In

Numerical Modeling of a Railway Wheel Profile

675

Fig. 5. Graphic dependence of maximum stress in R2 zone on the change in R4 .

case of non-uniform decomposition concentrating in a zone of maximum stress σi , the accuracy was achieved at 50,000 FE. Figure 2 shows that the graph of a function describing the dependence of maximum stresses in the R2 zone on transition radius R1 has two minima; the first minimum is deeper than the second one by 4.7%. It can be concluded (Tables 1, 2, 3, 4) that maximum stresses in the im zone of the wheel are most sensitive to changes in R1 . At a decrease in the stress value, a decrease in this radius decreases the wheel weight. The wheel weight decreased by 6.8 kg. The maximum level of stress intensity in the wheel rim zone of radius R2 decreased by 5.9% and reached its minimum at R1 = 35 mm. At the next stage, R6 values were varied at R1 = 35 mm. The data are presented in Table 5. Table 5. The influence of radius R6 on the value of maximum stress intensity in the wheel rim zone at R1 = 35 mm. Value of R6 (mm)

100

85

76

60

Wheel weight deviation from the nominal value (kg)

0

−6.85

−8.38

−8.89

Maximum values of stress intensity σi on radius R2 surface (MPa)

150

142

139.5

138.7

Variation of radius R5 did not change maximum stresses. The analysis showed that the wheel weight decreased by 8.9 kg. The maximum stress intensity value decreased by 7.9%.

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4 Conclusions The results show that for this set of axial section contours, the choice of a solid-rolled railway wheel profile using the uniform search method in the space of profiles with a piecewise constant curvature can reduce the wheel stress at the maximum points. From a mathematical point of view, the wheel profile characteristics are not optimal. At the same time, these characteristics make it possible to find a rational initial approximation for the optimal rail wheel profile contour with a flat-conical disk when trying to optimize it in a wider class of lines limiting the axial section profile.

References 1. Tsvik LB, Zapolsky DV (2013) Comparative analysis of the deformation of the disk portion of solid-rolled railway wheels of different structural design. In: Transportation: problems, ideas and perspectives, St. Petersburg State Univ. of Railways, St. Petersburg, 1–5 April 2013 2. Tsvik LB, Zapolsky DV, Zenkov EV et al (2013) Comparative analysis of deformation of disk part of whole-rolled railway wheels of various constructive design. Bull Res Instit Railw Trans 5:29–36 3. Akulich IL (1986) Mathematical programming examples and problems. Textbook for students of Economy, Higher School, Moscow 4. Grechneva MV, Balanovskiy AE, Gozbenko VE et al (2019) Quality and reliability improvement of tube-tube plate welded joints during welding by pulse pressure. IOP Conf Ser: Mater Sci Eng 560:012142. https://doi.org/10.1088/1757-899X/560/1/012142 5. Zenkov EV, Tsvik LB (2014) Calculation and experimental evaluation of strength characteristics of steel 50HFA under condition of two-axial strength using prismatic samples/Bulletin of Irkutsk State Technical University 4:27–33 6. Zenkov EV (2015) Development and implementation of practical methods tests materials under biaxial loading. Bull Irkutsk State Technical Univer 10:50–57 7. Tsvik LB, Zapolsky DV (2012) Features of modeling of stress-strain state of the solid-rolled railroad wheels with rectilinear generator disk portion. In: Automation and energy efficiency engineering and metallurgical industries, technology and reliability of machines, devices and equipment, VolGTU, Vologda, 25–30 June 2012 8. Kogaev VP, Makhutov NA, Gusenkov AP (1985) The calculations of machine parts and structures for strength and durability. Mechanical engineering, Moscow 9. Kuz’min P, Larionov LM, Kondratiev VV et al (2018) Use of the burnt rock of coal deposits slag heaps in the concrete products manufacturing. Constr Build Mater 179:117–124. https:// doi.org/10.1016/j.conbuildmat.2018.05.222 10. Burago NG, Nikitin IS, Nikitin AD et al (2019) The assessment of fatigue durability and critical plane determination for multiaxial cyclic loading at an arbitrary shift of phases. PNRPU Mech Bull 3:27–36. https://doi.org/10.15593/perm.mech/2019.3.03 11. Bondar VS, Abashev DR (2019) Some features of monotonic and cyclic loadings, Experiment and modeling. PNRPU Mech Bull 2:25–34. https://doi.org/10.15593/perm.mech/2019.2.03 12. Zienkiewicz OC, Taylor RL (2000) The Finite Element Method, 5th edn. The Basis, Butterworth-Heinemann, Berkeley 13. Zenkevich O (1975) Finite element method in engineering. Mir, Moscow 14. Govorkov AS, Zhilyaev AS (2016) The estimation technique of the airframe design for manufacturability. IOP Conference Series: Materials Science and Engineering 124:012014. https:// doi.org/10.1088/1757-899X/124/1/012014

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15. Shimkovich DG (2008) Femap & Nastran. DMK Press, Moscow, Engineering analysis by the finite element method 16. Rudakov KN (2011) FEMAP 10.2.0. Geometric and finite element modeling construction of structures. KPI, Kiev 17. Lavrentyieva M, Govorkov A (2017) Using a discrete product model to determine the design element junctures. MATEC Web Conf 129:03003. https://doi.org/10.1051/matecconf/201712 903003 18. Zenkov EV, Tsvik LB, Pykhalov AA (2011) Discrete stress-strain simulation states of plane cylindrical specimens with stress concentrators in the form of grooves. Bull Irkutsk State Technical Univers 7:6–12 19. Zenkov EV, Tsvik LB (2019) Verification of finite element model of deformation of laboratory sample for mechanical tests by method of digital images correlation. Lecture notes in mechanical engineering, p 1979–1987. https://doi.org/10.1007/978-3-319-95630-5_213 20. Zenkov EV, Aistov IP, Vansovich KA (2018) Analysis of strain state prismatic samples for mechanical testing of the biaxial stretching method digital image correlation. J Phys: Conf Ser 1050:012101. https://doi.org/10.1088/1742-6596/1050/1/012101

Features of Development of Structures of Extruders V. Kushnir(B) , N. Gavrilov, and I. Koshkin Baitursynov Kostanay State University, 47, Baitursynov St., Kostanay 110000, Kazakhstan [email protected]

Abstract. A brief overview of the use of extrusion technologies in the fields and industries and in the processing of various products, including animal and bird feed, was given. The advantage of single screw extruders, their production in various regions of the CIS countries and in Kazakhstan is noted. The technical characteristics of the extruders manufactured at “Agrotekhservis-12” (Republic of Kazakhstan) were presented. A number of disadvantages of single screw extruder designs have been identified. One of them is a relatively complicated spindle device, containing a large number of parts, which entails not only an increased time for repair work, but also additional difficulties in repairing, replacing failed parts and servicing the spindle. A new constructive solution that allows, without losing the main performance characteristics when processing specific types of raw materials, extending the life of the extruder by an average of 22%, in comparison with the base model of the PE-20 extruder, was proposed. Keywords: Extrusion · Technology · Extrusion process · Extruder · Screw design · Field waste processing

1 Introduction Single screw pressing mechanisms are energy-intensive technological facilities of the feed industry. They have become actively used in the extrusion of feed recently. The complexity and variety of feed processing is a feature of extruder presses. An urgent issue that depends on the structural-operational parameters of the extruder [1–4] is the desire to increase the productivity of the extruder press and the quality of the extrudate.

2 The Main Part Today, extruders are the most popular devices, because the versatility of this equipment allows its use in many areas and industries of production and processing of various products, including: production of amidoconcentrate additives; production of extruded compound feeds for cattle and small cattle; dog food production; production of dry food for fur animals; processing of cereals and legumes with cooling in a stream of air © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_78

Features of Development of Structures of Extruders

679

(using a special installation); processing of rye and sorghum crops; soybean processing; production of organo-mineral fertilizers; processing of biological waste by extrusion; processing of toxic leather wastes into a highly effective protein supplement; fishmeal production; production of instant soups based on extruded peas; production of milk powder substitute from plant components; production of egg powder from plant components; obtaining a karate-vitamin product from spruce needles; meat and bone meal production; processing waste from the production of alcohol and beer; production of granular, extruded fish cake floating and sinking (depending on the customer’s request); biofuel production; sunflower oil production and much more [1, 5–8]. Extrusion technologies also apply to the latest methods of processing grain, grain waste, crop waste, waste from the milling industry, and biological waste. In the most economically developed countries (USA, Japan, countries of Western Europe) extrusion technologies have become a priority in the development of the food and feed industry. Currently, various extrusion methods produce confectionery, as well as feed for poultry, animals, and fish. The only enterprise producing a model range of extruders in Kazakhstan is “Agrotekhservis-12” LLP (Director Borzenkov Aleksandr Petrovich), which produces the following types of extruders (Table 1). Additional equipment: feed mixer, feed hopper, strain gauge system (accuracy ± 50 gr.), and Dryer drum. The design of the extruder with an improved spindle arrangement is one of the developments in “Agrotekhservis–12” LLP. The utility model relates to the field of mechanical engineering, to devices for connecting shafts of power units with shafts of working bodies, and to spindles of devices whose shafts experience both radial and axial loads. An extruder for preparing extruded components for farm animals and birds is such a device (Fig. 1). Spindle of the extruder E-1000 “Bronto” is the closest analogue of the claimed utility model. The operation manual is E-1000 RE, “Cherkasy Elevator Mash” LLC, Ukraine (http://2184.ua.all.biz/ekstruder-e-1000-bronto-g276373) [9]. The spindle consists of an oil-filled housing, a shaft resting near the ends on tworow self-aligning radial roller bearings, and on an axial tapered roller bearing located between them [9–21]. The relatively complex spindle arrangement is a disadvantage of the known analogue containing a large number of parts, which entails not only an increased time for repair work, but also additional difficulties in repairing, replacing failed parts and servicing the spindle. The design of the known spindle is designed for a deliberately wide range of radial and axial loads on its shaft associated with the use of a wide range of feedstock for processing. However, when processing a specific type of raw material, there is no need to use such a complex and expensive device [22–24]. The development goal is to create a spindle that is simpler in design and operation without loss of basic performance characteristics when processing specific types of raw materials. The task is that in the inventive spindle, the spindle shaft is supported by two pairs of ball bearings located near its ends. A pair of deep groove ball bearings is used at one end of the shaft, and at the other end of the shaft, one of the bearings is a thrust ball bearing, and the second is a conventional deep groove ball bearing, also with increased

680

V. Kushnir et al. Table 1. Brief technical characteristics of the extruders.

The name of indicators

Performance 20 kg/h

Performance 70 kg/h

Performance 150 kg/h

Performance 350 kg/h

Performance 500 kg/h

Extruder electric motor power (kW/h)

3

9

18.0

37.0

55.0

Cutter electric motor power (kW/h)

By application

By application

0.75

0.75

1.1

Operating temperature range t, − C°

110–170

110–170

110–170

110–170

110–170

Dimensions (mm): length

1000

1250

1400

1700

2000

width

600

950

950

1200

1800

height

1000

1200

1200

1300

1750

Weight (kg) no 80 more

196

360

450

790

Feed drive

Mechanical

Mechanical

Mechanical

Mechanical forced

forced

Humidity of raw materials in %

14–30

14–30

14–30

14–30

14–30

Cost (tenge)

175 000

396000

764000

1638000

2480000

ultimate load. For example, deep groove ball bearings are single row, light series No. 208, and thrust ball bearings are medium series No. 8308 Table 2. The design of the proposed spindle is shown in Fig. 2. A shaft (3) resting on one end on a pair of deep groove ball bearings (8) is placed in an oil-filled housing (1), and on the other end it is placed on a deep groove ball bearing (8) and thrust ball bearing (6). The choice of specific brands of ball bearings depends on the raw material for which the extruder is designed, and the simplicity of design allows for quick replacement of bearings. The creation of a spindle that is simpler in design is a technical result, which makes it possible to ensure its reliable operation while significantly reducing its cost and operating costs. A spindle consisting of an oil-filled housing, a shaft resting on radial ball bearings located near the shaft ends and a thrust bearing is characterized in that the shaft ends are supported by two pairs of ball bearings, and a pair of radial ball bearings is used at one shaft end, and a pair is used at the second end of the shaft: persistent and deep groove ball bearings (Fig. 2).

Features of Development of Structures of Extruders

681

Fig. 1. General view of the extruder PE-20.

Table 2. Bearing specifications. Series and Bearing No.

Health factor C

Limit rpm

Permissible static load Qst. kg

208

39000

10000

1700

8308

78000

2000

11000

Fig. 2. Spindle Design. 1—housing; 2—centering ring of the front oil seal; 3—spindle shaft; 4—pin for connecting the spindle shaft and screw shaft; 5, 7—intermediate front bearing rings; 6, 8—spindle bearings; 9—retaining ring; 10—hole oil level; 11, 12—rear flanges; 13—spacer sleeve; 14—cam.

The power consumption of the extruder is interrelated with the friction costs in the working bodies when calculating the energy costs of manufacturing products. In the

682

V. Kushnir et al.

steady-state extrusion mode, the power consumption is an indicator of the stability of the process. Typically, control is based on the power consumed by the drive [1, 2]. The power (W) consumed by the extruder (N) is used to move the mass of material along the spiral channel to the head and beyond (N1 ), as well as to cut the material (melt) in the gap between the screw ridge and the inner wall of the cylinder (N2 ): N = N1 + N2 For a screw with a variable cutting depth:  3  π (t − e)Ljη 2 −7 n + A1 Pn N1 = 9, 8 · 10 · t

(1)

(2)

where A1 —is the direct flow constant, cm3 ; n—is the frequency of rotation of the screw, s−1 ; j—coefficient, cm2 2, 3π 2 D5 ln hh23 π 2 D2 − 4t (D + d3 )3 − (D + d2 )3 + 2 J = + π2 3(d3 − d2 ) (t + π 2 + D2 )(h2 − h3 )

(3)

The pressure drop in the head is the sum of the pressure values in those areas as in the calculations of the head resistance coefficient K. The calculation is shown above. The diameter of the screw shaft at the beginning of the pressure zone d2 , cm: d2 = D − 2h2

(4)

Power N2 is calculated as follows: N2 = 9, 8 · 10−7

π 3 D3 eLη 2 n δt

(5)

where L—is the screw length, cm; t—cutting step, cm; δ—is the gap between the cylinder wall and the screw ridge, cm In the power calculation formulas, the melt viscosity η appears, which is found by the shear rate as follows. Shear rate (s−1 ) of the spiral channel of the screw (for N1 ): γck =

π 2 (D − hcp ) · (D − 2hcp ) · n  hcp π 2 (D − 2hcp )2 + t 2

(6)

3) where hcp = (h2 +2 2 The shear rate in the gap between the screw face and the cylinder wall (for N2 ):

π 2 D2 n γσ = √ δ π 2 D2 + t 2

(7)

Features of Development of Structures of Extruders

For a screw with a variable cutting step, the value N1 is calculated:  2  π (d + h)3 d 2 η −7 2 (G − eR)n + A2 Pn N1 = 9, 8 · 10 · h

683

(8)

where G—is the coefficient, cm−1 G=

cos2 ϕ3 π(ϕ2 − ϕ3 ) 2.3 lg 2t cos2 ϕ2 · 360(d + h)

(9)

The angle of elevation of the spiral line at the beginning of the pressure zone ϕ2 is calculated: t2 ϕ2 = arctg (10) π(D − h) The cutting step at the beginning of the pressure zone t2 , cm: t1 + e(i − e) (11) i The angle of elevation of the spiral line at the end of the dosing zone ϕ2 is calculated t2 =

[1]: ϕ3 = arctg

t3 π(D − h)

(12)

The coefficient R, cm2 is calculated: R=

t22 cos2 ϕ2 π(ϕ2 − ϕ3 ) 2, 3 + lg π 2 (d + h) t32 cos2 ϕ2 180(d + h)t

(13)

To determine the viscosity of the melt in the screw channel, it is necessary to know the shear rate (s−1 ): γ =

π2  30h 4π 2 d 2 + (t2 + t2 )2

(14)

Power (W) consumed by a screw with a variable step to cut the melt in the gap (N2 ):    3 3 2 −7 π D (d + h)e 2(t2 − t3 ) + 2, 3t(lg t2 − lg t3 )ηn N2 = 4, 9 · 10 (15) ϕt To determine the viscosity of the melt in the gap between the screw ridge and the cylinder wall [1]: π 2 D2 n γδ =  δ 4π 2 D2 + (t2 − t3 )2

(16)

The engine power N dv of the extruder drive should be higher by an amount of efficiency η = 0,4…0,6 to compensate for unaccounted losses: to overcome friction, mechanical losses in the drive of the extruder: N (17) Ndv = 0, 4 . . . 0, 6

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3 Conclusions The theoretical calculation of bearings for strength is confirmed in practice during experimental work. Thus, the spindle, which is simpler in design and operation, allows, without losing the main performance characteristics when processing specific types of raw materials, to extend the life of the extruder by an average of 22%, in comparison with the base model of the PE-20 extruder.

References 1. Polishchuk VYu, Korotkov VG, Zubkova TM (2003) Designing extruders for agricultural units. Yekaterinburg, 200th 2. Van Zuilichem DJ, Stolp W (1986) Review of existing technologies for the preparation of extrusion products in tode and co-induction. Proceedings of the European Conference: Extrusion technology for the food industry. Dublin, Republic of Ireland: December 9–10, p 1–15 3. Yuriev VP, Zasypkin DV, Bogatyrev AN (1994) Physicochemical principles of extrusion food products. Thermoplastic extrusion: scientific foundations, technologies, equipment. Under the red. chl. RAAS AN Bogatyreva and V.P. St. George, “Step”, Moscow, p 5–24 4. Zubkova TM (2004) Methodological materials for modeling and optimization of single-screw extruders. RAAS, Moscow, p 34 5. Smith OV (1976) Extrusion cooking. In the book: New Protein Products. Corresponding Member of Altscus 2:86–121 6. Guy RG, Home AW (1988) Extrusion and co-extrusion of cereals. In: Nutritional structure. In: Blanchard JMV, Mitchell JR (eds) Its creation and evaluation. Elsevier Applied Science Publishers, Butterworths 18:331–349 7. Yuryev VP, Zasypkin DV, Alekseev VV, YaV Genin, Ezemitskaya MG, Tolstoguzov VB (1990) The structure of protein texturates obtained by thermoplastic extrusion. Narung 34(7):607–613 8. Gruzdev IE, Mirzoev RG, Yankov VI (1978) Theory of screw constructions. Publishing house Leningrad University, Leningad, pp 3–65 9. Operation manual for E-1000 RE, Cherkasy Lift Mash LLC, Ukraine. http://2184.ua.all.biz/ ekstruder-e-1000-bronto-g276373 10. Yun Chen (1993) Development of a method for calculating and studying mixing elements of single screw extruders. Disertation, MGAHM, Moscow, p 169 11. Gore VL, Me Kelvey JM (1958) Theory of screw extruders, Theory of rheology. Appendices, vol. 3, Academic Press, New York 12. Gavrilov NV, Kurmanov AK (2005) Device for the extrusion of roughage. Preliminary patent of the Republic of Kazakhstan for invention 15942, Astana, 15 July 2005, Bill. 7 13. Zubkova TM (1997) Research and optimal design of single screw pressing mechanisms. OSU, Disertation, Orenburg, p 165 14. Kartashov LP, Zubkova TM (2004) Materials on modeling and optimization of single screw extruders. Agropromizdat, Moscow, p 12 15. Kurmanov AK, Isintaev TI, Kurmanov BK, Khasenov YuB, Gavrilov NV (2007) Extruder. Provisional Patent 18519, Astana, 15 June 2007. Bill. 6 16. Gavrilov NV, Gavrilova MN (2008) Extruder for processing feed mixtures. Preliminary patent of the Republic of Kazakhstan 19144. Astana, 14 March 2008, Bill. 3

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17. Gavrilov NV, Shashubaeva AS (2013) Extruder for processing feed mixtures. Innovative patent for inventions 26996, Astana 18. Shilo IN, Romanyuk NN, Ageychik VA, Romanyuk VYu, Gavrilov NV, Kushnir VG, Gavrilova MN (2012) Extruder for processing feed mixtures. Patent for utility model “Republic of Belarus” 8631, 23 Jun 2012 19. Gavrilov NV, Gavrilova MN, Zhantugulov TZh (2008) Extruder for the processing of animal feed. Innovative patent for invention 19896, Astana, 15 August 2008, Bill. 8 20. Gavrilov NV, Zhantugulov TZh, Gavrilova MN (2010) Extruder for the processing of animal feed. Innovative patent for invention 23311, Astana, 15 Oct 2010, Bill. 12 21. Shilo IN, Romanyuk NN, Ageychik VA, Romanyuk VYu, Gavrilov NV, Kushnir VG, Gavrilova MN (2012) Extruder for the processing of animal feed. Utility Model Patent of the Republic of Belarus 8564, 28 Feb 2012 22. Gavrilov NV, Makarov SV (2013) Extruder for the processing of animal feed. Opinion on the grant of an innovative patent 27084, Astana, 05 Nov 2013 23. Kushnir VG, Gavrilov NV, Kim SA (2017) Experimental studies of the extrusion process of grain material. Eng Proc 206:1611–1617 24. Mauser F, Pfaller V, Van Lengerich B (1986) Technological aspects associated with specific changes in the characteristic properties of extrudates during HTSC extrusion cooking. Proceedings of the European conference: extrusion technology for the food industry, Dublin, Republic of Ireland, December 9–10, p 35–53

Research of Dynamics of Seat Air Suspension with Possibility of Vibration Energy Recuperation Under Action of Typical Harmonic Disturbances M. Lyashenko, P. Potapov(B) , and A. Iskaliev Volgograd State Technical University, 28, Lenin Avenue, Volgograd 400005, Russia [email protected]

Abstract. This paper presents the results of the modeling of the new system of the seat suspension operation. The advantages of the proposed suspension system are potentially good vibration insulation characteristics and the possibility of vibration energy recuperation. The main feature of the proposed system is the application of additional air volumes and the air motor connected to the tachogenerator for the recuperation of vibration energy in electric energy. Harmonic kinematic disturbances (a sinusoidal signal with various frequencies and amplitudes) were used to research operation of the proposed seat suspension. The results show that this seat suspension can effectively operate in most considered conditions and have better vibration insulation characteristics than a standard seat suspension. Moreover, the inner processes of seat suspension were studied and the values of recuperated energy are presented. The values of transmissibility for various conditions are also presented. Keywords: Seat suspension · Vibrations · Vehicle · Energy · Recuperator

1 Introduction At the present stage of the evolution of prospective wheel and tracked vehicles power ability, operational speeds and technological universality increase at the background of strict requirements to performance characteristics. It results in increased dynamical loads, more sophisticated and wider amplitude-frequency specters of disturbances on chassis, transmission, frame, cabin, and seat. An operator in his workplace suffers from various danger factors, namely, noise and vibration during work operations. These factors lead to health deterioration, fast fatigability, and decreasing of productivity. Thus, the development of advanced seat suspension systems is a topical problem. Existing standard seat suspensions protect the operator from vibrations by the dissipation of vibration energy in unregulated damping elements (transformation of this energy in heat). Thus, the vibration energy can be potentially stored and used or transformed. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_79

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So, the research of ways for improvement of characteristics of protection from the vibration of seat suspensions by using controllable elastic-damping system with vibration energy recuperation, that is, transforming of this energy into a useful one [1–11] is topical.

2 Model Description Authors proposed the seat air suspension [12] with the possibility of vibration energy recuperation (Fig. 1).

Fig. 1. Modeling scheme of proposed seat suspension: 1—mass on suspension; 2—air spring; 3— controllable electropneumatic valves; 4, 5—additional air volumes; 6—air motor (recuperator); 7—shock absorber; F grav —gravity force; Fspr—air spring force; F fr —friction force; M C — resistance (load) torque; Fa—inertia force.

The proposed seat suspension system includes the standard mechanism: scissor-type levers as the direction device, the air spring and the shock absorber, and additional proposed mechanism: two additional air volumes, controllable valves, and the air motor. The air motor can be used to drive an electric generator that is for recovering vibration energy to electric energy. Optimization analysis provides defining of capacities of additional air volumes. The capacity of these volumes is V 1 = V 2 = 4V p or V 1 = V 2 = 8V p in presented research. Here V P is the full capacity of the air spring. The mathematical model of the proposed seat suspension developed for computational research is described in [13]. Work of the standard shock absorber 7 and valves 3 provides absorption of vibration energy. Valves 3 open as follows: one of the valves transmits air from the spring volume 2 to the first volume 4 at the end of the pressure stroke, and another valve—from the second volume 5 to the spring volume 2 at the end of the rebound stroke. The air motor 6 (the energy recuperator) is installed between the additional air volumes 4 and 5. This recuperator performs useful work by the variable pressure difference of air pressure in mentioned air volumes. But this paper presents the research results obtained on the

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model of the seat suspension that doesn’t include the hydraulic shock absorber because preliminary research showed its disadvantages. DC tachogenerator TDP 0.2 LT-6 produced by Baumer [14] is used as the load device for the air motor in the presented model. Table 1 presents the main electric and mechanical characteristics of the tachogenerator. Table 1. Characteristics of DC tachogenerator TDP 0.2 LT-6. Parameter

Value

EMF gradient, mV/rpm

10

Assumed active load resistance in circuit at generator shaft speed ≤3000 rpm, Ohm ≥0 100 Anchor active resistance (at 20 °C), Ohm

3

Maximal speed of generator shaft, rpm

10000

Mass, kg

2.4

Generator shaft inertia moment, kg * m2

0.00011

The external load toque acting on the rotor of the air motor from the generator drive is calculated on the formulae, Nm (1): ML =

E2 , ω · (RA + RL ) · ηg

(1)

where E—EMF of the generator, V; RA —the anchor resistance, Ohm; RL —resistance in the load circuit, Ohm; ηg —generator efficiency (≈40% for micromachines with power up to 10 W [5]).

3 Research Results Range of numerical researches was made for verification of the possibility of use of the proposed method for controlling the elastic-damping characteristic of the seat suspension. The control is based on the correction of the characteristic at the ends of pressure and rebound strokes by the system, which includes additional air volumes. The valve system controls the airflow between mentioned air volumes. This airflow also drives the air motor to provide vibration energy recuperation. The developed mathematical model was the base for research of operation of the proposed seat suspension [12–15] under the action of the harmonic kinematic disturbance. Figures 2, 3, 4, 5 present examples of the obtained results. The research results show that amplitude of absolute displacement and acceleration of mass on the proposed seat suspension depend on the duration of the launch stage and steady operation of the pneumatic drive for vibration energy recuperation. If the drive constantly performs useful work, then mentioned amplitudes decrease. In the resonance and further in the underresonance zones of the disturbance frequencies (up to 1.2 Hz), the drive doesn’t have enough air pressure difference in additional air

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Fig. 2. Graphs of absolute accelerations of the mass on the standard and proposed air suspensions obtained under the action of the simulated harmonic sinusoidal signal with the frequency: a 1.2 Hz; b 1.6 Hz; c 2 Hz; d 6 Hz.

volumes which is necessary for fast launch. The suspension stroke with the determined vibration frequency and also the completeness of activation/deactivation of controllable valves create the necessary pressure difference. Existence of moment of resistance forces and loads causes stopping of the air motor. It is also influenced by the absence of conditions for creating timely pressure difference in additional volumes. Hence, mean-square values of absolute displacements and accelerations of the mass on the proposed seat suspension exceed similar parameters for the standard suspension in the described time range (as shown in Fig. 2a–d). Removal of the hydraulic shock absorber from the design led to the mentioned effect. Figure 4a–d presents characteristics of the processes in the suspension system under the action of described signal with various frequencies. It is possible to distinguish on the base of operation principal [12] several stages in the operation process of the system: pumping, the launch of the air motor (recuperator), and stable operation of the air motor. These stages influence the efficiency of energy recuperation process and operability of the suspension system. Necessary time for the recuperator launch decreases along with increasing of disturbances frequency. So, at the frequency 1.2 Hz time for the first launch is 3.4 s, and for the second—5 s, at the frequency 1.4 Hz—2.9 s, at the frequency 1.6 Hz time for the first launch is 2.8 s, and for the second—2.4 s, at the frequency 2 Hz—2.5 s, at the frequency 4 Hz—2.2 s, at the frequency 6 Hz—2 s, at the frequency 10 Hz—1.8 s.

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Fig. 3. Graphs of useful recuperator power, activation/deactivation of controlled valves and pressures in the spring volumes and additional volumes of the proposed seat suspension obtained under the action of the simulated harmonic sinusoidal signal with the frequency: a 1.2 Hz; b 1.6 Hz; c 2 Hz; d 6 Hz.

Fig. 4. a Transmissibility of the proposed seat suspension without the hydraulic shock absorber, with additional air volumes V 1 = V 2 = 4V p at the amplitudes of external kinematic harmonic disturbances:1—A0 = 0.015 m; 2—A0 = 0.02 m; 3—A0 = 0.025 m; b the average power of the recuperator at the harmonic action on the proposed seat suspension without hydraulic shock absorber, with additional air volumes V 1 = V 2 = 4V p at the amplitudes: 1—A0 = 0.015 m; 2—A0 = 0.02 m; 3—A0 = 0.025 m.

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Fig. 5. a Transmissibility of the proposed seat suspension without a hydraulic shock absorber, with additional air volumes V 1 = V 2 = 8V p at electrical resistances in the generator circuit: 1—RH = 100 ; 2—RH = 150 ; 3—RH = 1000 ; b Average power of the recuperator under the action of harmonic disturbance on proposed seat suspension without hydraulic shock absorber with additional air volumes V 1 = V 2 = 8V p at electrical resistances in the generator circuit: 1—RH = 100 ; 2—RH = 150 ; 3—RH = 1000 .

At the frequency of the harmonic disturbance 1.6 Hz (Fig. 3b), unstable work of the air motor is observed. The incompleteness of the opening/closing of controlled valves causes this unstable work. Disturbances with the frequency above 1.6 Hz (Fig. 3c, d) create conditions for stable operation of the air motor and hence for lesser mean-square values of amplitudes of absolute displacements and accelerations of mass on the proposed seat suspension in comparison with similar parameters of the standard seat suspension. Further influence of amplitude of external kinematic harmonic disturbances on characteristics of transmissibility (transmission coefficient) and average power of recuperation of the proposed seat suspension without a hydraulic shock absorber was researched (Fig. 4a, b). Increasing of the amplitude of the kinematic disturbance on the proposed seat suspension without a hydraulic shock absorber in the range from 0.015 m to 0.02 m leads to narrowing of the resonance zone. Transmissibility H(f) increases by 4% at the frequency 1.2 Hz (Fig. 4 a). Further increasing of disturbance amplitude up to 0.025 m led to decreasing by 1.2 times of maximal transmissibility H(f) down to value 1.546 and shift of resonance frequency from 1.2 to 1 Hz. The tendency of increase of the level of the recuperator average power along with increase of disturbances amplitude is observed almost in the whole frequency range from 1 Hz to higher. Maximal power 1.09 W was obtained at the disturbance amplitude A0 = 0.025 m at the frequency 6 Hz. Figure 5a, b presents the influence of an electrical load in the generator circuit on dependences of transmissibility and average power of recuperation of the proposed seat suspension from the frequency of harmonic disturbances. Change of electrical load resistance in the generator circuit has a small influence on the dependence of transmissibility of the proposed seat suspension from the frequency

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of kinematic harmonic disturbance. There are only some exceptions: frequency bands 1.6 and 2 Hz. Decreasing of active electric resistance in the generator circuit reduces transmissibility in those bands (Fig. 5a). Computational research shows that increasing of active load resistance in the generator circuit leads to reducing of the average power of the recuperator in almost whole considered frequency ranges of kinematic harmonic disturbances on proposed seat suspension (Fig. 5b).

4 Conclusions Computational research shows that the proposed scheme of the seat suspension system provides energy recuperation and also decreases vibrations of the spring mass. The most effective regime for operation of the proposed seat suspension is at disturbances with frequencies values above 1.6 Hz. The action of disturbances with amplitude 0.025 m and frequency 6 Hz can provide maximal recuperated energy. Also, the next ways for improving recuperation efficiency were found as a result of the research: • • • • •

using small additional air volumes; selecting optimal electrical load (active electric resistance) on the generator; minimizing air leakages from the system; decreasing inertia moment of the drive; decreasing “bad” resistance torques acting on the generator rotor (friction torques); etc.

In addition, the experimental research for the model verification was performed and model was accepted reliable. Further research would be aimed at the modeling other regimes of the suspension operation and system optimization.

References 1. Tiwari G, Saxena RK (2015) The regenerative energy suspension system. Int J Sci Eng Res 6(4):1249–1254 2. Segel L, Lu XP (1982) Vehicular resistance to motion as influenced by road roughness and highway alignment. Australian Road Res 12(4):211–222 3. Pan GY, Hao XL (2011) Research on active control of driver’s seat suspension system. In: International conference on vibration, structural engineering and measurement (ICVSEM 2011). Appl Mech Mater 105–107:701–705 4. Maciejewski I (2012) Control system design of active seat suspensions. J Sound Vib 331:1291–1309 5. Huseinbegovic S (2009) Adjusting stiffnes of air spring and damping of oil damper using fuzzy controller for vehicle seat vibration isolation. In: International Siberian Conference on Control and Communications (SIBCON – 2009), 27 March 2009 – 28 March 2009, Tomsk, Russian Federation, pp 83–92 6. Chernyshev VI (1994) Improvement of work conditions of vehicles operators by means of development and implementation of vibration protection systems with impulse control. Dissertation, Saint-Petersburg

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7. Posmetyev VI, Drapaluk MV, Zelikov VA (2012) Estimation of efficiency of application of system recovery of energy in car suspender. Scientific J KubSAU 76(02):1–14 8. Pozhidaev YuA, Kadoshnikov VI, Savochkina LV (2011) Damping devices designing for energy recovery. Vestnik Magnitogorsk state technical university named after G.I. Nosov 3:80–83 9. Pilipenko MV (2008) Rzrabotka matematicheskoi modeli avtonomnoy pnevmaticheskoy podveski siden’ya voditelya transportnogo sredstva c pryamym vkluchenniem vibrozashitnogo (Development of a mathematical model of an autonomous air suspension for a driver’s seat of a vehicle with direct inclusion of vibration protection). Tekhnicheskaya mekhanika 1:38–49 10. Liviu Serbu, Chandra S. Namuduri, Christopher J Mettrick, Joseph K Moore (2013) US Patents 8448952, 28 may 2013 11. Koenraad Reybrouck (2016) US Patent 9481221, 1 November 2016 12. Lyashenko MV, Shekhovtsov VV, Potapov PV et al (2018) RUS Patent 177004, 06 February 18 13. Lyashenko MV, Shekhovtsov VV, Iskaliev AI (2017) Mathematical model of a pneumatic relaxation of seat suspension with energy recuperation. Tract Agricult Mach 4:30–37 14. Lyashenko MV, Shekhovtsov VV Fedyanov EA et al (2019) Mathematical model of vehicle seat vibrations with energy recovery by means of a pneumatic consume. Energy Res Sav: Ind Trans 3(28):10–18 15. Lyashenko MV, Iskaliev AI (2018) Vibroprotection characteristics of the seat suspension with the possibility of vibration energy recuperation. In: Kalyaev IA, Chernous’ko FL, Prokhodko VM (eds) Progress of vehicles and transportation systems -2018. Intl. Scientific-practical conference, Volgograd, 9–11 October 2018, pp 71–73

Functional Tuning of Car Suspension D. Kushaliyev1(B) , L. T. Shulanbayeva1 , and B. A. Ermanova2 1 Zhangir Khan West Kazakhstan Agrarian Technical University, 51, Zhangir Khan Street,

Uralsk 090001, Kazakhstan [email protected] 2 Kazakhstan University of Innovative and Telecommunication Systems, 81, Manshuk Mametov Street, Uralsk 090000, Kazakhstan

Abstract. The reliability analysis of the car chassis showed that its elements have different durabilities within the operational period, i.e., some of them serve the entire life cycle or a significant part of it, while others have frequent turnover. These include non-recoverable elements, in particular, silent blocks and shock absorbers, the typical failure cause of which is wear and fatigue of the silent block and piston seal of the shock absorber. The equal resource increase and achievement of suspension unit characteristics in operating conditions can be obtained by improving the technology of restoring their working capacity by replacing worn-out elements with repair kits based on the new principles of tribocoupler operation. Thus, the studies are aimed at the development and implementation of suspension repair kits for silent blocks and piston seals of shock absorbers in the technological process of repairing the suspension. This makes it possible to increase the life of the vehicle suspension elements. Keywords: Bearing details · Ratchet effect · Spring liner · Gap

1 Introduction Work reliability and quality of technological and transport machines largely depend on the operational characteristics of plain bearings. The most important factor affecting the reliability of road transport to a large extent is the technical condition of the chassis. The basis for the improvement of automobile suspension elements is the result of theoretical and experimental studies of the design of a sliding bearing with a conical spring bush of the silent block and the technology of its manufacture, which ensure the achievement of operational characteristics of bearings at the level of the best world models, as well as the improvement of piston coupling of the shock absorber.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_80

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2 Relevance The analysis showed that bearings and shock absorbers are non-recoverable elements that absorb the largest share of wear. Improving their durability and manufacturing efficiency is a significant and urgent task. In a car, various groups of parts and assemblies are not equally reliable, some of them serve the entire maintenance cycle, others are part of it, and still others work very little time compared to the life of the car before overhaul [1–19]. In order to increase the durability and uniform reliability of the suspension units, it is necessary to improve these units with the restoration of their operability by using an upgraded repair kit. This approach is called a functional tuning [6].

3 Formulation of the Problem Theoretically substantiate the functional tuning of the restoration of the performance of the silent block and piston seals of the shock absorber by replacing the worn parts with conical spring inserts.

4 Theoretical Part The car tuning operation, the technical condition of its systems, and assemblies changes were the main reasons for which various types of wear such as plastic deformation, fatigue and temperature failure, fretting corrosion occur [7, 8]. This can lead to complete or partial loss of operability of the unit or part of the car, that is, to its failure or malfunction [9]. During operation, failures and malfunctions arise, the elimination of which is carried out through preventive and repair work, as well as through functional tuning. Preventive work is designed to maintain the product in good condition and prevent the occurrence of a failure, while repair work is aimed at restoring performance as a result of its occurrence, and functional tuning can also change and improve the performance of components and assemblies. The proposed design of the sliding bearing for the reciprocating motion of Fig. 1 consists of a shaft 1, an outer ring 2, and a spiral insert 3 located between them in the form of a coil spring. The spiral insert is made movable, conical with a cone angle of 1° to 5°, while the diameter of the spring wire d is equal to half the gap between the shaft diameter D and the diameter of the insert bore D + 2d . In addition, it is installed with an interference fit on the ends, as well with an interference fit on the inner and outer surfaces to ensure the constancy of the “ratchet effect” [10]. A patent [11] has been obtained for this design of a plain bearing for a reciprocating motion. The conical spring in the silentblock is designed to relieve the stresses in the rubber of the silent bobbin that arise when the load on the car changes, as well as a result of compression-rebound forces that occur on the road irregularities. Since the silentblock is fixed rigidly, there are strains in its rubber bushing that tend to break the rubber. Therefore, the spring insert, when the load is changed, will rotate in the desired direction, thereby relieving the stresses in the rubber bush of the silenblock, which in this design is intended

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Fig. 1. Conical sliding bearing for reciprocating rotary motion.

only for damping the forces, and does not work on twisting. This prolongs the life of the silentblock, which often breaks down much earlier than the shock absorber itself. Then calculating the conical spring conical liner, we assume that the spring is made up of a 65G spring wire of square cross section with a square side of 1,4 mm, and this wire was chosen because it is most suitable for the manufacture of a spring bush of the silent block of the rear shock absorber of a VAZ family car. When calculating the conical spring insert, the following assumptions are made: • absolute linear deformation of the spring fx is equal to 1 mm due to the insignificance of deformation of the spring liner in the silent block; • the length of the spring in the loaded state Hx is equal to H0 , since the spring is not loaded; • the angle of rise of the turns of the spring liner in the unloaded (free) state is adopted x = 1.83°; and • the initial angle of elevation of the axis of the helical beam of an unloaded spring α = α0 . Since the spring insert can be represented as a hard beam, the bending stiffness of the beam during bending can be calculated by the following formula: B = Eba3 /12

(1)

Since, in our case, the cross section of the used spring wire is a square, i.e., a = b. Further calculation was performed by the presented sequence of the spring liner as a rigid beam. Bending rigidity is B = Ea4 /12

(2)

where E = 20 × 104 MPa is the elastic modulus of the first kind. The torsional stiffness of the beam can be calculated by the following formula: C = ηba3 G = ηba3 E/2(1 + μ)

(3)

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Since a = b, then this formula can be represented as follows: Torsional rigidity: C = ηa4 G = ηa4 E/2(1 + μ)

(4)

where μ is the Poisson’s ratio of the material of the parts. Height (length) of spring in unloaded condition is l0 = π D0 / cos0

(5)

The working part length of the spring liner is H0 = l0 sin α0

(6)

Axial force, conical spring is compressed to the following limit: Pcb =

4 cos2 α0  cos0  ) C(sin α − sin α ) − B sin α(1 − 0 cos α D02

(7)

Permissible bending moment is given below: M = M0 = −

PD0 (B − C) sin 2α0 4(B sin2 α0 + C cos2 α0 )

(8)

The average value of the torsion of the spring is R = M /F

(9)

Return force when loading a conical spring with a constant step to Hx height is Fx =

fx · 2 · C + r) · (r2 + r1 )2

p · n · (r22

(10)

where fx = H0 − Hx ; x = 1, 2, 3; r1 r2 —the smallest and largest nominal average radius of the working part of the conical spring coil. Draft by P force of the conical spring is    P 4 0, 25(H0 − Hm ) 3 Pn.l. · 4−3· − n (11) λ≈ (1 − n) P Pn.l. where (r2 −r2 )ia, i—number of working turns; the force at which the drawdown begins. Hm is height of fully compressed conical coil spring which is given as follows:  Hm = (ia)2 − (r2 − r1 )2 (12) n= n—number of working spring turns.

r1 r2

(13)

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The calculated important value, affecting the durability of a tapered bearing, is the  permissible increase in the diameter D (padiyca f , ) of the spring ring, which in its final form is given as D(λ) = −



   1 cos(2α0) sin(α0)2 2 cos(2α0) λ2 − + −M 2C 2 cos(α0) C B 4B cos(α0)2

Pλ3 sin(α0 )

(14) The objective of experimental studies [12] was to study the effect of temperature and piston speed on the compression and rebound forces, i.e., the force on the rod during compression of the shock absorber and the force on the rod during rebound shock absorber.

5 Practical Significance Practical significance: The proposed repair set can be used in traditional (conventional) bearings, which consists in increasing the durability of the plain bearings by using conical spring liners in them. The innovative repair kit that is being developed facilitates the assembly of the product and improves its performance. The life of the sliding supports for the reciprocating-rotational motion applied in the upgraded silentblock shock absorber. The practical significance lies in the fact that it is easy to manufacture, assemble, and replace during repair after operation, and there is no process of jamming the bearing. Factories are tasked with increasing the reliability of car parts and assemblies. During the operational period, there are needs for various types of services, including external tuning, internal tuning, chip tuning, and motor tuning [6]. Functional tuning is designed to approximate the equidistance of various parts and assemblies that designers did not provide at the design stage, for example, turbochargers, cardan joints, shock absorbers, etc. Functional tuning also involves the use of repair kits in vehicle assemblies and units, for restoring their efficiency and often increasing their operational durability. When the temperature increases, the lubricant becomes more fluid, as a result of which the rebound and compression forces of the shock absorber can change. At a low temperature, the oil thickens, and hence the shock absorbers will transmit shocks and vibration to the car body and be delayed during the recoil process. From this, the comfort of the machine will deteriorate, and cracks may appear in the places where the shock absorbers are attached to the body, as well as dynamic loads on components and parts will increase. The speed change can also affect changes in compression and rebound forces, which in turn will affect the performance of the shock absorber. Figure 2 shows the shock absorber with a sealing element in the form of a spring insert which has a better compression and rebound response than the standard shock absorber. It follows that the replacement of the sealing element actually significantly affects the characteristics of the shock absorber, and to a greater extent it is affected by the condition of other elements (valves, etc.). However, the use of a spring sealing element will positively affect the life of the shock absorber, since the spring sealing element will provide more accurate and durable coupling of the piston-cylinder group

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Fig. 2. Piston assembly with copper-plated spring seal 65G steel grade

and, in addition, can be used in power hydraulic cylinders of transport technological equipment. The proposed innovative repair sets can be used in railway and automobile transport in suspension units, shock absorbers, steering, cardan shaft, in bearing units of aircraft, electrical contractors, sewing, mining, oil- and gas-producing and processing industries and some other, where traditional sliding and rolling bearings are used for heavy loads in a return-rotational mode. An innovative repair set, the main difference of this repair set is the provision of elastic interference instead of a gap on its working surfaces. The bearing is provided with a movable liner in the form of a helical conical spring (intermediate element), which in the oscillatory mode is forcibly rotated only in one direction and thus uniform wear and distribution of the lubricant are achieved: (1) reduction of the adhesion component of friction and (2) ratchet effect. The developed repair set allows you to automatically obtain the required interfaces, which, in turn, facilitates the assembly of the product and increases its efficiency. The durability of the sliding supports for the reciprocating-rotational motion is increased by two times. It is possible to use the results in another subject area—equipment for the extraction of oil, gas, and rocks.

6 Conclusions This design of a sliding bearing for reverse rotation has the following advantages: • it uses a spring piston ring, and hence a good sealing is ensured due to the labyrinth effect; • it increases the durability of the piston pair due to the use of tribological effects; • it increases the reliability and safety in operation due to the stability of rotation of the spring liner using the “ratchet effect”; • it reduces the cost of manufacturing and assembly of the product due to automatically obtained mates of the working surfaces, as well as by reducing the accuracy of manufacturing of the working surfaces of the parts;

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• it remains possible to adjust the compression of the spring liner during repair in order to compensate for wear; • the scope of use is expanding: this bearing can be used in various nodes of transport vehicles: shock absorbers, cardan shaft joints, in pivot suspension, steering units, etc.; • the durability of the bearing increases for two or three times due to the increased stability of the effect of non-toxicity, which is absent in the known designs of bearings; • it improves the distribution of lubricant due to the effect of the “oil siding thread”; • the repair and restoration of units are facilitated—the new bearing design allows the use of old parts (with traces of “false marking”) complete with new bearings of an unconventional design; • the bearing is easy to manufacture, assemble, and replace in case any repair occurs during its operation; and • it increases the turnaround mileage for two or three times.

Acknowledgements. The work was carried out within the framework of grant financing of the scientific project IRN: № AP 05133348.

References 1. Kragelsky IV, Dobychin MN, Kombalov VS (1977) Basics of calculations for friction and wear. Machine-building, p 526 2. Strecker William (2004) Troubleshooting Tilting Pad Thrust Bearings. Machinery Lubrication magazine, March-April 3. Sinanoglu Cem, Nair Fehmi, BakiKaramıs M (2005) Effects of shaft surface texture on journal bearing pressure distribution. J Mater Process Technol 168:344–353 4. Strecker William (2004) Failure analysis for plain bearings. Machinery Lubrication magazine, July-August 5. Yang BS, Lee YH, Choi BK, Kim HJ (2001) Optimum design of short journal bearings by artificial life algorithm. J. Tribol Int 34:427–435 6. Denisov AS (2015) Reliability of automobile engines in harsh climates and the potential of functional tuning. Scientific Rev 91–99 7. Prokhorov BV, Kostenkov VL, Chvanov AI et al (1989) Car VAZ-2108, 2109 and their modifications: technology for maintenance and repair, 2nd edn. Auto VAZ maintenance, Tolyatti, p 578 8. Smirnov VL, Prokhorov YuS, Boyur VS et al (2002) VAZ cars. Engines and their systems. Technology of maintenance and repair. ATIS, N. Novgorod, p 83 9. Savelyev VV (2005) Perfection of a car service by intensification of a preventive strategy: On the example of front-wheel drive VAZ cars: abstract of candidate thesis of technical sciences: 05.22.10. Volgogr. State tech. un-ty, Volgograd, p 163 10. Kushaliev DK, Vinogradov AN, Salimov BN, Hamsin AM, Adilova NB, Narikov KA (2014) Development of new friction bearing for swinging movement in knots of transport equipment and its processing by superfinishing. Life Sci J 11(1):286–290 11. Vinogradov AN, Kuranov VG, Kuranov VV, Kushaliev DK, Lin’kov ED (2013) Sliding bearing for reciprocating rotary motion. RU Patent 2499920, November 2013

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12. Vinogradov AN, Karakozova VA (1998) The methodology of experimental studies of transmission grease TAD-17 after exposure to low-energy laser and microwave fields. Restoration and hardening of machine parts: interuniversity. Scientific Collection; Sarat. State tech. un-ty, Saratov, p 6–11 13. Kostetsky BI (1970) Friction, greasing and wear in cars. Kiev, Technique, p 296 14. Kostetsky BI (1950) Durability of car details. Mashgiz, Kiev, Moscow, p 168 15. Kostetsky BI (1976) Superficial durability of materials at friction. Kiev, Technique, p 326 16. Spitsin NA, Sprishevsky AI (1961) Rolling bearings: help guide edited by. State scientifictechnical publishing house of mechanical-engineering literature, p 828 17. Borisov VI, Gor AI, Gudov VF (1972) Car “Volga” GAZ-24. Mechanical engineering, Moscow, p 384 18. Kuranov VG, Vinogradov AN, Denisov AS (2000) Depreciation and wea-free: monograph. Univ, Saratov, Saratov State tehn, p 136 19. Vinogradov AN, Kuranov VG (2003) Friction bearings for swinging movement on the basis of new tribological principles and effects. Interhigher education institution. sci.collection, Saratov State tehn. Univ, Saratov, Restoration and hardening of car details, pp 175–182

Approaches to Formation of Car Service Modes in Case of Complete or Insufficient Information on Operational Reliability of Car Elements M. Grigoriev(B) and V. Zenchenko Moscow Automobile and Road Construction State Technical University, 64, Leningradsky Prospect, Moscow 125319, Russia [email protected]

Abstract. The theoretical prerequisites and approaches to improving the methods for the formation of rational modes of servicing car elements at the initial stage of their using, which is characterized by a limited amount of information about the reliability of the elements under study (Stage I—production and start of operation), and their subsequent operation with the accumulation of information on reliability to a necessary amount (Stage II—subsequent operation) are considered, which allow ensuring a qualitative improvement of the developed standards. The calculation of the optimal modes of servicing car elements at the initial stage in the conditions of limited information on reliability (CLIR), which is done based on the use of minimax service strategies, is given. This problem was presented and solved from the point of view of the regenerating aperiodic process, which provides for the transition of car elements from a faulty state to a working one. A characteristic of the quality of functioning of the service strategy under study is a linear-fractional functional, which is the average specific loss. Since under the CLIR of car elements, the probability of failures is only partially known, the determination of optimal service modes is to find a guaranteed average gain, i.e., minimum specific losses. The calculation results of the studies based on the developed methodology confirmed that the obtained service intervals in the CLIR of new car elements have a high degree of reliability, and the obtained optimal periodicity of maintenance decreases. Keywords: Car service · Service modes · Reliability of car · Limited information · Minimax strategies

1 Introduction In modern conditions, active promotion of new models of cars of domestic and foreign production is carried out. The costs of maintaining operability and the level of reliability in the operation of cars equipped with new elements largely depend on the validity of the standards for their maintenance and repair. At the same time, it is important to reduce the time required for the development of scientifically based standards and their prompt © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_81

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correction in accordance with the actual conditions of car operation. Thus, it provides an increase in the operational reliability of vehicles with a reduction in the cost of its maintenance.

2 Research Methods In the process of formation of rational car service modes, the implementation of the following main steps is required [1]: • determination of the necessary list of preventive maintenance and repair works [2, 3]; • determination of labor costs during the maintenance and repair of a vehicle according to the formed list of works; • selection of the necessary technological equipment for maintenance and repair; • determination of optimal frequency of car service; and • formation of homogeneous groups (classes) of periodicities according to the list of maintenance and repair works with their subsequent assignment to a certain type of service or scheduled preventive maintenance [4, 5]. At the same time, the elements (assemblies, components, parts) of a vehicle that are of “critical reliability” or limiting reliability, by which the formation of rational service modes are carried out, are preliminarily identified [6]. Determining the optimal intervals for servicing car elements can be based on the use of approaches and methods in the conditions of A—complete availability of information on the reliability of car elements; B—limited information on the reliability of car elements; C—in the absence of information about it. Below are the principles and methods for implementing the issues under consideration in the framework of approaches A and B, i.e., in conditions of both complete availability of information on operational reliability and with its limitedness. In the first approach (A), which provides for the determination of the optimal service intervals for car elements in the presence of information about their operational reliability, the initial data for the implementation of the task in question are • • • •

mean time between failures (MTBF)—L; coefficient of variation of MTBF—ν; cost of monitoring the technical condition—C; cost of repair work aimed at eliminating failures (including the cost of spare parts and labor costs)—Sr .

For the presented initial data, the optimal periodicity of the element under consideration is determined from the expression, according to [7–9]  ν 2Kp ν  · L, (1) L=  1 + ν 2 (1 + ν)

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where Kp —coefficient taking into account the ratio of the costs of monitoring the technical condition and the cost of eliminating failures. Kp =

C . Sr

(2)

The implementation of such a technique gives fairly accurate results for ν ≤ 0.5 and Kp ≤ 0.4. With an increase in ν and Kp , the periodicity of maintaining the car element approaches the mean time between failures. Let us consider an example of determining the optimal periodicity of maintaining the car element for the following initial data. Based on the results of a complete finished cycle of reliability tests of the i-th element of the car, the following statistical characteristics of reliability indicators were obtained: • • • •

mean time between failures—L = 50 thousand km; coefficient of variation of MTBF—ν = 0.3; cost of monitoring the technical condition—C = 0.6 thousand c.u.; cost of repair work aimed at eliminating failures—Sr = 3.1 thousand c.u.

For the noted initial data, the coefficient taking into account the ratio of the costs of monitoring the technical condition and the cost of eliminating the failure will be Kp =

0.6 = 0.194. 3.1

The optimal maintenance interval of the considered car element, determined according to expression (1), will be  L=

2 · 0.194 · 0.3   1 + 0.32 (1 + 0.3)

0.3 · 50 = 23.6 thousand km.

A graphic illustration of the change in the optimal periodicity depending on the coefficient of variation ν is presented in Fig. 1, which shows that with its growth, the frequency of service should decrease. At the same time, under conditions of intensive modernization and updation of the model range of cars, it is not possible to obtain a full amount of information about their operational reliability at the initial stage of operation, which is the basis for the formation of preventive maintenance procedures for vehicles in order to reduce the cost of maintaining them in good condition. This requires the development and practical implementation of special applied methods that allow formulating and promptly adjusting the modes of servicing car elements in the conditions of an early period of their operation and the availability of a limited amount of information about operational reliability (approach B) [10]. Under these conditions, at the initial period of production and operation of a vehicle, the formation of optimal service modes can be carried out on the basis of the use of optimization methods based on the use of minimax service strategies, which provide optimal values of the indicators of operation of the car elements for the worst-case characteristics of their reliability. The noted principles allow us to trace the

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Fig. 1. Change in the periodicity of maintaining the car element depending on the time between failures.

improvement of service indicators as the completeness of the used information about the reliability of the system increases. At the same time, the minimax (maxmin) value provides guaranteed quality indicators, since for the selected periods and the frequency of preventive and restoration work of any option from a given class of reliability characteristics, the quality indicators are not greater (for minimax) or not less (for maxmin) than these values. The solution to this problem is considered from the point of view of the regenerating aperiodic process, which provides for the transition of the car elements from a faulty state to a working one. The random process, X(t), which describes the states of the elements under study and the diagram of its transitions are presented in Fig. 2. A characteristic of the quality of functioning of the service strategy under consideration from the point of view of representing the process X(t)  as regenerating is a linear-fractional functional, which is the average specific losses ¯ (Q, F) determined by the ratio of total losses to the time of normal functioning of the system during the regeneration period, i.e.,

Fig. 2. Transition diagram of X(t) process.



∞∞ (Q, F) = 0∞ 0∞ 0

0

(x, y)dQ(x)dF(y)

D(x, y)dQ(x)dF(y)

,

(3)

 where (Q, F)—average specific losses during the regeneration period; Q(x)—the distribution function of planned preventive measures; F(y)—the function of the probability of failure; D(x, y)—the function of the average time that the process X(t) spent in states

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 A0 and A1 ; and (x, y)—the average loss function for the process X(t) in states A2 and A3 . Since the probability of failures is only partially known in the conditions of limited information on the reliability of the car elements [11–13], the determination of the optimal intervals for monitoring the technical condition consists in finding the guaranteed average gain (minimum specific losses) from the following condition: 

 Q∗ , F ∗ = min

max

Q∈G F∈G(n,y,p)



(Q, F),

(4)

where G(n,y,p)—a class of distribution functions that at given points y = (y0 , y1 , …, yn ) take the values of the failure probabilities P = (p0 , p1 , …, pn ) and n—the number of points of the function F(y) underconsideration. In functional (3), the losses (x, y) are proportional to the time spent by the car in states A2 and A3 , and the function D(x, y) is the time spent in the states A0 and A1 , for which ⎫    SΣa = Sa · Ta + Ss.p. , when y ≤ x ⎪ ⎪ ⎪ (x, y) = ⎪ CΣp = Cp · Tp , when y > x ⎬ (5)

 , ⎪ x, when x ≤ y ⎪ ⎪ ⎪ D(x, y) = ⎭ y, when x > y where Ta—time spent on repair (a) work; Sa—loss per unit of time during the repair (expressed in terms of the cost of a standard hour); Ss.p.—the cost of spare parts (cost of the replaced part of a car); Tp—time spent on preventive (p) work; Cp—loss per unit of time during preventive work; and C Σp and S Σa —absolute costs during the control and diagnostic, preventive and repair work. For fixed intervals of preventive inspections Q(x), functional (3) is linearly fractional with respect to the mean time between failures of car elements F(y). Therefore, for given y = (y0 , y1 , …, yn ) and the corresponding failure probabilities  P = (p0 , p1 , …, pn ), there are probability jumps Pk = Pk+1 − Pk in the intervals yk , yk+1 . The solution of (3) and (4) based on the principles set forth in [14, 15] allows us to finally determine the values of the optimal service intervals for car elements in the conditions of limited information on their operational reliability using the following equation:   Pk+1 · SΣa + (1 − Pk+1 ) · CΣp Q∗ , F ∗ = min k , 0≤k≤n i=0 λi Pi + λk+1 (1 − Pk+1 )

(6)

 where Pk = Pk+1 −Pk —a jump in the probability of a failure in the interval λk ,λk+1) ; λi —the values of the argument of the distribution function of the MTBF for i = 0, k ; and Pk+1 —the probability of failure for the corresponding operating time λk+1 . Solution of (6) determines the minimum specific losses for maintenance and repair of car elements, which correspond to the optimal periodicity of monitoring their technical opt condition Lk in the range from k to k + 1 (Fig. 3).

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Fig. 3. Graphic illustration of the optimization of the control over the technical condition.

The given technique allows obtaining highly reliable data on the reliability indicators of new brands and models of cars of various classes at an early stage of their commissioning and in conditions of limited information on their operational reliability. Let us consider an example of determining the optimal periodicity of maintenance and repair of a car element in conditions of limited information on its operational reliability using the following initial data: time spent on preventive work on the considered car element—T p = 1 h; time spent on repair work on a car element—T a = 3 h; the cost of the standard hour of work during the repair of the considered car element—S a = 0.7 thousand c.u./hour; the cost of spare parts during repair work—S s.p. = 1.0 thousand c.u.; and the cost of a standard hour of work during preventive (control and diagnostic) work—C p = 0.6 thousand c.u./hour. Based on the collection of operational reliability data on 100 car elements under consideration, the statistics were obtained on the number of failures at run intervals (Table 1, Fig. 4). Table 1. Element failure rate distribution over vehicle runs. No.

Interval of a run, thousand km

Number of failures detected

1.

0÷10

10 failures

2.

10÷20

5 failures

3.

20÷30

15 failures

4.

30÷40

20 failures

Considering the number of accumulated failures, we obtain statistical characteristics of the probability of their occurrence on runs from 0 to li thousand km (Table 2, Fig. 5).

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Fig. 4. Interval distribution of the failure rate on the accumulated run of a vehicle. Table 2. Statistical characteristics of the probability of occurrence of failures of car elements on runs from 0 to li. No.

Interval of the run, thousand km

Accumulated number of failures

Probability of failure on the run—Pk

1.

0÷10

10 failures

10 failures/100 units = 0.1

2.

0÷20

15 failures

15 failures/100 units = 0.15

3.

0÷30

30 failures

30 failures/100 units = 0.3

4.

0÷40

50 failures

50 failures/100 units = 0.5

Fig. 5. Interval probability distribution of failures on the accumulated run of a vehicle.

The final initial data can be written as follows: lk = [l0 = 0; l1 = 10 th.km; l2 = 20 th.km; l3 = 30 th.km; l4 = 40 th.km], Pk = [P0 = 0; P1 = 0.1; P2 = 0.15; P3 = 0.3; P4 = 0.5]. The determination of the optimal periodicity of maintenance and repair (or their opt range) of the car element Lk is based on the use of the loss minimization functional  ∗ ∗ (Q , F ) according to expression (6).

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Initially, according to (5), the absolute costs of the diagnostic, preventive, and repair work are determined as given below: CP = CP TP = 0.6 · 1 = 0.6 thousand c.u. Sa = Sa Ta + Ss.p. = 0.7 · 3 + 1 = 3.1 thousand c.u.  Further, according to (6), the values of average specific losses (Q∗ , F ∗ ) are calculated for the run lk . The results of modeling the periodicity of servicing and its graphical illustration are presented in Table 3 and in Fig. 6. Table 3. The results of modeling the periodicity of servicing the car element. k

l k , thousand km.

Pk

k 

λi Pi

   Q∗ , F ∗ , thousand c.u./thousand km

i=0

0

0

0

0

0.094

1

10

0.1

0.5

0.056

2

20

0.15

3.5

0.055

3

30

0.3

9.5

0.063

4

40

0.5

17.5

0.072

Fig. 6. Optimization of the periodicity of servicing the car element.

 As from Table 3 and Fig. 6, a minimum of average specific losses (Q∗ , F ∗ ) is achieved for the run of 20 thousand km, which corresponds to the desired optimal opt periodicity of maintenance and related repair of the car element Lk .

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3 Research Results Comparing the results obtained with approach A with the results obtained using this technique of approach B, we can conclude that they converge. At the same time, due to the availability of only limited information on reliability (the lack of estimates of reliability indicators—the mathematical expectation of the mean time between failures, its standard deviation, and type of distribution law), the obtained standards are stricter (the optimal periodicity of maintenance decreases).

References 1. Zenchenko V, Grigoriev M (2020) Analysis of Trends and Processes of Auto Service Promotion. In: Popovic Z, Manakov A, Breskich V (eds), VIII international scientific siberian transport forum. TransSiberia 2019, Advances in Intelligent Systems and Computing, vol 1115, Springer, Cham. https://doi.org/10.1007/978-3-030-37916-2_56 2. Chernyaev IO, Grayevskiy I, Korabelnikov S (2018) The mechanism of continuous monitoring of compliance with environmental requirements imposed on vehicles in operation. In: Transportation research procedia, (Elsevier B.V.), pp 108–113. https://doi.org/10.1016/j. trpro.2018.12.051 3. Grayevskiy IS, Chernyaev IO (2018) The mechanism of continuous monitoring of compliance with environmental requirements for vehicles in operation. Vestnik grazhdanskikh ingenerov 6(71):180–184. https://doi.org/10.23968/1999-5571-2018-15-6-180-184 4. Vorobyov S, Chernyaev I, Nazarkin V, Filippov K (2017). Model of operation of motor vehicles based on monitoring of their performance characteristics. In: Transportation Research Procedia, (Elsevier B.V.), pp 695–701. https://doi.org/10.1016/j.trpro.2017.01.113 5. Chernyaev IO (2019) On the necessity and mechanism for forming technical operation systems of motor vehicles based on continuous control of their technical condition. Saint Petersburg State Univers Architecture Civil Eng 4(57):67–172. https://doi.org/10.24411/2078-13182019-14167 6. Grebennikov AS, Grebennikov SA, Konovalov AV et al (2008) Forecasting the service life of elements with the same name in a car as a function of the conditions of their interaction and nonuniformity of initial states. J Mach Manuf Reliab (37):87–93. https://doi.org/10.1007/s12 001-008-1018-8 7. YeS Kuznetsov (2003) Upravlenie tehnicheskimi sistemami (Management of engineering systems). Moscow Automobile and Road Construction State Technical University, Moscow, p 247 8. Kuznetsov ES, Boldin AP, Vlasov VM et al (2004) Technical operation of cars: textbook for Universities, 4th edn. Nauka, Moscow, p 535 9. Yakunin NN (2003) Metodologicheskie osnovy kontrolja i upravlenija tehnicheskim sostojaniem avtomobilej v jekspluatacii [Methodological bases of control and management of operational performance of motor vehicles]. Mashinostroenie, Moscow, p 178 10. Rementsov AN, Zenchenko VA, Nguyen MT (2010) An alternative approach to assessing the technical condition of electronic engine control systems. Bulletin of MADI (GTU) 4:27 11. Boldin AP (1994) Scientific basis of development and use of systems of external and built-in diagnostics in road transport. Dissertation, Moscow 12. Nikitin D, Asoyan A, Nikitina L (2018) A method for reliability improvement in air brake system of compressed air cars. In Transportation research procedia, (Elsevier B.V.), pp 533– 539. https://doi.org/10.1016/j.trpro.2018.12.156

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13. Ageeva EV, Sabelnikov BN, Shcherbakov AV, Pykhtin AI (2018) Improving the efficiency of the process of technical operation of vehicles by using the distance diagnostic method. Proc Southwest State Univers 22(6):6–13. https://doi.org/10.21869/2223-1560-2018-22-6-6-13 14. Zenchenko VA, Grigoriev MV (2004) Service modes of electronic engine control systems. Motor transport company (Avtotransportnoe predpriyatie) 8:16–21 15. Grigoriev MV (2004) Enhancement of operational reliability of electronic engine control systems (on the Example of Bosch M1.5.4 and Mikas 5.4 Systems). Dissertation, Moscow

Vibration Diagnostics of Swivel Suspension Elements of Automotive Vehicles A. N. Novikov, M. D. Tebekin, and S. V. Kolpakova(B) Orel State University Named After I.S. Turgenev, 95, Komsomolskaya St., Orel 302026, Russia [email protected]

Abstract. The paper presents a mathematical model for changing the technical condition of the ball joint of automotive vehicles. A design scheme is proposed, and assumptions and limitations for a mathematical model are determined. During the work, experimental and theoretical studies were carried out. To assess the reliability of the results obtained by theoretical methods, an experimental study was carried out on the developed installation using vibration methods. It has been found that in order to correctly measure vibration acceleration in the ball joint, it is sufficient to use a single vibration sensor «DH-3» in contact with the test sample parallel to the longitudinal axis of the ball pin. The comparison of curves of vibration acceleration dependence on the value of axial gap during mathematical modeling and experimental study showed that the largest divergence between them does not exceed 10%. This confirms the adequacy of the developed mathematical model of the change in ball joint technical condition and its compliance with the conditions of bench research. Keywords: Diagnosis · Mathematical model · Ball joint · Vibration acceleration · Software environment

1 Introduction A car suspension is a set of elements providing an elastic connection between the body (frame) and the wheels (bridges) of the car [1]. Mainly, the suspension is designed to reduce the intensity of vibration and dynamic loads (hits, shocks) acting on the person, the transported cargo, or structural elements of the car when it is moving on rough roads [2]. At the same time, it must ensure constant contact of the wheel with the road surface and effectively transmit the driving force and braking force without deviating the wheels from the corresponding position [3, 4]. Correct operation of the suspension makes driving comfortable and safe in the event of various problems, such as uneven road surfaces, changes in vehicle speed, load displacement, and external forces such as gusts of wind, rain, or snowfall, and much more [5]. Among the car suspension nodes, the ball joint is one of the main load-bearing nodes, the operability of such an element is also determined by the operating conditions, it connects the wheel and the suspension, and through this hinge all static and dynamic loads are transferred to the suspension and the car body [6]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_82

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2 Problem Formulation The ball joints used in the suspension of passenger cars are bearing mates, they receive and transmit significant forces in three planes: vertical (vehicle weight), longitudinal, and transverse—(when braking, accelerating, and turning). The reliability of the hinges in the suspension of a car ensures the reliability of the car as a whole, having a direct impact on its safety [7, 8]. The design of the ball joint determines the mobility of the stud 5 (Fig. 1) in two planes, and axial forces are transmitted through the polymer liner by the spherical head of the stud 1 to the body of the joint 3. In this case, gaps in the interface between the head and the liner are not provided, which is difficult to achieve in their production. To solve this problem, the finished joints are precisely crimped, which is part of the production and determines the necessary interference in the joint. Then the obtained interference is controlled in the hinge manufacturing process by checking the moments of rotation and swing of the stud relative to the body [9]. During operation, the hinges experience multi-cycle alternating loads, which leads to wear, reduced life, and the appearance of various defects (Fig. 1) [10].

Fig. 1. Defects of ball joints.

The main factor in the loss of operability of the hinge is the wear of the interface— “liner-stud head,” which causes an increase in axial clearance h [11]. The wear process is characterized by several factors which, in particular, depends on the friction conditions [12]. The studies of hinge samples dismantled from the suspension of passenger cars as a result of their loss of operability showed the main cause of failures—the destruction of the working layer of the polymer liner [13] and the growth of the gap in the studied interface. Exceeding the permissible values of the studied

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gaps is determined by the driver primarily subjectively by the appearance of knocks and extraneous noise from the suspension and chassis, vibrations on the steering wheel of the car, and deterioration of the vehicle’s handling while driving; however, these symptoms are also possible in the event of a malfunction of other elements of the chassis and steering. All these factors lead to a decrease in the durability of the suspension, and increased wear of wheel bearings and tires, which lead to a decrease in the active safety of the car [14]. In this regard, the study and the developed method for diagnosing hinges with various wear, giving reliable information about their technical condition is relevant.

3 Theoretical Part For the front MacPherson-type hinges of a passenger car, the axial clearance h is a parameter that determines its technical condition. The state of the hinge is considered ultimate [15] if the axial and radial clearances reach a value of 0.7 mm, while creating axial and radial loads on the stud of at least ± 981 N. These values cover ball studs with a diameter of an incomplete head sphere d = 25–35 mm. The dependence of the axial clearance h can be represented as a function:   (1) h = f F , FB , FB , N , μ , where, FP —axial loads directed along the longitudinal axis of the car, H; FB —lateral loads inside the ball joint, H; FV —vertical loads inside the ball joint, H; N —operating hours of the unit, expressed in kilometers of car; μ—coefficient of friction. A diagnostic sign that determines the technical condition of the hinge is the displacement of the stud inside the hinge body in a vertical plane due to the presence of a gap between the liner and the stud. This displacement during operation of the car leads to the development of a gap h, and dynamic impacts inside the hinge, which leads to the appearance of vibrations in the hinge. To diagnose the hinges, a special stand was used, which consists of two blocks. The first block displays the diagnosed mechanism, the second block—the actuating mechanism. To develop a mathematical model, we will present a stand for determining the technical condition of ball joints in the form of a structural scheme (Fig. 2). The mathematical model of changing the technical condition of the ball joint of the MacPherson-type front suspension of a car in the conditions of bench study can be presented in the form of a differential equation: m1 x¨ + b1 x˙ + c1 x + (˙x − y˙ )b2 + (x − y)c2 = 0,

(2)

where x—vertical mass displacement m1 , m; x˙ —mass velocity m1 , m/s; x—mass acceleration m1 , m/s2; y —kinematic effect of mass m2 (forced displacement of the «inertialess part of the installation»), m; y˙ —the speed of the «inertialess part of the installation»),

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Fig. 2. Design scheme of the suspension: 1—test bench frame, 2—elastic element with stiffness coefficient c1 , 3—diagnosed mechanism, 4—elastic element with stiffness coefficient c2 , 5— actuating mechanism, 6—damper with viscous resistance b2 , 7—vibration sensor, 8—damper with viscous resistance b1 .

m/s; b1 —viscosity in conjugation «lever-stand frame», m2 /s; b2 —viscosity in conjunction «stud head-polymer liner», m2 /s; c1 —the stiffness coefficient of the pair «leverframe of the stand», kg/s2; c2 —the stiffness coefficient of the pair «stud head-polymer liner», kg/s2. The following assumptions and limitations were used: • stiffness coefficient c1 is considered constant (the system is linear); • dry friction in the ball joint is neglected, and b2 = b1 ; • Actuator II provides a predetermined forced linear displacement of the ball stud 2, and therefore in the design scheme the mass m2 = 0; and • the polymer liner is an elastic medium c2 → ∞,n if |x − y| ≤ h; c2 = 0, if |x − y| > h.

y = yo sinωt.

(3)

We have carried out a mathematical transformation of the original differential equation to a dimensionless form and obtained the following equation: ξ¨ +

ε1 g1 g2 ε2 ξ˙ + 2 ξ = cos τ + 2 sin τ. η η η η

(4)

To solve the tasks, automated calculation systems were used. The main parameter under study is the dimensionless gap −, which depends on the dimensional gap h and mass displacement m1 —Eq. (5): = ZWi =

h , y0

(5)

at0 , y0 ω

(6)

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where ZWi —dimensionless vibration acceleration; a—dimensional vibration acceleration, m/s2 ; t0 = 0,001; c—step time to plot function. Using Eqs. 5 and 6, obtain the dependencies of vibration acceleration on the time of the experiment in the investigated range of axial clearance from 0.01 to 0.9 mm in ball joints. Their analysis allowed us to obtain a graph of the dependence of the magnitude of vibration acceleration on the magnitude of the axial clearance shown in Fig. 3.

Fig. 3. Graph of the dependence of the magnitude of vibration acceleration on the magnitude of the axial clearance obtained during mathematical modeling.

4 Experimental Studies The objective of the experimental studies was to conduct experiments to establish the relationship of the axial clearance in the hinge with the magnitude of vibration acceleration [16] in a laboratory bench study [17]. The basis of the stand is the right side of the MacPherson-type front suspension of a passenger car fixed at one point on the frame (pillar support bearing) and pivotally fixed at two points on the base (rubber sleeve and silent block) (Fig. 4). The experimental studies included the following equipment: a stand for testing and diagnosing suspension elements, DN-3 vibration sensors (Fig. 5), connecting wires and an analog-to-digital converter (ADC) with the necessary circuitry solutions, a computer with specialized software for signals processing SignalExpress LabVIEW, a device for controlling the gap in the hinge, including an ICh-10 dial indicator with a measuring tip, a bracket for mounting it on a stand, and test samples—30 hinge with varying degrees of wear. Processing of experimental results is reduced to an analysis of each graph obtained, in particular, to the indications of each cycle—maximum and average values of vibration

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Fig. 4. General view of the stand for the diagnosis of ball joints. a mechanical part, b hydraulic part: 1—vertical (main) hydraulic cylinder, 2—vertical hydraulic cylinder lever, 3—stub-axle steering, 4—stand frame, 5—lever arm, 6—emergency shutdown button, 7—horizontal hydraulic cylinder, 8—horizontal hydraulic cylinder lever, 9—controller, 10—hydraulic tank of the drive of the main hydraulic cylinder, 11—hydraulic distributor of the main hydraulic cylinder, 12—pressure gage, 13—main hydraulic cylinder drive pump, 14—hydraulic tank of the additional hydraulic cylinder drive, 15—additional cylinder drive pump, 16—electric motor of the additional hydraulic cylinder drive, 17—pump of main hydraulic cylinder drive.

Fig. 5. Installation of vibration sensors: a vibration sensors mounted on a stand; b general view of the vibration sensor. 1—stub-axle steering, 2—ball joint, 3—vibration sensors DN-3, 4—device for measuring axial clearance.

acceleration, vibration acceleration jumps. For analysis, use such signal characteristics as amplitude (lower and upper values), double amplitude (average and peak values), and period. Each experiment includes 12 cycles (zone 6). As a result of the experimental studies, a graph of the dependence of the magnitude of vibration acceleration on the magnitude of the axial clearance in the hinges is shown in Fig. 6. Analysis of the graphs shows that the maximum deviation of theoretical and practical results does not exceed 10%. As a result of approximating the graph shown in Fig. 6,

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Fig. 6. Results of experimental studies.

we can obtain the dependence described by the equation h = 0, 06 + 0, 005 a + 0, 00019 a2 − 0, 0000015 a3 . The resulting equation allows to determine the amount of clearance in the ball joint, depending on the parameters of vibration acceleration.

5 Conclusions As a result of the studies, the following results were obtained: 1. Numerical values of vibration acceleration are obtained for different values of axial clearance. 2. Based on the analysis of the graphs of the dependence of the maximum amplitude of vibration acceleration a on the time of the experiment, empirical dependences were obtained for test samples with an axial clearance of 0.01–0.9 mm to determine the actual value of the axial clearance h. 3. It has been established that for the correct measurement of vibration acceleration in a ball joint, it is sufficient to use one DN-3 vibration sensor installed in contact with the test sample parallel to the longitudinal axis of the ball stud. 4. Comparison of the graphs of the dependence of vibration acceleration on the value of the axial clearance in mathematical modeling and in experimental research showed that the largest discrepancy between them does not exceed 10%. This confirms the adequacy of the developed mathematical model for changing the technical condition of the ball joint and its compliance with the conditions of bench research.

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References 1. Raimpel J (1987) Car chassis: Suspension Elements. Moscow, p 288 2. Sert E, Boyraz P (2017) Optimization of suspension system and sensitivity analysisfor improvement of stability in a midsize heavy vehicle. Sci Technol, Int J, Eng 3. Lai CY, Liao WH (2002) Vibration control of a suspension system via amagnetorheological fluid damper. Modal Anal 8(4):527–547 4. Appleyard M, Wellstead PE (1995) Active suspensions: some background. IEE Proc -Control Theory Appl 142(2):123–128 5. Kavitha C, Abinav Shankar S, Ashok B, Denis Ashok S, Muhammad Usman Kaisan (2018) Adaptive suspension strategy for a double wishbone suspension through camber and toe optimization. Eng Sci Technol, Int J 21(1):149–158 6. Karaulin AL (2000) Car design. Chassis, Moscow, p 528 7. Ossa EA, Palacio CC, Paniagua MA (2011) Failure analysis of a car suspension system ball joint. Eng Fail Anal 18(5):1388–1394 8. Raimpel J (1989) Car chassis: Suspension structures. Moscow, p 328 9. Akhmadimov RM, Filkin NM (2009) A new approach in the design of a ball joint of a car suspension. Modern High Technol 4:23–25 10. Ossa EA, Palacio CC, Paniagua MA (2011) Failure analysis of a car suspension system ball joint. Eng Fail Anal 18:1388–1394 11. Kargin AA, Kosarov MV, Voinov AA (2008) Analysis of the study of ball joints in a car suspension. Penza State Univers 4:68–70 12. Akhmadimov RM, Filkin NM (2009) A new approach in the design of a ball joint of a car suspension. Modern High Technology 4:23–25 13. Mikhailovsky IA, Artyukhin VI (2007) Mastering the production and testing of ball studs of the front suspension of passenger cars from steel 41X1. Mat. 65th science and technology conf. Sat doc. T.1. Magnitogorsk, Moscow, p 23–25 14. Voskoboinikov YE, Gochakov AV, Kolker AB (2010) Filtration of signals and images: Fourier and Wavelet algorithms. Templan, Novosibirsk, p 195 15. Bleikhut R (1989) Fast digital signal processing algorithms. Publishing house “Mir”, p 448 16. Tebekin MD, Katunin AA, Novikov AN (2011) Russian Federation Patent 2483287, 31 May 2011 17. Zagudillin R (2009) Multisim. Labview, Signal Express, The practice of computer-aided design of electronic devices. Moscow, p 368

Indicator Analysis of Injection Process of Different Composition Mixtures of Diesel Fuel and Palm Oil at Changing of Speed Mode of Diesel Engine A. V. Kurapin(B) , E. A. Salykin, and K. E. Tshibanda Volgograd State Technical University (VSTU), 28, Lenin Avenue, Volgograd 400005, Russia [email protected]

Abstract. This article considers fuel supply for a diesel engine with mixtures of diesel fuel and palm oil of various compositions. The results of numerical experiments performed to study the effect of the palm oil addition in the mixture on the performance of the fuel supply process when the engine is running at different speed modes are presented. The calculations were made for three variants: for a constant value of the plunger active stroke, for a constant value of the mass cyclic feed of a mixture, and for a constant calorific value of a mixture. The values of all these parameters correspond to the operation of the system on pure diesel fuel at the appropriate speed of the crankshaft. It is shown that adjustment of the plunger active stroke in order to maintain a constant calorific value of the mixture is not required when the engine operates at the nominal speed mode. This conclusion is acceptable for all used mixtures because the deviations of the plunger active stroke do not exceed 3%. However, when the speed limit decreases and the proportion of palm oil increases, the change in the active stroke of the plunger increases and its maximum deviation exceeds 9%. Keywords: Diesel engine · Diesel fuel · Palm oil · Mixed biofuel · Fuel injection · Fuel supply · Speed mode

1 Introduction At the present time and for the period up to 2040–2050, internal combustion engines for transport purposes will remain the main consumer of motor fuels. In the structure of the fleet of these engines in the world today, the share of diesels is about 20%. And if in the United States that share is less than 3% as the result of the environmental scandal over Volkswagen’s diesel cars, in the EU countries 53% of cars are already diesel. In addition to Volkswagen, diesel cars have the largest share in sales of companies such as Volvo (80%), BMW (81%), Daimler (71%), and Renault and Peugeot (more than 50%) [1].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_83

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In modern conditions, fairly strict requirements are set for operational characteristics of diesel engines. The most important ones are fuel efficiency and exhaust toxicity. One of the most prospective ways to improve diesels in order to reduce the consumption of oil fuels and reduce harmful emissions is to adapt them to work on alternative fuels as renewable energy resources. One of the types of alternative fuels is biofuels (BF) of plant origin, among which vegetable oils play a huge role as fuel for transport diesels. Mixtures of vegetable oils with the diesel fuel (DF) are called biodiesel. Study and research of the use of these fuels as substitutes for general fuel are performed all over the world. In the European Union (EU) and the United States, oil methyl esters from vegetable oils, basically rapeseed oil, are named biodiesel fuels. Especially widely the methyl ester of rapeseed oil is used as biodiesel in France, Austria, and Germany [2–5]. In the US, esters of soybean oil are used. Also, research on the application of vegetable oils as a promising source of energy for diesel engines was initiated and is being actively developed in Russia [6–11]. These countries developed standards which regulate the composition and properties of biodiesel. The EU countries developed standards EN 41214, EN 590, (or 590:2000) and DIN 51606, in Russia—GOST R52368, adopted in 2005, in the USA—the standard ASTM 6751, adopted in 2002. For marking of BF and its mixtures with pure DF, foreign technical literature adopted marks consisting of letters and numbers. For example, B0 represents letters and numbers denote pure DF (0% biodiesel) and B100 denotes pure BF (100% biodiesel). Specific types of biofuels have the following designations. PB10 denotes a mixture of 10% palm oil and 90% pure DF; PB100 denotes pure palm oil; and PBJB5 denotes a mixture of fuel consisting of 5% palm oil, 5% jatrophic oil, and 90% pure DF. In the countries with a tropical climate, there is widespread production of palm oil. Currently, the palm tree (Elaeis guineensis) occupies a strong position in world agriculture, as one of the oilseeds produced in tropical countries. In the 2018/19 season, palm oil retained the first place in the world in terms of consumption among vegetable oils with a share of 34% [12]. In tropical countries such as Malaysia, Indonesia, Thailand, and others, there is active research on the use of palm oil as a fuel for diesels [2, 3, 13–19]. In connection with the above, theoretical and experimental studies of the operation of diesel engines using mixed fuel based on DF and palm oil are becoming highly relevant. 1.1 The Purpose and Objectives This work continues the research carried out earlier by the authors [20]. The objective of this study is theoretical analysis of the composition and properties of DF and palm oil fuel mixtures influence on the fuel injection process parameters at change of the diesel engine speed mode. During the research, the following tasks were set: 1. The analysis of the effect of the mixture composition on the parameters of the injection process at a constant value of the active stroke of the plunger that corresponds to the nominal cyclic feed on a clean DF when changing the speed mode of the diesel engine. 2. The analysis of the effect of the mixture composition on the parameters of the injection process at a constant value of the mass cyclic feed of the mixture which

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corresponds to the nominal cyclic feed on a pure DF when changing the speed mode of the diesel engine. 3. The analysis of the effect of the mixture composition on the parameters of the injection process during maintaining a constant calorific value of the mixture during changing of the speed mode of the diesel engine.

2 Object and Methods of Research In this study, the D-144 (4Q10.5/12) diesel engine fuel supply system is considered as an object of the numerical experiment. The fuel supply system specifications are presented in Table 1. Table 1. Technical specification of the test engine fuel feed system. Pump brand

UTN-5

The distance between the axes of plungers, mm 32 Diameter of the plunger, mm

8.5

Plunger stroke, mm

8

Number of pump elements

4

Nominal rotation speed of the pump, min−1

1000

Nominal volumetric cyclic flow, mm3

72

Nominal cyclic mass flow, g

0.06

Brand of nozzle

FD-22

Number of spray nozzle holes

4

Diameter of spray nozzle holes, mm

0.34

The maximum stroke of the needle, mm

0.265

The total effective area of the spray holes, mm2 0.218 Injection start pressure, MPa

17 ± 0.5

Diesel fuel (B0) and its mixtures with palm oil (PB) were used as fuel. PB additives make up 10, 20, 30, 40, 50, and 60% by volume. The resulting mixtures are designated, respectively, PB10, PB20, PB30, PB40, PB50, PB60, pure palm oil—PB100. The properties of the mixtures are shown in Table 2. To assess the influence of the properties of mixed fuel on the performance of the fuel supply process, numerical experiments were carried out using mathematical model integrated into the program complex (PC), “PC-Injection”, developed at the Bauman Moscow State Technical University, Department “Piston engines.” The mathematical model underlying the PC is based on proven methods and the results of original fundamental research of hydrodynamic processes in diesel fuel supply systems [21].

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Table 2. Properties of diesel fuel, palm oil, and their mixtures. Properties Kinematic viscosity at 40°C (cSt) at 100°C (cSt) Density at 20°C (g/cm3 ) Calorific value (MJ/kg)

B0

PB100 PB10

3.9

8.6

830.0 918.0 42.5

37.1

4.37 838.8 42.01

PB20 4.84 847.6 41.33

PB30 5.31 856.4 40.73

PB40 5.78 865.0 40.32

PB50 6.25 874.0 39.98

PB60 6.72 882.8 39.20

3 Results and Discussion Calculations show that differences in the properties of diesel fuel and palm oil have a noticeable effect on fuel delivery rates when their mixtures are used. Thus, an increase in the density of the mixture with an increase in the proportion of palm oil leads to an increase in mass cyclic fuel supply. Authors calculated the mass cyclic supply of Gc.mix for mixed fuel, consisting of diesel fuel and palm oil taking into account the density of the mixtures (see Table 2) when the diesel is running at the nominal speed at n = 2000 rpm and partial speed modes at n = 1800, 1600, and 1400 rpm. The results of the calculations are shown in Fig. 1a.

Fig. 1. a Change in the mass cyclic flow of the mixture Gc.mix in the function of the volume fraction of the PB; b change in the mass cyclic flow of the mixture Gc.mix in the function of the volume fraction of the PB at a constant plunger active stroke.

Computational researches of the fuel supply process with mixed fuel were performed to define the influence of that factor on the fuel supply parameters. The first calculations of the fuel supply process parameters were made for mixed fuel with constant active plunger strokes that correspond to the cyclic feedings on pure B0 (DF) at various frequencies of rotation of the crankshaft. The values of the plunger active stroke at different speeds of the crankshaft rotation operating on pure diesel fuel and the corresponding mass cycle feed are shown in Table 3. The results of the calculations are presented in Figs. 1b and 2a.

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Table 3. Values of the active stroke of the plunger and mass cycle feed on pure diesel fuel at different speeds of rotation of the crankshaft. The frequency of the crankshaft rotation, rpm Plunger active stroke, mm Mass cycle feed, g 1400

1.602

0.051

1600

1.694

0.055

1800

1.809

0.058

2000

1.93

0.06

Fig. 2. a Change in the maximum injection pressures Pin,max in the function of the volume fraction PB at a constant plunger active stroke; b Change in the maximum injection pressures Pin,max in the function of the volume fraction PB at a constant mass cyclic flow Gc.mix .

The analysis of these figures shows that the increase in the proportion of palm oil in the composition of the mixed fuel leads to increasing of mass cycle feed of the mixture and the maximum injection pressures. Calculations showed that the average injection pressures and the total feed duration also increased. These results are explained by increasing density and viscosity of mixtures along with the increase of the proportion of PB. It is necessary to pay attention to the large increase in the mass cyclic feed of the mixture (Gc.mix ) with an increase in the proportion of PB obtained during the hydrodynamic calculation (see Fig. 1b) in comparison with the mass cyclic feed of the mixture obtained only taking into account the mixture density (see Fig. 1a). This is due to a decrease in flow leaks through gaps in the plunger pair due to an increase in the mixture viscosity along with an increase in the volume fraction of palm oil. When the speed limit is reduced, the effect of the palm oil proportion in the mixture on the injection performance becomes more noticeable. So, at n = 2000 rpm Gc.mix increases by 0.0062 g, and at n = 1400 rpm by 0.0096 g (see Fig. 1b). The maximum injection pressures Pin,max contrarily increase significantly with an increase in the number of revolutions and the proportion of palm oil. So, at n = 1400 rpm, Pin,max increases by 2.2 MPa, at 2000 rpm by 4 MPa (See Fig. 2a).

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To maintain the mass cyclic feed of the mixture (Gc.mix ) at increasing the proportion of palm oil in it, it is necessary to adjust the high-pressure fuel pump by reducing the plunger active stroke. The change in the active stroke of the plunger in dependence of the proportion of palm oil in the mixture was calculated. Calculations were made in conditions of maintaining constant mass cyclic feed of the mixture that corresponds to the mass cyclic feed of pure DF at each engine speed mode. The results are presented in Table 3 and in Fig. 3a. The maximum fuel injection pressures for these conditions were also calculated (see Fig. 2b).

Fig. 3. a Change of the plunger active stroke in the function of the volume fraction PB at a constant mass cyclic flow Gc.mix ; b Change of heat introduced by the fuel into the combustion chamber Qmix in the function of the volume fraction PB at a constant cyclic mass flow Gc.mix .

As shown in Fig. 3a, the active stroke decreased from 1.93 to 1.7 mm at 2000 rpm, and from 1.6 to 1.36 mm at 1400 rpm, and the total feed duration also decreased. However, the maximum injection pressure increases with the increase in the proportion of palm oil in the mixture. For example, at n = 2000 rpm, the maximum injection pressure increases from 23.3 to 24.9 MPa (see Fig. 2b), which is due to an increase in the density and viscosity of the mixture. As the speed limit decreases, the increase in maximum injection pressures becomes less intense when the proportion of palm oil increases, and at n = 1400 rpm, the maximum injection pressures do not increase. Maintaining a constant mass cyclic feed of the mixture (Gc.mix ) at an increase in the proportion of palm oil leads to decrease in the amount of heat released during combustion of the mixture due to decrease in its calorific value, which reduces the power of the diesel engine. Figure 3b shows the change in the heat Qmix transferred with the fuel into the combustion chamber at a constant mass cyclic feed of the mixture Gc.mix corresponding to the mass cyclic feed Gc of pure diesel fuel at the corresponding frequency of the crankshaft (see Table 3). The calorific value of the mixtures is shown in Table 2. Thus, it is appropriate to adjust the plunger active stroke under the constant amount of heat transferred by the fuel into the combustion chamber. Authors performed calculations of the parameters of fuel supply process for mixed fuel taking into account this circumstance for a constant amount of input heat Qmix which corresponds to pure DF

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with a nominal cycle feed at a frequency of 2000 rpm and with partial cycle feeds corresponding to the frequencies of 1800, 1600, and 1400 rpm. The results of the calculations are presented in Fig. 4.

Fig. 4. a Change of mass cyclic flow Gc.mix in the function of the volume fraction PB at a constant amount of introduced heat; b Change of the plunger active stroke mix in the function of the volume fraction PB at a constant amount of introduced heat.

Thus, to keep constant quantity of input heat Qmix corresponding to pure diesel fuel at feeding mixtures of diesel fuel and palm oil, it is necessary to reduce the plunger active stroke as shown in Fig. 4b. Analysis of Fig. 4a shows that in this case, the mass cyclic feed of the mixture Gc.mix increases within smaller limits than when maintaining a constant plunger active stroke (see Fig. 1b). Also, calculations show that the average and maximum injection pressures increase within smaller limits than if the active stroke of the plunger was kept constant, but within larger limits than if the mass cyclic feed of the mixture is kept constant (see Fig. 2). The plunger active stroke is reduced within smaller limits than at maintaining a constant mass cyclic feed of the mixture (see Fig. 3a and 4b). However, when the speed of the crankshaft decreases the necessary reduction in the plunger active stroke becomes more significant. The total duration of injection under these conditions did not change much. The most suitable for practical use are the results of fuel supply calculations performed at maintaining a constant quantity of heat introduced with the mixed fuel into the combustion chamber, since, in this case, influence of the mixture composition on the power indicators of the diesel engine will be minimal. Obtained results for mentioned case: numerical values of the changes of mass feed of mixed fuel and adjusting injection pump setting—the plunger active stroke at changing the volume fraction of palm oil in the mixture and different frequencies of the crankshaft are given in Table 4.

4 Conclusion The performed research shows that in order to maintain a constant quantity of heat supplied with the mixed fuel into the combustion chamber, it is necessary to increase the mass cyclic feed of the mixture from 1.3% for the PB10 mixture to 8.28% for the

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Table 4. Deviations of the fuel injection pump adjustment parameters while maintaining a constant quantity of heat transferred with the mixed fuel into the combustion chamber with changes in the volume fraction of palm oil and the speed of the crankshaft. Deviations of adjusting Units B0 PB10 parameters

PB20

PB30

PB40

PB50

PB60

n = 2000 rpm Mass cyclic flow of the g fuel mixture %

0

0.00077 0.00153 0.00235 0.00319 0.00405 0.00492

0

1.29

2.56

3.93

5.34

6.78

8.23

Active stroke of the plunger

mm

0

0.013

0.025

0.035

0.043

0.052

0.058

%

0

0.68

1.32

1.86

2.29

2.78

3.02

Mass cyclic flow of the g fuel mixture %

0

0.00075 0.00151 0.00229 0.0031

0

1.29

2.6

3.94

5.34

6.76

8.23

Active stroke of the plunger

mm

0

0.015

0.03

0.043

0.055

0.065

0.082

%

0

0.83

1.68

2.43

3.13

3.72

4.74

Mass cyclic flow of the g fuel mixture %

0

0.0007

0.00143 0.00217 0.00294 0.00372 0.00453

0

1.28

2.61

3.96

5.37

6.79

8.27

Active stroke of the plunger

mm

0

0.02

0.039

0.057

0.074

0.09

0.106

%

0

1.2

2.37

3.5

4.59

5.64

6.7

Mass cyclic flow of the g fuel mixture %

0

0.00066 0.00133 0.00201 0.00279 0.00344 0.00419

0

1.3

2.63

3.97

5.51

6.8

8.28

Active stroke of the plunger

mm

0

0.024

0.048

0.071

0.091

0.114

0.134

%

0

1.53

3.11

4.67

6.06

7.71

9.19

n = 1800 rpm 0.00393 0.00478

n = 1600 rpm

n = 1400 rpm

PB60 mixture on average for all the considered crankshaft speeds. The corresponding decrease in the plunger active stroke increases with an increase in the proportion of PB in the mixture and with a decrease in the speed mode. Thus, for a PB60 mixture at n = 2000 rpm, the plunger active stroke decreases by 3%, and at n = 1400 rpm, the decrease reaches 9.19%. Thus, we can conclude that for the nominal speed mode of the diesel engine, the fuel injection pump adjustment is not required, since the deviations of the plunger active stroke are not large for all considered compositions of mixtures. At partial speed modes to maintain a constant quantity of heat introduced with the mixed fuel into the combustion chamber, it is necessary to adjust the fuel injection plunger active stroke downward. It provides maintenance of diesel engine power at an increase in the proportion of PB in the mixture.

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References 1. Otrazitsya li skandal vokrug Volkswagen na prodazhakh dizelnykh avtomobiley? (Whether the impact of the scandal on sales of Volkswagen diesel vehicles?). http://ru.euronews.com/ 2015/09/23/volkswagen-vw-scandal/ 2. Rebecca Andrade S, Ferreira G, Camargo D, Iglesias M (2016) “Thermodynamic properties of palm oil” (Elaeisguineensis) and evening primrose seed oil (therabiennis) as a function of temperature. Wold J Multi Res Dev 2(1):38–43 3. Esteban B, Riba JR, Baquero G, Rius A, Puig R (2012) Temperature dependence of density and viscosity of vegetable oils. Sciverse science direct (Biomass and bioenergy) 42:164–171 4. Claude Valery Ngayihi Abbe (2016) Contributin à la modelisation OD de la combustion Diesel application au biodiesel. Université de yaounde I, Thèse doctorale, GenieMécanique 5. Tarabet L (2012)b Etudes de la combustion d’un carburant innovant dans les moteurs à combustion interne de véhicules. Lyes Tarabet.—Ecoles des mines de NANTES. Universités de NANTES école, militaire polytechniques: theses doctorat (Energétiques). Les 23 Septembre 6. Markov VA, Gayvoronskiy AI, Grehov AV et al (2008) Rabota dizeley na netraditsionnyih toplivah (Operation of diesel engines on alternative fuels). Legion-Avtodata, Moscow 7. Aleksandrov AA, Arharov IA, Markov VA et al (2012) Alternativnyie topliva dlya dvigateley vnutrennego sgoraniya. (Alternative fuel for internal combustion engines). OOO NITs “Inzhener”, OOO “Oniko-M”, Moscow 8. Valeho PR et al (2014) Sravnitelnyie ispyitaniya alternativnyih topliv dlya dizelnyih dvigateley (Comparative tests of alternative fuels for diesel engines). Vestnik MGTU im. N. E. Baumana. Ser. “Mashinostroenie” 6:596 9. Vedruchenko VR, Kraynov VV, Litvinov PV (2016) Vliyanie svoystv raznosortnyih topliv dlya dizeley na harakteristiki toplivopodachi (The influence of the properties of different sorts of fuels for diesel engines on the characteristics of the fuel supply). Vestnik SibADI, Omsk 2(48):44–49 10. Priyandaka A, Valeho PI et al (2003) Eksperimentalnoe opredelenie kineticheskih konstant vosplameneniya rastitelnyih topliv v usloviyah DVS (Experimental determination of kinetic constants of ignition of vegetative fuels in the conditions of the internal combustion engine). Vestnik Rossiyskogo universiteta druzhbyi narodov: Inzhenernyie issledovaniya 1:29–31 11. Markov VA (2014) Vliyanie sostava smesevogo biotopliva na parametryi protsessa vpryiskivaniya topliva v dizele (The influence of composition of mixed biofuels on process parameters of injection of fuel in a diesel engine). Traktoryi i selhozmashinyi 12:3–9 12. Pal’movoe i soevoe maslo sostavlyayut bolee 60% mirovogo ob”yoma potrebleniya rastitel’nyh masel. (Palm and soybean oil account for more than 60% of the world’s vegetable oil consumption). https://www.oilworld.ru/analytics/worldmarket/305726 13. Januan J, Ellis N (2010) Perspectives on biodiesel as sustainable fuel. Renew Sustain Energy Rev 14:1312–1320 14. Namlizan N, Wong Wuttanasatian T (2014) Performance of diesel engine using diesel B3 mixed with crude palm oil. Sci World J, p 6 15. Nacatiozsezen Ahmet, Canakci Mustafa, Turkcan Ali, Sayin C (2009) Performance and combustion characteristics of a engine fueled with wasta palm oil and canola oil methyl esters. Fuel Elsevier Journal 88:629–636 16. Chuah LF, Abd Aziz AR, Yusup S, Bokhari A, Jaromir Klemes J, Abdullah MZ (2015) Performance and emission of diesel engine fueled by waste cooking oil methyl ester derived from palm olein using hydrodynamics cavitation. In: Chuah LF, Springer (Clean Techn Environ policy) 17:2229–2241 17. Song M et al (2012) Comparisons of NO emissions and soot concentrations from biodiesel— fuelled diesel engine. Fuel 96:446–453

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18. Rashid MM et al (2016) Performance and emission characteristics of a diesel engine fueled with palm, jatropha and moringa oil methyl ester. Ind Crops Prod 79:70–75 19. Prateepchaikul G, Teerawat A (2003) Palm oil as a fuel for agricultural diesel engines: comparative testing against diesel oil on. https://www.journeytoforever.org/biodiesel_SVO-palm. html 20. Salykin EA, Kurapin AV, Tshibanda KE, Dygalo VG, Slavutskiy VM (2018) Impact of diesel fuel and palm oil blend compositions on the performance of the fuel supply process in the diesel engine. IOP conference series: materials science and engineering, vol. 386, conference 1: The 102nd international scientific and technical conference “Intelligent Systems of Driver Assistance: Development, Research, Certification”, 18–19 April 2018, Nizhny Novgorod State Technical University, p 10 21. Grehov LV, Gabitov II, Negovora AV (2013) Konstruktsiya, raschet i tehnicheskiy servis toplivopodayuschih sistem dizeley (Design, calculation and technical services fuel supply systems of diesel engines). Legion-Avtodata, Moscow

Selection of Air Cooled Diesel Engine Boosting Level Considering Process Deviations of Parameters D. N. Ilyushin(B) , A. M. Lartsev, and E. A. Fedyanov Volgograd State Technical University, 28, Lenin Avenue, Volgograd 400005, Russian Federation [email protected]

Abstract. The problem of thermal factor and accordingly of achievable boosting level in air cooled engines is becoming acute as they get larger. This is due to the fact that as the engine volume is increasing, thermal emission from the cylinder is growing up and to a larger extent than the area of heat removal surface to cooling air. Among serially produced air cooled diesel engines the largest (diameter of cylinder D = 150 mm; piston stroke S = 160 mm) was diesel engine V-400. When selecting settings of such an engine it was important to know not only the maximum possible boosting level by mean effective pressure, but also to establish the required margin of this parameter in order to take into account the inevitable process variety of engine parameters in serial production. Taking as an example the above type of diesel engine, the article analyzes the impact of process variety in pressure charging and indicator indices of the working process on thermal condition of cylinder head. We have used the method of assessing the boosting level of diesel air cooled engine, considering the impact of pressure charging parameters on thermal condition of diesel engine at different values of air cooling downstream of compressor, engine settings by surplus air factor, and characteristics of fuel supply. Cylinder selection criteria were verified by thermal condition of the head based on which we should assess the maximum thermal condition of an engine as a whole. Keywords: Air cooled · Boosting level · Cylinder head · Technological variation

1 Introduction The world natural resources are mostly concentrated in vast and hard to access regions of Siberia, Far East, Extreme North, and the Arctic. At present, an interest in developing these areas has increased abruptly. This development is impossible without powerful and sustainable machinery, adapted to specific conditions of operation. For transport, construction, and auxiliary equipment used in extreme climatic zones, as well as remote areas with hard supply conditions of materials, necessary for operation, certain advantages are offered by air cooled engines, first of all running on diesel fuel. In some cases, © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_84

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such engines are preferred for special equipment. At the same time, diesel air cooled engines due to their design have lower values of mean effective pressure than diesel engines of the same size with liquid cooling. This makes it important and vital for engine engineering the task of boosting diesel air cooled engines and creating their versions with maximum possible boosting level by pressure charging, observing, of course, all safety and ecological requirements. The variety of process parameters by cylinders of diesel engine and variety of turbo compressor parameters are caused by one reason: extreme deviations (variety, error) of original parts and assembly quality. Production (process) variety of parameters in systems, details, and machinery as a whole is due mostly to production causes. Production deviations of parameters are sometimes called as original deviations or process deviations. Variety of parameters in an item depend on perfection degree of technological processes, quality of machining equipment, training of production personnel, and general culture of fabrication. Using as an example diesel engines 8DVT-330, V-400, V-450, we have analyzed the impact of process variety of pressure charging and inter-cylinder differences in the indicator process on permitted boosting level of diesel air cooled engines. As shown above [1], boosting limit by power of diesel air cooled engines is limited first of all by maximum permitted thermal condition of cylinder head, where maximum temperature of the head fire bottom is criterion for determining the boosting limit.

2 Object of Research The object of our research is 8-cylinder, V-shaped diesel air cooled engines 8DVT-330, V-400, V-450 [2]. Parameters of cylinder-piston groups of the above engines: cylinder diameter 150 mm and piston stroke 160 mm. Rated speed of crankshaft rotation n is 1700 min−1 . Engines vary by rated power. Rated power values for the above diesel engines are given in Table 1. Table 1. Rated power of engines under research. Engine

Rated power Ne (kW)

8DVT-330 272 + 15 V-400

307 + 15

V-450

330 + 15

3 Impact of Process Variety of Pressure Charging on Thermal Condition of Cylinder Head To identify the impact of process variety [3] of pressure charging pk on permitted boosting limit, we performed comprehensive tests of diesel engine 8DVT-330.

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To assess the impact of pressure charging variety on engine performance and to determine range pk , in which the engine runs without visible deterioration of key indices, we carried out bench tests of 100 8DVT-330 engines with TKR 8,5C-7 turbo compressors [4]. Variation of engine power depending on variation of pressure charging is shown in Fig. 1.

Fig. 1. Variation of rated power Ne of diesel engine 8DVT-330 depending on variation of pressure charging.

During tests it was noted that the required, as per engine specifications, power Ne = 276,5 ± 1,5 kW was maintained as long as pressure charging was within limits 0,077 MPa ≤ Pk ≤ 0,083 MPa. When pressure charging exceeded 0,090 MPa, turbo compressors TKR 8,5C-7 often surged [5–9]. Specific effective fuel consumption had no visible changes, remaining close to 1,5 g/(kW*h). Statistical assessment made it possible to establish the permitted variation range for 8DVT-330 engine of pressure charging when using TKP 8,5C-7 from the point of insuring sufficient power and reliable operation of the diesel engine. It should be noted that within the range of pressure charging variation 0,077 MPa ≤ Pk ≤ 0,083 MPa, maintaining required rated power Ne = 276,5 ± 1,5 kW, there were more than 60% of tested engines. For this range of pressure charging variety, we made calculations of temperature fields for cylinder head fire bottom. The calculation ignores the impact on engine thermal conditions and relation of pressure charging to counter pressure at outlet Pk /Pt . Parameters of calculated engines are given in Table 2. Calculation results of engines and cylinder head thermal condition are given in Table 3. Used in Table 3 are the following designations: • • • •

α—excess air factor; Ga —engine air consumption per hour; Pz —maximum combustion pressure; Tz —maximum temperature in combustion chamber;

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Table 2. Parameters of calculated engines. Ne (kW) n Pk (MPa) Pt (MPa) Pk /Pt (min−1 ) 275

1700

0.077

0.0811

0.95

278

1700

0.083

0.0874

0.95

Table 3. Calculation results of engines. Ne (kW)

α

Ga (kg/hour)

Pz (MPa)

Tz (K)

Twch (K)

Tmax (K)

275

1.74

1609

9.29

1816

488

590

278

1.78

1660

9.44

1800

482

581

• Twch —weighted average temperature in cylinder head; and • Tmax —criterion (maximum) temperature of cylinder head. As we can see in Table 3, the rise of maximum temperature in cylinder head bottom of turbo compressor with worst characteristics was 590–581 = 9°. Using in an engine turbo compressors of one model but with a variety of consumption and pressure characteristics, we can have not only the variation of rated power within specifications tolerance, but also variation of temperature in cylinder head bottom, which under extreme levels of boosting might result in diesel engine failure due to destruction of cylinder head [10–13].

4 Impact of Variety in Process Characteristics on Temperature Field of Cylinder Head Tests on assessing the impact of process variety on cylinder head temperature were done at V-400 engine with turbo compressor S3A « Schwitzer » in the power range of Ne = 309-330 kW (modifications of diesel engine V-400 and V-450). During tests eight cylinders of diesel engine were indicated. Two cylinder heads were installed at B-400 engine [14], prepared to indicate low and high pressures in the combustion chamber. Heads, fitted with pressure sensors, were installed consecutively on cylinders under the following pattern: 1–2, 3–4, 5–6, and 7–8. To increase the mean effective pressure during engine boosting, the rotation speed of crankshaft was maintained permanent: n = 1700 min−1 . As a result, the process variation is expressed by variation of maximum combustion pressure Pz [7, 15–17]. Figure 2 shows, experimentally determined by means of indication, variation of maximum combustion pressure by cylinders of diesel engine at two levels of boosting Similar picture of inter-cylinder differences at two levels of boosting confirms that the differences are not due to the boosting level, but are caused by specific design features of engine and non-uniform cyclic feed by engine cylinders.

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Fig. 2. Variation Pz by cylinders: ▲—V-400; —V-450.Nof cyl—no. of. indicated cylinder

Assessment of the impact degree from variety of indicating process values by cylinders of diesel engine on thermal condition of cylinder head shows that the differences in indicating process by cylinders and first of all differences in dynamics of thermal radiation, reflected by variation of Pz , affect significantly the thermal condition of cylinder heads [8]. As you can see in Table 4, variation of Pz by 9% at the same cyclic feed corresponds to 19 K of criterion temperature variation. Table 4. Engine parameters, considering process variations by cylinders. Ne n qcycle (mg) α (kW) (min−1 )

Pz (MPa) Tz (K) Pk (MPa) Tk (K) Twch (K) Tmax (K)

309

1700

176

2,06 11,06

1658

0,21

367

477

574

299

1700

176

2,06 10,06

1507

0,21

368

464

555

According to the layout diagram of V-400 diesel engine, cylinders 4 and 8 have the worst cooling conditions [18, 19]. Cylinder 4 has higher Pz , and accordingly heat transfer coefficient from gases inside cylinders, so it has the highest combustion rate. This judgment confirms selection of cylinder 4 by cylinder head temperature for assessing thermal condition of diesel engine as a whole [20, 21]. Used in Table 4 are the following designations: • qcycle —fuel cyclic feed; • Pk —boosting pressure; and • T k —air temperature at engine inlet. Considering significant impact of process variety on temperature field of cylinder head, you should, when selecting boosting level of diesel air cooled engines, take into account the process variety, having a safety margin by criterion temperature of at least 6%.

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5 Conclusion We have analyzed the impact of process variety in turbo compressor parameters on characteristics of diesel engine, the impact of inter-cylinder differences in indication process of particular cylinders of multi-cylinder diesel engine on thermal condition of cylinder head, and identified selection criteria of cylinder, whose head thermal condition should be considered in assessing extreme thermal condition of engine as a whole. When using a turbo compressor of one model you may come across a major variation of cylinder head temperature field due to process variety of turbo compressor parameters. Using an engine turbo compressors of one model but with different consumption and pressure characteristics, we can have not only lower power, which will be within the permitted technical range, but also higher temperature of cylinder head bottom, which under certain boosting levels may affect its reliability. When selecting settings of air cooled engines it is important to have a certain margin of mean effective pressure in view of inevitable process variety in performance of serially produced engines.

References 1. Vasiliev AV, Lartsev AM, Fedyanov EA (2017) Ocenka teplovogo sostoyaniya golovki cilindra dvigatelya vozdushnogo ohlazhdeniya pri ego forsirovanii (Assessment of the thermal state of the cylinder head of an air-cooled engine during its forcing) Truck, Moscow 2. Menshenin GG (2006) Povyshenie tekhnicheskogo urovnya i nadezhnosti dizel’nyh dvigatelej vozdushnogo ohlazhdeniya 8CHVN15/16 s uchetom rezul’tatov ekspluatacii (Improving the technical level and reliability of air-cooled diesel engines 8CHVN15/ 16, taking into account the results of operation: monograph) VPI (branch) VolgSTU, Volgograd 3. Lartsev AM (2013) Osobennosti proizvodstva dvigatelej vozdushnogo ohlazhdeniya bol’shoj moshchnosti (Features of the production of air-cooled engines of high power) Engine building, St. Petersburg 4. Rein VF (1989) Rezul’taty priemo-sdatochnyh ispytanij sta dvigatelej 8DVT-330: tekhnicheskaya spravka (The results of acceptance tests of a hundred engines 8DVT-330) Volgograd engine factory, Volgograd 5. Lartsev AM (2014) Ocenka effektivnyh pokazatelej dvigatelya vozdushnogo ohlazhdeniya V-400 pri ego forsirovanii (Evaluation of the effective performance of the air-cooled engine V-400 during its forcing). Engine building, St. Petersburg 6. Vasilyev AV, Lartsev AM, Fedyanov EA (2020) Evaluation of possible limits of forcing of high-capacity air-cooled engines. 5th international conference on industrial engineering, ICIE, Sochi 7. Paul Tholen, Irolt Killmann (2017) Investigations on highly turbocharged air-cooled diesel engines. Jpn, Tokyo 8. Wladyslaw M, Konrad B (2007) Analysis of thermal loads on air cooled engine. J KONES Powertrain Transp, p 143 9. Nomura T, Matsushita K, Fujii Y, Fujiwara H (2014) Development of temperature estimation method of whole engine considering heat balance under vehicle running conditions, SAE Int J Engines 10. Cheng DB, Li Za, Zhi TG, Tao Db (2018) Coupled heat transfer between air-cooling and cylinder head engine, EEA—Electrotehnica, Electronica, Automatica

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11. Li B, Hong J, Sun J, Xu H, Qiu Z, Pan S (2009) Numerical simulation for flow and heat transfer of engine coolant. Hsi-An Chiao Tung Ta Hsueh, Journal of Xi’an Jiaotong University 12. Ha C, Li Y, Xb Y (2007) Numerical simulation study on steady heat transfer of fluid-solid coupled system in diesel engines. Transactions of the Chinese Society of Agricultural Machinery, Nongye Jixie Xuebao 13. Ramasubramanian S, Raja VKB (2017) Review on enhanced heat transfer techniques using modern technologies for 4S air cooled engines, 2nd international conference on frontiers in automobile and mechanical engineering; Sathyabama University, Chennai, India 14. Opredelenie pokazatelej rabochego processa dizelya V-400 po vsem cilindram na nominal’nom rezhime i pri ego forsirovanii do 450 (Determination of indicators of the working process of the V-400 diesel engine for all cylinders in the nominal mode and when it is forced to 450 h.p.) (1990) Volgograd engine factory, Volgograd 15. Shchinnikov PA, Mikhaylenko AI, Sinelnikov DS (2016) Experimental estimation of surface heat transfer coefficient for air-cooled internal combustion engine, 11th international forum on strategic technology. IFOST 2016, Novosibirsk, Russian Federation 16. Rittenhouse JA, Rowton AK, Ausserer JK, Polanka MD, Litke PJ, Grinstead KD (2014) Preliminary thermal loss measurements for a small internal combustion engine. 52nd Aerospace Sciences Meeting: Science and Technology Forum and Exposition, SciTech, United States 17. Ji F-Z, Du F-R, Xu B, Yang S-C (2014) Research on thermal state of air-cooled piston engine for aviation. Chinese Internal Combustion Engine Engineering 18. Mˇardˇarescu VG, Ispas N, Nˇastˇasoiu M (2014) Considerations about designing of an air cooled cylinder head for a direct injection small diesel engine, INMATEH—Agric Eng 19. Yan T, Yobby J, Vundavilli R (2014) Optimal design of IC engine cooling fins by using genetic algorithm. ASME international mechanical engineering congress and exposition, Proceedings (IMECE), Montreal, Canada 20. Vasiliev AV, Lartsev AM, Fedyanov EA, (2016) Metod ocenki izmeneniya teplovogo sostoyaniya golovki cilindra dvigatelya vozdushnogo ohlazhdeniya pri ego forsirovanii (A method for assessing changes in the thermal state of the cylinder head of an air-cooled engine during its forcing). News of MSTU MAMI. Ser. Transport vehicles, transport and technological means and power plants, Moscow 21. Krstic B, Rasuo B, Trifkovic D, Radisavljevic I, Rajic Z, Dinulovic M (2013) An investigation of the repetitive failure in an aircraft engine cylinder head, Engineering Failure Analysis

Analysis of Constructive Reliability and Maintainability of the Contemporary Electronic Control Units of the Active Safety Systems V. Dygalo(B) , M. Lyashenko, and O. Kosov Volgograd State Technical University, 28, Lenin Avenue, Volgograd 400005, Russia [email protected]

Abstract. Considering the operating conditions of the automated brake system computer, one can note that the working conditions are unfavorable. Despite the fact that manufacturers strive to provide a high level of protection for units, car owners set operating modes that, in some parameters, exceed the values provided for manufacturers. This leads to failures of the electronic control unit. The article considers the analysis of designed reliability and maintainability of modern unit controls systems, and active safety of the Bosch and Continental-Teves illustrates two designs used most frequently in the automotive industry. In addition, it should be noted that the cost of these units is quite high, which increases the relevance of the maintainability of electronic control units. In addition, the operation of these systems in conditions different from the design leads to operation in supercritical modes. For example, the intersection of large irregularities is located on the road at high speed and with a high repetition rate. This can lead to the damage in the electronic components, especially surface mounting and conductors, caused by vibration. Keywords: Vehicle · Active safety system · Designed reliability assessment

1 Introduction The first sign that the active safety system (ASS) is faulty is the indication of the icon on the instrument panel, which burns for more than 6 s, and also when the vehicle is moving. This means that the system detected an error by means of self-diagnostics and disabled the ASS functions. In such cases, it is necessary in an urgent order to diagnose the ASS system to determine the cause of the malfunction. If computer diagnostics does not see the ASS unit when it is requested, or there are a lot of errors in it, then most often it indicates a malfunction of the ASS electronic control unit [1].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_85

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As a rule, the main causes are constant vibration and large temperature changes in the engine compartment. It is possible to distinguish four characteristic variants of non-serviceability: 1. 2. 3. 4.

ASS does not turn on. ASS turns on, finds an error in itself or in its nearest environment and turns off. The ASS turns on, works, and then finds an error and turns off. ASS turns on, works, and then finds an error and continues to work.

Errors can be critical and not critical from the point of view of ASS. A very clear example of a critical error is the disappearance of the signal from the wheel sensor. If the signal from the wheel disappears, the ASS does not know what is happening to this wheel and turns off, so as not to aggravate the road situation by inappropriately distributing the braking force along the wheels [2, 3]. When inoperative, the system continues to poll the wheel sensor. And if the signal is resumed, and is sufficiently stable, then the ASS is switched back on. In the event that the fault is serious, the system will no longer turn on. The survey will be discontinued. But after the ignition is switched off (the ASS is de-activated) and the ignition is switched on again, the system according to the algorithm will restart and find the error again to disconnect, notifying the driver by means of indication. If the fault is rectified (and as a result of the error), the ASS will work in the normal mode. There is a persistent misconception that information about all detected errors is written into the ASS’s memory and can be read from there. There are ASS units that do not fix error codes. Accordingly and understand why the failure of such blocks is difficult. [4] The main reasons for the failure of the SAB electronic units: • Overvoltage is the main cause of failure. If a short circuit occurs in the electrical circuit of one of the solenoids, the overvoltage can disable the entire control unit. • Often external factors are also causing damage—rust, mechanical damage or overheating, and severe shock or vibration (microscopic cracking in printed circuit boards) can be one of the reasons for the failure of the computer. • Moisture is one of the worst enemies of the electronic control unit, because, penetrating inside, the liquid provokes a short circuit of electrical circuits, which leads to overvoltage [5]. • Corrosion of connecting elements and metal parts results from moisture dropping inside the computer body. • Luft of the bearings of the hubs located very close to the electronic sensors has an extremely negative effect on the system, it is necessary to follow the state of the suspension of the machine. • Malfunction of the wiring or the generator can lead to disconnection of the automatic warning system by the automatic protection system. • Repair of the ASS system in uncertified repair shops can lead to serious problems. • When painting the car, drying in the chamber without dismantling the control unit of the ASS can result in a breakdown of the latter. • Poor maintenance of the brake system leads to a breakdown of the system, for example, when replacing the brake fluid, the battery of the hydraulic unit must be discharged.

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Symptoms of ASS system failure [6] are as follows: • • • • •

Indication of the bulb (ABS/ESP) during the movement. Indication of the bulb (ABS/ESP) after warming up the engine. Indication of the bulb (ABS/ESP) after cleaning the engine compartment. Continuous indication of the bulb (ABS/ESP) during braking. There is an error of the ASS block when driving on an uneven surface.

2 Basic Faults of the Unit 1. One or more sensors on the wheels do not work, and the replacement of the sensors does NOT lead to the elimination of the defect. 2. Speedometer, odometer does not work. 3. The fault indicator SAB lights up when the engine warms up, the first few minutes on the “cold” SAB is working properly. 4. The pump is constantly running (a distinctive sound is heard under the hood). 5. Diagnosis reveals an open in the pump circuit. Two indirect reasons that can lead to errors in the work of the SAB are as follows: • Installation of tires of different sizes and • Wear and/or incorrect adjustment of the wheel bearing. The electronic control unit is a complex component of the car’s design and the types of its breakdowns are different [7]: • • • • •

There is no possibility of viewing the wheel sensor. There is no connection with the control of the units, the XX mechanism, or the valves. There is no reaction to the test, the sensors “do not see” the control unit. There are physical damages—sgo-reli flash, transistors, or tracks. There is no communication with the scanner, diagnostic modules, and other control units.

The main requirement for the ASS ECU installed on the car is reliability. No less important requirements—the ability to work in virtually all known conditions of operation, maintainability, small gabarites, weight, and power consumption. Consequently, the cost of the computer for use on the car is higher compared to a car with analogous characteristics used in conventional stationary objects [8].

3 Maintainability Analysis Analysis ASS ECU showed that manufacturers use various technological solutions in the production of electronic filling of blocks, which ultimately affects the reliability and repairability of the system.

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According to the structural design, the IS is divided into hulls with terminals, hull-less terminals, and uncorrupted ones. A number of separate functional microcircuits, united by the type of manufacturing technology, voltages of power supplies, input and output resistances and signal levels, structural design and ways of fastening or mounting, form a series of ICs [4]. Usually the IS series includes such a set of functional microcircuits from which it is possible to build a complete device. There are also a series of special microcircuits designed to work in specific conditions, or special purpose (specialized integrated circuits), active security systems are a vivid example of such solutions. Chassis integrated circuits perform a number of functions, the main ones of which are protection from climatic and mechanical effects; shielding from interference; simplification of the processes of assembly of microcircuits; and unification of the original structural element (microcircuit) in dimensional and installation dimensions [9]. The main drawback of both cabinet microcircuits and the devices built on them is a large volume of auxiliary structural elements: housings, terminals, sealing elements, heat sink, etc., which do not carry a functional load. The use of case microcircuits leads to unproductively large expenditures of useful volume and mass of the device and reduces by one or two orders of magnitude the density of the assembly of the elements compared to the density of their placement in the crystal or on the substrate. However, this production technology increases the reliability and maintainability of the computer ASS working in heavy conditions. An example is the product of Continental-Teves. The board of the ESP MK-60 control unit manufactured by Continental-Teves is shown in Fig. 1.

Fig. 1. Control-board ESP MK-60 manufactured by continental-teves.

In order to increase the degree of effective use of the volume and mass of microelectronic digital devices in recent years, open-frame semiconductor and hybrid ICs have become widespread [10]. This principle is used in the production of Bosch units (Fig. 2).

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Fig. 2. Controller board manufactured by Bosch (ABS 5.3).

Open-frame IPS is a sub-substrate with one of the methods of integral technology applied on it. For the implementation of the installation between the card-free ICs on the substrate, contact areas are provided (Fig. 2). Hybrid chipless microcircuits represent a relatively large size si-tally or ceramic substrate (base), in which the passive part (interconnects, rezis) is produced by spraying, and the active part (diodes, transistors, crystals of semiconductor microschemes) is glued to the allocated places and soldered to the rest of the circuit by jumpers. On the perimeter of the substrate are located contact pads (Fig. 2). The use of open-frame integrated circuits along with a sharp decrease in the overall dimensions and mass of the equipment created on their basis leads to an increase in the labor intensity of its production and, consequently, the cost, the need to provide additional measures of protection, and sealing that dramatically reduces the reliability and maintainability of the computer ASS [8]. These shortcomings are practically devoid of the widely distributed leadless enclosures with reduced sizes or micro-cases that are used by Continental-Teves. In modern ASS designs, the micro-computer ECU is already traditionally located on the hull of the hydraulic unit (Fig. 3). In the course of development of the ASS, the overall dimensions and mass of the hydraulic unit and the ECU decreased, and for today they are comparable in size. Since the dimensions of the hydraulic unit ASS cannot be further reduced significantly, the use of open-body IC to reduce the size of the computer seems inappropriate, since in this case the cost increases and the maintainability of the computer decreases. Compared with open-frame hybrid chips, SMD (surface mount technology) circuit boards are subject to repair without the use of expensive equipment Fig. 4. The main board of the electronic control unit is the main and most expensive part. Its damage causes a malfunction of the entire system. Repair of contact areas, oxidized tracks, and a failed contact group requires extensive engineering knowledge, special equipment, and high accuracy.

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Fig. 3. General view of the hydraulic unit (right) and the computer (left) ASS.

Fig. 4. Controller board manufactured by Bosch (ESP 5.7).

Problems with contact areas can raise due to the ingress of liquids, vibration, and impact. From a strong impact or vibration, chips can move and fly off contact lanes. The repair of the microcircuit boards requires a thorough diagnosis to identify all the damaged areas and a long process of repair. Soldering BGA chips or reballing is the process of reconstructing an array of balls on the bottom of the board. It is because of high dynamic loads, there may be a problem

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with the pads and their peeling. The recovery procedure can be divided into the main stages: • • • •

dismantling of the defective microelement after preheating; cleaning of the carrier board from the remnants of the old solder; rolling of new contact conclusions; and installing the new component in place.

It should be noted that the quality of soldering significantly depends on the quality of the equipment and consumables used for re-installation. In addition, BGA soldering requires extensive work experience, knowledge of the element base, a good view of the worker performing repairs, and professional infrared or thermal air stations.

4 Technology of Repair The repaired board is placed on a horizontal platform, which has a lower heating by an infrared emitter of local action. This radiator is sent to the BGA chip to be soldered. The solder is heated to a temperature of about 200o to facilitate the dismantling of the element. The main heating is carried out from above with the help of a locally directed flow of hot air. Usually, the temperature is set in the range of 330–360 0C for mediumsized chips. The procedure takes about a minute. Heating is carried out at the edges of the board, excluding the center of the microcircuit. This is necessary to prevent the crystal from overheating. It is necessary to control the time and intensity of processing the IC by air. Since the layout of the elements is very dense, there is a possibility of overheating of neighboring elements. To do this, they are covered with a special protective film or foil [7]. After this, the microscheme is dismantled. For this purpose, a “hoist” chip is used, which is included in the set of the station. This accessory is necessary for the separation of the repair chip from the printed circuit board. The stage is very responsible. If there is insufficient heat, there is a risk of damage to the conductive paths. The next step is to clean the electronic board and the chip from the remains of the old pri-pawn. It is very important not to spoil the solder mask, otherwise it may spread the solder along the tracks. For removal, a soldering iron with a “wave” attachment is used. Its use is effective, and allows you to achieve the best possible result. Further, the BGA soldering technology involves rolling new pin leads on the chip. It is possible to use ready-made balls. But the often-touch pad consists of hundreds of conclusions. Therefore, in the industrial case, use is made of specialized screen areas in which the chip is fixed. When reballing an important element is high-quality solder paste. Such specimens, when heated, give an even and smooth ball. And substandard pastes break up into a large number of small balls. The final procedure for soldering the BGA microscheme is to install it in place. The element is installed, starting from silk-screen printing, applied to the board itself or mounting racks. Then the microcircuit is heated by hot air and, due to the surface tension forces from the action of molten solder, is fixed in the initial part of the dismantling. For this reason, the circuit moves a little, taking up a “comfortable position.”

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At this, repair procedures are completed. The board is flushed with flux and checked for efficiency. Thus, it is possible to restore the efficiency of the electronic control unit of the active safety systems.

References 1. Dygalo VG, Revin AA (2006) Virtual’no-phisicheskaya tekhnologiya laboratornykh ispytaniy system activnoy bezopasnosti avtotransportnykh sredstv (Virtual physical technology of laboratory tests of active safety systems for vehicles: monograph). Volgograd, VolgGTU, p 316 2. Revin AA (2002) Teoriya ekspluatatsionnykh svoistv avtomobiley I avtopoezdov s ABS d rezhime tromozheniya (Theory of operational properties of cars and road trains with ABS in braking mode). Volgograd, VolgGTU, p 372 3. Dygalo VG, Revin AA (2012) Tekhnologii ispytaniy sistem aktivnoy bezopasnosti avtotransportnykh sredstv (Technology testing of systems of active safety of vehicles. Mashinostroenie, Moscow, p 387 4. Dygalo VG, Lyaschenko MV, Boyko GV, Dygalo LV (2018) Application of virtual physical modeling technology for the development of elements of the autonomous (unmanned) vehicles’ systems. IOP Conference Series: Materials Science and Engineering, Vol. 315, International Automobile Scientific Forum (IASF-2017): Intelligent Transport Systems, Moscow, 18–19 October, 2017, p 11 5. Revin AA, Dygalo VG, Lyaschenko MV, Boyko GV, Dygalo LV Methods of monitoring the technical condition of the braking system of an autonomous vehicle during operation. IOP Conference Series: Materials Science and Engineering, vol 315, International Automobile Scientific Forum (IASF-2017): Intelligent Transport Systems, Moscow, 18–19 October, 2017, p6 6. Revin AA, Dygalo VG (2001) Issledovanie tromoznoy dinamiki avtomobilya metodami kompleksnoy tekhnologii modelirovaniya (Research of brake dynamics of the car by methods of complex modeling technology). Volgograd, VSTU, p 122 7. Maier M, Müller K (1995), ABS 5.3: The new and compact ABS5 unit for passenger cars, SAE Technical Paper Series 950757. Robert Bosch GmbH 8. Emig R, Goebels H, Schramm HJ (1990) Antilock braking systems (ABS) for Commercial vehicles—status 1990 and future prospects, SAE Technical Paper Series 901177, Robert Bosch GmbH 9. Bosch, Automotive Braking Systems (1995) Robert Bosch GmbH 10. Dygalo VG, Larin ES, Nikitin YuM (2018) Primenenie elektronnykh komponentov dlya diagnostiki tormoznykh system avtomobilya (The use of electronic components for the diagnosis of vehicle braking systems). Razvitie social’nogo I nauchno-tekhnicheskogo potentsiala obschestva: proceedings of intern. scientific-practical, Moscow, 15 January 2018, p 846–850

Simulation of Change in Reliability of Rope System Motion Mechanism in Mobile Ropeway Complex A. V. Lagerev1 , V. I. Tarichko2 , and I. A. Lagerev1(B) 1 Academician I.G. Petrovskii Bryansk State University, 14, Bezhitskaya Ul, Bryansk 241036,

Russia [email protected] 2 Bryansk Automobile Plant JSC, 1 Staleliteynaya Ul, Bryansk 241038, Russia

Abstract. The article presents a method of computer simulation for the process of changing the reliability indicators over time in the key node of the mobile cable car complex—the mechanism of movement of the cable system. The method is based on a specially developed mathematical probabilistic model. This allows us to predict the kinetics of reliability indicators of both the movement mechanism as a whole and its individual structural elements, taking into account the time and amount of repair and restoration work, as well as simulate the stage of operation of the life cycle of this mechanism. The calculation of the probability of smooth operation of the movement mechanism and its individual elements at an arbitrary moment of time is based on the solution of the Chapman–Kolmogorov linear differential equation system, which is periodically rebuilt in the time moments of scheduled repairs of the mobile ropeway complex. The article presents the results of calculations in relation to the designed complex of mobile ropeways. Keywords: Rope system · Motion mechanism · Reliability kinetics · Repair · Simulation

1 Introduction Ropeways as a system of above-ground transport have been widely used in many countries of the world as a continuous mode of transportation for freight and passengers [1–3]. At present, they are an important element of modern infrastructure ensuring effective use of a wide range of intelligent off-street transport and logistics technologies in a highly urbanized environment of large cities and metropolises [4]. Most ropeways in use are fixed ropeways, which are designed for long-term use within the area of their installation. Relocation of freight ropeways, for example, is quite rare during their service life. However, there are mobile ropeways intended for frequent relocation due to the technological peculiarities of production processes supported by them. Among such mobile structures, there are technical devices that have already been © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_86

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implemented in practice and have proved their effectiveness in long-term operation [5, 6]. Even more mobile constructions of ropeways are known only as technical proposals and patents [3, 4]. A promising type of mobile ropeway is mobile ropeways complex [7]. Their equipment is located on base chassis (usually on heavy wheeled or tracked vehicles) and can, therefore, be used to quickly establish crossings over water barriers, ravines, canyons, and swampy terrain. Figure 1 shows a model of the mobile complex based on wheeled chassis. The design of mobile ropeway systems does not provide for the installation of any intermediate supports and includes only the end supports combined with the motion and tension mechanisms of the rope system. Mobile ropeways and complexes are intended for use in places or in conditions where it is impossible or not desirable to establish capital structures (bridges, overpasses, tunnels, embankments, etc.), for example, when performing construction and installation or repair works of autonomous objects [3], when dealing with natural or man-made disasters [8], when doing forestry works in mountainous or difficult to reach areas [5, 6, 9], when carrying out agricultural works in challenging natural conditions [10], and when carrying out loading and unloading operations on water transportation means [11].

Fig. 1. Mobile ropeway complex model (scale 1:72).

2 Statement of the Research Task Scientific research of ropeways is a complex problem as they include several important aspects—technical, economic, social, and legal. Most of the known studies were devoted to engineering problems of design and calculation of basic structural elements of ropeways, for example, analysis of bearing rope dynamics and strength [12, 13]. It should be noted that the operating loads acting on the bearing elements of the ropeways and the metal structure of ropeways have a pronounced random and non-stationary character. The main reason is the effect of stochastic wind load [14]. Also, for example, study [15] considered issues of social and economic impact of ropeways construction on the

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development of adjacent territories, studies [16, 17] develop the economic justification and optimization of ropeways construction costs, and study [18] investigates the issues of legal registration of ownership for air space and land for ropeways. The problem of ensuring safe transportation of people and goods is important for the design and operation of ropeways and complexes. Forecasting and analysis of emergencies risks in the operation of major components or ropeways, in general, are usually based on the application of the well-known method of failure tree [3, 19]. The main problem of this method’s successful application is that quantitative calculations of failure probability for technical systems of ropeways and complexes require data on failure probabilities for each structural component of these systems. Such information is extremely limited, as it is based on statistical processing of available data on occurred failures and does not take into account the duration of service life to failure. As a result, the data on the probability of uninterrupted operation of structural elements—necessary to predict the risk of emergency situations—are average and do not fully reflect individual features of the structure, modes, and service life of ropeways and complexes, as well as the efficiency of the repair activities carried out. In order to improve the reliability of the initial data—necessary for carrying out the risk analysis for ropeways and complexes—the study has developed a method of computer simulation of the process of major unit reliability indicators changing, i.e. of the rope system motion mechanism.

3 Mathematical Model The motion mechanism of the mobile ropeway complex consists of a significant number of elements that are potentially dangerous in terms of their failure during the operation process. By their purpose and place in the structure, they belong to one of three systems: mechanical, hydraulic, or electrical. The total number of potentially dangerous elements in each of them is nmech , nhyd , and nel accordingly. During operation, the mechanism may be in one of the following possible conditions at any certain moment: • one functional state S0 (it is characterized by the fact that all potentially dangerous elements are in the working condition and the properties of the working fluid comply with the requirements of the operational documentation); • one of several non-functional states S1 , S2 , . . . , Sm , . . . , SM (each state is characterized by the fact that one corresponding element m is in the non-functional state whereas the remaining elements are in the functional state). Thus, the total number of possible states of the mechanism is M = nmech + nhyd + nel + 2.

(1)

The probability of subsequent failure of an arbitrary element q before the recovery of the occurred failure of the element m is negligible. Therefore, the graph of possible states and their connecting transitions during operation of periodically repaired ropeways motion mechanism will be as shown in Fig. 2a. The quantitative characteristic of the

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transition of the mechanism from a functional state S0 to a non-functional state Sm caused by the failure of the element m is the failure rate of this element λm . The quantitative characteristic of the reverse transition from non-functional state Sm to functional state S0 caused by the restoration or replacement of the previously failed element m is the repair rate of this element μm .

Fig. 2. a Graph of possible states and transitions; b kinetics of motion mechanism’s trouble-free operation probability: 1—without repairs; 2—with repairs.

Probabilities of the motion mechanism being at an arbitrary moment of operation in all possible states S0 , S1 , . . . , Sm , . . . , SM can be determined using the system of Chapman–Kolmogorov equations [20]. It is a system of ordinary differential system of first-order equations. For the graph in Fig. 2a, this system is expressed as follows: ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨

⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬

⎡

m=M λm ⎢− ⎢ m=1 ⎢ λ1 ⎢ ⎢ λ2 ⎢ ... ⎢ =⎢ ... dPm ⎢ ⎪ ⎪ ⎪ dτ ⎪ ⎢ ⎪ ⎪ λm ⎪ ⎢ ⎪ ⎪ ⎪ ⎪ ... ⎪ ⎢ ⎪ ⎪ . .. ⎪ ⎪ dP M −1 ⎪ ⎢ ⎪ ⎪ ⎪ ⎪ ⎣ λM −1 dτ ⎪ ⎭ ⎩ dP M dτ λM dP0 dτ dP1 dτ dP2 dτ

μ1

μ2 . . . μm . . . μM −1

−μ1 0 . . . 0 0 −μ2 . . . 0 ... ... ... ... 0 0 . . . −μm ... ... ... ... 0 0 ... 0 0 0 ... 0

... 0 ... 0 ... ... ... 0 ... ... . . . −μM −1 ... 0

⎤ ⎧ ⎫ μM ⎥ ⎪ P0 ⎪ ⎪ ⎪ ⎪ ⎪ ⎥ ⎪ ⎪ ⎪ P1 ⎪ ⎪ ⎥ ⎪ ⎪ 0 ⎥ ⎪ ⎪ ⎪ ⎪ ⎪ P 2 ⎪ ⎥ ⎪ ⎪ 0 ⎥ ⎪ ⎨ ⎬ ... ⎥ , ... ⎥ · ⎥ ⎪ Pm ⎪ ⎪ ⎪ ⎪ ⎥ ⎪ 0 ⎥ ⎪ ⎪ ⎪ ... ⎪ ⎪ ⎪ ⎪ ⎪ ... ⎥ ⎪ ⎪ ⎥ ⎪ ⎪ P ⎪ M −1 ⎪ ⎪ ⎪ ⎦ ⎩ 0 ⎭ PM −μM (2)

where P0 , P1 , . . . , Pm , . . . , PM are the probabilities of the mechanism being in the corresponding possible states; λm is the failure rate of element m; and μm is the repair rate of element m. To solve the system of differential equations (Eq. 2), it is necessary to set initial conditions. They include many probabilities Pm at the time the motion mechanism is put

Simulation of Change in Reliability of Rope System Motion

into operation (at τ = τ0 = 0). The initial condition vector is ⎫ ⎧ ⎫ ⎧ ⎪ ⎪ ⎪ 1 ⎪ ⎪ ⎪ ⎪ P0 (τ = τ0 ) ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ 0 ⎪ (τ = τ ) P 1 0 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ . . . . . . ⎬ ⎬ ⎨ ⎪ ⎨ = 0 . Pm (τ = τ0 ) ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ...⎪ ... ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ 0 (τ = τ ) P ⎪ ⎪ ⎪ ⎪ M −1 0 ⎪ ⎪ ⎪ ⎭ ⎭ ⎩ ⎪ ⎩ 0 PM (τ = τ0 )

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(3)

The system (Eq. 2) allows to predict the process of change in time for the probability of trouble-free operation of the ropeways motion mechanism as PMech (τ ) = P0 (τ ).

(4)

The sum of all other probabilities P1 , . . . , Pm , . . . , PM expresses the probability of the motion mechanism being in a non-functional state QMech (τ ): QMech (τ ) = 1 − PMech (τ ) =

m=M 

Pm (τ ).

(5)

m=1

The ratio Pm (τ )/QMech (τ ) can be considered as a relative individual contribution of the failure of element m into the reduction of the overall level of reliability of the motion mechanism at an arbitrary moment τ . The system (Eq. 2) solution under the initial condition (Eq. 3) adequately describes the change in time of reliability indicators prior to the first repair or maintenance τr,1 (Fig. 2b). At the moment τr,1 , one or more elements are restored or replaced. Therefore, the probabilities of them being in a non-functional state are spasmodically decreasing from value Pm (τr,1 − 0) = Pm (τr,1 ) to value Pm (τr,1 + 0) = 0. The probability of the motion mechanism being in the functional state spasmodically increases from P0 (τr,1 − 0) = P0 (τr,1 ) at the sum of the probabilities Pm (τr,1 ) of the restored elements. Therefore, from the moment τr,1 the integration of the system of differential equations (Eq. 2) should be carried out under a new vector of initial conditions: ⎧ ⎫ i=m ⎫ ⎪ ⎧ r,1 ⎪ ⎪ ⎪ ⎪ ⎪ P0 (τr,1 + 0) ⎪ P0 (τr,1 ) + Pi (τr,1 ) ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ i=1 ⎪ ⎪ ⎪ ⎪ (τ + 0) P 1 r,1 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ P1 (τr,1 ) ⎨ ⎬ ⎬ ⎪ ⎨ ... , (6) = ... ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ Pm (τr,1 + 0) ⎪ ⎪ ⎪ ⎪ ⎪ 0 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ... ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ . . . ⎪ ⎪ ⎭ ⎪ ⎩ ⎪ ⎪ PM (τr,1 + 0) ⎩ ⎭ PM (τr,1 ) where mr,1 is the number of elements of the motion mechanism that have been restored as planned at the time of operation of the mobile ropeway system τr,1 . Similarly, the vector of initial conditions (Eq. 6) changes for other moments τr,n . Thus, the process of predicting changes over time for the motion mechanism reliability

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during the planned restoration or replacement of the elements (curve 2 in Fig. 2b) is reduced to the successive integration of the system of equations (Eq. 2) within consecutive time intervals τr,n ≤ τ ≤ τr,n+1 with periodic reformation of the vector of initial conditions (Eq. 6) at the starting point of each such interval τr,n . Despite planned repairs and maintenance, in real conditions of operation there are occasional failures of elements of transport devices [21]. They require unscheduled restoration or replacement of failed elements during the next repairs or maintenance of the hydraulic drive τr,n (Fig. 2b). This circumstance distorts the picture of the kinetics of reliability indicators, as it requires additional appropriate adjustment of the vectors of initial conditions for the moments of time τr,n : ⎧ ⎫ i=m j=n ⎧ ⎫ ⎪ r,n r,n ⎪ ⎪ P0 (τr,n ) + Pi (τr,n ) + Pj (τr,n ) ⎪ ⎪ ⎪ ⎪ P0 (τr,n + 0) ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ i=1 j=1 ⎪ ⎪ ⎪ ⎪ (τ + 0) P 1 r,n ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎬ ⎬ ⎨ P1 (τr,n ) ... , = . . . ⎪ ⎪ Pm (τr,n + 0) ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ 0 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ... ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎭ ⎪ . . . ⎪ ⎪ PM (τr,n + 0) ⎩ ⎭ PM (τr,n )

(7)

where nr,n is the number of accidentally failed τr,n−1 ≤ τ ≤ τr,n elements of the motion mechanism that have been restored or replaced during operation τr,n .

4 Test Analysis of the Mathematical Model The developed method of forecasting the change of mobile ropeways complex motion mechanism reliability was implemented in the form of a computational complex “Kinetics of mobile ropeway complex motion mechanism reliability.” Test evaluation of the features of its use for reliability analysis and the adequacy of the obtained results were carried out for the motion mechanism of the mobile complex 200 m long with hydraulic frequency-throttle regulation of the speed of cargo below 100 kN [22]. The name of potentially dangerous structural elements included in the design of the considered motion mechanism and the failure rates λm of these elements are given in Table 1. The data used for the test calculation were taken from [23–25]. Figure 3 shows the results of calculation of the diagram of change in time of failurefree operation probability for the motion mechanism Pmech (τ ) during the first repair cycle of the mobile ropeway complex (0 < τ < Trep = 12000 h). Diagrams 2 and 3 produced by simulating a random process of damaging-restoration of functional properties of the motion mechanism taking into account its planned repairs, there are spasmodic changes Pmech (τ ) in moments of time evenly distributed with a period of 1500 h. They correspond to the moments of recovery time of elements τr,i , and the value of the spasmodic change is determined by the amount of repair—the number and list of restored elements. The greatest value Pmech (τr,i ) is characteristic for the moment of major repairs, as it provides for the maximum amount of restoration work. However, overhaul does not allow to reach the initial value of the probability of trouble-free operation of

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Table 1. Composition and failure rate of motion mechanism elements. Constructive element

Failure rate 106 , h−1

Hydraulic system Axial piston hydraulic motor

9.5

Unregulated pump

13.5

Adjustable throttle

2.1

Pressure valve

5.8

Hydraulic distributor

2.5

Filter

0.7

Check valve

5.7

Pressure pipelines

4.0

Drain pipelines

1.8

Pipe connections

0.4

Hydrotank

1.2

Mechanical system Transmission

0.2

Shoe brake

1.7

Worm reducer

0.3

Couplings

0.8

Ropeway pulley

0.05

Deflecting rollers

0.05

Bearing units

2.0

Electrical system Packet switch

0.1

Automatic switch

0.15

Controllers

0.2

Electric cables

0.01

Safety devices

3.0

the motion mechanism Pmech = 1, since overhaul may not include restoration work for a number of structural elements with a low failure rate (e.g. transmission, worm reducer, electrical cables, switches, etc.). Pmech (τr,i ) = Pmech (τr,i + 0) − Pmech (τr,i − 0).

(8)

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Fig. 3. Change in time of trouble-free operation probability for the motion mechanism: 1— without repair; 2—failure recovery; 3—repair as required by the repair documentation.

5 Conclusion The developed method of computer simulation for the process ropeway system motion mechanism reliability changing for mobile ropeway complex is expedient to be used when planning repairs to such mechanisms to assess their technical effectiveness and ensure the required reliability indicators. The method has a number of advantages: • it allows to predict the change of reliability indicators throughout a period of time— both for the motion mechanism as a whole and for its individual structural elements taking into account the time and scope of repairs; • it allows to simulate the operational stage of the motion mechanism life cycle; and • it allows to obtain initial information (probability of uptime operation of all potentially dangerous structural elements) for the analysis of operational risks of the motion mechanism using a fault tree at an arbitrary time of operation of the mobile ropeway complex. The expansion of the proposed approach for forecasting changes in the reliability indicators characterizing the operability of the entire mobile ropeway complex throughout a period of time, and planning repair activities period and scope are promising directions for further research. Acknowledgements. The study was supported by President Grant for Government Support of Young Russian Scientists No. MD-422.2020.8.

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20. Težak S, Toš Z (2010) Reliability analysis of operation for cableways by FTA (fault tree analysis) method. Promet-Traffic & Transportation 22:163–173. https://doi.org/10.7307/ptt. v22i3.272 21. Ross SM (2014) Introduction to probability models. Academic Press, New York 22. Nikitin OF (2007) Nadezhnost, diagnostika i ekspluatatsiya gidroprivoda mobilnykh obektov (Reliability, diagnostics and operation of hydraulic drive of mobile objects). MGTU, Moscow 23. Lagerev AV, Tarichko VI, Lagerev IA (2019) Modelirovanie rezhimov raboty gidroprivodov s chastotno-drosselnym regulirovaniem mobilnykh transportno-peregruzochnykh kanatnykh kompleksov (Modeling operation modes of hydraulic drives with frequency-throttle regulation of mobile transport and overloading ropes complexes). Nauchno-tekhnicheskiy vestnik Bryanskogo gosudarstvennogo universiteta 4:462–480. https://doi.org/10.22281/2413-99202019-05-04-462-480 24. Denson W, Chandler G, Crowell W et al (1991) Nonelectronic parts reliability data. IIT Research Institute, Chicago 25. Failure rate of elements. Directory (2018). https://areliability.com/intensivnost-otkazov-ele mentov-spravochnik/. Accessed 15 Jan 2020

Interaction of a Large Tire with the Soil A. V. Vasilenko(B) , S. A. Ivanov, and V. I. Gilmutdinov Voronezh State Technical University, 20 Let Oktyabrya, Voronech 394006, Russia [email protected]

Abstract. The paper presents the results of an experimental study into the interaction of a wheel propulsion device equipped with large-sized pneumatic tires with the ground surface. To conduct full-scale experiments while studying the influence of the characteristics of a pneumatic tire on the parameters of the calculation model, special stands with rectilinear and circular trajectories of a single wheel were used, which allow testing a single wheel in conditions as close as possible to real. It was found that the contact surface of the wheel with large tires can contain several zones of deformation of the soil surface, which, in turn, can be represented by a combination of cylindrical and flat surfaces. In addition, it is shown that in the zone of loading the wheel, the deformation vector of the soil surface has a sufficiently large angle of deviation from the direction of the gravity vector. Taking these features into account when constructing a calculation model will improve the modeling adequacy of the process of interaction of large tires with a supporting surface. The research results allow one to justifiably expand the field of mathematical modeling of the wheel interaction with various types of supporting surfaces. Keywords: Wheel propulsion · Experimental stand · Pneumatic tire · Single-wheel experimental study · Wheel drive · Large tire · Pneumatic tyre · Ground surface · Mutual deformation · Engine load · Surface load · Support surface · Support load

1 Introduction In the modern, high-tech world, it is possible to achieve high-performance indicators, both in the productivity of the work performed, and as a result of economic profit, only if costs are minimized at all stages of the product life cycle. In order to achieve high-performance indicators, strict compliance with all stages of the life cycle is a prerequisite. Both the cost and reliability of the developed product depend on the depth of development of the design and product modeling stages. The easiest way to increase reliability is to increase the safety margin. But this necessarily leads to higher product prices and lower product competitiveness. Therefore, only a precise definition of the parameters necessary for product development can ensure an optimal balance of product reliability and cost. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_87

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In the development of transport and technological machines, the interaction of the engine and the support surface plays an important role in the efficiency of work. The interaction of the wheel propulsion of transport-technological machines with the ground support surface largely depends on the propulsion design, the characteristics of the pneumatic tire, and many other parameters [1–9]. At the same time, the interaction parameters of the propulsion device and the supporting surface have a major impact on the traction dynamics of the machine and the processes taking place in its other systems. When designing such machines, one has to deal with process modeling to select the optimal design parameters. The aim of this work was an experimental study of the process of interaction of the wheel and the ground support surface. In addition, a more detailed study of the mutual deformation of the wheel and the bearing surface allows us to suggest refinement of the design interaction scheme, taking into account the features of the characteristics of tires with a diameter of more than 1.5 m.

2 Justification of Selection of Research Object As objects of study, the mechanical and other characteristics of a single-wheel propulsion with large pneumatic tires with an outer diameter of 1.5–2.6 m, designed for use on transport and technological machines of large unit power, were considered. When driving on a supporting surface, the wheel mover is exposed to external forces and moments that cause complex deformations of the pneumatic tire, in particular, its carcass and belt. In turn, the shell of the pneumatic tire is loaded with excessive internal air pressure and deformations that occur in the contact area cause a change in internal pressure, partially redistributing their effect on the rest of the shell. Solving the problem of determining the mechanical properties of a pneumatic tire by a calculation method, even using modern methods of numerical analysis, presents significant difficulties [2, 10, 11]; therefore, experimental methods for determining the mechanical properties of a pneumatic tire remain relevant. The process of interaction of a wheel equipped with a deformable pneumatic tire and a supporting surface is a task complicated by slipping and, as a consequence, by the presence of nonholonomic bonds of mutually deforming bodies [6, 7, 12–17]; therefore, to solve practical problems approximate models are often used to find engineering solutions when analyzing the traction qualities of a wheel propulsion. As an approximate model of the interaction of the wheel with the soil surface, the model proposed in [10, 18, 19], assuming that the soil surface is deformed only in the vertical direction, is most often used. Such an assumption agrees quite well with experimental results, for tires with a diameter of up to 1.4 m [10]. Deformations of a pneumatic tire caused by external forces and moments can be represented as a combination of simple components: radial, lateral, circumferential (tangential), and angular [2–4, 8–17], To assess the radial deformation of a pneumatic tire, its value, measured under the center of the wheel, called normal deformation, is normally used. For the case of rectilinear movement of the wheel, the most significant are the radial, circumferential, and angular deformations.

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It should be noted that when modeling the processes of interaction between the wheel and the soil surface, a model is often used with the representation of contact areas in the “loading” and “unloading” zones, where the contact surface is represented by two mating cylindrical bodies of the “hard” wheel [1, 7, 20]. This assumption significantly simplifies the computational complexity, while allowing you to take into account the main processes that occur in contact and, on the other hand, allows you to get an engineering method for calculating the wheel operation in traction mode.

3 Description of the Model and Experimental Installation Experimental studies of the interaction of pneumatic tires with various types of supporting surfaces were carried out during tests of a single-wheeled propulsion device on special stands, in a mode of movement close to free. The stands allow testing a singlewheel propulsion in all known modes, with passport values of vertical load, on various types of supporting surfaces [1]. The complex of measuring equipment allows you to register the basic parameters of the interaction of the wheel during the test. In Fig. 1, a general view of the test setup with the tire 29.5–29 F-114 is shown. In addition, the presence of a special in-wheel sensor made it possible to continuously measure and record the value of the main components of the pneumatic tire deformation—radial and tangential [15].

Fig. 1. General view of the test setup with tire 29.5-29 F-114.

As a result of the tests, the strain values for tires with diameters from 1.5 to 2.6 m were obtained. The most characteristics are the results of processing strain measurements for tires 37.5–39 mod. F-7.

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In Fig. 2. the trajectories of the movement of the tread surface point of the pneumatic tire 37.5–39 mod. F-7 are presented for various values of the central reference point slip coefficient (CRP) [1, 20] when the wheel moves along dense loam at internal air pressure pw = 0.2 MPa (C = 14–15 beats; Gk = 92 kN).

Fig. 2. The trajectories of the point of movement of the tread surface of the pneumatic tire 37.5– 39 mod. F-7 at different values of the CRP slip coefficient when the wheel moves through dense loam with an internal air pressure pw = 0.2 MPa (C = 14-15 strokes; Gk = 92 kN).

The trajectory of movement of a point on the surface of the wheel located in the central plane of rotation is in the nature of a cycloid deformed by the presence of slippage. In this case, the tangent constructed to an arbitrary point on the trajectory gives a visual representation of the direction and magnitude (along the radius of curvature) of the speed of movement of the selected point. Considering that joint deformation of the soil and the surface of the pneumatic tire occurs in the wheel loading zone (area with x > 0), it can be argued that the resulting trajectory can also be attributed to particles of the soil surface. To bind the trajectories to the supporting surface, the figure additionally shows the track parameters. Artwork has no text along the side of it in the main body of the text. However, if two images fit next to each other, these may be placed next to each other to save space. For example, see Fig. 1. An analysis of the trajectories obtained for two values of the CRP slip coefficient shows that in both cases the displacements are associated with the presence of the horizontal component of the strain vector, which is in good agreement with the results obtained previously [4–6, 14, 18, 21]. Moreover, an increase in slippage leads to a

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noticeable decrease in this component, and with a significant slippage, its value can be neglected, i.e. consider only the case of vertical soil deformation, as suggested in [1, 2, 12–14, 19, 22]. Figures 3 and 4 show the profiles of the contact surface of the tire 37.5–39 mod. F-7 and the relationship between its curvature and the longitudinal contact coordinate when the wheel moves on different types of soil surface, with a vertical load on the wheel axis Gk = 92 kN.

Fig. 3. The profile of the contact surface of the tire of 37.5–39 mod.F-7 and the relationship between its curvature and the longitudinal coordinate of the contact at the air pressure in the tire pw = 0.32 MPa on loose soil, θo = 0.98.

The relationships are obtained as a result of numerical differentiation of the surface deformations of the pneumatic tire in the contact area. The presence of a gap in the functions of curvature indicates a flat contact area. Moreover, the length of the flat section decreases with an increase in internal pressure and a decrease in soil strength. The torque applied to the wheel in traction mode, on the contrary, slightly increases its length. The graphs additionally plotted lines of constant radius, the value of which is determined in accordance with the model of the wheel proposed in [1, 20]. In general, the obtained results allow us to conclude that when considering the model of wheel interaction, not only the horizontal, but also the vertical component of the deformation of the soil surface, with regard to tires with a diameter of more than 1.5 m, is considered.

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Fig. 4. The profile of the contact surface of the tire of 37.5–39 mod.F-7 and the relationship between its curvature and the longitudinal contact coordinate at air pressure in the tire pw = 0.2 MPa on dense soil for different values of the coefficient of slippage of CRP.

4 Conclusion As a result of experimental studies of the characteristics of the wheel propulsion, relationships are obtained that allow more accurately to predict the behavior of the tested tires, especially in traction mode. The study of the trajectory of the motion of points on the surface of the tire with a size of 39.5–39 during rolling along a dense loam indicates the appearance of a flat zone in the contact, which is inclined in the direction of wheel movement and use a simplified model to simulate the process of interaction of the wheel with the surface An experimental study of the trajectory of the surface points of tires with a diameter of more than 1.5 m when driving on tight loam indicates the appearance of a flat zone in contact of the wheel with a supporting surface inclined in the direction of wheel movement, which allows us to use this refinement to construct a design scheme for modeling the wheel interaction process with a soil surface. The results can be used both in the design of large tires and in modeling the loads arising in the transmission of wheeled vehicles of high power.

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References 1. Ulyanov NA, PIssssssss N, Vasilenko AV et al (1982) Stands for testing large pneumatic tires. Constr Road Mach 6:21–22 2. Becker MG (1973) Introduction to the theory of systems terrain—the machine. Mechanical Engineering, Moscow 3. Ageikin YS (1972) Cross-country wheel and combined propellers. Mechanical Engineering, Moscow 4. Jhonson KL (1962) Tangential Tractions and Microslip in Rolling Contact Phenomen. Symposium Amstedam-London-New York, p 6–28 5. Babkov VF, Bezruk VM (1976) Fundamentals of soil science and soil mechanics. Higher school, Moscow 6. Brazhnik BM, Zuckerberg SM (1973) The influence of the design of the lugs on the working parameters of high-performance tires. Car Des 9:34–36 7. Glagolev NI (1964) Friction and wear when rolling cylindrical bodies. Eng J Acad Sci USSR 4:45–48 8. Pirkovsky YuV (1963) The study of the influence of the drive design to the front axles on the traction and economic qualities of high-traffic vehicles. Dissertation, University of Moscow 9. Pirkovsky YuV (1965) Some questions of rolling automobile wheels. Automot Ind 12:26–29 10. Arzhayev GA, Balaka MN, Vasilenko AV et al (2013) Kinematic relations when rolling elastic wheel on a flat deformable bearing surface. Scientific Bulletin of the Voronezh State university of architecture and civil engineering. High technologies. Ecology, p 102–109 11. Kolbasov AF (2011) Some topical issues of the car tires. Basic research 8–1. http://fundam ental-research.ru/ru/article/view?id=26799. Accessed 30 Jan 2011 12. Bernstein R (1913) Probleme einer experimentallen Motor-pflugmechanik. Der Motorwagen 9:59–63 13. Harris TA (1971) An analinical method to predict sliding in trust-loaded Angular contact ball bearings. Trans. ASME 93:28–31 14. Bocharova NF, Tsitovich IS (1983) Designing and calculation of wheeled vehicles of high passability. Mechanical Engineering, Moscow 15. Nikulin PI, Arzhayev GA, Vasilenko AV et al (1986) Deformation measurement of a pneumatic tire of a moving wheel. VINITI Scientific Works 9:54–61 16. Omelyanov AE (1948) The use of pneumatic wheels on agricultural machinery. Agric Mach 5:37–39 17. Chudakov EA (1948) Rolling of car wheel. Publishing House of the Academy of Sciences of the USSR, Moscow 18. Poletaev AF (1964) Rolling drive wheels. Tractors Agric Mach 1:21–22 19. Goberman PA (1979) Theory, design and calculation of construction and road machines. Mechanical Engineering, Moscow 20. Ulyanov NA (1982) Wheeled propellers of construction and road machines. Mechanical Engineering, Moscow 21. Ishlinsky AYu (1942) The theory of resistance to rolling and related phenomena. Publishing house of the conference on friction and wear, p 37–40 22. Kopelevich LM (1962) Analysis of the slippage of the drive wheels of the car when driving on deformable soils. Siberian Road Institute 33:105–119

Improving Technical Readiness of Wheeled and Tracked Vehicles in Severe Climatic Conditions A. A. Gorbunov1(B) and A. M. Burgonutdinov2 1 Perm National Research Polytechnic University, 29, Komsomolskij Prospect, Perm 614990,

Russia [email protected] 2 Perm Military Institute of the National Guard Troops of the Russian Federation, 1, Gremyachij Log, Perm 614112, Russia

Abstract. The article is devoted to the topical issues of increasing the technical readiness of wheeled and tracked equipment in harsh climatic conditions. The high technical readiness of the rolling stock depends on the condition of the batteries. Only the comprehensive application of insulation and heating can ensure the proper level of battery life at negative temperatures. The research proposes a solution for the rolling stock of non-Arctic performance, which under the conditions of operation is not advisable to convert to the Arctic, but it is necessary to ensure high technical readiness for one or two coldest 5-day periods with an air temperature of up to −35°C. The equipment requirements are formulated to solve this problem. The theoretical justification of the battery heater algorithm has been carried out. An algorithm is developed to calculate the parameters of cooling and heating of batteries, cooling and heating time, the amount of heat given, and the received heat. The insulation material for the battery is selected. A test calculation of insulation efficiency on the battery cooling time is performed. The power calculation and the choice of the type of heating element of the battery are carried out. The efficiency of the heater in the low-temperature freezer is checked. Keywords: Wheel and track equipment · Arctic performance · Battery · Thermal conductivity heater · Low-temperature camera · Insulation · Heat · 5-day

1 Introduction A significant part of the country’s wheel and track equipment (more than 60%) more than 5 months a year works in low temperatures. Severe climatic conditions have a negative impact on the performance of rolling stock. Due to a number of economic reasons and design features, the bulk of the rolling stock of domestic production (except for the “Arctic” equipment) is designed for reliable and effective operation in winter at temperature; the ambient air is not lower than −30°C. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_88

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When the air temperature drops below −30°C, the operation of wheeled and tracked cars becomes more complicated and there is a need for their additional equipment, as well as the mandatory provision of special winter fuel and lubricant. The mobile staff, operated in winter, require special maintenance, and driver and technical staff require at least short-term theoretical and practical training

2 Relevance, Scientific Significance with a Brief Overview of Literature Studies on the impact of climate factors on battery life show that issues of relationship between operating patterns and extreme cold climate conditions and their long-term impact on materials’ batteries are not sufficiently studied and remain open. Analysis of faults and failures, as well as predicting the reliability of battery in low temperatures is one of the main tasks that can be solved through organizational and technical measures, which will result in an increase in the technical readiness of the vehicles [1]. Lower ambient air temperature reduces the reliability and performance of batteries. This is due to the increase in the viscosity of the electrolyte when cooled, which is accompanied by an increase in resistance of the passing electric current, and at the same time the mixing that is required for the fresh electrolyte to enter the active mass of electrodes pores is complicated [2]. At low temperatures, battery conditions deteriorate dramatically. Cold batteries are constantly undercharged. Even at a temperature of −10°C, a 50% battery can be charged up to 60–70% of the nominal capacity. At a temperature below −30°C, the rechargeable current of the battery is reduced by 20–30 times compared to the temperature of +20°C [3]. However, the allowable level of AB discharge in the cold season should not exceed 25% to eliminate the risk of electrolyte freezing [4]. Another reason for the reduction in battery charge is the installation of additional electrical equipment, which consumes the generator’s power reserve provided by the design, and when the engine is not launched, the batteries are discharged. Additional electricity users include satellite monitoring systems and tachographs that consume up to 0.5 A [5], pre-launch heaters, and air heaters that consume up to 10–15 A during operation [6]. With sufficient vehicle life throughout the day, it is possible to ensure an adequate level of battery charge by applying insulation and heating, implemented in various ways [7].

3 Setting a Task The technical readiness of vehicles in cold climates depends directly on the condition of the batteries. To ensure the required level of rechargeable batteries in cold climates, it is necessary to develop a heater and insulation. Algorithm for solving the problem:

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• Determine the working conditions of the heater and make an algorithm for its operation • Determine battery cooling times for specified conditions • Determine the characteristics of the insulation to maintain the temperature of the batteries, conduct a check calculation of the cooling time with the insulation • To pick up a type of heater for batteries, to calculate the power • Check the efficiency of the battery heater. Conditions and algorithm of the heater. The temperature of the heater is −10°C, as a significant reduction in the power of the charging current occurs when the battery is cooled below this temperature [8]. The temperature of turning off the heater is +25°C; this temperature is accepted to provide a reserve of heat when the battery cools down after hours. The battery heats from −35°C to −10°C to 4 h and is caused by a battery charge rate of at least 75% and a limit of no more than 20% of the generator’s power (200 w) to the battery [9]. The heater consists of two plates located on the long sidewalls of the battery. Battery protection should ensure that the heater is turned off when the engine is turned off. Initial data for calculations: • Battery Tyumen 6ST-190L, specifications in Table 1 [10, 11] Table 1. Characteristics of the Tyumen 6ST-190L battery. Parameter

Value

L × W × H, m 0.518 × 0.228 × 0.238 Weight, kg

63.14

• • • •

Car is working for 12 h from 08:00 to 20:00 [12] Engine operating time is 9 h Car downtime is 12 h—from 20:00 to 08:00 The temperature of the surrounding air is the coldest 5-day event for the city of Perm −35°C [13] • Battery heating temperature by heater is 25°C 3.1 Structure A significant part of the country’s wheel and track equipment (more than 60%) more than 5 months a year works in low temperatures. Severe climatic conditions have a negative impact on the performance of rolling stock. Due to a number of economic reasons and design features, the bulk of the rolling stock of domestic production (except for the “Arctic” equipment) is designed for reliable and effective operation in winter at temperature the ambient air is not lower than −30°C.

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When the air temperature drops below −30°C, the operation of wheeled and tracked cars becomes more complicated, and there is a need for their additional equipment, as well as the mandatory provision of special winter fuel and lubricant. The mobile staff, operated in winter, require special maintenance, and driver and technical staff require at least short-term theoretical and practical training. Determining the cooling time of the battery without insulation will be carried out according to the formula 1. τ=

Q Q

(1)

where Q the amount of heat emitted when the battery is cooled; Q specific amount of heat emitted when the battery is cooled Transform (1) into the form (2): τ=

4L(CEL · mEL + CL · mL + CC · mC ) · mB   3 0,25 Pr g·β·t·L ·λ·F 2 V

(2)

where is the heat capacity of lead, CL = 0.13 kJ/(kg·K) [14]; mass of lead in the battery 6ST-190, mB = 43.1 kg [15]; the heat capacity of the electrolyte at a density of 1.27 kg/m3 , CEL = 3.3 kJ/(kg·K) [9, 14]; electrolyte mass in the battery 6ST-190, mEL = 15.24 kg [14]; mEL the heat case of the battery 6ST-190 from polypropylene, CC = CC 0.46 kJ/(kg·K) [14]; the mass of the battery case 6ST-190 from polypropylene, mC = mC 4.8 kJ/(kg·K) [15]; the mass of the battery 6ST-190 in running order, mB = 64.14 kg; mB L × B × H length, width, height battery, L = 0.518 m, B = 0.228 m, H = 0.238 m; initial temperature of the battery wall, tW = 25°C [16]; tW ambient temperature, tA = − 35°C [16]. tA g is the acceleration of gravity, g = 9.81 m/s 2 ; T is the absolute ambient temperature, K; Pr is the Prandtl number, Pr= 0.705 [14]; λ is the thermal conductivity coefficient battery, λ= 8.92 W/(m·K) [15] CL mB CEL

According to the results of the calculation, the cooling time of the non-insulated battery from tW = 25°C to tA = − 35°C will be 4.487 s, or 74 min and 47 s. Therefore, to prevent the battery from cooling in the intershift time, it is necessary to install an

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insulation. The insulation material should be fire-resistant, dielectric, and acid-resistant, no more than 20 mm thick. The mullito-silica fiber of the MKKPP-130 has been selected as the insulation material, and the characteristics are presented in Table 2 [17]. Table 2. Characteristic MKKPP-130. Parameter

Value

Application temperature, 0C

−180 … 1150

Density, kg/m3

130

Thermal conductivity, W/(m · K) 0.039 Heat capacity, J

1.047

Thickness, mm

20 ± 5

For the outer layer of the insulation, the flint KT-11-30 K fabric is selected, and characteristics are presented in Table 3 [18]. Table 3. Characteristic KT-11-30 K. Parameter

Value

Application temperature, °C

−200… 1000

Surface density, g/m2

300 ± 30

Thermal conductivity, W/(m·K) 0.04 0.35 ± 0.05

Thickness, mm

The efficiency of the insulation will be assessed by the test calculation of the cooling time of the battery with the insulation according to Eq. (3): τ=

Q

(3)

QI

where Q the amount of heat emitted when the battery is cooled; QI specific amount of heat emitted when the battery is cooled with insulation Convert (3)–(4): τ= where

2(CL · mL + CEL · mEL + CC · mC ) · mB · F



δI λI

+

δT λT

+

l λ

 ,

(4)

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δI λI δT λT

767

the thickness of the insulation layer, m; coefficient of thermal conductivity of the insulation, W/(m·K); the thickness of the outer layer of tissue, m; coefficient of thermal conductivity of the outer layer of insulation, W/(m·K);

According to the calculation, cooling time of the insulated battery with tW = 25°C to tA = − 35°C will be τ = 109515,412 s or 17 h 45 min, which meets the requirements. To maintain the temperature of the battery within the specified range, a heater is needed. The heater must meet the following requirements: • • • • •

the ability to quickly install and remove; high flexibility, strength, and impact resistance; resistance to acids; explosion protection; minimum thickness.

This is the requirements of the polymetallic resistive amophore heating element; the characteristics are presented in Table 4. Table 4 Heating element characteristics Parameter

Value

Application temperature, °C

−70 … + 65

Working surface temperature, °C 37.5 ± 2.5 Power consumption

40

Supply voltage, V

12 … 15

Current strength, A

3

Resistance, Ohm

4,6

L × W×H, m

0.513 × 0.185 × 0.004

To calculate the power of the heater, determine the amount of heat needed to heat the battery from tW = − 35°C to tA = − 10°C according to (5): QI = CB · mB · (tW − tA ), where tW initial temperature of the battery, °C; tA the final temperature of the battery, °C The amount of heat will be 1452220 J.

(5)

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Using formula (6), according to Table 4, calculate the heating time of the battery from tW = − 35°C to tA = − 10°C. QH = I 2 · R · t → t =

Q , ·R

I2

(6)

where I the current strength, A; R the resistance of the heater, Ohm; t the time of application of power, s The battery heats from tW = − 35°C to tA = − 10°C with one heater will be 9 h and two heaters in 4.5 h. This will provide a battery charge even under the most adverse conditions—when cooling down to a temperature of 35°C.

4 Practical Significance, Suggestions, and Results of Pilot Research As a result of measurements, the total power of the battery heater was 90 w, with a current strength of 6.7A and a voltage of 13.4 V, Fig. 1a. The heater was powered by a charger [19]. A programmable thermoregulator W1209, with a resistive temperature sensor, was used to control the heater [20].

Fig. 1. a check the power of the heater; b checking the heater in a low-temperature chamber.

The efficiency of the heater is checked in a low-temperature chamber. The battery was cooled for 24 h, to a temperature of −26°C, Fig. 1b. Since heating occurs linearly, 1 degree requires the same amount of heat, regardless of the temperature of the heating; the temperature of the heater was checked on the site from tW = − 26°C to tA = − 1°C. The heating time was 4 h, which confirms the theoretical calculations.

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5 Conclusions The following conclusions have been obtained as a result of the work. Requirements for a non-Arctic transport battery heater have been determined. Based on the analysis of the features of batteries and vehicles, an algorithm of the heater is proposed, providing the required level of charge at a temperature of up to − 35°C, theoretically justified are the temperature of switching on, the temperature of the switch, and the heating time. A thermal calculation algorithm has been developed for insulating batteries, allowing to determine the time of heating and cooling and the amount of heat being sputed and given away. A heater and a battery heater have been developed and tested. The heater and heater allow the battery to be charged at a temperature below −10 degrees Celsius and prevent it from cooling below −10°C during the intershift time (up to 12 h). The proposed solution may have practical significance and, when implemented, will improve the technical readiness of wheeled and tracked equipment of non-Arctic performance at temperatures of −35°C.

References 1. Akimov SV, CHizhkov YuP (2007) Elektrooborudovanie avtomobilej i traktorov (Electrical equipment for cars and tractors). Za rulem, Moscow 2. Ustinov PI (1952) Akkumulyatornye batarei (Rechargeable battery). Gosenergoizdat, Leningrad 3. Sapozhenkov NO (2015) Izmenenie temperatury avtomobil’nyh akkumulyatornyh batarej v zimnij period (Changing the temperature of car batteries in the winter). Inzhenernyj vestnik Dona 3:21–30 4. Yutt VE (2006) Elektrooborudovanie avtomobilej (Electrical equipment for cars). Goryachaya Liniya—Telekom, Moscow 5. Pankratov NI (1985) Ekspluataciya akkumulyatornyh batarej pri nizkih temperaturah (Battery operation at low temperatures). Avtomobil’nyj transport 2:16–19 6. TekhnoKom (2011) AvtoGRAF Sistema sputnikovogo monitoringa i kontrolya transporta: Rukovodstvo pol’zovatelya v.7.1 (Autograph system for satellite monitoring and control of transport: user’s Guide V. 7. 1). TekhnoKom, CHelyabinsk 7. Pevnev NG (2017) Podderzhanie zaryazhennosti akkumulyatornyh batarej s cel’yu povysheniya zhizneobespechennosti avtomobilej (Maintaining battery life in order to improve the life support of vehicles). Tekhnika i tekhnologii stroitel’stva 11:10–16 8. SHAAZ (2004) Rukovodstvo po remontu PZHD30-1015006 RK (Liquid diesel heater pzhd 30. Repair manual pzhd 30-1015006). SHAAZ, SHadrinsk 9. Mishchenko KP, Radvel’ AA (1974) Kratkij spravochnik fiziko-himicheskih velichin (Brief reference of physical and chemical quantities). Khimiya, Leningrad 10. NIISF (2000) SP 131.13330.2012 Stroitel’naya klimatologiya (Construction climatology). NIISF, Moscow 11. Standartinform (2009) GOST R 53165-2008 (MEK 60095-1:2006) Batarei akkumulyatornye svincovye starternye dlya avtotraktornoj tekhniki. Obshchie tekhnicheskie usloviya (Leadacid starter batteries for automotive equipment. General specifications). Standartinform, Moscow

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12. Standartinform (1979) GOST 23619-79. Materialy i izdeliya ogneupornye teploizolyacionnye mullitokremnezemistye steklovoloknistye. Tekhnicheskie usloviya (Materials and products of refractory heat-insulating mullite glass-fiber. Technical conditions). Standartinform, Moscow 13. Stekloplastik NPO (1999) TU 5952-151-05786904-99 Tkani kremnezemnye (Silica fabrics). NPO Stekloplastik, Moscow 14. Mintransa R (2018) Prikaz Mintransa Rossii ot 20.08.2004 N 15 Ob utverzhdenii Polozheniya ob osobennostyah rezhima rabochego vremeni i vremeni otdyha voditelej avtomobilej (On approval of the Regulations on the specifics of working hours and rest time for car drivers). Mintransa Rossii, Moscow 15. Batarei akkumulyatornye svincovye starternye. Instrukciya po ekspluatacii FYAO. 355.009 IE (Lead-acid starter batteries. Operating instructions). https://search.rsl.ru/ru/record/010096 88424. Accessed 15 Jan 2020 16. Davosyan MA (1962) Akkumulyatory i batarei svincovye (Lead-acid batteries and batteries). CINTI EP, Moscow 17. Afanas’ev SN (2001) Akkumulyatornye batarei. Ekspluataciya na vooruzhenii i voennoj tekhnike (Rechargeable battery. Operation in service and military equipment). PVI VV MVD Rossii, Perm’ 18. Tyumenskij akkumulyatornyj zavod (2012) Instrukciya po ekspluatacii batarei akkumulyatornoj starternoj NAKI 563412.012 (Operating instructions for the battery starter battery) Tyumenskij akkumulyatornyj zavod, Tyumen’ 19. Zaryadnoe ustrojstvo serii Kulon.Modeli-707d, 715d. Instrukciya po ekspluatacii (Pendant series charger. Model 707d, 715d. The manual). BLAST, Sankt—Piterburg 20. W1209 Thermostat Board. https://github.com/TG9541/stm8ef/wiki/Board-W1209. Accessed 15 Jan 2020

Modeling the Equipment for Mechanical Bulk Products Sorting L. V. Konchina(B) , M. G. Kulikova, and A. V. Borisov National Research University “MPEI” in Smolensk, Energy Travel 1, 214013 Smolensk, Russia [email protected]

Abstract. This paper considers a dynamic model of the process of mechanical bulk products’ separation in the form of a mechanical system on an elastic base. This model allows sorting grains, cereals, and other bulk products when sifting through grates and sieves and distributing them by size class. As an object of study of sorting equipment used in the processing of agricultural raw materials, we considered a vibrating screen machine. To conduct the analytical study of the processes arising from the screen movement, we proposed a dynamic model consisting of a screening surface located on an elastic base at some angle relative to the horizontal plane, of screened mass, and of vibration exciter. The bulk product is fed from above and moves through the screens, passing through several gratings or grids with different cell diameters. As the parameters determining the displacements of the mechanical system under study, we considered the ones adopted when modeling vibrations of the sprung rolling stock: bouncing, lateral bearing, twitching, pitching (galloping), and wagging. Differential equations of motion of the presented mechanical system with elastic bonds are obtained under the condition that the center of mass of the screen is displaced relative to the geometric center of symmetry on the screening surface. For this, we used the center of mass motion theorem and the one on the change of the kinetic momentum in a mechanical system of theoretical mechanics. The proposed system of differential equations of motion of a mechanical system makes it possible to numerically solve the problem, to determine its individual parameters, and to stable equipment positions. Keywords: Equipment modeling · Fractionation · Vibrating screen machine · Vibrating screen · Vibration exciter · Unbalance

1 Introduction Food industry currently occupies one of the leading places in the Russian economy. Current trends in improving product quality demand the use of modern equipment for sorting grain, malt, cereals, and other bulk products in grain processing, canning, food concentrate, and other food industries [1]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_89

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There is a wide range of equipment depending on the principle of separation (suction separators, winders, vibrating machines) [2, 3]. In production conditions, the process of bulk products separation is carried out using special equipment, such as a vibrating screen or screen [4, 5]. The vibrating screen machine is a type of sorting equipment. Screens and vibrating screen machines are intended to carry out the process of separation of bulk products and materials. Product is divided into size classes as it’s being sifted through gratings and sieves. Gratings are installed motionlessly; various types of motion are provided for screens: rolling rotation or vibration [6]. Screen housings of the vibrating screen machine make reciprocating movements. Bulk product is fed from above and moves through the screens, passing through several gratings or grids with different cell diameters. Under the influence of gravity and vibration of the desktop, the product is divided into several fractions of varying particle sizes.

2 Materials and Methods For an analytical study of the processes that occur during the motion of the considered mechanical system, it is necessary to draw up a design scheme, to carry out mathematical modeling of the motion process. In this paper, we propose a dynamic model, consisting of a screening surface located on an elastic base at some angle relative to the horizontal plane, of screened mass and of vibration exciter (vibrating screen machine). We adopted as parameters that determine displacements of the mechanical system under consideration, the ones adopted in the simulation of rolling stock vibrations: bouncing, lateral bearing, twitching, pitching, and wagging. For research, we used the center of mass motion theorem and the one on the change of the kinetic momentum in a mechanical system of classical mechanics.

3 Results and Discussion In this paper, in order to study mechanical processes that occur during the vibrating screen motion, we consider a model consisting of a screened surface, of a screened mass, and of a vibration exciter, the geometric parameters of which are shown in Fig. 1. The presented mechanical system is positioned on an elastic base at an angle α relative to the horizon. The longitudinal and transverse horizontal displacements of the center of mass of the mechanical system are denoted as x and y, respectively, and the vertical by z, and the rotation angles relative to the main central axes of inertia are denoted as follows: ψ around the transverse axis x, θ around the longitudinal axis y, and around the vertical axis z. In the considered model for displacements, the following terms can be used that accurately enough reflect the essence of these displacements adopted when modeling vibrations of a sprung rolling stock in [7]: • bouncing is linear movement of mass along the axis z; • lateral bearing is linear mass displacement along axis x;

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z

β О x

θ

α

ψ

y

l l1

Fig. 1. Geometrical parameters of a mechanical system

• twitching is linear movement of mass along axis y; • longitudinal pitching or galloping ψ are angular displacements of the mass relative to the axis x; • lateral pitching θ is angular displacement of the mass relative to the axis y; • wagging β is angular mass displacement relative to the axis z. Thus, the dynamic model of the screen is represented by a mechanical system with elastic bonds. In this case, elastic bonds are springs experiencing strain-compression tensile with stiffness ck (k = 1,2,3,4). In addition, when unbalances rotate, centrifugal forces arise, which determine the disturbing force P, which gives the following projections on the coordinate axis: Py = P sin ωt, Pz = P cos ωt, P = md rω2 ,

(1)

where ω is the unbalance rotational velocity, rad/s; t is the time, s; md is the unbalance mass, kg; and r is the eccentricity of the unbalance mass relative to its rotation axis, m. The following parameters were taken as generalized coordinates of the mechanical system: • zc is the vertical coordinate of the center of mass of the system; • ψ, θ , β are the angular motions relative to coordinate axes. Differential equations of motion of the system (under the assumption that the center of mass of the screen is displaced relative to the geometric center of symmetry on the screening surface) can be written in general form using theorems on the center of mass motion and on the change of the kinetic momentum in a mechanical system in projections on the coordinate axis n  d 2 zc Fize (2) M 2 = dt i=1

Jx

d2 ψ dt 2

=

n  i=1

− → Mx F ei ,

(3)

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 − d2 θ →e  Fi , = M y dt 2

(4)

 − d2 β →e  Fi , = M z dt 2

(5)

n

Jy

i=1 n

Jz

i=1

index “e” means that it is external forces that are considered; M is the mechanical system mass (the total mass of the screening surface, of the screened mass and of the vibration exciter), kg; Jx , Jy , Jz are the central moments of inertia of the mechanical system relative to the axes Cx, Cy, and Cz under the assumption that the axes pass through the center of mass of the system (point C). For the mechanical system under consideration, we wrote differential equations of motion in the following form [8–16]: M

d2 zc = nmd ω2 r cos ωt − Mg cos α + (P1z + P2z + P3z + P4z ), dt 2

(6)

n −  d2 ψ → e Pk , = M + M x x dt 2

(7)

 →  d2 θ e − = M y Pk , dt 2

(8)

−  d2 β → Jz 2 = Mze Pk , dt

(9)

Jx

k=1

n

Jy

k=1 n

k=1

the value n takes into account the number of unbalance; l, l1 are the distances between geometric axes of elastic elements (Fig. 1), m; g is the acceleration of gravity; P1z , P2z , P3z , P4z are projections of the restoring forces P1 , P2 , P3 , P4 on the axis z; M e is the moment developed by an electric engine. For systems with linear characteristics of elastic elements P1 , P2 , P3 , P4 , the first approximation can be represented as follows: d1 d2 P2 = c2 · 2 + b2 , dt dt

(10)

d3 d4 , P4 = c4 · 4 + b4 , dt dt

(11)

P1 = c1 · 1 + b1 P3 = c3 · 3 + b3

k = fk (zk , zc , θ, ψ), k = 1, n,

(12)

where c1 , c2 , c3 , c4 , b1 , b2 , b3 , b4 are coefficients that determine stiffness and viscous resistance of elastic elements.

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The model proposed by the authors of this paper does not specify any quantity and quality indicators of vibration exciters, electric engines of a mechanical system. The parameters proposed herein in order to describe the motion of the screen are different from already known and adopted parameters presented in [4, 5]. The resulting system of differential equations of a mechanical system motion allows for the numerical solution of both the problem as a whole and the determination of its individual parameters, but also it makes it possible to determine zones and stability positions by means of the methods proposed in [17, 18]. The numerical solution of the problem in a first approximation (provided that the deviations of the angle β = 0) showed that the motion relative to axes x and y is oscillatory, and changes in the angles θ and ψ are insignificant. The change in the axis z also takes place according to sinusoidal law (Figs. 1, 2, 3). The results obtained indicate the adequacy of the considered model of mechanical system (Fig. 4).

Fig. 2. Graph of displacement of the center of mass of the system relative to the axis z(m) over time t(s).

Fig. 3. Graph of change in the angle ψ(rad) over time t(s).

Fig. 4. Graph of change in the angle θ(rad) over time t(s).

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4 Conclusions 1. The use of differential equations of system motion, obtained using general theorems of system dynamics, allows us to solve both the problem as a whole and to determine individual parameters. 2. Using the proposed model will allow one to find out optimal working conditions of the screening equipment in order to ensure stability. 3. The developed model can be used to solve problems of product fractionation in food and processing industries.

References 1. Bracacescu C, Gageanu I, Popescu S, Cagatay Selvi K (2016) Researches concerning impurities separation process from mass of cereal seeds using vibrating sieves in air flow currents. Proceedings of 15th international scientific conference “Engineering for Rural Development”, Jelgava, Latvia, p 364–370 2. Rus Fl (2001) Separation operations in the food industry, Publishing Transylvania University of Brasov, p 75–101 3. Kulikova MG, Konchina LV (2017) Modeling of process equipment in the food industry. Nat Tech Sci 5(107):126–127 (In Russian) 4. Nukeshev S, Slavov V, Kakabayev N, Amantayev M (2018) Mathematical modelling in 3D of opener with scatterer of the grain-fertilizer seeder. MECHANIKA 24(6):840–844. https:// doi.org/10.5755/j01.mech.24.6.22476 5. Ene Gh, Sima T (2013) Aspects regarding sifting materials on vibrating sieves I; II; J Synth Theor Appl Mech 4(1):15–25, 2:99–112 6. Omarov TI (2010) Investigation of dynamic processes in the mechanisms of variable structure of rail technological and transport machines: the author’s abstract on the competition for the scientific degree of Doctor of Technical Sciences: 01.02.06. Almaty, Institute of Mechanics and Engineering Science of the Ministry of Education and Science of the Republic of Kazakhstan 7. Borisov AV (2015) Automated development of three-dimensional models of exoskeletons with links of variable length Mechatronics, automation, control 16(12):828–835 8. Borisov AV (2018) Mechanics of the spatial model of an exoskeleton and an anthropomorphic robot. Questions of defense equipment. Scientific and technical journal. Technical means of countering terrorism 16(3–4):46–55 9. Rumyancev SA, Azarov EB (2005) Mathematical model of non-stationary dynamics of the system “vibromachine-electric drive” in the case of drive from asynchronous motors with a short-circuited circuit) Transport of the Urals: Scientific and Technical Journal 1(4):2–7 (In Russian) 10. Rumyancev SA (2003) Dynamics of transient processes and self-synchronization of movements of vibrating machines). UrB RAS, Ekaterinburg 11. Omarov TI, Ibraev SM (2004) Dynamic study of the mechanisn of movement of rail cars: guidelines for the implementation of the SRS at the course “Dynamics of cars”. KazNTU, Almaty 12. Omarov TI (2010) Research of dynamic processes in mechanisms variable structure rail transport and technological machines: abstract of doctor technical Science: 01.02.06. Almaty, Institute of mechanics and machine science, MER RK

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13. Omarov TI (2010) Vibrational model of trolley rolling stock. Bull Eurasian Nat Univ 4(77):311–314 14. Rumyantsev SA (2003) Dynamics of transients and self-synchronization movements of vibration machines. Uro RAS, Yekaterinburg 15. Rumyantsev SA, Azarov EB (2005) Mathematical model of non-stationary dynamics of the “vibrator-electric drive” system in the case of a drive from asynchronous motors with a closed loop. Transport of the Urals. Scientific and Technical Journal 1(4):2–7 16. Omarov TI (2010) Determination of the parameters for the dynamic model of the mechanism of movement of rail cars. Vestnic KazNPU named after Abai’s 1(29):182–186 17. Omarov TI (2006) Frictional self-oscillations in the transmission of the movement mechanism of a rail car. Proceeding of the IX all-Russian Congress on theoretical and applied mechanics. Nizhny Novgorod, p 175–180 18. Omarov NI, Felsky VI (2005) Static indeterminability and dynamic loads of the rail car transmission. Tr. Intl. forum on the science, technology and education, Moscow, p 103–106

Method of Calculating the Stress–Strain State of the Cylinder Head of a Liquid-Cooled Transport Diesel Engine A. N. Gotz and V. S. Klevtsov(B) Vladimir State University Named After Alexander Grigorjevich and Nikolay Grigorjevich Stoletovs (VlSU), 87, Gorky Street, Vladimir 600000, Russia [email protected]

Abstract. In the internal combustion engine, the details surrounding the combustion chamber—the cylinder head and the piston—are exposed to stresses from the action of variable gas force and variable heat load due to the combustion of fuel in the combustion chamber, while the temperature stresses are much higher than the stresses from the power load. Therefore, at the design stage of the new design of the internal combustion engine is calculated on the durability of heat-stressed parts, as they limit the reliability of the piston engine. The stages of creating and preparing a solid-state model of the cylinder head to create a finite element model are shown on the example of the diesel 8CHN12/13 (KAMAZ 740.75-440). The shape of the elements for the finite element model of the cylinder head was chosen from the condition of reducing the design time. It is shown that the high-frequency temperature fluctuations that occur as a result of the working process of the piston engine do not affect the thermal strength of the cylinder head, and the influence is exerted by high-frequency temperature fluctuations due to changes in the operating modes of the engine. The changes in the main characteristics of the aluminum alloy, from which the cylinder head is made, with temperature changes and with cyclic thermomechanical loads of low frequency are presented. It is shown that when the temperature increases, the endurance limit of the material decreases under low-frequency loads. Keywords: Cylinder head · Thermal state · Stress–strain state · Diesel · Finite element · Aluminum alloy

1 Introduction When operating a transport diesel engine in unsteady conditions in the cylinder head and piston, there are stresses not only from the variable gas force, but also variable temperature stresses caused by the temperature difference in the individual sections of these parts, since the thermal state in the combustion chamber changes over time. Note that as the calculations showed [1, 2], often, the temperature stresses of heat-stressed © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_90

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parts are much higher than the stresses from power loads. Therefore, at the design stage of a new piston engine with the specified in the terms of reference indicators of durability calculation of durability is the cylinder head or piston is given quite a lot of attention [3, 4]. Let us consider the method of selection of initial data in the calculation of thermal and stress–strain state of the cylinder head of a transport diesel engine using the finite element method and using the software package Solid Works, taking into account the nature of loading during Assembly, as well as in operation [5, 6].

2 Purpose of Research To offer a technique of a choice of initial data at the calculation of thermal and stress– strain state of a cylinder head of the transport diesel engine of liquid cooling taking into account the loadings arising when you are pressing of saddles and sleeves of valves, installation of injectors, fastening of a head at Assembly, and also at work of the diesel engine in operation.

3 The Proposed Method of Research Since the calculation is carried out in Solid Works software complexes [5, 6], it is necessary to build a solid-state 3D model of the cylinder head (CH) before constructing a finite element model (CAM). Building a 3D model of the CH can be carried out in three ways: direct, reverse, and combined [7, 8]. The direct method is to build a solidstate model according to the drawings of CH. The reverse is in sizing and building a 3D model on the finished product. Since CH is a complex spatial detail with complex internal geometry (cavity cooling intake/exhaust ducts, oil line), to build the most accurate solid model you need to know the exact size of internal cavities. Let us consider in more detail the combined method of determining the parameters on the example of the 8CHN12/13 Hz diesel engine (KAMAZ 740.75–440). Overall dimensions and dimensions of the superstructure CH are taken from the drawings. To clarify the geometry of the internal cavities, the head must be cut into several horizontal layers. It should be borne in mind that the cutting tool has its own thickness, which must be taken into account and compensated for when building a 3D model. Otherwise, the resulting dimensions and geometry will be distorted. At the same time, increasing the number of cuts allows more accurately simulate the internal cavities of the CH, while introducing an error due to extrapolation of the cut material. When constructing a 3D model based on the reverse engineering method, special attention should be paid to the location and correctness of the statement of the sizes of small chamfers, fillets, automatically constructed surfaces (operation pulling on sections with a curve forming [2, 5, 6]). You should also pay attention to the elements of zero thickness. Figure 1 shows the stages of creating a solid-state model of 8CHN12/13 Hz diesel in a reversible way-by cutting into five layers. Based on the created solid-state three-dimensional model (see Fig. 1 b), a finite element model (CAM) of CH is constructed using the SolidWorks Simulation software. As shown by the experience of using FEM in calculating the CH of air-cooled diesel

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Fig. 1. The result of building a solid model: a—cut into five-layer cylinder head, b—solid 3D model of the cylinder head.

[1, 2], it is most appropriate to use four-node tetrahedron in the CAM (Fig. 2), the use of which helps to reduce the design time compared to other CE [3, 4, 7, 8] and also allows more accurately describe the geometry of the CH compared to hexahedrons or pentahedrons (eight and six nodal elements).

Fig. 2. Four-node tetrahedron for the finite element.

When constructing a CAM, it is necessary to reduce the size of the sides of the finite element (FE) in places of stress concentration (inter-valve jumper, jumper between pipelines and the nozzle installation hole, etc.) and in sections of a sharp temperature drop. After the construction of the CAM CH, diesel 8CHN 12/13 (740.75-440) consists of 2805 finite elements and 47,347 nodal points (Fig. 3).

Fig. 3. Finite element model CH.

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To determine the maximum temperature of the loading cycle, it is necessary to specify the characteristics of the material from which the CH is made. In this particular case, the CH is made of aluminum alloy Ak9CH (AL4) [9–11]. For calculations of the heat-stressed deformed state, it is necessary to know not only the main characteristics of the material, but also the laws of change of these characteristics depending on temperature. The changes in the modulus of elasticity E, the ultimate tensile limit σ v and yield point σ 0, 2 , the coefficients of linear thermal expansion α and thermal conductivity λ, as well as the mass heat capacity C from temperature T are given in Table 1 [12, 13]. Table 1. Change of physical and mechanical properties of aluminum alloy Ak9CH (AL4) T, °K

E, MPa

σv , MPa

σ0,2 , MPa

α, 1/K

λ,W/(m °K)

C, J/(kg °K)

293,16

72,000

317

170

0,0,000,209

152

714

373,16

66,900

307

150

0,0,000,217

155

755

423,16

66,500

292

130

0,0,000,221

156

776

Density μ = 2650 kg/m3 , Poisson ratio μ = 0.33

The mechanical properties of the aluminum alloy Ak9Ch (AL4) deteriorate significantly when heated from 300 to 423 °K, the ultimate tensile limit σ v decreases from 317 MPa to 292 MPa, the yield point σ 0, 2 —from 170 MPa to 130 MPa, and the modulus of elasticity E—from 0.72 105 MPa to almost 0.66 105 MPa [12–14] (Fig. 4). All this leads to a sharp decrease in the durability of the CH [15].

Fig. 4. Change of their properties of alloy Ak9ch (AL4) at temperature change.

The coefficient of thermal expansion α and the coefficient of thermal conductivity λ are less dependent on temperature. In Fig. 5, graphs of low-cycle fatigue of aluminum alloy at temperature change of the tested samples are given. Since the CH undergoes mechanical and thermal loading during operation of the engine under real conditions of low frequency, and the results given in Fig. 5 can be used in calculating the durability of CH. The validity of the use of these data for the conditions of high-speed diesels is justified in the work [12].

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Fig. 5. Fatigue curves for alloy under cyclic thermomechanical loads of low frequency (1/30 Hz).

Let’s divide conditionally all stresses arising in sections of CH from Assembly to operation of the engine in operation on the stresses caused by mechanical action, and also caused by temperature difference: (a) stresses caused by mechanical action on CH: press-fit seats and the valve; tighten the nuts or bolts securing the injector; tightening of bolts or studs CH; gas power; (b) the stress caused by the temperature difference in the cross sections of CH. Let us consider in more detail how to determine the stresses caused by mechanical action on CH. When the seats and valve sleeves are installation by to press in the CH has a contact pressure, because they are connected during hot landing, while the outer diameters of the seats and valve sleeves are larger than the diameter of the hole, where these parts are installed (Fig. 6). Pressing can be carried out under pressure or due to the temperature difference of parts 1 and 2 (see Fig. 6).

Fig. 6. Coupling when pressing two cylindrical parts: 1—internal part; 2—external part.

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When part 1 is installed in the inner surface of the part 2 (CH), there is a contact pressure, the value of which can be determined using the formula of Lame [16–18], since the mating parts have the same length. Since the valve seats and bushings are made of gray cast iron, and the CH is made of aluminum alloy, an additional contact pressure arises on the contact surface due to the difference in the α Al and α gci coefficients of linear thermal expansion of aluminum alloy and gray cast iron, respectively. Finally, the contact pressure p on the CH surface (see Fig. 6-detail 2) equals [19, 20] p=

δ−(αAl −αgci )td2 d 2 2 1 1+k1 1 1+k2 E1 ( 1−k 2 − μ1 ) + E2 ( 1−k 2 1 2

+ μ2 )

,

(1)

where δ is the difference between the diameters of the parts (tensioner in the connection of parts 1 and 2) (see Fig. 6); α Al and α gci —the coefficients of linear thermal expansion of aluminum alloy and gray cast iron, respectively, 1/deg; d is the diameter of the surface openings in CH; d 2 —external diameter of a saddle or sleeve valve; E 1 –modulus of elasticity of gray cast iron (part 2), which made the saddle and the valve; k 1 = d 1 /d is the ratio of the inner diameter of the seat or the valve to the diameter of the mounting surface of CH; μ1 is the Poisson’s ratio for gray cast iron; E 2 –module for aluminum alloy CH; k 2 = d/d 2 is the ratio of the diameter of mounting surface CH to conditional diameter d 2 (we assume using the principle of Saint-Venant [6] that the mating parts have the same thickness); μ2 is the Poisson’s ratio for the material CH. When installing the injector, the nut is tightened, and the force is assumed in the form of a uniformly distributed pressure within the pressure cone [17–19] at the point of contact of the nozzle sealing washer with the support surface of the CH [19]. If we denote F f - the surface area of the injector on the inner surface of CH, m2 , then on this surface acts uniformly distributed load: Pg = pz − p0 ,

(2)

where pz is the maximum combustion pressure in the design mode, MPA; p0 is the atmospheric pressure, MPA. Forces from tightening bolts fastening heads’ cylinders (in our case cylinder heads are individual) are determined by in dependence from magnitude gas forces Pg : Pg = (pz − p0 )Fp ,

(3)

where F p —piston area, m2 . If the head is multi-cylinder (is common to several or all cylinders), then Pg is multiplied by the number of cylinders. The force coming on one bolt is correspondingly equal to Pb = Pg /ib =

(pz − p0 )Fp ib

where ib is the number of bolts holding the cylinder head.

(4)

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The tightening force of the fastening bolt CH at a given coefficient of the stock density of the joint is equal to [19] ss Q0 = ν(1 − χ )Pb ,

(5)

where χ is the coefficient of the main load of the threaded connection (usually χ = 0.2…0.4) [2, 3]. To ensure the density of the joint between the CH and the cylinder block, take ν = 1.2…2.5—with soft gaskets; ν = 2.5…3.5—with metal gaskets; ν = 3.0…4.0—with flat metal gaskets [2, 3]. The main load factor can be calculated by the formula [17]:  λd χ= , (6) (λd + λb )  where λ d is the sum of the coefficients of compliance of contracted items (the system case) [17]; (λd + λb )—the sum of the coefficients of compliance of contractible parts and bolt (Fig. 7). The coefficient of compliance of thin intermediate part (gasket) λd was determined by the formula: λd =

l1  , Ed π4 (a + l1 tg α)2 − d02

(7)

where l1 is the thickness of the gasket; a is the outer diameter of the bearing surface of the nut (bolt head); tgα = 0.4…0.5 (for the pressure cone); and d 0 is the diameter of the bolt hole; E d is the elastic modulus of the gasket, N/m2 . To determine the gas pressure force, the maximum combustion pressure pz was selected in the design mode of the engine.

Fig. 7 Cylinder head-mounting scheme: 1—CH; 2—gasket; 3—cylinder block.

To determine the temperature stresses arising in sections of CH at the engine’s operation requires the solution of the nonstationary heat conduction problem with the choice of the boundary conditions describing the thermal interaction of the surface of HZ and environment [1] that will allow us to determine the heat-stressed state of CH.

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Since in [1, 14, 15] the method of calculating the heat-stressed state is considered in sufficient detail with the indication of the accepted boundary conditions, this section of the calculation is not provided in this article. Complex heat exchange in the diesel engine is nonstationary, which is due to changes in the temperature and pressure of the working mixture not only during the cycle, but also under different operating conditions. In addition, the transport diesel about 80…90% of the time works on non-stable modes. However, the change in temperature in CH caused by the working process (highfrequency fluctuations) does not significantly affect the stress–strain state of the cylinder head. Calculation and simulation performed only when the diesel engine is running in different engine modes. Stresses from mechanical loads and thermal stresses are added up according to the principle of independence of the action of forces. The thermal stress– strain state of cylinder heads is discussed in detail in [1, 2, 4], and in [21–24] methods for modeling the thermal state in order to clarify the calculation for durability.

4 Conclusion The proposed method of selecting the initial data for calculating the stress–strain state of the cylinder head of a liquid-cooled transport diesel engine, taking into account the mechanical loads acting on the cylinder head elements and arising when you are pressing in CH of the seats and valve sleeves, the installation of injectors, fixing the head on the block case during Assembly, as well as when the diesel engine is in operation from the action of gas and inertial forces, allows calculating the strength and predicting the reliability of the CH in operation.

References 1. Gotz AN, Ivanchenko AB, Prygunov MP, Frantsuzov IV (2013) Modeling of the heat–stressed state of the cylinder head of an air–cooled tractor diesel. Fundamental Research. http://fun damental-research.ru/ru/article/view?id=31686. Accessed 26 Jul 2018 2. Gotz AN, Prygunov MP (2014) Modeling of the heat–stressed state of the cylinder head of a tractor diesel. Tractors and agricultural machinery. M Russ 10:19–22 3. Gotz AN, Glinkin SA (2016) Conditions of loading of pistons of internal combustion engines and the reasons of formation of cracks on an edge of the combustion chamber Tractors and agricultural machines. M Russ 10:12–16 4. Gotz AN, Glinkin SA (2016) Criteria for destruction of heat–stressed parts of piston engines and review of methods for assessing the durability of pistons. Tractors Agric Mach. M RUSS 11:14–18 5. Alyamovsky AA (2010) COSMOSWorks. Fundamentals of structural strength calculation in SolidWorks environment. DMK Press, Moscow 6. Alyamovsky AA (2010) Engineering calculations in Solid Works Simulations. DMK Press, Moscow 7. Morozov EM, Nikishov GP (2008) Finite element Method in fracture mechanics. LKI/URSS, Moscow 8. Donchenko AS, Morganyuk VS, Averchenkov EA, Kharchenko VK, Isaev EV (1983) Calculation of the stress–strain state of the tractor diesel piston under cyclic loading. M Russ, p 39–44

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9. Morozov NF (1984) Mathematical problems of the theory of cracks. Nauka, Moscow 10. Birger IA, Shor BF, Demyanushko IV (1975) Thermal Resistance of machine parts. Engineering, Moscow 11. Rumb VK, Medvedev VV (2006) Forecasting of durability of details of ship diesels. Dvigatelestroyeniye 4:29–34 12. Abramchuk FI, Marchenko AP, Razleytsev NF (1992) Modern diesel engines: improved fuel efficiency and long–term strength. Technika, Moscow 13. Klyuev VV (1995) Engineering. Machine reliability, Mashinostroenie, Moscow, Encyclopedia, p 592 14. Donchenko AS (1985) To the calculation of the diagram of nonisothermal deformation of piston alloy AL25. Problems of Strength 3:103–107 15. Collins J (1984) Damage to materials in structures. Analysis, prediction, prevention. Mir, Moscow, p 624 16. Serensen SV, Kulaev VP, Nadarevic RM (1975) Bearing capacity and calculations of machine parts for durability. Engineering, Moscow, p 488 17. Birger IA, Shorr BF, Iosilevich GB (1993) Calculation of the strength of machine parts. Handbook. 4th edn. Mashinostroenie, Moscow, p 640 18. Iosilevich GB, Lebedev PA, Streljaev VS (2013) Applied mechanics. Mashinostroenie, Moscow, p 576 19. Gotz AN (2017) Numerical methods of calculation in power engineering: textbook. FORUM: INFRA–M, Moscow, p 352 20. Kogaev VP, Makhutov NA, Gusenkov AP (1985) Calculations for strength and durability. Mashinostroenie, Moscow, p 224 21. Lazarev EA, Ivashchenko NA, Perlov ML (1988) Features of thermal and stress–strain state of pistons of tractor diesel. Build Engine 7:3–5 22. Voznesensky NP, Logvinenko AYa (1969) To the question of the nature of the stress state of cylinder heads when working tractor engines. Tractors Farm Mach 4:6–8 23. Voznesensky NP, Logvinenko AYa (1971) On the causes of destruction and the choice of material cylinder heads diesels. Tractors, Farm Mach 2:13–14 24. Grishin DK, Vallejo Maldonado PR, Chaynov ND, Lodnya VA (2010) Mathematical modeling of the thermal state of the head of a high–speed small–size diesel engine with direct injection. Tractors Farm Mach 8:28–30

Specifics of Rock Excavation Process Using Open-Pit Excavator O. Lukashuk1(B) , K. Letnev1 , and A. Komissarov1,2 1 Ural Federal University, 19 Mira Street, Yekaterinburg 620002, Russia

[email protected] 2 Ural State Mining University, 85, Khokhryakova Street, Yekaterinburg 620014, Russia

Abstract. The article considers specific features of the rock excavation process carried out by an open-pit front-shovel excavator in terms of determining what operation modes of its main mechanisms (mechanisms of lifting and thrusting) are most rational for the excavation purposes. It is shown that their joint action during excavation forms a kinematic chain which connects the main mechanisms and a bucket and consists of their driven links and elements of the operational equipment. It was established that operation parameters of the main mechanisms depend on kinematic properties of a transmission mechanism, which includes the kinematic chain itself. Relations were obtained for the purposes of evaluating such rational velocities of lifting and thrusting which would ensure the bucket (top of its cutting edge) followed a path set for the excavation. The results of the research should allow to develop a system to control drives of the main mechanisms. Keywords: Front-shovel operational equipment · Rock excavation process · Main mechanisms · Transmission mechanism · Rational lifting and thrusting velocities

1 Introduction The process of rock excavation is carried out by coordinating operation of two main mechanisms of an open-pit excavator (lifting and thrusting mechanisms) in order to move its bucket and simultaneously extract a layer of rock under constantly changing working conditions. It is hindered and limited by psychological and physical abilities of an excavator operator. And, as experience of using open-pit excavators demonstrates, the duration of a working cycle in specific conditions considerably exceeds its design value. In the current period of market economy, the task of increasing the efficiency of openpit excavators by utilizing all of their technological capabilities becomes even more actual than ever. The main trend in solving this problem is to establish for the main mechanisms the laws of their motion during excavation. Known methods of determining those are based on formal approaches—fuzzy logic, artificial intelligence, and so on [1–8]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_91

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2 The Goal and Tasks of the Research The goal of this research is to determine kinematic and dynamic characteristics of the excavation process by finding out how operation parameters of the main mechanisms (velocities of lifting and thrusting) change to make the bucket (top of its cutting edge) follow a set path. The tasks would be • to justify a mathematical model of the transmission mechanism formed during excavation; • to find such lifting and thrusting velocities which could provide a necessary bucket (cutting edge) motion along a set path. The object of the research is a mechanical system which includes the main mechanisms (lifting and thrusting) and transmission mechanism. Its subject is to determine functional relations between those parameters which define the bucket (cutting edge) position within an open-pit and operation parameters of the main mechanisms (lifting and thrusting velocities). And the research methods are adopted from the theory of machines and methods, mathematical modeling, and calculating experiment.

3 Solution of the Research Tasks A kinematic chain is formed during excavation, which consists of driven links of the main mechanisms (rack gear of the thrusting mechanism, head block of the boom, section of the lifting rope which comes off the head block) and elements of the operational equipment (saddle bearing, dipper stick, bucket rigidly fixed to the stick and bucket suspension) [9, 10]. Structural analysis of the kinematic chain was carried out. The following assumptions were taken: • the head block of the boom could be practically considered as a driven link of the lifting mechanism since the speed of a point where the lifting rope comes off the block is equal to the lifting speed, and also, kinematically, it is a crank; • the lifting rope (its fragment) is a weightless, inextensible fiber in the form of a variable-length rod; • the bucket suspension represents a solid body which is pivotally connected with the bucket and forms a common rod with the rope. The structural analysis of the kinematic chain resulted in the following statements: • a kinematic pair formed by the lifting rope and head block is equivalent, relative to the speed, to a revolute pair (joint), which is instantaneous in this case; • the «stick-bucket» link forms a two-degrees-of-freedom connection with the excavator stand (boom) in the form of translational (stick-saddle) and revolute (saddle-boom) pairs;

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• the kinematic chain includes four movable links: two cranks (rack gear and head block), rod (lifting rope and bucket suspension) and «stick-bucket» link; • the chain forms a two-crank-and-rod mechanism with the stand. Thus, in the process of excavation, a transmission leverage is formed (Fig. 1), which converts the motion of driven links of the main mechanisms into the motion (movement) of the bucket [2]. Lever mechanisms differ from other mechanisms by featuring «individual» kinematic properties which depend on the structural schematic of a mechanism, type of kinematic connections between links and geometry (lengths) of the links. The main characteristics of the leverage are kinematic and dynamic transfer functions (gear ratios) which determine the dependencies between kinematic and dynamic parameters of driven and driving links [11, 12].

Fig. 1. Structural schematic of electromechanical system of open-pit excavator: LD, TD—drives of lifting (LM) and thrusting (TM) mechanisms

Degrees of freedom (mobility) are calculated for the transmission mechanism as S = 3n − 2P5 = 3 · 4 − 2 · 5 = 2

(1)

where n = 4 is number of pairs as movable links; P5 = 5—number of fifth class kinematic pairs (one degree of freedom). The mechanism with two degrees of freedom (two generalized coordinates) can have either two initial links (if generalized coordinates are set to coordinates of two links) or one initial link (if it forms a two-degrees-of-freedom pair with the stand) [4]. As an initial link, a «stick-bucket» is selected here, and, therefore, positions of all links in both the transmission mechanism and main mechanisms are determined from the «stick-bucket» position. Thus, the process of excavation is characterized by a common transmission mechanism of the main drives [5, 6] which includes the main mechanisms and transmission mechanism (Fig. 2). Generalized coordinates of the common transmission mechanism are set to coordinates at the top of the bucket cutting edge in the XOY coordinate system (point K – X K and Y K ), where the OX-axis coincides with the excavator datum level, and the OY axis—with the rotation axis of its slewing platform. Then, kinematic analysis of the transmission mechanism was carried out on the basis of a graph-analytical method by drawing diagrams of the mechanism and its velocity vectors. To find the velocities of working motions (lifting and thrusting), it is necessary to specify the laws of motion for the initial link (that is a trajectory of the bucket movement

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Fig. 2. Schematics of transmission mechanism: 1—“stick-bucket” link; 2, 3—crank; 4—lifting rope; V E , V L , V T —velocities of excavation, lifting, thrusting

(top of its cutting edge) and excavation speed) along with the dimensions of transmission mechanism links. Since the thrusting velocity changes its direction depending on the bucket position in a pit, so it follows that the form of a vector velocity diagram and the type of dependencies used to determine the velocities of working motions change, too. Such dependencies which could help to assess kinematic transfer functions (relations between lifting and thrusting velocities and excavation speed) are expressed in a general form as KTFT =

VT = f1 (XK , YK , lC , lV , ψ, α, ϕ1 , ϕ2 , γ , δ, ε); VE

(2)

KTFL =

VL = f2 (XK , YK , lC , lV , ψ, α, ϕ1 , ϕ2 , γ , δ, ε), VE

(3)

where KTFT , KTFL are kinematic transfer functions of thrusting and lifting motions; lC , lV —lengths of constant and variable links; ψ—slope angle of a tangential trajectory for the bucket movement at the point K; α, ϕ 1 , ϕ 2 , γ , δ, ε—angles determining the positions of links. To determine operation parameters of the main mechanisms, a computing experiment was carried on an EKG-20A open-pit excavator made by JSC «Uralmashplant». The forces of lifting and thrusting were to be evaluated via equations of statics for specified external forces.

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Initial data for the calculation were • coordinates of the «stick-bucket» link, that is, the point K (top of the bucket cutting edge)—X K and Y K ; • velocity of excavation—V E = 1 m/s; • slope angle of a tangential trajectory for the bucket movement at the point K – ψ = 60°; • radiuses of excavation at the excavator datum level for initial, intermediate, and terminal trajectories—RE.DL = 9, 12 and 15 m; • maximum excavation height—H E.MAX = 17 m; • tangential force of resistance to excavation—F R = 230 kN. Table 1 cites the results of computation to work out an open pit of 17 m in height and A = 6 m in stope width. The data cited above show that operation parameters of the main mechanisms change significantly while depending on both the excavation radius (X K coordinates) and excavation height (Y K coordinates). Ranges of velocities for working motions are thrusting velocities −0.87 m/s ≤ V T ≤ 0.84 m/s and lifting velocities 0.01 m/s ≤ V L ≤ 0.95 m/s. The set given in the table of such calculated lifting and thrusting velocities which enable the bucket (top of its cutting edge) to move along a specified path is a fragment of a simulation model for the process of excavation in a pit. This simulation model could be expressed graphically in the form of hodographs for lifting and thrusting velocity vectors (Fig. 3). It would also help to determine an algorithm of digital control which should form control commands to be sent to the drives of the main mechanisms. Thus, the simulation model of excavation obtained from the computing experiment would allow to evaluate operation parameters of the main mechanisms at any point of the excavator work area for specified power-force parameters realized at the bucket and specified trajectories of its movement (top of its cutting edge).

4 Conclusion The methodology suggested here to calculate operation parameters (velocities of lifting and thrusting) of the main mechanisms of an open-pit excavator via a computing experiment allows to evaluate actual velocities of their working motions in specific mining and technological conditions of operation (pit dimensions, bucket trajectory types, and so on). Determining correlations between operation parameters of the main mechanisms in the process of excavation could serve as a basis in development of an adaptive system of digital control for the drives of the main mechanisms which would help to increase the efficiency of excavator operation in specific conditions by properly coordinating velocities of working motions (lifting and thrusting).

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Table 1. Operation parameters of the main mechanisms for an EKG-20A excavator with the excavation height of H E = 17 m. №

Coordinates of point K

Velocities of lifting and thrusting

Forces of lifting and Powers of lifting and thrusting thrusting forces

X K, m

V L , m/s

F L , kN

Y K, m

V T , m/s

F T , kN

PL , kW

PT , kW

Initial trajectory (X K0 = 9 m) 1

9.0

0

0.95

−0.87

290

−630

275

550

2

10.15

2

0.92

−0.81

350

−620

331

490

3

11.30

4

0.84

−0.70

420

−605

352

421

4

12.45

6

0.70

−0.51

520

−580

359

292

5

13.60

8

0.52

−0.19

700

−555

366

106

6

14.75

10

0.50

0.19

975

−590

489

110

7

15.90

12

0.66

0.50

1270

−700

826

348

8

17.05

14

0.80

0.70

1560

−850

1220

578

9

18.20

16

0.89

0.81

1810

−1005

1580

795

10

18.80

17

0.91

0.84

1910

−1060

1770

923

Intermediate trajectory (X K0 = 12 m) 11

12.0

0

0.90

−0.72

517

−411

468

296

12

13.15

2

0.85

−0.61

560

−402

478

246

13

14.30

4

0.78

−0.45

595

−395

464

177

14

15.45

6

0.70

−0.23

674

−346

472

80

15

16.60

8

0.65

0.04

755

−294

487

11

16

17.75

10

0.66

0.29

838

−217

550

64

17

18.90

12

0.69

0.50

886

−95

613

48

18

20.05

14

0.68

0.65

896

115

608

74

19

21.20

16

0.49

0.75

890

497

433

371

20

21.80

17

0.25

0.78

960

806

218

638

Terminal trajectory (X K0 = 15 m) 21

15.0

0

0.85

−0.55

690

−207

586

114

22

16.15

2

0.80

−0.42

722

−187

577

78

23

17.30

4

0.74

−0.24

754

−152

559

37

24

18.45

6

0.69

−0.04

791

−91

544

4

25

19.60

8

0.64

0.16

835

9

538

1

26

20.75

10

0.60

0.35

885

156

528

54

27

21.90

12

0.51

0.50

937

372

474

186 (continued)

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Table 1. (continued) №

Coordinates of point K X K, m

Y K, m

V L , m/s

28

23.05

14

0.32

0.62

1010

685

327

423

29

24.20

16

0.08

0.70

1180

1130

43

793

30

24.80

17

0.01

0.74

1350

1420

225

1057

Velocities of lifting and thrusting V T , m/s

Forces of lifting and Powers of lifting and thrusting thrusting forces F L , kN

F T , kN

PL , kW

PT , kW

Fig. 3. Hodographs for velocities of working motions while moving the bucket up to a design excavation height: VL, VT—velocities of lifting and thrusting

References 1. Babakov SE, Pevzner LD (2012) Algorithmizing control of excavator bucket movement while digging by means of fuzzy logic. Min Equip Electromech 9:8–17 2. Komissarov AP, Letnev KY, Lukashuk OA (2017) Analyzing two-crank leverages of operational equipment in open-pit excavators. Technological Equipment for Mining and Oil-Gas Industry: Proceedig of XIV International Science and Technology Conference “Readings in memory of V. R. Kubachek”. UrSMU Publishing, Ekaterinburg, 20–21 Apr 2017, pp 41–46 3. Koryukov AA (2013) Geometric model for operational equipment of open-pit excavator to calculate stresses on electric drives and control bucket position. News of higher education. Min J 3:106–113 4. Levitskiy NI (1979) Theory of mechanisms and machines. Science, Moscow, p 576 5. Lukashuk OA, Letnev KYu, Komissarov AP (2017) Determining operation modes for drives of main mechanisms in open-pit excavators. News of Higher Education. Min J 5:52–58

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6. Lukashuk OA (2019) Laws of forming operation parameters of main mechanisms of open-pit excavator during rock excavation. Min Equipment Electromech 3:14–17 7. Malafeev SI, Tikhonov YuV (2015) Intellectualization of open-pit excavator. Min Info-Anal Rev 11:107–115 8. Pevzner LD (2014) Automated Control of heavy-duty single-bucket excavators. Mining, Moscow, p 400 9. Pevzner LD, Babakov SE (2015) Algorithm of digging control for open-pit excavator (mechanical shovel) using fuzzy logic. Min Info-Anal Rev 1:263–271 10. Poderni RY (2007) Mechanical equipment of open-pits, 6th edn., rev & sup. MSMU Publishing, Moscow, p 680 11. Bender FA, Sawodny OA (2014) Predictive driver model for the virtual excavator. In: The 13th international conference on control, automation, robotics and vision (ICARCV), pp 187–192 12. Lee B, Kim HJ (2014) Trajectory generation for an automated excavator. In: Proceedings of the 14 International conference on control, automation and systems (ICCAS/14). Seoul, pp 716–719

Temperature Condition of Car Exhaust System at Low Ambient Temperatures M. G. Boyarshinov and N. I. Kuznetsov(B) Perm National Research Polytechnic University, 29, Komsomolsky Prospect, Perm 614990, Russia [email protected]

Abstract. The main reason for the condensate formation in the exhaust system of transport and technological vehicles is the deposition of excess moisture contained in the hot exhaust gas on the cold walls of the exhaust system at low ambient temperatures. An experimental study was made for the time dependences of the temperature of the exhaust system elements of transport and technological vehicles on various negative ambient temperatures during the engine warm-up at idle speed. The temperature was measured with a special equipment OVEN MV1108A, OVEN AC4, and SCADA OwenProcessManager software. The characteristic features of the unsteady temperature change of the exhaust system elements in the conditions of negative values of the ambient temperature are revealed. An analysis of the experimental data showed that the experimentally obtained temperature– time dependences when using dimensionless indicators differ slightly. This made it possible to construct a mathematical model of the temperature dependence of the exhaust system elements on the engine operating time for the entire research range. Keywords: Exhaust gases · Exhaust system · Temperature · Condensate

1 Introduction In a modern city, car operation is usually characterized by prolonged downtime in traffic jams and long engine idle. When operating in cold winter conditions, the exhaust system walls remain cold and water vapor moving along the exhaust system together hot exhaust gases condenses on cold inner surface of this system [1–3]. As a result during prolonged operation of the engine at low-speed accumulation of condensate is observed in the exhaust system of transport and handling machines [4]. Frequent prolonged warming up of the car in winter conditions, driving in short runs, subsequent long-term parking at air temperatures below 0 °C are dangerous, because depending on the design features of the exhaust system elements, formation, accumulation in significant quantities, and freezing of condensate in the exhaust system are possible, what leads to the formation of an ice plug inside the exhaust system or at its © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_92

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outlet and, as a consequence, the inability to start the engine [5, 6]. The same problem occurs in autonomous fluid engine preheater. The consequence of this is a violation in the cold winter season of the delivery schedules of vital products, materials, medicines, fuel, foodstuffs to remote northern settlements and areas, the planned delivery of passengers to places of residence and work is violated, the terms of construction and repair work are disrupted, road maintenance is deteriorating, and so on. The presence of condensate in the exhaust system leads to intense corrosion of parts of this system: pipes, mufflers, and resonators. When repairing parts of the exhaust system welding is carried out [7–10]. With temperature differences in the winter due to the presence of condensate microcracks form in the weld points, which increase in size over time, and as a result the welds burn out. This leads to increased noise, high toxicity, and increased exhaust emissions of freight and passenger vehicles. As a result, these problems in the exhaust systems lead to negative consequences for urban residents and the environmental situation as a whole. In the service enterprises of the Perm Region and other regions in the autumn– winter period, complaints are repeatedly recorded in connection with the occurrence of the problem under discussion. The same problem exists and is widely discussed in the northern regions of the Urals and Siberia. Condensate is formed when hot exhaust gases [11–15] moving in the exhaust system come into contact with the walls of this system, which have a temperature close to the temperature of the surrounding air. The composition of the exhaust gases contains water in the vapor state, which is formed during the combustion of fuel (more than 1.2 kg per 1 kg of burnt fuel, [16]), which enters the engine with air from the atmosphere (up to 0.05 kg per 1 kg of burnt fuel in depending on the ambient air temperature [16]), as well as due to chemical reactions occurring in the catalytic converter.

2 Experimental Procedure Since the main reason for the formation of condensate inside the exhaust system is the temperature difference between the exhaust gases and the walls of the exhaust tract, the authors performed a series of experiments to determine the temperature of the elements of the exhaust duct system during engine warm-up when it is idling [17]. The temperature of the elements of the exhaust system was measured using special equipment [18–20]. The analog input module OVEN MV110-8A is designed to read and convert an electrical signal from temperature sensors to Celsius degrees. The USB/RS485 OVEN AC4 automatic interface converter communicates between the MV 110-8A input module and a personal computer, which is used to collect, store, convert, and display experimental research results. The temperature of the exhaust system elements is measured by thermocouples (Fig. 1) with an operating range from –50 to +500 °C. Experimental studies were carried out in the following sequence: • before the start of the measurements, the temperature of the exhaust system and other components of the vehicle was equal to the ambient temperature, for which the vehicle was kept at the site for at least 8 h before the measurements; • a “cold” engine was started, the temperature of which (like the temperature of the exhaust system) is equal to the temperature of the ambient air;

Temperature Condition of Car Exhaust System at Low

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Fig. 1. Location of thermocouples when measuring the temperature of the exhaust system elements

• engine idling for 30 min, during which the temperature was automatically recorded at the studied points of the exhaust tract. Experience in the practical operation of the vehicle under investigation shows that this time is enough to warm the engine to operating temperature. To reduce the influence of secondary factors on the process of heating and cooling elements of a car, experiments were carried out in a territory protected from the wind. An experimental study was conducted for an exhaust system consisting of an exhaust manifold that simultaneously serves as a preliminary catalytic converter; the middle part of the exhaust system, consisting of a lower catalyst and a front silencer; intermediate pipe and rear muffler. Thermocouples are installed on the outer surface of the elements of the exhaust system (Fig. 1).

3 Experimental Results The results of determining the dependence of the temperature of the exhaust system elements on time at ambient air temperatures –3 °C, –6 °C, and –9 °C are presented in Fig. 2. Analysis of the data obtained shows that at negative ambient air temperatures the temperature distribution of the examined elements of the exhaust system is of the same type. At the point of placement of the first thermocouple, an intense rise in temperature is noted at the initial stage of engine warming up. Next, there is a gradual decrease in temperature from the location of the second thermocouple to the last fourth thermocouple, which corresponds to the physical interpretation of cooling the exhaust gas as it moves from the exhaust manifold to release into the atmosphere. By the end of the 30-min time interval, a general decrease in temperature is observed and its value for all elements of the surface of the exhaust system reaches stationary values. In the locations of the third and fourth thermocouples, the elements of the exhaust system warm-up to stationary temperatures rather quickly, and then the temperature remains practically unchanged during the entire considered time interval. Apparently, in the areas where these thermocouples are located, favorable conditions may exist for the formation and accumulation of condensate.

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Fig. 2. Dependence on time t of the temperature of the elements of the exhaust system at ambient temperatures –3 °C (a), –6 °C (b), and –9 °C (c);  —thermocouple 1, —thermocouple 2, o—thermocouple 3, ♦—thermocouple 4

Temperature Condition of Car Exhaust System at Low

799

It was found that with a decrease in ambient temperature, an increase in the maximum value of the surface temperature of the exhaust system is simultaneously observed. Such an increase in the temperature of the surface of the exhaust system with a decrease in the negative ambient temperature is apparently due to more intensive engine operation and a later exit to the operating thermal regime.

4 Analysis of the Experimental Results For further analysis, the following values are introduced: T max —the maximum temperature of the considered element of the exhaust system and t max —time to reach the temperature T max of the same element of the exhaust system. Using the entered values, the dimensionless temperature (1) and time values are considered (2) θ= τ=

T Tmax t tmax

(1) (2)

Figure 3 shows the dependences of the dimensionless temperature θ the surface of the elements of the exhaust system on the dimensionless time τ at ambient air temperatures –3 °C, –6 °C, and –9 °C during warming up at idle speed of the car engine.

Fig. 3. The dependence of the dimensionless temperature θ on the dimensionless time τ of the elements of the exhaust system at ambient temperatures –3 °C (a), –6 °C (b) and –9 °C (c); —thermocouple 1, —thermocouple 2, o—thermocouple 3, ♦—thermocouple 4

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Figure 4 shows the curves describing the averaged dependences θ (τ ) for each of the ambient temperatures. The weak difference in the obtained dependences suggests the possibility of constructing a universal mathematical dependence between the dimensionless temperature θ and time τ to describe the process under study. Using the least squares method to approximate the obtained curves with a polynomial of degree 4 leads to the expression θ = −0.0696τ 4 + 0.6345τ 3 − 2.0253τ 2 + 2.5369τ − 0.0956.

(3)

The resulting expression can be used to approximately describe the time dependence of the temperature of the exhaust system elements.

Fig. 4. Averaged dependences of dimensionless temperatures θ on dimensionless time τ of the exhaust system elements at ambient temperatures –3 °C (), –6 °C (), and –9 °C (o)

5 Conclusion An experimental study was carried out to determine the temperature of the exhaust system elements at the stage of unsteady operation of an automobile engine at negative ambient temperatures. In an experimental study, it was found that lowering the ambient temperature leads to a slower heating of the car engine and, at the same time, to an increase in the temperature of the exhaust system elements. Based on the experimental data, dependences on the dimensionless time of the dimensionless temperature of the exhaust system elements are constructed. It turned out that the averaged curves practically coincide over the considered time intervals. This made it possible to obtain an approximate mathematical description of the dependence of temperature on time at the considered time intervals and ambient air temperatures.

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References 1. Condensate-free technology. Longer life (2019) http://www.ernst-hagen.de/htmlen/produkteserienschalldaempfer-kondensatfrei.php Accessed 15 Nov 2019 2. Kuznecov NI, Petuhov MYu, Haziev AA (2014) Razrabotka rekomendacij po ekspluatacii avtomobilej v usloviyah megapolisa (Development of recommendations for the operation of cars in a metropolis). Problemy tekhnicheskoj ekspluatacii i avtoservisa podvizhnogo sostava avtomobil’nogo transporta, Moscow, pp 227–233 3. Kuznetsov N, Petukhov M, Khaziev AA, Laushkin AV (2015) Problem of accumulation and freezing of condensate in the exhaust gases of cars at low temperatures. Dev Technol Automot Eng 47–55. https://doi.org/10.4028/www.scientific.net/AMM.838.47 4. Kuznecov NI, Petuhov MYu, Shcheludyakov AM (2012) Ob osobennostyah zapuska dvigatelya legkovogo avtomobilya v sovremennom megapolise pri nizkih temperaturah okruzhayushchej sredy (On the features of starting a car engine in a modern metropolis at low ambient temperatures). Vestnik PNIPU. Ohrana okruzhayushchej sredy, transport, bezopasnost’ zhiznedeyatel’nosti 1:137–143 5. Reshenie suda № 2-1747/2015 2-1747/2015 ~ M-374/2015 M-374/2015. (2015) Delo № 2-1747/2015 ot 24 iyulya 2015 g. http://sudact.ru/regular/doc/UP2TFt0dJ9Vj. Accessed 13.04.2019 6. Reshenie Kurchatovskogo rajonnogo suda g. CHelyabinska. (2011) Delo № 2-6/11 ot 13 aprelya 2011 goda. http://sudact.ru/regular/doc/p7OrtXeRoBdy. Accessed 13 Apr 2019 7. Curà F, Mura A (2012) Aging characterization of metals for exhaust systems. Int J Automot Technol 13(4):629–636. https://doi.org/10.1007/s12239-012-0061-0 8. Li MC, Wang SD, Ma RY et al (2012) Effect of cyclic oxidation on electrochemical corrosion of type 409 stainless steel in the simulated muffler condensates. J Solid State Elecrochem 16(9):3059–3067. https://doi.org/10.1007/s10008-012-1746-z 9. Curà F, Mura F, Sesana R (2015) Experimental investigation of fatigue and aging performance of automotive exhaust flexible couplings. Proc Inst Mech Eng Part C: J Mech Eng Sci 229(7):1215–1223. https://doi.org/10.1177/0954406214549268 10. Abdoli M, Rahimi H, Fail Godarzizadeh AJ (2011) Investigation of failure in automotive exhausts. Anal Preven 11:679. https://doi.org/10.1007/s11668-011-9502-8 11. Boyarshinov MG, Lobov NV, Kuznecov NI, Martem’yanov AO (2018) Temperaturnyj rezhim sistemy vypuska otrabotannyh gazov avtomobilya v usloviyah ponizhennyh temperatur (The temperature regime of the exhaust system of the vehicle in low temperatures). Vestnik PNIPU. Transport. Transportnye sooruzheniya. Ekologiya 3:5–16. https://doi.org/10.15593/ 24111678/2018.03.01 12. Heil B, Enderle C, Herwig H, Strohmer E, Margadant A, Ruth W (2002) The exhaust system of the Mercedes SL500. MTZ Worldwide 63(1):2–5. https://doi.org/10.1007/BF03227514 13. González NG (2016) Condensation in exhaust gas coolers. Energy and thermal management, air conditioning, waste heat recovery. Springer, Cham. https://doi.org/10.1007/978-3-31947196-9_9 14. Hashimoto R, Mori G, Yasir M, Tröger U, Wieser H (2013) Impact of condensates containing chloride and sulphate on the corrosion in automotive exhaust systems. BHM BergHuettenmaenn Monatsh 158(9):377–383. https://doi.org/10.1007/s00501-013-0180-6 15. Bosch. Gasoline-engine management Basics and components (2001) Automotive Aftermarket Business Sector, p 432 16. Laushkin AV, Haziev AA (2012) Prichiny obvodneniya motornogo masla v ekspluatacii (Reasons for flooding engine oil in operation). Vestnik MADI 1:63–67

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17. Boyarshinov MG, Kuznecov NI (2019) Temperaturnyj rezhim sistemy vypuska otrabotavshih gazov avtomobilya pri ponizhennyh temperaturah okruzhayushchego vozduha (The temperature regime of the exhaust system of the vehicle at low ambient temperatures). Progressivnye tekhnologii v transportnyh sistemah, p 776 18. Kuznecov NI (2017) Kolichestvennaya ocenka soderzhaniya v otrabotavshih gazah vody, postupayushchej v dvigatel’ s atmosfernym vozduhom (Quantification of the content in the exhaust gas of water entering the engine with atmospheric air). Vestnik PNIPU. Transport. Transportnye sooruzheniya. Ekologiya 1:77–87. https://doi.org/10.15593/24111678/2017. 01.06 19. http://www.owen.ru/catalog/modul_vvoda_analogovih_signalov_owen_mv110_8a/335 02416. Accessed 04 Oct 2019 20. Novickij PV (1991) Ocenka pogreshnostej rezul’tatov izmerenij (Estimation of errors of measurement results). Publishing house Energoatomizdat, Leningrad, p 304

Analysis of a Quarry Mobile Diesel Generator Station During the Moving of an Excavator S. I. Malafeev1,2(B) and S. S. Malafeev3 1 “Joint Power” Company, Ltd., PO Box 142, Moscow 111672, Russia

[email protected] 2 Vladimir State University Named After Alexander and Nikolay Stoletovs, 87, Gorky Str.,

Vladimir 600000, Russia 3 Vladimir Polytechnic College, 11, Oktyabrsky Ave., Vladimir 600001, Russia

Abstract. The results of calculation and analysis of an autonomous quarry station with a voltage of 6.3 kV for powering excavators and drilling rigs during movement are considered. Structurally, the station is made in the form of a removable module of a closed design, which is installed in place of the standard body of the base truck. The module has two compartments and a transition pad. A diesel engine and its support systems (fuel, air, cooling, lubricating, and starting) are installed in the front compartment. A transformer and a high-voltage cabinet are located in the rear compartment. The system of electrical equipment provides all types of protection to ensure the safe operation of the station. The results of station power calculations for the movement of various excavators are presented. To control the mobile station, modern means of automation and remote control were used. A specialized computer provides remote start-up and shutdown of the unit, engine support, adjusting the parameters of the regulators, measuring the parameters of the generated electricity, recording processes during the run, generating a history file, remote monitoring, including using the Internet. The control of the electric equipment of the excavator during the movement provides for speed limits when moving uphill or downhill in accordance with the energy capabilities of the diesel generator station. Keywords: Excavator · Power supply · Electric drive · Engine · Generator · Control

1 Introduction In open-pit mining, excavators using electric energy sources are widely used [1–3]. These include electric mechanical shovels and draglines and electro-hydraulic excavators [4– 10]. Power supply of such excavators is carried out from stationary or mobile lines [11]. A feature of the operation of mining machines is their frequent movement when changing the site of excavation [12]. For the movement of machines usually use special cable connections to connection points in quarries. In the absence of electric lines in © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_93

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places of movement of excavators, autonomous mobile diesel power plants are used. Such stations can also be used to power electric excavators in areas that are not provided with stationary power lines. The operation of the diesel generator station during the power supply of the excavator, both when loading the rock mass and when moving, has the following features: • non-stationary nature and a wide range of load power changes; • complex modes of starting powerful loads; • workload with energy recovery, for example, when the excavator moves downhill when driving. In bidirectional energy transfer in a local electric network, a buffer energy storage device and an energy processes control system are required [13]. Under these conditions, questions of rational choice of the power of a diesel engine and a synchronous generator of an electric autonomous station and development of algorithms for controlling the operation of an excavator to coordinate the modes of an energy source and a consumer are of particular interest. The article presents the results of a study of an autonomous diesel station designed for use in mining enterprises when driving mining excavators, carried out by the “Joint Power” Company, Moscow.

2 Analysis of the “Mobile Station—Excavator” System When moving an excavator, usually only movement drives work, the installed power of which is 20–30% of the total installed power of the main movement drives (hoist, crowd, and swing). At the same time, the electric equipment of the auxiliary needs of the excavator also works, the power of which depends on the type of excavator and its operating mode and amounts up to 25% of the power of the main drives [14]. The process of connecting the excavator to a power source depends on the control system used. Most of the excavators currently operating use the Ward Leonard drive system with a network synchronous motor. When connecting an excavator, an asynchronous start of the synchronous motor is performed, or a preliminary acceleration of the drive motor is started using one of the generators of the multi-machine unit. In electro-hydraulic excavators, series reactors are used to facilitate start-up. In modern excavators with semiconductor energy converters and active rectifiers, the rational interaction of the drives and the supply network is provided by the control system [15, 16]. 2.1 Calculation of the Power of the Station When Moving the Excavator Since a career autonomous station is used to move various excavators, when choosing equipment, various possible modes of its operation must be taken into account. Consider the forces of resistance to movement and power processes when driving an excavator with a mass m. The resistance to movement of the excavator is determined by the formula [17]. F = F1 + F2 + F3 , where F1 is the movement resistance, F1 = (0.05 − 0.07) mg;

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g is the acceleration of gravity; F2 is the soil deformation resistance, F2 ≈ 0.1 mg; F3 is the resistance to movement during ascent or displacement force during descent, F3 = mg sin α; α is the angle of rise (descent) to the horizon. Mechanical power when moving considering F1 = 0.05 mg is equal to Pm = (F1 + F2 + F3 )v = (0.15 + sin α)mgv, where v is the speed of movement. The moment of resistance to rotation is determined by the formula Ms = (0.6 − 0.65) µmg, where μ is the soil resistance coefficient. At μ = 0.5 we have Ms = (0.3 − 0.325) mg. Mechanical power when turning the excavator at an angular speed of Ω is equal to Ps = Ms Ω. The table shows the results of calculating the power of excavators during the movement in different conditions. Data on masses, speeds of movement, and climbing angles are taken from the technical descriptions of mining machines. Additionally, when calculating the power of a power plant, the power consumption of own needs should be taken into account. It depends on the type of excavator and the operating mode of the equipment. Approximately, the power consumed by auxiliary equipment is 70% of the power of the auxiliary transformer. The powers calculated for driving at maximum speed and maximum uphill angle correspond to maximum power values. These values determine the maximum load of the diesel generator station. When the excavator moves downhill or when braking, mechanical–electrical energy conversion by the movement drives occurs. The generated electrical energy enters the local AC network. The receivers of this energy are a step-down transformer for auxiliary needs with an auxiliary excavator electrical equipment connected to it and a synchronous generator of an autonomous station. The generator enters engine mode and rotates the crankshaft of the diesel engine. As a result, the “engine braking” mode takes place. The energy potential of such braking is determined by the mechanical efficiency of the diesel engine ηm.d , which is 88–91%. Therefore, the maximum power of electromechanical energy conversion by a diesel generator station, taking into account the efficiency of a synchronous generator ηc,Γ , is equal to P1 =

1 − ηm.d Pd , ηs.g

where Pd is the rated power of the diesel engine;

(1)

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ηs.g is the efficiency of synchronous generator. All recovered electrical energy must be converted into other types of energy, mainly mechanical and thermal. In this case, the power of converting electrical energy into mechanical energy directly by an autonomous station should not exceed the value of P1 . The calculation data shown in Table 1 indicate that a mobile station with an installed equipment capacity of 0.7–0.8 MW can be used to move excavators. In this case, the speed of movement and the uphill angles should be limited. Table 1. Power plant capacity when moving excavators Excavator

Mass, kg Movement Speed, km/h

Ascent angle, deg

Power, kW

EKG-5

0.197 × 106

0.55

12

44

109

131

21

EKG-8

0.373 × 106

0.45

12

69

169

250

32

EKG-10

0.41 × 106

0.7

13

115

289

274

53

EKG-12

0.43 × 106

0.8

13

134

343

288

63

EKG-15

0.672 × 106

0.75

13

205

507

450

96

EKG-18P

0.75 × 106

1.0

12

306

756

502

143

EKG-20K

0.77 × 106

1.0

12

314

776

515

147

EKG-32P

1.05 × 106

1.0

13

428

1060

703

200

EKG-35

1.25 × 106

1.08

12

535

1336

836

252

EX 3600

0.353 × 106

2.1

30

438

1304

236

511

EX 5600

0.518 × 106

2.1

30

643

1930

347

750

Movement without ascent

Uphill movement

Turn, 2 rpm

Descent recovery

2.2 Functional Diagram of the “Mobile Station—Excavator” System Figure 1 shows a simplified diagram of the operation of electrical equipment during the moving of an excavator with AC electric drives [18]. It shows a truck with a diesel

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generator station installed on it, containing a diesel engine, a synchronous generator, and an electrical switchgear; electric cable and excavator. The high-voltage input device of the excavator is connected via cable to the mobile station. Two transformers are used to power the excavator equipment. T1 provides power to the main drives, and T2 provides power to Auxiliary Equipment. In order to simplify the drawing, the excavator diagram shows only the drive: Motor 1 and Motor 2, transistor converters TC and control units. The excavator is controlled by two command devices and controller. The drives are powered by a local direct current network organized by means of an active rectifier (AFE) with an inductor L. The diagram shows a capacitor C in a DC link, a transistor converter for emergency power drop TCF, Equipment Status Controller, and Monitor. The TCF converter is used for emergency discharge of energy and converting it into heat using the block of resistors R. The CAN network is designed to exchange data between system components. The equipment state controller collects and processes data on the state of all components to form control and data transfer commands to the excavator information and diagnostic system. The monitor is located in the driver’s cab and is designed to display the processes and status of electrical equipment. Electrical Diesel Generator Equipment

Car

Excavator

Cable

Higt voltage input

T2

Monitor Equipment Status Controller

Auxiliare Equipment

CAN BUS T1

L1

C TC

TC

M

M

AFE

Command Devices

Controller

Control Unit Control Unit

Motor 1

R

TCF

Motor 2

Fig. 1. Functional diagram of the electrical system “autonomous station—excavator”.

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When driving the excavator, the “Run” mode is activated. In this case, the control of the movement drives is carried out by the driver using the command devices. The output signals of the control devices and go to the inputs of the controller, which is also connected to the local CAN network and receives data on the consumed active power. The controller output signal in the form of a serial digital code with identification numbers of the receivers is transmitted to the inputs of the converter control units. The speed reference signals for the movement drive are formed depending on the position of the command devices with correction for active power at the input of the excavator. The power at the input of the excavator depends on the movement speed, the slope of the road, the coefficient of friction of the roadway, and the mode of movement. When driving on a flat road or when going uphill, energy is consumed from a diesel generator station. The power of the station is limited by the nominal value of the diesel engine power. Therefore, the active power consumed by the excavator must not exceed the value P2 = ηs.g Pd . Thus, when driving an excavator, the active power at the input must not exceed modm.d ulo the value P1 = 1−η ηs.g Pd during recovery and values P2 = ηs.g Pd when consumed. This condition is provided by adjusting the speed of movement of the excavator by correcting the reference signal for driving the controller. During the drive of the excavator, the power at the input of the machine is constantly m.d measured and compared with two settings: P1 = − 1−η ηs.g Pd and P2 = ηs.g Pd . The first setting P1 corresponds to the maximum power that can be provided during engine braking. The second setting P2 corresponds to the maximum power that a diesel generator station can provide. The power range 0 ≤ P ≤ P2 corresponds to the normal operation of the diesel generator station. The power range P1 ≤ P ≤ 0 corresponds to the permissible mode of operation during energy recovery. If the active power exceeds the value P2 or the active power exceeds the value P1 during energy recovery, the speed reference for the drive is corrected so that the active power is limited within P1 ≤ P ≤ P2 . The graph of the current power value is simultaneous with the settings P1 and P2 displayed on the driver’s monitor. Active power control allows the driver to optimize the process of driving the excavator. 2.3 Electrical Safety During the Operation of a Mobile Station The local electric network with a mobile diesel generator has an isolated neutral. Such a network should be provided with special means of control and protection [19]. Protection against electric shock consists of basic protection, protection in the event of a malfunction, and additional protection. Basic protection eliminates direct contact with the energized (active) parts of the installation using reinforced double insulation, guards, and galvanic separation of power and control circuits. Protection in the event of a malfunction in the event of a failure of the main insulation, for example, during an earth fault, eliminates the occurrence of hazardous voltage on the conductive parts of the electrical installation by automatically shutting down the installation. All open conductive parts of a mobile electrical installation, its housing, and other third-party conductive parts are reliably connected to the housing of an autonomous mobile station. When the station body and the excavator are driven, they are interconnected by a protective

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conductor. Other electrical installations are not connected to the generator. To protect against single-phase earth faults, protection using a zero-sequence voltage is applied. The self-grounding of the installation provides stable operation of the protection against earth fault [20]. Additional protection provides increased electrical safety and disconnection of the power source and the formation of alarms for personnel in cases of failure of the main protection; failure of protection in the event of a malfunction, with increased danger under adverse conditions. Additional protection is provided by duplication of automatic protective shutdown devices, the use of sound alarm devices, and personal protective equipment.

3 Conclusion and Direction of Further Work The mobile career station was designed and implemented by the “Joint Power” Company, Moscow. The power unit used an 800 kW diesel engine and a 6.3 kV synchronous generator with a power of 750 kVA. The station has been successfully tested in the testing range and quarry. The direction of further work is modeling and experimental study of the starting modes of powerful drive units, optimization of the power unit operation according to the criterion of efficient use of energy resource.

References 1. Hustrulid W, Kuchta M, Martin R (2013) Open pit mine planning and design, vol 1—fundamentals. CRC Press, London, New-York, Leiden 2. Czaplicki JM (2010) Mining equipment and systems. Theory and practice of exploitation and reliability. CRC Press, Balkema, London, New-York, Leiden 3. Awuah-Offei K (2018) Energy efficiency in minerals industry. Best practices and research directions. Springer International Publishing AG. https://doi.org/10.1007/978-3-319-54199-0 4. P&H 2650 CX Hybrid Shovel (2016) Joy Global 5. Malafeev SI, Novgorodov AA (2016) Design and implementation of electric drives and control systems for mining excavators. Russ Electri Eng 87(10):560–565. https://doi.org/10.3103/S10 68371216100035 6. Uno K, Imaie K, Maekawa K et al (2013) Development of mining machinery and future outlook for electrification. Hitachi Rev 62(2):99–106 7. Rodriguez J, Moran L, Pontt J et al (2004) Operating experience of shovel drives for mining applications. IEEE Trans Ind Appl 40(2):664–671. https://doi.org/10.1109/TIA.2004.824508 8. Enache M-A, Campeanu A, Enache S et al (2019) Dynamic state of starting for a high-power asynchronous motor used for driving a surface mining excavator. The XIth international symposium on advanced topics in electrical engineering, 28–30 March, Bucharest, Romania, pp 1–6 9. Aqueveque P, Wiechmann EP, Henríquez JA et al (2016) Energy quality and efficiency of an open pit mine distribution system: evaluation and solution. IEEE Trans Ind Appl 52(1):580– 588. https://doi.org/10.1109/TIA.2015.2464172 10. Enache M-A, Campeanu A, Enache S et al (2019) Dynamic state of starting for a high-power asynchronous motor used for driving a surface mining excavator. The XIth international symposium on advanced topics in electrical engineering, 28–30 March 2019, Bucharest, Romania, pp 1–6

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11. Bise CJ (2013) Modern American coal mining. Methods and applications. Published by the Society for Mining, Metallurgy and Exploration, Inc., Englewood 12. Morley LA (1991) Mine power systems. Information Circular 9258 (United States Bureau of Mines). Washington 13. Dorsett WA, Dillinger JB, Liten MJ et al (2019) Mining machine and energy storage system for same. Pat US No 10449849, 22 Oct 2019 14. Malafeev SI, Malafeev SS (2019) Investigation of electric power processes during the operation of a mining excavator. In: 2019 international conference on industrial engineering, applications and manufacturing (ICIEAM), 25–29 March 2019. https://doi.org/10.1109/ici eam.2019.8743002 15. Pandit P, Mazumdar J, May T, Koellner WG (2010) Real-time power quality meashurements from a conventional AC Dragline. IEEE Trans Ind Appl 46(5):1755–1763. https://doi.org/10. 1109/TIA.2010.2057470 16. Malafeev SI, Konyashin VI (2019) Induction motor drives for electric mining shovels: synthesis, design and research. In: 2018 International conference on industrial engineering, applications and manufacturing (ICIEAM), 15–18 May 2018, pp 1–6. https://doi.org/10.1109/ici eam.2018.8728598 17. Wong JY (2001) Theory of ground vehicles. Wiley 18. Malafeev SI, Serebrennikov NA (2018) Method of controlling electrical equipment at excavator driving. Pat RU 2670964. Bull. 33 19. Olszowiec P (2014) Insulation measurement and supervision in live AC and DC unearthed systems. Lecture notes in electrical engineering. Springer International Publishing, Switzerland. https://doi.org/10.1007/978-3-642-29755-7 20. Malafeev SI, Mamaj VS, Mikrjukov VI et al (1998) Power-mains directional ground-fault protective device. Pat RU 2122268. Bull. 32

Experimental and Theoretical Approach for Evaluation of Thermal Loading of Car Brake Discs V. Dygalo(B) and I. Zhukov Volgograd State Technical University, 28, Lenin Avenue, Volgograd 400005, Russia [email protected]

Abstract. The article describes two main approaches to assessing the thermal loading of friction pairs—experimental and theoretical for evaluating friction pairs in terms of the phenomenon of fading. Most of the kinetic energy of a car with ABS is extinguished due to friction in the braking mechanism. Overheating of the brake mechanism, namely, its friction pairs, leads to the occurrence of critical fading, accompanied by a sharp decrease in braking torque. Reducing the influence of this phenomenon is a very difficult task both from the point of view of taking into account the cost of the brake mechanism and its minimal complexity. The authors propose the use of cryogenic treatment of brake discs to reduce the influence of thermal stress on the occurrence of fading, as well as comparing the results of theoretical and experimental evaluation of friction pairs of the brake mechanism. Modern methods of calculating temperature values and obtaining experimental data have been applied, allowing one to increase the accuracy of thermal load estimation. Keywords: Anti-lock braking system · Braking mechanism · Thermal loading · Fading · Cryogenic treatment · Finite element method

1 Introduction The wide equipping of automobiles with automated brake systems, in addition to the obvious advantages in terms of active safety, gives rise to a number of problems caused by changes in the working process [1]. An increase in specific power and an increase in the mass of cars (such as crossovers) lead to an increase in the kinetic energy, which must be extinguished during braking. Unlike the traditional way to use braking, the main part of the kinetic energy of a car with ABS is extinguished due to the friction in the braking mechanism during operation of the ABS, which inevitably leads to an increase in their thermal load, especially when manufacturers of car brake systems use traditional elements of the basic models with unification.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_94

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From literary sources, it is known that overheating of brake friction pairs contributes to the emergence of critical fading, accompanied by a sharp decrease (up to 50%) in the friction coefficient of brake linings, as well as increased wear of the counterbodies, with the formation of macroscales [2].

2 Theoretical Approach To solve the problems associated with the phenomenon of fading, after the designer using calculation methods has identified a problem associated with increased heat load of the brake system, it is necessary to make changes to the design. Estimated estimation methods were considered by the authors in [3]. One of the ways can be a change in the surface area of the friction pairs of the brake mechanism, which can entail a change in neighboring nodes (hub, rim), which leads to an increase in the cost of the finished structure. The next approach to solving the problem of increased thermal stress of the brake mechanisms can be the use of materials of friction pairs whose properties can avoid these problems. But materials with higher characteristics have a higher cost [4]. For example, brake discs made of composite materials instead of antifriction gray cast iron used in production vehicles. As a cheaper way to improve the properties of the material, the authors propose cryogenic treatment of brake discs made of gray antifriction cast iron. In order to verify the positive effect on the properties of the brake mechanism of cryogenic treatment of the brake disk, it is necessary to test the samples and draw conclusions based on the values obtained. The research model repeats the test design for frictional heating and is the same for the calculated and experimental models [5]. The bottom line is that two samples of the disk and the shoe, respectively, movable (rotation) and the stationary samples, are pressed against each other with a certain force, as a result of which there is a braking moment and heat is generated between the disk–shoe pair (Fig. 1). Points with a maximum temperature are located on the disk; therefore, there is no need for a block (a fixed sample) in a three-dimensional model when simulating the thermal regime in FEM.

Fig. 1. Test scheme for friction pairs of the brake mechanism.

The brake pads for the initial data were selected by Ferodo model FDB527 in which the friction mixture FER4904 is used. In the pads under consideration, the friction code

Experimental and Theoretical Approach for Evaluation of Thermal

813

for this material is GG, which means that the coefficient of friction for the cold and hot pads is the same and lies in the range 0.45–0.55. This fact indicates the stability of the frictional properties of the material at various temperature conditions, which is an indicator of high-quality friction material used for a modern serial passenger car. The material of the disk is AChS-4 antifriction cast iron—the same for the calculated and experimental models. The thermal conductivity of gray antifriction cast irons is in the range from 54 to 45 W/m °C at a temperature range of 20–400 °C and decreases with increasing temperature. In this regard, to perform the calculation, we take the average value of the coefficient of thermal conductivity of 50 W/m °C [6]. Heat transfer by conductivity obeys the Fourier law, which establishes that the rate of heat conduction Qtrans is proportional to the heat transfer area (A) and the temperature gradient (dT /dx) [7] or Qtrans = −KA(dT /dx),

(1)

where K is the thermal conductivity in W/m °C. For most materials, K varies with temperature. The coefficient increases with temperature in gases at low pressures but can either increase or fall in metals and liquids. To apply heat loads in the form of a heat flux W/m2 to a part, it is necessary to calculate the friction work performed per unit time to the disk area [8]. Work is defined as follows: A = N · μ · S;

(2)

The power is determined from the relation P = N · μ · V;

(3)

where N is the normal clamping force of a stationary sample (pads) to the movable (disk) in N; V is the friction surface of the rolling sample in m/s. Based on the data obtained, we calculate the supplied heat capacity or power per unit area (Table 1). Next, it is necessary to determine what part of the total thermal power of the disk block arising in the friction pair is brought to the disk. For example, in article [9], such a ratio is given that 69% is brought to the disk, and the rest to the block without justification of the reasons why this ratio is approximate to practice. To determine the temperature field pattern of the test sample when thermal loads are applied to it, an application was used using the SolidWorks Simulation finite element method [10]. We focus on the fact that in addition to performing verification calculations, the program is designed specifically for performing design calculations, since SolidWorks represents a complex of the complete product life cycle of PLM (Product Lifecycle Management) [11]. And the developer of the brake system initially uses such packages as Simulation, which is part of the general PLM system. We carry out the construction of a three-dimensional model of assembly of a test sample mounted [12] on the spindle of a friction machine together with parts of a friction

814

V. Dygalo and I. Zhukov Table 1 Initial data of the thermal model of friction pairs

Parameter

Units measuring

Value

Load

N

400

Friction linear velocity

m/s

1.84

The surface area of the rolling sample

m2

6782 × 10−4

Power supplied to the rolling sample

W

368

Heat flow

W/m2

542,581

Coefficient of friction

0.5

machine that participate in thermal processes and can affect the surface temperature of the sample (Fig. 2).

Fig. 2. Three-dimensional model of assembly of a test sample installed on the friction machine SMC—2.

The task of thermal loads was carried out in the following way. There are three heat transfer mechanisms; these mechanisms are as follows: • Conductivity, • Convection, and • Radiation. Thermal analysis calculates the temperature distribution in a particular body due to the action of some of these mechanisms, or all of them together. In all three mechanisms, thermal energy flows from a medium with a higher temperature to a medium with a lower temperature. Let us arrange the heat loads and heat losses on different surfaces of the model, setting the initial data and limitations. Based on the foregoing, we apply the heat flux power to the movable test specimen allocated between the disk (movable test specimen) and the block (fixed) (Fig. 3).

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Thermal radiation is the thermal energy emitted by bodies in the form of electromagnetic waves due to their temperature. The Stefan–Boltzmann law establishes that the integrated radiation ability of a completely black body, or E b , is determined by the ratio [13]: Eb = σ T

(4)

where σ is the Stefan–Boltzmann constant, and T is the absolute temperature of an absolutely black body. The spectral variation of the radiation of an absolutely black body is described by the Planck distribution. By integrating the Planck distribution law over all wavelengths (λ), the Stefan–Boltzmann law is obtained. If a completely black body with a surface area A is immersed in a medium with an ambient temperature Ta, then the net velocity of the heat source radiated by a completely black body is given by the ratio [14]:   (5) Qr = σ A Ts4 − Ta4 , Ts > Ta where T s —Absolute temperature of a black body, T a —Absolute ambient temperature (ambient temperature).

Fig. 3. Heat transfer to the environment with a temperature of 25 °C through radiation from the surfaces of a movable sample. Emissivity 0.8.

A heated movable sample transfers a certain amount of heat to the environment. The amount of heat depends on the emissivity of the body, which is determined by the

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emissivity. In this case, the coefficient was taken equal to 0.8 based on a number of reference data and such a parameter as the degree of blackness (Fig. 4).

Fig. 4. Heat transfer to the environment from the surfaces of a movable sample to the environment through forced convective heat transfer coefficient. Convective heat transfer 300 W/m2 K.

From those surfaces through which thermal energy is scattered by radiation, energy is also scattered by forced convection. One of the main parameters determining this amount of heat is the convective heat transfer coefficient, which is usually a reference parameter. The spindle shank also transfers heat to the environment through forced convection. Part of the surface of the shank is located under the spacer and the movable sample; therefore, to simplify the model, we take the average value of the convective heat transfer coefficient. The spindle and distance washer give off heat to the environment through a convective heat transfer mechanism. Due to the fact that the spindle of the friction machine has a continuation and is structurally connected with the rest of the friction machine in such a way as a reducer and a reducer with a bed. Taking into account all the mates and details, a rather complex system is obtained. We will simplify it by reducing the convective heat transfer from 300 W/m2 K to 250 W/m2 K [15]. The friction machine spindle transfers part of the heat to the environment through a radiation mechanism. Based on the reference data and the shade of the spindle parts and the spacer washer, an emissivity of 0.7 is set. It is less than the emissivity of the movable

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sample, which is made of cast iron, and when the surface of the sample is thermally oxidized, its color has a darker emission spectrum compared to the steel of which the spindle and spacer ring are made (Fig. 5).

Fig. 5. Diagram of temperature distribution in degrees Celsius of simulation results.

The result of the study is a plot of the temperature field of the assembly unit, which gives an exhaustive picture of the temperature of parts. Of primary interest is the maximum surface temperature of a moving sample, namely, the maximum temperature and the surface on which the points with the maximum temperature are located. The extremum is

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located on the working surface of the sample, the area of contact with a stationary sample (block). The temperature of the remaining layers of the sample gradually decreases at a distance of the contacting surface. Moreover, there is a sharp decrease in the surface temperature of the spindle of the friction machine and the spacer ring in comparison with the movable sample [16]. As mentioned above, the experimental research scheme repeats the theoretical one and is made in accordance with RD 50-662-88 [17], where a set of methods for evaluating the frictional compatibility of lubricants and (or) structural materials used in rubbing materials is established. Tests are carried out in accordance with this regulatory document during frictional heating.

3 Experimental Approach As a rotating sample, we used disks with a diameter of 36 mm and a thickness of 6 mm obtained from the original brake disc of a Lada Granta automobile by waterjet and turning [18]. This made it possible to obtain the roughness and accuracy of the test surface comparable to the working surface of the original brake disc. One of the factors that confirms the adequacy of the tests carried out is the materials of friction pairs. A chemical analysis of the data of brake discs was carried out, which showed full compliance of the chemical composition with the requirements of the regulatory documentation for this brand of cast iron; all parameters were in the middle of the allowable ranges (Fig. 6).

Fig. 6. A frame of thermal video received by the SAT HotFind-L thermal imager: 1—temperature at the center point of the video detector, 4—maximum temperature in the captured area.

A movable sample is a disk that rotates at a constant speed of 1000 rpm (16.6 s−1 ) [19]. A fixed sample fixed in the carriage is pressed against it, which is a rectangular segment of the brake pad. In the experiment, two manufacturers of brake pads were used slightly below the average (Riginal company) and the upper price segment with verified authentication (Ferrodo company).

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The heat load of the friction pairs during the test was estimated using the SAT HotFind-L [20] thermal imager. Of great interest is the surface temperature of the moving sample; then, the imager was tuned specifically for it. The emissivity correction coefficient is chosen to be 0.7, which, according to the documentation for the thermal imager, corresponds to processed gray cast iron (Fig. 7).

Fig. 7. The maximum temperature values of moving samples for 5 min for a combination of different moving and fixed samples.

A comparison of the experimental and calculated values of the maximum temperatures of the moving sample indicates a minimum deviation of the two values. When considering Figs. 5 and 7, it is worth paying attention that the region with the maximum temperature is on the same surfaces in the calculation model and the experimental sample.

References 1. Revin AA, Zhukov IS, Shkarupelov VS (2012) Methodology of monitoring the technical condition of the braking system of the car with ABS during operation. Izvestia VSTU, seriya: nazemnye transportnye sistemy 89(5):90–93 2. Automotive handbook. Bosch. 3rd edition, Knizhnoe izdatelstvo Za rulem, Moscow, 2012 3. Turbin IV, Epishkin VE, Solomatin NS (2014) Effect of friction coefficient on tribotechnical characteristics of disc brake friction pairs. In: Proceedings of the conference. Perspektivnyye napravleniya razvitiya avtotransportnogo kompleksa: sbornik statey VIII Mezhdunarodnoy nauchno-proizvodstvennoy konferentsii, pp 124–128 4. Kokonin SS, Obizhaev GY, Okulov BS et al (2001) High loaded multidisc brakes and factors determining the efficiency and smoothness of their work. Tyazheloe mashinostroenie, pp 19–26 5. Bezyazychnyy VF, Lyubimov RV (2000) Experimental study of the processes of destruction of the surface layers of the metal in the steady-state process of fretting wear. Collection of scientific papers TSTU Mekhanika i fizika friktsionnykh kontaktov 7:24–28 6. Revin AA, Dygalo VG (2014) Creation of the main operational properties of vehicles in braking mode. Avtomobilnaya promyshlennost 11:3–5

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7. Chichinadze AV (1970) Thermal dynamics of friction. Mashinostroenie, Moscow 8. Chichinadze AV (1967) Calculation and investigation of external friction during braking. Mashinostroenie, Moscow 9. Chichinadze AV, Hebda MI (1990) Tribotech handbook, vol 3 t.2. Mashinostroenie, Moscow 10. Chichinadze AV, Hebda MI (1989) Tribotech handbook, vol 3 t.1. Mashinostroenie, Moscow 11. Voloaca S, Fratila G (2012) Concerns regarding temperature distribution obtained by experiments and finite element analyses for types of brake discs. U.P.B. Sci Bull Series D 74(3):33 12. Gudz GS, Eremenko PI (1979) Investigation of the temperature condition of brake mechanisms by modeling. Avtomobilnaya promyshlennost 10:20–22 13. Pershin VK, Fishbejn LA (2005) Simulation of thermal conditions in the friction interaction of the wheel and brake pad. Trasnport Urala 4:34–44 14. Starostin IP (2005) Numerical solution of the problem of thermal conductivity in friction pairs with a small overlap coefficient. Matematicheskoe modelirovanie 7:23–30 15. Gudz GS, Zahara IY, Tarapon OG (2009) A new approach to modeling the temperature condition of automotive ventilated brake discs during cyclic braking. Collection of scientific papers modelirovaniya v ehnergetike NANU im. G.E. Puhova: Modelirovanie i inform. Tekhnologii 51:37–42 16. Alekseev GN (2005) General heat engineering. Vysshaya shkola, Moscow 17. Revin AA, Zhukov IS, Shkarupelov VS (2012) Methods for determining the full braking operation carried out by the braking mechanism of the car with abs. Izvestiya VSTU, seriya: nazemnye transportnye sistemy 21(124):21–24 18. Tarasik VP (2006) The theory of the motion of the automobile: textbook for universities. BHV-Peterburg, Sankt-Peterburg 19. Tumasov AV, Groshev AM, Kostin SY, Saunin MI, Trusov YP, Dygalo VG (2011) Investigation of the properties of active vehicle safety by imitation modeling. Zhurnal avtomobilnykh inzhenerov 2:34–37 20. Revin AA, Poluektov MV, Radchenko MG, Zabolotnyy RV (2013) The influence of the ABS workflow on the durability of the vehicle chassis elements: monograph. Mashinostroenie, Moscow

Opportunities for Increasing the Operability of Heavy Vehicle Transmissions by Using Thermodynamically Stable Power Semiconductor Devices I. Savin1(B) , R. Polyakov1 , and Fu Sheng-ping2 1 Orel State University Named After I S Turgenev, 95, Komsomolskaya St., Orel 302026, Russia

[email protected] 2 Xiamen University of Technology, 600 Ligong Road, Jimei District, Xiamen, Fujian Province

361024, China

Abstract. In an electric transmission, the engine mechanical energy is converted into electrical energy in the generator, and then again converted into mechanical energy in the traction motors. This requires multiple energy conversion: thermal energy of fuel—mechanical energy of fuel—mechanical energy of ICE—electrical energy of a generator—mechanical energy of a transmission—electrical energy of a traction motor—mechanical energy of a propeller (wheel). For the conversion of electrical energy, power semiconductor devices (PSD) are widely used. These simple devices have high efficiency and are simple in design; however, they have a significant drawback. One type of failure is the breakdown of a semiconductor structure along a chamfer, as a result of which plasma can form on the chamfer of the semiconductor structure at large values of the blocking reverse voltage. This plasma, having melted the PSD case, comes out and damages the nearest devices, which leads to the need for more expensive repairs. Keywords: Semiconductor devices · Thermodynamically stable · Electromechanical drive · Electromechanical transmission · The released plasma · Case non-rupture

1 Introduction In enterprises engaged in the open development of minerals, in recent years, the process of introducing heavy-duty mining dump trucks using an electric drive as a transmission has been actively ongoing. Traditional traction electric drives of direct current are known even to people far from career equipment. In comparison, an AC drive can improve the reliability of the truck and reduce the cost of the life cycle and one-ton kilometer of traffic. This is achieved by increasing the operating life of the elements of the electromechanical and converting parts of the drive, increasing the traction and braking forces, expanding the speed range of their effective action, and increasing the maximum speed of the loaded truck and the efficiency of the electric drive as a whole. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_95

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2 General Provisions Hybrid electromechanical drive, as an independent direction in the development of transmissions for automobile transport, arose in the first half of the last century. The most widespread on heavy-duty mining dump trucks, a drive on sequential excitation electric motors, was received only in the 60s of the twentieth century. And here, for its foundation, a serial electric motor is perfectly suited, the natural mechanical characteristic of which is almost ideal for traction purposes. These engines can operate without overheating with a large number of starts per hour for any duration of inclusion, and the service life of the collector brushes of such engines with continuous operation of the pushers is 500–800 h [1]. For all its advantages, the DC electromechanical transmission has a number of disadvantages, which at a certain stage were a deterrent to the further large-scale development of this area. Technological features of the production of DC traction machines of especially high power of 1000 kW and more do not justify the creation of mining dump trucks with a carrying capacity of more than 250 tons using DC motors for a number of reasons: • weight and size indicators violate the layout balance; • collector reliability is reduced at high operating currents; • price increases disproportionately to increased capacity [2]. Moreover, increasing operational safety requirements requires fundamentally new approaches to traction drive control systems to implement optimizing algorithms for acceleration, movement, and braking. Indeed, in an electric transmission, it is very simple to dissipate the braking energy into the brake resistors and blow the heat out with fans. If on such a dump truck it is braked with mechanical brakes, then there will be 500 m of brakes [3]. And since the cars work in open cast mines with long descents, the problem of braking is very acute in them. Thus, the electromechanical transmission “at the same time” also solves the problem with the brakes. The use of power semiconductor devices facilitates the task of switching electric currents on an electric motor. From the whole variety of known electric motors, it is not easy to choose a specific one that would better fulfill its functions on a dump truck. Asynchronous, synchronous, inductor, valve—each of them has its own advantages and disadvantages [4].

3 The Use of Power Semiconductor Devices in Mining Trucks The simplicity of the design of the induction electric motor gives it high reliability, on the one hand, but at the same time, the formation of the desired traction characteristic is problematic, especially in the zone of low rotational speeds. This problem can be solved by a synchronous motor, but it is impossible to get rid of the presence of a sliding contact without increasing the overall dimensions [5]. A sliding contact is certainly not a collector, but if reliability is above all, then asynchronous is beyond competition, but again there are problems with traction moments at low speeds. These problems can be solved, but such a solution affects the price not for the better. If we consider a

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permanent magnet motor, then this is the champion among the considered motors in terms of traction and dynamic characteristics, but permanent magnets are not cheap, and they are not indifferent to temperature conditions [6]. Definitely, it cannot be said that any one traction engine will win. However, the fact that the traction electric AC drive, already in operation today on hundreds of mining dump trucks in the world, will force out tomorrow the drive on collector electric motors, is beyond doubt. For various problems, different solutions, but power converters for all options, are approximately the same in complexity and cost, although they differ in circuitry solutions. In recent decades, there has been a massive transition to AC motors with frequency converters due to greater total reliability and the lack of the need to service the engine collector. Thus, a typical structure of alternating current electric traction of such a dump truck can be represented as follows [7] (Fig. 1):

Fig. 1. Block diagram of an AC electric drive.

An internal combustion engine rotates a generator that generates electricity. A generator is usually either based on a synchronous or asynchronous machine [8, 9]. After the generator there is a converter, which makes a constant from the alternator current. Also in such a converter there is a control unit of the pathogen, which regulates the current in the excitation winding of the generator and thereby adjusts to different engine speeds and the removed power. In fact, such a pathogen is a half-bridge of power semiconductor transistors with a control system. In this case, the traction and braking characteristics of the truck are (Fig. 2). As can be seen from the characteristics, the necessary force on the wheels at certain points must be increased to critical values [10]. To do this, the current strength switched by power semiconductor devices for the electric motor increases, which, in turn, can cause a breakdown of the semiconductor element and failure of not only the power device, but the transmission as a whole, since the transistor case does not have high thermodynamic stability, since high-temperature plasma formed during the reverse short circuit current, especially in the area of the chamfer of the semiconductor structure, propagates inside the body and fuses thin cuffs to outpour and goes outside, damaging

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Fig. 2. Block diagrams of an AC electric drive: first—traction on wheels, second—wheel brake force.

all nearby equipment [11, 12]. As a result, it is necessary to repair the dump truck in an inaccessible place—a quarry, which in turn leads to the downtime of the entire working shift (Fig. 3):

Fig. 3. Semiconductor device with a hole from the released plasma.

The invention relates to the field of semiconductor technology and can be used to create power semiconductor diodes, thyristors, photothyristors, and other devices with high thermodynamic stability at reverse short-circuit currents [13, 14]. Thus, the task was to develop the design of the case of a power semiconductor device with high thermodynamic resistance, which would prevent the exit of plasma from the case of the device [15]. The result of the solution of the problem is the proposed design of a power semiconductor device with high thermodynamic stability, comprising a housing formed of a

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ceramic ring and thin copper cuffs connecting the ring and two current-carrying electrodes, between which there is a semiconductor element with fused temperature compensators, a contact strip, and a centering insulating ring [16]. The device is characterized in which the centering insulating ring is made with two protrusions covering the rectifier element on both sides, while the width of the protrusion entering the chamfer of the semiconductor structure is equal to or greater than its width, and one protrusion is pressed against the semiconductor structure by an additional ring of heat-resistant material [17] (Fig. 4):

Fig. 4. Thermodynamically stable semiconductor device, where 1—steel ring, 2—a protective ring.

4 Experiment To check the thermodynamic stability of the case, tests were carried out according to the following scheme [18] (Fig. 5):

Fig. 5. Electrical circuit for testing the device.

G1 is an alternating current source having an appropriate short-circuit power; S 1 , S 2 high-power keys; F1 fuse instead of S 2 ;

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L1 T1 RM P1 M1

inductor; high-power transformer; non-inductive shunt; an oscilloscope; testing device Verification Conditions:

• body temperature of the tested device: +25 °C; • the semiconductor element was previously mechanically damaged so that the breakdown passes along the chamfer of the structure; • the tightness of the housing was 10–7 Pa m3 /s; • current rise rate—25 A/µs; • the control circuit has been opened. The key S 1 was closed at time t 1 , so that the device was fed back voltage. In this case, the reverse current was constantly increased at a rate limited by the variable inductance L 1 . At time t 2 , switch S 2 was closed, limiting the current amplitude to I RM [19, 20]. The results showed that these samples withstood short-circuit currents of more than 140 kA, and the protective index of the housing stability was more than ix2 · t = 40 · 106 A2 · s, which is more than 5 times higher than the thermodynamic stability of conventional instrument designs [21, 22] (Fig. 6).

Fig. 6. The device after tests.

5 Conclusion The tests carried out proved the stability of the device body to thermodynamic loads, which in turn allows the use of power semiconductor devices in thermodynamically stable cases without risk in various fields.

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References 1. Kvaginidze VS, Petrov VF, Koretsky VB (2003) Repair manufacturability of heavy-duty mining dump trucks in coal mines of the North. Publishing house of the Moscow State Mining University, Moscow, p 289 2. Savochkin VA, Dmitriev AA (1990) Statistical dynamics of transport and traction machines. Mechanical Engineering, Moscow, p 320 3. Belokurov VN, Gladkov OV, Zakharov AA, Melik-Sargsyants AS (1987) Dump trucks. Mechanical Engineering, Moscow, p 216 4. Chebovsky OG, Moiseev LG, Nedoshivin RP (1985) Power semiconductor devices: Reference. Energoatomizdat, Moscow, p 401 5. Efremov IS (1984) Theory and calculation of the traction drive of an electric vehicle Higher. School, Moscow, p 383 6. Bogdanov KL (2009) Electric traction vehicle Training Edition. Automobile and Road State Moscow Technical University (MADI), Moscow, p 57 7. Volkswagen AG (2011) Fundamentals of electric car drives VAG self-study program, No. 499. Translation and layout of Volkswagen Group Rus. Volkswagen AG, Wolfsburg, p 68 8. Kurbasov AS, Sedov VI, Sorin LN (1987) Proektirovanie tiagovykh elektrodvigateley (Design of traction motors). Transport Publ., Moscow, p 536 9. Kopylov IP, Klokov BK, Morozkin VP, Tokarev BF (2002) Proektirovanie elektricheskikh mashin (The design of electrical machines). Vysshaya shkola Publ., Moscow, p 757 10. Drubel O (2013) Converter applications and their influence on large electrical machines. Springer, Berlin, p 190 11. GOST 2582–81 (1981) Mashiny elektricheskie vrashchayushchiesya tyagovye. Obshchie tekhnicheskie usloviya (State Standard 2582–81. Rotating electrical machines for rail and road vehicles. General specifications). Standartinform Publ., Moscow, p 37 12. Gemke RG (1975) Neispravnosti elektricheskikh mashin (Malfunction of electric machines). Energiya Publ., Leningrad, p 296 13. Avilov VD (1995) Metody analiza i nastroyki kommutatsii mashin postoyannogo toka (Methods of analysis and setting of commutation of DC machines). Energoatomizdat Publ., Moscow, p 237 14. Avilov VD (2013) Optimizatsiya kommutatsionnogo protsessa v kollektornykh elektricheskikh mashinakh postoyannogo toka (Optimization of switching process in collector electrical machines DC).OmGUPS Publ., Omsk, p 356 15. Veltman A, Pulle D, De Doncker R (2016) Direct current machines. Fundamentals of electrical drives, power systems. Springer, Cham, p 341 16. Kothari D, Nagrath I (2010) Electric machines, 4th edn. New Delhi, Tata McGraw Hill Education, p 778 17. Bogoslovsky AS (2014) Power semiconductor rectifiers. Military Publishing House, Moscow, p 208 18. Levinson AZ (1990) Semiconductor rectifiers. Gosenergoizdat, Moscow, p 115 19. Mazel KB (2004) Rectifiers and voltage stabilizers. Gosenergoizdat, Moscow, p 121 20. Rudenko VS, Senko VI, Chizhenko IM (1983) Conversion technology [Text]: textbook for universities, 2nd edn. Head Publishing House, Kiev, Vishka school, p 431 21. Preobrazhensky VI (1986) Semiconductor rectifiers, 2nd edn. Energoatomizdat, Moscow, p 136 22. Slavik I (1989) Design of power semiconductor converters: Per. Energoatomizdat, Moscow, From Czech, p 222

Development of Operational Opportunities for Two-Stage Torque Converters N. N. Trushin(B) Tula State University, 92 Lenin av., Tula 300012, Russia [email protected]

Abstract. Hydrodynamic torque converters are widely used in the transmissions of various purposes self-propelled vehicles. Torque converters are most efficient in trucks, haulers, tractors, and other heavy and utility vehicles operating in variable road conditions and off-road. Torque converters have the ability to automatically control the engine torque, but their torque transformation capabilities are relatively low, which requires the torque converter to be coupled with a multistage gearbox. In addition, the efficiency of the torque converters is significantly lower compared to mechanical gears. In order to increase the efficiency of hydromechanical transmissions, the article discusses technical solutions to develop the operational properties of an automobile and tractor torque converter. The paper proposes a torque converters design featuring two automatic switchable turbines depending on the gear ratio of the torque converter and the conditions of movement of the self-propelled machine. Those solutions make it possible to obtain two ranges through a joint operation of the transmission with the vehicle engine. Keywords: Self-propelled vehicle · Torque converter · Quality improving

1 Introduction Hydromechanical transmissions (HMT), containing a torque converter, a mechanical speed gearbox, and a hydraulic control system are widely used in the transmissions of self-propelled vehicles for various purposes. The useful properties of torque converters are well manifested in machines operated in a cyclic mode with variable loads in poor road conditions and off-road. Torque converters carry execute a continuous automatic change of torque, absorb shock, and vibration, facilitate machine control [1]. Single-stage torque converters containing three impellers: a centrifugal pump, a centripetal type turbine, and a reactor have been most common in the transmissions of self-propelled vehicles [2]. They are characterized by a relatively simple design and low cost. A significant drawback of the most common serial automobile and tractor singlestage torque converters is the relatively narrow range of automatic change of the engine torque: the maximum values of the torque transformation coefficient for such devices usually range from 1.8 to 2.5. In individual designs of single-stage torque converters, © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_96

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the transformation coefficient reaches 3.5–4 [3]. Another disadvantage of single-stage torque converters is the relatively low coefficient of performance (COP) in the range of low and medium gear ratios [4]. The insufficient torque transformation range in many cases requires the torque converter to be coupled with a manual multistage planetary or shaft-type gearbox. The number of stages in the HMT gearboxes of cars reaches 8–9, and the HMT gearboxes of trucks and buses have up to 12–16 steps or more [5]. At the same time, an increase in the number of steps in the gearbox leads to such negative properties as a complication of the transmission control system and increase in the power take-off of the drive engine for the implementation of auxiliary functions [6]. It is also known that with the increase in the number of stages in the gearbox, the transmission operating time at the lower stages is reduced [7].

2 Problem Statement Multistage torque converters have higher transforming properties within small gear ratios (0–0.5). Multistage torque converters are divided into two-stage and three-stage, in which two or three turbines are simultaneously connected to the output shaft, respectively. The maximum values of the torque transformation coefficient in multistage torque converters reach 4.5–6.5 [5]. Increasing the maximum value of the transformation coefficient of more than 4 in a multistage torque converter allows reducing the number of stages in a mechanical gearbox and thereby simplifying the HMT and its control system. Various types of multistage torque converters of various types have gained some popularity in transport, mining and construction machinery: such as Lysholm-Smith [8], Twin Disc [9], Brockhouse-Salerni [10], Packard [11], SRM (Svenska Rotor Maskiner) [12], Volvo [13]. Such torque converters are used in transmissions of heavy vehicles, buses, tractors, tanks, diesel locomotives, etc. In Russian transport engineering, two-stage torque converters are used in unified hydraulic transmissions for shunting locomotives of the 1200 hp family [14]. A separate reactor is coupled to each turbine in multistage torque converters so that the torques on each turbine have the same direction. Thus, a two-stage torque converter usually has five impellers: one pump, two turbines, and two reactors. Threestage torque converters have six to seven impellers: one pump, three turbines, and two or three reactors. A large number of impellers results in high gear ratios (over 0.5), the parameters of multistage torque converters sharply deteriorate due to the increased level of hydraulic losses. Complex variants of two-stage torque converters are known, which are capable of switching over to the hydraulic clutch mode with gear ratios of more than 0.8 (e.g., the Brockhouse-Salerni or Packard Ultramatic torque converters). However, in the clutch mode, complex multistage torque converters also demonstrate lower efficiency compared to single-stage complex torque converters due to the relatively large number of rotating impellers. As previously noted, another significant drawback of single-stage torque converters is their relatively low efficiency [5]. Therefore, in order to increase the transmission efficiency, many torque converters have a locking mode, which reduces the period of their active work, despite the rejection of damping properties.

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The parameters of multistage torque converters sharply worsen within high gear ratios (more than 0.6) due to an increase in hydraulic losses. Typically, in two-stage torque converters, the pump is a centrifugal type, the first-stage turbine is an axial type, and the second-stage turbine is a centripetal type. The axial-type turbine works more efficiently within small gear ratios (from 0 to 0.4) of the torque converter, and the centripetal type turbine works in the range of high gear ratios (more than 0.6) and in the fluid coupling mode [5]. To eliminate the inhibitory effect of the first-stage turbine with gear ratios of above 0.5 and in the fluid coupling mode, it was proposed to connect this turbine to the output shaft of the torque converter using a freewheel [15]. However, in the clutch mode, twostage torque converters have lower efficiency compared to single-stage torque converters due to the relatively large number of rotating impellers [5]. The latter drawback can be overcome by blocking the two-stage torque converter using the appropriate coupling after entering the fluid coupling mode. A torque converter was selected according to USSR patent No. 116957 as a prototype for design. It comprises a pump connected to a drive shaft, a first-stage turbine connected to a driven shaft by a freewheel, a second-stage turbine, a first reactor installed between the first- and second-stage turbines, and a second reactor installed between the secondstage turbine and the pump. The first and second reactors are rigidly connected to each other and to the stationary body with a freewheel [15]. The kinematic diagram of the initial two-stage torque converter is shown in Fig. 1.

2

3

4

1

10

5

6

7

8

9

Fig. 1. Kinematic diagram of a complex two-stage torque converter designed by S. M. Trusov

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The initial torque converter contains five impellers: pump 1, turbine of the first stage 2, first reactor 3, turbine of the second stage 4, and second reactor 5. The pump is connected to drive shaft 6. First turbine 2 is connected to driven shaft 9 with freewheel 7, and second turbine 4 is directly connected to driven shaft 9. Reactors 3 and 5 are rigidly connected to each other, and reactor 5 is also connected to housing 10 with freewheel 8. The first-stage turbine is of axial type, it works effectively within small gear ratios (0–0.6), and the second-stage turbine is of the centripetal type, its effective working area is within high gear ratio (0.6–0.98). To eliminate the inhibitory effect of the first-stage turbine with a gear ratio of more than 0.6 and in the hydraulic clutch mode, this turbine is especially connected to the driven shaft of the torque converter with a freewheel 7, which allows the first-stage turbine to rotate freely in the flow of the working fluid, providing a relatively small hydraulic resistance. The pump and turbines are located symmetrically relative to each other, which allows the torque converter operating effectively in the fluid coupling mode. This torque converter has two rigidly connected reactors, oppositely located in the circle of the working fluid. Therefore, a special structural element is necessary for the rigid connection of oppositely located reactor tracks. These circumstances complicate the overall design of the torque converter and reduce its efficiency both in the torque transformation mode and in the fluid coupling mode.

3 Results of Engineering The engineering task is to simplify the design of the initial two-stage torque converter and to increase its efficiency in the entire range of torque transformation and in the fluid coupling mode. The task was achieved due to the fact that in the original two-stage torque converter, which contains a centrifugal type pump, an axial-type turbine of the first stage and a centripetal-type turbine of the second stage, the turbines are connected to the driven shaft using individual freewheels, and the reactor is installed only between the second-stage turbine and the pump. The reactor between the turbines of the first and second stages is removed. Figure 2 shows the kinematic diagram of the designed torque converter in the variant of two automatically switched turbines and one reactor [16]. Torque converter 1 contains centrifugal pump 2 connected to drive shaft 3, first-stage turbine 4 of the axial type, connected with freewheel 5 to driven shaft 6, second-stage turbine 7 of the centripetal type, connected with freewheel 8 to driven shaft 6, reactor 9 installed between turbine 7 and pump 2. Reactor 9 is connected to stationary shaft 11 with freewheel 10, which in turn is connected to housing 12. Optional coupling 13 is designed to block hydraulics from transformer 1 by connecting drive shaft 3 and driven shaft 6 in order to increase the efficiency of the transmission with the steady movement of the self-propelled machine. The designed two-stage torque converter operates as follows: The drive motor (not shown in the diagram) through drive shaft 3 drives pump 2, which creates the flow and pressure of the working fluid. The working fluid first flows into first turbine 4, and then into second turbine 7. Within small gear ratios (0–0.6), axial type turbine 4 operates more efficiently, which has higher values of efficiency and torque transformation coefficient compared to centripetal-type turbine 7. The working

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1

4

13 7

2

9

3

5

8

10

11

12

6

Fig. 2. Kinematic diagram of the designed torque converter

fluid, leaving turbine 4 and entering turbine 7, creates a negative torque on turbine 7. To eliminate the inhibitory effect of turbine 7 on driven shaft 6, freewheel 8 disconnects turbine 7 from driven shaft 6. The torque on driven shaft 6 is only created by first turbine 4. As the self-propelled vehicle accelerates and the gear ratio of the torque converter increases, the sign of torque on turbine 7 becomes positive, and it also comes into operation. Within large gear ratios (of more than 0.6) and in the hydraulic clutch mode, turbine 7 of the centripetal-type works more efficiently than turbine 4 of the axial type. In this case, turbine 4 can rotate faster than turbine 7 and disconnect from driven shaft 6 using freewheel 5. The torque converter switches to the hydraulic clutch mode using freewheel 10, breaking the connection between reactor 9 and fixed shaft 11 within high gear ratios (of more than 0.8). In order to increase the transmission efficiency, the torque converter can be blocked with the help of clutch 13. Figure 3 shows graphs of changes in torques at the output of the torque converter depending on changes in the gear ratio [17]. The graphs show that within small gear ratios the torque on the second turbine is negative, and the torque on the driven shaft is generated only by the first turbine. As the gear ratio increases, the torque on the first turbine decreases to 0, while the torque on the second turbine increases and becomes positive. Thus, the torque converter in question has the following characteristic states during operation:

Development of Operational Opportunities for Two-Stage

833

Torque ratio

First turbine torque

Resultant torque

Second turbine torque

0

Speed ratio

Fig. 3. Graphs of changes in torque on the torque converter turbines

1. within small gear ratios, the turbine of the first-stage operates, the turbine of the second-stage is disconnected from the driven shaft; 2. within average gear ratios on the driven shaft the turbines of the first and second stages operate simultaneously; 3. within large gear ratios, only the second-stage turbine works, the first-stage turbine is turned off; 4. the torque converter operates in the fluid coupling mode. The operational capabilities of the torque converter can be expanded due to operational changes in its transparency [4]. As a rule, the torque converter parameters are selected based on the average operating conditions of the transmission of a self-propelled vehicle. However, the various operating conditions of self-propelled vehicles require an operational change in the transparency of the torque converter during operation due to the following considerations. When choosing the joint operation of the engine and torque converter, various options for combining their characteristics are possible. So, for example, to obtain good economy with steady traffic in good road conditions, it is advisable to enter the input revolutions, which the engine and the torque converter pump develop with full fuel supply and a stopped turbine, to choose as low as possible. In this case, the slip decreases during operation of the integrated torque converter in the fluid coupling mode and the hydraulic transmission efficiency increases. On the contrary, for

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quick acceleration and better use of engine power, it is advisable to select the input speed as high as possible. High values of efficiency can also be claimed when moving a transport vehicle in adverse road conditions and in off-road conditions. Changing the transparency of the transmission with the constant transparency of the torque converter is carried out using a multistage gearbox. In the 1950s, General Motors proposed using reactor rotary blades in automotive torque converters to regulate inlet revolutions. When using rotary blades, the angle of exit of the working fluid from the reactor can vary from 15° to 85°. The position of the reactor blades is usually set depending on the amount of fuel supply to the engine: full pressure on the fuel pedal corresponds to a small angle of the blades, while slight pressure corresponds to the installation of the reactor blades at a large angle [18]. Torque converters with rotary reactor blades are not widely used due to the significant complexity of the design. This drawback can be overcome by using the blade system of single-stage four-wheel torque converters with two reactors, but at the same time, the reactors do not work simultaneously, but separately from each other. In this case, the torque converter acquires the ability to operate in two different operating modes, corresponding to different values of the input revolutions. The blades of one of the reactors are profiled with a small exit angle of the working fluid, and the blades of the other reactor with a large exit angle of the working fluid. The entry angles of the working fluid into the blades of both reactors are the same or approximately equal. Thus, depending on which reactor is currently active, various transparency properties of the torque converter and various ranges of joint operation of the torque converter and the engine are registered. The design of such a torque converter and the HMT control system in each operating mode ensures the operation of only one of two reactors: the active reactor is blocked with the HMT housing, while the inactive reactor rotates freely in the flow of the working fluid. As a result, with two reactors the torque converter operates alternately with either one or the other reactor [19]. Figure 4 is a kinematic diagram of a two-stage torque converter with switchable reactors [20]. The positions of elements 1–8, 13 correspond to the positions in Fig. 2. Torque converter 1 contains two reactors 9 and 10, which are installed on freewheels 11 and 12, respectively. The torque converter activation brakes are designated as 14 and 15. In the first torque converter operation mode, one of the brakes, for example, brake 14 is turned off; reactor 10 in the absence of a rigid connection with the body will freely rotate in the flow of the working fluid. Active brake 15, in this case, includes reactor 9, and the torque converter will operate in the same load mode. In another case, brake 15 is on and brake 14 is off. Reactor 10 will be turned on, and reactor 9 becomes inactive and will freely rotate in the flow of the working fluid. In this case, the torque converter will operate in a different load mode. The operation of the torque converter with switchable reactors in the fluid coupling mode with any active reactor is provided using freewheeling mechanisms 9 and 10. Manual or automatic control of brakes 14 and 15 is also provided using the HMT hydraulic system.

Development of Operational Opportunities for Two-Stage

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1

4

13 7

2 14

10

9

3

8

5

15

11

12

6

Fig. 4. Kinematic diagram of a torque converter with switchable reactors

4 Conclusion Compared with traditional two-stage torque converters, the designed one has a simpler design due to the removal of the reactor between the turbines of the first and second stages. An additional freewheel is a unifying element, which slightly complicates the design of the torque converter. The independent operation of the turbines at the first and second stages makes it possible to optimally profile their blades and thereby provide higher values of efficiency in the entire range of gear ratios. The symmetrical arrangement of the pump and turbine ensures the efficient operation of the torque converter in the fluid coupling mode. The latter allows borrowing elements of blade systems from serial singlestage torque converters. Compared with twin-turbine torque converters, the proposed one does not have a summing mechanical transmission, which is also its advantage. The properties of the considered torque converter allow halving the number of steps in the mated mechanical gearbox. Acknowledgements. The authors thank the personnel of the Research Library at Tula State University, and of the Tula Region Research Library for their assistance with the references and patent search, and innovative design development. The results of the research project are published with the financial support of Tula State University within the framework of the scientific project № 2019-22.

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References 1. Hossay P (2020) Automotive innovation: the science and engineering behind cutting-edge automotive technology. CRC Press/Taylor & Francis Group, Boca Raton FL 2. Maddock D (2014) Automotive torque converters. In: Encyclopedia of automotive engineering (online version). Wiley, pp 803–826 3. Nanney MJ (2007) Light and heavy vehicle technology, 4th edn. Elsevier, Oxford 4. Trusov SM (1977) Automotive Torque Converters. Mashinostroeniye, Moscow 5. Mazalov ND, Trusov SM (1971) Hydromechanical gearboxes. Mashinostroeniye, Moscow 6. Fischer R et al (2015) The automotive transmission book. Springer, Heidelberg 7. Truhanov VM et al (2001) Transmissions of tracked and wheeled vehicles. Mashinostroeniye, Moscow 8. Lysholm AJR (1933) Hydraulic variable speed power transmission. US Patent 1900118, 7 Mar 1933 9. Shorts WF (1955) Vehicle power transmission. US Patent 2727601, 20 Dec 1955 10. Gatiss AL (1950) Improvements in or relating to hydraulic transmission apparatus. GB Patent 640727, 26 Jul 1950 11. Micsh HL, Lucia CJ (1953) Transmission. US Patent 2,630,893, 10 Mar 1953 12. Ahlen KG (1954) Hydrodynamic torque converter. US Patent 2,690,053, 28 Sept 1954 13. Kronogard S-O (1964) Hydrodynamic torque converter. US Patent 3,154,924, 3 Nov 1964 14. Hydromechanical Transmissions. Design, Production, Operation (1980) Mashinostroeniye, Moscow 15. Trusov SM (1959) Torque converter. USSR Patent 116957 16. Trushin NN (2019) Torque converter. RF Patent 2682694. 20 Mar 2019 17. Kelley OK (1957) Hydrokinetic torque converter and gearing. US Patent 2782659, 26 Feb 1957 18. Kelley OK (1957) Transmission. US Patent 2814214, 26 Nov 1957 19. Trushin NN, Orlov AB (1996) Controlled complex torque converter. RF Patent 2065103:10 20. Trushin NN, Antsev VY, Obozov AA (2019) Improving automotive torque converter quality. In: Proceedings of ICIE 2019 II:727–735. https://doi.org/10.1007/978-3-030-22063-1_78

Conveyor Belt Vibrations G. G. Kozhushko(B) , M. D. Lukashuk, and O. A. Lukashuk Ural Federal University, 19, Mira Street, Yekaterinburg 620002, Russia [email protected]

Abstract. Transportation of bulk materials using belt conveyors has reached the point where the modern requirements of modern industry to achieve higher performance are limited due to the fact that machine designers can not develop dynamically stable conveyors, which can be considered one of the main problems in our time. The belt speed and width are the two main parameters that can provide the required performance. At a certain speed, width, and tension of the belt, there is an unstable transverse and longitudinal vibration. Vibration with a higher amplitude can be so strong that it can reduce the service life of not only the roller bearings of the conveyor but also its frame due to dynamic loads. The purpose of this study is to study the lateral vibrations of the conveyor belt. Evaluating the boundaries of stable resonant operation is an important prerequisite for determining the failure zones of the conveyor. Keywords: Conveyor belt · Vibration · Lateral vibrations · Roller bearings · Boundary value problem

1 Introduction Wider usage of conveyor transport in mines and quarries is one of the major factors in increasing the engineering level and efficiency of the mining industry. In recent years, most mines transition to continuous or cyclic-continuous transportation. Rise of freight flows and transporting lengths made it necessary to design high-production belt conveyors which are lengthier and more powerful than before by selecting more expensive synthetic or rubber cable belts. It is known that materials of conveyor belts feature physically and geometrically nonlinear, anisotropic properties. Many research groups conducted dynamic analysis on large belt conveyors in order to lower their cost price and optimize performance. At first, a conveyor belt was modeled as an elastic solid, then—as a viscoelastic solid to factor in viscoelastic properties of the belt-coating layer. Designing and using systems of high-speed belt conveyors are often marked by the necessity of solving the problems of start–brake modes, loading and unloading transported material, restraints set by dynamic loads on elements of roller bearings, as well as providing stability of such belt motion which would exclude the possibility of operating in resonance or almost resonance modes. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_97

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There exists a sufficient number of proofs that lateral belt vibrations, on one hand, cause damage to the machine structure, on the other, could be controlled by correctly selecting design parameters and operation modes. Correct positioning of tension rolls seems to be the most practical way of obtaining a non-resonance belt. Conveyors could be equipped with additional devices which would allow eliminating lateral vibrations, but, due to mechanical constraints set by the design, such an approach is too expensive.

2 Theoretical Part Downtime of belt conveyors under maintenance at factories leads to serious financial losses. It is mainly caused by requisite repair works or inspection of metal parts carried out on conveyors and their belts. A belt cannot be handled until the conveyor comes to a complete halt, with losses in productivity and efficiency of equipment usage which ensue. Wear of a belt after a short period of working time occurs due to those many factors affecting it, among which its vibrating motion is one of the major constituents. Uncontrolled (related to uncontrollable processes) vibration of machine components which exceeds allowable limits (belt velocity and loading uniformity) causes damage and leads to emergency state. Consider forced lateral vibrations of conveyor belts—they are excited via conveyor rollers and feature an eccentricity due to either production error or having transported material stuck onto rollers. The dissipation of energy for lateral belt vibrations could be expressed in the form of hysteresis (structural) damping. The concept used here to give a complex representation of the elasticity modulus or flexural rigidity of the belt is supposed to have an aperiodicity and proportionality of energy dissipation in one cycle of vibrations in a hysteresis loop area [1–7]. Main equations of conveyor belt motion are derived using principles taken from nonlinear mechanics of deformed solids [8–12]. Lateral vibrations of a conveyor belt in motion could be expressed in the form of ∂ 2w ∂ 4w ∂ 2w = α 2 − β(1 + iη) 4 + g, 0 ≤ x ≤ l, 0 ≤ t ≤ ∞, (1) 2 ∂t ∂x ∂x   where α = Sgq−1 ; S = S − v2 q g; β = Dx g q; w(x, t) is a belt deflection at the cross section x; S,v—a belt tension and its motion velocity, respectively; Dx , η—a flexural rigidity of the belt in the direction of x-axis and reduced coefficient of damping, respectively; q(x, t)—a linear load to the belt from the proper √ weight of transported material, which is further considered as q(x, t) = const; i = −1; g = 9,81 m/c2, t—time. Boundary conditions, which correspond to kinematic excitation of the belt ends at rollers due to imbalance of rolls, would be described as w(t, 0) = δ1 exp(ω1 t + ϕ1 ); w(t, l) = δ2 exp(ω2 t + ϕ2 ), where δ1 , δ2 , ω1 , ω2 , ϕ1 , ϕ2 are the frequency amplitudes and initial phases of vibrations at the left and right ends, respectively [13–17]. The design diagram is shown in Fig. 1. = ∂w(t,l) = 0; at the starting point in time w(0, x) = Suppose ∂w(t,0) ∂x ∂x = 0. Solution of the boundary problem (1) is to be sought after in the form w0 (x); ∂w(0,x) ∂t

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Fig. 1. Design diagram to study forced lateral vibrations of a conveyor belt excited via rollers

of w(t, x) = w(x) + (l − x)l −1 δ1 exp(i(ω1 t + ϕ1 )) + xl −1 δ2 exp(i(ω2 t + ϕ2 )) + ζ (x, t), where w(x) is a stationary form of the belt deflection; ζ (x, t)—a new unknown function which complies with the boundary problem [18]; ⎫ ∂ 2ζ ∂ 2ζ ∂ 4ω ⎪ ⎪ = α 2 − β(1 + iζ ) 4 + f (t, x)⎪ ⎪ ⎪ ∂t 2 ∂x δx ⎪ ⎬ ∂ζ (t, l) ∂ζ (t, 0) (2) = = 0⎪ ζ (t, 0) = ζ (t, l) = 0, ∂x ∂x ⎪ ⎪ ⎪ ⎪ ∂ζ (0, x) ⎪ ζ (0, x) = ζ0 (x); = ζ1 (x)⎭ ∂t where ⎫ l−x x ⎪ 2 2 f (t, x) = δ1 ω1 exp(iω1 t) + ∂2 ω2 exp(iω2 t)  f1 + f2 ⎪ ⎪ ⎪ ⎪ l l ⎪ ⎬ l−x x (3) δ1 − δ2  ζ01 + ζ02 ζ0 (x) = ω0 (x) − ω(x) ¯ − ⎪ l l ⎪ ⎪ ⎪ l−x x ⎪ ⎭ δ1 i − δ2 i⎪ ζ1 (x) = − l l The solution ζ (x, t) of the boundary problem (2) could be expressed as ζ = ζ1 + ζ2 , where ζ1 is the solution (2) for f = f 1 , ζ0 = ζ01 ; ζ1 ζ2 —the solution (2) for f = f 2 , ζ0 = ζ02 . Every boundary problem is solved separately for ζ1 and ζ2 . Let us find ζ1 = ζ1 (t, x) : ⎫ ∂ 2 ζ1 ∂ 2 ζ1 ∂ 4 ζ1 ⎪ ⎪ = α 2 − β(1 + iζ ) 4 + f1 (t, x)⎪ ⎪ ⎪ ∂t 2 ∂x δx ⎪ ⎬ ∂ζ1 (t, l) ∂ζ1 (t, 0) = = 0⎪ ζ1 (t, 0) = ζ1 (t, l) = 0; ∂x ∂x ⎪ ⎪ ⎪ ⎪ ∂ζ1 (0, x) ⎪ ζ1 (0, x) = ζ0 (x); b = ζ11 ⎭ ∂t ∞Express 2the functions f1 and f2 in the form of Fourier series f1 (t, x) = l=1 b1j δ1 ω1 ϕj (x) exp(iω1 t), where ϕj are eigenforms of vibrations which correspond to a j-th mode; 

b1j = (l − x)l

−1

l  x 1 − ϕj (x)dx; , ϕj (x) L1 = l

0

(4)

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b2j = xl

−1



l

, ϕj (x) L2 =

xl −1 ϕj (x)dx.

(5)

0

ζ1 (t, x) =

∞

ζ1j ϕj (x) exp(iωt)

(6)

j=1

Suppose the frequencies of exciting forced vibrations at the left and right rollers are equal since they are determined by the speed of belt  motion. Therefore, if there is no slipping of the belt on rolls, ω1 = ω2 = ω = V r, where r is the radius of rollers. Substituting (6) into (2) (and it is easy to notice that the boundary conditions (3) are true due to the choice of functions ϕi (x), j = 1, 2, . . .), we get [19–22] ∞  ∞ ∞ 

∂ 2 ϕj ∂ 4 ζj −ω2 ζ1j ϕj (x) expiωt = αζ1j 2 expiωt − β(1 + iη)ζ1j 4 expiωt ∂x ∂x j=1

j=1

+

∞

j=1

b1j δ1 ω2 ϕj (x) expiω1 t

l=1

After transformations, the expression obtained should be multiplied by ϕi (x) and integrated by x within the range from 0 to l. After canceling the expression by exp(iωt), we get −ω2 ζ1j =

∞

αxij ζ1j − β(1 + iη)λj ζ1j + b1j δ1 ω2 .Φ

(7)

i=1

Setting constraints on (7) using its j-th member, we get −ω2 ζ1j = αxij ζ1j − β(1 + iη)λj ζ1j + b1j δ1 ω2

(8)

In which case, the Fourier series coefficient is expressed as ζ1j =

b1j δ1 ω2 β(1 + iη)λj ζ1j − αxij ζ1j − ω2

(9)

Let us define p2j = βλ4j − αxjj , p1j = ηβλ4j x and rewrite (9) in the form of    b1j δ1 ω2 p2j − ω2 + p1j b1j δ1 ω2  ζ1j =  =  2 2 p2j − ω2 + p1j p2j − ω2 + p1j ⎡ ⎤ 2 2 b1j δ1 ω p1j p2j − ω ⎣ ⎦ =  − i  2  2 2 2 2 2 p2j − ω2 + p1j p2j − ω2 + p1j p2j − ω2 + p1j  b1j δ1 ω2 (1) =  (10) exp iθ j 2 2 p2j − ω2 + p1j

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where θj(1) is a phase angle, that is a lag of belt motion from an excitation vector at a left  −1 (1) roller, tgθj = −p1j p2j − ω2 .   The expression (10) could be written as ζ11 = Re(ζ1i )+iJm ζ1j , where a real compo−1   2 2 and an imaginary nent of shifting is Re(ζ1i ) = b1j δ1 ω2 p2j − ω2 p2j − ω2 + p1j   −1     2 2 component is determined as Jm ζ1j = b1j δ1 ω2 −p1j p2j − ω2 + p1j . Retaining only the first member of the row (8), we get by a certain approximation b1j δ1 ω2 ϕ1 exp[i(ωt + θ1 )] ζ1 = ζ11 ϕ1 (x) exp(iωt) =  2 2 p2j − ω2 + p1j

(11)

while the accuracy of evaluating the belt displacement via this formula increases, the closer it gets to the resonance frequency of the harmonic profile ϕj (x) [23–26]. Now let us suppose that j = 1, j = 2 and retain in the row (7) the first two members (by the i index):  −ω2 ζ11 = αx11 ζ11 + αx21 ζ12 − β(1 + iη)λ41 ζ11 + b11 δ1 ω2 ; −ω2 ζ12 = αx12 ζ11 + αx22 ζ22 − β(1 + iη)λ42 ζ12 + b12 δ1 ω2 with x12 = x21 . It follows ⎫   ⎬ βλ41 − αx11 − ω2 + iβηλ41 ζ11 − αx21 ζ12 = b11 δ1 ω2 ;⎪   ⎭ −αx12 ζ11 + βλ42 − αx22 − ω2 + iβηλ42 ζ12 = b12 δ1 ω2 ⎪ then a system of algebraic equations could be obtained: a11 ζ11 + a12 ζ12 = ξ1 ; a21 ζ11 + a22 ζ12 = ξ2 , solving which we get ζ11 =

ξ1 a22 − ξ2 a12 ξ2 a11 − ξ1 a21 ; ζ12 = , a11 a22 − a21 a12 a11 a22 − a21 a12

(12)

where a12 = a21 = −αx12 . It allows us to find a more accurate approximation: ζ1 = ζ11 ϕ1 (x) exp(iωt) + ζ12 ϕ2 (x) exp(iωt).

(13)

Solving the function ζ2 = ζ2 (t, x) requires a complete repetition of the procedures (12), (13) while substituting indices of the eccentricity of the right roller δ2 (from 1 to 2), along with functions and coefficients within those expressions. Similarly, with (11), retaining the first member of the row, we get b2j δ2 ω2 ϕ1 exp[i(ωt + θ2 )] ζ2 = ζ21 ϕ1 (x) exp(iωt) =  2 2 p2j − ω2 + p1j

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3 Conclusion Designing a belt conveyor requires dynamic analysis to be used in order to predict the location of lateral vibrations. Equations are cited which determine the motion of a working belt. Although certain parameters which affect vibration deviate, all in all, the system is deterministic by its nature, that is until higher amplitudes of vibration appear. Huge interest in engineering developers would represent a boundary of stability for such a design. The paper considers various constraints which should be set to get a dynamically stable project. Suggested engineering solutions have to refrain from rendering the design too complex or raising costs of a conveyor and its operation. At the same time, solving such problems would allow to richen the theory of mechanical system vibration, achieve longer service life for rollers (affected by dynamic processes), prevent the belt from leaving unprompted its guide. Obtained modal parameters of the system (eigenfrequencies and forms of vibrations at principal modes) are the grounds of practical recommendations to select such parameters of conveyor complexes and their operation which would exclude the possibility of working in resonance or almost resonance modes. Analyzing and resolving consequences of vibrations affecting a conveyor, ensuring smooth workings of the machine are all important for the purposes of improving and maintaining its equipment in an operable condition.

References 1. Galkin VI, Sheshko EE (2017) Lentochnye konveyery na sovremennom etape razvitiya gornoy tekhniki (Belt conveyors at the modern stage of development of mining machines). Mining J 9:85–89 2. Tarasov YD (2013) Povyshenie tyagovogo usiliya lentochnyh konveyerov s uvelichennymi dlinami, uglami naklona i proizvoditelnostiyu (Raising the traction power of belt conveyors with increased lengths, inclinations and performances). J Mining Equipment Electromech 5:46–48 3. Galkin VI, Sazankova ES (2013) Vliyanie parametrov prostranstvennoy trassy lentochnogo konveyera na ustoychivost dvizheniya lenty (Impact which parameters of the space route of a belt conveyor has on the stability of belt motion). J Mining Equipment Electromech 7:6–9 4. Galkin VI, Sheshko EE, Sazankova ES (2015) Vliyanie tipov i harakteristik lent na ekspluatatsionnye parametry spetsialnyh lentochnyh konveyerov (Impact of types and characteristics of belts on operating parameters of specialized belt conveyors). Mining J 8:88–91 5. Papoyan RL (2012) Tekhnicheskie usovershenstvovaniya na konveyernom transporte (Technical improvements in conveyor transport). J Mining Info Anal Bull 8:228–233 6. Korneev SV, Dolgih VP (2016) Metodika tyagovogo rascheta shahtnyh lentochnyh konveyerov na osnove kompyuternogo modelirovaniya soprotivleniy dvizheniyu tyagovogo organa (Method of traction calculation of belt conveyors used in mines on the basis of computer-aided modeling of tractive resistance). News High Educ. Min J 3:81–87 7. Dmitriev VG, Cherednik PN (2016) Programmnyy kompleks dlya tyagovogo rascheta i analiza puskovyh i tormoznyh rezhimov lentochnyh konveyerov (Software package for traction calculation and analysis of starting and breaking modes of belt conveyors). J Mining information and analysis bulletin) 2:25–35 8. Hearn EJ (1997) Mechanics of materials. An introduction to the mechanics of elastic and plastic deformation of solids and structural materials. Part 2, 3rd edn. UK

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9. Filippov AS, Drobyshevsky NI, Kamenskay DD, Kisselev AE, Moiseenko EV (2014) Endto-end technology of modeling a melt-structure interaction during IVMR in VVER with HEFEST-URAN toolkit. In: Proceedings of the 22nd international conference on nuclear engineering, ICONE22, 7–11 July 2014, Czech republic, Prague 10. Paris PC, Tada H (1983) The application of fracture proof design methods using tearing instability theory to nuclear piping postulating circumferential through wall cracks. NUREG/ CR-3640 11. Filippov AS, Drobyshevsky NI, Strizhov VTh (2009) Simulation of vessel—with—melt deformation by SOCRAT/HEFEST Code. In: 17th International Conference on Nuclear Engineering, ICONE 17, 12–16 July 2009, Brussels, Belgium 12. Naumova EV, Prinz VYa, Golod SV, Seleznev VA, Soots RA, Kubarev VV (2009) Manufacturing chiral electromagnetic metamaterials by directional rolling of strained heterofilms. J Opt A Pure Appl Opt 11:074010 13. Wang BH, Liu JP, Lu S (2014) Analyzed development of the high-power and high-speed belt conveyor. J Min Mach 42(1):27–30 14. Trufanova IS (2014) Promezhutochnyy privod kak sredstvo sovershenstvovaniya lentochnogo konveyera (Using an intermediate drive as a way of improving a belt conveyor). J Min Equipment Electromech 6:13–16 15. Roberts AW (2001) Recent developments in belt conveying—bulk solid and conveyor belt interactions. In: Levy A, Kalman H (eds) Handbook of conveying and handling of particulate solids. Elsevier Science, pp 225–233 16. Yardley ED, Stace LR (2008) Belt conveying of minerals. Woodhead Publishing Ltd., Cambridge 17. Voytyuk IN, Proskuryakov RM, Kopteva AV (2012) Perspektivy primeneniya sovremennyh informatsionnyh tekhnologiy i tekhnicheskih sredstv izmereniya v sistemah upravleniya lentochnym konveyernym transportom (Prospects of using modern information and measuring technologies in control systems for belt conveyor transport). J Min Info Anal Bull 6:223–227 18. Nordel LK, Ciozda ZP (1984) Transient belt stresses during starting and stopping: elastic response simulated by finite element methods. J Bulk Solids Handling 4(1):93–98 19. Kuleshov MV, Syromyatnikov VS (2017) Optimization of the conveyor drive parameters under stochastic loads. Proc Higher Educ Inst. Machine Build 10/691:69–76 20. Monastyrskiy VF, Monastyrskiy SV, Kiriya RV (2008) Optimizatsiya energoemkosti transportirovaniya nasypnyh gruzov lentochnymi konveyerami (Optimization of power intensity of transporting bulk loads by means of belt conveyors). In: Papers of Seminar 21 of the “Mining Week-2007” Symposium, pp 304–309 21. Serpil K, Gerdemeli I, Cengiz C (2012) Analysis of belt conveyor using finite element method. In: Scientific proceedings of the IX International congress on machines, technologies, materials 22. Zür TV (1986) Viscoelastic properties of conveyor belts; modeling of vibration phenomena in belt conveyors during starting and stopping. J Bulk Solids Handling 6(3):553–560 23. Kozhushko GG (1992) Mehanika deformirovaniya i prognozirovanie resursa rezinotkanevyh lent konveyerov gornorudnyh predpriyatiy (Mechanics of deformation and prediction on lifespan of rubberized-fabric belts of conveyors at mining enterprises). Dissertation Abstract, Ural State Mining University, Yekaterinburg 24. Podporin TF (2016) Metodika rascheta prodolnoy ustoychivosti dvizheniya lenty v rezhime ustanovivshegosya dvizheniya na bremsbergovom konveyere so slozhnym po prochnostnym harakteristikam konturom lenty (Method of calculating the longitudinal stability of belt used in a brake incline conveyor which functions in the mode of steady motion and utilizes a belt of a complex profile characterized by its strength impact). J Min Equipment Electromech 6:20–29

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Property-Based Identification and Separation of Rocks in the Drilling Process and Shipment A. A. Shigina1(B) , A. O. Shigin2 , and A. A. Stupina1 1 Siberian Federal University, 3, Vuzovsky Lane, Krasnoyarsk 660025, Russia

[email protected] 2 Siberian Federal University, 95, Krasnoyarsk Worker, Krasnoyarsk 660025, Russia

Abstract. The development of a dynamic technology for monitoring and controlling the quality of the extraction and processing mineral raw materials based on deposit modeling and ore flow control is relevant for large mining and metallurgical plants, where ore from several mines is sent to the processing plant. There exists a problem connected with all parts coordination of the technological process from the geological model of the deposit, mining faces, ore depots, and the shipment system to the concentrating mill and metallurgical plant. By assessing the physicomechanical properties of rocks and their ratios during the drilling of blastholes, it is possible to determine the composition of the rock mass. The scheduling system monitors the movement of rock mass components from blasting to shipment to ore passes. An intelligent rig system identifies the properties of certain rocks according to their properties and their combination. With the help of the dispatching system, a portion controlled ore shipment occurs with the ore accumulation of the particular composition. Keywords: Types of polymetallic ores · Physical properties · Identification · Portioned shipment

1 Introduction The development of a dynamic technology for monitoring and controlling the quality of the extraction and processing mineral raw materials based on deposit modeling and ore flow control [1, 2] is relevant for large mining and metallurgical plants [3], where ore from several mines is sent to the processing plant [4]. There exists a problem connected with all parts coordination of the technological process from the geological model of the deposit, mining faces, ore depots, and the shipment system to the concentrating mill and metallurgical plant. A representative object for the implementation of such a system is the Polar Division of PJSC MMC Norilsk Nickel, one of the largest mining enterprises in Russia and the world [4]. For this plant, the development of the effective technology for controlling ore flows [4] is especially important since multicomponent ores are mined and processed at its deposits and there is a need to maintain the targets © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_98

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for some metals [5]. A separate problem is the dilution of mined ores [6]. It should be solved by separating the host ore or filling mixtures from the ore starting from mining faces, so that the waste rock does not fall into one ore pass with the ore, reducing its quality. Separation of ores and gangue at the drilling and shipment stages of ores from the mining face is a complex problem that should be solved using intelligent systems that evaluate the characteristics of the rocks directly while drilling [7, 8]. The development of intelligent technology for monitoring and controlling the quality of ore flows in the extraction and processing of multicomponent ores [2] involves achieving the main goal. It is the development of the system for evaluating the mineral composition of rocks in real time while drilling, their movement during the blasting process and the portioned shipment of ore portions to ore passes with the ore shipment of the particular quality to specialized processing plants. The following tasks should be solved for this goal achievement: 1. Study conditions for the rocks separation in mines of the Polar Division of JSC MMC Norilsk Nickel [9], including the study of the ore flow formation. Study of the composition and physical and mechanical properties of the mined ores and contained minerals; 2. Study the structure of the operating unit and the automation system of the Sandvik DL-430 drilling machine, equipped with a hydraulic perforator and hydraulic feed mechanism [10, 11] with an evaluation of the possibility of measuring the mechanical properties of the rock using standard equipment and standard measuring tools; 3. Development of principles for determining the strength and density of drill rocks using the operating unit and sensors of the drilling machine; 4. Development of the methodology for determining rocks while drilling, casting [12], and shipment; 5. Development of methods for digital control of the separation accuracy of ore flows with the formation of ore passes of the necessary quality and composition.

2 Analysis of the Problem of Useful Ore Components Loss and Dilution at Extremely Different Ore Quality Ores mined at the mining enterprises of the Polar Division of MMC Norilsk Nickel PJSC are multicomponent [13] and they can significantly differ both in the content of useful components (Fig. 1) and in mineral composition that determines the efficient concentrating technology. Mining enterprises of the JSC MMC Nornickel are developing three deposits of sulfide copper–nickel ores [2]: 1. Norilsk—1 (underground mine “Zapolyarny,” open-pit mine “Medvezhy Ruchey”); 2. Talnakhskoye (underground mine “Komsomolsky” including “Komsomolskaya,” “Skalistaya,” and “Mayak” mines”); 3. “Oktyabrskoye” (underground mines “Taimyrsky” and “Oktyabrsky”).

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Fig. 1. The content of useful components in the extracted ores.

Ores of various quality and composition are processed in two mills. At the Norilsk Concentrating Mill (NCM), ore concentrating is carried out according to gravity–floatation technology according to three technological schemes [2]. At the Talnakh Concentrating Mill (TCM), ore concentrating is carried out by the flotation method [2]. Rich ores are from “Oktyabrsky,” “Taimyrsky,” and “Skalisty” mines. Moreover, any deviations from the required content of useful components in the ore and its mineral composition lead to significant losses of metals. So with a decrease in the mass share of nickel in ore from 4.5 to 1%, an average decrease occurs [14]: • Quality of the same name concentrate decreases from 13 to 8.2%; • Extraction of nickel in a concentrate decreases from 77.5 to 57%; • Yield of nickel concentrate decreases from 27 to 7%. At the same time, the yield of tailings increases from 30 to 75%. To increase the efficiency of the technology, ores are averaged and the mixture of the required quality is prepared [15, 16]. It requires energy-intensive, capital-intensive, and labor-intensive resources. At the same time, significant losses of useful components are inevitable. Obtaining ores with previously known characteristics from mining enterprises will avoid significant losses of metals. A significant impact on the decrease in the quality of ores is exerted by the inevitable ingress of enclosing rocks into the ore using the technology of mining a deposit with the explosion of overlying rocks [6, 17] and filling mixtures using the technology with a hardening tab [6, 17]. At the same time, up to 17% of the gangue can enter the ore [6]. In the absence of intelligent automated technology for the gangue separation in the mine, the latter inevitably falls into ore passes and goes to the mill. This reduces the efficiency of mining enterprises and processing plants.

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3 Evaluation of the Ores Identification Possibility for Further Separation of Various Physical and Mechanical Properties Depending on the structure and mineral composition, as well as the content of non-ferrous and precious metals [5], ores are divided into: • • • •

disseminated ore (average composition of Ni 0.4–0.5%, Cu 0.7–0.8%), cupriferous (average composition of Ni 0.9–1.5%, Cu 2.0–3.2%), rich (average composition of Ni 2.5–3.5%, Cu 3.5–4.5%), selective ores (the richest in the composition of non-ferrous and precious metals are ores from the “Oktyabrsky” mine).

Ore mining is carried out at seven mining enterprises [2], which process three deposits and produce commodity ores of various compositions. Salable production and consumers of mining enterprises are given in Table 1. Table 1. Production consumers. Mining enterprise

Salable production

Consumer

“Zapolyarny” mine

Disseminated ore

Norilsk concentrating mill

“Medvezhy ruchey” pit

Disseminated ore

Norilsk concentrating mill

“Komsomollyskaya” mine

Cupriferous and disseminated ores

Norilsk concentrating mill

“Skalistaya” mine

Rich ore

Talnakh concentrating mill

“Mayak” mine

Disseminated and rich ores Norilsk concentrating mill, Copper plant

“Taymirsky” mine

Rich ore

Talnakh concentrating mill, Copper plant

“Oktyabrsky” mine

Rich, Cupriferous and disseminated ore

Talnakh concentrating mill, Norilsk concentrating mill

According to Table 1, it is clear that the capabilities and technologies of the concentrating mills differ significantly and it is necessary to separate the ore flows at the exits from the mines. Studies have shown that the physical and mechanical properties of ores and enclosing rocks differ significantly [18] and can be fairly accurately identified by two parameters: strength and density. These parameters are often inversely related. This allows one to obtain important digital markers [19] for identifying ore components with sharply different combinations and property values. The physical and mechanical properties of ores are well studied [20]. The density of ores has the following values: • Density of rich ores is 4.1 t/m3 ; • Density of disseminated ores is 3.05 t/m3 ; • Density of cupriferous ore is 3.3 t/m3 ;

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The value of the rock strength ratio according to the M. M. Protodyakonov scale is as follows: • • • •

For rich ores is from 5 to 7; For cupriferous ores is from 10 to 12 (up to 16); For disseminated ores is from 5 to 10; For enclosing rocks is from 5 to 10. Thus, ores are determined by the following property ratios:

• rich ores are identified by a combination of the following properties: high density, low strength; • cupriferous ores are identified by a combination of the following properties: low density, high and very high strength; • disseminated ores are identified by a combination of the following properties: low density, average strength values. The enclosing rocks have similar strength values. To distinguish disseminated ores from gangue, one should take into account that gangue has a slightly lower density of 2.5–2.8 t/m3 . An intelligent system installed in the on-board computer of a drilling machine, using these digital markers, distinguishes in the rock mass and builds a map of the location of ores with the necessary properties on the well grid by combining identified fields with a specific ore composition.

4 Development of Principles for Evaluating the Strength and Density of Drilled Rocks Sandvik DL-430 drilling rigs are used at the mining enterprises of the JSC MMC Nornickel for drilling blast holes (Fig. 2). This is a single boom electro-hydraulic drilling rig for extensive underground sewage processing and deep drilling. The robust boom has 3-m parallel drilling coverage. Using the 360° rotation mechanism, full parallelism is achieved, and the wide coverage of the tilt forward and backward provides the ability to perform a variety of drilling tasks. It is equipped with an automation system and an on-board computer. This machine uses a hydraulic hammer for drilling. While drilling, the automated system maintains pressure on the discharge line of the hammer drill at a constant level. It is necessary to measure the feed rate of the operating unit in discrete time intervals to evaluate the strength of rock in real time. For this, it is necessary to measure the flow rate of hydraulic fluid on the discharge line of the hydraulic cylinder of the feed mechanism using a flow meter (Fig. 3). The feed rate is directly dependent on the flow rate of the fluid supplied to the hydraulic cylinder of the feed mechanism and is inversely proportional to the strength of the drill rock. Thus, the strength of the drill rock in real time is determined according to formula (1): σt.r =

k S =k· , MPa vd Qg.f

(1)

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Fig. 2. Drilling module Sandvik-430. (1—punch; 2—feeder; 3—boom; 4—pipe manipulator).

Here, σ c.r is the compressive strength of the rock, MPa; vd is the drilling speed, m/min; S is the cross-sectional area of the hydraulic cylinder of the feed mechanism, m2 ; Qg.f is the flow rate of the hydraulic fluid of the pump in the hydraulic cylinder of the feed mechanism, m3 /min; k is the design coefficient, depending on the design of the drilling tool and perforator.

Fig. 3. Drilling speed meter (flow meter) for indirect evaluation of rock strength, subject to constant pressure of the feed mechanism.

To maintain a constant pressure level in the perforator while drilling, a pressure manometer is installed in the hydraulic system of the drilling rig; its readings are duplicated in an automated system. It is necessary to measure a parameter characterizing the recoil energy to evaluate the density of the drill rock. It is necessary to use a shock sensor installed in the hydraulic system of the hydraulic perforator to measure the shock pressure (Fig. 4). The sensor measures pressure fluctuations when a hammer is hit. At the moment of impact, a sensor shows a peak value. Peak values in different cycles of the drill differ depending on the density and strength of the rock being destroyed (Fig. 5). In this case, the averaged strength of drill rocks is determined by measuring the drilling speed using a flow meter (Fig. 3). By comparing the strength measured through

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Fig. 4. Mechanism for evaluating the characteristics of the rocks based on the standard hydraulic perforator drilling rig Sandvik-430. (1—shank; 2—piston; 3—case; 4, 6—chambers; 5, 11— pressure head highway; 7—spool; 8—chamber; 9—channel; 10, 13—hydraulic accumulator; 12, 15—drain highway; 14—hole in the spool; 16, 17—channels; 18, 19—piston shoulder; 20— pressure manometer of the feed line for indirect determination of rock strength. 21—pressure manometer measuring impact pressure for indirect evaluation of rock density).

Fig. 5. The graph of the pressure of the impact of the hammer while drilling.

the drilling speed and the impact pressure measured through the impact sensor with reference values, the system evaluates the relative value of the rock density. By the ratio of the calculated strength and relative density of the rock, the system evaluates and fixes the pass of a certain type of ore or gangue.

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5 Methodology for Evaluating Areas of Specific Types of Rocks While Drilling, Milling (Explosion), and Shipment Using the big data analysis on the properties of drill rocks and comparing combinations of strength and density of drill rocks at certain time intervals with digital markers, the on-board computer accurately determines the location of rock types along with the depth of the well (Fig. 6). The coordinates of the beginning and end of the areas of certain types of rocks are determined.

Fig. 6. Fixing the alternation of certain types of rocks in the well while drilling.

While drilling a grid of wells, the coordinates of the beginning and end of the regions of certain types of rocks are combined into the boundaries of the volume regions of certain types of rocks. The union of these regions makes up a volumetric tomogram of the rock mass (Fig. 7).

Fig. 7. Building a tomogram of the rock mass while drilling a grid of wells.

According to mining technology, explosives are calculated. This calculation is advisable to perform an intelligent system taking into account certain strength characteristics and areas of certain types of rocks. Explosion of the rock mass with predetermined properties and structure will help to get a controlled explosion to obtain the optimal size of the pieces and minimal expansion of the rock with the formation of explosion with a known structure and location of areas with the known types of rocks. As a result of the calculation of explosives and the application of the rock mass transformation algorithm in the explosion, the intelligent system builds an explosion diagram (Fig. 8). Thus, the intelligent system of the on-board computer based on the drilling rig receives a tomogram of the rock mass along the grid of wells. On its basis, it determines the quantitative content of individual types

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of ores. The system performs automatic calculation of explosives, simulates the transformation of rock mass after an explosion, and determines the explosion scheme with the determination of the accumulation areas of the certain types of rocks. The system determines a specific ore pass into which it is necessary to ship the ore and remembers the corresponding digital marks for each area of accumulation of the same type of rocks.

Fig. 8. Digital diagram of the explosion of the rock mass after detonation with the determination of accumulation areas of certain types of rocks.

6 Control System of the Addressed Portioned Shipment of Various Types of Rocks It is necessary to use a transport complex and digital communications on-board computers of a drilling rig and load–haul–dump (LHD) to develop of a comprehensive technology for pre-concentration by separating different types of ores, starting from the drift with the loading of some passages with ore with the particular characteristics and quality. There are no opportunities to organize free wireless communication in the cramped conditions of the mine and its constant transformation. In this regard, it is necessary to organize wireless communication by installing wireless communication units at forks in the mine close to the drift and at the LHD unloading points. Fixed wireless communication units are necessary for the control system of address portioned shipment of various types of rocks (CSAPS dispatching system). This system operates as follows. It is necessary to complete the calculation of the digital scheme of the explosion of the rock mass at the moment of drilling completion in the on-board computer of the drilling rig. Then, the intelligent drilling rig system transmits the received information to CSAPS. This system is pre-connected with LHD, digitally attached to the drift for further unloading the rock mass. CSAPS transmits a rock diagram of the rock mass explosion and a loading command to the LHD on-board computer. In the on-board computer of the LHD, an explosion scheme and the placement of the LHD in the mine with digital marks of the drift and ore passes appear. The camber scheme

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is displayed on the PDM operator monitor and the remote control monitor. An operator of the LHD focuses on the unloading of certain areas of the explosion using augmented reality video displayed on the monitor. Certain rocks types are shown by lightening in the form of various colors shading on the video from the LHD video camera, which removes rock mass explosion in real time (Fig. 9).

Fig. 9. Lightening of the rock mass explosion on the LHD monitor determining accumulation areas of certain type rocks.

Having loaded the ore, an on-board computer displays a digital mark of the ore pass where the loaded ore must be shipped. This digital mark is pre-attached to the submerged part of the explosion by an intelligent rig system. When passing the wireless unit near the drift, the LHD transmits information about the shipped part of the explosion to CSAPS. Then a computer adjusts the digital explosion scheme based on the shipped part. The next LHD loads the updated digital explosion scheme to the on-board computer with the help of the wireless unit and it is sent for loading. The loaded LHD delivers the rock to a specific ore passage to which the loaded rock is attached with a digital mark. A driver of certain LHD sees on the screen with these digital marks a number of the ore run to which the ore must be delivered. Along the route to the ore pass, the LHD passes by a wireless stationary electronic receiver–transmitter, while the map of the rock mass explosion is updated taking into account the shipped portion.

7 Quality of Addressed Portioned Shipment of Certain Types of Rocks 7.1 CSAPS Performance Verification System A system for monitoring the correctness of ore uploading is required to ensure the reliability of CSAPS. This system operates as follows. In the on-board LHD system, the next to be shipped, a specific ore pass, a digital mark is fixed with a number of the ore pass. Approaching the appropriate ore pass, the LHD unloads the bucket, while the on-board system reads the wireless digital ore pass mark and remembers it to confirm the shipment. In case of compliance with the digital mark of the ore and LHD, the

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information is updated and the LHD should be slaughtered for the next shipment. In the case of a mismatch of digital marks (LHD arrived at an inappropriate ore pass), a system captures and remembers the error, ties it to the driver’s personality to control the quality of operation. The error is duplicated on the screen and the light signal. If it arrives at the wrong ore pass, the system can block the unloading of the bucket into the wrong ore pass and signals to follow the previously defined ore pass. As a result, the system controls the shipment of the ore with the particular properties to certain ore passes. 7.2 Intelligent System Performance Evaluation The evaluation of the developed system should be done to reduce the loss of recoverable useful components and reduce dilution. The extraction of nickel is the most indicative for the processing of copper–nickel ores. It is known that with an increase in the nickel content in ore from 1 to 2%, a substantial increase in recovery occurs from 56 to 72% [15]. A system that determines the composition and quality of the ore obtained will avoid accidental contact with the concentrating mill of raw materials with characteristics that do not correspond to the technology and avoid metal losses of up to 22%. Monitoring the process of loading and unloading certain portions of ore from the explosion of the rock mass will eliminate the ingress of gangue into the ore pass with ore of known quality and composition. The hit of waste rock taking into account the error of the system within 6% is possible. The ore processing at the concentration plants will decrease to 11% decreases in concentrating mills from 17 to 6%. Taking into account the output volumes of mining enterprises of the JSC MMC Norilsk Nickel (Fig. 10), the reduction in ore processing while maintaining the plant’s productivity is 1.9 million tons per year. Taking into account the released capacities of concentration mills the output of the mineral processing plant of JSC MMC Norilsk Nickel may grow by the appropriate value.

Fig. 10. Extraction volume of various types of ores by mining enterprises of the JSC MMC Norilsk Nickel.

Acknowledgements. This article was prepared as part of a research carried out with the financial support of the Russian Science Foundation according to the research project No. 19-7100028 within the framework of the Competition of 2019 “Conducting initiative research by young scientists.”

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References 1. Temkin IO, Myaskov AV, Konov IS et al (2019) Construction and functioning of digital platform for transportation control in opencast mines. Gornyi Zhurnal 11 2. Makarov VA, Malinovsky EG, Katzer II et al (2016) Intelligent technology for monitoring and controlling the quality of ore flows in the extraction and processing of multicomponent ores. Siberian Federal University, Krasnoyarsk, p 191 3. Kozhiev HH (2006) Reconstruction of the mining technological diagram in the increasing stability direction of the ore composition. Mt Info Anal 8:31–33 4. Balandin VV, Erlykov GP, Simonin PV et al (2019) Oktyabrsky mine is the largest mining division of the polar division of Norilsk nickel. Gornyi Zhurnal 11 5. Sluzhenikin SF (2011) Platinum-copper-nickel and platinum ores of Norilsk Region and their ore mineralization. Russ J Gen Chem 81:1288–1301 6. Tapsiev AP, Freudin AM, Uskov VA et al (2014) Resource-saving geotechnologies for thick gently dipping complex ore deposits in the Norilsk region. J Min Sci 5:123–136 7. Stupina AA, Shigina AA, Shigin AO et al (2016) Control by technological mode parameters with an intellectual automated system. IOP Conf Ser: Mater Sci Eng 8. Shigin AO, Shigina AA, Bovin KA et al (2018) Roller bit drilling optimization. Int J Mech Eng Technol 9(7):1358–1366 9. Arshavsky VV, Tapsiev AP (2003) Mining technology perfecting in mines of the Norilsk industrial region. Non-ferrous Metals 3 10. Turgel DK (2007) Underground mining machinery and equipment. Yekaterinburg. Ural State Mining University, p 302. http://www.giab-online.ru/files/Data/2011/online/Underground_ mining.pdf 11. Marysyuk VP, Ryshkel IA, Trofimov AV et al (2019) Investigation of the distribution of particle size distribution of blasted rock mass at the Oktyabrsky mine. Gornyi Zhurnal 11 12. Spiridonov EM, Korotayeva NN, Kulikova IM et al (2011) Palladoarsenide Pd2 As—a product of mayakite PdNiAs destruction in norilsk sulfide ores. New Data Miner 46:48–54 13. Kozhiev HH (2006) The influence of the quality of mined ore on its enrichment. Mt Inf Anal 8:27–28 14. Kozhiev HH (2006) Enlarged calculation of the ore quality management system efficiency. Mt Inf Anal 8:29–30 15. Tapsiev AP, Anushenkov AN, Uskov VA et al (2010) Improvement in productivity of surface stowing facilities for mines of the transpolar branch of the Norilsk Nickel joint-stock company. J Min Sci 46(3):265–270 16. Marysyuk VP, Darbinyan TP, Andreev AA (2019) Effectiveness evaluation of changes in the development system during the extraction of sulfide copper-nickel ores at the Oktyabrsky mine. Gornyi Zhurnal 11 17. Spiridonov EM (2005) Genesis of Pd, Pt, Au, and Ag minerals in magmatic Norilsk sulfide ores, XV All-Russia conference on experimental mineralogy, Nauka, Syktyvkar, pp 317–319 18. Köhler J, Pagani1 A, Stricker D (2010) Detection and identification techniques for markers used in computer vision. In: Visualization of large and unstructured data sets—IRTG workshop, vol 10, pp 36–44 19. Cemekhman LS, Fomichev VB, Yertseva LN et al (2010) Atlas of mineral raw materials, technological industrial products and commercial products of the Norilsk Nickel Polar Division. Publishing House Ore and Metals, p 336 20. Shigina AA, Shigin AO, Stupina AA et al (2016) Model of rock drilling process in terms of roller cone bit remaining life. Int J Appl Eng Res (IJAER) 11(19):9792–9799

Development of Control Systems for Screw Propellers Y. Liberman, N. Shonokhova, and O. Lukashuk(B) Ural Federal University, 19, Mira Street, Yekaterinburg 620002, Russia [email protected]

Abstract. Nowadays, a need arises more and more often to develop new hardto-rich areas, which place a demand on special properties of machinery—first of all, such as cross-country capacity, maneuverability, and remote-control. A rotary screw all-terrain vehicle (ATV) is a high-passability terrestrial vehicle for off-road driving. The paper solves the problem of reducing overall dimensions of a propeller, which drives a rotary screw ATV; design variations of screw propellers with their motor fitted inside are proposed. Three types of propellers were designed: with a variable-speed motor, a stepper motor, and bicycle wheel-motor. The main design feature of such propellers is a motor within the propeller remaining stationary while a hollow body of revolution with a helical spiral ribbon, becoming a movable structural element. The description and analysis of special control systems as well as the principles of selecting individual units of the system are given. Logic control circuits for stepper and variable-speed motors were developed. Step-pulse systems with spiral motors on stepper drives allow constructing compact snow-and-swamp-mobiles with their lifting capacities higher (at least by 1.5–2 times) than those of similar vehicles with pulse-counting systems or spiral motors on bicycle wheel-motors. Keywords: Screw propeller · Stepper motor · Variable-speed motor · Wheel-motor · Roller-motor · Control system

1 Introduction A rotary screw all-terrain vehicle (ATV) or screw-propelled vehicle is an off-road vehicle, which drives along using a rotary screw propeller [1–4]. The designs of such propellers include two or more Archimedes’ screws made of very durable materials and situated on the sides of an ATV body. At the moment, there exist many engineering variations of rotary screw ATVs [5–8]. But all of them have large overall dimensions and mass, which is explained by the fact that their motor is separated from the propeller, while control is handled by an operator from within a cab. There are several problems which this paper tries to solve: designing a compact propeller by placing a motor within the propeller body, placing an operator away from the vehicle, and developing a remote-control system. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_99

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2 Solution of the Problem The problem of reducing overall dimensions of a propeller could be solved by positioning the motor within its body, thus allowing to reduce the size. The task might be accomplished by using a general asynchronous drive. But existing drives are high-speed types which are unstable at lower revolutions, requiring the integration of a high-ratio reduction gear. And the simplest variant would be a conveyor drive roller with a comb coiled around it. That principle was implemented in the design of a wheel-motor on a universal asynchronous drive made in the Bauman Moscow State Technical University. But positioning the motor within a propeller is a drawback in itself since planetary gears used in such designs are heavy and complex to maintain [9]. Figure 1 shows a screw propeller with a variable-speed motor whose prototype is a roller-motor. This propeller is characterized by higher reliability and smoother running but has its own drawbacks such as required precise manufacturing of its parts, high labor coefficient of repair and maintenance, and all other things aside, increased mass due to a large number of auxiliary constructive elements. Another variant of a gear-motor would be a bicycle wheel-motor (Fig. 2). A bicycle wheel-motor is a gearless or geared engine forming a magnetic field which makes it rotate due to interaction with constant spindle magnets. Its many windings are grouped into three, alternated round a cycle, while magnets are positioned opposite to them. To start the rotation, voltage is applied to the windings, thus activating them when they close in on a magnet. The wheel-motor is selected by catalog [10]. The principle behind its operation reminds one about a stepper motor. This design was awarded a patent for useful model [11].

Fig. 1. Screw propeller with a variable-speed motor.

Drives used in wheel-motors have power limitation of 2 kW. To increase the power of developed designs, low-speed motors of higher power could be chosen, which would allow to eliminate the need for a reducing gear pass—one of such stepper motors is shown in Fig. 3. The design of this propeller is similar, in terms of its layout, to a roller-motor—a stepper motor is situated within the propeller body. The stepper motor is selected by catalog [12]. Its body [2] is mounted within the propeller on bearings (5), which allows it to remain stationary relative to the vehicle platform since it is rigidly connected to a stand (4), which, in its turn, is rigidly connected to the propeller frame.

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Fig. 2. Propeller with wheel-motors.

The second stand of the propeller (3) is mounted in the frame on a bearing (6). The motor (2) is located in the center of the propeller body (1) in order to evenly distribute loads coming from the motor weight onto the stands. The developed design has such advantages as reliability and precision when it comes to following a set path, but there is a drawback—it does not run smoothly (due to specifics of stepper motor operation). The design was also patented [13].

Fig. 3. Propeller with a stepper motor.

A block-diagram of stepper motor control is presented in Fig. 4. It consists of a programmable pulse generator (1), subtraction-based pulse counter (2), OR (3), AND (4), «inhibit» (5) elements, circular pulse distributor (6), power amplifier (7), and stepper motor (8). There are two modes of operation in this pulse-step system: following a specified trajectory or moving without any travel constraint. The system of variable-speed motor control is shown in Fig. 5. The speed of motor rotation is managed by a typical motor controller (4), whose master input is wired via a comparator and analog commutator (3) to the output of a code-voltage convertor (1). And the master input of the analog commutator (3) is connected with the output of ORunit (9). The system allows to control the motor in two modes: performing a set motion or moving without any constraint.

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Fig. 4. Block-diagram of stepper-motor control.

Fig. 5. Block-diagram of variable-speed motor control.

The control systems shown here differ by how they control rotary speeds of their motors—controlling the stepper-motor speed involves changing the rate of feeding control signals to the motor windings, while in the case of a variable-speed motor, it is about changing the resistance or voltage in the electric circuit. Thus, the system with a stepper motor has a speed master control and circular pulse distributor, and the second one—a «code-voltage» convertor. All those elements could be implemented in several ways and require further consideration in order to select a more proper variant in terms of reliability requirements. The speed master control is assigned a task of feeding pulses at a specified rate into the interpolator—they determine the rotary speed of an end effector (a propeller in this case). The unit maintains programmed constancy of profiling execution speed along with acceleration and deceleration. For vehicles which use a low-frequency stepper drive, responding to maximal 800 Hz of control pulses, as a rule, there is no need for smoother acceleration or deceleration when passing from one rotation frequency to another. The speed master control of such vehicles is simplified and consists of a block of generators whose pulse rate is determined by a speed-programming code.

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The block is intended for generating rectangular pulses at a specified rate. It consists of n multivibrators working in an automatic mode. Their vibration frequencies vary by 1,19 times. Depending on the required motion speed, the control signal is sent to one of the «Speed coding» inputs. Since there are continuous pulses coming from the generators, speeds are switched by interrupting the feed of control signals at one input and starting to send them to another. The proposed logic circuit of stepper-motor control is presented in Fig. 6. It includes a programmable pulse generator (block 1), subtraction-based pulse counter (block 2), OR (3), AND (4), «inhibit» (5) elements, and circular pulse distributor (block 6).

Fig. 6. Logic circuit of stepper-motor control.

The programmable pulse generator (1) is set up using a specified speed code, then the control signals come to the AND elements (4 and 40). If both inputs of either contain the same signal (both 1 or both 0), then their output will hold 1. The subtract-based pulse counter (2) is set up with the movement code. Every signal coming to it is subtracted from that set value, and when the counter becomes empty (no more signals present), the control signals stop coming from the counter output to the OR element (3). The latter has as many inputs as the counter (2) has outputs. If any input of the OR element receives 1, then its output will contain 1, too. If the pulse counter (2) is switched off, then the signal is sent to the AND element (40) in order to get the motor rotating without a constraint of pulse count. If the movement code is set, then signals are passing from the pulse generator to the AND element (4), then continue on to the inhibit element (5), to the pulse counter, and to AND (4*) and «inhibit» (5*) elements. If the second input of the AND element (4*) contains 1, then the motor will be rotating in the inverse direction (a revers). Then the signals go to the circular pulse distributor (6), which sets up the rotation, then to a power amplifier (7) (since they are control signals of lower power), on to a stepper motor (8). One special feature of this block-diagram is a circular pulse distributor intended for setting up the direction of motor rotation.

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A block-diagram to control a variable-frequency motor is shown in Fig. 7. The diagram consists of a «code-voltage» converter (1), subtract element (2), analog commutator (3), motor controller (4), variable-frequency motor (5), pulse sensor (6), inhibit element (7), pulse counter (8), and OR element (9).

Fig. 7. Logic circuit of variable-frequency motor control.

The converter (1) is set up with a speed code, and its output gets a value of voltage, which passing through the subtract element (2), corresponds to the direction of motor rotation. Then the voltage goes to the analog commutator (3), which is in charge of closing the circuit and is managed directly with a signal from the OR element (9). Then the signals pass on to the motor controller (4), then to the variable-frequency motor (5). The controller (4) is mounted within the wheel-motor body but shown as a separate element of the diagram. The output shaft of the motor or gearbox is equipped with the pulse sensor (6), which is required to control the number of motor revolutions (to move along the path). The sensor relays the signals to the inhibit element (7), then to the pulse counter (8) and OR element (9). If the pulse sensor (6) is transmitting no signals to the inhibit element, the motor stops. If «one» is fed as a control signal to the input «Rotation 0,1» and no signals are coming from the pulse sensor, then that signal goes straight to the OR element (9) and the motor will be rotating without constraint on its rotary speed.

3 Conclusion Pulse-step systems with spiral motors on stepper drives make it possible to develop compact snow-and-swamp-mobiles with their lifting capacities higher (at least by 1.5–2 times) than those of similar vehicles with pulse-counting systems or spiral motors on

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bicycle wheel-motors. At the same time, they have one substantial drawback: if such a snow-and-swamp-mobile is affected by a strong magnetic field or electrical noise, its reliability turns out to be lower than that of bicycle wheel-motor systems. This fact is subject to their higher complexity and presence of many elements prone to lose pulses due to such interference or other factors. All variations of propellers considered above are intended for various conditions of operation—for example, the propeller with a variable-frequency motor would be more useful for the purposes of driving across loose earth or snow since higher mass of the propellers should create additional traction. The propeller with bicycle wheel-motors is better at moving over the water or swamps since such a design allows to lighten a vehicle and to put up a sort of air cushion underneath the propellers to make it more buoyant. Anyway, both systems are equivalent and can be used to control propellers, but the type of motor depends on the conditions of operation.

References 1. Oshima M, Komoto M, Nakamura M (1982) Development of archimedean screw tractor. Proc Annu Offshore Technol Conf 71–75 2. Osi´nski D, Szykiedans K (2015) Small remotely operated screw-propelled vehicle. Adv Intel Syst Comput 351:191–200 3. Naletov ID (2017) Screwmobiles, their advantages and universality. SPbPU science week: proceeding of the scientific conference with international participation. Saint-Petersburg, Peter the Great St. Petersburg Polytechnic University, pp 239–242 4. Screwmobiles: the rarest all-terrain vehicles. https://www.popmech.ru/technologies/11541vvinchivayas-v-gryaz-shnekokhod/. Accessed 19 Jan 2020 5. Lishchenko TV, Iglin PV, Khomyakov AL (2018) Perspective development of rotary screw allterrain vehicles. Society. Science. Innovation: Proceeding of the XVIII All-Russian theoretical and practical conference, Vyatsky State University, Kirov, pp 530–536 6. Karaseva SA (2014) Calculating main parameters of propellers for rotary screw amphibians. Cars Road Infrastruct 2(2):18 7. New technology. https://masterok.livejournal.com/584743.html. Accessed 19 Jan 2020 8. Gridin DS, Gridin KS, Razumov MS (2014) Analyzing existing designs of all-terrain vehicles. Innovations in Construction from the Perspective of Younger Specialists: Proc. of the International Science and Technology Conference, p 90–96 9. Glagolev SN (2014) Building machines, mechanisms and equipment. Direct-Media, Moscow, p 396 10. Gearboxes and Gearmotors: Industrial Catalogue. Ch. 2. VNIITEMR, Moscow, 1989, p 60 11. Liberman YaL, Zakharova NA (Shonokhova NA) (2016) Screw propeller. Patent Russian Federation 161941. Bull 14 12. GOST 16264.5-85 (2016) Stepper motors. General specifications (rev 1, 2). Standartinform, Moscow, p 80 13. Liberman YaL, Zakharova NA (Shonokhova NA) (2017) Screw propeller. Patent Russian Federation 167625, Bull 1

Management of Transport and Logistics System Based on Predictive Cognitive and Fuzzy Models A. Asanov1(B) and I. Myshkina2 1 MIREA—Russian Technological University, 78, Vernadsky Avenue, Moscow 119454, Russia

[email protected] 2 Kazan Federal University, 18, Kremlyovskaya Street, Kazan 420008, Russia

Abstract. The article offers an approach to solving particular controlling problems that arise in the management of cargo transportation. The proposed approach makes it possible to predict the possibility of emergency situations during transportation and the duration of cargo transportation, on the basis of which the optimal route can be selected. To predict the occurrence of accidents, vehicle failures, and driver errors, a fuzzy cognitive model is constructed that allows taking into account a large number of heterogeneous factors. The forecast model for estimating the duration of transportation is based on the results of a survey of experts, and fuzzy logic is used to formalize expert estimates. A fuzzy hierarchical model is used to reduce the number of fuzzy products. The article also provides a methodological example showing the results of applying the cognitive approach to specific data. Keywords: Controlling · Transport system · Cargo transportation · Optimal route · Cognitive model · Fuzzy model · Situational management

1 Introduction The quality of production processes management, including transport and logistics, is given unflagging attention. One of the ways to solve the problem of improving management efficiency is controlling [1] a functionally separate direction in process management, aimed at the future state of the system/process. Controlling is one of the mechanisms of the market economy, which is designed to anticipate (evaluate in advance) the economic and commercial situation in order to take timely measures to optimize the activities of the business entity in order to achieve the set goals. Therefore, in order to avoid errors and ineffective solutions when using controlling, it is necessary to assess the difficulties and emergency situations in time and find ways to eliminate them in a timely manner. The peculiarity of decision-making in the management of transport and logistics systems is that decision-making is carried out in conditions of uncertainty, lack of sufficient information about the possible states of objects and entities involved in the operation

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_100

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of such systems. Moreover, an important subject that affects the success of such systems is a person, for example, a dispatcher and/or a driver of a vehicle that performs cargo transportation. Professional qualities, personal, psychological, health status, possible reactions to situations that arise during the movement, etc.,—all these indicators undoubtedly have an impact on the possibility of emergency situations in the process of cargo transportation. The task of taking these indicators into account when making decisions is poorly formalized and, together with the need to take into account a large number of other heterogeneous indicators, requires the development of new approaches and the use of adequate methods. Modern research on the management of transport and logistics systems actively uses artificial intelligence methods to account for possible uncertain situations. For example, fuzzy logic and fuzzy cognitive models are used to predict the success of transport projects related to the construction of new roads and to predict the consequences of the introduction of new transport technologies [2–5]. Artificial neural networks are used to evaluate vehicles in real-time tracking systems and during pre-flight checks [6, 7]. In this paper, we consider one of the tasks of controlling the management of transport and logistics systems; the task is of predicting the possibility of emergency situations during transportation using fuzzy cognitive maps, as well as forecasting the duration of cargo transportation using fuzzy models, on the basis of which a particular strategy for performing a transport and logistics operation can be adopted, in particular, the choice of the optimal route is made. It should be noted that most of the studies related to this topic are mostly devoted to specific aspects of this problem. This includes assessing the professional qualities of the driver [8], predicting the condition of the car [9, 10], etc. For a comprehensive analysis and prediction of risks arising in the process of cargo transportation, to take into account a large number of heterogeneous influencing factors, it is advisable to use cognitive modeling.

2 Cognitive Model for Predictive Assessment of Emergency Situations During Cargo Transportation 2.1 Application of Cognitive Modeling in the Management of Transport Systems The cognitive approach is an approach to the study of processes, phenomena, objects in any subject area when the main attention is focused on the processes of representation, storage, processing, and interpretation of knowledge [11]. The cognitive approach is based on the construction of special (cognitive) models of the system under study and the use of a scenario approach. It allows to analyze possible scenarios for the development of situations (the states of the system and the environment), to assess the degree of achievability of the goals set when managing poorly structured systems. A cognitive map is a mathematical model of a system presented as a weighted oriented graph that allows describing the subjective perception of this system by a person or group of people. The complexity of managing the transport and logistics system is due to the need for rapid management decisions in conditions of uncertainty, the presence of a large number of factors that affect the system; the lack of sufficient quantitative information about the behavior of the system, as well as a large number of factors that affect the

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system; in addition, management decisions should allow predicting the possible risk of emergency situations that can lead to severe environmental consequences, human casualties, and material losses. Due to the specifics of transport systems, which are, in fact, poorly structured systems, it becomes appropriate to conduct a qualitative analysis of the possible consequences of decisions made using cognitive modeling. In this paper, we have studied the possibility of using the cognitive modeling methodology to solve one of the tasks, that is forecasting the possibility of emergency situations in the process of cargo transportation based on the analysis of quantitative and qualitative information about internal and external factors that affect the possibility of an emergency, a failure in the operation of the vehicle and the delivery time of the cargo. The features of functioning of any vehicle as a complex technical system are the following [12]: • the vehicle functions only in conjunction with the person (driver), i.e., they form a human–machine system that belongs to the class of ergatic systems • the operation of the vehicle, its system, and the driver is affected by a large number of non-stationary and subjective factors that are difficult to take into account. The cognitive model allows to take into account heterogeneous, poorly formalized factors when predicting the possibility of emergency situations in the process of cargo transportation. It also makes it possible to analyze probable situations that may arise during cargo transportation depending on the state of the vehicle, the driver’s state, the external environment, the route and cargo characteristics, etc. 2.2 Fuzzy Cognitive Model-Building for Predictive Assessment of Emergency Situations During Cargo Transportation Fuzzy cognitive model for predictive assessment of emergency situations during cargo transportation [11, 13–15]: Φ = where G =  is an oriented graph (digraph), V is a set of vertices, and V = {Vl } = {Pi } ∪ Tj ∪ {Gh } are the selected three groups that correspond to control, intermediate, and target vertices. Control vertices describe the current situation and, in turn, include the following groups of factors: the condition of the vehicle, the driver, external environment (weather, pavement quality, etc.), characteristics of the route, and cargo. The target vertices correspond to abnormal situations that may occur during cargo transportation, which may include an increase in the delivery time, the possibility of an emergency,  a failure in the operation of the vehicle.  and E = eij , i, j = 1, M is a set of arcs, M—total number of vertices.   Y = Y Vl , l = 1, M —set of vertex parameters V [the value of vertices Th is a quantitative assessment of factors that describe the current situation (the vehicle in question, the selected driver, route features, cargo, etc.)]. The vertices take values from the interval

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n

Y Pi ∈ [0; 1]. Scaling of the natural values of the vertices Y Pi can be implemented using the formula:  n n Y Pi − Y Pi  .  min Y Pi =  n  n Y Pi − Y Pi max

min

The value Gh is an assessment of the possibility of emergency situations; Y Gh ∈ [0; 1] or Y Gh ∈ [−1; 1].   Effects weights W = wji (i = 1, M , j = 1, M ) between each pair of vertices take values from the interval [−1; 1]. Positive weight value wij indicates that there is a direct connection between vertices: the increase in the value of the vertex Vi leads to an increase in the value of the vertex Vj , and vice versa, the decrease in the vertex value Vi reduces the value of the vertex Vj . Negative weight value wij indicates that there is feedback between vertices: the increase in the value of the vertex Vi reduces the value of the vertex Vj , and vice versa, the decrease in the vertex value Vi leads to an increase in the value of the vertex Vj . Calculation of the forecast estimation of occurrence of emergency situations in the process of cargo transportation includes the following stages: Stage 1 Building a cognitive model. Stage 2 Setting the initial values of the control vertices. Stage 3 Recalculates the values of all vertices (except for vertices corresponding to performers). Model of cognitive map calculation stages [11]: ⎛ Yi (t + 1) = f ⎝k1 · Yi (t) + k2 ·

M 

⎞ Yj (t) · wji ⎠,

(1)

j=1

where Yj (t + 1) Yj (t) are the values of the jth vertice at the calculation stage t + 1 and t; wji is the weight of the connection between vertices Vj and Vi ; f (·) is a non-linear, monotonically increasing function that converts the value of an input argument in the interval [0;1] or [–1;1], and this determines the range of possible values of the target vertices; k1 and k2 characterize the contribution of the corresponding components to the calculation of the new vertex value (0 ≤ k1 ≤ 1, 0 ≤ k2 ≤ 1). Calculation using the Formula (1) is carried out until the values of all vertices stop changing. Figure 1 shows a fragment of a cognitive model for predicting the occurrence of emergency situations during cargo transportation. Table 1 shows a description of the vertices of this cognitive map and an interpretation of the maximum value of the vertices corresponding to one.

3 Predictive Estimation of the Duration of Cargo Transportation and Selection of the Optimal Route The deviation of the delivery period from standard can be caused by a whole set of factors, some of which are given in the previous section of this article. It is possible to estimate

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Fig. 1. Fragment of a cognitive model for predictive assessment of emergency situations during cargo transportation.

the approximate delivery time by interviewing experts or by using the cognitive model, discussed above, to assess how much the delivery time may increase depending on the current situation. Another approach to formalizing expert evaluations that allows using qualitative evaluations can be based on fuzzy logic. To calculate the forecast estimate of the delivery time from one point to another point, a fuzzy model can be built using fuzzy products of the form: If A1 is A˜ i11 AND . . . AND An is A˜ i1n Then T is T˜ 1i1 , where Aj (j = 1, n) are input linguistic variables corresponding to influencing factors i (A˜ jk are values of linguistic variables Aj ), T is an output linguistic variable “Delivery Time” (T˜ i1 are values of a linguistic variable T ). For a large number of input variables, it is advisable to build fuzzy hierarchical models in order to reduce the number of rules [15]. A possible way to build such a model in the case of four input linguistic variables is shown in Fig. 2 (V1 and V2 are intermediate linguistic variables, RB is a rule base). If there are different routes from the starting point to the final point, the obtained forecast estimates of the duration of transportation between possible route points allow to find the optimal route (according to a complex criterion that takes into account a

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Table 1. Some vertices of the cognitive map for predictive assessment of emergency situations in the process of cargo transportation. Vertex number

Vertex name

Vertex number

Vertex name

1 (intermediate vertex (initial value is zero))

Driver errors in the 10 handling of the vehicle (1—a large number of errors)

The quality of the road surface (1—road surface is good)

2

The experience of the 11 driver (1—a long experience)

Traffic flow rate on the route (1—high traffic intensity)

3

Number of road accidents caused by the driver (1—a large number of road accidents)

12

Weather conditions during transportation (1—good weather conditions)

4

The level of the driver’s health (1—the driver is absolutely healthy)

13

Number of vehicle breakdowns (1—a large number of breakdowns)

5

Number of road accidents caused by a vehicle malfunction (1—a large number of road accidents)

14

Restricting and prohibiting signs on the route (1—a large number of limiting and prohibiting signs)

6

The service life of the 15 vehicle (1—a long service life)

The duration of the route (1—long route duration)

7

Cargo volume (1—large cargo volume)

16 (target vertex)

Delivery time (1—significant increase in delivery time)

8

Nature of cargo (1—a dangerous cargo)

17 (target vertex)

Occurrence of emergencies (1—greater possibility of an emergency)

9

The speed limit (driving style) (1—extreme driving mode)

18 (target vertex)

The failure of the vehicle (1—greater possibility of vehicle malfunction)

complex of qualitative and quantitative factors). In this case, the optimal route will take into account the possible risks of emergency situations in the process of cargo transportation, i.e., the elements of situational management will actually be used [16].

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In a more advanced version, it is possible to embed a special decision support subsystem in the architecture of on-board information and control systems for modern and advanced heavy-duty vehicles [17].

A1

RB1

V1

RB2

V2

RB3

T

A2 A3 A4 Fig. 2. Variant of implementation of the fuzzy hierarchical model.

4 Methodological Example of Predictive Assessment of Emergency Situations in the Process of Cargo Transportation In this section, we will study some of the situations that may occur when organizing cargo transportation, and assess the possibility of emergency situations based on the cognitive map shown in Fig. 1. Let the influence weights between map vertices have the following values: w21 = −0.8, w21 = −0.8, w31 = 0.7, w41 = −0.4, w51 = 0.5, w61 = 0.4, w10,1 = −0.4, w1,17 = 1, w1,18 = 0.7, w13,1 = 0.4, w6,18 = 0.7, w78 = 0.8, w28 = −0.8, w89 = 0.8, w15,9 = 0.8, w9,10 = −0.8, w9,17 = 0.8, w14,9 = 0.6, w10,15 = −0.8, w10,11 = −0.4, w12,10 = 0.4, w11,17 = 0.4, w12,17 = −0.5, w13,16 = 0.5, w13,18 = 0.8, w14,16 = 0.5, w18,16 = 1, w17,16 = 1, w18,17 = 0.8. As a function f (·) in (1) a hyperbolic tangent was chosen to calculate the vertex values, k1 = k2 = 0.9 v (1). Let us find the values of the target vertices for the “ideal” situation corresponding to the best values of the managed vertices. In this situation, we have the following values of the corresponding vertices: Y V2 = 1, Y V3 = 0, Y V4 = 1, Y V5 = 0, Y V6 = 0, Y V7 = 0, Y V8 = 0, Y V9 = 0, Y V10 = 1, Y V11 = 0, Y V12 = 1, Y V13 = 0, Y V14 = 0, Y V15 = 0. The qualitative description of this situation is as follows: the driver has a long driving experience, good health, and has not been involved in road accidents, observes the rules of the road, the route is easy, the weather conditions for the trip are good, etc. Changes in values during the calculation process and established values of target vertices V16 , V17 , V18 are shown in Fig. 3a. In the “worst” situation, we have the following values of the corresponding vertices: Y V2 = 0, Y V3 = 1, Y V4 = 0, Y V5 = 1, Y V6 = 1, Y V7 = 1, Y V8 = 1, Y V9 = 1, Y V10 = 0, Y V11 = 1, Y V12 = 0, Y V13 = 1, Y V14 = 1, Y V15 = 1. Changes in the values during the calculation and the established values of the target vertices are shown in Fig. 3b.

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Figure 4 shows the changes in values during the calculation process and the established values of target vertices for an arbitrary situation with the following values of managed vertices: Y V2 = 0.9, Y V3 = 0.3, Y V4 = 0.7, Y V5 = 0.3, Y V6 = 0.9, Y V7 = 0.6, Y V8 = 0.6, Y V9 = 0.4, Y V10 = 0.6, Y V11 = 0.6, Y V12 = 0.8, Y V13 = 0.1, Y V14 = 0.2, Y V15 = 0.5. It is obvious that the obtained values correspond to the expected estimates of the considered situations.

Fig. 3. a The value of the target vertices for the “ideal” situation; b target vertex values for the “worst-case” situation.

Fig. 4. Values of target vertices for an arbitrary situation.

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5 Conclusion The cognitive approach makes it possible to forecast the occurrence of emergency situations, taking into account a large number of heterogeneous influencing factors, and to improve the quality of decisions made in the management of cargo transportation. One of the advantages of using fuzzy cognitive maps for this problem is the ability to formalize and describe very complex situational constructions. At the same time, the implementation/configuration of cognitive models is limited only by our capabilities/limitations in identifying a sufficient amount of numerical data that corresponds to real situations that arise in the process of cargo transportation. The proposed approach can also be applied when selecting drivers and vehicles for cargo transportation. The direction of further research is to expand the set of factors taken into account, improve the methodology for building cognitive models based on the results of a survey of experts and retrospective data, and explore the possibilities of using different types of cognitive models.

References 1. Horvath P (2006) Controlling. Vahlen, München 2. Zhang P, Jetter A (2018) A framework for building integrative scenarios of autonomous vehicle technology application and impacts, using Fuzzy Cognitive Maps (FCM). In: PICMET 2018—Portland international conference on management of engineering and technology: managing technological entrepreneurship: the engine for economic growth, Proceedings. https://doi.org/10.23919/picmet.2018.8481747 3. Ba˘gdatlı MEC, Akbıyıklı R, Papageorgiou EI (2017) A fuzzy cognitive map approach applied in cost–benefit analysis for highway projects. Int J Fuzzy Syst 19(5):1512–1527 4. Tsadiras A, Zitopoulos G (2017) Fuzzy cognitive maps as a decision support tool for container transport logistics. Evolving Syst 8(1):19–33 5. Rozenberg IN (2015) Cognitive management of transport. The State Counsellor 2:47–52 6. Akhmetvaleev AM, Katasev AS, Podolskaya MA (2018) Neural networks collective model and software package to determine person’s functional state. CASPIAN J Control High Technol 1(41):69–85 7. Akhmetvaleev AM, Katasev AS (2018) Neural network model of human intoxication functional state determining in some problems of transport safety solution. Comput Res Model 10(3):285–293 8. Fedorov DS (2011) Theoretical aspects of methodology for the selection of professional drivers, using hardware-software systems. SibADI Bull 3(21):11–15 9. Kokorev GD (2018) Forecasting the automobile state on the basis of approximation of its elements parameters change. Sci J Kuban State Agrarian Univ 121(07):1434–1452 ´ 10. Swiderski A, Jó´zwiak A, Jachimowski R (2018) Operational quality measures of vehicles applied for the transport services evaluation using artificial neural networks. Eksploatacja i Niezawodnosc–Maintenance Reliab 20(2):292–299 11. Vasilev VI, Ilyasov BG (2009) Intelligent control systems. Radio Engineering, Moscow 12. Asanov AZ, Valiev DH, Savinkov AS (2012) Integration and intellectualization of on-board control systems for heavy-duty vehicles. In: Problems of control and modeling in complex systems: proceedings of the XIVth international conference, SNTs RAN, Samara, pp 524–531 13. Myshkina IYu, Asanov AZ, Grudtsyna LYu (2015) Evaluation and selection of personnel based on clear and fuzzy cognitive models. Int J Soft Comput 10:448–453

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14. Asanov AZ, Myishkina IYu (2012) Cognitive modeling in the task of assessing the compliance of a job applicant with qualification requirements. Bull Comput Inf Technol 12:2–34 15. Borisov VV, Kruglov VV, Fedulov AS (2007) Fuzzy models and networks. Goryachaya liniya –Telekom, Moscow 16. Pospelov DA (1986) Situational management: theory and practice. Nauka, Moscow 17. Asanov AZ (2017) Modern architecture board information and control systems of heavy vehicles. Russian Technol J 5(3):106–113

The Study of Influence of Hole Diameter Within the Inclined-Corrugated Contact Elements on the Hydraulic and Heat-Mass Transfer Characteristics of Cooling Toweraper A. Dmitriev1 , I. Madyshev2(B) , and A. Khafizova2 1 Kazan State Power Engineering University, 51, Krasnoselskaya Street, Kazan 420066, Russia 2 Kazan National Research Technological University, 68, Karl Marx Street, Kazan 420015,

Russia [email protected]

Abstract. This paper deals with the study of circulating water cooling processes in evaporative cooling towers, widely used in various industries. This paper deals with the studies within the inclined-corrugated contact elements, operated with the contactless evaporative cooling technology. The authors studied the heat-mass transfer and hydrodynamic processes under the condition of countercurrent movement of two phases. The comparative results of hydraulic resistance with the previously obtained results for the inclined-corrugated plates with 5 mm diameter of holes were conducted and with those that are widely used in the production process of units are shown in this paper. The heat efficiency coefficient and the efficiency coefficient of water evaporation were determined. An increase in the diameter of holes allows to reduce the hydraulic resistance. The high efficiency of heat-mass transfer processes for the inclined-corrugated contact elements is observed at a wide range of rates of 1.7–3 m/s, the irrigation density of 12–31 m3 /(m2 h). The developed checker filling units with the inclined-corrugated contact elements provide a sufficiently high efficiency of cooling the water in the proposed design of cooling tower. Keywords: Inclined-corrugated contact elements · Cooling toweraper · Heat efficiency coefficient · Heat-mass transfer

1 Introduction The water is widely used as a refrigerant for cooling the process equipment at the industrial enterprises due to its high heat capacity. A huge amount of natural water is used for the process purposes, which has a significant impact on the world water reserve and the environment. In order to solve these problems, the recycling (circulating) water supply system, which is cooled mainly in cooling towers, is used by industrial enterprises. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_101

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The recycling water supply system allows to reduce the natural water consumption significantly [1–4]. The performance efficiency and service life of process equipment, as well as consumption of raw materials, fuel, and electricity depends on the cooling tower operation efficiency. Most often, the industrial enterprises use fan (mechanical draft) cooling towers, where the liquid is cooled by the interaction of water and atmospheric air. The main cooling element of cooling tower is the filler, on the surface of which the liquid phase interacts with the gas one. There is a wide range of design options for the fillers [1, 5–18], which meet high requirements and have a number of advantages. However, when cooling the water, a very important factor should be also taken into account, i.e., biological pollution, caused by the development of anaerobic bacteria and microorganisms in the water. In order to prevent biofouling on the filler surface, a chemical method against microorganisms is often used, i.e., using chemical reagents. The reagents enter the water environment causing the death of bacteria. However, this method has some drawbacks: to maintain the bacterial balance in the water environment, and a huge amount of reagents is required, which is very expensive from an economic point of view. Moreover, some microorganisms can adapt to the water environment with chemical reagents in it. In this regard, the authors have the following task: to develop a design of cooling tower so that the cooling of liquid can be quite effective and the use of chemical reagents can be significantly reduced [19–21].

2 Description of the Device and Its Operation In order to solve this task, the design of evaporative reagent-free cooling tower with the inclined-corrugated contract elements was developed. The peculiarity of this cooling tower is that the main cooled liquid flow moves along the radiator and interacts with the air through the wall that does not allow microorganisms to get the necessary nutrients. Also, the recycling water is cooled by the cooled liquid flow along the piping wall. The design of non-contact evaporative cooling tower is shown in the research paper [22]. The developed cooling tower operates as follows: the used process water is fed to the filer unit and divided into 2 flows so that the main part of liquid moves along the pipes, being cooled by the air flow and by transferring the heat to the liquid film, flowing down the pipes. The remaining part of liquid, 5–6% of hot water total amount is distributed over the inclined-corrugated checker filling unit, interacting with the air flow, and is cooled by the liquid evaporation. After that it enters the drainage basin. In addition to the hot water, the water from the drainage basin is fed to the second liquid flow through the inlet point to the checker filling units, so the system has a liquid circulation, and the water level in the basin is maintained. In this case, the small flow is an additional one, filling up the evaporated part of liquid in the drainage basin. This liquid flow acts as a refrigerant for the main hot water flow. The efficiency of recycled water cooling in pipes largely depends on the water cooling degree within the cooling tower filler, which is affected by its design. The filler consists of vertical checker filling units with pipes, arranged in several rows (Fig. 1). The liquid enters the checker filling units through a single inlet point on the wall side surface. The checker filling is a rectangular box with corrugated plates 1 placed in it. The plates are

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arranged perpendicular to each other at an angle of 90°, forming a zigzag in the profile. The plates are the inclined-corrugated contact elements with the horizontal corrugations of a rounded profile, on the surface of which there is a moving liquid turbulence at a relatively low flow rate. A row of hot water pipes is located between the plates. The liquid is distributed within the checker filling as follows: the water moves from the top to bottom, along the surface of pipes and in the form of liquid film moves along the perforated plates, forming a Z-trajectory. A part of liquid falls through the plate holes with further dripping onto the liquid film surface on the below plate and pipes. After that it breaks with the formation of new water drops. The air is pumped by the fan from the bottom up, passes through the plate holes by pushing out the water drops in different directions, thereby spraying the liquid over the entire volume of checker filling and the outer surface of pipes. The air flow has a chaotic character of movement (indicated by a dashed line in Fig. 1). It should also be noted that the upper plate of each checker filling is also a separating device, thereby reducing the entrainment of liquid from the cooling tower into the atmosphere.

1 2

Fig. 1. The layout of a row of checker fillings: 1—corrugated plate; 2—pipe.

As a result of this design solution, the water within the checker filling is distributed independently and quite evenly, thereby significantly reduces the need to install the spraying devices. Therefore, the maintenance costs for these devices are reduced, as well as the energy costs for pumping the processing medium.

3 Description of the Study and Its Results In order to conduct the experimental study of heat-mass transfer processes under the condition of countercurrent movement of two phases, as well as to study the hydrodynamic processes, an experimental apparatus was developed. The experimental apparatus is a checker filling, consisting of two contact stages with the inclined-corrugated plates and a total height of 340 mm. The corrugated plates have a rounded profile with a radius of 7.5 mm. The rounded holes are executed within the side surfaces and the upper part of corrugations. The dimensions of the studied apparatus in the cross section are 100 × 100 mm. The apparatus, used for the previous research, had the holes with 5 mm diameter within the plates. The obtained results are shown in the research paper [23]. In this paper, the diameter of holes was changed to 6 mm and a number of studies were also conducted.

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The conducted studies are focused on determining the hydraulic resistance in the contact device, obtaining the experimental data when changing the fictitious air flow velocity, liquid and gas flow rates, depending on the irrigation density of contact device. One of the main tasks is also to compare the characteristics with those, obtained in the course of previous research, as well as to compare the checker fillings, with those, widely used in the production process. The experiments were conducted on the air–water system basis. The water was fed to the upper central part of the first contact stage at various rates. The liquid temperature at the inlet and outlet of apparatus was measured by means of a two-channel meter-regulator OWEN 2TRM1. The water flow rate was measured by means of a variable area flow meter. The fictitious cooling air flow velocity (for the full cross section of apparatus) was measured by means of thermal anemometer testo 405i and varied within the range of 1.57–3.15 m/s. The irrigation density varied within the range of 12–37 m3 /(m2 h). The air temperature was within the range of 26.2–27.3 °C; the hot water temperature—35.1 to 42.8 °C. In the course of experiment, the relative air humidity was measured by means of thermohygrometer testo 605i and varied within the range of 37.5–39.6%. The pressure drop, according to the height of contact stages, was measured by means of differential pressure gauge testo 510i. The obtained values of hydraulic resistance (Fig. 2) of inclined-corrugated contact elements indicate that the liquid bubbling is quite intensive, which confirms the efficiency of processes. Also, as a result of experiment, it was found that the range of operating gas rates is quite wide from 1.7 to 3 m/s, and the hanging (suspension) state starts at high rates and is observed when the irrigation density is equal to 37 m3 /(m2 h). 3

ΔP/H, kPa/m

2.5

1 2 3 4

2 1.5 1 0.5 0

W0, m/s 1

1.5

2

2.5

3

3.5

Fig. 2. The change in the hydraulic resistance of inclined-corrugated contact elements, depending on the fictitious air flow velocity at different irrigation densities q, m3 /(m2 h): 1—0; 2—12; 3—31; 4—37 and the diameters of holes within the corrugations: dashed lines—5 mm; solid lines—6 mm.

The authors also compared the hydraulic resistance of these plates with the plates where the diameter of holes within the corrugations is 5 mm (Fig. 2), as well as with

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other types of contact devices (Fig. 3). As a result of comparison, it can be stated that: the hydraulic resistance of inclined-corrugated contact element with 5 mm diameter of corrugation holes increases sharply when the rate is 1.7 m/s and, then, a hanging state comes, which cannot be referred to a plate with 6 mm diameter of corrugation holes. The range of operating rates in the contact devices with the inclined-corrugated plates is noticeably greater than that of their analogs [12–14]. According to the figures, an increase in the diameter of holes allows to reduce the hydraulic resistance, but an increase in the irrigation density reduces the range of operating rates and as a result, the hanging state comes faster. For a more complete and clear picture of design operation efficiency, the heat efficiency coefficient and the efficiency coefficient of water evaporation were also determined, as well as the comparison with the previously obtained results for the inclined-corrugated plates with 5 mm diameter of holes were conducted. As shown in the research paper [24], the heat efficiency coefficient in the evaporative cooling tower was determined by the following formula: ηL =

tL0 − tLk , tL0 − tLp

(1)

where t L0 —the water temperature at the cooling tower inlet, °C; t Lk —the water temperature at the cooling tower outlet, °C; t Lp —the water equilibrium temperature, i.e., dew point temperature (the theoretical limit of water cooling), °C. The efficiency coefficient of heat-mass transfer apparatus upon water evaporation was determined by the following formula: E=

xk − x0 , xp − x0

(2)

where x 0 , x k —the moisture content of saturated air at the cooling tower inlet and outlet, kg/kg; x p —the equilibrium moisture content of saturated air, kg/kg. The dependencies shown in Fig. 4 tell us about a sufficiently high heat efficiency coefficient at low irrigation densities for the corrugated plates with 5 and 6 mm diameter of holes, which is at the same level with the analog. With a further increase in the irrigation density, the efficiency coefficient decreases, while the corrugated plate with 5 mm diameter of holes has higher efficiency coefficient than the plate with 6 mm diameter of holes. The efficiency of heat-mass transfer processes is also characterized by the heat-mass transfer efficiency coefficient, the dependency of which is shown in Fig. 5. In the course of early studies, it was found that the highest efficiency of heat-mass transfer for the corrugated plates with 5 mm diameter of holes is observed at an irrigation density of 15–25 m3 /(m2 h), achieving the heat-mass transfer efficiency of 98%. When studying the corrugated plates with 6 mm diameter of holes, the decrease in cooling efficiency by 25% was observed, which is associated with the decrease in the air flow velocity, passing through the holes that reduce the degree of penetration and filtration of air through the water flows. However, these values of heat-mass transfer efficiency coefficient indicate the competitiveness of devices with its analogs, used in the production process.

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2

ΔP/H, kPa/m 1.75

1 2 3 4

1.5 1.25 1 0.75 0.5 0.25

W0, m/s

0 0

0.5

1

1.5

2

2.5

3

3.5

Fig. 3. The dependency of hydraulic resistance of inclined-corrugated contact elements on the fictitious air flow velocity and the type of contact device when the irrigation density is equal to q = 30 m3 /(m2 h): 1—the pall ring, d = 50 mm; 2—the Rashig rings, d = 100 mm; 3—checker filling «Injekhim-2002»; 4—the inclined-corrugated contact element with a hole diameter of 6 mm. 0.35

ηL 1 2 3

0.3 0.25 0.2 0.15 0.1 0.05 0 0

1

2

3

4

5

6

Lm/Gm

Fig. 4. The dependence of the change in thermal efficiency on the ratios of mass flow rates of liquid and gas phases at different irrigation densities q, m3 /(m2 : h): 1—12; 2—24; 3—37 and the diameters of holes within the corrugations: dashed lines—5 mm; solid lines—6 mm.

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E

0.9

1 2 3

0.8 0.7 0.6 0.5 0.4 0.3 0.2

0

1

2

3

4

5

6

Lm/Gm Fig. 5. The dependence of the heat and mass transfer efficiency on the ratios of mass flow rates of liquid and gas phases at different irrigation densities q, m3 /(m2 h): 1—12; 2—24; 3—37 and the diameters of holes within the corrugations: dashed lines—5 mm; solid lines—6 mm.

4 Conclusion In the course of experimental studies, the design parameters of elements were changed and compared. As a result, it can be stated that the contact devices with inclinedcorrugated plates, the diameters of which are equal to 5 and 6 mm, can be used in the production process, depending on the parameters of technological process. The high efficiency of heat-mass transfer processes for the inclined-corrugated contact elements is observed at a wide range of rates of 1.7–3 m/s, the irrigation density of 12–31 m3 /(m2 h), using the plates with a diameter of corrugation holes equal to 6 mm. The cooling efficiency of heat-mass transfer processes on the plates with 5 mm diameter of corrugation holes is higher, but the range of operating rates is smaller. The developed checker filling units with the inclined-corrugated contact elements provide a sufficiently high efficiency of cooling the water, flowing along the pipes in the proposed design of cooling tower. Moreover, such design of cooling tower allows to reduce the costs for installation of liquid spraying devices, as well as to reduce the use of chemical reagents. Acknowledgements. The reported study was funded by the grant of the President of the Russian Federation, project number MK–417.2019.8.

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Foamed Heat-Insulating Materials V. A. Smoliy(B) , E. A. Yatsenko, and A. A. Chumakov Platov South-Russian State Polytechnic University (NPI), 132, St. Prosvescheniya, Novocherkassk 346428, Russia [email protected]

Abstract. The current development of the oil and gas industry’s mechanical engineering is described. A brief description of the “hot” pumping of oil through the pipeline from the place of its production is presented. The description of the thermal insulation technology used for pumping oil using polyurethane foam and galvanized steel is given. On its basis, the necessity of using foamed thermal insulation materials, for example, foam glass in the oil and gas engineering industry as a thermal insulation of pipelines for the transportation of hydrocarbon raw materials (oil) is justified. The physical and mechanical properties of foam glass are described, which clearly show its advantage over other thermal insulation materials. The developed technology of production of foam glass using raw materials of the Russian Far East and for the harsh climatic conditions of this region is presented. The graph of foaming of foam glass is given. For evidence of the use of foam glass as the insulation of pipelines, the authors made a thermal design of a pipeline section with the given initial data and the graphical dependence proved the effectiveness of foam glass for the insulation oil pipelines in the Far Eastern and Northern regions of the Russian Federation. Based on the research, the corresponding conclusion is made. Keywords: Insulation · Pipeline · Pumping · Foam glass · Density · Foaming

1 Introduction Oil and gas engineering is a growing and extensive industry that originated in the late nineteenth century. Currently, this branch of mechanical engineering produces technological equipment, as well as special complete technological lines and installations for the chemical, petrochemical, oil and gas industries. A special place in the oil and gas sector of mechanical engineering is occupied by pipelines. At the moment, in connection with the increase of oil production in the far Eastern and Northern regions of the Russian Federation, there is your problem of transporting hydrocarbons over long distances, and this is due to increased oil viscosity at low temperatures, causing it to thicken, and flow speed inside the pipeline is greatly reduced. Therefore, it is necessary to provide thermal insulation along its entire length to reduce heat loss. Usually, the insulation of pipelines is carried out with polyurethane foam, which is applied in a single layer. The thickness of © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_102

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the polyurethane foam layer depends on the diameter of the pipe itself and the area where the pipeline is planned to be laid, for the diameter of the oil pipeline of 1020 mm and in the Far North and Far East, it is used 100 mm. Inside the polyurethane foam, there is a signal cable of the operational remote control system, which allows using special devices to detect areas that need repair before an accident occurs. For additional protection of the thermal insulation material from external damage, additional protection is mounted on top of it. For this purpose, a shell made of thin-sheet galvanized steel is used; it is made with a first-class zinc coating according to GOST 14918 or with a zinc coating not lower than class 450 according to GOST R52246. These are formed metal casings that protect thermal insulation materials on pipelines, process equipment, and various containers from atmospheric influences, mechanical damage, and ultraviolet radiation. But this type of thermal insulation has a number of disadvantages, the main of which is that heat passes through the polyurethane foam over time, and the steel eventually begins to rust under the influence of the environment, which also affects the thermal insulation layer [1–4]. Therefore, the most promising for high-quality and long-lasting insulation of pipelines are foam insulation materials, in particular, foam glass, which is a porous heat and sound insulation material with a true porosity of up to 85–95%, consisting of gaseous and porous phases. The solid phase is glass that forms thin walls of individual cells several micrometers thick. The cells are filled with a gas phase whose gas pressure at room temperature is approximately 30.3–40.5 kPa. Foam glass with closed pores is used for thermal insulation [5–15]. The main advantages of foam glass in comparison with other thermal insulation materials are durability, water resistance, relatively high mechanical strength, noncombustibility, and biological resistance. Foam glass is easily machined: cutting, sawing, drilling, grinding, and bonding with each other and with other materials, which expands the scope of application. Foam glass as a thermal insulation material with a thermal conductivity equal to that of the best thermal insulation materials, exceeds them in a number of other indicators. Foam glass is water-tight, has high mechanical strength, non-flammable, and meets sanitary requirements—does not rot and does not mold. The thermal insulation properties of foam glass are due to • low density—140 to 200 kg/m3 ; • high closed porosity—the amount of solid phase is 5–15%, and gaseous—85 to 95%; • water absorption—3 to 5%. The mechanical properties of foam glass depend on the average density and pore diameter, and for a fine-porous material with a density of 180–200 kg/m3 , the strength limits are MPa: compression—0.88; bending—0.59 to 0.69; tensile—0.44 to 0.49. Thermal insulation foam glass is characterized by high frost resistance—up to 50 cycles of alternate freezing to −50 °C and thawing at 20 °C [9, 13].

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2 Main Part 2.1 Technology for Producing Foam Glass Research scientists of the Department of General chemistry and technology of silicates of the Platov South-Russian State Polytechnic University (NPI) have developed a technology for producing foam glass based on raw materials and for the harsh climatic conditions of the Russian Far East [16–18]. The essence of the method for obtaining this material consists in sintering a mixture of powdered raw materials and special additives that contribute to the formation of the gas phase when heated. During the heat treatment of the mixture, when the temperature in the kiln reaches the softening temperature of the main components of the charge, sintering of the silicate raw material particles begins, while the particles of the pore-forming agent are blocked by the softened glass-like material. When the decomposition temperature of the blowing agent is reached, the gas phase begins to be released, which foams the glass mass. In all places of the caked body where the particles of the pore-forming agent were blocked, pores appear due to the release of gases (Fig. 1). The shape of the pores and properties of the resulting foam glass largely depend on the concentration and type of the used pore-forming agent. The properties of the developed foam glass are shown in Table 1.

Fig. 1. Microstructure of the developed foam glass.

Table 1. Properties of the developed foam glass. Name

Value

Density, kg/m3

150–600

Strength, MPa

0.8–5.0

Thermal conductivity coefficient, W/m · K 0.06–0.12 Water absorption, %

3–5

Foaming of foam glass occurs in accordance with the graph shown in Fig. 2.

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Fig. 2. The temperature–time interval for the production of foam glass: 1—loading; 1–2—heating; 2–3—foaming; 3–4, 5–6—cooling;4–5—stabilization; 6—unloading of samples.

2.2 Thermal Calculation of an Oil Pipeline with Foam Glass Insulation To prove the effectiveness of the developed foam glass as a heat-insulating material in hot oil refining, a thermal calculation was performed [19, 20] of the oil pipeline with the following initial data: • • • • • •

temperature at the inlet of the pipeline t 1 = 90 °C; temperature at the outlet of the pipeline t 2 = 70 °C; ambient temperature t amdient = −30 °C; oil product consumption (volume) V = 0.378 m3 /s; the length of the pipeline L = 4000 m; the outer diameter of the pipeline D = 1240 mm = 1.24 m.

Foam glass was chosen as a thermal insulation material. The thickness of the insulation layer δ = 100 mm = 0.1 m. The outer diameter of the insulation layer D = D + 2δ = 1.34 m. In accordance with GOST 31447–2012, pipelines are made of 09G2C steel with a wall thickness of δ = 14 mm = 0.014 m. When pumping, the oil has a certain flow temperature calculated using the formula (1): toil = tamdient +

ln

t1 − t 2 t1 − tambient t2 − tambientt

(1)

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where t oil t1 t2 t ambient

oil flow temperature, °C; oil temperature at the inlet to the pipeline, °C; oil temperature at the outlet of the pipeline, °C; ambient temperature, °C.

But the temperature of the oil flow is not enough to know what kind of insulation should be used. Therefore, we determined the heat transfer coefficient of the pipes. We used a simplified formula (2) for large diameter pipes Dn > 500 mm: K=

1 α1

+

1  δi

λi

+

1 α2

(2)

where K α1 δi λi α2

heat transfer coefficient of the pipes, W/(m2 · K); heat transfer coefficient from oil to the wall, W/(m2 · K); the thickness of tube wall, m; coefficient of thermal conductivity of steel, 50 W/(m2 · K); coefficient of heat transfer from the pipe wall to the environment, W/(m2 · K).

The final temperature in the pipeline (with a heat transfer coefficient K = 0.501 W/(m2 · K) corresponding to the thickness of the insulation layer δ = 100 mm) was calculated using the formula (3): tfin = tin −

KF taverage Gc

(3)

where t fin t in K F t average G

the final temperature of flow in the pipeline, °C; flow temperature at the inlet of the pipeline, °C; heat transfer coefficient of pipes, W/(m2 · K); the total surface of the pipeline, m2 ; temperature head, °C; mass flow, kg/s.

The final temperature at the end of the pipeline section under consideration will be 70.66 °C with a heat transfer coefficient K = 7.712 W/(m2 · K) and an insulation thickness δ = 5 mm [8, 9]. Table 2 shows the calculation of the final temperature of the oil product for different heat transfer coefficients and thermal insulation thickness. According to the table above, we construct a graphical dependence of the final temperature of the oil product flow on the thickness of the thermal insulation layer, shown in Fig. 3.

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The thickness of the insulation layer δ, cm

Heat transfer coefficient K, W/(m2 · K)

0

Outlet temperature t out , °C

31.615

26.28

0.5

7.712

70.55

1

4.392

78.52

2

2.360

83.69

3

1.613

85.65

4

1.226

86.68

5

0.988

87.32

6

0.828

87.75

7

0.712

88.06

8

0.625

88.29

9

0.557

88.48

10

0.502

88.72

11

0.457

88.75

12

0.419

88.85

13

0.387

88.94

14

0.360

89.01

15

0.336

89.08

16

0.316

89.13

17

0.297

89.18

18

0.281

89.23

19

0.266

89.27

20

0.253

89.31

21

0.241

89.34

22

0.230

89.37

23

0.220

89.39

24

0.211

89.42

25

0.203

89.44

26

0.195

89.46

27

0.188

89.48

28

0.181

89.50

29

0.175

89.52

30

0.169

89.54

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Fig. 3. Dependence of the final temperature of the flow of petroleum products in the pipeline on the thickness of the insulation layer.

3 Conclusion Thus, the foam glass produced from raw materials of the Far East of Russia is promising for use in thermal insulation of pipelines, since it is superior in its physical and chemical properties of traditionally used materials and when you use foam glass insulation reduces the conductivity and increases the temperature of the flow of oil output, which has a positive impact on the throughput and minimizes heat loss to the environment. Acknowledgements. The work was carried out at SRSPU (NPI) with the financial support of the Russian scientific Foundation under agreement No. 18-19-00455 “Development of technology for integrated protection of pipelines for oil and gas operated in the Russian Far East” (head-Yatsenko E.A.).

References 1. Garina EP, Garin AP, Batsyna YaV, Shpilevskaya EV (2020) Obespecheniye ekonomicheskoy bezopasnosti ustoychivogo razvitiya predpriyatiya mashinostroyeniya (Ensuring economic security of sustainable development of machine-building enterprises). Econ Entrepreneurship Law, 37–52 2. Osnovnyye trebovaniya k teploizolyatsii truboprovodov neftyanoy i gazovoy otrasli (Basic requirements for thermal insulation of pipelines in the oil and gas industry). https://1cert.ru/stati/osnovnye-trebovaniya-k-teploizolyatsii-truboprovodov-neftyanoyi-gazovoy-otrasli,free. Accessed 03 Feb 2020 3. Izolyatsiya trub nefteprovodov (Isolation of oil pipeline pipes). https://www.kzit.ru/company/ articles/izolyatsiya_trub_nefteprovodov/,free. Accessed 03 Feb 2020

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4. Aliev RA, Belousov VD, Nemerow AG (1998) Truboprovodnyy transport nefti i gaza (Pipeline transport of oil and gas). Moscow 5. Kudinov VI (2004) Osnovy neftegazopromyslovogo dela (Fundamentals of oil and gas industry). Izhevsk 6. Elagina OY, Ageeva VN, Buklakov AG (2019) Some aspects of heat-insulating materials application on systems of oil fields steam pipelines. Neftyanoe Khozyaystvo-Oil Ind, 87–89 7. Dadashov I, Loboichenko V, Kireev A (2018) Analysis of the ecological characteristics of environment friendly fire fighting chemicals used in extinguishing oil products. Pollut Res, 63–77 8. Zakharov SL, Yunusov KB, Levin SN (2016) Material for protection of oil products against evaporation. Chem Petrol Eng, 69–70 9. Demidovich BK (1972) Proizvodstvo i primeneniye penostekla (Production and application of foam glass). Minsk 10. Zarubina LP (2012) Teploizolyatsiya zdaniy i sooruzheniy. Materialy i tekhnologii (Thermal insulation of buildings and structures. Materials and technologies). Saint-Petersburg 11. Perspektivnyye otechestvennyye razrabotki: penosteklo – novaya tekhnologiya zhdet vnedreniya (2000) (Promising domestic developments: foam glass-a new technology is waiting to be introduced). Ind Constr Rev, 13–14 12. Gorlov YuP, Merkin AP, Ustenko AA (1980) Tekhnologiya teploizolyatsionnykh materialov (Technology of heat-insulating materials). Moscow 13. Bobrov YL, Ovcharenko EG, Shoikhet BM, Petukhova EYu (2003) Teploizolyatsionnyye materialy i konstruktsii (Thermal insulation materials and structures). Moscow 14. Yatsenko EA, Ryabova AV, Goltsman BM (2019) Development of fiber-glass composite coatings for protection of steel oil pipelines from internal and external corrosion. Chernye Metally, 46–51 15. Ivanov KS, Korotkov EA (2017) Investigation of the effect of a layer of granulated foam-glass ceramic on the temperature conditions of frozen soil. Soil Mech Found Eng, 349–355 16. Ventrella A, Smeacetto F, Salvo M et al (2012) Characterization of new glass coated foam glass insulating tiles by standard tests. J Mater Eng Perf, 2380–2388 17. Yatsenko EA, Goltsman BM, Smoliy VA et al (2019) Integrated protection of pipelines using silicate materials. In: International multidisciplinary scientific geo conference surveying geology and mining ecology management, SGEM, pp 507–514 18. Yatsenko EA, Goltsman BM, Smoliy VA (2018) Peculiarities of the use of siliceous raw materials of the Russian Far East in the integrated pipeline protection. MATEC Web Conf 242:01016 19. Gorlov YP (1989) Tekhnologiya teploizolyatsionnykh i akusticheskikh materialov i izdeliy (Technology thermal insulation and acoustic materials and products). Moscow 20. Guidance document RD 39-30-139-79 Metodika teplovogo i gidravlicheskogo rascheta magistral’nykh truboprovodov pri statsionarnykh i nestatsionarnykh rezhimakh perekachki n’yutonovskikh i nen’yutonovskikh neftey v razlichnykh klimaticheskikh usloviyakh (Method of thermal and hydraulic calculation of main pipelines in stationary and nonstationary modes of pumping Newtonian and non-Newtonian oil in different climatic conditions)

Computer Simulation of Microprofile Strain Under Orthogonal Impact at Constrained Load. Part 1 N. V. Vulykh1(B) and A. N. Vulykh2 1 Irkutsk National Research Technical University, 83, Lermontov St., Irkutsk 664074, Russia

[email protected] 2 Irkutsk State Agrarian University named after A.A. Ezhevsky, 1/1, Molodyozhny, Irkutsk

664038, Russia

Abstract. The improvement of surface plastic deforming technology is pertinent in the machine-building technology and constitutes optimization of deforming processes while forming microgeometry of the surface. Today the requirements for processing accuracy, surface finish, fatigue strength, and durability of products are becoming more demanding. The paper presents the processes of the local surface strain of machine components. It is stated that, after edge-cutting machining, real surface of machine components is longitudinally V-shaped. It is shown that the mechanism of how the microshape changes is not sufficiently investigated yet due to its volatility and other obstructive factors. The authors provide the mechanism of how the microroughness model changes its shape under the strain impact commensurate to the initial microshape height. Also, the paper shows how the microshape height reduction affects the base angle of the deformed microshape, relative width of the contact area, and behavior of the microshape valley point under constrained load. Lead, tin, aluminum, and copper are used as the material for samples. Keywords: Surface microprofile · Roughness modeling · Finite-element modeling · Elasto-plastic strain · Constrained strain

1 Introduction Traditionally, the surface plastic strain is executed with a local deforming tool (ball, roll, disk, diamond-pointed indentor, etc.). With that, the tool usually impacts the component orthogonally. Plastic local impact allows for finishing and strengthening treatment of various components, of simple and complex shapes. Real surface of components is never completely smooth. Instead, it always has microroughness that constitutes its microrelief. Properties of that microrelief—dimensions, shape, and locations of irregularities—are determined by the method and conditions of surface treatment. A failure to take account of the initial roughness may close the door on © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_103

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appraising the effect of process parameters on the surface quality of finished products. It is clearly seen in surface plastic strain processes when the draft value is commensurate with the microroughness height. In such a case, what is strengthened is not the general volume of the metal but geometrical elements of the surface layer. In fact, it is a difficult task to study the strain of irregularities on real products due to surface irregularities, uneven distribution of microelevations by height, etc. As known [1, 2], edge-cutting machining gives most irregularities than the V-shape. It should be noticed that for lathed surfaces having the roughness Ra = 2.5–20 μm, it is likely that all profile peaks may simultaneously contact a flat counterbody [3]. High homogeneity of the profile after lathe work was mentioned in [4]. Therefore, it is safe to use a regular longitudinally V-shape profile for modeling the surface layer after edge-cutting machining. One of the problems related to the deforming processing of plastically deformed surfaces is that the way how the microprofile changes its shape which is not well studied due to its volatility and other factors. Due to this, a relevant objective is to improve the surface plastic strain technology by taking account of the technological background in formation of the surface microgeometry. That said, the purpose of this paper is to determine the mechanism of how the microroughness model changes its shape under different degrees of the strain impact commensurate with the initial microprofile height.

2 Materials and Methods As widely known, computer modeling based on the finite-element method is a fruitful way to analyze the strain-stress behavior of the microroughness model [5, 6]. One of the most versatile and commonly used programs executing the finite-element method is ANSYS Workbench [7, 8]. The geometry of the studied area was gradually formed in the program pursuant to the plan of exposing the rough surface of Sample 3 to the impact of a rigid tool, Indentor 1 (see Fig. 1). Deforming processing in ANSYS is a real vertical travel of the indentor and complex microprofile shape change through time.

Fig. 1. Physical model of exposing microroughness to the rigid tool impact: 1—indentor; 2— device body; 3—sample.

To make the microprofile shape change more illustrative, the scale ratio is 300. Microprofile height h equaled to 6 mm, length D—20 mm, base angle α—30°. These microrelief parameters were measured as is (with respect to the scale ratio) after lathe

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machining. The sample was made from soft metals more prone to changing shape under strain than medium-rigidity metals. Besides, the shape-change ability of soft metals (e.g., lead, copper, tin, etc.) is practically beneficial as those metals are used as soft surfaces that ensure the integrity and tightness of high-pressure vessels [9–11]. Deforming tool angle β (Fig. 1) was equal to 0° as it imitated the deforming ball or roll with a radius sufficient to ensure simultaneous strain of 5 microelevations of the Sample [12, 13]. The width of the microprofile base is commensurate with its height which is one of the factors ensuring a quality picture of the microprofile shape change; it is also practically valuable in terms of surface strain. Strain goes in constrained conditions as the microprofile element is considered the element of a surface of the deformed sample. In this case, the finite-element method uses the following sample properties: type— rough plate; strain diagram—bilinear; other parameters are given in Table 1. Table 1. Sample properties. Material

Elastic modulus, E, MPa

Poisson’s ratio, μ

Flow stress, σ T , MPa

Lead

17,000

0.42

10

200

Tin

55,000

0.33

12

785

Aluminum

69,000

0.33

30

1150

Copper

120,000

0.33

60

3000

Strengthening modulus, Et, MPa

Indentor Properties: type—smooth plate; material—steel XX15, hardened steel; elastic modulus E = 2.11 × 105 MPa; Poisson’s Ratio μ = 0.3; material strain diagram—bilinear, featuring flow stress σT = 2000 MPa, strengthening modulus Et = 20,000 MPa. To accelerate the finite-element method, Indentor was taken as a rigid body (see Fig. 2a) consisting of 20 finite elements. One of the key features of the process is the deep elasto-plastic strain of the sample. To fulfill the objective correctly, the following process conditions were provided: 1. Sample and Indentor material: elasto-plastic. 2. Sample and Indentor grid: hexagonal, with additional nodes introduced on finiteelement edges of the sample. 3. Friction coefficient in the sample-Indentor contact area: 0.2 [14]. 4. The sample grid is denser in the contact area (see Fig. 2a). 5. To avoid boundary effects on the sample’s side edges, the sample width was taken higher than the microprofile height. Boundary conditions (see Fig. 2b): 1. Travel across the sample’s butt end only along oX-axis (Displacement C, D). 2. Travel across the sample’s side edges only along oZ-axis (Displacement E, F).

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Fig. 2. Sample finite-element grid (5576 finite elements, 27,445 nodes) (a); method for setting conditions and load (b).

3. Sample’s bottom plane fixed (Fixed Support A). The microprofile was deformed by setting the Indentor’s vertical displacement of 0.5 h (Joint Displacement B) (see Fig. 2b), as it is known [10, 15–17] that for low base widths, Indentor’s displacement higher than 0.5 h is likely to lead to complete smoothening of the microprofile, with further Indentor penetration (not allowed by the task).

3 Results and Discussion Figure 3 shows how the microprofile strain εh affects the relative width I D , vertical displacement I h of the microprofile valley point, and change of the deformed microprofile base angle α d , where ID = DDi ; Ih = Shi ; εh = 100% at h = 6 mm (see Figs. 1 and 4). The calculation helped find out that an increase in the strain leads to an increase in the relative microprofile width. With that, until the strain degree reaches 20%, the width grows almost linearly to 0.15–0.225, and after (20–25)% the increase intensity grows and reaches 0.786–0.925 (depending on the microprofile material). The vertical displacement of the microprofile valley point does not change before the 10% strain for tin, aluminum, and copper microprofile and 20% for lead microprofile, and then the

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valley point elevates (the softer the material, the fastest the elevation). At the 35–37% strain, the valley point elevation is quite similar for all materials and totals 0.08–0.09. Under further strain, the valley point elevates even higher and reaches 0.213–0.275, depending on the microprofile material. The static position of the valley point at the initial deformation stage with the further vertical displacement is explained by the following [18]: at the vertical displacement of the Indentor by εh (see Fig. 3), a microprofile contact area Di , forms underneath it (see Fig. 4), accompanied by the formation of a plastic strain area of contact with the bottom border outlined by half-arcs (see Fig. 5).

Fig. 3. Effect of the microprofile strain on the relative valley width ID (a); vertical displacement of the valley point (b); microprofile base angle (c); 1—lead; 2—tin; 3—aluminum; 4—copper.

Fig. 4. Microroughness model shape change: undeformed microprofile (a); microprofile after the ith strain (b); D is the valley width; Di is the valley width after the ith strain; h is the microprofile height; S i is the valley elevation after the ith strain; α d is the deformed microprofile base angle.

Thus, when the metal is displaced from the microprofile peaks, a spare surface of the plastic strain area will get positioned at BC (see Fig. 5). Upon the superposition of

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Fig. 5. Lueder-Chernov’s bands of microprofile strain.

points of C and S, bands of adjacent irregularities will meet and strain areas of adjacent irregularities interact which will cause the valley point S elevation (see Figs. 4 and 5). Deformed microprofile base angle α d remained unchanged until the strain degree reached 15% for the lead microprofile and 20–30% for the tin, aluminum, and copper microprofiles. Then, when the strain degree reached 40%, the angle increased to 34° for copper, 35° for aluminum, 36° for tin, and 41° for lead. At the 50% draft, the angle reached (57°–80°), depending on the microprofile material. Figure 6 illustrates the impact of the flow stress of the microroughness model on the relative width I D , vertical displacement I h of the microprofile valley point, and change of the microprofile base angle αd at the 50% draft. As seen from Fig. 6, at the maximum microprofile draft, the increase in the flow stress of the microroughness model from 10 to 60 MPa leads to a decrease in the microprofile base angle, as well as the relative width and vertical displacement of the microprofile valley point. This means that, the stronger the microprofile, the highest its ability to preserve the initial shape. Besides, it should be noticed that as the flow stress of the microroughness model increases from 10 to 12 MPa, and the microprofile shape significantly stabilized at the moment when lead was replaced by tin. Namely, the relative width of the deformed microprofile decreased from 0.925 to 0.847 (by 8.5%), vertical displacement of the valley point decreased from 0.275 to 0.25 (by 9%), deformed microprofile base angle decreased from 80 to 65° (by 19%). This shape change reduction under strain may be explained by the significant increase in elastic properties of the microprofile. While lead’s elastic modulus came to 17,000 MPa, tin’s elastic modulus totaled 55,000 MPa. Besides, lead’s strengthening modulus (785 MPa) is almost 4 times as high as tin’s (200 MPa) (see Table 1). As the microroughness model is symmetric, Fig. 7 illustrates only halves of bands of lead deformed irregularities (the most plastic material) and copper deformed irregularities (the strongest material), allowing for monitoring the deformed state at its extremes. Bands are shown for vertical oY-axis and horizontal oX-axis for the 50% strain. From the analysis of bands, it is seen that at the 50% strain (against the initial microprofile height), the microprofile plastically horizontally deformed from 0.9 mm for copper and to 1.05 mm for lead, on both sides from the profile peak (see Fig. 7a, b), and the profile peak deformed by 3 mm (0.5 h) (see Fig. 7c, d). Figure 7c, d also shows how the microprofile valley elevated, though a small void area remained. With that, the void depth came to 1.4 mm (or 3% of the initial microprofile height) for the lead microprofile, and 1.8 mm (or 30% of the initial microprofile height) for the copper microprofile.

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Fig. 6. The impact of the flow stress of the microroughness model on the relative width I D —1; vertical displacement I h of the microprofile valley point—2; and microprofile base angle α d —3.

Fig. 7. Microprofile plastic deformation distribution fields: (oX, ε h = 50%; a Lead; b Copper); (oY, εh = 50%; c Lead; d Copper).

4 Conclusion By analyzing the results of modeling the deformed state of the three-dimensional microprofile in XOY plane at the 50% strain of the initial height in ANSYS Workbench drives to the following conclusions:

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1. As part of this analysis, the mechanism of the shape change of the lead, tin, aluminum, and copper microprofile was described. 2. It was found out that the valley point starts to elevate at the 10–20% strain of the microprofile and reaches the value of 0.213–0.275 of the initial profile height, depending on the microprofile material. 3. The relative microprofile width reached 0.786–0.925 of the initial microprofile width (depending on the microprofile material). With that, the horizontal microprofile strain on both sides from its peak came to from 0.9 mm for copper models (the strongest material), and to 1.05 mm for lead models (the least strong material). 4. The deformed microprofile base angle reached 57° for copper models and 80° for lead models. 5. With that, the void depth came to from 1.4 mm (or 3% of the initial microprofile height) for the lead microprofile, and to 1.8 mm (or 30% of the initial microprofile height) for the copper microprofile. 6. At the maximum microprofile draft, the increase in the flow stress of the microroughness model from 10 to 60 MPa leads to a decrease in the microprofile base angle, as well as the relative width and vertical displacement of the microprofile valley point. Side surfaces of the microprofile did not contact. It should be noticed that at the further microprofile strain, its full smoothening will likely to take place from the elevation of valleys and approach of the side surfaces.

References 1. Proskuryakov Yu (1971) Technology of metal hardening and gaging treatment. Machine Construction, Moscow 2. Suslov A (1977) Engineering support of connection contact stiffness. Nauka, Moscow 3. Dyomkin N (1970) Rough surface contacting. Nauka, Moscow 4. Schneider Yu (1972) Formation of regular microreliefs on parts and their operation properties. Machine Construction, Leningrad 5. Vulykh NV (2017) Analysis of the stressed condition of rough layer in response to local and axially symmetrical plastic deforming. Irkutsk State Technical University Bulletin, vol 21, no 11(130) 6. Zaides SA, Kuang LH, Kyong NK (2018) The quality evaluation of the strengthened surface plastic deforming by rollers with various constructions. Irkutsk State Technical University Bulletin, vol 22(1) 7. Basov K (2002) ANSYS, in examples and tasks. Computer Press, Moscow 8. Xiaolin C, Yiijun L (2014) Finite element modeling and simulation with ANSYS workbench. CRC Press 9. Pogodin VK, Livshits VI, Drevin AK (1974) Experimental research of sealing conditions for the thor-plane sealing joint. Mashinovedeniye 1 10. Livshits OP, Gridin GD (1980) Impact of the sealing surface microrelief on the tightness of high-pressure vessel seals. Paper presented at the technological control of the machining quality and operational properties of machine components, Kyiv 11. Nikolaeva EP, Mashukov AN (2017) Evaluation of residual stresses in high-pressure valve seat surfacing. Chem Pet Eng 53(7–8):459–463. https://doi.org/10.1007/s10556-017-0363-1

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12. Vulykh NV, Gorbunov AV (2012) Centrifugal rolling of flexible shafts to achieve minimum roughness and maximum surface loading capacity. Irkutsk State Technical University Bulletin, vol 10(69) 13. Vulykh NV (2020) Centrifugal rolling of flexible shafts for achieving best possible roughness of the surface. In: Radionov A, Kravchenko O, Guzeev V, Rozhdestvenskiy Y (eds) Proceedings of the 5th international conference on industrial engineering. ICIE 2019, vol 2. Lecture Notes in Mechanical Engineering. Springer, Cham, pp 1079–1088. https://doi.org/10.1007/ 978-3-030-22063-1_115 14. Kragelsky I, Vinogradova I (1962) Friction coefficients. Reference book. Mashgiz, Moscow 15. Gridin GD (1980) Ensuring tightness of separable joints of high-pressure vessels with soft coatings. Dissertation, University of Kuibyshev 16. Vulykh NV, Ryzhikov IN, Caocao P, Saiganov TM (2019) Determining the critical displacement of the die when deforming an ideally rigid-plastic microprofile under constrained impact. Paper presented at the lifecycle of structural materials. University of Irkutsk, 24–26 Apr 2019 17. Vulykh NV (2019) Microprofile model form changing research at axisymmetric deformation with account of scale factor. In: Radionov A, Kravchenko O, Guzeev V, Rozhdestvenskiy Y (eds) Proceedings of the 4th international conference on industrial engineering. ICIE 2018. Lecture Notes in Mechanical Engineering, Springer, Cham, pp 1161–1168. https://doi.org/ 10.1007/978-3-319-95630-5 18. Hill R (1956) The mathematical theory of plasticity. State publishing house of technical and theoretical literature. Moscow

The Algorithm for Calculating the Milling Error by Mathematical Modeling Method When Machining the Parts N. I. Oleynik1 , E. V. Malkova1,2 , and S. Yu. Popova1,2(B) 1 South Ural State Agrarian University, 48, Sonya Krivaya St., Chelyabinsk 454080, Russia

[email protected] 2 South Ural University of Technology, 9a, Komarovskiy St., Chelyabinsk 454052, Russia

Abstract. The article deals with the accuracy of shaping processes. To do this, it is necessary to define quantitative relationships between machining errors and the reasons that cause them. A mathematical model makes it possible to widely use the modeling method, which represents the same experiment, but it is carried out analytically. The essence of developing a mathematical model means that the real system is simplified, schematized, and described using the mathematical tools. The set of elements, the relationship between the elements, as well as the possible states of each element and the essential characteristics of the states and relations between them are determined. The system of restrictions on the values of controlled parameters is defined. The mathematical description of the errors in shaping is based on the idea of a technological system as a combination of coordinate systems with superimposed relationships. And the formation of errors is considered as spatial displacements and rotations of coordinate systems built on parts or nodes, the dimensions of which are constituent links in the dimensional chain. The closing link of the dimensional chain is the relative position of the coordinate systems built on the tool cutting edges and technological bases of the workpiece machined. The algorithm for calculating the milling error using mathematical modeling is proposed. Keywords: Accuracy · Machining error · Mathematical modeling · Milling · Machining conditions

1 Introduction The increasing rapidity of changing the manufactured products and related to this the increase in the frequency of changing the technological processes, machines, equipment, apparently, result in the need for developing those methods for studying the mechanism of machining errors formation and their calculations, which would combine high accuracy and low time consumption. These requirements are satisfied by the method of mathematical modeling, which is especially effective provided the computer software © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_104

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is used. The issues of modeling the processes of shaping are considered in the papers [1–5]. Modeling is an integral part of modern computer-aided design (CAD) systems, on the basis of which it is improved and developed [6, 7].

2 Theoretical Justification The mathematical model contains the functional relationships between optimization parameters and the requirements for the part to be machined, organizational requirements and constraints due to the limited capacities of the technological system [8, 9]. Let us consider the solution of a typical problem for accuracy using mathematical modeling based on the models developed by the coordinate system method with deforming constraints [10–14]. When designing technological operations for choosing a processing mode, it is important to know the expected machining error. The analysis of regulatory documents on the choice of cutting modes shows the absence of any data indicating a relationship between cutting modes and processing accuracy. The only exception is the feed, the choice of which is associated with the roughness of the treated surface, which is clearly not enough. The methodology for solving the problem related to selecting processing mode elements that provide a given accuracy consists in developing a mathematical model of the mechanism for generating processing errors, assigning processing mode elements according to reference and regulatory data; in calculating the expected error; in comparing its value with the tolerance if the tolerance is exceeded; in making the adjustments to the processing modes that ensure the error position within the tolerance field [15, 16]. Let us consider the choice of the milling mode elements that provide the specified accuracy when machining on a vertical milling machine model 6P12 designed for milling the planes, various kinds of grooves, slots, etc. To solve this problem, we develop a mathematical model of the mechanism related to machining errors formation [10, 16]. In Fig. 1, a vertical milling machine is shown, where the closing link during milling is the distance between the cutting edges of the mill and the adjusting base of the workpiece. Provided the milling is carried out due to the longitudinal movement of the table, the spindle and the working table have one degree of freedom among the parts included in the dimensional chain. The spindle rotates, and the table makes a translational–reciprocal motion. The determination of displacements along the axes and rotation angles around the axes as a result of the installation and static tuning is carried out on the basis of the technique described in the reports [17, 18]. After developing the coordinate systems on the main bases of parts (the main bases coincide with the technological ones for any workpiece) and excluding the parts, we obtain the equivalent circuit shown in Fig. 2. The system developed on vertical guides (auxiliary bases) of the machine stand is considered as a fixed coordinate system  N , in which all movements of the remaining coordinate systems are carried out. Using the obtained equivalent scheme (Fig. 2), we write the equation of relative motion of the cutter tooth tip in the coordinate system  t developed on the workpiece technological bases [18, 19].

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Let us consider the mill rotates in accordance with the law ω = ω(t), and the table moves progressively in accordance with the law s = s(t), then −1 −1 −1 R = McW Mc2 Mc1 MW [Mm M0 Mv Mω Mc r Wm − M0 Mv Mω Mc r m + Mv Mω Mc r 0 + Mω Mc r v − Mc1 Mc2 McW r c1 + Mc2 McW r c2 m

− McW r cW − Mc1 Mc2 McW sx + r c − r N ] m

(1)

where R is the radius vector that determines the position of the tooth top of milling −1 −1 −1 , Mc2 , Mc1 are the inverse matrices of cutter in the workpiece coordinate system; McW the rotations of the coordinate systems of the parts included in the workpiece branch; M ω is the rotation matrix of the spindle coordinate system according to the law ω = ω(t); S x is the displacement vector of table coordinate system by longitudinal feed according to the law s = s(t); M m , …, M c are the matrixes of rotations of coordinate systems of tool branch details under the influence of external factors;r 3m , . . . , r c are the radius vectors connecting the starting points of the coordinate systems of the tool branch parts; −1 −1 , …, Mc3 are the matrix of the coordinate systems rotations of parts related to Mc1 the workpiece branch under the influence of external factors;r c1 , . . . , r n are the radius vectors connecting the starting points of the parts coordinate systems.

Fig. 1. Vertical milling machine.

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Fig. 2. Equivalent scheme.

Let us introduce the factors generating the processing error into the equation of motion. In this regard, we will consider the forces acting directly during milling. These forces include cutting forces, gravity, inertia, as well as the torque transmitted to the cutter and the feed transmitted to the table through the kinematics of the machine. To introduce these forces and moments into the model, it is necessary to know in which coordinate systems they act, as well as the points of their application, the direction of action and their magnitude. Cutting forces act simultaneously on the workpiece and the mill; therefore, their effect is considered in the coordinate systems of the cutter M and the workpiece W. During milling the application point, direction and magnitude of the resultant cutting forces acting on the milling teeth will be changed depending on the position of the workpiece on the table, the configuration of the surface being machined, the number of the milling teeth. Therefore, in order to determine the variables listed above, it is necessary to specify the corresponding dependencies. These dependencies are based on the contact angle ϕc, which determines the number of simultaneously working milling teeth; however, the contact angle can vary due to the variable milling width. The difficulty of specifying the dependence determining the number of simultaneously working teeth is explained by the random nature of the change in the milling width from one type of workpiece to another. The milling width is a function of the workpiece configuration, its installation on the machine table, and the relative position of the milling machine and the workpiece. Having determined the position of the workpiece in the coordinate system of the machine table, the contour of the workpiece is divided into sections that can be described by corresponding equations. The next step is to determine the coordinates of the milling cutter contact points with the contour lines of the workpiece surface machined. To do this, it is enough to solve a

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system of equations that includes the equation of a given section of the machined surface contour and the equation of a circle with a diameter equal to the diameter of milling cutter. Knowing the angle ϕt between the cutter teeth and the contact angle ϕc of the milling cutter with the workpiece, you can calculate the number of simultaneously working teeth using the formula zt = ϕc/ϕt. Knowing the number of simultaneously working teeth, it is easy to calculate the value of the resultant cutting forces, its direction, and coordinates of the application point. Let us find the reactions at each reference point of each coordinate system in the equivalent circuit. Let the Qth coordinate system of the equivalent circuit is acted by the external forces P 1 , . . . , P n , that is, a system of cutting forces on each cutter tooth located at a fixed time in the cutting zone; G is the part weight on which the Qth coordinate system is created (Fig. 3).

Fig. 3. The coordinate system Q influenced by the system of forces.

To find the reactions at the reference points of the Qth coordinate system, we define the main vector RQ RQ and the main moment of the external forces system W Q relative to its beginning: RQ = RxQ + RyQ + RzQ ; W Q = WxQ + WyQ + WzQ RxQ =

n 

Pxj + GxQ ; WxQ =

j=1

RyQ =

n 

n  j=1

(3)

j=1

Pyj + GyQ ; WyQ =

j=1

RzQ =

n    Pxj zj − Pzj xj + GxQ zQ − GzQ xQ

(2)

n    Pyj zj − Pxj yj + GyQ zQ − GxQ yQ ;

(4)

j=1

Pzj + GzQ ; WzQ =

n    Pzj zj − Pyj zj + GzQ yQ − GyQ zQ , j=1

(5)

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where x j , yj , zj are the coordinates of the points of the application of the external forces; Pxj , Pyj , Pzj are the projected external forces on the coordinate axes of the j-th coordinate system; RxQ , RyQ , RzQ are the projected main vector on the axis of the coordinate system; W xQ , W yQ , W zQ are the projected vector of the main moment on the coordinate system axis. Let us set up a system of static equilibrium equations ⎧ 6 ⎪ ⎪ ⎪ RxQ + NxQj = 0; ⎪ ⎪ ⎪ j=1 ⎪ ⎪ ⎪ 6 ⎪ ⎪ ⎪ NyQj = 0; ⎪ RyQ + ⎪ ⎪ j=1 ⎪ ⎪ ⎪ 6 ⎪ ⎪ ⎪ NzQj = 0 : ⎨ RzQ + j=1 (6) n ⎪ ⎪ ⎪ WxQ + (NxQj zQj − NzQj xQj ) = 0; ⎪ ⎪ ⎪ j=1 ⎪ ⎪ ⎪ n ⎪ ⎪ ⎪ WyQ + (NyQj xQj − NxQj yQj ) = 0 : ⎪ ⎪ ⎪ j=1 ⎪ ⎪ n ⎪ ⎪ ⎪ ⎪ W + (NzQj yQj − NyQj zQj ) = 0 zQ ⎩ j=1

where N xQ , N yQ , N zQ are the reactions of the j-th reference point of the coordinate system in the directions X, Y, Z; x Qj , yQj , zQj are the coordinates of the j-th reference point of the Qth coordinate system. Solving the system of equations for the reactions N xi , N yi , N zi will help to determine the desired reactions at the reference points of the Qth coordinate system. In order to proceed to the calculation of reactions in the following coordinate system Q − 1, it is necessary previously to determine the movements of reference points, the position of the Qth coordinate system relative to the (Q − 1)th coordinate system, to form the NQ rotation matrix of the Qth coordinate system; to determine the main moment W Q−1 and the main vector RQ−1 of the external forces relative to the (Q − 1)th coordinate system. The reaction calculation for the (Q − 1)th coordinate system is carried out in the same way as for the Qth coordinate system according to the static equilibrium equation. Knowing the reactions and the stiffness at the reference points, one can calculate the elastic displacements of the latter; the stiffness at the reference points is determined experimentally [11].

3 Research Results Thus, the algorithm for calculating the milling error is the following. Input data is entered. The first group includes the processing conditions: cutting depth; minute feed; spindle rotational speed; cutter diameter; the number of cutter teeth; sharpening geometry; milling cutter resistance; workpiece material; cutting tool material; workpiece material hardness; milling width B over the workpiece sections; and the distance Li to the cross sections from the end face of the workpiece from the side of

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the milling cutter entrance to the cutting zone. The second group includes data which characterize the technological system: stiffness at the reference points; reference points coordinates related to the elements of technological system; the elements starting points coordinates in the coordinate systems; and the number of elements. The third group implies a system of restrictions imposed on the technological system: allowable values of the components of the cutting forces; power; speed on the resistance of the cutting tool; feed rate limited by surface roughness requirements. The fourth group deals with the precision and dimensional parameters of the workpiece: processing tolerance; a specified part size. After entering the initial data, the variable L is assigned the value L1, that is, the workpiece is displayed in the specified section. Then the milling cutter is rotated through the angle ω1 so that the cutter tooth is aligned with the first point of the first section of the workpiece, and the value ω1 is assigned to the variable ω. The number of cutter teeth in the cutting zone is determined. This helps to calculate the cutting forces acting on the mill and the workpiece and to calculate the movements and rotations of coordinate systems in the equivalent scheme. The calculations are carried out in the following order: the reactions are determined at the parts reference points in the technological system; the movements of parts reference points in the technological system are calculated; rotation angles of coordinate systems are determined and rotation matrices are formed; the values of radius vectors connecting the starting points of coordinate systems are determined. According to the relative motion equation, one can calculate the value of the radius vector which determines the position of the tip of the cutter tooth at a given point on the machined surface in the case of elastic displacements. The processing errors at a given point are determined as the difference between the given value of the radius vector and the calculated value [20]. Having determined according to the handbooks the elements of the cutting mode recommended for the given processing conditions, the milling error R = Rm − R. at each point of the obtained surface is calculated. If it turns out that, where T is the tolerance for deviation RRR, then it is necessary to make adjustments to the values of one of the elements in the milling mode (as a rule to the longitudinal feed). For this purpose, the error calculations are repeated with a smaller value of the feed rate S l , and its value decreases until the equality R = T is achieved.

4 Conclusion The mathematical model helps to make it possible to widely use the modeling method, which includes the same experiment, but it is carried out analytically and helps to set up quantitative relationships between processing errors and the reasons that cause them. Thus, the real system is simplified, schematized, and described using the mathematical apparatus; it helps to find a set of elements, the relationship between the elements, as well as the possible states of each element and the essential characteristics of the states and the relations between them. The formation of errors is considered as spatial displacements and rotations of coordinate systems built on parts or nodes, the dimensions of which are constituent links in the dimensional chain. Thus, the proposed algorithm for calculating the milling error using mathematical modeling helps to prevent the error occurrence in the process of machining the parts.

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References 1. Bazrov BM (1978) Tekhnologicheskie osnovy proektirovaniya samopodnastraivayushchihsya stankov (Technological basis for the design of self-adjusting machines). Mashinostroenie, Moscow 2. Bazrov BM (1984) Raschet tochnosti mashin na EVM (Calculation of the accuracy of computer machines). Mashinostroenie, Moscow 3. Reshetov DN, Portman VT (1986) Tochnost’ metallorezhushchih stankov (Precision of metal cutting machines). Mashinostroenie, Moscow 4. Solomentsev YuM, Kosov MG, Mitrofanov VG (1984) Modelirovanie processov mekhanicheskoj obrabotki (Modeling of machining processes). NIImash, Moscow 5. Solomentsev YuM, Kosov MG, Mitrofanov VG (1985) Modelirovanie tochnosti pri avtomatizirovannom proektirovanii metallorezhushchego oborudovaniya (Accuracy modeling in computer aided design of metal cutting equipment). VNIITEMR, Moscow 6. Avraamova TM, Bushuev VV, Gilovoy LYa et al (2011) Metallorezhushchie stanki (Metal cutting machines: a textbook). Mashinostroenie, Moscow 7. Pronikov AS, Averyanov OI, Apollonov YuS et al (1086) Proektirovanie metallorezhushchih stankov i stanochnyh sistem (Design of metal cutting machine tools and machine systems. Reference book). MSTU named after N.E. Bauman, Mashinostroenie, Moscow 8. Averchenkov VI, Gorlenko OA, Ilyitsky VB et al (1988) Sbornik zadach i uprazhnenij po tekhnologii mashinostroeniya (A collection of tasks and exercises on mechanical engineering technology: textbook). Mashinostroenie, Moscow 9. Koshin AA, Rakovich AG, Sinitsyn BI (1988) Sistemy avtomatizirovannogo proektirovaniya tekhnologicheskih processov, prisposoblenij i rezhushchih instrumentov (Computer aided design systems for technological processes, devices and cutting tools). Mashinostroenie, Moscow 10. Levin AI (1968) Matematicheskoe modelirovanie v issledovaniyah i proektirovanii stankov (Mathematical modeling in research and design of machine tools). Mashinostroenie, Moscow 11. Bazrov BM (2005) Osnovy tekhnologii mashinostroeniya (Fundamentals of machine construction). Mashinostroenie, Moscow 12. Polyakov AN (2006) Ispol’zovanie sistemy MATLAB v matematicheskom proektirovanii stankov. Bazovye polozheniya sistemy (Using the MATLAB system in the mathematical design of machine tools. Basic provisions of the system). OSU, Orenburg 13. Balakshin BS (1966) Osnovy tekhnologii mashinostroeniya (Fundamentals of machine construction technology). Mashinostroenie, Moscow 14. Semenov BP, Tikhonov AN, Kosenok BB (1996) Modul’noe modelirovanie mekhanizmov (Modular modeling of mechanisms). SSAU, Samara 15. Dunaev PF, Lelikov OP (2008) Konstruirovanie uzlov i detalej mashin (The design of nodes and parts of machines). Academy, Moscow 16. Dunaev PF (2006) Raschet dopuskov razmerov (The calculation of tolerances). Mashinostroenie, Moscow https://www.iprbookshop.ru/5138. Accessed 1 Dec 2019 17. Tokarev VV, Skrebnev GG (1998) Matematicheskoe modelirovanie processov rezaniya, rezhushchego instrumenta i ASNI (Mathematical modeling of cutting processes, cutting tools and ASSR). VolgSTU, Volgograd 18. Manuylov PA, Semenov BP, Kosenok BB (1990) Invariantnost’ modul’nyh vektornyh modelej. Matematicheskoe modelirovanie v mashinostroenii (Invariance of modular vector models. Mathematical modeling in machine constructing). Conference reports, Tolyatti

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19. Kuzmin VV (2008) Matematicheskoe modelirovanie tekhnologicheskih processov sborki i mekhanicheskoj obrabotki izdelij mashinostroeniya (Mathematical modeling of technological processes of assembly and machine products processing). Higher School, Moscow 20. Semenov BP (1989) Analitika elementarnyh vektornyh modulej (Analytics of elementary vector modules). Moscow Aviation Institute, Moscow

Improving Surface Quality in Honing Low-Carbon Steels Pre-treated by Hydrogen Absorption O. A. Kursin, X. B. Pham, and A. A. Zhdanov(B) Volgograd State Technical University, 28, Lenin Ave., Volgograd 400005, Russia [email protected]

Abstract. One of the most important tasks of technical progress in the field of mechanical engineering is to improve the reliability and durability of machines and mechanisms. Its solution is closely connected with the improvement of technological methods and means of finishing parts, i.e., with the technological provision of high accuracy of their geometric shape, low surface roughness, better physical and mechanical condition of the surface layers of metal, and a reduction in the time of the technological process. It is at the final operations that the surface layer of the parts is formed, which determines their performance properties. Currently, for finishing large-sized hydro- and pneumatic cylinders made of low-carbon coldresistant perlite and stainless austenitic steels of the oil and chemical industry. Rolling is often used in production instead of honing. However, the rolling of the holes gives the lowest dimensional accuracy and geometric shapes. During the rolling process, it is possible to re-seal the surface, which leads to the formation of microcracks and destruction of the surface during operation. In the process of honing such steels, bulges, and metal flows are formed, and the roughness increases, which is a consequence of the high plasticity of the material being processed. In this case, to ensure the quality of the treated surface, it is necessary to apply multiple machine–manual finishing or polishing, which increases the complexity of finishing operations. Therefore, it is necessary to improve the process. Keywords: Honing · Low-carbon steel · Surface hardness · Hydrogen absorption

1 Introduction The problem of increasing the efficiency of the honing process of large-sized pneumatic and hydraulic cylinders made of low-carbon cold-resistant and austenitic corrosionresistant steels is relevant, as it is associated with ensuring the reliability of these critical products [1, 2]. The article suggests that before the process of finishing the abrasive treatment of the internal surfaces of large cylinders to produce pre-hydrogenation at room temperatures in the electrolytic bath in a low-concentration sulfuric acid solution with a low current © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_105

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density. The main interrelated parameters of the process are studied: the hardness of the flooded surface, the depth of the hardened layer, the time of flooding, the current density in the electrolytic bath, and the concentration of the solution. Low-temperature hydrogenation increases the efficiency of the finishing process by reducing the total processing time, reducing the height of the microsurfaces of the treated surface and significantly reducing energy consumption. The proposed preliminary process of hydrogenation of the surface layer of large-sized steel parts can also be used for honing small-sized products.

2 Relevance Honing “soft” stainless steel 12H18N10T (AISI 321) and frost-resistant steel 09G2S gives a poor surface quality, i.e., lapping along the machining mark (Fig. 1) and scouring are observed.

Fig. 1. Lapping along the machining mark: (1) the abrasive grain; (2) lapping along the machining mark.

Various studies [3–10] proved that the characteristics of honed surface microrelief depend on the hardness of the workpiece material (Fig. 2), which indicates the need to increase the surface hardness. The ways to increase the surface hardness are nitridation [11], carburizing [12], nitrocarburizing [13], and laser alloying of the surface layer [14]. However, these methods have common drawbacks, i.e., a decrease in the corrosion resistance of products due to the knocking out of chromium atoms by carbon or nitrogen atoms and thermal deformation due to heating of large-sized long products to temperatures of 700–950 °C. To eliminate these drawbacks, we propose a low-temperature method of hydrogen absorption [15–19] in an electrolytic unit under room conditions.

3 Purpose and Objective The purpose of the work is to improve the process of honing large-scale hydro- and pneumatic cylinders made of low-carbon steels by pre-low-temperature (20–25 °C) hydrogenation of their working surfaces. To achieve this goal it is necessary to solve the following tasks:

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Fig. 2. Dependence of arithmetic average surface roughness Ra on surface hardness in steels honing.

• Consider the physical and chemical basis of the method for increasing the hardness of the treated surfaces of steel products by pre-heating low-temperature water cooling; • Create a pilot plant for low-temperature saturation of the product surface with hydrogen; • Investigate the influence of the main parameters of the hydrogenation process in a wide range of changes: the current density, the concentration of the electrolytic solution, and the process time on the increase in the hardness of the treated surface; • Investigate the effect of the hydrogenation process on the depth of hydrogen penetration into the metal structure; • Construct a mathematical model of the dependence of the roughness parameter Ra on the modes of flooding during honing with pre-flooding; • Identify rational modes of the honing process with preliminary hydrogenation, excluding the embrittlement process, and ensuring improvement of the surface treatment quality of products made of 09G2S and 12H18N10T steels and increasing the productivity of the process as a whole.

4 Theoretical Relevance We used sulfuric acid, H2 SO4, with the catalyst NH4 CNS (thiourea) as electrolysis [20]. The cathode was a billet hydrotreated, and the anode was a titanium rod (Fig. 3). The solution under the influence of the catalyst and action of the cathode voltage segregated hydrogen on the surface of the steel (billet); the hydrogen diffused into metal. At present, hydrogen has been generally accepted to diffuse in metals in an ionized state in form of proton. If the energy state of the metal atoms was such that the proton could not be retained by their electric field, then hydrogen moved in the lattice from one atom to another under the action of their thermal vibrations.

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Fig. 3. Process of hydrogen absorption of articles.

Since adsorption is a process preceding the diffusion, any change in the state of the surface that affects the adsorption intensity must also change the diffusion rate. Indeed, the effect of the physical state of the surface and metal structure on diffusion is very important. Providing a surface with roughness by mechanical means, chemical etching (H2 SO4 acid) or other methods increases the area available for adsorption, which significantly increases the rate of gas diffusion at low pressures. The mechanism of activated adsorption under the action of thiourea and cathode voltage was a set of parallel multi-stage competing reactions. To simplify the task in our work, we offered some basic equations: H2 O + NH4 CNS + e = CNS− + NH4 OH + Hads

(1)

H2 SO4 + H2 O = 2H3 O+ + SO2− 4

(2)

H3 O+ + e = H2 O + Hads

(3)

2H3 O+ + 2e = 2H2 O + H2

(4)

In the presence of the CNS− and SO4 2− anions, the attraction of metal atoms and weakening of metal compounds occurred near the metal surface, and even the chemical compounds Me-CNS and Me-SO4 were partially formed. Thereby, a proton of a small radius (hydrogen) easily penetrated into the metal lattice. The protons in Eq. 3 were less active than the ones from thiourea according to Eq. 1. In the absence of a catalyst (thiourea), the proton only passed from the hydrosonium (H3 O) ions to the metal, so a slower diffusion rate was observed.

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In vacancies, interstitial sites, segregation lines, and spots, where the lattice was disturbed, these ions were connecting into hydrogen molecules; and thereafter, in these spots, respectively, a high pressure arose, a micro-hardening took place, the internal compression stress increased, and hardness on the surface enhanced. But the hydrogen proton had a weak connection with metals, so 2 weeks later, hydrogen left metal and hardness on the surface restored. Increasing the current density and sulfuric acid concentration caused an increase in the amount of hydroxonium H3 O+ that reached the cathode. The amount of releasing gas enhanced according to Eq. 4 and of adsorbing ions per unit of the contact area according to Eqs. 1 and 3. This gas did not have time to come out and took up space on the surface, decreasing the area available for adsorption. When the rate of increase of hydrogen adsorption intensity was less than the rate of reduction of hydrogen adsorption area, a decrease in the rate of the surface diffusion was observed. So, the possibility of adsorption and hardness on the surface reduced. With time, the hardness of the surface layer enhanced due to the increase in the amount of hydrogen. In our investigation, 1 h later, there was observed no large increase in hardness on the surface, since a saturated state of hydrogen was reached. Possible depth of penetration was also investigated. Experimental data showed that for one hour, hydrogen penetrated 09G2S to a depth of up to 0.8 mm and into 12H18N10T to a depth of 0.5 mm. Hydrogen penetrated the austenitic grade steel deeper than pearlite grade steel. This could be explained by a low rate of diffusion with a face-centered lattice in austenitic steels, with hydrogen ions to easily pass from one metal atom to another due to the isotropic deposition of hydrogen atoms in the cube center.

5 Practical Relevance Our research study and construction of a mathematical power-law model made it possible to identify the rational schedule of hydrogen absorption with the contact time of 1 h, sulfuric acid concentration of 1 standard solution, and current density of 2.8 A/m2 . At the same time, it was possible to increase the hardness on the surface of articles made of the 09G2S steel by 50% and the 12H18N10T steel by 60%. Subsequent processing by honing was carried out on the OF-38A machine at a speed of reciprocal motion of the honing stone equal to 8 m/min, rotation speed equal to 45 m/min, and abrasive stones BP 72X5X4 WA F120 O 6 V A. When honing, the layer of 0.2 mm was being removed for 2 min. The results of the experiments were measured by means of the PM7 profilograph profilometer (ABRIS). Some profilograms of the surface processed by conventional honing and honing with hydrogen absorption pre-treatment are shown in Figs. 4, 5, 6, and 7. The profilograms show that an increase in the hardness of the product surface by hydrogen absorption made it possible to reduce the roughness Ra parameter of articles from 12H18N10T steel to 50% and 09G2S to 40%.

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Fig. 4. Profilogram of the normalized 12H18N10T steel surface processed by conventional honing (Ra = 1.14 µm).

Fig. 5. Profilogram of the normalized 12H18N10T steel surface processed by honing with hydrogen absorption pre-treatment (Ra = 0.59 µm).

Fig. 6. Profilogram of the normalized 09G2S steel surface processed by conventional honing (Ra = 1.34 µm).

6 Conclusions Based on the study of the phenomenon of hydrogen penetration into the surface layers of metals and the associated changes in their structure and strength properties, it is established that the process of low-temperature hydrogenation has two stages in time. The first stage of the initial increase the hardness occurs due to the penetration of hydrogen

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Fig. 7. Profilogram of the normalized 09G2S steel surface processed by honing with hydrogen absorption pre-treatment (Ra = 0.76 µm).

atoms into the crystal lattice of the metal, changing its volume, which leads to an increase in the hardness. The second stage is the ultimate saturation of hydrogen and its interaction with defects in the metal structure, changes in the energy of the metal bond, the formation of hydrides, which ultimately leads to embrittlement of the interfacial boundaries, and a decrease in strength properties. The influence of the main parameters of the hydrogenation process (current density, concentration of the electrolytic solution, and process time) on the increase in the hardness of the treated surface and the decrease in the roughness parameter Ra was studied in a wide range on the created pilot plant. It was found that the hardness increases by 50–60% (by steel 09G2S hardness increased to HB 210, on steel 12H18N10T to HB 280). As a result, the Ra roughness parameter after honing is reduced by 30–35%.

References 1. Kulikov SI (1973) Honing. Russia, Moscow 2. Babichev AP (2013) Honing. Volgograd, Russia 3. Kao SCh (2018) Improving the process of honing the holes of large-sized hydro-pneumatic cylinders by preliminary low-temperature hydrogen treatment of the surfaces to be machined. Volgograd State Technical University, Desertation, p 110 4. Kremen ZI, Dugin VN, Medvedev VV (1983) The quality of the surface layer in machining abrasive bars. J Vestnik Mashinostroeniya, 73–75 5. Kudoyarov RG (2006) Improving the quality of parts in diamond honing. J Mach Tools 5:35–37 6. Matalin AA (1949) Roughness of the surface of parts in instrument manufacture. Russia, Moscow 7. Melnikova EP (2003) The influence of technological factors on the surface quality in finishing abrasive machining. J Tekhnologiya Mashinostroeniya 3:13–16 8. Novikova MP, Orlov PN (1977) Handbook of metalist. Russia, Moscow 9. Gai EK, Jieimuzu B (1994) Method of honing. Patent of Japan 6155282, 6 March 1994 10. Richter A (2006) Honing in on perfection. J Cut Tool Eng 8:204–205 11. Lakhtin YM (1976) Steel nitrogenization. Russia, Moscow 12. Gulyaev AP (1986) Metallography. Russia, Moscow, p 544 13. Przhenosil B (1969) Ni-carbing. Russia, Moscow 14. Grigoryants AG (1986) Technological processes of laser processing. Russia, Moscow

916 15. 16. 17. 18. 19. 20.

O. A. Kursin et al. Smith D (1848) Hydrogeninmetals. Chicago Sieverts A, Moritz H (1941) Zeit anorg chem, vol 247 Kuznetsov VV (1993) Hydrogen absorption of metals in electrolytes. Russia, Moscow Sinyutina SE, Vigdorovich VI (2002) Some aspects of hydrogenation. Tomsk, Russia Galaktionova NA (1966) Hydrogen in metal. Russia, Moscow Kursin OA (2017) Investigation of ways to improve the quality of surfaces of products from low-carbon steels at finishing abrasive machining. Russia, Volgograd, p 104

Research on the Process of Forming Cylindrical Surfaces of Holes During Milling Finish with End Mills Using a Circular Interpolation Strategy V. A. Stelmakov(B) , M. R. Gimadeev, and D. D. Iakuba Pacific National University, 136, Tihookeanskaya St., Khabarovsk 680035, Russia [email protected]

Abstract. The development trend of modern engineering production is manifested by automation and mechanization based on the widespread use of CNC machining centers. The use of such centres in a multirange production mode ensures implementation of functionally linked technological transitions (operations) for processing the vast majority of the surfaces of a workpiece during a single installation, in compliance with the principle of unity of bases, which provides for achieving higher processing accuracy. In modern engineering, one of the most labor-intensive operations is the processing of holes, which are subject to high technological requirements for accuracy in size, shape, and location. CNC machining centers offer the option of using various milling strategies to produce high-precision holes. Such strategies are a circular interpolation strategy and a screw interpolation strategy. In this paper, we consider the main factors affecting the accuracy of the shape of the holes obtained by milling using a circular interpolation strategy. Mathematical models have been developed for calculating the magnitude of the shape error associated with the process of instrument penetration into the workpiece material and the elastic deformation of the tool during the final treatment. Keywords: NC center · Form deviation · End mill · Elastic tool deformation · Machining strategies

1 Introduction The development trend in modern engineering production is its automation and mechanization based on the widespread use of CNC machining centers. The use of such centers in a multi-nomenclature production makes it possible to carry out a set functionally related technological transitions (operations) for machining the vast part of the majority surfaces from one installation in compliance with the principle unity bases, which allows achieving higher machining accuracy. This leads to a reduction in the composition of © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_106

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the necessary machine tools, a reduction in the production area, a reduction in the path traveled by the product during manufacture, and a reduction in the production cycle of the part. One of the most time-consuming operations in modern engineering is the processing of holes, which are subject to high technological requirements for accuracy in size, shape, and location. However, if the workpiece has a sufficient number of holes of various diametric sizes, then to ensure the specified accuracy, each hole has to have a drill, a reamer, and a boring tool corresponding to the diametrical size, pre-configured for the corresponding diameter. These circumstances indicate an “overload” tool store [1–10], and since most of the base member elements, including holes, must be machining on one installation, it is necessary to make timely replacement of cutting tools, which leads to reduction in productivity, increase in auxiliary time in this operation, and increase in the cutting tool range. With a limited capacity of tool stores, technological requirements of cutting tool nomenclature expansion make it necessary to expand functional capabilities of the used cutting tool. This unconditional requirement is best met by the technological capabilities of the end hard alloy mills [2, 11, 12]. CNC machining centers offer the possibility of using various milling strategies to produce exacting holes. Such strategies are circular interpolation strategies and a screw interpolation strategy. However, due to the active development and updating control systems for metal-cutting equipment and the dynamic characteristics of machining centers (drives, digital systems, etc.), there are currently no or outdated practical recommendations for choosing milling strategy, technological parameters, and machining modes necessary to ensure a given precision and surface quality [3, 4, 13]. The purpose of the work is to study factors affecting the quality and accuracy of the hole surfaces obtained during finishing milling with a circular interpolation strategy.

2 Method As materials for the manufacture of smooth cylindrical holes, carbon steels with a carbon content of C = 0.2–0.35% were used, the chemical composition of the steel is shown in Table 1, aluminum alloy of grade AMg6. Table 1. The chemical composition steel used. Fe%

C%

Si%

Mn%

Cr%

Ni%

Cu%

Mo%

Al%

Co%

Ti%

99.2

0.2

0.3

0.45

0.18

0.04

0.04

0.01

0.002

0.012

0.002

As the tool material, H10F carbide was used marked by Sandvik Coromant, the closest Russian analogue is VK10 used for processing gray cast irons, non-ferrous metals, and alloys. For the processing of carbon steels, the GC1620 hard alloy was used, the closest Russian analogue is T15K6.

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Deviations from the roundness and cylindrical forms were examined at the Roundcom-41C installation. According to the measurement results, hole polar diagrams were constructed, allowing one to judge the processing technology and the features of the tool used. The measurement procedure is as follows: samples are mounted on a precision swing spindle located under the part. When the table rotates, each point on its surface forms a reference circle. Deviations from the measured part roundness located on the spindle are evaluated by moving the dipstick, resulting in a surfaces polar diagram. Material processing experiments were conducted at a three-coordinate multipurpose processing center with CNC DMC 635 V ecoline, and a five-coordinate processing center with CNC DMU 50 ecoline. The processing centers are equipped with the Heidenhain ITC 620 CNC system, a powerful spindle up to 8000 min−1 , with a power of 13 kW. The X, Y, and Z positioning accuracy is 0.008 mm. The determination of the main factors contributing to the formation of deviations from roundness was determined using harmonic analysis. Using this approach, the signal reflecting the part profile is represented as a Fourier series, and the factors affecting the roundness deviation parameter are the decomposition coefficients [13–20]. P(n) =



r(θ ) exp

jnθ , T

(1)

where n is the number of irregularities on the part section profile. The case n = 0 corresponds to the nominal part radius (the pin touches the surface); n = 1 reflects the eccentricity with the part is mounted in a roundness measurement instrument; n = 2 reflects ovality; n = 3–5 reflects the form deviation due to the fixing part during machining; n = 6–20 reflects vibration caused by insufficient rigidity technological system; n = 20–100 reflects the machining features (the growth formation), and n = 100–1000 reflects structure material defects.

3 Results and Discussions The value of the deviation from roundness and cylindricality parameter in the finish milling strategy with circular interpolation is greatly influenced by the process of cutting the mill into the workpiece material, the elastic pressing of the mill and its profile. The numerical value of each component is influenced by various factors, for the determination of which it is necessary to analyze each component of the error separately. From the kinematics analysis with circular interpolation strategy, we can conclude that the error value of the cut-through tool is influenced by the following factors: R-cut— the plunge-cutting radius, α—the angle initial point plunge-cutting, F-cut—the feeding plunge-cutting (Fig. 1). The cutting radius of the tool into the workpiece material is important because it determines the smoothness of the cutting process while reducing the possibility of impact, vibration, and instantaneous load on the machining center drive. In practice, the described parameter is selected by the technologist in the preparation of the control program based on his personal experience, which leads to a reduction of accuracy and quality of the hole to be treated (Fig. 1a).

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Fig. 1. Graphs of the main factors affecting the value of the plunge-cutting error: from the value plunge-cutting radius a, from the value angle initial point plunge-cutting radius, b, from the value feeding plunge-cutting, c, graphic surface d.

The next parameter for the study was the angle initial point plunge-cutting radius (Fig. 1b). This parameter has the following geometric meaning: on the plunge-cutting circumference, a point is defined at a given angle from the initial point, to which the tool from the positioning point follows with linear interpolation and starts plunge-cut along the radius when it is reached. Accordingly, in order to ensure a smooth insertion process and reduce the probability vibrations during finishing due to a sharp decrease in plunge-cutting force, it is recommended to choose the value angle initial point plunge-cutting radius as maximum possible. The next parameter for the analysis was the supply set when the tool was cut into the workpiece material (Fig. 1c). This process parameter is set throughout the path when the tool is cut into the workpiece material. When the finishing start point is reached, the drives of the processing center are accelerated to the value of the working supply, which leads to an increase in the cutting force during this transition, which may negatively affect the accuracy of the obtained hole shape. In order to determine the optimal range of values for the three variables described above, which affect the deviation from roundness in milling, we will use a ternary graph (Fig. 2d). Such graphs are used to study the linkage between several variables, in an experimental study of response dependencies relative to three factor variables.

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On the basis of the described studies, a multi-factor regression analysis was carried out, which resulted in a regression model, which allows to determine the value of plungecutting error depending on the selected values of three variables:  = 21.04 − 3.32 · R − 3.94 · α − 7.68 · F − 0.07 · R · α + 0.17 · R · F + 1.72 · α · F − 0.57 · R · α · F;

(2)

The next research stage was the determination elastic tool deformation. At the stages smooth plunge-cutting and the finishing hole with circular interpolation, elastic releasing tool E from the cutting force arising during processing appear (Fig. 2), the value of it increases as the tool reaches the finish point, after which the value cutting force becomes «constant». An increase in the value cutting force is directly related to an increase in the size of the material to be cut with one mill tooth. The increase in the thickness cut-off layer directly depends on the size of the selected plunge-cutting radius, on the selected value working supply and supply for plunge-cutting, the diameter tool, the metal transition for finishing, etc.

Fig. 2. Scheme for the formation of an error in the geometric shape associated with elastic tool compressions.

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The presented loading scheme is a variable stiffness system with one degree of freedom in the area of which the distributed load P acts: ⎧ 2 ⎪ ⎨ d ε = M0 (z) ; for ε (0) = C; dz 2 EJx0 (z) (3) ⎪ ⎩  M0 (z) = k(z) · M (z) ε (0) = D; To bring a system with variable stiffness to a system with constant stiffness, it is necessary to add the following forces system: ⎧ ⎪ ⎨ R = (k2 − k1 ) · P      ; (4) b b ⎪ M = k2 · l − − l1 − k1 · l − − l1 ·P ⎩ 2 2 To determine the function of the reduced bending moment, we use the method of initial parameters: M0 (z) = MA · z 0 − RA · z + M · (z − l1 )0 − P · (z − l1 );

(5)

Hence, we get the second-order differential equation:

1 d 2ε 0 0 = · M · z − R · z + M · − l − P · − l (z (z ) ) A A 1 1 ; dz 2 EJx0

(6)

By integrating the expression twice, we get:



k2 · l − 2b − l1 − k1 · l − 2b − l1 · P · (z − l1 )2 z2 z3 · −P· + 2 6 2

(k2 − k1 ) · P · (z − l1 )3 (7) − + C · z + D; 6 ⎛

1



b ε(z) = · ⎝P · l − 2 EJz0



Since the value of the angle of tool deflection at the starting point is very small, in further calculations, we take C = 0, based on this, the equation takes the following form:



2 3 k2 · l − 2b − l1 − k1 · l − 2b − l1 · P · (z − l1 )2 z z ε(z) = · ⎝MA · − RA · + 2 6 2 EJz0

(k2 − k1 ) · P · (z − l1 )3 + D; − 6 ⎛

1

(8)

To determine the effect of a minute supply on the amount of elastic tool squeezes, experiments were carried out during which the values of the deviation parameter from cylinders during processing with different values of feeding per tooth were measured for the following materials: steel (the composition of which is given in Table 1) and aluminum of AMg6 grade.

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Having analyzed the data presented in Fig. 3, it can be concluded that the experimental values of the maximum bending of the tool differ from the calculated ones by no more than 15%. This percentage of discrepancy is explained by the influence of other factors on the shaping process, such as the roughness of the cutting edge of the tool, the vibration effect of the tool during operation.

Fig. 3. The dependence elastic releasing on the working supply: steel 20 (a), AMg6 (b).

According to the experimental results, it was found that the index of deviation from roundness is significantly influenced by such geometric and technological parameters of the end mill as the cutting radius, the angle of the starting point of the cutting radius and the supply set when cutting the tool into the workpiece material. For the above parameters, in order to determine the optimal range of their values selection and increase the accuracy of processing, a multi-factor regression analysis was carried out, the result of which was a regression model and a surface graph, characterizing it. It should also be noted that the mathematical model of the process of elastic deformation of the cutting tool during milling with the strategy of circular interpolation was checked during the study of the index of deviation from the cylinders, the maximum percentage of deviation of experimental and theoretical values was 15%.

4 Conclusions 1. The following dependencies of the plunge-cutting error value from technological and geometric parameters of the end milling tool at finishing by the circular interpolation strategy were established experimentally: • with an increase in the tool plunge-cutting radius, the value plunge-cutting error decreases; therefore, for finishing, it is necessary to select the maximum radius value; • reducing the value of angle tangent to the plunge-cutting radius leads to an increase in the error value, and therefore, for finishing, it is advisable to apply the value angle in the range up to 180° (included), while the boundaries range depend on the diameter of the cutting tool. • the tool supply does not have a noticeable effect on the value of plunge-cutting error over the range its choice of 50–90% of the working, but with its values over

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the range of 10–50% of the working, there is an extreme character of the error value growth. 2. It has been found that the model of the elastic deformation process of the cutting tool in milling with the strategy of circular interpolation can be used in calculating the hole shape deviation when machining with the end hard alloy tool.

References 1. Leonov SL (2012) Modelirovanie protsessa frezerovaniia otverstii na stankakh s ChPU (Modeling the process of milling holes on CNC machines). Polzunovskii Vestnik 1(1):177–180 2. Stel’makov VA (2017) Modelirovanie protsessa formoobrazovaniia tsilindricheskikh otverstii poluchennykh metodom frezerovaniia na stankakh s ChPU (Modeling the process of forming cylindrical holes obtained by milling on CNC machines). Electronic Scientific Edition “Uchenye zametki TOGU” 8(2):321–327. https://pnu.edu.ru/media/ejournal/articles-2017/ TGU_8_159.pdf 3. Stel’makov VA (2015) Issledovanie prichin vozniknoveniia pogreshnostei formy pri obrabotke otverstii frezerovaniem (Investigation the causes mold errors when machining holes by milling). Problems and achievements in innovative materials and technologies of mechanical engineering: materials of the International scientific and technical conference, pp 257–259 4. Davydov VM, Kabaldin IuG (2003) Kontseptual’noe proektirovanie mekhatronnykh modulei mekhanoobrabotki (Conceptual design of mechatronic machining modules). Dal’nauka Publ., Vladivostok, p 251 5. Stel’makov VA (2016) Metod otsenki tochnosti gladkikh tsilindricheskikh otverstii po diametral’nomu razmeru i otnositel’nomu polozheniiu ikh osei (Method for assessing the accuracy smooth cylindrical holes by the diametric size and relative position their axes). Uchenye zapiski Komsomol’skogo-na-Amure gosudarstvennogo tekhnicheskogo universiteta. Nauki o prirode i tekhnike, I-1(25):73–81 6. Kabaldin IuG (2000) Matematicheskoe modelirovanie samoorganizuiushchikhsia protsessov v tekhnologicheskikh sistemakh obrabotki rezaniem (Mathematical modeling self-organizing processes in cutting systems). Dal’nauka Publ., Vladivostok, p 195 7. Dunin-Barkovskii IV Kartashova AN (1978) Izmereniia i analiz sherokhovatosti, volnistosti i nekruglosti poverkhnosti (Measurements and analysis surface roughness, waviness and noncircularity). Mashinostroenie Publ., Moscow, p 232 8. Uaitkhauz D (2009) Metrologiia poverkhnostei. Printsipy, promyshlennye metody i pribory (Surfaces metrology. Principles, industrial methods and devices). Dolgoprudny, “Intellekt” Publ., p 472 9. Stel’makov VA (2016) Poluchenie zadannykh parametrov sherokhovatosti pri sverlenii i frezerovanii tsilindricheskikh otverstii (Obtaining the specified roughness parameters during drilling and milling cylindrical holes). Uchenye zapiski Komsomol’skogo-na-Amure gosudarstvennogo tekhnicheskogo universiteta. Nauki o prirode i tekhnike I-1 (25):66–72 10. Stel’makov VA (2015) Issledovanie vliianiia rezhimov obrabotki na tochnost’ formy otverstii, poluchennykh frezerovaniem (Study the influence processing modes on the accuracy the shape of the holes obtained by milling). Informatsionnye tekhnologii XXI veka, pp 50–55 11. Stel’makov VA (2015) Issledovanie prichin vozniknoveniia pogreshnostei formy pri obrabotke otverstii frezerovaniem (Investigation the causes mold errors when machining holes by milling). Problems and achievements in innovative materials and technologies of mech. eng.: materials of the International scientific and technical conference, pp 257–259

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12. Kim C-J (2004) Mechanisms of chip formation and cutting dynamics in the micro-scale milling process. Dissertation, University of Michigan, p 111 13. Downs RA (1993) Surface topography measurement using fringe-field capacitive profilometry. Dissertation, University of Washington, p 136 14. Lou S, Jiang X, Scott Paul J (2014) Morphological filters for functional assessment of roundness profiles. Meas Sci Technol 25(6):1–16 15. Tokyo Seimitsu Co. Ltd. (2006) Application guide manual for roundness and cylindrical profile measuring instrument. Tokyo, p 96 16. Altintas Y, Engin S (2001) Generalized modeling of mechanics and dynamics of milling cutters. Ann CIRP 50(1):25–30 17. Kountanya RK (2002) Process mechanics of metal cutting with edge radiused and worn tools. Dissertation, The University of Michigan, Ann Arbor 18. Rahman M, Kumar AS, Prakash JRS (2001) Micro milling of pure copper. J Mater Proc Tech 116:39–43 19. Chuzhoy L, DeVor RE, Kapoor SG, Bammann DJ (2002) Microstructure-level modeling of ductile iron machining. ASME J Manuf Sci Eng 124:162–169 20. Kitahara T, Ishikawa Y, Terada T, Nakajima N, Furuta K (1996) Development of micro-lathe. Mech Eng Lab Rep 50(5):117–123

Cutting Forces and Roughness During Ball End Milling of Inclined Surfaces M. R. Gimadeev(B) , V. A. Stelmakov, and V. V. Gusliakov Pacific National University, 136, Tihookeanskaya St., Khabarovsk 680035, Russia [email protected]

Abstract. Ball end milling of complex surfaces is common in the mould and aerospace industries. A significant influential factor in complex surface machining by ball end milling for roughness, part accuracy and tool life is the cutting force. This work is devoted to the analysis of cutting forces and roughness parameters that arise during milling with a ball end tool with a variable surface angle (γ ). A model of the cutting force and motion of the tool is formulated taking into account the inclination of the surface. The factors affecting the magnitude and nature of surface roughness during milling with a ball end tool are investigated. It has been experimentally established that the reduction in amplitude roughness parameters occurs with an increase in the inclination angle. Instantaneous values of cutting forces were measured in the range of values of variable feeding per tooth (fz) and angle of surface inclination (γ ). The study showed that the forces of cutting and roughness are highly dependent on the inclination of the surface, both in quantitative and qualitative terms. This observation is also supported by the model developed. Keywords: Ball end milling · Dynamics · Surface inclination · Surface roughness

1 Introduction Currently, processing curved surfaces using ball end tools is the subject of numerous studies. Ball end tool is widely used in the manufacturing of dies and moulds for the aerospace industry, in manufacturing of wing parts from aluminium alloys and composites. It follows from numerous studies that in curvilinear milling, the change in the inclination of the ball end cutter relative to the workpiece (determined by the angle of inclination of the surface—γ ) significantly affects the cutting forces [1, 2], the wear of the tool [3, 4], as well as the roughness of the surface to be treated [5, 6]. From the point of view of the above effects, cutting with a surface inclination of γ = 0° is most undesirable since the cutting speed at this position of the tool and part is close to zero. At the same time, the treated material is not cut but is ploughed and subjected to large elastic and plastic deformations. This ploughing mechanism can cause excessive © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_107

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mechanical load on the cutter, which can lead to skimming as well as deterioration of surface roughness. Therefore, it is recommended to treat with an inclined spindle or an inclination of the surface to be treated. These recommendations avoid negative effects by increasing the cutting speed while improving tool resistance and chip formation, which in turn results in improved surface quality. Numerous studies show that the actual surface roughness differs significantly from the theoretical model, which is the result of the kinematic–geometric projection of the cutter on the workpiece. These discrepancies are caused by tool vibrations associated with the deflection of the cutter and a change in the geometry of the cutting zone [7].

2 Model of Cutting Forces and Vibrations There has been significant research reported in modelling mechanics of milling [8–12] but little work has been done on the mechanics of ball end milling. To determine the instantaneous movements of the ball end tool associated with the deviations of the cutter caused by the cutting forces F, it is necessary to solve the following differential equations of motion: mx · x¨ (t) + cx · x˙ (t) + kx · x(t) = Fx (t) my · y¨ (t) + cy · y˙ (t) + ky · y(t) = Fz (t) · sin γ + Fy (t) · cos γ

(1)

mz · z¨ (t) + cz · z˙ (t) + kz · z(t) = Fz (t) · cos γ − Fy (t) · sin γ During milling of inclined surfaces, tool oscillations are defined in directions perpendicular to tool axis of rotation and collinear vector of feed motion y(t) perpendicular to tool axis of rotation and vector of feed motion x(t) parallel to tool axis of rotation z(t). In Eq. 1 mi is modal mass, ci is damping coefficient, F x , F y , F z is instantaneous cutting forces in coordinates of process equipment, k i is stiffness coefficient. The rigidity of the process system refers to the ratio of the cutting force component directed normal to the surface being machined to the displacement of the cutting edge of the tool relative to the same surface of the workpiece and in the same direction. To determine these cutting forces, a mechanical model of the cutting force is used, developed by Lee and Altintas [13–15]. In this model, to set the resulting force acting on the i-th infinitesimal segment of the cutting edge, a lot of curvilinear coordinate systems are used, perpendicular to the tangents to the spherical surface. The detailed geometry of the helical ball mill is shown in Fig. 1a–d. Figure 1a shows tangential dF tj , radial dF rj , axial dF aj cutting forces, acting j-th tooth and tool coordinates for a ball end mill. The inclination angle λ of a milling cutter with a spherical initial tool surface along the cutting edge is shown in Fig. 1a, chord L 2ch , segment angle F1 and arc length larc in Fig. 1c. dFtj = Kte dlj + Ktc dSzj dFrj = Kre dlj + Krc dSzj dFaj = Kae dlj + Kac dSzj

(2)

where K te , K re , K ae —edge specific coefficients, K tc , K rc , K ac —specific coefficients of shift, dlj —infinitely small cutting edge length, S zj —cross-sectional area of the section [16].

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Fig. 1. Geometry and tool coordinates for a ball milling cutter a scheme of cutting forces; b tool coordinates for ball end; c cross-sectional area; d cross-sectional area of the given figure.

Cross-sectional area (Fig. 1c, d) can be calculated by formula: Szj = L2ch · haver

(3)

where L 2ch —length of the second chord, h aver —average chip thickness (Fig. 1d).   2   H L1ch 2 L2ch = 2 · + (4) 2 4 haver = fz · sin A

(5)

Length of the first chord L 1ch , arc length l arc and circle segment angle F1 : L1ch = 2 · sin ·

larc ·R 2R

(6)

Cutting Forces and Roughness During Ball End Milling

1 · R 2   H 1 = 2 arccos 1 − 2 · 2R larc =

Angle A (Fig. 1d) to calculate the average chip thickness, you can calculate:   H A = arctan L1ch /2

929

(7) (8)

(9)

Find the equation of the cutting edge on the spherical (radius R) of the original tool surface (Fig. 1a). The radius vector r of the current point of the original tool surface is ⎡

⎤ R sin ϕ cos  ⎢ R sin ϕ sin  ⎥ ⎢ ⎥ r=⎢ ⎥ ⎣ R cos ϕ ⎦

(10)

1 The equation of the cutting edge will be sought as the equation of a curve located on the original tool surface and intersecting the meridian at an angle (90° − λ). Parametric equation of the form  = (ϕ) describes a certain line on the sphere. If  = 0°, these lines are meridians, and if  = 90°—parallels. The cosines of the angles between the axes of the XYZ coordinate system of the tool and the tangent line to the curve  = (ϕ) on the original tool surface are: dX cos ϕ cos  dϕ − sin ϕ sin  dϕ  = dS dϕ 2 + sin2 ϕ d2 cos ϕ sin  dϕ − sin ϕ cos  dϕ dY  = cos β = dS dϕ 2 + sin2 ϕ d2 − sin ϕdϕ dZ = cos δ = dS dϕ 2 + sin2 ϕd2 cos α =

(11)

where dS—cutting edge arc differential. In particular, the cosines of the angles between the coordinate axes and the tangent line to the meridian (for  = const) on the original instrumental surface are represented as dependencies developed by the author Radzevich [17]: dX = cos ϕ cos  dS dY cos β = = cos ϕ sin  dS dZ cos δ = = − sin ϕ dS cos α =

(12)

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According to the formulas sin ϕ = cos ϕ =

2 tan ϕ2 1 + tan2

ϕ 2 1 − tan2 ϕ2 1 + tan2 ϕ2

(13)

we get the result: 1 ( + C) chq cos ϕ = thq( + C) sin ϕ =

(14)

where ch—hyperbolic cosine, th—hyperbolic tangent. We set the condition that  = λ. Then the equations of the cutting edge are represented in parametric form as follows: R cos λ chq(λ + C) R sin λ Y = chq(λ + C) Z = Rthq(λ + C)

X =

(15)

To determine the infinitesimal length of the cutting edge, you can use the expression proposed in [14–16] as  

dl = r 2 (ψ) + r  (ψ)2 + z  (ψ)2 dψ (16) where

r(ψ) =

1 − (ψ cot λ − 1)2

−R(ψ cot λ − 1) cot λ r  (ψ) =  1 − (ψ cot λ − 1)2

⎫ ⎪ ⎪ ⎪ ⎪ ⎬

⎪ ⎪ ⎪ ⎪  2 2 2 2 ⎭ z (ψ) = X + Y + (R − Z) cot λ

(17)

When milling at an angle of inclination γ > 0°, three tool cutting zones are distinguished depending on the angle of rotation of the tool  (Fig. 2): • for circuit Fig. 2a, angle 1     L1ch fz /L1ch 1 = 2 · arccos 1 − 2 L1ch − − 2 2       L1ch fz /L1ch + 2 180 − 2 · arccos 1 − 2 L1ch − − 2 2

(18)

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• for circuit Fig. 2b, d, angle 2 is taken as 1/8 of a full revolution or 45°, this value was obtained when modelling the cutting process for a ball end mill with the number of teeth z = 2, fz = 0.4 mm/tooth, ae = 0.4 mm, then

ψ = 2π − 1

(19a)

π − 2 (19b) 2 From the above reasoning and Fig. 2, it is seen that in the case of milling, the tool cuts only in zone 2. This means that when milling with the angle of inclination of the surface, the active number of teeth can be less than one, pulsating forces can occur and the cutting process becomes uneven and intermittent. Based on the foregoing, in this paper, we consider the process of milling with a ball end mill inclined surfaces with an angle γ , in the range from 10° to 70°. In this case, it is worth considering the effective diameter Dcap (Fig. 2c). Calculation of cutting speed V C , respectively: π · Dcap · n Vc = (20) 1000 At the same time, the effective diameter Dcap is calculated as  if γ = 0◦ , then Dcap = 2 H · (D − H )

 ⎧ Dcap = 2D cos ω = 2 · R · cos 90◦ − γ ⎪ ⎪ ⎨ (21) or, if γ > 0◦ , then ⎪ ⎪ ⎩ D = L = 2 · sin · larc · R cap 1ch 2R ψ=

3 Experimental Details Machining was carried out on samples made of steel 45 (similar C45, 1045), diameter carbide end mill with a diameter D = 12 mm and number of teeth z = 2 of the company Sandvik Coromant. The milling tool made of fine-grained tungsten carbide had an antiwear coating TiAlN and the following parameter was λ = 30°. The feed per tooth was fz = 0.4 mm/tooth, the allowance for all samples was ap = H = 0.2 mm, the lateral pitch ae = 0.4 mm. To ensure equal cutting speed V C , for various tilt angles of the machined surface, the rotation frequency (n) was varied in the range from 1478 to 8000 min–1 . To solve the differential Eq. 1 of motion, the parameters m, c, k were determined using the shock test, the calculations were performed according to the dependencies of the authors, Lee and Altintas [13, 18], and thus the following parameters were obtained: m = 0.059 Ns2 /m, s = 30.6 Ns/m, k = 14,619,352 N/m. The study measured cutting forces (F x , F y , F z ). For experimental research, technological equipment with CNC DMG DMU 50. Surface roughness measurements after machining were performed using a profilometer SURFCOM 1800D. The measurements were carried out along various paths to find the maximum values of the roughness parameters.

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Fig. 2. Cut segment and contact area a for the first pass; b for the second and subsequent passes; c effective diameter when milling inclined surfaces; d cutting process diagram.

4 Results and Discussion Figure 3 shows a comparison of measured and calculated cutting forces (Fx, Fy, Fz) versus time for various values of the surface angle γ . From Fig. 3, it can be seen that the angle of inclination of the surface γ significantly affects the cutting forces, both in quantitative and qualitative terms. With increasing angle γ , the limiting immersion area of the tool in the workpiece (determined by the working angle ψ and the active number of teeth zc ). Therefore, pulsating forces may be present in the finishing milling by the ball end tool, since for a surface angle of γ > 0°, the number of active teeth is very often less than one (zc < 1). Analysing the obtained data (both calculated and measured), it can be established that a decrease in the force values occurs with an increase in the angle of inclination [19–21] from 10° to 40°, however, with a further increase in the angle of inclination, the

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Fig. 3. Cutting forces a measured at γ = 10°; b calculated for γ = 10°; c measured at γ = 40°; d calculated for γ = 40°; e measured at γ = 70°; f calculated for γ = 70°.

forces increase. In addition, the force F x is most sensitive when the angle of inclination of the surface changes. From Fig. 3, it is also seen that the cutting forces calculated on the basis of the developed model are in good agreement with the measured ones. Nevertheless, it was found that the shape of the curve of the experimental dependence differs from theoretically calculated by the formulas obtained above by no more than 10% for γ = 10° and 70°, and less than 15% for γ = 40°. These discrepancies are probably due to the accuracy of the calculation of specific cutting force coefficients. An analysis of profilograms (Fig. 4a–f) after the above experiment allows to conclude that the surface microrelief after processing with a ball end mill has a regular profile [20], while the roughness of the tool has practically no effect on the surface roughness, so as insignificant, and some manifestation is observed only in the direction of the sidestep. This is evidenced by the presented profilograms, where the distance between the segments of the profile (hollows and protrusions) is equal to the specified feed rate f z = 0.4 mm/tooth. The milling scheme and the surface obtained during processing on which the measurements were made are shown in Fig. 5. The measurement results are presented in Table 1. Thus, an analysis of the experimental data summarized in Table 1 allows us to conclude that the distribution of the parameters Ra, Rz, Rt, Rq, Rp, Rc and Rv tend to decrease in numerical value with an increase in the angle of inclination, while the minimum values correspond to the angle tilt 40°. With an increase in the processing angle to 70°, the values of the altitude parameters increase to 10–20% higher than the minimum values.

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Fig. 4. Profilograms of surfaces after milling with different angles of inclination γ a γ = 10°, direction f z ; b γ = 10°, direction ae ; c γ = 40°, direction f z ; d γ = 40°, direction ae ; e γ = 70°, direction f z ; f γ = 70°, direction ae .

Fig. 5. Diagram of milling and measured pattern on the die surface a measured at γ = 10°; b measured at γ = 40°; c measured at γ = 70°.

The reduction in the quality of the machined surface (Fig. 4), in this case, can occur due to the effects of squeezing the cutting tool and an increase in the amplitude of oscillations of the technological system [20] (Fig. 3) during milling. It was also found

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that an increase in forces in the direction ae (X) and f z (Y ), is observed when milling the surface γ > 40°. This can be explained by the distribution of components of the cutting force along the cutting edge, which depends on the inclination of the surface. It is worth noting that the appropriate choice of the angle of inclination of the surface can improve the quality of the surface. Based on the foregoing, we can conclude that the ranges of rational values of the angle of processing are from 10° to 40°. Table 1. Experimental parameters of surface roughness for angles 10°, 40° and 70°. Cutting pattern/surface

Figure 5a

Parameter (angles 10°)

Ra, µm

Maximum values measured in the direction:

f z 0.820

3.397

3.580

2.248

0.953

3.093

1..149

399.709

ae 0.629

2.749

3.055

1.716

0.737

2.568

1.033

410.073

Cutting pattern/surface

Figure 5b

Parameter (angles 40°)

Ra, µm

Maximum values measured in the direction:

Rz, µm Rt, µm Rp, µm Rq, µm Rc, µm Rv, µm Rsm, µm

f z 0.602

2.486

2.690

1.569

0.698

2.227

0.917

413.681

ae 0.663

2.847

2.975

1.634

0.760

2.502

1.213

390.628

Cutting pattern/surface

Figure 5c

Parameter (angles 70°)

Ra, µm

Maximum values measured in the direction

Rz, µm Rt, µm Rp, µm Rq, µm Rc, µm Rv, µm Rsm, µm

Rz, µm Rt, µm Rp, µm Rq, µm Rc, µm Rv, µm Rsm, µm

f z 0.675

2.815

2.955

1.902

0.796

2.658

0.913

366.595

ae 0.941

4.393

4.900

2.510

1.123

3.552

1.883

394.226

5 Conclusions In this paper, the influence of the tilt angle of the machined surface on cutting forces, vibrations and microrelief parameters is investigated. A model of cutting force and vibration is formulated, including kinematic and geometric parameters. The study showed that the cutting forces and vibrations of the cutting tool depend on the angle of inclination of the surface, both in quantitative and qualitative aspects. The cutting forces calculated on the basis of the developed model, with a high degree of accuracy are consistent with the measured ones. However, there are discrepancies between theoretical and practical

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values that result from the occurrence of the radial cutter beat phenomenon. Therefore, in order to increase the accuracy of the developed power model, the phenomenon of radial beat should be taken into account. It has been experimentally proven that it is desirable to apply the inclination of the surface to the horizontal plane, when milling with a spherical tool, to an angle of up to 40°, which, in addition to the forces, reduces the surface roughness parameter groups Ra, Rz, Rv, Rp by an average of 1.4 times, in the feed pattern compared to 10° and in the direction of the lateral pitch compared to 70°.

References 1. Fontaine M, Devillez A, Moufki A, Dudzinski D (2006) Predictive force model for ball-end milling and experimental validation with a wavelike form machining test. Int J Mach Tools Manuf 46:367–380 2. Lamikiz A, Lopez de Lacalle LN, Sanchez JA, Salgado MA (2004) Cutting force estimation in sculptured surface milling. Int J Mach Tools Manuf 44:1511–1526 3. Toh CK (2004) A study of the effects of cutter path strategies and orientations in milling. J Mater Process Technol 152:346–356 4. Subrahmanyam KVR, San WY, Soon HG, Sheng H (2010) Cutting force prediction for ball nose milling of inclined surface. Int J Adv Manuf Technol 48:23–32 5. Lopez de Lacalle LN, Lamikiz A, Sanchez JA, Arana JL (2002) Improving the surface finish in high speed milling of stamping dies. J Mater Process Technol 123:292–302 6. Ko T, Kim JHS, Lee SS (2001) Selection of the machining inclination angle in high-speed ball end milling. Int J Adv Manuf Technol 17:163–170 7. Wojciechowski S, Pelic M, Twardowski P (2012) Cutter displacements as a main factor in surface texture generation during cylindrical milling of hardened steel. In: ICSM 2012 International conference on surface metrology, Annecy—Mont Blanc, France, 21–23 March 2012 8. Altintas Y, Spence A (1991) End milling force algorithms for CAD systems. CIRP Ann 40(1):31–34 9. Armarego EJA, Deshpande NP (1991) Computerized end milling force predictions with cutting models allowing eccentricity and cutter deflections. CIRP Ann 40(1):25–29 10. Kline WA, DeVor RE, Zdeblick WJ (1980) A mechanistic model for the force system in end milling with application to machining airframe structures. In: North American manufacturing research conference proceedings, Dearborn, MI, Society of Manufacturing Engineers, vol XVIII, p 297 11. Koenigsberger F, Sabberwal AJP (1961) An investigation into the cutting force pulsations during milling operations. Int J Much Tool Des Res 1:15–33 12. Tlusty J, MacNeil P (1975) Dynamics of cutting forces in end milling. CIRP Ann 24(1):21–25 13. Lee P, Altintas Y (1996) Prediction of ball–end milling forces from orthogonal cutting data. Int J Mach Tools Manuf 36:1059–1072 14. Altintas Y, Lee P (1998) Mechanics and dynamics of ball end milling. Trans ASME J Manuf Sci Eng 120:684–692 15. Altintas Y, Lee P (1996) A general mechanics and dynamics model for helical end mills. Ann CIRP 45(1):59–64 16. Bouzakis KD, Aichouh P, Efstathiou K (2003) Determination of the chip geometry, cutting force and roughness in free form surfaces finishing milling, with ball end tools. Int J Mach Tools Manuf 43:499–514 17. Radzevich SP (2001) Fundamentals of surface generation. Rastan, Kiev

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18. Altintas Y (2000) Manufacturing automation, metal cutting mechanics, machine tools vibrations and CNC design. Cambridge University Press, Cambridge, MA 19. Gimadeev MR, Davydov VM, Nikitenko AV, Sarygin AV (2019) Formirovanie parametrov sherohovatosti na osnove korrelyacionnyh svyazej pri chistovom frezerovanii prostranstvenno-slozhnyh poverhnostej (The formation of roughness parameters based on correlation in the clean milling of spatially complex surfaces). Uprochnyayushie Tehnologii I Pokrytiya 6(174):243–248 20. Gimadeev MR, Davydov VM (2018a) Obespechenie kachestva poverhnosti pri mehanoobrabotke slozhnoprofilnyh detalej (Ensuring surface quality during machining of complex parts). Tehnologiya Mashinostroeniya 11:6–9 21. Gimadeev MR, Davydov VM (2018b) Correlation of roughness indicators during milling with a spherical tool. Tyazheloe Mashinostroenie 9:24–29

Optimization Criteria for Modeling of Gear Hone Tooth Engagement and Processed Gear in Terms of Specific Sliding and Contact Pattern Size Yu. Bagaiskov(B) Volzhsky Polytechnic Institute (branch) of the Volgograd State Technical University, 43a Engels St., Volzhsky, Volgograd Region 404130, Russia [email protected]

Abstract. Abrasive shavers (gear hones) are applied for gear tooth honing in case of finish processing of lateral faces of hardened gear teeth; they are manufactured from resin bond abrasive materials using uncontrolled casting. Shaver teeth feature contact and bending strains during operation; the total strain value increases significantly from the teeth roots to the tips. Besides, the sliding parameters and the contact area pattern size of the engage teeth vary depending upon the strain values. It can be demonstrated using a geometric model of abrasive shaver teeth profiles contacting with a gear being processed. Due to elastic deformation, the shaver tooth center shifts, which affects the values of the main engagement parameters, primarily the radii of curvature. The values of specific sliding and the contact area pattern size of the tooth-tip profiles decrease and distribute more uniformly along with the teeth height. The influence of such a phenomenon on the gear tooth honing parameters can be anticipated. The optimization criteria are suggested in order to estimate the performance level, quality, and accuracy of processing by the relation of specific sliding values and the contact pattern size. Considering the criteria values, the abrasive shaver parameters and the honing process can be designed optimally. Keywords: Gear hone · Elastic deformation · Specific sliding · Contact pattern · Engagement model · Optimization · Metal removal

1 Introduction An abrasive shaver (a gear hone) consists of an effective abrasive ring and a metal hub and is manufactured by uncontrolled and pressure casting of abrasive compositions based on a resin bond, including epoxy, acrylic, and urethane bonds [1–4]. Abrasive shavers are operated according to the rolling method with reversing, radial load, and axial advance. The diagonal sliding velocity in the engagement of shaver teeth and processed gear results from the tangential, radial, and axial motion components and ensures removal of metal from the lateral faces of the part teeth [5–8]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_108

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2 Relevance of Deformation Accounting It is common knowledge that elastic strains emerge in the engagement of shaver teeth and processed part (gear) teeth, similarly to metal tooth gears, due to the relatively elastic abrasive-polymeric material of the shaver teeth [9, 10]. Such strains are divided into contact, bending, and tooth-root strains in the rim of the shaver’s abrasive-polymeric ring [11]. Calculation and experimental studies made it clear that the overall strain along the teeth height does not distribute uniformly. Besides, the contact component distributes in the most uniform manner, with a slight increase near the pitching point. On the other hand, the bending strain and the root strain rise sharply from the tooth root to the tip (by 5–6 times) ensuring general irregularity in the distribution [12, 13]. Comparing the elastic deformation values of gear–hone teeth with the errors of the gears processed (profile error f fr = 0.02–0.03 mm for average-sized gears of accuracy degree 7–8) and the metal removal values (0.005–0.020 mm), it may be concluded that they are commensurate at hone material elasticity modulus E0 < 6000 MPa [14].

3 Theoretical Analysis of Gearing Conditions Hone teeth deformation alters their operation conditions, sliding parameters, and size of the contact pattern with the machined gear faces [15]. The diagram of the velocity components in point K is shown in Fig. 1. Velocity components VK0 and VK1 are the absolute velocity of the hone and hear teeth, respectively, at point K; VTO and VT 1 are the tangential components of the absolute velocity and located in the plane perpendicular to the engagement line at an angle  to each other. Relative sliding velocity Vs of hone and gear teeth is determined according to tangential velocity components VTO and VT 1 and using the following formula:  2 + V 2 − 2V V cos  Vs = VTO (1) TO T 1 TO Ê

VN VK1

VT1

VS

VTO

VKO

Fig. 1. Sliding velocity Vs of the shaver and part teeth profiles with consideration of the velocity components.

Specific sliding of hone and gear teeth in the contact point: ϑ0 =

Vs Vs ; ϑ1 = VTO VT 1

(2)

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Analytical studies of a geometric engagement model of shaver teeth profiles with the teeth made of a conditionally elastic material and processed gear teeth were carried out (Fig. 2). This model allows reproducing the nature of the interaction between shaver and gear teeth in the presence of shaver–teeth elastic strains. Contact loads result in bending of a shaver tooth during operation and in shifting/turning of the tooth center axis by the specific angle θ . The angle value is proportional to the strain value.

4 Analytical Research Results The sliding parameters, υ0 , υ1 , on the profiles of the shaver teeth and gear, correspondingly, are calculated depending on the contact point position along with the teeth height [16]. Variations of the sliding parameters with respect to the elasticity modulus E0 of the shaver composite material and the normal force Pn are investigated. As is known, the specific sliding, according to this model, determines the sliding nature and conditions in the contact points K 0 and K 1 and thus enables simulating the rate of metal removal from the part tooth face, as well as the shaver tooth material loss. As anticipated [17, 18], the specific sliding values of the shaver teeth and the processed part teeth at their rims and roots are 2.5–4 times as high as in the pitching point similarly to toothed gears. As the value of the shaver material elasticity modulus E0 decreases down to 100 MPa, meaning that the shaver tooth strain increases, specific sliding variations along the teeth height become more uniform and even higher along with the part tooth height. Influence of the hone teeth elastic deformation value on size variation of contact area S in the engagement is significant [19]. As E0 decreases, the value of S increases by (E0 /E01 )2/3 , wherein (E0 /E01 ) is the decrease extent of the E0 value. Thus as E0 changes from 2000 to 100 MPa, the S value near the pole increases by more than seven times. If hone teeth bending deformation is considered in addition to contact deformation, especially at E0 ≤ 500 MPa, even more uniform variation of S along the teeth height was found [14]. The results of the conducted analytical studies confirmed the correspondence of the sliding parameters and the contact pattern area of the hone and gear teeth with the hone’s geometry and elastic behavior during operation [16]. Variation of the sliding parameters and the contact pattern area can characterize intensity and uniformity of metal removal and hone material wear, fullness of machining, and quality of the machined surface, in other words, the main gear honing parameters. Since the optimization criteria were established on the basis of those parameters, it was possible to provide an integrated analytical relationship between the hone’s geometry and elastic behavior and the gear honing parameters. This enables determination of the optimal tool parameters for processing a particular part with corresponding requirements or the optimal scope of using a hone with particular parameters.

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Fig. 2. Geometric model of the contact of the shaver and part teeth profiles at deformation.

The optimizing criteria can be distinguished into groups according to the main gear honing requirements: • • • •

The maximum removal metal amount The minimum hone wear The accuracy resulted from machining the involute gear profile The roughness and fullness of machined gear tooth faces.

The gear honing optimization criteria based on assuming the linear variation of the specific sliding values along the height of hone and gear teeth are used in works [14, 20]. However, the analytical studies mentioned above demonstrated the availability of prominent extremes—the minimum values of υ0 and υ1 —near the engagement pole. Selection of the optimization criteria was substantiated herein with consideration of this provision. The gear-honing performance optimization criterion can be expressed by the value of specific sliding on the part tooth profile near the pole as it maximizes: K1 = |ϑW 1 | → max

(3)

The maximum values of the sliding parameters, which determine the hone material wear amount and pattern, were mainly observed on the hone tooth head. For this reason,

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the hone wear optimization criterion, similarly to [20], was taken equal the sum of the specific sliding values in those points of the hone tooth profile as it maximizes:   (4) K2 = |ϑa0 | + ϑf 0  → min Selection of the tooth gear accuracy optimization criterion after honing is based on the fact that variation of specific sliding υ1 along the tooth height determines the uniformity of metal removal from lateral faces. As variations of υ1 , in most cases, are minimal near the engagement pole, the profile accuracy on the gear tooth head and dedendum was studied separately. The relationship between the contact pattern sizes and the amount of load in contact, which behavior in engagement also affects the teeth accuracy (especially in case of double-tooth contact), was reviewed above. Since certain non-uniformity in changing of the contact profile area S along the height was established in analytical studies, this factor must be considered for accuracy assessment of machined gears. Relative differences of specific sliding values in lower contact point υf 1 or on gear tooth top υa1 and pitch diameter υW 1 (K 3 and K 4 ) [20], as well as the differences of the contact pattern areas in the top and lower points (Sa1 and Sf 1 ) on the gear tooth (K 5 ), as they tend to 0, are taken as the profile accuracy optimization criteria of the gear teeth machined by hones:   ϑf 1  − |ϑW 1 | →0 (5) K3 = |ϑW 1 | K4 =

|ϑa1 | − |ϑW 1 | →0 |ϑW 1 |

(6)

Sa1 − Sf 1 →0 SW 1

(7)

K5 =

The contact pattern area is the main parameter generalizing the influence of multiple factors on gear quality after gear honing. It depends on the hone and gear geometry, hone material elasticity modulus, and paired relationship of the contacts. As contact pattern area of hone and gear teeth extends, the number of abrasive grain peaks involved in metal removal increases, the grid of machining marks becomes denser, and quality of the resulting faces increases. That is why the ratio of the contact pattern area SW 1 near the pole and the reference area m2 characterizing the machined surface is used for roughness optimization parameters of those faces: K6 =

SW 1 → max m2

(8)

The prevailing criteria depend on the requirements for machining of parts. The values of the gear honing optimization criteria K 1 –K 6 are calculated using formulas (2–8) and according to the values of the hone material elasticity modulus E0 , specific normal force Pn , and paired relationship of the contacts in the engagement of hone and gear teeth obtained, in their turn, according to the design data of variation of specific sliding and the contact pattern area of hone teeth with various degrees of elasticity and the machined gears along with the teeth height.

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5 Analysis of the Results The analysis revealed that increase in the metal layers removed from the gear teeth lateral faces (increase in the K 1 criterion) should be first of all expected at increased operating load. Hone wear value (decrease in the K 2 criterion) should decrease if a tool with low E 0 is used. Accuracy of the gear teeth involute profile after gear honing, disregarding the distribution peculiarities of their initial errors, can be ensured (in case of comprehensive consideration of the criteria K 3 and K 5 ) by decreasing the hone material elasticity modulus E0 and increasing the force Pn . Thus, it can be concluded that post-honing accuracy of gears increases at higher elastic deformation of the hone teeth. Roughness decrease of machined gear teeth faces (increase in the criterion K 6 ) is possible as the hone material elasticity modulus E0 and increased force Pn (at increased elastic deformation of the hone teeth material) decrease and in case of a higher paired relationship of the teeth contacts. Figure 3 depicts the optimization criteria values in terms of tooth gear accuracy (K 3 , K 5 ) and machined face roughness (K 6 ) depending on the hone material elasticity modulus E0 (the K 1 , K 2 , and K 4 criteria depend on E0 insignificantly). The criteria gain optimum values (K 3 and K 5 tend to zero, K 6 tends to maximum) as the elasticity modulus value decreases.

Fig. 3. Relationship between criteria K 3 (1), K 5 (2), and K 6 (3) and the hone material elasticity modulus E0 .

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6 Conclusions Thus, analytical modeling generally confirmed the theoretic provisions regarding the efficiency of using hones with a lower elasticity modulus of their materials (increased elasticity) for designing. The obtained correspondence between the main gear honing parameters and all the affecting factors determine the optimum hone designing directions with consideration of the hone material degree of elasticity and according to the set requirements. Using the suggested optimization criteria for changing the specific sliding values and the machining area size in hone–gear engagement, enables determination of the optimum hone geometry and elastic behavior, planning of the metal removal rate to achieve the maximum capacity, high accuracy, and good quality of hardened gear machining.

References 1. Garshin A, Fedotova S (2008) Abrasive materials and tools. Manufacturing Procedure: Instructional Aid, Polytechnic University Press, SPb 2. Schegolev V, Ulanova M (1984) Elastic abrasive tools. Mashinostroenie, Leningrad 3. Kovalchuk Yu (1984) Design basis and manufacturing process of abrasive and diamond tools. Mashinostroyenie, Moscow 4. Ostrovsky V (1981) Theoretical basis of grinding. Leningrad State University Press, Leningrad 5. Kalashnikov A, Morgunov Yu, Kalashnikov P (2014) Aspects of the cylindrical gear honing process. Reference Guide. Eng J 6:3–9 6. Kalashnikov A, Morgunov Yu, Kalashnikov P (2012) Modern methods for machining gears. Spektr Publishing House, Moscow 7. Kalashnikov A (2013) Gear honing. RITM: Repair Innov Tech Modernization 10(88):22–29 8. Fessler A, Wunderlin V, Zlenko N (1993) Honing process development. Industrial Academy, Dübendorf, Switzerland 9. Airapetov E, Genkin M, Kolin I (1971) Flexibility of straight-tooth Spur gearing. Vibroacoustic activity of gear mechanisms, pp 13–59 10. Zablonsky K, Filipovich S (1976) Tooth stiffness analysis of spiral gears. News of Higher Institutions. Engineering, pp 75–79 11. Bagaiskov Yu (2018) Study of total elastic deformation of gear hone tooth. In: Fundamentals of mechanics: proceedings of the international research to practice conference, Novokuznetsk, MS RDC, pp 92–96 12. Bagaiskov Yu (2017) Elastic contact deformation of gear hone tooth lateral faces. In: Fundamentals of mechanics: proceedings of the international research to practice conference, Novokuznetsk, MS RDC, pp 126–129 13. Bagaiskov Yu (2018) Bending deformation analysis of gear hone tooth lateral faces. MATEC Web of Conferences, vol 224. International conference on modern trends in manufacturing technologies and equipment 2018, Sevastopol, Russia 14. Bagaiskov Yu, Shumyacher V (2005) Performance increase of devices made of abrasive composite materials Volzhsky Institute of Civil Engineering and Technologies (branch) of Volgograd State University of Architecture and Civil Engineering, Volgograd 15. Schigolev A (1975) On the cutting rate of gear-tooth honing of Evolute Spur gears and reliability issues. Omsk Polytechnic Institute, Omsk, pp 69–78

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16. Bagaiskov Yu (2006) Designing of gear hones with consideration of composite-material tooth deformation. Mech Eng 5:32–36 17. Alekseeva N (1997) Designing involute gears for aircrafts. Moscow Aviation Institute, Moscow 18. Galkin P, Nikitina L (2008) Mechanism and machine theory. Gears train design and analysis. Publishing House of the Tambov State Technical University, Tambov 19. Taramykin Yu (1966) Momentary tooth contact shape and area in case of gear honing. In: Collection of works by ENIMS Postgraduates, M., pp 188–197 20. Manunin V, Bogomolov N, Kislov Yu (1979) Influence of gear hone geometry on tooth gear accuracy. In: Works of WNIIASh/VNII of abrasive materials and grinding: studies of the grinding, polishing and finishing processes, pp 39–50

Twist Drilling FEM Simulation for Thrust Force and Torque Prediction I. S. Boldyrev(B) and D. Y. Topolov South Ural State University, 76, Lenin ave., Chelyabinsk 454080, Russia [email protected]

Abstract. Drilling is one of the most common processes in metalworking. The cutting forces that occur during the drilling process have a significant impact on the accuracy and quality of the holes. Uncompensated radial cutting forces lead to an increase in the diameter of the hole being machined, which reduces its accuracy. And when machining laminated materials, excessive axial cutting force leads to a stratification of the composite and reduces the quality of the hole. In this regard, the task of determining or predicting cutting forces is currently quite relevant. This article proposes a method for calculating cutting forces when drilling aluminum homogeneous and isotropic alloy 6061-T6 using the finite element method in the Lagrangian formulation. The calculation results are compared with calculations using empirical formulas and the results of experiments of other authors. The influence of the chip separation criterion type and material model on cutting forces during drilling were also investigated. Keywords: Twist drilling · FEM · Cutting force · Simulation · Torque

1 Introduction In mechanical processing, the drilling process is one of the main operations in the production of machine parts and equipment. This process, the geometry of drills, the mechanics of the drilling process has been well studied in recent years. Cutting forces during drilling affect the quality and accuracy of the holes. Previously, Parsian et al. applied a mechanistic approach to predicting cutting forces during drilling [1]. Hamade et al. applied the same approach to determining cutting forces when drilling aluminum. It consists of defining empirical power equations and corresponding coefficients [2]. Giasin et al. investigated the axial cutting force when drilling fiber-reinforced composites using the finite element method [3]. Matsumura et al. proposed a model of cutting forces for drilling multilayered materials [4]. Wang et al. determined the coefficients in power equations for the calculation of cutting when drilling [5]. Watson proposed a model of drilling on the cutting edges and chisel of the drill and compared it with experimental data [6]. Marusich et al. modeled the process of drilling with carbide drills using the finite element method [7]. Merino-Perez et al. investigated the effect of cutting speed and © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_109

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material properties on cutting forces when drilling CFRP composites [8]. Sreenivasulu et al. simulated the formation of chips when drilling aluminum 6061-T6 alloy [9]. Patra et al. used neural networks to predict the state of the tool based on the measurement of axial cutting force [10]. Uhlmann et al. investigated deep drilling with spiral drills [11]. Mathew et al. investigated the temperature distribution in the material being processed [12]. Sultan et al. studied the formation of chips when drilling stainless steel with spiral carbide drills [13]. Beer et al. investigated the effect of tool geometry on cutting forces when drilling Inconel 719 alloy [14]. Sambhav et al. have created geometric models of spiral drills with various forms of sharpening the back surface [15]. Abouridouane et al. investigated the machinability of ferritic–pearlitic steels [16]. Abele et al. has been optimizing the geometry and design of spiral drills based on numerical simulation [17]. Girinon et al. used commercial packages (Abaqus) to simulate the drilling process and cutting forces [18]. Gaikhe et al. predicted the axial force and the moment of cutting when drilling fiberglass [19]. Diaz-Alvarez et al. proposed a numerical approach to thermomechanical modeling of the drilling process. Previously, for the 6061-T6 alloy, the finite element method was used mainly for modeling free orthogonal cutting [20]. When drilling, chip formation conditions make it difficult to use FEM. In addition, usually in the process of calculating the elements forming the chips are usually removed from the calculation, as they reach the limit deformation. This article also proposes to use the FEM in the Lagrangian formulation to simulate the drilling process for 6061-T6 aluminum alloy and to predict the axial cutting force and torque.

2 Analysis of Factors Affecting the Cutting Forces During Drilling The working process of metal cutting consists of the dynamic and kinematic interaction of two solids—the workpiece and the cutting tool. The surface layer of metal, which is cut from the workpiece, is subjected to intense plastic deformation, as a result of which the material of the cut layer in a partially or completely destroyed state is removed from the workpiece in the form of cut chips. During the cutting process, new surfaces continuously appear on the workpiece and on the cutting chips. In contrast to turning, it is not one main edge that takes part in the cutting of chip, but two and additionally a chisel edge. Each edge has a cutting force that can be decomposed into three mutually perpendicular components. The cutting force acting on the main edge is decomposed into a force F z , tangent to the circle on which the edge point is located, a radial F y force passing through the axis of the drill, and F x force parallel to the axis of the drill. Pair of tangential forces creates torque M. On the other main edge operates a similar system of forces. The cutting force acting on half of the chisel can also be decomposed into three forces. However, due to the relatively small influence exerted on the power characteristics when drilling two components, they are not taken into account. Auxiliary edges in cutting chips are not significant. However, due to the fact that the auxiliary clearance angle is zero on the chamfers of the drill, there is friction between them and the hole wall. Make the sum of the projections of the acting forces on the axis X, which coincides with the axis of the drill. The specified amount of projections is the axial force when drilling. Axial force counteracts feed motion. It is calculated on the strength of the details of the feed mechanism of the drilling machine. For large

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overhangs, the axial force causes a longitudinal bending of the drill. We make the sum of the moments of the acting forces relative to the X-axis. The specified sum of the moments is called the cutting resistance torque when drilling (the cutting torque). Under the effect of cutting torque, the drill twists. The radial forces of F y , acting on both main blades of the drill and directed toward each other, should theoretically be balanced. However, due to the inaccuracy of sharpening the drill (different angles in terms of the length of the main edges), the forces of F y are not equal. Therefore, a resultant force directed towards a greater force appears. Under the action of the resultant, the diameter of the hole increases as compared with the diameter of the drill. This increase in a hole diameter causes another macro-geometric error—leading the drill away from the geometric axis of the hole since the drill will no longer be centered in the hole with its chamfers. Hole diameter increase and withdrawal of a hole from a geometric axis are always inherent in drilling holes with double-blade screw drills. The influence of the structural elements of the drill on the power characteristics of the drilling process is different. Most of the torque falls on the main edge of the drill. The chisel accounts for most of the axial or thrust force. By changing the magnitude of the axial force and torque can be judged on the state of the drill during the cutting process. If there is a sharp increase in torque, then this corresponds to the predominant wear of the main edges of the drill. The sharp increase in axial force indicates the predominant wear of the chisel. With an increase in feed and drill diameter, the cross-sectional area of the chip cut by the main edges increases, as a result of which the axial force and torque increase. However, just as with turning, the feed and the diameter of the drill do not have the same effect on thrust force and torque. Since in any type of work, the thickness of the chip affects the components of the cutting force less strongly than the width, then the feed to the axial force and torque also affects less than the diameter of the drill. The main influence on the axial force and torque is exerted by the angle of inclination of the helical groove ω, the point angle of the drill 2ϕ and the angle of inclination of the chisel. Increasing the angle of inclination of the helical groove reduces both the axial force and the torque, but the axial force decreases more intensively. The effect of the angle ω on Fx and torque is noticeable only at angles ω < 30°–35°. A further increase in angle ω practically does not affect the change in F x and torque. The experimentally established influence of angle ω on axial force and torque is due to the fact that an increase in angle causes an increase in the rake angle of the drill, which reduces the cutting force on the main edge and its components. The effect of the point angle on F x and torque when drilling is similar to the effect of side cutting edge angle F x and F z forces when turning. As the angle 2ϕ increases, the ratio of the width of chip being cut to thickness decreases. This should reduce the force F z on the main edge and, as a consequence, the magnitude of the torque. Just as when turning, an increase in the angle 2ϕ when drilling results in an increase in the angle between the main edge and the direction of feed movement, which increases the axial component of the cutting force on the main edges and the axial force. The angle of the chisel on the axial force and torque affects the most difficult. On the one hand, an increase in the angle causes a reduction in the length of the chisel, which should somewhat reduce the torque and more significantly axial force. On the other hand, as the angle increases, the length of the main edges and their sections with a small static rake angle increase. The latter should lead to an increase in both torque and

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F x . Such a contradictory influence of the ϕ angle leads to the fact that with its increase the axial force increases continuously, and torque decreases initially and then decreases.

3 3D FEM Model Description The original 3D finite element drilling model is presented in Fig. 1. Modeling was done in the LS-Dyna package. The model consists of a square workpiece 50 × 50 mm, 10 mm thick and HSS twist drill. The material of the workpiece is aluminum alloy 6061-T6 (the Russian equivalent of the alloy AD33 according to GOST 4784-97). The mechanical properties of the material of the workpiece: density of 2700 kg/m3 , a tensile elasticity modulus of 68,900 MPa, an elongation of 25%, a yield strength of 270.2 276 MPa. Material model (strain curve)—bilinear kinematic hardening (* MAT_PLASTIC_KINEMATIC). The first part of the curve is linear elastic, the second is linear hardening with a hardening modulus of 200 MPa [21]. A high-speed steel (HSS) twist drill with a diameter of 7.5 mm was used as a tool. Geometrical parameters of the drill: helix angle 30°, point angle 118° clearance, clearance diameter 7.3 mm, flute length 50 mm, core thickness 2 mm. The simulation was carried out with the following cutting conditions: cutting speed 310 m/min, feed 0.64 mm/rev. The workpiece and drill were meshed by a finite element mesh. The element type is an eight-node hexahedron at the workpiece and a four-node shell element at the drill. The deformations of the drill were not taken into account in the calculation, the material of the drill is of the RIGID type. For adequate modeling, it is necessary to apply a chip separation criterion. In this case, and in order to exclude material failure in triaxial compression, the maximum principal strain of the workpiece deleted elements was 25%.

Fig. 1. Twist drill and workpiece FEM-model at the initial moment of time.

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4 Results of Numerical Simulation The results of numerical simulation of drilling of the alloy 6061-T6 are presented in Figs. 2 and 3. Figure 2 represents the distribution of equivalent stresses in the workpiece at the final moment of simulation. Figure 3 depicts thrust force and torque values during the simulation. The calculation time for a 6-core processor was 2.5 h. As a result of the simulation, it was possible to obtain distribution curves for axial force and torque. For comparison, the results of the experiment are as follows: thrust force 700 N, torque 500 Nm [2]. As a result of the simulation, the following conclusions can be drawn. The results on thrust force differ by experiment no more than 15%, while for torque, there is no convergence. Such a discrepancy in terms of the torque can be explained by the fact that in the process of simulation, elements that have reached the limit state are removed from the calculation. Since the torque is created mainly by the friction of the guides of the twist drill on the workpiece, when the corresponding elements are removed, it becomes close to zero. To study the influence of the model of the processed material in the simulation, the Johnson–Cook model with the following parameters was also used: A = 324.2 MPa, B = 113.8 MPa, N = 0.41, C = 0.003, M = 1.35, strain rate effect was not considered. The failure model parameters for Johnson–Cook model are as follows: D1 = –0.76, D2 = 1.44, D3 = –0.46, D4 = 0, D5 = 1.5 [21]. As the simulation results showed, the material model has little effect on the force characteristics of the cutting process. However, the experiment shows that such a relationship exists [2].

5 Conclusion and Further Research Modern methods of modeling the cutting process using the finite element method have now been significantly developed, making it possible to predict the shape and size of chips and the machined surface, the stress–strain state, the temperature field, the projections of the cutting force, residual stresses, if necessary, even with additional energy. However, the simulation results, especially 3D, coincide with the experiment more qualitatively than quantitatively. The most likely reasons for this situation are imperfect algorithms for modeling fracture and friction, as well as inaccuracies in the preparation of the initial data. The results of numerical simulation showed that the finite element method in the Lagrangian formulation with the removal of elements that have reached limit strain makes it possible to predict the axial cutting force when drilling an aluminum alloy with an accuracy of 20%. As for the torque, the result is unsatisfactory. This is due to the fact that during the simulation the chip is not modeled and it is not possible to calculate the component force F z . This is a disadvantage of the proposed approach. To overcome this drawback, it is necessary to use other FEM implementations, in particular meshless methods, such as SPH, SPG, EFG, or FEM in the ALE formulation. This study can be useful in predicting the accuracy of drilling holes, as well as to assess the quality of the machined surface when machining composites.

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Fig. 2. FEM model: Von Mises stress distribution in workpiece at the final moment of simulation.

Fig. 3. a FEM model: thrust force and torque prediction.

Acknowledgements. South Ural State University is grateful for financial support of the Ministry of Education and Science of the Russian Federation (Grant No. 9.5589.2017/8.9).

References 1. Parsian A, Magnevall M, Beno T et al (2014) A mechanistic approach to model cutting forces in drilling with indexable inserts. Procedia CIRP 24:74–79 2. Hamade RF, Seif CY, Ismail F (2006) Extracting cutting force coefficients from drilling experiments. Int J Mach Tools Manuf 46:387–396

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3. Giasin K, Ayvar-Soberanis S, French T, Phadnis V (2017) 3D finite element modelling of cutting forces in drilling fibre metal laminates and experimental hole quality analysis. Appl Compos Mater 24:113–137 4. Matsumura T, Tamura S (2013) Cutting force model in drilling of multi-layered materials. Procedia CIRP 8:182–187 5. Wang M, Gao L, Zheng Y (2014) An examination of the fundamental mechanics of cutting force coefficients. Int J Mach Tools Manuf 78:1–7 6. Watson AR (1985) Drilling model for cutting lip and chisel edge and comparison of experimental and predicted results. I—initial cutting lip model. Int J Mach Tool Des Res 25(4):347–365 7. Marusich TD, Usui S, Stephenson DA (2007) Finite element modeling of drilling processes with solid and indexable tooling in metals and stack-ups. In: Proceedings of the 10th CIRP international workshop on modeling of machining operations, pp 51–58 8. Merino-Pérez JL, Royer R, Merson E et al (2016) Influence of workpiece constituents and cutting speed on the cutting forces developed in the conventional drilling of CFRP composites. Compos Struct 140:621–629 9. Sreenivasulu R, SrinivasaRao C (2018) Modelling, simulation and experimental validation of burr size in drilling of aluminium 6061 alloy. Procedia Manuf 20:458–463 10. Patra K, Jha AK, Szalay T et al (2016) Artificial neural network based tool condition monitoring in micro mechanical peck drilling using thrust force signals. Precis Eng. https://doi. org/10.1016/j.precisioneng.2016.12.011 11. Uhlmann E, Richarz S (2016) Twisted deep hole drilling tools for hard machining. J Manuf Process 24(1):225–230 12. Mathew NT, Vijayaraghavan L (2018) Modelling of temperature distribution in the work material during drilling under sustainable environment. J Manuf Process 36:309–318 13. Sultan AZ, Sharif S, Kurniawan D (2015) Chip formation when drilling AISI 316L stainless steel using carbide twist drill. Procedia Manuf 2:224–229 14. Beer N, Ozkaya E, Biermann D (2014) Drilling of inconel 718 with geometry-modified twist drills. Procedia CIRP 24:49–55 15. Sambhav K, Tandon P, Dhande SG (2012) Geometric modeling and validation of twist drills with a generic point profile. Appl Math Model 36(6):2384–2403 16. Abouridouane M, Klocke F, Dobbeler B (2017) Characterisation and modelling of the machinability of ferritic-pearlitic steels in drilling operations. Procedia CIRP 58:79–84 17. Abele E, Fujara M (2010) Simulation-based twist drill design and geometry optimization. CIRP Ann 59(1):145–150 18. Girinon M, Valiorgue F, Karaounic H, Feulvarch E (2018) 3D numerical simulation of drilling residual stresses. C.R Mecanique 346:707–711 19. Gaiche V, Gaiche YS, Patil JP (2018) Prediction of thrust force and torque in drilling of glass fiber reinforced plastic using mechanistic force model approach. Procedia CIRP 77:187–190 20. Diaz-Alvarez J, De-La-Cruz-Hernandez A, Diaz-Alvarez A et al (2015) Numerical modelling of the thermal effects on material in drilling processes Ti6Al4V alloy. Procedia Eng 132:427– 432 21. Boldyrev IS, Schurov IA, Nikonov AV (2016) Numerical simulation of the aluminum 6061T6 cutting and the effect of the constitutive material model and failure criteria on cutting forces’ prediction. Procedia Eng 150:866–870

Modeling Abrasive Grain Interaction with Machined Surface A. M. Kozlov(B) , S. K. Ambrosimov, and A. A. Kozlov Lipetsk State Technical University, 30, Moskovskaya Street, Lipetsk 398055, Russia [email protected]

Abstract. Grinding is the most common type of surface finish for parts. Abrasive grains on the tool working surface have a different spatial orientation with regard to the machined surface; as a result of which, one part of them cuts off the material, another part only deforms it, and the remaining part does not participate in the operation because it falls into the grooves previously cut by other grains. The nature of abrasive grain interaction with the machined surface significantly affects the formation of longitudinal and transverse roughness. Until recently, researchers determined the type of abrasive grains involved in the operation on the basis of mainly experimental studies. Previous theoretical studies made it possible to determine only the total number of active grains, i.e., those taking part in the operation. This article proposes to consider the type (cutting or deforming) of grain interaction with the machined surface with an account of the grain’s spatial orientation. Mathematical dependencies that determine the arrangement of grain in the tool’s working space are presented. With the account of the proposed approach, a method is presented for determining cutting and deforming abrasive grains on the tool working surface on the basis of computer modeling, as well as modeling results in comparison with data from other researchers. It is established that by changing the tool design or the kinematic cutting pattern, it is possible to increase the number of cutting grains and increase machining productivity. Keywords: Modeling · Cutting and deforming abrasive grains

1 Introduction The development of mechanical engineering leads to the development of high-strength materials which in most cases can be machined by grinding only. Such machining requires various kinematic schemes [1, 2] and tool designs. When ground, the material is cut off with a combination of a large number of separate abrasive grains arranged on the work surface of the tool. Each of these grains is chaotically arranged and interacts differently with the machined surface. The nature of abrasive grain interaction with the machined surface significantly affects the formation of longitudinal and transverse roughness. The microrelief of the surface of parts working © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_110

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in mobile contact conditions affects their wear [3], and, in some cases—the quality of the resulting products [4]. For these reasons, it is quite difficult to model the microrelief of a ground surface.

2 Problem Statement In modeling the process of forming the microgeometry of a ground surface, it is common to consider the interaction of not all active (in contact with the workpiece surface) abrasive grains with the cut-off layer, but that of a single grain [5–9]. In the contact of the tool’s work surface with the machined profile, not all abrasive grains interact equally with the workpiece surface. It should be taken into account that some of the grains will be cutting, others—due to their geometry or arrangement—will be deforming, and the rest will not be in contact with the work surface because their path will coincide with the grooves formed by other grains [10]. Researchers distinguish between the tool’s cutting and deforming working elements and apply this approach to edge-cutting machining processes [11, 12]. Thus, the development of a grinding process model with an account of the nature of abrasive grain interaction with the machined surface will improve the modeling accuracy and outline the ways to increase the quality and productivity of machining.

3 Theoretical The technology of obtaining abrasive grains leads to their shape having an arbitrary contour. Depending on the research objectives, the grain shape approximation can be represented by different figures. It is convenient to use the ball shape for roughing and that of an ellipsoid of revolution for finishing [13]. It is more practical to use an ellipsoid of revolution as a model because it is possible to obtain different geometric shapes: spherical, plate, needle, etc. only by changing the dimensions of the ellipse semi-axis. The abrasive grain is randomly arranged in the tool surface. In this regard, a number of researchers [8, 11] believe it to be unlikely that the abrasive grain in the bond is oriented perpendicular to the work surface. It was experimentally found that the range of variation of the grain inclination angle to the machined surface norm is within ±45 [13]. In order to describe the interaction of the abrasive grain with the work surface, it is necessary to determine its arrangement on the abrasive surface (Fig. 1). Using the ellipse equation, the abrasive grain profile without taking into account its inclination in radial coordinates relative to the center of the grinding wheel  2 2 R(ϕ) =

a ·b b2 +a2 ·tg 2 ϕ

cos ϕ

,

(1)

where a, b are the semi-axes of the ellipsoid of revolution, ϕ and R are the radius vector angle and the radius vector of the grain arrangement in radial coordinates, respectively.

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Fig. 1. Schematic diagram of abrasive grain arrangement in space during operation: 1—grain, 2—sidewalls, 3—transverse roughness, 4—longitudinal roughness.

Given the inclination angles (ϕ V , ϕ S ) of the main axis of the ellipsoid  2 2 R(ϕ) =

a ·b b2 +a2 ·tg 2 (ϕ+ϕs )

cos(ϕ + ϕs )

(2)

The arrangement of a single grain in the plane of the principal movement vector ν  y(t) = s · R · cos · t + R(ϕ) + h (3) R where s R v t h

is the coefficient: at peripheral grinding = 1; at cup wheel lace grinding s = 0; is the abrasive wheel radius; is the tool’s linear velocity; is the point in time for which the grain arrangement is determined; is the component taking into account the arrangement of abrasive grains in the working layer of the grinding wheel.

In the contact interaction of the abrasive grain with the machined material, part of it is cut off and a groove with a cross section S cut is formed on the surface. Another part of the machined material is not cut off, but is only plastically deformed and forms the so-called “sidewalls” (Fig. 2) on both sides of the groove with an area S def [14–16]. Thus, the abrasive grain frontal projection area is divided into two—of a cutting operation character and of a deforming one. Chip shrinkage is conditionally neglected. If the cut section S cut takes the largest part of the abrasive grain cross section, the grain is considered cutting, and if the sidewall area S def is predominant, the grain is deforming.

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Fig. 2. Diagram of forming the cutting and plastic deformation zones in introducing the abrasive grain in the work surface.

In order to determine the number of cutting and deforming grains on the working surface of the abrasive tool, dependencies were obtained to be used for computer simulation. To simulate the location of abrasive grains in the surface layer of the tool, we used the results of studies presented in [17]. According to these studies, the grain distribution in height obeys the Fermi–Dirac function for the distribution of electrons in a solid: y(x) =

k1 exp[B · (M − x)] + 1

(4)

where M = 0.098 dz + 0.0264, B—coefficient depending on the grain size dz: B = 13/dz. Taking the total number of abrasive grains equal to Z, the percentage of cutting grains Z p will be determined as the ratio of the number of grains with a cutting area of the front surface to the total number of active grains   Z k3=1 1(Sp [k3]>0)  × 100% Zp =  (5) Z k3=1 1((Sp [k3]+S∂ [k3])>0) where the unit indexes after the summation signs indicate that the action is performed only when the condition of grain contact with the work surface is met. The number of deforming grains   Z 1 k3=1 (Sp [k3]>0, at Sp =0)  × 100% Zp =  (6) Z k3=1 1((Sp [k3]+S∂ [k3])>0) The number of active grains in contact with the work surface may increase if cutting occurs in intersecting directions, e.g., as at circular grinding with the lace of the cup

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wheel [18] (Fig. 3a), with a displacement of the tool’s and the part’s axes h—Fig. 3b. If instead of the round shape of the tool, a polyhedron with the number of faces n is used (Fig. 3c) [19], there will be more intersections of the trajectories of the abrasive grain movement.

Fig. 3. Diagram of circular grinding with cup wheel lace.

4 Results The modeling results of determining the number of active (cutting and deforming) grains in the contact zone of the tool and the workpiece are presented in Table 1 compared with the data obtained by other researchers [20–22]. Table 1. Modeling results. Grain Number of working grains, 1/mm2 fineness Source [20]

[21]

[22]

Authors Cutting

Deforming

16

1.70

1.449 1.223 0.881

1.23

25

1.35

0.836 0.863 0.420

1.00

40

0.36

0.464 0.429 0.225

0.331

It follows on from the table that the theoretical approaches used by other researchers to determine the number of working grains yield only their total number without distinguishing between cutting and deforming grains. Since, when two sides of the face grinding wheel are in operation, the abrasive grains of one side are working according to the pattern similar to that of the straight wheel periphery, for this side, there will not be any fundamental changes in the number of working grains and the ratio of cutting and deforming grains for this side. A different situation will arise when the other side of the abrasive tool is in operation when the tool’s and the part’s axes are displaced. The larger this displacement, the greater the part of the grains will perform the cutting and deformation work because their cutting speed vector will have a certain intersection angle with the machining traces left by the

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grains of the first side. The graphs (Fig. 4) show the results of modeling the number of grains participating in the operation for the tool side which work after the first side has formed the roughness profile on the product. It follows on from the graphs that the number of active grains increases. An increase in productivity of up to 40% when using a cup abrasive wheel industrially for grinding cylindrical parts was noted by Bakul [23].

Fig. 4. Change in the number of active grains depending on grain size and intersection angle (above) and axial displacement and number of working elements. Grain fineness 40, 25, and 16 for variants 1, 2, 3, respectively.

5 Conclusion In the described model of cutting with a single abrasive grain, it is proposed to determine the nature of its interaction, cutting or deforming, with the machined surface depending on its orientation with regard to the machined surface. This makes it possible to more

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accurately model the roughness parameters of the ground surface during the finishing of critical parts. The conducted research shows that by changing the tool design or the kinematic cutting pattern, it is possible to increase the number of cutting grains which will reduce the roughness of the machined surface and increase the productivity of machining.

References 1. Kozlov AM, Kozlov AA (2009a) Shaping the surface topology of cylindrical components by means of an abrasive tool. Russ Eng Res 29(7):743–746 2. Kozlov AM, Kozlov AA, Vasilenko YuV (2016) Modeling a cylindrical surface machined by a non-circular face tool. Procedia Eng 150:1081–1088. https://doi.org/10.1016/j.proeng. 2016.07.07.218 3. Kozlov AM, Kozlov AA (2009b) Increasing wear resistance of shafts by forming the type of direction of their surface irregularities during grinding. Bull Saratov State Tech Univ 3(41):112–114 4. Kozlov AM, Telegin VV, Kozlov AA (2018) The influence of roll working surface topography on wear resistance and quality of cold rolled grain-oriented steel. J Chem Tech Metal 53(5):943–994 5. Shipulin LV (2013) Improving the design technique for the operations of flat grinding by the periphery of the wheel based on complex process modeling. Modern problems of science and education. https://science-education.ru/ru/article/view?id=9014. Accessed 2 Apr 2019 6. Yashkov VA (2018) Modeling the interaction of cutting abrasive grains with the surface of the part. Modern high technology. https://top-technologies.ru/ru/article/view?id=37356. Accessed 26 Nov 2019 7. Kozlov AM, Efremov VV (2004) The formation of microrelief during processing with an abrasive tool. News of higher educational institutions. Mech Eng 1:59–64 8. Gorlenko OA, Bishutin SG (1998) Determining the number of active grains during grinding. STIN 11:18–19 9. Zakharov OV, Khudobin LV, Vetkasov NI et al (2016) Abrasive-jet machining of large hollow components. Russ Eng Res 36(6):469–471 10. Maslov EN (1974) Theory of material grinding. Mashinostroenie, Moscow 11. Naerman MS (1976) Progressive processes of abrasive, diamond and elbor machining in mechanical engineering. Mashinostroenie, Moscow 12. Ambrosimov SK (2019) Methods of deforming-cutting pulling and tools with elastic deforming elements. Bull Lipetsk State Tech Univ 1(35):56–61 13. Lavrinenko VI (1997) The spatial arrangement of high-strength material grains in the grinding wheel abrasive layer. High-Strength Mater 5:72–78 14. Bogdanov AYu, Bogdanov VV (2000) A generalized probabilistic approach to the kinematics of the grinding process. Fundamental and applied technological problems of machine building - Technology-2000. In: Transactions collection of international scientific-technical conference in Oryol, OryolSTU, Oryol, pp 115–117 15. Korchak SN (1974) The performance of the grinding process of steel parts. Mashinostroenie, Moscow 16. Orobinsky VM (2000) Abrasive machining methods and their optimization. Mashinostroenie, Moscow 17. Kurdyukov VI, Agapova NV (2001) Finding the law of grain density distribution in the upper layer of the abrasive circle. Processes of abrasive processing, abrasive tools and materials. Shlifabraziv-2001, Volzhsky, pp 26–29

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18. Svitkovsky FYu, Ivanova TN, Osipova TI (2000) Theoretical studies of the cutting profile of the diamond face tool surface. Bull IzhSTU 2:17–19 19. Kozlov AM, Ponomarev ON, Efremov VV (2005) Combined face grinding wheel. RF Patent 2249500, 10 Apr 2005 20. Filimonov LN (1979) High speed grinding. Mashinostroenie, Leningrad, p 248 21. Bishchutin SG (2002) Predicting the state of the surface layer of ground parts. Ref Eng J 8:59–61 22. Redko SG, Korolev AV (1970) The formation of the ground surface profile. News Univ Eng 7:159–163 23. Bakul VN (ed) (1976) Synthetic diamonds in mechanical engineering. Naukova Dumka, Kiev

On the Formation of Groove Geometry Defects Due to Transverse Vibrations of End Mills A. A. Dyakonov1 , S. V. Sergeev2 , and A. V. Baev1(B) 1 South Ural State University (NRU), 76, Lenina Avenue, Chelyabinsk 454080, Russia

[email protected] 2 Branch of South, Ural State University (NRU), in Zlatoust, 16, Turgeneva St., Zlatoust

456209, Russia

Abstract. Currently, the issue of increasing the intensity of machining is relevant in production. However, an increase in the cutting modes almost always leads to defects. Thus, the setting of optimal modes is uppermost in the work of engineers. The article discusses the mechanism of the appearance of defects in the form and size of narrow deep grooves due to transverse vibrations of the mill. It illustrates an example of a product designed with such grooves, the requirements to which were not met by machining operations. The article shows possible trajectories of vibratory displacements of the cutting part of the tool in the transverse plane due to the synchronization of transverse and longitudinal vibrations of the cutting part. Based on the described model, it has been revealed that the stability of the milling process cannot be ensured when the handling radius of the mill is nine times more than its diameter. We have established the nature and degree of the dependence of the defects in the form and size of the machined groove on the specified cutting modes. The obtained results of the study allowed us to adjust the cutting modes set in a real technological process and to avoid defects in the manufacture of the product. The adjustments allowed us to stably meet the requirements of the part drawing, to exclude defects during milling operations, and to avoid additional locksmith operations. Keywords: Vibrations · Vibratory displacement · Defect of form · Milling stability · Cutting modes

1 Introduction An analysis of the machining operations of products designed with narrow deep grooves showed that the requirements to the accuracy of the shape and arrangement of surfaces are not met in most cases when the handling radius of the mill exceeds its five diameters. A successful assurance of the accuracy of the machined surfaces when designing technological processes largely depends on the experience of the process engineer, since the use of various reference books, for example, Reference book of Guzeev V. I. “Cutting modes for CNC-controlled turning and milling and boring machines” or reference book © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_111

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of Kosilova A. G. “Manufacturing engineer’s reference book,” containing empirical and averaged data, does not guarantee a positive result in specific machining conditions. Despite the fact that a number of authors [1–3] indicate that vibrations are an important component of the cutting process, and a significant number of works study the stability of the milling process [4–10], this factor is not taken into account in such reference books. The specified requirements to the accuracy and roughness of surfaces are often provided with either “blindly” based on the experience of the technologist or the performers resort to using the test run method, which leads to an increase in the time needed to prepare for the manufacture of the product, and to an increase in the likelihood of defects. Welding is used to save defective expensive parts, that is, a material is deposited on the necessary surfaces, and then they are re-formed. This changes the structure of the material and reduces the performance of the product.

2 Structure For example, enterprises engaged in the manufacture of molds have deviations in the geometry of narrow deep grooves when machining a “punch” part, a fragment of which is shown in Fig. 1. Such surfaces are typically machined with low-rigidity end mills. In particular, the deviation of the size from the drawing requirements is 1.5 + 0.06, the actual size is from 1.52 to 1.68, the deviation of the parallel alignment of the groove walls is up to 0.15 mm (conical breakdown).

Fig. 1. Fragment of a part.

From the standpoint of vibrational cutting mechanics [11], a peculiar feature of the milling process is that the tool teeth unevenly cut the layer of a material, and only several tool teeth are involved at any time. Besides, constantly changing cutting forces generate stable transverse vibrations of the mill ω. However, in addition to transverse vibrations, the milling process also involves longitudinal vibrations, which arise due to the influence of a variable axial cutting force connected with radial “shaking” of the cutting part of

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the tool. Different frequency ratios of the resulting vibrations can lead to a significant defect in the form and size [12]. Transverse and longitudinal vibrations of the cutting tool are connected parametrically, and the appearance of a defect in the shape of the machined groove in the form of a conical breakdown in the cross section depends on the amplitude of the transverse vibrations in the direction perpendicular to the feed movement (Fig. 2).

Fig. 2. Scheme of the longitudinal variable force action on the end mill.

Let us compose an equation of movement of the mill’s axis of mass in the direction perpendicular to the feed movement, taking into account the influence of longitudinal vibrations. Assessing the vibratory displacements of the cutting part of the tool, we should pay attention to the trajectory of its axis of mass. To this end, we compose an equation of movement of the cutting part in a plane perpendicular to the feed direction.  y = A · cos(ωt + ϕ) (1) z = Az · cos(2ωt + ϕz ) where A and Az are the mill’s vibration amplitudes in perpendicular directions; ϕ and ϕz are the initial vibration phases. When the mill’s axis of mass makes transverse vibrations ω, there inevitably appear vertical displacements, which frequency is twice larger than the frequency of the transverse ones (Fig. 3) [13]. Since the longitudinal force Z in the technological system changes with a frequency, which is twice larger than the frequency of the mill’s transverse vibrations (see Fig. 3), it performs work with each cycle, and the energy of the system will constantly increase. This, in turn, leads to an increase in the vibration amplitude at periodically changing process parameters, i.e., the so-called parametric resonance develops in the

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Fig. 3. Vibratory displacements of the end mill’s axis of mass.

system [12]. This is preconditioned by the continuous flow of energy into the system, and, in other words, it shakes itself. In this case, an increase in the amplitude of the mill leads to a conical breakdown of the groove (Fig. 4) [13].

Fig. 4. Conical breakdown of the groove.

With this in mind, let us transform the system of equations (1) and obtain the following equation: z 2y2 − =0 2 A AZ

(2)

This equation is an equation of the Lissajous closed curve, provided that the frequencies of the tool’s transverse and longitudinal vibrations are multiple. Figure 4 shows the

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trajectories of the tool’s axis of mass with a frequency phase ratio of 1:2 (Fig. 5a) 1:3 (Fig. 5b) 3:4 (Fig. 5c). However, if there is no multiple relationships between the frequencies, the trajectory of the tool’s axis of mass will not be closed, and there will be areas filled with the trajectory of the tool.

Fig. 5. Lissajous curves with a frequency phase ratio of: a 1:2 b 1:3 c 3:4.

Thus, the ratio of the frequencies of the considered vibrations significantly affects the nature and size of the defect. So, when modulated vibrations are excited, the amplitude increases and the frequency decreases, which occurs before the system leaves the resonance area, and when it falls into the stability area, the frequency of transverse vibrations begins to increase again and the system returns to the instability area. This means that transverse vibrations become frequency-modulated. The control of the mechanism, which contributes to the amplification of such vibrations by the frequency mismatch, allows us to significantly reduce the groove breakdown and to increase its accuracy. To illustrate this mechanism, let us compose an equation of movement of the mill’s axis of mass in the direction perpendicular to the feed movement, taking into account the influence of longitudinal vibrations. T R ∂ 2y · sin 2θ + · cos 2θ + (μ + 2q · cos 2θ ) · y = 2 ∂θ m m where q, μ are the dimensionless coefficients:

(3)

4jy 4ky = 2 (4) mω2 ω 2jz (5) q= mω2 where m is the reduced mass of the end mill. The coefficient μ characterizes the ratio of the system’s eigenfrequency at the average value of the parameter jy to the parameter change frequency, and q characterizes the parameter change degree. They fully determine the movement stability. The zone of the change in q and μ can be divided into areas corresponding to stable and unstable movements (Fig. 6). The stability areas are shaded in the figure. So, to determine the stability of the movement described by Eq. (3), we should calculate the coefficients q and μ, apply the obtained values to the diagram and establish whether the system falls into a stable or unstable area [13]. After comparing the dimensionless coefficients q (5) and μ (4), we obtain: μ=

3D q = μ l

(6)

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where D is the diameter of the mill; l is the handling radius of the mill. Despite the fact that many works [14–20] deal with the increase in the milling process stability, as can be seen from Eq. (6), when the handling radius is 9 times larger than its diameter, the parameter q will be significantly less than the parameter μ. This means that in the Ains–Strett diagram, the cutting conditions for such ratios of the tool sizes will almost always correspond to an unstable area. Based on the aforesaid, we found an approximate equation of the boundaries of the first instability area: (μ − 1)2 − q2 = 0

(7)

In this case, the following equation corresponded to instability: (μ − 1)2 − q2 < 0

(8)

Fig. 6. The boundary of the first instability area (Ains–Strett diagram fragment).

Figure 6 shows the boundaries calculated by Eq. (7). For comparison, the dashed line also shows the exact boundary according to the Ains–Strett diagram. The boundaries of other areas are calculated similarly. To remove the technological system from the area of “dangerous” resonant frequencies, it is enough to limit the feed or cutting speed. Thus, we can significantly reduce the amplitude of the tool’s vibratory movements, which in turn will lead to a decrease in the conical breakdown of the groove. However, an excessive decrease in the cutting modes leads to an increase in the time needed to manufacture the product, therefore, to an increase in its cost, which may be unacceptable in modern

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conditions. Thus, it is necessary to find a balance when the time needed to manufacture the product will be minimal, and the accuracy requirements will be met. Based on the described recommendations, we adjusted the machining parameters, in particular, reduced the feed by 44% from 0.08 to 0.045 mm/rev (millimeter/revolution), and reduced the cutting speed by 25% from 120 to 90 m/min (meters per minute). As a result, when the product (Fig. 7) is manufactured in the updated modes, the requirement to the width of the groove is met. We also managed to significantly reduce the groove breakdown from 0.15 to 0.02 mm.

Fig. 7. Re-manufactured product.

3 Conclusions We established the possibility and determined the reasons and conditions for the existence of synchronization of frequencies of rotational and vibratory movements of end mills during machining of narrow deep grooves, which predetermines a decrease in accuracy during such machining. We also found a desynchronization phenomenon consisting in the fact that the frequency of the tool’s transverse vibrations begins to deviate from the frequency of its longitudinal vibrations when a parametric resonance occurs, and the transverse vibrations become frequency-modulated. In this case, a gradually expanding groove is formed. The practical application of the described model allows us to control the machining accuracy at the stage of designing machining processes. This allows us to significantly reduce the cost of manufacturing products due to the reduction of the time needed to prepare the production and manufacture, as well due to the reduction of defects.

References 1. Poduraev VN (1970) Obrabotka rezaniem s vibraciyami (Vibration Cutting). Mashinostroenie, Moscow 2. Kumabe D (1985) Vibracionnoe rezanie (Vibration cutting): per. s yap. S.L. Maslennkova. Mashinostroenie, Moscow

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3. Tverskoj MM (1982) Avtomaticheskoe upravlenie rezhimami obrabotki detalej na stankah (Automatic control of the processing modes of parts on machines). Mashinostroenie, Moscow 4. Gao G, Wu BH, Zhang DH, Luo M (2013) Mechanistic identification of cutting force coefficients in bull-nose milling process. Chin J Aeronaut 26:823–830 5. Grossi N, Sallese L, Scippa A, Campatelli G (2015) Speed-varying cutting force coefficient identification in milling. Precis Eng 42:321–334 6. Yue C, Gao H, Liu X (2017) Research on the stability of the machining process based on the dynamic cutting force coefficient. J Mech Eng 53:193–201 7. Jiang SL, Sun YW (2018) A multi-order method for predicting stability of a multi-delay milling system considering helix angle and run-out effects. Chin J Aeronaut 31:1375–1387 8. Wu S, Yang L, Liu XL et al (2017) Effects of curvature characteristics of sculptured surface on chatter stability for die milling. Int J Adv Manuf Technol 89:2649–2662 9. Tang X, Peng F, Yan R et al (2017) Accurate and efficient prediction of milling stability with updated full-discretization method. Int J Adv Manuf Technol 88:2357–2368 10. Xie Q (2016) Milling stability prediction using an improved complete discretization method. Int J Adv Manuf Technol 83:815–821 11. Pankin AV (1961) Obrabotka materialov rezaniem (Cutting materials). Mashgiz, Moscow 12. Lakirev SG, YaM Hilkevich, Sergeev SV (1993) Vibracionnaya mekhanika processov sverleniya – bureniya i novye dinamicheskie ehffekty (Vibrational mechanics of drilling processes—drilling and new dynamic effects). Chelyab. gos. tekhn. un-t, Chelyabinsk 13. Sergeev SV (2004) Povyshenie ehffektivnosti vibracionnyh processov pri mekhanicheskoj obrabotke razlichnyh materialov: monografiya (Improving the efficiency of vibration processes during the machining of various materials: monograph). YUUrGU, Chelyabinsk 14. Lei N, Soshi M (2017) Vision-based system for chatter identification and process optimization in high-speed milling. Int J Adv Manuf Technol 89:2757–2769 15. Gurdal O, Ozturk E, Sims ND (2016) Analysis of process damping in milling. Procedia CIRP 55:152–157 16. Tajalli SA, Movahhedy MR, Akbari J (2014) Chatter instability analysis of spinning micro-end mill with process damping effect via semi-discretization approach. Acta Mech 225:715–734 17. Ozoegwu CG, Omenyi SN, Ofochebe SM (2015) Hyper-third order full discretization methods in milling stability prediction. Int J Mach Tools Manuf 92:1–9 18. Jin G, Qi H, Li Z, Han J (2018) Dynamic modeling and stability analysis for the combined milling system with variable pitch cutter and spindle speed variation. Commun Nonlinear Sci 63:38–56 19. Totis G, Albertelli P, Sortino M (2014) Efficient evaluation of process stability in milling with spindle speed variation by using the Chebyshev collocation method. J Sound Vib 333:646–668 20. Comak A, Budak E (2017) Modeling dynamics and stability of variable pitch and helix milling tools for development of a design method to maximize chatter stability. Precis Eng 47:459–468

Peculiarities of Process Conditions and Rail Grinding Modes I. Yu. Orlov1(B) , S. A. Krukov1 , and N. V. Baydakova2 1 Volzhsky Polytechnic Institute (Branch) of Volgograd State Technical University, 42a, Engels

Street, Volzhsky 404121, Volgograd Region, Russia [email protected] 2 Volzhsky Branch of National Research University Moscow Power Engineering Institute, 69, Lenin Avenue, Volzhsky 404110, Volgograd Region, Russia

Abstract. The scientific article analyzes the known materials used for the manufacture of railway rails and the problems encountered in their operation. As a result of rolling stock wheels acting on rails, various defects occur on them. Grinding technology is used to eliminate them. It has been found that the load on the abrasive wheels has a variable character and by adjusting the speed of movement of the rail grinding train, the pressing forces of the wheels, it is possible to influence the removal of the rail metal. The resulting dependencies describe this regularity. During the operation of the track, the physical and mechanical properties of the metal change significantly along the section of the rail head. A sharp change in hardness at certain sections of the rail head will contribute to the tightening of operating conditions for the grinding wheels. Studies carried out to evaluate the operational properties of the ground surface of the rails have shown that, in order to ensure increased operational resistance of the rails, it is necessary to form surface roughness during grinding taking into account their initial hardness and operating conditions. Based on the analysis, carried out to study the process of grinding railway rails with wheels of existing technologies of metal processing, wear of materials, it can be concluded that the wheels should be produced on a bakelite binder from abrasive materials of high wear resistance. Keywords: Grinding wheel · Rails · Abrasive tool · Defects · Performance

1 Introduction Currently, in the Russian Federation, more than 80% of all freight turnover takes place on railways. Taking into account the climatic factor, the conditions of operation of the rail are the heaviest in the world. Several main grades of steel produced by different methods of smelting (M, K, E) and doped with vanadium (F), silicon (C), chromium (X), and titanium (T) are used for making railway rails. Of the following variations of alloys— M76, M76F, M76T, K76, K76F, K76T, E76, E76F, E76T makes the profiles of rails of © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_112

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P50 and P65 series making 75% of all supporting frameworks of broad gage railroad tracks. Mechanical properties of rail steels: hardness after volume hardening reaches up to 60 HRC on Rockwell scale; Impact viscosity—2.5 kg/cm2 ; Ultimate strength of steel reaches 1000 MPas. Such properties provide good impact resistance and sufficient resistance to cyclic loads, allowing for decades of track operation without replacement. However, due to the impact of the wheels of the rolling stock on the rails, there are defects in the form of mechanical surface damages, collapse and peeling of the metal, as well as wavy wear of the contacting surfaces and wear of the transverse profile of the rail.

2 Main Part In order to eliminate the above-mentioned defects, rail grinding trains with cars equipped with bogies with grinding heads having electric motor, abrasive wheel, parallelogram suspension with pneumatic cylinder are used. The efficiency of grinding depends directly on the quality of the rail grinding wheels. In modern RShP the method of power grinding at which the circles rotating with skorostyyu3600 rpm nestle on rails with effort about 7.5 kN ÷ 9.6 of kN depending on an operating mode (Fig. 1) [1] is used.

Fig. 1. Diagram of interaction of grinding wheel and rail head: 1—grinding wheel; 2—rail head.

The contact force is selected from conditions of high cutting capacity of wheels and minimization of thermal defects on rails. Load is indirectly estimated by current load of electric motors of abrasive wheels drive. For conditions of the definition of indicators of circles current loading of electric motors of the drive of abrasive circles for main carts makes 23 A and 25 ÷ 27 A, working on the over the surface the skating. The results of measuring the current loads of the abrasive wheel drive motors during grinding show that

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the load on the wheels is variable (the control system controls the value of the physical load on the wheels indirectly controlling the current), the average value corresponding to the task with accuracy not exceeding the value specified by the system developer. As a result of operational tests carried out by FSUE “VNIKTI”, there were obtained dependencies of removal of rail metal per wheel from speed at different forces of pressing abrasive wheels (Fig. 2) at speeds of 5, 6.5, 7.5 km/h. Dependence of rail metal removal on speed of movement for currents 26 and 27 A on smoothing bogies are obtained experimentally—by calculation method.

Fig. 2. Dependence of metal removal on motion speed [2].

It follows from the graphs presented in Fig. 3 that by adjusting the speed of movement and the pressing forces of the wheels, it is possible to influence the removal of the rail metal.

Fig. 3. Dependence the area of removal of metal on train speed [2].

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These dependencies can be analytically described by the following equations. The relationship in Fig. 2 is expressed by the equation: T = 0.51 · S 1.5

(1)

And the dependency in Fig. 3 is described by: F = 2.4 · S −1

(2)

At current intensity of 23–26 A. One condition of wheels operation is absence of clamps on treated surface of rails. Maximum thickness of removed metal layer from rail head in one pass at hardness of steel 400 HB and train speed 5 km/h shall be 0.2 mm; current loadings of electric motors—25 ÷ 27 of amperes. Wheel resistance—not less than 6 h, and average wear of wheels up to 70% of wheel height. Significant differences in operation of abrasive tool during rail grinding compared to grinding in stationary conditions on machines introduce significant changes in natural conditions: ambient temperature, depending on the time of year, can vary from 20– 40 °C to −10 to 50 °C, and air humidity from 15 to 90%. Such changes in temperature and humidity can significantly alter the structural and mechanical characteristics of the grinding wheels used. Note also that when the ambient temperature in the rail butt joints changes, the clearance value will increase or decrease. With increased gaps between rails at the points of their docking, the grinding wheel will experience impact loads resulting in the chipping or destruction of its working surface. During rail track operation physical and mechanical properties change considerably along rail head cross section. Figure 4a shows the hardness distribution by rail profile after operating time of 450 million tons gross. A sharp change in hardness at certain sections of the rail head will also promote to tighten the working conditions of the grinding wheels [3, 4]. In the work [3] the reasons and mechanism of defects formation in the rail head, as well as influence of various factors in grinding on fatigue strength, wear resistance and overall durability of rails are quite fully considered. The regulatory and technical documentation on rail grinding regulates roughness and burn marks on the treated surface, which together determine the physical condition and quality of the rail surface after their grinding. A study to evaluate the operational properties of the surface of the rails after grinding showed that in order to ensure increased operational resistance of the rail, it is necessary to form surface roughness during grinding taking into account their initial hardness and operating conditions. On the basis of the works of M. H. Akhmetzanov, M. A. Frishman, E. P. Bondarenko, etc., which determine the stressed states of the rail head during operation taking into account the type of loading depending on the curvature of the track section and its location, the values of surface roughness are determined, which ensure improvement of operational properties of the rails. By way of example, Table 1 shows the values of the required roughness of the rail head portions lying on the inner thread of the curved track portion with a radius greater than 500 m (see Fig. 4b).

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Fig. 4. Rail diagram a Hardness by rail profile [3]. b Conditional diagram of load on rail.

Table 1. Required roughness of rail head sections lying on the internal curved section of the track with radius more than 500 m [3]. Sections of profile and Characteristic view of their boundaries at angles the destructions in the of grinding heads profile area inclination, ϕ, in degrees

Recommended roughness on a plot the profile, Rz, micron

The hardness at the plot the profile HB 340 ÷ 400

400 ÷ 460

>460

I

−60 to −15

–

35–40

35–40

35–40

II

−15 to −10

Wear

16–20

16–20

16–20

III

−10 to −5

64–68

54–58

44–48

IV

−5 to −1.5

Formation of transverse cracks

64–68

54–58

44–48

V

−1.5 to + 8

Contact fatigue destruction

54–58

48–54

40–44

VI

+8 to +20

–

35–40

35–40

35–40

The analysis of the presented data in Table 1 indicates the complexity of process grinding due to the non-uniformity of the load on the rails and the required roughness Rz on the parts of the head and rail profile. In order to form the cross profile of the rail head shown in the figure in Table 1, it is necessary to use multi-instrument processing with flat grinding scheme lateral of the grinding wheel. For this purpose, grinding wheels mounted on profiling bogies and wheels on smoothing bogies are used on rail trains.

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However, the working equipment of the existing rail grinding trains and the abrasive tool used do not fully ensure the efficiency of the work in the railway conditions. It should also be noted the peculiarities of the modes of the rail grinding process in cutting depth, longitudinal feeding and operating speed of the wheel rotation. The cutting depth is selected depending on the grinding path width and current load of the motor (see Fig. 5).

Fig. 5. Dependence of electric motor current load on cutting depth t and grinding track width B [3].

The longitudinal feed of the grinding wheel to the straight depends on the operating speed of the rail grinding train, which currently composes 6–8 km/h. To implement a high-performance process, it is necessary to increase this speed to 12–15 km/h. It is known that the grinding of the rails is carried out by the end wheels on the bakelite bundle at a rotational speed of 50 m/s. To improve grinding performance, it is recommended to increase this speed to 100 m/s [4]. However, one of the main factors limiting the increase in cutting speed is the strength of the grinding wheel.

3 Conclusions Based on the analysis carried out to study the grinding process of railway rails by grinding wheels on existing technologies of metal processing, wear of composite materials, it can be concluded that the wheels should be produced on a bakelite binder from abrasive material of high wear resistance, for example, from zirconium-electric corundum with high content of zirconium dioxide [5–20]. In order to increase the efficiency of the rail grinding operation, it is necessary to carry out a set of research, technological, engineering works based on the analysis of studies in the field of improving the properties of abrasive material, study of the

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influence of fillers, evaluation of the operation of the abrasive tool for rail grinding, classification of defects of the rail rolling surface, to create an effective technology of wheel production and carrying out a set of comparative and qualification tests of wheel performance indicators, in the following directions: 1. Selection of strong and wear resistant abrasive grains and rational grain compositions of molding mixtures for making tools; 2. Experimental study of technological possibilities of using slimes (metal processing wastes) for production of non-working and working parts of the circle; 3. Study of the effect of various fillers on the thermal conductivity index of the abrasive wheel; 4. Study of physical and chemical processes taking place during polycondensation of bakelite binder for correction of production process and development of method of calculation of bakelization mode; 5. Development of a method of heat treatment of bakelite circles.

References 1. Albrecht VG, Krysanov LG, Abdurashitov AY, Schmiga YuN (1999) Profile processing of rails by grinding trains with active working bodies. Technoforum, Moscow 2. Abdurashitov AY, Krysanov LG, Kamensky VB (2001) Profile grinding of rails, Transport. Moscow 3. Ilina AS (2013) Justification and development of scientific and methodological bases of highperformance technology of rail grinding in conditions of railway track. Dissertation, Saratov State Technical University named after Gagarin YuA 4. Aksenov VA, Ilin AS (2007) Technological peculiarities of the process of grinding rails in the way and their influence on the operational stability of rails. J Siberian State Univ Commun Routes 17:216–221 5. Baidakova NV, Orlova TN (2017) Procedia engineering. Ser. “International conference on industrial engineering, ICIE 2017”, pp 188–193 6. Baidakova NV, Orlova TN (2017) Procedia engineering. Ser. “International conference on industrial engineering, ICIE 2017”, pp 194–199 7. Shumyacher VM, Slavin AV, Kryukov SA (2016) Procedia engineering. Ser. “2nd international conference on industrial engineering, ICIE 2016”, pp 916–919 8. Slavin AV, Kryukov SA (2016) Procedia engineering. Ser. “2nd international conference on industrial engineering, ICIE 2016”, pp 911–915 9. Kryukov SA, Kryukova AS (2017) Procedia engineering. Ser. “International conference on industrial engineering, ICIE 2017”, pp 200–203 10. Kryukov SA, Kryukova AS (2017) Procedia engineering. Ser. “International conference on industrial engineering, ICIE 2017”, pp 204–209 11. Kryukov SA, Tkach MA (2017) Procedia engineering. Ser. “International conference on industrial engineering, ICIE 2017”, pp 200–203 12. Bauman HN (1956) Am Ceram Soc Bull 10:35 13. Bird GA (1994) Oxford: Science Publications, p 350 14. Hasselman DB, Amer HJ (1969) Ceram Soc 4:215 15. Kezdi A (1969) Handbuch der Bodenmechanik, pp 97–101 16. Konig W, Bottler E (1978) INFOS 91:45

976 17. 18. 19. 20.

I. Yu. Orlov et al. Konig W, Lorts W (1975) CIRP 24:231–235 Suto T, Waida T (1973) Bull Mech Eng Lab 8:1–11 Tobochnik J, Chapin PM, Chem J (1988) Physics 88:58–62 Moser M, Peters J (1973) Ann CIRP 1:103–105

Thermal Processes in Surface Plastic Deformation of Difficult-to-Cut Materials N. Papsheva and O. Akushskaya(B) Samara State Technical University, 244, Molodogvardeiskaia Str., Samara 443100, Russia [email protected]

Abstract. The paper presents data from the study of the influence of methods and modes of surface plastic deformation (SPD) on the temperature of the contact region during titanium alloy processing. It shows that, as a result of deformation and the work of friction forces, heat is generated. In this case, the overall temperature field is influenced by the geometrical parameters of the part to be processed, the time of the previous treatment, the total thermal power of the sources and the nature of heat exchange with the environment. A generalized solution is given for determining the maximum contact temperatures during ball rolling and ultrasonic hardening by the method of moving sources. The authors find out that the maximum discrepancy between theoretical and experimental data, as a rule, does not exceed 12–16%. Obtaining the temperature of the contact region makes it possible to check the selected modes by the maximum possible heating temperature, which is especially important when using optimal modes of surface plastic deformation. Keywords: Ultrasound · Hardening · Ball rolling · Contact area · Titanium alloy

1 Introduction Surface plastic deformation processing (ball rolling, ultrasonic hardening, diamond burnishing, etc.) is one of the effective methods to increase the reliability and durability of machine parts from difficult-to-cut materials (including titanium alloys) used to manufacture parts operating in extreme conditions [1–7]. As is known, titanium alloys have a special combination of physical and mechanical properties: high specific durability and heat resistance, low heat and thermal diffusivity, etc. Due to the low thermal conductivity, titanium alloys are characterized by a concentration of heat in the near-contact region, which can lead to a decrease in operational characteristics. To study thermal phenomena during ball rolling and ultrasonic hardening, materials of two structural groups were used: OT-4 alloy and VT6 and VT9 alloys.

2 Determination of Maximum Contact Temperatures Intensive processing regimes due to a significant increase in the temperature of the surface layer cause thermoplastic deformations, which reduce favorable residual compressive © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_113

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stresses, and in some cases contribute to the formation of residual tensile stresses [8– 10]. The combined effect of high pressures and temperatures can lead to structural transformations. During ball rolling and ultrasonic hardening as a result of deformation and the work of friction forces, heat is generated, which is spent on heating the tool, the workpiece and on heat exchange with the environment [11, 12]. The work of friction caused by the movement of the tool on the machined surface, during ultrasonic hardening by a ball freely installed in the socket and by ball rolling is very small in comparison with the work of deformation and can be neglected. Heat transfer to the environment with an error of 1% can also be neglected [13, 14]. In the quasi-stationary stage of the process at the set thermal mode, we assume that the parts of the tool in contact with the part turn out to be warmed up to the maximum temperature, since they are constantly exposed to heat. Moreover, the contact area is continuously moving relative to the part, meeting all the time with unheated points. Therefore, the temperature gradients in the direction of the deforming tool are much smaller than the gradient in the part. Thus, the heat sink to the tool in the steady state can be neglected without a significant decrease in accuracy [15, 16]. Therefore, for ultrasonic hardening and rolling ball it can be stated that Q ≈ Qp . Sources of heat generated as a result of plastic deformation are local under these SPD methods. In ultrasonic hardening, a variable periodic force with a frequency of ultrasonic vibrations is superimposed on a constant static force created by a deforming tool (indenter). In accordance with this, the thermal power should be considered a timedependent variable [14]. Since the general work consists of work carried out by constant Pst and periodic force, in accordance with the principle of superposition, we consider two independent sources of heat. The power of the first is determined as follows Pst KV 1000 , (1) M 60 where K—coefficient of friction; V—speed; M—mechanical equivalent of heat. The power of the source when rolling the ball is determined similarly. The work of the plastic introduction of the indenter, produced by a variable periodic force, is performed with a frequency of Ñ cycles per minute. In this case, the average power of the source q1 =

Aω , (2) M where A—the work of plastic implantation; ω—the frequency of cycles. During each cycle, the indenter deployment effort changes. Consequently, the power of the source also changes. To calculate the maximum temperatures, it is necessary to determine the largest (amplitude) power of the source q0 . We assume that the change in effort, and, accordingly, in power occurs according to a cosine law. Then q0 (t) =

f (t) = q0 cos ωt

(3)

When studying the temperature fields formed during the SPD, the temperature in the deformation zone is considered as the result of the combined action of two fields: the

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local one, which occurs at the time of deformation of a certain part of the part and the general one arising from the heat influx from previously deformed sections [17]. The general temperature field is influenced by the geometric parameters of the workpiece, the time of the previous processing, the total thermal power of the sources, the nature and intensity of the heat exchange with the external environment. The distribution of sources in the part has practically no effect on the overall field. Therefore, for each specific case, the total heating can be determined by any known dependence, using the most simple method for schematizing the shape of the source and the type of the motion. So, the local temperature field is determined by the shape of the sources and the distribution law of the power of their heat generation and practically does not depend on the other factors listed above. We accept that the heat source has a spherical shape and its intensity is distributed normally in three spatial coordinates. In this case, we can write   qm (4) exp −kR2 , F(x, y, z, t) = cγ where qm —the maximum heat release intensity; c—the heat capacity; γ —the specific weight; k—the coefficient of concentration of thermal power, characterizing the shape of the curve of the normal distribution; R—radius vector of the point being considered. For hardening with the application of ultrasound, it is recommended that the radius of the indent be taken equal to the conditional heating spot r n , where the heat release qi is 0.05 of the highest intensity in the center of the indent. In this case k=

3, 0 2 rH

(5)

Since the shape of the part practically does not affect the local temperature field, we take the surface of the part processed to be flat, representing the product itself in half-space −∞ < x < ∞; −∞ < y < ∞; z ≥ 0. The surface z = 0 of the half-space is assumed to be adiabatic, and the initial temperature is assumed to be zero. The intensity of the sources during the ball rolling can be considered constant in time, with ultrasonic hardening, a periodic change in intensity occurs. In this case, the most interesting is the maximum temperature in the steady-state stage of the SPD process. We determine the local component of the temperature field at the maximum temperature of the deformation zone. We assume that the maximum value of the contact temperature is close to the temperature of point 0 (0, 0, 0), at which the intensity of the heat sources is greatest. It should be noted that at high speeds of the source, the temperature maximum can be slightly shifted from the central point (0, 0, 0) in the direction of the lag along the axis OX. Assuming in the equality X = Y = Z = 0 and noting that in this case  (6) R1 = R2 = R = ξ 2 + η2 + s2

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we find the image of the maximum contact temperature for an arbitrary distribution of sources [18–20] ∞  ∞ 1 ds F(ξ, η, s, p) T (p) = T (0, 0, 0, p) = 2π α −∞ 0     √ Vξ R p+α 1 dξ dη exp − exp − √ R 2a α

(7)

2

where α = V4a ;—coordinates of the points of location of heat sources at time points; p—Laplace transform parameter. With ultrasonic hardening, two independent heat sources operate. The temperature T 1 arises from the action of a constant power source q1 . Temperature fluctuations T (t) are superimposed on it, which arise as a result of an additional action, which depends on time and changes according to the sinusoidal or cosine laws of the variable source q0 (t). If we assume that the intensity of a variable power source q0 (t) varies in time with frequency ω in a cosine dependence, then the total thermal power q0 (t) = q1 + q0 cosωt, ,

(8)

where q0 —the amplitude value of the variable component of thermal power. The resulting temperature T (t) in the quasi-stationary stage of the process can be written as the sum of the constant component of temperature T 1 arising from a constant source q1 and the variable component T 0 (t) from the action of the source q0 (t) , T (t) = T1 + T0 (t).

(9)

In this case, each component of the contact temperature can be searched separately, solving two independent tasks. To determine the variable component of the steady-state temperature T 0 (t), we use (with some modifications) the method proposed in [8]. It is more convenient to present the dependence of the oscillating power of the source on time in a complex form, assuming q0 (t) = q0 exp(iωt).

(10)

To calculate the maximum temperature of the contact region T (t) during ultrasonic hardening, a constant component of the contact temperature should be added to the amplitude value of the variable. The local temperature thus found is added to the overall field temperature, which is determined each time depending on the processing conditions and the shape of the workpiece:          2qcp l Vs l Vs l Vs l Vs l ch K0 + sh K1 , (11) T= πλ 2Q 2Q 2Q 2Q where l is half the width of the contact strip (imprint radius); qcp —the average heat flux equal to the heat power referred to the middle of the surface of the belt; λ—the coefficient of thermal conductivity, K 0 (x) and K 1 (x) are the MacDonald functions of zero and first orders, respectively; V s is the velocity of the source.

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The temperature during SPD in the contact zone was studied in the ANSYS software package using the finite element method. The task is axisymmetric elasto-plastic and has a three-dimensional (3D) character, but to simplify the calculation, it is performed in a two-dimensional (2D) model. The solution obtained for the section (2D) applies to the entire model. Contact interaction of two surfaces is simulated: spherical (tool) and flat (part). The axis of the sphere is fixed in the direction of the x-axis, the cylinder is fixed on the lower surface in all directions. The force Fn that acts on the surface of the sphere is determined during loading by the displacement of this surface along the y-axis. Tool material (ball material)—ShH15 steel; the processed material is titanium alloy VT-9. Properties of materials: isotropic elastic ball with modulus of elasticity E 1 = 2.2 × 105 MPa and Poisson’s coefficient ν 1 = 0.33, simulated part isotropic elastic-plastic with modulus of elasticity E 2 = 1.18 × 105 MPa, Poisson’s coefficient ν 2 = 0.35, breaking point σ v = 1300 MPa. We break the surfaces into finite elements, creating a finer mesh at the contact points. The results of determining the temperature in the contact region are presented in Fig. 1.

Fig. 1. Temperature distribution during SPD of titanium alloy VT-9 a ball rolling: V = 50 m/min, pH = 1500 N, b ultrasonic hardening: V = 50 m/min, Pst = 250 N, c ultrasonic hardening: V = 100 m/min, Pst = 250 N.

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As you can see, with ultrasonic hardening, the maximum temperature does not exceed 170 °C, and when ball rolling—180 °C, which indicates the identical effect of both methods on the temperature under optimal processing conditions. At the same time, with an increase in speed from 50 m/min to 100 m/min during ultrasonic hardening, the temperature in the contact zone increases from 174 to 596 °C, while the heating zone decreases significantly, since due to the low thermal conductivity of the VT-9 alloy and the high processing speed the heat flow does not have time to spread deep into the metal. In the process of an experimental study of temperature, the basic parameters of the process of ultrasonic hardening and ball rolling—the value of the static (normal) force and speed—were changed. The analysis of the results obtained theoretically and experimentally showed their good convergence. From the graphs shown in Fig. 2, it follows that the maximum temperature in the contact zone is determined by the force and processing speed, i.e., parameters that determine the amount of heat released in the contact area. During ultrasonic hardening with an increase in force from 100 N to 350 N and a speed from 15 m/min to 50 m/min, the maximum temperature rises from 600 to 1700 °C. During ball rolling, a similar dependence is observed.

Fig. 2. Dependence of the temperature in the contact zone on the effort and speed during ultrasonic hardening of the alloy OT-4: 1. V = 15 m/min; 2. V = 30 m/min; 3. V = 50 m/min, empty circle—experimentally; filled circle—in theory.

3 Conclusion A generalized solution is proposed for calculating the maximum contact temperatures during ball rolling and ultrasonic hardening by the method of moving sources. It was found that the maximum discrepancy between theoretical and experimental data, as a rule, does not exceed 12–16%. Determination of the temperature of the contact region makes it possible to check the selected modes by the maximum possible heating temperature, which is especially important when using optimal modes of surface plastic deformation.

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References 1. Nerubaj M, Kalashnikov V, Shtrikov B (2005) Physico-chemical methods of processing and assembly. Mechanical engineering, Moscow 2. Gubanov V (2010) Finishing and hardening of parts by smoothing. Strengthening Technol Coat 8:3–5 3. Kazantsev V, Kudryashov B, Nigmetzyanov R, Prikhodko V, Fatyukhin D (2009) Ultrasonic surface plastic deformation. Bulletin of the Kharkov National Automobile and Highway University, Kharkiv 4. Gubanov V, Gerasimov V (2006) Comparative evaluation of the quality of processing of cylindrical surfaces by cutting and smoothing. Technol Mech Eng 3:17–18 5. Gubanov V, Marfitsyn V, Orlov V, Shirtladze A (2008) Smoothing technology. Repair Restor Modernization 11:36–38 6. Gubanov V, Orlov V, Maslov D (2005) A new way of finishing by pressure. Technol Mech Eng 12:20–21 7. Dvoivnev A, Barats F, Aleksandrov S (2007) Improvement finishing and hardening treatment Surface diamond burnishing. Autom Mod Technol 4:36–39 8. Vologin M (2002) The use of ultrasound and explosion during processing and assembly. Mechanical engineering, Moscow 9. Markov A (1989) Ultrasonic processing of materials. Mechanical engineering, Moscow 10. Smelyansky V (2002) Mechanics of hardening of parts by surface plastic deformation. Mechanical engineering, Moscow 11. Gubanov V (2002) The formation of residual stresses when ironing parts with a wear-resistant tool. Strengthening Technol Coat 7:6–9 12. Ovseenko E (2011) The surface layer of non-rigid parts hardened by surface plastic deformation. Bulletin of the Kharkov National Automobile and Highway University, Kharkiv 13. Reznikov A (1986) Thermophysics of the processes of mechanical processing of materials. Mechanical engineering, Moscow 14. Reznikov A, Reznikov L (1990) Thermal processes in technological systems. Mechanical engineering, Moscow 15. Barats A, Kochetkov V (2013) Cooling of the deformation zone during finishing and hardening treatment by increasing the heat flux into the tool. Strengthening Technol Coat 6:33–37 16. Papsheva N, Akushskaya O (2012) The effect of SPD on the temperature in the contact area. SSAU, Samara, pp 303–305 17. Barats I, Maslyakova I, Barats F (2011) Mathematical models of technological thermophysics and physical interactions. SSTU, Saratov 18. Ilyicheva O (2012) The technology of logical modeling and analysis of complex systems. Eng Bull Don 4 19. Dec G (1989) Guide to the practical application of the Laplace transform. Science, Moscow 20. Neumoina N, Belov A (2006) Thermal processes in a technological cutting system. Polytechnic, Volgograd

Nonlinear Matching Between Forming Motions as the Basis for Machining Composite Surfaces with Simple Shape Tools S. K. Ambrosimov(B) and A. M. Kozlov Lipetsk State Technical University, 30, Moskovskaya Street, Lipetsk 398055, Russia [email protected]

Abstract. The article presents a classification of levels of matching between forming motions, three main levels of matching are distinguished. It provides a detailed description of the main forming diagrams with two linearly matched motions implemented in machining threads and gears, as well as two nonlinearly matched forming motions implemented in machining shaped surfaces and cams. The principles and possibilities of nonlinear forming based on nonlinear generation with the use of three complex-matched feed motions in the same plane are outlined. The options of generation with different cutting edge sliding factors in relation to the machined surface are analyzed. Forming with nonlinear profile generation makes it possible to machine complex surfaces like cams, toothed gears with different tooth shape with tools having a simple shape of the generating surface, with rectilinear cutting edges, e.g., side, cylindrical, and angular milling cutters. Machining with such tools on CNC machines makes it possible to significantly increase the profile machining precision due to the rectilinear cutting edges and to reduce or increase the cutting edge length or the profile length of the generating surface due to the profile slip of the tool. In the latter case, it reduces the thermal load on the cutting edge. Keywords: Machining complex-profiled surfaces · Nonlinearly matched forming motions · Nonlinear generating machining

1 Introduction A series of relative motions of the workpiece and of the tool’s generating surface required to obtain a given surface of the part represents the kinematic forming diagram. The tool’s generating surface, the kinematic forming diagram, and the actual surface shape are mathematically interrelated in such a way that the surface enveloping the considered sequential positions of the nominal surface of the part is the tool’s generating surface [1]. The forming kinematics consists of a kinematic diagram characterized by (i) a certain mutual direction of the constituent forming motions which are determined by the degree of freedom of the machine equipment, (ii) the quantitative relation between © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_114

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motions, and (iii) its reference to the generating surface. By moving the generating surface according to the kinematic forming diagram, a machined surface is obtained. An important factor in the method of forming is the ratio between the forming motions, the so-called matching. Matching between motions is a property that determines the inner structure of a kinematic diagram as a certain functional relation between the speeds of elementary motions or between the tool motions against the workpiece; the property is essential in forming a nominal surface. This ratio may be different for different machining methods.

2 Problem Statement The existing classifications of kinematic diagrams do not take into account the levels of matching between the forming motions and the cutting edge sliding during machining. Motions are matched in the machining of parts with a recurring profile, e.g., threaded, involute, etc. pieces, as well as of complex-shaped surfaces of dies, turbine blades, and cams. Usually, two motions are matched, e.g., when the main motion and the feed motion are matched, this is typical of hobbing; when two feed motions are matched, this is typical for milling-shaped surfaces using a radius end mill and for turning via hob peeling. Matching is ensured by machine tools with rigid kinematics. This either preserves a constant ratio between the speeds of matched motions or makes the ratio between the speeds of the motions change according to the law determined either by the copier form or the CNC machine program.

3 Theoretical Three levels of matched motions are distinguished. The zero level, i.e., the lack of matching, is characterized by that any ratio may be set between the speeds of forming motions to machine the surface, which, within certain limits, affects only the parameters of surface roughness and not the shape of the machined surface. The first level of matching is characterized by a constant certain ratio of motion speeds, i.e., when the speed of one motion to obtain the necessary surface increases, the speed of the other must increase equally. It is typical of tooth generation methods where forming is achieved via enveloping. On the second level of matching, the speed ratio of forming motions changes in time according to a certain law in the process of machining. The second level is used to machine shaped surfaces in matching the motions according to the program or the copier. For example, when machining dies, molds, ship propellers with radius end mills, the milling is traverse, and the XOY motions are nonlinearly matched (Fig. 1). When the tool is moving in the machining plane, the interrelation between two feed motions is constantly changing on the AA1 interval: the ordinate y1 motion is higher than the abscissa x 1 motion, and on the interval A1 A2 vice versa. In recent years, three nonlinearly matched motions have increasingly been used for milling composite surfaces. This machining requires that in order to increase the cutting speed, on some intervals, the workpiece is rotated in the XOY plane through an angle ϕ, which requires a three-axis matching of motions at a time.

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Fig. 1. Diagram of milling a shaped surface with two and three complex-matched forming motions.

Machining with three complex-matched motions can be used to form complexprofiled surfaces [2–6], e.g., toothed gears and other parts with a recurring profile. The cutting edge sliding factor P is determined by a value equal to the ratio of the cutting edge displacement speed in relation to its tip V 0 to the speed of the tip in the direction of feed V 1 or to the machined surface formation rate in the feed motion plane. Figure 2a, b presents two diagrams of machining a radius surface with a tool with a straight cutting edge whose cutting motion is perpendicular to the plane of the drawing with two matched feed motions in the plane of the drawing—(i) the workpiece rotation at a speed of ω = V 1 /r and (ii) reciprocating tool motions with the cutting edge displacement speed in relation to its tip V 0 . In the general case, for instance, if the profile rotation radius R exceeds the surface radius r, forming is possible only with three forming motions: one rotating and two reciprocating. Each diagram shows three contact points of the tool cutting edge A1 , A2 , A3 and the corresponding three points of the workpiece B1 , B2 , B3 , and the tool is shown in two successive positions. In the diagram (Fig. 2a), the cutter rolls along the machined surface at a speed of the vertex of the cutting edge, the greater the rate of formation of the machined surface in the plane of feed (displacement of the cutting edges A1 A2 , A2 A3 greater than the corresponding displacements of the workpiece B1 B2 , B2 B3 ), i.e., the sliding factor is greater than one. So it can be stated that the sliding speed (the relative motion speed) will be equal to V 01 = V 0 − V 1, while a cutting edge of greater length (A1 A3 ) is required to machine a part of the surface of a certain length (B1 B3 ). A special case is generating machining when the relative feed speed (sliding speed) is zero. With a further decrease in the cutting edge displacement speed in relation to the tip of the tool, at a constant surface formation speed, the sliding speed changes (Fig. 2b),

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Fig. 2. Diagrams of generating a radius profile when milling with a cylindrical mill. a The sliding factor is greater than one; b the sliding factor is less than one.

the profile interval of a certain length B1 B2 is machined with a cutting edge section of a shorter length A1 A2, etc. When the relative motion speed V 01 reaches the value V 1 , the tip stops moving in relation to the cutting edge V 0 = 0, and the surface formation speed V 1 is equal to the feed motion speed and to the relative motion speed (Fig. 3a), with the sliding factor 0 equaling zero, i.e., P = V 0 /V 1 . On the one hand, this significantly reduces the tool life, whereas on the other hand, it simplifies the method kinematics and the tool design. With a further decrease in V 0 , V 0 < 0 (Fig. 3b), the cutting edge length may be less than the interval of the machined surface, equal to it or greater, but the relative sliding speed in this case will change from −V 1 do −∞. The sliding factor is different for real methods of machining via nonlinear forming motions. For instance, when generating teeth and slots, three types of sliding are simultaneously implemented: in the area of the wheel tip 0 < P < 1, at the pitch point P = 1, and at the tooth root P > 1.

Fig. 3. Diagrams of generating a radius profile a the sliding factor is zero; b the sliding factor is less than zero.

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The analysis of the kinematic diagrams and of the nominal surfaces of complexprofiled parts made according to these diagrams makes it possible to conclude that the simpler the kinematic diagram [7–14], the more composite is the generating tool surface and vice versa. Thus, recurrent complex-profiled surfaces like gears, cams, etc. can be machined with universal tools with a simple shape of the generating surface, e.g., side mills or slab mills (Fig. 4), via three complex-matched forming motions with the sliding factor greater than one. The workpiece should move in such a way that when machining any point, the position of the rectilinear generator of the milling cutter generating surface be tangential to this point.

Fig. 4. Diagram of profile generation with three nonlinearly matched forming motions.

For example, at some interim point in time, the tool cylindrical generating surface touches the profile radius interval at the point A1 . In order to machine the profile interval from point A1 to Bi , the milling cutter must hold such a position in relation to the machined profile that the point Ai coincides with the point Bi and at the same time the rectilinear generator A1 Ai touches the profile on the interval A1 Bi at the point Bi . Since the machining is performed on the CNC machine and the position of the milling head with the tool is invariable, forming motions are performed due to the motion of the table with the workpiece. Thus, for machining the profile from A1 to Bi at a constant tool position, the table with the workpiece must rotate through an angle of ϕ and move axially through the values X and Y, i.e., the point Bi moves to the position Bij and the point Ai moves to the position of Aij . Since the cutting edge interval A1 Ai is shorter than the machined curved interval A1 Bi , machining is performed with a sliding factor of less than one.

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4 Conclusions The application of nonlinear matching makes it possible to simplify the cutting tool design, to apply tools with rectilinear generators of generating surfaces. It increases the precision of machining shaped surfaces in comparison with their machining with shaped tools when it is more difficult to guarantee the precision of curved profiles. A number of authors have proved that the cutting edge temperature depends on the motion speed of its tip in relation to the cutting surface [15–17], i.e., during slip generation, the temperature decrease depends on the cutting edge relative motion speed (the slip speed). A lower temperature, as well as an increase in the overall length of the main cutting edge, increases the cutting tool life [18–20].

References 1. Abrosimov SK (2006) Synthesis of new machining methods based on the orientation of forming motions in relation to the machined surface. STIN 4:2–7 2. Abrosimov SK (2001) A method of machining composite curved surfaces. RU Patent 2167746, 27 May 2001 3. Abrosimov SK (2005) Simulating the tool motion trajectory for machining composite surfaces. STIN 12:23–24 4. Abrosimov SK (2006) Simulating tool motion trajectories in machining surfaces like die impressions. STIN 8:33–35 5. Abrosimov SK, Kosenkov MA (2013) Improving the efficiency of machining of complex contours milled with rocking motion feed using CAD/CAM systems. In: Applied and fundamental studies proceeding. 2th international academic conference. Publishing House “Science and Innovation Center” and the International Journal of Advanced Studies, pp 198–203 6. Abrosimov SK, Meshcheryakov VN (2013) Improving the system of valve electric drive of CNC machine tools to provide efficient methods of milling. News High Educ Inst Chernozem Reg 4:9–13 7. Granovskii GI, Granovskii VG (1985) The cutting of metals. Vysshaya Shkola, Moscow 8. Ermakov YM (2003) Integrated methods for efficient machining. A technologist’s library, Mechanical Engineering, Moscow 9. Danilov VA (1995) The shaping machining of composite surfaces by cutting. Science and Technology, Minsk 10. Radzevich SP (2001) The forming of part surfaces. Fundamentals of the theory, Rastan, Kiev 11. Rodin PR, Lincoln GA, Tatarenko NM (1976) The machining of shaped surfaces on CNC machines. Tekhnika, Kiev 12. Petrushin SI The principles of forming with cutting blade tools. Tutorial, Tomsk State University, Tomsk 13. Lashnev SI, Borisov AN, Emelyanov SG (1997) A geometric system of surface formation with cutting tools. Kursk State Technical University, Kursk 14. Vasin SA, Vereshchaka AS, Kushner VS (2001) The cutting of materials: the thermomechanical approach to the system of relationships when cutting. Moscow Bauman State Technical University, Moscow 15. Vorontsov AL, Sultan-Zade NM, Albagachiev YA (2011) Development of a new theory of thermal cutting processes. Determination of thermal fields and contact temperatures when cutting materials. Part 2. J Mech Eng 4:73–80 16. Krivoruchko DV, Storchak MG (2012) The surface temperature of chips. Bull Nat Tech Univ Ukraine 64:56–62

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17. Tashlickii NN (2005) Features of wear of carbide tools in intermittent cutting. Eng Bull 7:55–56 18. Ambrosimov SK, Gribkov RV (2019) Deformation-cutting pulling with the cutting edge displacement in relation to the cutting surface. Bull Lipetsk State Tech Univ 2(40):41–46 19. Zelinsky VV, Borisova EA (2012) Establishing the prevailing types and causes of cutting tool wear. Eng Life Saf 2:55–60 20. Kosenkov MA (2013) Investigation of disk tool wear and temperature modeling in the contact zone during milling with the displacement of the cutting edge tip in relation to the cutting surface. Friction Lubr Mach Mech 10:38–40 21. Golembaevsky AI (1986) Foundations of systematology of ways of forming machining in mechanical engineering. Science and Technology, Moscow

Chip Formation Analysis in Finish Turning of Alloy and PM Hardened Tool Steels Using Coated and Uncoated PBCN Tools M. Ociepa1(B) , M. Jenek1 , and O. V. Yagolnitser2 1 University of Zielona Gora, 4, Szafrana ul., Zielona Gora 65-516, Poland

[email protected] 2 Moscow State Technological University “STANKIN”, 1, Vadkovskiy Lane, Moscow 127055,

Russia

Abstract. The article presents analysis of influence of the type of cutting blades made of composite materials based on cubic boron nitride (CBN) on the selected parameters of chip formation process during finish turning of hardened tool steels: Sverker21® (SV21) alloy steel and Vanadis 4 EXTRA SuperClean® (V4) powder metallurgy steel. The analysis showed smaller value of the average chip thickening coefficient Kh and friction coefficient μ after machining of V4 powder metallurgy steel by all tested blades, and over the entire range of the studied tool feed rates, as compared with SV21 alloy steel. The value of the sliding angle  was found to be smaller for all studied variables during machining of SV21 alloy steel. The highest intensity of changes in the values of all studied parameters was found for uncoated blades 7025 during machining of V4 powder metallurgy steel. Keywords: Hard machining · PCBN · Chip shape · PM · CBN coatings

1 Introduction Environmentally clean technologies are used more and more often in the industrial manufacture of machine parts [1]. The aspects related to ecology in a broad sense that influence decisions regarding the choice of optimal production methods, as well as issues related to energy efficiency of the process and minimization of the amount of waste generated during the production process, directly affect the cost efficiency of the production process [2–4]. Powder metallurgy (P/M) is one of the most rapidly developing areas related to manufacturing technologies and finds application, in particular, in aviation, automotive, tool, and machine industries. Smaller energy consumption and formation of less quantity of waste result in cost efficiency of its use as compared to traditional methods of manufacturing semi-finished products [5, 6], and also comply with the accepted global trends of environment friendliness [7]. Steadily growing interest is observed in recent years in regard to using powder metallurgy tool steel in different industries, primarily due to the well-defined chemical © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_115

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composition and high purity of this type of material [8, 9]. According to Erden et al. [10], P/M steels are characterized by improved microstructure properties as compared to conventional steels from the point of view of the most uniform distribution of carbides in the base material, as well as finer grain size. Even greater opportunities for application of P/M steels are also seen due to their high mechanical strength and wear resistance. The problem with components made of P/M steel is their low machinability [8]. Machinability is a concept that is difficult to define, and it means the set of measurable quantitative and qualitative parameters which analysis indicates feasibility of machining the material [11]. Machinability of P/M steel is regarded as low, comparable to machinability of forgings [8, 11]. This leads to more rapid wear of cutting tools, resulting in lower economic efficiency of machining of this group of materials. The two most debated aspects of low machinability of P/M steel relate to its low thermal conductivity due to porous structure, as well as repetitive micro-strikes of the blade against the material being processed—the lack of continuity of structure results in “quasi-interruption” of cutting. Low thermal conductivity of the processed material causes high temperatures in the cutting area, affecting the cutting blade and leading to its rapid wear. Micro-strikes of the blade against the processed material can cause cracks on the used protective coating and its rapid abrasive wear, resulting in increase of the final cost of manufactured finished parts [1]. According to Obikawa et al. [1], Salak et al. [12], this is one of the reasons for the still low popularity of these materials in production. The mentioned “quasi-interruption” of cutting can, however, be a reason for obtaining advantageous shapes of chips as compared to machining of traditional materials. The described aspects necessitate the application for processing of P/M steel of tools with substantially high durability and resistance to abrasive wear. These include, first of all, cutting blades made of polycrystalline cubic boron nitride (PCBN), which show very high efficiency in terms of their high strength, resistance to oxidation [13, 14], good thermal conductivity, and resistance to temperatures up to 1500 °C [15]. They are also chemically neutral in regard to iron and iron alloys, and chemically stable at high temperatures [16], what makes possible to use them in highly efficient processing of P/M steel. Tools made of PCBN are divided into two groups: the so-called BL group with low percentage of crystalline boron nitride (CBN) in the blade material (40–70%), and the so-called HL group with high, above 70%, CBN content [14, 16]. Machining of “hard” materials, that is, having hardness above 45 HRC according to [17, 18], is performed using dedicated cutting tools, which include tools made of PCBN. “Hard machining” of materials entails, in particular, reducing the time for preparation and manufacturing process, as well as increasing the efficiency of machining, which results in noticeable economic benefits. Moreover, these benefits are further increased due to no need for use of metal working fluids during machining, what makes this type of machining environmentally friendly [2, 17]. The use of protective coatings on the cutting blades (PVD or CVD) allows more efficient machining of P/M steels [17, 19]. Tools with coating compared to tools without coating are characterized by higher permissible mechanical and thermal load, reduced friction between the tool and the chip, and increased wear resistance of the blade in a

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wide temperature range in the area of the contact of the cutting edge with the processed material [20]. The objective of this study was a comparative analysis of the effect of cutting blades made of PCBN with coating and without coating on the characteristics and selected parameters of chips after finish turning of improved tool steel: P/M steel and alloy steel.

2 Experimental Approach 2.1 Workpiece Materials The following high-carbon tool steels were used in the research: P/M steel Vanadis® 4 Extra SuperClean (hereinafter: V4; C ~ 1.4%, Si ~ 0.4%, Mn ~ 0.4%, Cr ~ 4.7%, Mo ~ 3.5%, V ~ 3.7%), and alloy steel Sverker® 21 (hereinafter: SV21; C ~ 1.55%, Si ~ 0.3%, Mn ~ 0.4%, Cr ~ 11.3%, Mo ~ 0.8%, V ~ 0.8%). Samples in the form of rollers with dimensions ø = 50 mm, l = 20 mm were subjected to the process of thermal improvement according to the requirements of the manufacturer of both steels, providing hardness 60 ± 2 HRC. In case of P/M steel V4, the resulting structure is characterized by the presence of small carbide particles uniformly distributed in the base (Fig. 1b). While for alloy steel SV21, the resulting structure is characterized by presence of large primary carbide particles and small secondary carbide particles formed during tempering (Fig. 1a).

Fig. 1. Structure of heat-treated alloy steel SV21 (a) and P/M steel V4 (b).

2.2 Investigation Method and Tools Machining was done with the following cutting parameters: V c = 160 m/min, ap = 0.2 mm, f 1–5 =0.05; 0.075; 0.1; 0.125; 0.15 mm/rev. The cutter PDJNR2020K11 (κr = 93°, α = 6°, γ = −6°) with replaceable plates DNGA 110408 (r ε = 0.8 mm) was used in the study. Dry machining was performed. Machining was done using new cutting blades for each variable. Characteristics of the cutting blades are presented in Table 1. Scanning microscope JEOL JSM-6400 was used for metallographic studies. The chip thickness was measured ten times using ball micrometer with a measuring error of ±0.004 mm.

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Material type

CBN 7025

CBN 7015

CBN 020

Machining type

Continuous and semi Continuous interrupted

Continuous

PCBN structure

60% CBN (1.3 μm) in ceramic binder

50% CBN in ceramic binder

50% CBN in ceramic binder

Coating

NONE

TiN

TiAlN

Chamfer

BN = 0.1 mm GB = 20°

BN = 0.1 mm GB = 30°

BN = 0.13 mm GB = 25°

Cutting edge radius (r n )a

21.7 μm

17.17 μm

25.26 μm

a Average of 3 measurements

3 Results and Discussion 3.1 Chip Shape Change of the chip shape during machining of alloy steel SV21 (a) and P/M steel V4 (b) depending on the type of cutting blade and feed rate f is shown in Fig. 2.

Fig. 2. Chip shape depending on the type of cutting blade and feed rate f for: a SV21; b V4.

Analysis of changes in chip characteristics during turning of both materials (Fig. 2) shows that the shape of chips is more advantageous in case of machining P/M steel V4. For this material, the range of feed rate f for which the chip is obtained as short spirals or separate short fragments is large and applies to all studied cutting blades at feed rate above 0.1 [mm/rev.]. Such chip shape, according to [21], is easy to remove from the cutting area and does not damage the surface of the machined material during machining. In case of alloy steel SV21, advantageous shape of chips was obtained during machining using the blade MBC020 at feed rate f = 0.05 and 0.075 [mm/rev.], and using the blades 7015 and 7025 during machining at feed rate f = 0.15 [mm/rev.]. The least advantageous shape of chips in the form of long spirals, strips, or long straight segments was obtained mainly during machining of P/M steel V4 at feed rate below 0.1 [mm/rev.]

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and during machining of alloy steel SV21 using the blades 7015 and 7025 at feed rate below 0.15 [mm/rev.], and for the blade MBC020 during machining at feed rate above 0.075 [mm/rev.]. Such chip shape can damage the machined surface, resulting in increase of surface roughness and change of performance properties. 3.2 Characteristics of the Chip Formation Zone The main parameters describing the process of chip formation include: • Average chip thickening coefficient K h, determining the speed of the chip along the surface of the blade advance, • Sliding angle  determining the changes occurring on the surface of the material and tool wear, • Coefficient of friction μ on the rake face determining, in particular, temperature in the cutting area. Figure 3, 4 and 5 shows in succession the values of coefficient K h , sliding angle , and coefficient μ during machining of alloy steel SV21 (a) and P/M steel V4 (b).

Fig. 3. Values of average chip thickening coefficient K h depending on the cutting blade and feed rate f for: a SV21; b V4.

The smallest value of average chip thickening coefficient K h over the entire range of studied feed rates f and for all studied cutting blades was obtained during machining of P/M steel V4 (Fig. 3b). Depending on the value of feed rate f , it was, at the average, by 10–26% smaller than during machining of alloy steel Sv21 (Fig. 3a). The smallest change in the intensity of the analyzed parameter depending on the increase of feed rate f for P/M steel V4 was obtained during turning by blades 7015 coated with TiN, the largest change—during machining by uncoated blades 7025. For SV21 material, the intensity of change in the value of this parameter depending on increase of feed rate f was similar for all types of blades. The smallest value of sliding angle  over the entire range of studied feed rates f and for all studied types of the cutting blade was obtained for machining of alloy steel SV21 (Fig. 4a). Depending on feed rate f , it was, at the average, by 6–24% smaller as compared to machining of P/M steel V4 (Fig. 4b). The smallest change in the intensity

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Fig. 4. Value of sliding angle  depending on the type of the cutting blade and feed rate f for: a SV21; b V4.

Fig. 5. Value of the friction coefficient μ depending on the type of the cutting blade and feed rate f for: a SV21; b V4.

of the analyzed parameter depending on the increase of feed rate f for P/M steel V4 was obtained during turning by blades MBC020 coated with TiAlN, the largest change— during machining by uncoated blades 7025. For SV21 material, the intensity of change in the value of this parameter depending on increase of feed rate f was similar for all types of blades. The smallest value of friction coefficient μ over the entire range of studied feed rates f and for all studied cutting blades was obtained during machining of P/M steel V4 (Fig. 5b). Depending on the value of feed rate f , it was, at the average, by 10–28% smaller than during machining of alloy steel SV21 (Fig. 5a). The smallest change in the intensity of the analyzed parameter depending on the increase of feed rate f for P/M steel V4 was obtained during turning by blades 7015 coated with TiN, the largest change—during machining by uncoated blades 7025. For SV21 material, the intensity of change in the value of this parameter depending on increase of feed rate f was similar for all types of blades.

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4 Conclusions Basing on the analysis performed, the authors formulated the following conclusions: • The most advantageous shape of chips is obtained during machining of P/M steel V4 at feed rate f in the range of 0.1–0.15 [mm/rev.] regardless of the type of cutting blade used. • The value of average chip thickening coefficient K h and friction coefficient μ over the entire range of studied feed rate and for all types of studied cutting blades was the smallest during machining of P/M steel V4. • The smallest value of sliding angle  over the entire range of studied feed rate and for all types of studied cutting blades was obtained during machining of alloy steel SV21. • The largest intensity of change of the values of studied parameters was obtained for uncoated blades 7025 during machining of P/M steel V4.

References 1. Obikawa T, Ohno T, Yamaguchi M et al (2012) Wear characteristics of cutting tools in turning of sintered steel under different lubrication conditions. Key Eng Mater 523–524:13–18 2. Shvartsburg LE, Butrimova EV, Yagolnitser OV (2017) Energy efficiency and ecological safety of shaping technological processes. Procedia Eng 206:1009–1014. https://doi.org/10. 1016/j.proeng.2017.10.586 3. Shvartsburg L, Yagolnitser O, Butrimova E (2018) Integrated approach to providing for environmental friendliness and safety of the technological processes. MATEC Web Conf 224:01090. https://doi.org/10.1051/matecconf/201822401090 4. Zaborowski T, Shvartsburg L, Ivanova N, Ryabov S (2018) Ecoenergetic cutting techniques. Manag Prod Eng Rev 9(4):70–75. https://doi.org/10.24425/119547 5. Senthur Prabu S, Choudhary A et al (2014) Experimental study od dry sliding wear behaviour of sintered Fe-C-W P/M low alloy steels. Procedia Mater Sci 5:809–816 6. Nizam Khan M, Narayan S, Rajeshkannan A (2019) Influence of process parameters on workability characteristics of sintered Al and Al-Cu composites during cold deformation. AIMS Mater Sci 6(3):441–453 7. Shvartsburg LE, Butrimova EV, Yagolnitser OV (2017) Quantitative evaluation of the effectiveness of best available technologies of form-shaping. MATEC Web Conf 129:01027. https:// doi.org/10.1051/matecconf/201712901027 8. M’Saoubi R, Czotscher T et al (2014) Machinability of powder steels using PCBN inserts. Procedia CIRP 14:83–88 9. Selvakumar N, Mohan Raj A, Narayanasamy R (2012) Experimental investigation on workability and strain hardening behaviour of Fe-C-0.5 Mn sintered composites. Mater Des 41:349–357 10. Erden MA, Gunduz S et al (2017) Wear behaviour of sintered steels obtained using powder metallurgy method. Mechanika 23(4):574–580 11. Alizadeh E (2008) Factors influencing the machinability of sintered steels. Powder Metall Met Ceram 47(5):304–315 12. Salak A, Vasilko K et al (2006) New short time face turning method for testing the machinability of PM steels. J Mater Process Technol 176:62–69

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13. Slipchenko K, Turkevich V et al (2018) Superhard pcBN materials with chromium compounds as a binder. Procedia Manuf 25:322–329 14. Ociepa M, Jenek M, Feldshtein E (2018) On the wear comparative analysis of cutting tools made of composite materials based on polycrystalline cubic boron nitride when finish turning of AISI D2 (X153CrMoV12) steel. J Superhard Mater 40(6):396–401 15. Arsecularatne J, Zhang L, Montross C (2005) Wear and tool life of tungsten carbide, PCBN and PCD cutting tools. Int J Mach Tools Manuf 46:482–491 16. Slipchenko K, Petrusha I et al (2018) Investigation of the mechanical properties and cutting performance of cBN-based cutting tools with Cr3C2 binder phase. Procedia CIRP 72:1433– 1438 17. Sivaraman V, Prakash S (2017) Recent developments in turning hardened steels—a review. In: IOP conference series: materials science and engineering, pp 197 18. Ociepa M, Jenek M, Leksycki K (2019) The phenomenon of material side flow during finish turning of EN X153CrMoV12 hardened steel with tools based on polycrystalline cubic boron nitride. J Superhard Mater 41(4):265–271 19. Uhlmann E, Braeuer G et al (2004) CBN coatings on cutting tools. Res Dev Germany: Ann German Acad Soc Prod Eng 11:45–48 20. Zlamal T, Mrkvica I, Szotkowski T, Malotova S (2019) The influence of the surface treatment of PVD coating on its quality and wear resistant. Coatings 9(7):439 21. Maruda RW, Krolczyk GM et al (2016) Chip formation zone analysis during the turning of austenitic stainless steel 316L under MQCL cooling condition. Procedia Eng 149:297–304

Numerical Modeling of Metal Thin Layer Upset Forging with Extrusion into in Forging Cavity Under Stiffening Rib O. A. Nikitina1(B) and T. M. Slobodyanik2 1 Nosov Magnitogorsk State Technical University, 38, Lenin Ave., Magnitogorsk 455000,

Russia [email protected] 2 National Research Technology University NUST “MISIS”, 4, Leninsky Ave., Moscow 119049, Russia

Abstract. The authors conduct a stress-deformed state analysis of the material thin layer upset forging with extrusion into a forging cavity under the stiffening rib. A detailed analysis of the deformation ratio distribution and stress ratio distribution on the vertical axis of symmetry of a stiffness rib at various stages of calculation is provided. Also, a brief analysis of the deformation ratio distribution and stress ratio distribution in external forging fibers is conducted. A numerical experiment is made applicable to plane upset forging of the blank with the initial width of the body h0 = 16.13 mm to a final width h4 = 12.5 mm through intermediate stages with h1 = 15.5 mm, h2 = 14.5 mm, and h3 = 13.5 mm. At the same time, the cavity width under the stiffening rib is assumed as being equal to a final thickness of a forging body, the radius of the cavity conjugating with a deformed plane of forging 15 mm. The stiffening rib finite calculation height was 30 mm. During the research the authors quantitatively estimated stress changing and deformation ratio in external fibers and on the stiffening rib vertical axis of symmetry at forging. The calculation results were displayed in the form of distortion of a finite element grid and the isoline images of the considered values in the blank material. Keywords: Computer modeling · Areas of defects · Finite elements · Stamping long panels

1 Introduction The effective activity of enterprises in various industries is guaranteed by the efficiency of the equipment use. A rational design and effective use of equipment are considered in the research papers [1–10]. Forging and stamping production development requires a lot of parts of complex configuration with a thin body and high stiffening ribs, having sufficient rigidity and small weight. Defect-free forging according to a rational technology scheme is the purpose of © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_116

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development and implementation for each product item. Recently, the design process and production of aluminum alloys forging have been increasing. Mastering a new technology for long panel stamping involves great material and energy resources for experimental work conduct in industrial conditions [11]. Computer modeling of technological processes allows reducing costs. The finite elements method are often used for solving the problems of large plastic deformations. Numerical modeling results are the distributions of the deformation ratio and stress ratio in the forging fibers at various stages of upset forging. They allow studying the nature of the distribution of these values in the blank material and identifying the most difficult zones for forging. In addition, computer modeling allows predicting the areas of defect formation at long panel stamping. The analysis of a stress–strain state at upset forging with flowing into a forging cavity under a stiffening rib, conducted by the finite element method, is described in article [12, 13]. The detailed analysis of ratio deformation and stress distribution in external forging fibers at different stages of upset forging is conducted [14]. In this paper the authors perform a detailed analysis of the distributions of deformation ratio and stress ratio in the forging fibers on the stiffness rib vertical axis of symmetry at the various stages of upset forging.

2 Main Part A numerical experiment is carried out applicable to the alloy 1024. The blank in forging was divided into 480 elements and deprived of broadening. The array of input data also includes tension modulus of a forging material E f = 2 × 105 MN/m2 , the one of a blank material E b = 0.746 × 105 MN/m2 , Poisson’s coefficient ν = 0.3, the forging temperature—320 to 400 °C, the blank temperature—400 °C, the coefficient of friction between a blank and forging—μ = 0.15. A numerical experiment is made applicable to the plane upset forging of the blank with the initial width of the body h0 = 16.13 mm to the final width h4 = 12.5 mm through intermediate stages with h1 = 15.5 mm, h2 = 14.5 mm, and h3 = 13.5 mm. At the same time, the cavity width under a stiffening rib was assumed as being equal to the final thickness of a forging body, the radius of cavity conjugating with a deformed plane of forging—15 mm. The final calculated stiffening rib height was 30 mm. During the research, the authors quantitatively estimated stress changing and deformation ratio in external fibers and on the stiffness rib vertical axis of symmetry forging. They also assessed the pressure of forging on the blank. The calculation results were displayed in the form of distortion of a finite element grid and the isolines images of the considered values in the blank material. A brief analysis of the deformation ratio distribution and stress ratio distribution in external forging fibers provided the following results. During upset forging a maximum deformation ratio was fixed in a middle part of the body width, on the left and right of the stiffening rib, while the minimum ratio deformation was fixed on a conjugate part of the plane deforming surface of forging with a radius part of the cavity under the stiffening rib. In the proximity to the middle plane of the stiffening rib the deformation ratios increase again, which does not contradict [15]. With the increase in the rib height

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and the reduction of forging, the blank compressive stress in the external forging fibers increases monotonically similar to the distribution of the deformation ratio at each stage of calculations. The minimum values of deformation ratio at the second, third, and fourth stages are almost the same on the bands of a forging body. Stresses in the considered zone have variable values: they increase at the first, second, and third passes by 50–52%, while at the final pass the stress increment is 20–25%. It is necessary to analyze the distributions of deformation ratio and stress ratio in the forging fiber on the stiffness rib vertical axis of symmetry at the various stages of calculation (Fig. 1).

Fig. 1. Distribution of deformation ratio in the forging fibers on the vertical axis of symmetry of the stiffness rib at different stages of upset forging: 1—h1 = 15.5 mm, 2—h2 = 14.5 mm, 3—h3 = 13.5 mm, 4—h4 = 12.5 mm.

The minimum values of deformation ratio do not qualitatively change with the increase in the rib height (Fig. 2, node number 225 of the computational finite element grid) and are located in the zone of symmetry above the rib (node number 991 of the computational finite element grid). With the increase of the rib height, the deformation ratio values increase in a suprarib zone, their difference is 60–70%. Stress ratio distribution differs in many respects from the deformation ratio distribution (Fig. 3): maximum stress values are in the radius

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Fig. 2. Computational finite element grid.

zone (node number 225 of the computational finite element grid). During the initial stage of calculations, stress does not change qualitatively along the rib. The increase in stress occurs on the subsequent stages of calculations. The minimum values are located in the area close to a deformable surface (nodes number 991, 82 of the computational finite element grid). Stress distribution on the axis of the stiffening rib is heterogeneous: stressdeformed state transforms from compression in the supra-rib zone into the tension in the rib lower zone. This does not contradict the distortions of the computational coordinate grid (Fig. 4). The numerical experiment allowed revealing the area of defect formation in the forging cavities of long panels. Sink mark is the most common defect of a supra-rib zone of forging cavities in long panels.

3 Conclusions The analysis of the stress–strain state at upset forging with flowing into a forging cavity under the stiffening rib showed that the method presented is suitable for the calculation of the plastic forming of forge pieces with a prominent lateral surface. Computer modeling [16] allows obtaining the shape and size of the initial part blank. The analysis of the results of computer modeling allowed identifying two factors affecting the defect development: the radius of the body conjugating with the stiffening rib and the rib width.

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Fig. 3. Stress distributions in the forging fibers on the vertical axis of symmetry of the stiffness rib at different stages of upset forging: 1—h1 = 15.5 mm, 2—h2 = 14.5 mm, 3—h3 = 13.5 mm, 4—h4 = 12.5 mm.

Fig. 4. Computational coordinate grid distortion at different stages of upset forging: a h0 = 16.13 mm, b h1 = 15.5 mm, c h2 = 14.5 mm, d h3 = 13.5 mm, e h4 = 12.5 mm.

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Fig. 4. (continued)

References 1. Zarubina EM, Nikitina OA, Slobodyanik TM (2018) Organization of training for small and medium business entrepreneurs in an industrial city. In: Proceedings of the international scientific conference “Far East Con” series “advances in economics, business and management research”, pp 132–134 2. Nikitina OA, Kharitonov AO (2013) Determination of rational parameters of the forming process of plastic mass. In: 21st century technologies in food, processing and light industry, vol 7, pp 5 3. Nikitina OA, Slobodyanik TM (2007) Using Baumol’ s model in management of enterprise’ s capital. Appl Math Econ Tech Res 1(1):72–73 4. Nikitina OA, Slobodyanik TM (2015) Analysis of power of mechanisms of overturning wagons. Min Inf Anal Bull (Sci Tech J) 9:183–186 5. Slobodyanik TM, Nikitina OA (2018) Projecting of the planetary gear in mining equipment. Min Inf Anal Bull (Sci Tech J) 7:46–52 6. Slobodyanik TM, Nikitina OA (2018) Projecting of low costing actuators in mining machines. Min Inf Anal Bull (Sci Tech J) 7:115–120

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7. Nikitina OA, Litovskaya YuV, Ponomareva OS (2018) Development of the cost management mechanism for metal products manufacturing based on budgeting method. Acad Strateg Manag J 17(5):1–7 8. Gerasimova AA, Radyuk AG, Titlyanov AE (2015) Creation of a diffusional aluminum layer on the narrow walls of continuous-casting molds. Steel Trans 45(3):185–187 9. Slobodyanik TM, Balakhnina EE (2020) Dynamic analysis of elementary differential gear with rigid links. IOP Conf Ser Mater Sci Eng 709:033066 10. Slobodyanik TM, Balakhnina EE (2020) Dynamic analysis of elementary differential gear with elastic links. IOP Conf Ser Mater Sci Eng 709:044008 11. Nikitina OA (2005) Development of design methodology for stamping of aluminum panels with single-sided fins using the vertical hydraulic presses. Moscow State University of Steel and Alloys, Moscow, Disertation 12. Solomonov KN, Nikitina OA (2003) New developments in technology for die forging. Izvestiya Ferrous Metal 3:22–25 13. Li Gunghin, Lei Chun, Sun Sheng, Guan Tingdong (1989) A system of CAS/CAD system for die forging process. J Jpn Light Metals 7:295–300 14. Nikitina OA, Slobodyanik TM (2019) Numerical modelling of the material layer upset forging with extrusion under the stiffening rib into forging cavity. Lect Notes Mech Eng 1071–1077 15. Altan T, Fyorentino R (1972) Calculation of forces and stresses during die forging. Eng Des Technol 4:64–77 16. Maiorova TV, Ponomareva OS (2015) The methodology of economic evaluation of enviromental management of metallurgical industry. Bull Magnitogorsk Tech State Univ G.I. Nosov 4(52):112–116

Calculation of the Stress–Strain State of the Polymer Material in the Cutting Zone O. Erenkov(B) , I. Lopushanskii, and D. Yavorskii Pacific National University, 136, Tikhookeanskaya Street, Khabarovsk 680035, Russia [email protected]

Abstract. This article presents the results of theoretical studies of the stress–strain state of polymeric materials in the cutting zone during turning. The commonality of the processes of destruction and cutting of materials is substantiated. The scheme is given to determine the components of the cutting force during turning. To calculate the orthogonal projections of the cutting force, the hypothesis of the equality of the tangential stresses during cutting and during compression or tension is used. An expression is obtained that allows one to evaluate the stress–strain state of the material in the cutting zone. This expression is consistent with the known patterns of destruction of solid polymer materials. Thus, dependence is obtained for the shrinkage coefficient expressed in terms of the physical constants of the material being processed. Keywords: Polymeric materials · Turning · Cutting force · Cutting zone · Stress · Shrinkage coefficient

1 Introduction Currently, there is a significant number of theoretical and experimental studies of the polymeric materials destruction process under the mechanical load action [1–7]. The solid destruction is generally the result of overcoming the interaction forces between its atoms and molecules which can occur under the influence of thermal energy, mechanical stress, radiation, electrical discharges, etc. The materials processing by cutting and polymers in particular can be represented as a kind of fracture process. And this process is accompanied by a dynamic effect of the cutting tool edges on the surface to be treated. The commonality of the fracture and cutting processes was established in the works of V. A. Kudinov, Yu. G. Kabaldin, V. N. Poduraev [8–11]. The authors substantiated theoretically and proved experimentally the occurrence of both processes when the acting stresses exceed the tensile strength of the material. The results of numerous studies [12–17] found that when cutting any solid materials, the formation of chips is preceded by the creation of a stress–strain state of the material in the cutting zone. Such a state is created by the cutting edge of the tool that has introduced and moving in this processed material. As the tool is introduced into the material, © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_117

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the stress in the cross section of the workpiece becomes more critical, the material is destroyed under the action of elastic and plastic deformation with the formation of a main crack.

2 Stresses in the Cutting Zone When studying the chip formation zone it was found that significant compression deformations arise in the volume of the future chip element before fracture occurs along the cleaving plan. These deformations cause the material of the shear layer to flow along and perpendicular to the front surface of the tool. Failure will occur when compressive stresses exceed the yield strength of the deformable material. The normal stress on the conditional shear plane, causing compression of the material during cutting, can be defined as σcd = Fc∂n sin β/ab,

(1)

where a is the thickness of the slice; b is cut width; β is the shear angle; Fc∂n is normal force (perpendicular to the conditional plane of shear). The shear angle β can be determined by the ratio tgβ = cos γ /(k − sin γ ), where k is the value of the coefficient of the material shrinkage; γ is the front angle of the cutting edge of the tool. In this case, the normal force Fc∂n can be determined through the force R of chip formation according to Fc∂n = R sin(β + ω),

(2)

where ω is the angle of action, i.e. the angle between the chip forming force vector and the cutting speed vector (Fig. 1). To determine which you can use the dependence ω = C − arctg

cos γ , k − sin γ

(3)

where k is the shrinkage coefficient of the chips, which is determined experimentally; C is a constant value, which, characterizing the invariability of the sum of angles ω+β = C for practically applied cutting conditions [9]. Thus, the definition of normal stresses is reduced to the determination of chip formation force, i.e., the force with which the front surface of the tool acts on the chips. It is convenient to  determine the chip formation force through its projection on the axis (Fig. 1), i.e., R = Pz2 + Px2 + Py2 . The classical approach to determining the stress–strain state in the chip formation zone does not always take into account the axial component of the cutting force Pz. However, in the case of polymer materials processing the axially directed force Pz has a significant effect on the material cutting process course o and the formation of the processed surface quality indicators. Over the past few decades, a number of works have been published in the literature in which cutting forces are analytically associated with the physical and mechanical characteristics of the material being processed. In this paper, to calculate the orthogonal

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Fig. 1. Scheme for determining the cutting force components during turning

projections of the cutting force, we use the technique proposed by N. N. Zorev. The basis of this technique is the hypothesis that the tangential stresses are equal when cutting and when compressing or stretching, provided that the relative shifts are equal [15]. According to Kudinov [11], the main component of the chip formation force can be calculated as   (4) Pz = τy st ctgβ + tg(β + ω) , where s is the feed; t is the cutting depth; τ y is the plastic shear resistance of the chip material. The remaining projections of the chip formation force are calculated as Px = Pz KX , Py = Pz KY ,

(5)

where KX , KY are the coefficients characterizing the ratio of the chip formation force projections on the coordinate axis:   (μ cos ν − sin γ ) sin β − (cos γ + μ cos ν sin γ ) sin λ + μ sin ν cos λ cos β ; KX = (cos γ + μ cos ν sin γ ) cos λ − μ sin ν sin λ   (μ cos ν − sin γ ) cos β + (cos γ + μ cos ν sin γ ) sin λ + μ sin ν cos λ sin β KY = . (cos γ + μ cos ν sin γ ) cos λ − μ sin ν sin λ (6) These expressions are obtained from the analysis of the forces equilibrium conditions on the tool front surface for the most general case of cutting. Here μ is the average coefficient of friction. The model presented in [16] made it possible to obtain a physical equation that takes into account the relationship between the shear angle and the average coefficient of friction, μ, μ = tg(90◦ + γ − 2β).

(7)

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The chip deflection angle ν determines the orientation of the force R relative to the front surface of the tool. This angle can be calculated as ν = η − V −0.08 arctg(tgλ cos η + tgγ sin η).

(8)

The coefficient η is determined from the expression:  s r (9) + tg(0.5β) sin2 β, sin 2η = t t where λ is the angle of the main cutting edge inclination; r is the radius of the tool transition cutting edge curvature. Given this assumption and taking into account Eq. (5) the chip formation force R in the general case is defined as  (10) R = Pz 1 + KX2 + Ky2 , where Pz the main component of the cutting force: cos ω . Pz = τy st sin β cos(β + ω)

(11)

As is known it is easy to determine [16] τy value with a sufficient degree of accuracy from the data of polymeric material tensile testing. In mechanical tests, the polytrophic relationship between shear stress τ and shear ε is well observed τ = Aεm ,

(12)

The extrapolation of this dependence to the region of large deformations inherent in the cutting process (ε = 2.5) gives values close to τy . Therefore, we can use the relation τy = A2.5m .

(13)

In addition, an approximate dependence can be used to determine τy τy =

0.6σb , 1 − 1.7ψB

where σb is the tensile strength; ψB uniform relative narrowing of the sample. Given (5) and (5) we define the chip formation force as  Pz μ2 + 1. R= (cos γ + μ cos ν sin γ ) cos λ − μ sin ν sin λ

(14)

(15)

Then the normal stress on the conditional plane taking into account (1), (4), and (11), is determined from the expression:  τy tg(β + ω) cos ω σcd = μ2 + 1. (16) (cos γ + μ cos ν sin γ ) cos λ − μ sin ν sin λ Thus, expression (16) is obtained, which allows one to evaluate the stress–strain state of the material in the cutting zone. This expression is consistent with the known patterns of destruction of solid polymer materials. By changing the stress–strain state, it is possible to control the process of chip formation during cutting of a polymer material, which affects the quality indicators of the surface layer.

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3 Shrinkage Coefficient The surface quality of the at polymer materials turning largely depends on the deformation nature and magnitude of the processed material during processing. Is known shrinkage of the chips is the external manifestation of the deformation process in the presence of significant plastic stresses. The degree of chips shrinkage is estimated by the value of the shrinkage coefficient [5]. Shrink coefficients take different values for different materials and conditions and are the basis for a comparative qualitative analysis of the factors influence on the chip formation nature [8, 18]. The mechanical stress acting on the material is the main factor affecting the structural strength and the destruction process of the polymer material as already noted [18, 19]. In this regard, the relationship between the magnitude of the applied stresses and the shrinkage coefficient of the chip is of scientific and practical interest. At the present stage, physical ideas about the strength of polymeric materials are based on the kinetic concept of strength. The main relation of the kinetic theory of destruction is written in the form of an empirical equation Zhurkova [20]:  U0 − γ σ , (17) t = t0 exp KT where U 0 is the activation energy of the fracture process elementary breaking act in the absence of stress, which is close in magnitude to the chemical bonds energy for polymers; γ is a coefficient depending on the material nature and structure and the γ values change with a variation in the material structure; t 0 is the time of atoms thermal vibrations in solids; K is the Boltzmann constant; T is the absolute temperature; σ is the average stress in the sample. The concept of chip formation frequency had been introduced in the work [8]. This concept is used as one of the characteristics of the materials machining process and is determined by the expression: 1000V , (18) 60kh where V is the cutting speed; k is the shrinkage coefficient of the chip; h is the thickness of the chip element. We represent the chip formation frequency parameter as the transition frequency of the shifted material element into the chip. Based on the established [8–11] commonality of the solid materials destruction and cutting processes the chip formation parameter is equal to the frequency of bond breaking and is expressed by the following dependence: fcmp =

1 . (19) t Solving together (17)–(19) with respect to the shrinkage coefficient we obtain   −γ σ 103 Vt0 exp U0kT K= . (20) 60h Thus, the dependence (20) is obtained for determining the shrinkage coefficient of the chips, expressed through the physical constants of the processed material and taking into account the stress state level of the workpiece material in the cutting zone. fcmp =

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4 Conclusion In this work, we obtained formulas of very important and interrelated characteristics of polymer composite materials cutting process such as material stress in the cutting zone and the chip shrinkage coefficient. Based on the magnitude of the material stress–strain state it is possible to justify the selection of the pre-treatment parameters of the workpiece by external influences and make the right choice of the tool geometric parameters. The chip shrinkage coefficient allows to evaluate the nature of the chip formation process and to predict the type of chip produced. In general knowledge and accounting of the stress in the cutting zone and the chips shrinkage coefficient will ensure the required quality of the processed surface and the productivity of the polymer materials turning process. Acknowledgements. The reported study was funded by RFBR according to the research project № 20-08-00039.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Kaminsky AA (1988) Mechanics of the destruction of polymers. Naukova Dumka, Kiev Fuji T, Dzako M (1982) Mechanics of the destruction of composite materials. Mir, Moscow Cherepanov GP (1983) Mechanics of the destruction of composite materials. Nauka, Moscow Kartashov EM, Tsoi B, Shevelev VV (2002) Structural—statistical kinetics of polymer destruction. Chemistry, Moscow Ratner SB, Yartsev VP (1982) Physical mechanics of plastics. Nauka, Moscow Ogibalov PM, Lomakin VA, Kishkin BP (1972) Polymer mechanics. Publishing house of Moscow University, Moscow Askadsky AA (1983) Chemical structure and physical properties of polymers. Chemistry, Moscow Kabaldin YuG, Shpilev AM (1998) Self-organizing processes in technological systems for machining diagnostics and control. Dalnauka, Vladivostok Kabaldin YuG, Oleinikov AI, Shpilev AM, Burkov AA (2000) Mathematical modeling of selforganizing processes in technological systems of cutting processing. Dalnauka, Vladivostok Poduraev VN (1974) Cutting of hard-to-handle materials. Higher School, Moscow Kudinov VA (1967) Dynamics of machine tools. Mechanical Engineering, Moscow Erenkov OYu, Kovalchuk SA, Gavrilova AV (2007) Combined method of plastic work piece machining based on a pretreatment mechanical down. Rare Met 26:20–24 Rosenberg AM (1990) The mechanics of plastic deformation in the processes of cutting and deforming drawing. Naukova, Dumka Ivakhnenko AG, Kuts VV (2013) Predesign studies of metal cutting systems. South-Western State University, Kursk Zorev NN (1966) Questions of the mechanics of the process of metal cutting. Mashgiz, Moscow Yacheritsin PI (1990) Theory of cutting. Physical and thermal processes in the technological system. New Knowledge, Minsk Davim JP (2013) Nontraditional machining processes: research advances. Springer Science & Business Media, New York Erenkov OYu, Faleeva EV, Erenkov SO (2012) Studies of the influence of cutting parameters on the type of chips during the turning of polymeric materials. Bull Mech Eng 9:68–70

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19. Ahmad J (2009) Machining of polymer composites. Springer Science & Business Media, New York 20. Zhurkov SN (1987) Kinetic nature of the strength of solids. Solid State Phys 29:156–160

Research on Formation of Microgeometry of Work Surface of Grinding Wheel T. N. Ivanova1,2(B) and Witold Biały3 1 Tchaikovsky Branch of Federal State Budgetary Educational Institution of Higher Education “Perm National Research Polytechnic University”, 73, Lenin Av., Tchaikovsky 617764, Russia [email protected] 2 Federal State Budgetary Institution of Science “Udmurt Federal Research Center, Ural Branch of the Russian Academy of Sciences”, 34, Tatyana Baramzina St., Izhevsk 426067, Russia 3 Silesian University of Technology, 26, Roosevelta Street, Zabrze 41-800, Poland

Abstract. As a grinding wheel rotates, every grain acquires a certain trajectory of movement, sequence, and duration of contact with a machined part. The grains can be divided into four groups: working, contacting, screened, and non-operational ones. The main characteristics of formation of the microrelief of the wheel work surface depend on the law of difference in altitude of cutting edges and corner radiuses of their tops. The studies on the kinematics of interaction between a grinding wheel and a machined surface during face grinding showed that overlapping of scratches across the width occurs at a smaller depth. The cutting depth of a grinding wheel does not depend on the value of longitudinal and cross feed, but it is determined by the law of grain distribution in the volume of abrasive layer as well as the shape of the tops of abrasive grains. It is established that abrasive grains, located in the work surface layer to the cutting depth, are in the most unfavorable conditions due to their small amount and highest difference in altitude. It leads to an increase in the size of the chip, occurrence of the highest cutting forces, and wear of grains. Keywords: Grains · Grinding wheel · Microrelief · Work surface of the wheel

1 Introduction The possibility of chip removal is governed by the section thickness, properties of metal under deformation speed, geometric parameters of cutting edges of the wheel. Randomized geometry and arbitrary location of cutting edges on the work surface of grinding wheel allow the application of probabilistic-statistical approach for description of regularities of the grinding process [1–20]. The main characteristics of formation of microrelief of work surface of the wheel depend on the law of difference in altitude of cutting edges and corner radiuses of their tops. In general, cutting edges of a wheel are expressed as a random variable. There © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_118

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are different opinions about the law of difference in altitude of cutting edges of work surface of the wheel. Some researchers accept the equal probability law, considering that abrasive grains are uniformly located in the cutting layer of the wheel, while the others prefer the normal distribution law and still there are ones, who accept complex laws. It can be explained by errors of methods and relief measuring equipment as well as simplification during statistical description of relief and parameters of grinding process [1–9, 12]. 1.1 Theoretical Part To determine the difference of altitude of cutting edges of the wheel it is necessary to consider uniform distribution of grains in the volume of the wheel, the influence of wheel dressing, and the nature of its wear in the grinding process, when several cutting edges are formed on grains in the external layer of the wheel. What is more, the role of the binder should be considered too, because in some cases it allows formation of several cutting edges on the tops of the abrasive grains and retains them on the surface of the wheel, while in the other cases it does not. In most grinding operations, only the upper part of the wheel microrelief takes part in work, which constitutes not more than one tenth of a profile height for grit size 100/80. Consequently, the formation of several cutting edges occurs in an external part of the profile during wheel dressing and wear. Then the amount of cutting edges in the external part will increase and change the law of difference in altitude. That is why it can be assumed that the shape of distribution density curve of cutting edges and its asymmetry will depend on the strength of grain retaining by the binder, grain size, their brittleness and conditions of wheel dressing and grinding. The analysis of the most widespread distribution laws (normal, log-normal, exponential, gamma and beta distribution, Rayleigh distribution, Weibull distribution, etc.) shows that two-parameter beta distribution is the most optimal distribution type for a description of all possible cases of the law of difference in altitude of cutting edges on the work surface of the wheel. It is applied for random variables limited from two sides. This distribution has special cases, which represent uniform, triangular, parabolic, and asymmetrical distribution with positive and negative skew [1–5]. The distribution of corner radiuses of tops of abrasive grains can be described by beta or gamma distribution, log-normal distribution and Rayleigh distribution. The law of distribution of corner radiuses of tops of abrasive grains on the work surface of the wheel can be found experimentally. To do this, it is necessary to project cutting grains of the wheel on a polished surface of a sample in the process of rotation. The projection of traces of separate grains on the surface of the sample will be seen under a microscope (Fig. 1). The grains of the wheel located in an external layer will encounter a sample in different points according to a difference in altitude. By measuring scratches displacement on the sample, we can separate the grains whose difference in altitude is fractions of a micron. Let us consider the sequence of grain cutting into a surface (Fig. 2). The scratch of the most protruding grain was accepted to be the beginning. In sections 1–1 and 2–2, which show projections of all grains of the wheel on the given level of cutting, we can observe the traces from separate protruding grain tops without kinematical overlapping.

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Fig. 1. Scheme of sample surface scratching by grinding wheel.

These sections are shown as separate scratches, the shape of which is similar to the shape of the grain top in a plane being perpendicular to the cutting speed vector. However, in sections 2–2, 3–3, and 4–4 (Fig. 2) the tops of grains overlap increasingly, causing the scratch to show the traces of their collective action, which makes it impossible to determine the shapes of the tops of separate grains depending on the shape of the scratch. It is clearly demonstrated after full overlapping of scratches in section 5–5 (Fig. 2c, g). 1.2 Experimental Part Depending on the number and the character of combined movements as well as the shape of machined part, grains make movements along complex trajectories of relative displacement during the cutting process. The traces of a set of trajectory curves of grains stay on the machined surface. The process of allowance removal by abrasive machining represents the combination of cutting under high plastic deformations and friction under high unit pressure and considerable heat emission. With the wear of an abrasive layer of a grinding wheel, the grains that were previously screened appear on the surface and come in contact with the machined surface. In an abrasive wheel there are no grains, which are not engaged in work of deformation of the machined material. As the same grains in different moments of time can be both removing chip and displacing the material plastically, they are usually are not considered separately from the contacting ones. Using distribution law and taking screening phenomenon into account, the amount of cutting grains in a surface layer is limited and constitutes few percent from the total number of grains in the wheel, while immediately contacting grains amount to several tens.

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Fig. 2. Scheme of formation of sequential group scratches in the sections of plane.

Along with a surface layer, let us single out a working layer. The working layer should be considered as the space under the binder of the tool, in which protruding grain tops are placed. It is worthwhile to additionally separate a surface working layer, in which the tops of the grains directly deepen inside a machined material. In the working layer of the tool, the main work on grinding is fulfilled and the machined material is separated. The products of its dispersion, resulting slurry (remains of abrasive grains and binder), and lubricant-cooling fluid accumulate in the working layer. In connection with these, to reach the optimal grinding the next inequality must be true: Surface working layer < working layer That is the cutting depth of grains of surface working layer always must be less than the depth of grain protrusion under the binder. Consequently, we have subordinating layers: Surface working layer < working layer < surface layer.

Research on Formation of Microgeometry of Work

The minimal number of scratches for their merging into one groove will be  π 2 Lm π Dwl = , Zmin ≥ 2 t 4 πt

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(1)

where t—penetration depth, Dwl —diameter of the grinding wheel. Equation (1) is used for a calculation of the minimal number of grains, placed on some circumference in a staggered order, with an average distance between them being Lm . Equation (1) demonstrates that during wheel construction it is necessary to keep the distance between the grains in accordance with the grinding depth. Thus, for example, to remove the allowance t = 0.01 mm if the distance between the grains is L m = 1 mm it is enough to have Z min = 100 and wheel diameter Dwl = 30 mm. The size of the wheel will increase, if the calculation is based on condition for obtaining longitudinal irregularities, which are not exceeding a specified value Ra . Installed, that grinding wheel grains 1, 2, 3, 4 under cutting depth t c > form overlapping scratches. After the end of the grinding process irregularities with a respect to surface level of the part II–II still remain, they are equal to Ra . The number of grains  π Dw π Dkp = . (2) Z0 = Lm 2 Ra The distribution of grain tops along the grinding width to the depth h0 is determined by profilograms of scratches (Fig. 3a). At the length 0.8 mm there are seven collective scratches, formed by three or more grain tops (I, IV, VII). Obviously, the tops of the grains do not overlap before reaching the depth h, so it can be said that the number of grains, located on the one circumference is Z = 1. Then, the kinematic interaction between a grinding wheel and a flat part (pic. 3) comes down to the scheme of scratching by the one grain. In the depth interval from h to hi , when scratches merge along the grinding width, the probability of occurrence of several scratches located one after another grows. In this case, the difference in altitude of grains with a respect to rotation circumference is saved.

Fig. 3. a Profilogram of irregularities; b graph of grain tops distribution along the depth of diamond layer AC6 100/80 M04 4 (FEPA D126 125/106 K75 m).

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Let us estimate the probability of occurrence of m = 1, 2, 3 … grain tops one after another on the surface of an elementary wheel with diameter d and width b, which is commensurate with an average width of grain tops on the considered depth hi . If we take into account that in the real tool a grain can be located with any geometry with a respect to an external working surface, we accept a sphere of certain radius as an equivalent shape of grain, considering all its external points are cutting. Therefore, the calculation of b value will be carried out basing on the assumption that grains are globules with the diameter d 0 . In this case we have the next equation for radial tops  2  b = 2 1/3d0 h = √ d0 h. 3

(3)

Equation (3) shows an increase in the calculated value b and the growth of probability that grains will hit one after another as the abrasive wheel deepens in a surface layer. Using the data from surface scratching (Fig. 3) we determine total amount of cutting grains in the layer Z i for different ti by drawing the tangent line. Then their density is found according to the formula λs = π DZwli B , where Dwl is a wheel diameter, B is a wheel width. Having determined these parameters and knowing the wheel area, the Poisson parameter can be defined: b as = λs bπ Dwl = Zi . B

(4)

So, the probability of grain locating on an elementary circumference of the wheel with the width b is determined according to the formula  m   Zi Bb b exp −Zi . (5) Pm = m! B The results of the calculations of probability that separate working grains are located on the one circumference of rotation on different levels of surface working layer are shown in Table 1. The number of working grains is demonstrated graphically on Fig. 3b. Before reaching the depth h0 = 6 µm, grain distribution follows some monotonous curve (Fig. 3b), which reflects the growth of grain density along the depth of a surface layer. Then the grain distribution gradually starts lagging behind the curve due to a higher degree of overlapping of grain tops by each other. To the layer depth h on the one circumference of rotation there is mainly one grain. For the top in form of globules, two grains are located only on 7% of the width b. There are no grain tops on 82% of the width b, that is why grinding wheel penetrating to the depth hi = 12 µm leaves scratches without overlapping (Fig. 2, sections 1–1 and 2–2). The greater the depth is, the higher the number of grains located one after another is. Thus, for h = 21 µm there are circumferences with 6–8 grains, though most of them still have 1–2 cutting tops. Only in case of great grinding depths hi = 0.03–0.05 mm, there are 2–4 grains on the one circumference, though circumferences of width b with 9–11 working tops, still remain. When the layer depth is h = 0.1 mm the number of grains placed on the one circumference reaches approximately 8–10, while the maximal value is 28–30 grains. If m = 0

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Table 1. Probabilistic assessment of the number of grains, located on the one circumference of rotation AC6 100/80 M04 4(FEPA D126 125/106 K75 m). Probability Pmi , %, under m, which is equal Depth (µm) h = 12 h = 21 h = 30

h = 50

h = 100

0

61.9

22.1

5.5

3.7

–

1

29.7

33.3

16.0

12.3

–

2

7.1

23.8

23.2

20.0

–

3

1.1

12.7

22.3

22.1

–

4

0.1

4.8

16.2

18.2

–

8

–

–

0.7

1.3

0.1

9

–

–

–

0.4

0.3

37.4

91.1

144.8

263.8

561.8

Z i (cps) b (mm)

0.064

0.083

0.100

λs (cm2 )

3.4

8.4

3.3

as

0.48

1.52

2.89

0.130 23.9 3,29

0.180 51.0 20.2

the condition of missing of grains on interval b saves its value up to layer depth h = 50 µm. So, if h = 0.1–0.13 mm the probability of missing of cutting tops reaches 1–4%. Overlapping (merging) of scratches occurs when h = 21 µm, which should be explained by the phenomenon of displacement of metal from the scratch to its lateral sides and an increase in the overlapping effect. By increasing the diameter, it is possible to reduce the difference in altitude of grains along the width and the circumference of a grinding wheel. As a result, the probability of missing of grains on a circumference of rotation decreases to insignificant values. It has been established that in the abrasive wheels due to the distribution on the elementary circumferences of rotation there can be a different number of cutting tops of the grains—from the one grain to several tens or even hundreds of pieces. That is why in case of small number of grains (Z ≤ 10) during surface grinding, the value of longitudinal feed must be limited so that the total length of scratches made by the whole amount of grains Z would not be significantly different from S. To provide the conditions for scratches merging the penetration depth must exceed the diameter of the circle. In fact, scratches on the width b under Z = 1 are not merging and this results in occurrence of areas on a grinded surface that was not machined. However, in case of grinding with cross feed these areas will be cut by the width b with considerably bigger number of grains. This will happen, if there are not too many areas with Z = 1. Thus, 250 if Dwl = 250 mm and the grinding depth is t = 0.5 µm, Zmin ≥ π2 0.5×10 −3 = 1100 pcs. There is no abrasive wheel which diameter and grit size comply with mentioned condition at depth of surface working layer h = 0.5 µm. During grinding with this depth, separate grooves are formed. To make them merge along the width and to form new grinded surface, they must penetrate to the depth t ≥ h. Thus, for the wheel with

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diameter 63 mm, grit size AC6 100/80 4 (FEPA D126 125/106 K75 m) this depth is π 63 ≈ 86 pcs. The calculations show that at this depth h = 0.021 mm and Zmin ≥ 2 0.021 there are no circumferences of width b with such an amount of grains. Obviously, for scratches merging along the length (they have already merged along the width) it is necessary to penetrate more deeply. The studies on the kinematics of an interaction between a grinding wheel and a machined surface during flat face grinding have shown: 1. Overlapping of scratches along the width occurs at a smaller depth, i.e., considerably earlier than along the length. The provision of scratches merging in one groove happens on the greater penetration depth than in case of overlapping of scratches along the width. 2. Cutting depth of grinding wheel does not depend on the value of longitudinal and cross feed, but it is determined by the law of grain distribution in the volume of abrasive layer as well as the shape of the tops of abrasive grains. 3. Abrasive grains located in the surface working layer to the cutting depth are in the most unfavorable conditions due to their small amount and the highest difference in altitude. The chip with the greatest length and section width is formed and the biggest cutting forces along with highest wear of grains occur in this layer. 4. The grain tops located in the layer of preliminary penetration are insensible of work mode of grinding wheel. In finish and rough grinding, they are similarly loaded, that is why grain resistance in this layer cannot be increased by decreasing cutting modes.

References 1. Ivanova TN, Dement ev VB, Nikitina OV (2018) Research on operation mode of abrasive grain during grinding. MEACS IOP Publishing IOP Conf Ser Mater Sci Eng 327:042045. https://doi.org/10.1088/1757-899x/327/4/042045 2. Volkov DI (2009) Theoretical model of stressed state of the surface layer of workpieces in creep-feed grinding. Vestnik of PA Solovyov Rybinsk State Aviation Technical University 3. Zakharov OV, Balaevand AF, Kochetkov AV (2017) Modeling optimal path of touch sensor of coordinate measuring machine based on traveling salesman problem solution. Procedia Eng 206:1458–1463 4. Tyuhta AV, Vasilenko YV, Kozlov AM (2016) Ways to enhance environmental flat grinding by improving the technology of the coolant supply. Procedia Eng. https://doi.org/10.1016/j. proeng.2016.07.217 5. Kozlov AA, Kozlov AM, Vasilenko VYu (2016) Modelling of machined surface during the grinding of noncircular end abrasive tool. Bull South Ural State Univ 54–62 6. Artemov II, Zverovschikov AE, Nesterov SA (2017) Strategy for evaluating the manufacturability of product design for high-tech high-tech engineering industries. Bull Rybinsk State Aviat Technol Acad named after PA Solovyov 1(40):286–290 7. Zakharov OV, Khudobin LV, Vetkasov NI, Sklyarov IA, Kochetkov AV (2016) Abrasive-jet machining of large hollow components. Russian Engineering Research

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8. Rezchikov AF, Kochetkov AV, Zakharov OV (2017) Mathematical models for estimating the degree of influence of major factors on performance and accuracy of coordinate measuring machines. MATEC Web Conf 129:01054 9. Sklyarov IA, Zakharov OV, Kochetkov AV (2016) Increasing the efficiency of diagnostics of gas pipelines based on preliminary abrasive cleaning. Chem Petrol Eng 52:1–5 10. Hanmin Shi (1984) Effects of some non-linear factors on machine tool chattering and their mathematical models. J Huazhong Univ Sci Technol (Nat Sci Ed) 12(6):101–112 11. Gonzalo O, Peigne G (2006) High speed machining simulation of thin-walled components. In: Fifth international conference on high speed machine, pp 525–536 12. Ivanova TN, Korshunov AI, Božek P (2018) The influence of chemical composition of toughto-machine steels on grinding technologies. Manag Syst Prod Eng 26:172–177. https://doi. org/10.1515/mspe-2018-0028 13. Biały W, Maruszewska EW, Kołodziej S (2018) Product defectiveness analysis using methods and tools of quality engineering. In: Cross-border exchange of experience production engineering using principles of mathematics. Publisher Department of Mathematics and Descriptive Geometry, VŠB—Technical University of Ostrava, pp 7–16 14. Sitko J, Biały W (2017) Problem of improvement the quality of products with use industrial waste. In: The quality aspects of materials, technology and management. Oficyna Wydawnicza Stowarzyszenia Mened˙zerów Jakósci i Produkcji. Cz˛estochowa, pp 129–135 15. Hou ZB, Komanduri R (2003) On the mechanics of the grinding process. Part I. Stochastic nature of the grinding process. Int J Mach Tools Manuf 43:1579–1593 16. Hou ZB, Komanduri R (2004) On the mechanics of the grinding process. Part II. Thermal analysis of fine grinding. Int J Mach Tools Manuf 44:247–270 17. Hou ZB, Komanduri R (2004) On the mechanics of the grinding process. Part III. Thermal analysis of the abrasive cut-off operation. Int J Mach Tools Manuf 44:271–289 18. Jin T, Stephenson DJ (2003) Investigation of the heat partitioning in high efficiency deep grinding. Int J Mach Tools Manuf 43:1129–1134 19. Malkin S, Xu X (2001) Comparison of methods to measure grinding temperatures. J Manuf Sci Eng 123:191–195 20. Hecker Rogelio L, Liang Steven Y (2003) Predictive modeling of surface roughness in grinding. Int J Mach Tools Manuf 43:755–776

Possibilities of Technology Grinding Steel Parts T. N. Ivanova1,2(B) 1 Tchaikovsky Branch Perm National Research Polytechnic University, 73, Lenina st.,

Tchaikovsky 617764, Russia [email protected] 2 Udmurt Federal Research Center, Ural Branch of the Russian Academy of Sciences, 34, Tatyany Baramzinoi st., Izhevsk 426067, Russia

Abstract. Grinding is the process characterized by high-thermal intensity that leads to defects formation. Recent achievements in the field of reducing thermal intensity of grinding process do not solve the problem of high-productivity faultless grinding of heavily-machined steel sheets, which represent one of the factors hindering effectiveness of machining. Thus development of scientific grounds for creation of high-productivity faultless grinding techniques, based not only on conventional methods and their improved versions but new industrial equipment as well, is an academic task of great industrial and economic importance. In the article the analytical dependence between grinding modes, thermal processes, coolant influence, and surface finish is determined on basis of complex study of rules, by which thermal processes during grinding of thin plates of heavily-machined steels are developing. The new types of grinding tools with intermittent working surface are designed, which allow in practice extending technological possibilities of faultless face grinding of flat surfaces. The requirements for stable achievement of surface finishes Ra = 0.2 ÷ 0.4 µm are specified. The science-based method of creating an optimal technological process of grinding of heavily-machined steel sheets by intermittent cutting surface grinders with direct coolant feed into cutting zone is developed, this method allows to set processing modes and choose grinder characteristics for every technological situation, characteristic for particular grade of steel and grinding conditions and provide conformity of parts on finishing stage to necessary requirements. Keywords: Grinding · Thin plate · Cutting fluid · Temperature · Grinder with intermittent working surface · Productivity · Quality · Heavily-machined steel

1 Introduction As a result of analysis of technological problems, characteristic to face grinding of thin plates made of heavily-machined steels, it was discovered that large surface of contact between grinder and processed part impairs conditions of chip forming, and creates

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_119

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unfavorable conditions for cutting zone cooling, blocks heat exchange. This particularly influences the efficiency of grinding of thin plates made of complex alloy martensitic steels, high strength, carburized steels, corrosion-resistant steels, and austenitic steels with heat-resistance and heat-proof properties. Quality of part surface layer during grinding is provided by selecting rational mode of grinding process, grinding wheel parameters, composition of coolant, and choosing method of cooling. 1.1 Theoretical and Experimental Party Direct influence on service parameters of thin plates is applied during grinding by processes of heat formation and plastic deformation in working zone, the degree of their influence depends in its turn on intensity of the tool action onto part, time of tool and part contact, relative velocity of their displacement, and so on. The mentioned parameters vary significantly when using different processing schemes. The heat formation process during grinding is characterized by rapid temperature rising with speed of hundred thousand of degree per second. After immediate heating there follows cooling of surface layers with the same speed, which causes changes in physical and mechanical parameters and geometry of surface layer of the thin plate [1–21]. One of the most important criteria in setting of optimal mode and maximum productivity mode of faultless face grinding of heavily-machined steel sheets is the temperature of grinding, to avoid defects on the plate surface it should not exceed critical values T °crit . Determining of T °crit requires to carry out complex experiments, and therefore to determine maximum productivity mode of faultless grinding other criteria may also be used: structure of ground surface, which characterizes presence or absence of defective layer though it can be defined after great number of tests; wear rate of wheel abrasive layer. To find the optimal mode there determined are the dependence between ground surface temperature of the plate T °part and modes or dependence between material removal rate Q and conditions of face grinding: ⎡  0.5 ⎤ ⎛

0.5 ⎞  υ z υpart [x − 2dn]2 + z 2 x2 + z 2 υ ◦ q part ⎥ ⎜ ⎟ ⎢ part exp − K0 ⎣ Tpart = ⎦ · ⎝1 + ⎠ ≤ Tcrit 2π λ 2a 2a 2a ◦

◦

n Tcrit = CT υwheel /Q

(1)

where υ wheel —velocity of grinding wheel; υ part —velocity of part; x—length of contact zone; d—protrusion of grit above the bond; q, a, λ—physical parameters of part material and coolant; n—shares of heat absorbed by chips, wheel and coolant; z—width of surface to be ground; C T —general factor, accounting factors, indicating, respectively, influence of contact area, material to be processed, wheel characteristics, cooling. The value of optimal productivity can be obtained from conditions of material removal rate, minimum prime cost of operation or required surface finish: 1/(x+1)  (2) Q = A/K q where A—factor, accounting for specific consumption of diamonds, K q —factors, accounting for influence of wheel grade and grade of processed material on diamonds consumption.

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The optimum productivity mode is chosen if it provides no defects on processed surface. Cutting zone temperature can be significantly reduced, if one can provide quantization of grinding by intermittent surface of wheel cutting part. In this case temperature field tends to heat saturation in steps, and therefore the process can be broken off from time to time, till temperature reaches maximum, so temperature can be limited by any preset value. The time interval till start of next cycle should be such that the processed surface cools down to its initial temperature. Such process can be performed if the cutting surface of the grinder is broken into series of interchanging bulges and hollows. The same degree of temperature reduction may be obtained at different combinations of bulge and hollow width. This fact allows choosing geometry of intermittent surface grinder with regard not only to thermal intensity of the process, but also wheels durability as well [1–8]. Causes of temperature reduction at change of grinding by tool with solid working surface for grinding by tool with intermittent one are as follows. First, it is lower rate of heat formation. Power of heat formation is proportional to tangential component of cutting force Pz , which during grinding by intermittent cutting surface grinder is by 20– 30% lower than that of solid working surface wheel. Second, hollows of the intermittent surface grinder are designed so that during contact of one cutting bulge with processed surface the temperature cannot be set and reach its maximum. During pause in contact, duration of which depends on width of the hollow, contact zone of the part cools down. Then there follows heating, and so on. The less is relation of bulge width to hollow width in grinder, the less is the temperature. Third, coolant is fed directly in the contact zone, which can be obtained during conventional grinding with great difficulties. Thus heat dissipation in cooling media is more intensive during intermittent grinding than during grinding with solid wheel. The results of temperature field calculation for flat grinding by means of tool with intermittent work surface and by ejecting lubrication fluid for cooling in front of cutting area are shown on Fig. 1. Consumption of the lubrication fluid Qcool = 0.35 L/s, outflow velocity υ = 3.76 mps, steel 12XH3A (Russia) (USA 3415, Germany 1.5732, 12Ni14, Poland 12HN3A) (a = 0.06 sm2 /s, λ = 7.2 W/(m K)), wheel speed υ wheel = 20 mps, detail speed υ part = 1.5 m/min, wheel radius R = 75 mm, width of contact area 5 mm. It is evident that maximum temperature while grinding by tool with entire cutting face is being 290 °C. The highest temperature on the depth x = 1 mm does not increase more than by 50 °C (Fig. 1a). When grinding by intermittent tool with ejecting lubrication fluid for cooling, maximum temperature decreases by 15–20%. Moreover, changing of thermal field, representing temperature curves crossing for fixed depths, has occurred. Figure 1b Curve x = 0, corresponding to surface temperature, crosses curves, which represent the temperature of deeper layers. It means that after passing the source, temperature of deeper layers turns out to be greater than surface temperature. When x = 0 thermal gradient changes its direction after passing the source and some part of heat flow goes in upward direction to lubrication fluid for cooling. Temperature curves of deeper layers slightly deform. If heat transfer is present, penetration depth of high temperatures in grinding by means of intermittent tool decreases. Analysis of isotherms (bottom side of the graph Fig. 1) proves that part of heat flow goes deep inside the detail and causes

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Fig. 1. Temperature profile of flat grinding of steel 12XH3A a tool with entire cutting face b intermittent tool with ejecting lubrication fluid for cooling, z-axis coordinated in points of contact, x-depth of thermal flow amplitude.

its heating-up, and as for other part, it goes to surface of the detail and then inside the cooling agent. That is why the detail surface heats up to high temperatures under the source. Using of cooling considerably decreases penetration depth of high temperatures and total heat content of grinded detail. Surface roughness parameter Ra decreases when grinder with intermittent cutting surface is used. This can be explained by the fact that cutting grains of intermittent grinder are sharper, and that coolant action is more effective, which creates of more stable cutting profile and reduces friction forces. The chips are extracted from grinder hollows under action of cutting fluid jet, coming from inside the tool. Increasing the number of hollows in cutting layer diminishes the parameter Ra . To provide Ra = 0.1 − 0.32 µm, optimal area of hollows should not exceed 30% of working area. With change of longitudinal feed from 2 to 6.5 m/min the surface roughness parameter Ra increases (Fig. 2a), but the absolute value of Ra when working with intermittent surface grinder is by 30–40% less, and by 10–20% less in height than that obtained when working with solid grinder. Value of Ra increases with increase in cutting depth (Fig. 2b) as the thickness of removed chips increases. Thus condition of maximum productivity and minimum surface finish is fulfilled on account of variation of grinding modes and geometry of wheel cutting layer. The hardness dependence on the abrasive tool speed shows that when the wheel speed is changed from 18 to 24 m/s, the surface layer hardness changes insignificantly. When the wheel speed is further accelerated to 38 m/s the hardness decreases by 250– 300 H/mm2 relative to the basic hardness. When the cutting depth is increased from 0.01 to 0.05 mm, the thickness of a metal layer with a changed structure ranges from 40 to 100 µm at grinding with the NCCS wheel with grooves; when the NCCS wheel with holes is used, the metal layer thickness is in the range of 60–100 µm, and when the CCS-wheel is used, it is in the range of 90–300 µm. During grinding, structural changes take place in metal due to the action of heat in the studied range of cutting depths. In the thin surface layer (about 0.005 mm) the hardness

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Fig. 2. Dependence of surface finishes during grinding heavily-machined steel 12XH3A with cooling from: a part velocity; b wheel velocity. Solid line—intermittent grinder with hollows in working layer, dashed line—solid grinder with flow coolant feed. 1–12 hollows, 2–8 hollows; 3–6 hollows.

is similar to the basic hardness (H 100 = 570 H/mm2 ); then it abruptly decreases down to 470–500 H/mm2 . The microstructure analysis of the sample surface shows that on the surface a white zone, in which etching does not take place, appears, and in deeper layers it transforms into a tempered troostite-sorbite structure. The thickness of the tempered layer changes within the range of 15–200 µm depending on the conditions and methods of grinding. The decrease in the hardness at a certain depth of the surface layer is due to the structural transformations and the specific volume decrease. After thermal treatment, in its initial state, the studied steel has small residual compressive stresses in the surface layer (about 6 MPa). In the process of grinding, the redistribution of stresses takes place (Fig. 3). For example, after grinding with small depths, residual tensile stresses are maximal on the surface. After grinding with depth of cutting t > 0.03 mm, the zones with maximal residual tensile stresses shift into deeper layers which have maximal degree of tempering. In a thin plastically deformed layer the tensile stresses are significantly less than maximal.

Fig. 3. The depth distribution of residual stresses in the surface layer after grinding: a the NCCS wheel with grooves on the abrasive layer; b the NCCS wheel with holes; c the CCS-wheel. Wheels 12A2 150 × 32 × 40 AC6 80/60 M2-01 4 (Russia) (FEPA D126 125/106 K75 m), components from steel 12Cr18Ni9, υ wheel = 34 m/s, υ p = 8 m/min, 1—depth of cutting t = 0.01 mm; 2—t = 0.02 mm; 3—t = 0.03 mm; 4—t = 0.04 mm.

The grindability of components made from high-strength steels with the use of abrasive CCS-wheels is poor; the wheels rapidly get blunted, lose their cutting capability, and burn the work surface. As the abrasive grains of the CCS-wheel become blunt during

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grinding components from high-strength steels, the height of fine irregularities grows to Ra = 2.4 µm. The use of lubricoolant decreases the surface roughness by 8–10%. As a result of research the science-based method of creating an optimal technological process of grinding of heavily-machined steel sheets by intermittent cutting surface grinders with direct coolant feed into cutting zone is developed, this method allows to set processing modes and choose grinder characteristics for every technological situation, characteristic for particular grade of steel and grinding conditions. On the basis of performed theoretical and experimental research new designs of face grinding tools with intermittent working surface are suggested, their application allows to reduce temperature in cutting zone by 30–40%, cutting forces by 20–30%, parameter of surface roughness in 1.8–2.2 times and to increase durability of tool in 3–5 times. Thus, the decrease of the thermal stress of the face grinding process decreases the total stress of the surface layer. We have proved that for decreasing the temperature in the contour of the contact between a grinding wheel and a component it is very important to use NCCS wheels and to supply lubricoolant directly to the cutting zone. The experimental studies on the determination of residual stresses appearing during grinding hard-to-machine materials show the regularity of the formation of heat residual stresses.

References 1. Zakharov OV, Balaevand AF, Kochetkov AV (2017) Modeling optimal path of touch sensor of coordinate measuring machine based on traveling salesman problem solution. Procedia Eng 206:1458–1463 2. Tyuhta AV, Vasilenko YV, Kozlov AM (2016) Ways to enhance environmental flat grinding by improving the technology of the coolant supply. Procedia Eng. https://doi.org/10.1016/j. proeng.2016.07.217 3. Kozlov AA, Kozlov AM, Vasilenko VYu (2016) Modelling of machined surface during the grinding of noncircular end abrasive tool. Bulletin of the South Ural State University, pp 54–62 4. Ivanova TN, Dolganov AM (2007) The modern snap in technology of diamond face grinding of flat surfaces: monograph. Institute of Economics UrB RAS Publ, Izhevsk, p 387 5. Zakharov OV, Khudobin LV, Vetkasov NI, Sklyarov IA, Kochetkov AV (2016) Abrasive-jet machining of large hollow components. Russian Engineering Research 6. Rezchikov AF, Kochetkov AV, Zakharov OV (2017) Mathematical models for estimating the degree of influence of major factors on performance and accuracy of coordinate measuring machines. MATEC Web Conf 129:01054 7. Sklyarov IA, Zakharov OV, KochetkovAV (2016) Increasing the efficiency of diagnostics of gas pipelines based on preliminary abrasive cleaning. Chem Petrol Eng 52:1–5 8. Hanmin Shi (1984) Effects of some non-linear factors on machine tool chattering and their mathematical models. J Huazhong Univ Sci Technol (Nat Sci Ed) 12(6):101–112 9. Gonzalo O, Peigne G (2006) High speed machining simulation of thin-walled components. In: Fifth international conference on high speed machine, pp 525–536 10. Ivanova TN, Korshunov AI, Božek P (2018) The influence of chemical composition of toughto-machine steels on grinding technologies. Manag Syst Prod Eng 26(3):172–177. https://doi. org/10.1515/mspe-2018-0028 11. Hou ZB, Komanduri R (2003) On the mechanics of the grinding process-Part I. Stochastic nature of the grinding process. Int J Mach Tools Manuf 43(15):1579–1593

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12. Hou ZB., Komanduri R (2004) On the mechanics of the grinding process-Part II. Thermal analysis of fine grinding. Int J Mach Tools Manuf 44(2/3):247–270 13. Hou ZB, Komanduri R (2004) On the mechanics of the grinding process-Part III. Thermal analysis of the abrasive cut-off operation. Int J Mach Tools Manuf 44(2/3):271–289 14. Jin T, Stephenson DJ (2003) Investigation of the heat partitioning in high efficiency deep grinding. Int J Mach Tools Manuf 43(11):1129–1134 15. Malkin S, Xu X (2001) Comparison of methods to measure grinding temperatures. J Manuf Sci Eng 123(2):191–195 16. Hecker Rogelio L, Liang Steven Y (2003) Predictive modeling of surface roughness in grinding. Int J Mach Tools Manuf 43(8):755–760 17. Svitkovskij FJu (1986) Choice of characteristics of diamond wheels in accordance with thermal mode of grain operation. Cutt Tool Issue 34:68–74 18. Dement ev VB, Ivanova TN, Dolganov AM (2017) Dolginov temperature of heating and cooling of massive, thin, and wedge-shaped plates from hard-to-machine steels during their grinding. J Eng Phys Thermophy 90(1):102–109. https://doi.org/10.1007/s10891-017-1544-7 19. Volkov DI (2009) Theoretical model of the stress state of the surface layer of components at deep grinding. Solovyov Rybinsk State Aviat Technol Acad 1:52–63 20. Ivanova TN, Dement ev VB, Nikitina OV (2017) Research on operation mode of abrasive grain during grinding. MEACS. https://doi.org/10.1088/1757-899X/327/4/042045 21. Volkov D.I (2009) Theoretical model of stressed state of the surface layer of workpieces in creep-feed grinding. Vestnik of P. A. Solovyov Rybinsk State Aviation Technical University

Calculation of Allowance Value for Grinding with Flap Wheels of Shot-Treated Surface to Ensure Required Roughness V. P. Koltsov1(B) , V. B. Rakitskaya1 , and E. V. Tardybaeva2 1 Irkutsk National Research Technical University, 83, Lermontov St., Irkutsk 664074, Russia

[email protected] 2 Baikal State University, 11 Lenin St., Irkutsk 664003, Russia

Abstract. In the aircraft industry to obtain the necessary form of long panels and sheathing, the technology of shot peen forming and subsequent grinding with flap wheels is successfully implemented. Due to the impact of the shot, a specific microgeometry is formed on the treated surface, a characteristic feature of this microgeometry is the occurrence of numerous shot dimples with various diameters and depths. Since the depth of the shot dimples is much higher than the valleys of the surface microroughness, formed as a result of previous processing, these dimples increase the surface roughness. When grinding with flap wheels, depending on the value of the allowance on the treated surface, a new microrelief is formed in the form of a combination of the traces of the abrasive grains of the flap wheels during grinding and the remaining dimples from shot peen forming. Since the dimples have a shape close to spherical with a much larger radius of curvature than their depth, at each stage of grinding, depending on the allowance, the curvature of the dimples has a significant impact on the formation and the value of roughness of the treated surface. The paper presents a methodology for creating a digital model of roughness during grinding with flap wheels of the surface treated by shot peen forming in dependence to the allowance for grinding, and presents a numerical method for determining the required allowance for obtaining the required values of roughness. Keywords: Shot peen forming · Grinding with a flap wheel · Optical method of three-dimensional scanning · Surface roughness after shot peening · Allowance for grinding · Shot indentations

1 Introduction For obtaining complex curvilinear surface forms of panels and sheathing, as well as operations of hardening, the shot peen forming and shot peen hardening is widely used [1–11]. Grinding with flap wheels is an obligatory part of the technological process of

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_120

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forming long large-sized surfaces such as panel and sheathing. It is carried out in order to improve the quality of the initial surface obtained after shot peen forming [12–15]. As a result of shot flow impact on the workpiece surface, a specific surface roughness profile characterized by numerous dimples of shot of different diameters and depths is formed [16–18]. At the same time, the distribution of dimples on the treated surface is chaotic (random) (Fig. 1) [19].

Fig. 1. Digital model of the sample surface after shot peen forming.

The results of the study of numerous samples treated with shot peening showed that due to the low degree of coverage (up to 40%) in shot peen forming the metal influx formed around the dimples is commensurate with the microrelief height of the surface obtained by the previous operation—milling, as well as the rare and nonexistent overlap of dimples. During grinding, first of all, a layer of the surface microrelief from the previous operation (milling) and the influx formed as a result of shot peen processing is removed, and when the grinding process continues, the subsequent layers of the surface in areas not covered with dimples are removed. Dimples in the form of voids have a form close to spherical with radii in workpiece surface (up to 0.3 mm), much greater than the depth of the hole (tens of microns), so the area covered by dimples on the treated surface and the volume of the metal is not directly proportional to the depth of cut. Thus, by increasing the thickness of the removed layer of material during grinding, the area and the degree of surface coverage of the remaining dimples decreases and the number of abrasives of flap wheels simultaneously participating in the grinding process becomes

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greater. This leads to an increase in the volume of the material to be removed, which in turn requires a constant increase in the forces and cutting power during grinding. Cutting forces and power are stabilized on the degree of approach to the complete removal of traces of dimples.

2 Formation of Model of Allowance for Desired Roughness The model of the allowance for the required roughness during grinding with flap wheels of the surface treated with shot peen forming is formed on the basis of the roughness model. For forming this roughness model, it is first needed to obtain a data on the surface after shot peen forming. Since the dimples formed as a result of the impact of shot are of different diameters and depths, as well as randomly located on the treated surface, a two-dimensional evaluation of the roughness does not give a valid result, since the surface roughness within the base length in different directions is different. In this case, the roughness is estimated by a three-dimensional method within a given base area. This means that the data on the surface after shot peen forming should be three dimensional, and the base area of roughness in this case can be determined experimentally as the degree of stabilization of the degree of coverage and has a value inversely proportional to the degree of coverage of shot dimples. Digital three-dimensional description of the shot-treated surface can be obtained using a digital microscope, such as the Bruker contour GT-K1 three-dimensional optical profilometer (Fig. 2), which allows to present in detail the entire scanned surface and its microrelief profile in any normal plane.

Fig. 2. Digital three-dimensional optical profilometer.

In Fig. 1, a typical image of the scanned surface treated with shot peen forming and a microrelief profile passing the center of one dimple in the longitudinal and transverse direction are presented. With this digital model, all the necessary surface parameters,

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including the number and size of dimples in the sample surface, as well as the depth of each dimple can be obtained. To analyze and describe the formation of roughness during grinding with flap wheels the shot-treated surface, we have developed a model of the dimple profile (Fig. 3) [20].

Fig. 3. Scheme of the main parameters of the workpiece profile after milling, shot peen forming, and grinding with flap wheels, where hi is the depth of the ith dimple; hp —the allowance removed during grinding; hk —the dimple depth after grinding; hk  —the depth of the dimple from the center plan after grinding taking into account the shot peen forming (SPF); hk  —is the distance between the center plan after grinding without taking into account shot peen forming (Pp ) and the center plan after grinding (Pk ); r i —the radius of the dimple in the center plan after milling (P0 ); r k —the radius of the dimple in terms of the center plan PP ; r k  —is the radius of the dimple in sample surface of the center plan Pk ; V k —volume of voids in the dimple after grinding under the center plan Pk ; V k  —the volume of the dimple void after grinding above the center plan Pk .

This model represents the formation of a ball trace of radius Ri after indentation into the surface treated by milling (Fig. 3—the original relief), as well as the further formation of a new surface (after subsequent grinding) in the form of a combination of the traces of the abrasives of the flap wheels (Fig. 3—relief after grinding) and the remains of the dimples after removing the layer of material with thickness hp . With the help of this model, the displacement (position) of the center plane is determined by the volume of voids (the total volume of voids of dimples is determined by their depths obtained using the Bruker Contour GT-K1 profilometer) formed by the traces of shot impact, and on the basis of the position of the center plane the surface roughness within the base area is determined by the Eq. 1 [20]. 

hk =

  m 2  π  1  hi − hp · Ri − · hi − hp , · Fb 3

(1)

i=1

where m is the number of remaining dimples after grinding with flap wheels with the allowance hp . At a known value of the thickness of the material to be removed and the position of the center plane, according to [20] the arithmetic mean deviation of the profile within the base area Sage in accordance with the thickness of the material (allowance for grinding) to be removed can be determined by the following expression: Sage = 0.5Sa_gr +

m    2π  1   2  hi − hp − hk · Ri − · hi − hp − hk , · Fb 3 i=1

(2)

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where S a_gr —the arithmetic mean deviation of the profile within the base area of the surface treated by grinding without taking into account the shot dimples. Equation 2 is valid only if there is a sufficient total volume of voids of the remaining dimples after grinding, which provides a displacement of the center plane, that is, m    2π  1   2  hi − hp − hk · Ri − · hi − hp − hk ·  0.5Sa_gr Fb 3

(3)

i=1

According to Eq. 2, it is not difficult to notice that the surface roughness after grinding depends on the number and depth of the remaining dimples, the assigned value of the allowance and S a_gr . In relation to the surface (with the roughness S a_gr ) treated by grinding with flap wheels without shot peen pre-treatment, during grinding after removal of the layer of material, the thickness of which exceeds the peak of the profile valleys created by previous treatment, the surface roughness becomes reachable [21] and depends on the mode of grinding processing. The value of the reachable roughness during grinding with flap wheels can be set experimentally for each processed material with a specific flap wheel and grinding mode. And so, on the basis of equations 1–2 the value of the arithmetic mean deviation of the surface profile is calculated depending on the allowance for grinding on the basis of data on dimples of the scanned shot-treated surface. Figure 3 shows the result of the approximate calculation of roughness depending on the value of the allowance for grinding. The calculation is carried out for the base area of 15 mm*15 mm of the sample of aluminum alloy BT 95. According to the technology of manufacturing large and curved aircraft panels and sheathing, the sample was first milled to the purity of the surface Ra 0.4, after milling is processed by a ball steel shot with a diameter of 3.5 mm on the shot peening machine of contact type DUF-4 M with processing mode: speed of shot peen wheel is 1200 rpm, longitudinal feed is 2.5 mpm. After shot peening, the treated sample surface is scanned on a three-dimensional optical profilometer to obtain the necessary data on the dimples (in this case, total dimple number is 120 with a depth of 3.2–90.5 µm, the total degree of coverage of dimples −10.66%). The roughness value in Fig. 4 obtained taking into account the remaining dimples and the nominal surface at a definite allowance value. As mentioned above, in order to obtain the final value of the roughness on the treated surface during grinding after the shot peen forming, it is necessary to take into account the reachable roughness of the surface-grinded areas not covered by dimples. Based on the obtained dependence on the graph the dependence of the allowance on the value of roughness: a = 49.24e−14.7Sa

(4)

Equation 4 is of a particular nature for one mode of shot peen forming and a specific material to be processed. However, this approach is common to all modes and processed materials in the implementation of the technology of shot peen forming with subsequent grinding with flap wheels.

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Fig. 4. The actual dependence of the displacement of the center plane and the arithmetic mean deviation of the profile on the allowance.

3 Conclusion Dimples formed as a result of shot peen forming play a crucial role in the formation of the roughness of the treated surface in the implementation of the technology of shot peen forming with subsequent grinding with flap wheels. The proposed approach is creating a model of the allowance for grinding with flap wheels after shot peen forming allows to assign a needed allowance value for the desired value of surface roughness.

References 1. Pashkov AE (2005) Tehnologicheskie svjazi v processe izgotovlenija dlinnomernyh listovyh detalej (Technological connections in the manufacturing process of long sheet metal parts). IrGTU, Irkutsk 2. Pashkov AE, Chapyshev AP (2003) Uchet vlijanija struktury zony obrabotki pri drobeudarnom formoobrazovanii (Taking into account the influence of the structures of the processing zone during shot-impact shaping). Interuniversity collection of scientific articles “Technological mechanics of materials”, IrGTU Publ., Irkutsk, pp 22–27 3. Koltsov VP, Starodubtseva DA, Kozyreva MV (2015) Analysis of cuttings and part surface roughness dependences under flap wheel machining according to factorial experiment results. Vestnik of Irkutsk State Tech Univ 1(96):32–41 4. Likhachev AA, Gerasimov VV, Pashkov AA (2015) Implementation of shot peen forming control system on contact type installations. Vestnik of ISTU 12(107):19–25

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5. Pashkov AA (2015) Automation of large scale panels shootblasting process morphogenesis on contact type installations. Vestnik of P. A. Solovyov Rybinsk State Aviat Tech Univ 4:34–39 6. Diak AU (2015) Promising methods to determine surface coverage under shot peening. Vestnik ISTU 12(107):19–25 7. Diak AU (2014) Promising methods to determine surface coverage under shot peening. Vestnik ISTU 7(90):12–17 8. Vinh LT, Starodubtseva DA, Koltsov VP, Hoang NT (2018) Determination of the degree of shot coverage after shot peen forming by image processing. Sci J Syst Methods Technol 2(38):32–37 9. Koltsov VP, Vinh LT, Starodubtseva DA (2018) Surface roughness formation during shot peen forming. IOP Conf Ser Mater Sci Eng (MEACS 2017) 327:042125 10. Koltsov VP, Starodubtseva DA (2017) Investigation of traces of interaction between flap wheel and aluminum alloy plain surface. Procedia Eng 473–478 11. Koltsov VP, Starodubtseva DA, Vinh LT, Son PX (2018) Step-by-step surface roughness formation during shot peening and subsequent grinding with flap wheels. Adv Eng Res Int Conf Avia Mech Eng Transp (AviaENT 2018) 158:386–390 12. Dimov UV, Poashev DB (2015) Cutting forces in machining by elastic abrasive wheels. Vestnik ISTU 7(102):47–55 13. Dimov UV, Poashev DB (2015) Cutting zone temperature under elastic fap disc machining. Vestnik STU 2(97):38–42 14. Koltsov VP, Vinh LT, Starodubtseva DA (2019) Determination of the allowance for grinding with flap wheels after shot peen forming. In: Material of international conference on innovations in automotive and aerospace engineering, p 632 15. Koltsov VP, Vinh LT, Rakitskaya VB (2020) To determination of removable material during grinding with flap wheels after shot peen forming. In: International conference on modern trends in manufacturing technologies and equipment 2019 (ICMTME 2019), Sevastopol 16. Koltsov VP, Vinh Le Tri, Starodubtseva DA (2017) To the problem of shot peening coverage degree determination. Vestnik Irkutsk State Tech Univ 11(130):45–52 17. Husu AP, Vitenberg JuR, Pal’mov VA (1975) Sherohovatost’ poverhnostej: teoretikoverojatnostnyj podhod (Surface roughness: a probabilistic theory). Nauka Publ, Moscow 18. Koltsov VP, Starodubtseva DA, Chapyshev AP (2017) By definition, the value of the allowance during deburring abrasive mop panel surface after shot peen forming. Bull Kazan State Tech Univ named after A.N. Tupolev 73(1):25–30 19. Koltsov VP, Vinh Le Tri, Starodubtseva DA (2018) Mathematical model of surface profile arithmetic mean deviation formation at shot peen forming. Vestnik Irkutskogo gosudarstvennogo tehnicheskogo universiteta 2(133):26–33 20. Koltsov VP, Vinh LT, Starodubtseva DA (2018) Formation of the surface roughness during grinding with flap wheels after shot peening. In: International conference on modern trends in manufacturing technologies and equipment, vol 224. Sevastopl 21. Podahev DB (2014) Optimization of finishing of details from high-strength aluminum alloys by the elastic abrasive tool. Dissertation, Irkutsk National Research Technical University

Phasechronometric Turning Monitoring System Testing in Industrial Conditions D. D. Boldasov, A. S. Komshin, and A. B. Syritskii(B) Bauman Moscow State Technical Umiversity, 2nd Baumanskaya st., Moscow 105005, Russia [email protected]

Abstract. The paper describes the process of obtaining the LITZ LTC 15TS lathe phasechronometric portrait. This is one of the testing stages for prototype phasechronometric system for diagnosing the cutting process. The choice of the phasechronometric approach is explained by its high measurement accuracy due to the reference to the time and frequency standard, as well as high noise immunity. The measuring system, which accurately implements the measurement time intervals, has been developed. It works in conjunction with a high precision rotary encoder LIR-152A. The features of various machine operating modes in phasechronometric representation are considered: idling, turning, transient. The paper describes the process of developing a tool for measuring time intervals for obtaining primary measurement information. An experiment is also described with turning of a titanium alloy Ti–Al-V (according to BS marking), including the analysis of the chronogram of spindle rotation during the transition process—cutting of the tool into the workpiece. Keywords: Turning · Diagnostics · Phasechronometric method

1 Introduction Despite the great interest in the problems of diagnosing the technical condition of lathes, the problem of monitoring and predicting the failure of individual elements of the machine drive is relevant. In literary sources and patents, you can find at least a dozen diagnostic methods based on measuring various parameters of the cutting process or the operation of a lathe. One of the most described of them is the method of vibration diagnostics, which allows you to identify deviations from the normal functioning of the machine, both during the operation of the machine and in the process of testing equipment at idle. However, it is not a secret that certain diagnostic methods have inherent difficulties, and in some cases also drawbacks [1]. This can be either the high price of the measuring channel of the diagnostic system, or the relatively low accuracy of measurements and other subtleties. The importance of creating such systems is also determined by the fundamental principle: tool failure will necessarily lead to the failure of the entire technological © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_121

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system [2, 3]. Research in the field of diagnostics of the state of a tool [4] shows that 20% of the unscheduled downtime of equipment is caused by a tool breakdown. In addition to losses from downtime, tool wear can lead to deterioration of the surface quality and even the size of the workpiece being processed beyond the tolerance field. When using monitoring systems for the state of the instrument, the risk of defectiveness on these grounds is reduced. When machining difficult-to-handle materials such as titanium alloys, the need to monitor the condition of the tool is crucial. Titanium has a good combination of lightness and strength, which is maintained even at high temperatures, and exceptional corrosion resistance. These characteristics of it were the main reason for the wide distribution in the industry. Titanium found its main application in the aerospace industry (both in engine building and in the manufacture of aircraft bodies). Also, titanium is used, mainly due to its outstanding strength properties, for example, in the manufacture of steam turbine blades, superconductors, in rocket science, its corrosion resistance has found application in shipbuilding, chemical and petrochemical industries, biomedicine, etc. However, despite the high applicability of titanium, it is an expensive material compared to most others because of the difficulty in smelting and manufacturing billets. On the other hand, the high cost is compensated by the long service life and its characteristics [5]. According to [6], when processing critical parts made of titanium: 1. It is necessary to control the cutting speed, feed and wear along the rear surface on the finishing passes; 2. Tool breakage during the finishing operation can cause damage to the surface of the part; 3. Mating sections on the instrument are voltage concentrators. The cutting process can affect the surface quality of the part, which during operation will lead to deformation of thin-walled elements or to a decrease in the fatigue strength of critical rotating parts (discs/shafts). However, despite the high relevance due to the above factors, today the problem of creating an effective system for monitoring tool wear has not been resolved. The lack of engineering solutions that have undergone a deep introduction in the industry in this area is caused by the shortcomings of existing methods. They are usually divided into direct and indirect [7]. Direct methods directly allow you to measure wear parameters using contact or noncontact (mainly optical) methods. This approach is difficult to implement directly in the cutting process, since it is necessary to stop processing, which leads to an increase in operating time and, consequently, to a decrease in productivity. Indirect methods are more effective, including the measurement of various physical parameters correlated with the state of the instrument. There are known descriptions of diagnostic methods based on measuring the cutting force, power consumed by the engine, analyzing the quality of the machined surface, the trajectory of the axis of the machine spindle, chemical analysis of the tool surface, methods of vibro-acoustic and vibrodiagnostics, as well as various combinations of various methods, for example, an analysis-based method of vibro-acoustic signal in combination with temperature measurement in the cutting zone [8]. A thorough analysis of these methods individually leads to the conclusion that

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each of them has significant shortcomings that impede the widespread introduction of one or another approach to monitoring the state of the tool in the production process. So, for example, the vibration diagnostics method is characterized by problems with the installation of primary transducers. In particular, the sensor should be installed in such a way that all joints separating the cutting zone and the installation site of the accelerometer should be fixed. At the same time, part of the information is inevitably lost and the situation is likely when it contained data on the state of the cutting tool [9]. As there are difficulties in the implementation of the method based on the measurement of cutting force, the unpopularity of the installation of dynamometric devices is indicated. This is due to the complexity of the design of the machine, reducing the versatility of the equipment and the occurrence of problems with the rigidity of the elastic system and with the reliability of the devices themselves. In order to compensate for the shortcomings of individual methods, many researchers propose options for monitoring systems that include modules for measuring several parameters at the same time. This is justified in terms of obtaining more information about the processing process, although it is not without drawbacks. Most of these systems incorporate a significant number of sensors (cutting forces, acoustic emissions, power, vibration sensors), which seriously complicates their installation on the machine and reduces the reliability of the technological system. And especially, it is necessary to note additional difficulties with the parallel processing of large arrays of measurement data. From the foregoing, there is a need to find alternative methods for monitoring the tool. The use of a phasechronometric diagnostic method for assessing tool wear during processing can be such an alternative approach due to its advantages relative to “traditional” monitoring and diagnostic methods.

2 Method Description The phasechronometry method (PCM) is as follows: the duty cycle (for which one revolution of the shaft is taken) is divided into equal intervals and the transit time of each phase is measured, thereby forming a series reflecting the instability of the duty cycle [10–12]. The system diagram is shown in Fig. 1. The duty cycle breakdown is carried out using the LIR-158A angular displacement sensor. The analog signal from the sensor is fed to the input of the digitizing subsystem, where a differential measurement circuit is implemented, which allows you to subtract interference from the signal and increase its amplitude. The signal passes through a low-pass filter based on the operational OPA725 (TI), and then passes to the input of the analog comparator TLV320 (TI), where a rectangular signal is generated. Since the necessary accuracy of measuring time intervals is at the level of 10–7 s, and at the stage of digitization, signal distortion is possible, the analog part should not introduce an error in the measurement result more than at the level of 10–8 from. The required level of accuracy is ensured by the right choice of operational amplifier and comparators. The total error from all components of the analog board does not exceed 4 × 10–8 s. Next, the signal is fed to the input of the DE0-Nano-SoC FPGA (Altera), which is using a crystal oscillator (50 MHz), the time between the state changes of the analog

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comparator (from logical 0 to logical 1 and vice versa) is measured. Further, the measured intervals are processed using a special algorithm and a criterion for assessing the state of the turning plate is formed. Using FPGAs based on System-on-Crystal (SoC) allows you to raise the file system and implement the information processing algorithm directly on the FPGA without the need to use a single-board computer, which reduces the cost and complexity of the system architecture, as it eliminates the development of an algorithm for controlling the interaction of FPGAs and OK.

Fig. 1. System schematic.

For experimental research, the choice of a turning tool from the manufacturer Sandvik is considered, since this manufacturer provides a large amount of information on the processed material, as well as the results of research on processing using its own tool. Based on information on the behavior of titanium alloys during cutting, it was proposed to divide experimental studies into several stages: 1. The first stage is the removal of the phasechronometric portrait of the machine (idling, transients, cutting); 2. The second stage is turning of two titanium billets under identical conditions to study the repeatability of the indications of the phasechronometric system; 3. The third stage is the turning of titanium billets until critical wear of the turning plates is achieved. This article will describe the results of the first stage of work. The study of phasechronometric portraits of various lathes is an important step in the development of a system for monitoring the turning process. In this case, a phasechronometric portrait can be understood as a set of machine operation features isolated from rotation chronograms under various operating modes (idling, turning, transient processes).

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3 Experimental Results Experimental studies were carried out at the production base of the FINVAL Group Engineering Technology Center using a LITZ LTC 15TS turning machining center with drive power up to 7.5 kW and rotation speed up to 6000 rpm. The choice of this machine was primarily determined by the convenience of developing and installing snap-in phasechronometric systems. The snap-in itself was developed by the scaling method, since its design is similar to that described in a previously published article [13]. The type of installation is shown in Figs. 2 and 3.

Fig. 2. Tool mounted on machine spindle.

The first stage of experimental research was the recording of a phasechronometric portrait [14] at idle at various speeds of rotation (407, 512, 629, 769, 865, 989, 1258, 1538 rpm). Based on the obtained measurement information, chronograms were constructed for each value of the rotation speed. To build chronograms [15, 16], data intervals of 10 thousand values were taken (2 spindle turns). Figure 4 shows the result in the form of a rotation chronogram for a rotation speed of 629 rpm. It can be noted that the results are repeatable from turn to turn, which indicates the stability of the phasechronometric portrait of the machine, which allows the use of the machine idle record as data for comparison. This makes it possible to realize on the basis of a phasechronometric system functions for automatically determining the moment of cutting a tool into a workpiece and exiting it (precision recording of the time of the beginning and end of the turning process).

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Fig. 3. Installed phasechronometric sensor on the machine.

Fig. 4. Idle chronogram at 629 rpm.

Also, during the measurements, the moments of transition from one speed to another were recorded. Such a transition was most clearly observed when changing the rotational speed from 1065 to 1256 rpm, which is shown in Fig. 5. The chronogram shows a small “dip” in the range of 30,000–50,000 values. This behavior of the graph can be explained by the following: when the engine spindle accelerates at a certain point in time, the speed becomes higher than the set value, and the CNC system equalizes the speed to the required number of revolutions. Data with similar detail (5000 measurements per revolution) can be used to evaluate the quality of the pair “machine drive + CNC system”. Next, the longitudinal turning of the outer surface of the cylindrical billet was carried out, the material of which was selected is a Ti–Al-V titanium alloy. The choice of this material is due to the fact that in the field of titanium alloys processing with Sandvik tool it acts as a workability standard [6], and also the resistance time of various plates of this manufacturer was established for this material.

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Fig. 5. Spindle acceleration chronogram.

Turning parameters and cutting conditions: tool—interchangeable inserts type SNMG 12 04 12-SMR 1115; holder MSBNR2020K12; cutting depth—1 mm; feed 0.4 mm/rev; cutting speed—43.5 m/min. Figure 6 shows the chronogram of turning with a diameter of 32 mm at a spindle speed of 395.6 rpm, and also Fig. 7 shows the chronogram at the time of cutting the tool into the workpiece.

Fig. 6. Turning chronogram (diameter 32 mm).

The spindle speed is different only to maintain the same cutting speed so that the turning conditions are the same. The charts show the repeatability and frequency from turn to turn (Fig. 6), while the nature of the chronogram is comparable to damped oscillations. Frequency is also observed during transients, such as cutting a tool into a workpiece (Fig. 7). A chronogram built on 16 spindle revolutions can be divided into three zones. Zone 1—idle spindle, zone 2—transient when cutting the tool into the workpiece, zone 3—steady metal cutting. From the chronogram, you can calculate the

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Fig. 7. Turning chronogram (diameter 20 mm).

number of revolutions during which a transition period was observed. When multiplied by the value of the longitudinal feed, it is possible to estimate the length of the surface processed under conditions of unstable cutting—2.8 mm. In the case of fine turning of this part, particular attention should be paid to surface quality control.

4 Conclusion The results allow us to draw conclusions: the phasechronometric method does not require complex preparation for use for various models of lathes, the PCM is suitable for a detailed study of cutting processes in order to improve the quality of processing. At the next stage of work, studies will be carried out proving the correlation of the readings of the PCM system and the quality of the treated surface. Such results will make it possible to implement a processing quality monitoring system before conducting control tests (measurements). Acknowledgements. The authors wish to acknowledge the assistance during experimental research to the N. Efremova, Director of the FINVAL Group Engineering Technology Center and M. Kasatkin M ,Deputy Director.

References 1. Ghasempoor A, Moore T and Jeswiet J (1998) On-line wear estimation using neural networks. Proc Inst Mech Eng B 212:105–112 2. Sinopalnikov V, Grigoriev S (2005) Nadejnost I diagnostika technologicheskich system (Reliability and diagnostics of technological systems). Moscow 3. Altintas Y (2012) Manufacturing automation: metal cutting mechanics, machine tool vibrations, and CNC design. 2nd ed. Cambridge 4. Silva R, Reuben R, Baker K, Wilcox S (1998) Tool wear monitoring of turning operations byneural network and expert system classification of a feature set generated from multiple sensors. Mech Syst Signal Process 12:319–332

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5. Machado A, Wallbank J (1990) Machining of Titanium and its alloys—a rewiev. Proc Instn Mech Engrs 204:53–59 6. Sandvik Coromant AB (2011) Technical manual 7. Romashev A (2014) Klassifikaciya sposobov monitoringa sostoyaniya rejuschego instrumenta (Classification of methods for cutting tool state monitoring). Aktualniye Prob V Mashinostroenii 1:178–186 8. Makarov V, Shokhrin A, Potyagailo O (2011) Influence of cutting conditions and tool wear on the cutting parameters for numerically controlled machine tools. Russ Eng Res 31:69–73 9. Kozochkin M, Sabirov F (2009) Attractors in cutting and their future use in diagnostics. Meas Tech 52(2):166–171 10. Syritskii A (2016) Measurement of the wear of a cutting tool by phase chronometer method in the course of working. Meas Tech 59(6):595–599 11. Boldasov D, Potapov K, Syritskii A (2016) Phase-Chronometric Diagnostics of Metal-Cutting Lathes. Russ Eng Res 36(8):668–672 12. Boldasov D, Lazarev N, Syritskii A (2015) Izmeritelniy blok fazochronometricheskoy sistemi monitoring processa tokarnoi obrabotki (Measuring unit of a phasechronometric system monitoring of the turning process). Pribori 10:6–9 13. Potapov K, Syritskii A (2014) Realizaciya izmeritelnoy fazochronometricheskoy sistemi dlya diagnostikitechnicheskogo sostoyaniya tokarnikh stankov (Implementation of a measuring phase-chronometric system for diagnosing the technical condition of lathes). Pribori 5:13–18 14. Syritskii A (2017) Phasechronometric measuring technologies application for turning tool wear monitoring. MATEC Web Conf 129:01049 15. Kiselev M, Komshin A, Syritskii A (2018) Predicting the technical state of a turning tool on the basis of phase-chronometric measurement information. Meas Tech 60(11):1081–1086 16. Kiselev M et al (2018) Technical diagnostics functioning machines and mechanisms. IOP Conf Ser Mater Sci Eng 312:012012

Optimizing the Design of a Grooving Tool Plate S. V. Grubyi1(B) and P. A. Chaevskiy2 1 Bauman Moscow State Technical University, 2nd Baumanskaya St., Bldg. 5, Block 1,

Moscow 105005, Russia [email protected] 2 LLC “Company RITS”, Bolshaya Semenovskaya St., Bldg. 40, Moscow 107023, Russia

Abstract. A method for optimizing the design of a shaped replaceable polyhedral plate of a grooving tool was clarified. Criteria and limit values for choosing an optimal design of the shaped groove plate were suggested. A method to apply criteria for choosing an optimal design was laid out based on the example of a replaceable polyhedral plate of a given shaped profile. Common grooving tools featuring brazed plates, with a geometry compliant to GOST 18884-73, were reviewed as a basic option. A change from common grooving tools with brazed plates using cutters with replaceable polyhedral plates was justified. Models of a tool holder block and a replaceable polyhedral plate to process a given profile were developed. The suggested criteria allow us to define the most efficient design solution in each particular case and may be employed in various industries. Keywords: Grooving tool · Design optimization · Optimization criteria · Prefabricated cutter · Replaceable polyhedral plate

1 Introduction Improving the efficiency of machining remains one of the most relevant research topics whose results may be found in papers [1–5]. Modern products manufactured by machine-building enterprises contain a lot of components with grooves. These components vary greatly according to the shapes and sizes and are made of various materials. The grooves often have a shaped profile that needs to be processed using a shaped tool. Shaped grooves are processed with solid, composite or prefabricated hard-alloy cutters or mills, depending on the type of component. Tool providers offer tools of various designs for grooving. For example, such tooling resource centers as Iscar, SANDVIK Coromant, SimTec, Paul HORN, Carmex, WIDIA, DENITOOL offer various cutter options with replaceable polyhedral plates (RPP) for groove turning in their catalogs. The tools provided by such companies have various design features and can be used within the premises of machine-building enterprises. The biggest disadvantage of such tools is a rather high price, which means that processing of relevant parts requires more funds when these tools are used. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_122

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When processing hard-to-machine materials, brazed-tip cutters and solid mills show low efficiency due to their low safety factor. The prerequisites for the strength calculation of the tool are outlined in several papers, while considering the possibility of analytical calculation of power loads and cutting temperatures [6–10]. Therefore, the issues of development, production and application of prefabricated cutters designed in Russia are up to date for those companies and firms that set and solve tasks of reducing the cost of production and manufacturing expenses. Common grooving tools featuring brazed plates, with a geometry compliant to GOST 18884-73, were reviewed as a basic option. These cutters are used in some enterprises for this type of operation. Cutters of this type of construction suffer from a number of serious drawbacks: the need for resharpening to restore cutting properties, which leads to the necessity of employing additional qualified personnel and using special-purpose equipment; a relatively short tool run between sharpenings due to the impracticability of using wearresistant coatings on brazed plates; No special geometry of the front surface required to ensure optimal chip formation; extended auxiliary tool change time compared to products having RPP, etc. These disadvantages suggest the need for replacement of such cutters with tools featuring advanced designs with RPP. RITS Company LLC specializes in the implementation of effective cutting tool designs at modern machine-building enterprises. RITS joined forces with the Bauman Moscow State Technical University and conducted research to justify the implementation of advanced turning tools with RPP and re-place the brazed cutters. The results of the research are presented in the article [11]. The research conducted did not address in great detail the issues of designing advanced cutting tools with RPP. This article suggests considering the tasks as follows: • Develop criteria and restrictions for optimizing the design of a prefabricated shaped grooving tool; • Developing a method for designing a prefabricated shaped groove cutter. The proposed method may be illustrated using the example of replacing the cutter with brazed shaped plates as shown in “Fig. 1” with an RPP cutter.

Fig. 1. Shaped cutter profile.

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2 Criteria and Their Limit Values to Optimize the Design of a Prefabricated Shaped Grooving Tool Developing the design of a prefabricated shaped grooving tool assumes the design of a replaceable plate to process a given profile. 2.1 Choosing the Position of the Plate According to the Type of Installation Relative to the Workpiece By the type of installation relative to the workpiece, one can differentiate a radial Fig. 2 and tangential Fig. 3 position of the plate.

Fig. 2. Radial.

Fig. 3. Tangential.

The radial position of the plate provides for installation perpendicular to the axis of the workpiece. When the plate is positioned tangentially, the cutting force PZ is directed along the larger side of the plate section, which increases the strength. The advantage of such an arrangement is that the cutting plate can withstand higher cutting forces than in the radial arrangement when the cutting forces are directed along a smaller cross section of the cutting plate. Based on these advantages, we choose the tangential position of the plate.

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2.2 Choosing a Plate Shape The shaped plates are as a rule needed in small amounts, and therefore, large investments in a special mold for production won’t be effective. It is advisable to choose a standard plate shape for designing a shaped RPP. The shaped profile will be formed by grinding following pressing and sintering of the plate. A criterion for the overall stability of the RPP is suggested to choose the plate shape. This criterion is determined by the number of main cutting edges on the plate. The number of main cutting edges on the plate should be as large as possible. The boundary conditions determining the number of main cutting edges are geometric values of the cutting wedge and shaped profile required. In the example given, the front angle value of 5° and back angle value of 5° are proposed. Tool providers use PPR shapes shown in Fig. 4 for grooving tools. It should be kept in consideration that the shapes of the groove and cut-off plates shown in Fig. 4 are not optimized for the production of small batches of shaped plates as pressing is accompanied by chip splitters on the front surface and there is no way to form plates with small thickness using molds of this type. This is a significant drawback in the event where the plate is positioned tangentially as workpieces with the minimum thickness, close to the thickness of the finished RPP, reduce the cost of raw materials and the volume of ground materials.

Fig. 4. RPP shapes of tool providers for grooving tools.

The standard shapes of RPP shown in Fig. 5 were taken into account.

Fig. 5. Common RPP shapes.

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When reviewing the plate shapes, let us consider standard sizes with nearby diameter values of the inscribed circles: CNMA 120408, TNMA 220408, SNMA 120408, PNMA 110408, HNUA 110412. “Fig. 6” shows the shapes in question with the required geometrical parameters of the cutting part. The PNMA 110408 plate cannot ensure the required processing depth, and the HNUA 110412 plate has too small side base edges after the formation of the cutting head.

Fig. 6. Plates with required geometric properties.

2.3 Choosing the Plate Mounting System The labour intensity and cost of producing a special tool holder vary depending on the type of plate mounting chosen. The standard tool holders may not be used as the application area is restricted. The standard tool holders for the plate shapes in question will not allow processing of the groove. Plate mounting types are reviewed in many papers, e.g., in [12, 13]. A criterion of mounting unit production costs is suggested to select the type of plate mounting. The cost of the mounting unit includes the cost of producing the tool holder and the cost of all fasteners. Let us have a look at the plate mounting types: Figure 7 shows a mounting diagram with clamping from the top. A plate without a hole is positioned in the holder on the support and two side surfaces with a clamp located on the support surface only. The simple mounting system consists of a tool holder, a clamp, and a clamp screw. A product design featuring a cover chip breaker and a hardalloy support plate is possible. Such design has following disadvantages: no fastening on the side surfaces, difficult chip removal, misalignment in the direction of cutting and fastening forces, low accuracy of positioning of RPP top when it is rotated or changed.

Fig. 7. Mounting system C. Clamp from the top.

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Figure 8 shows a mounting system with an extra stiff clamp. A plate with a hole is positioned in the holder on one support and two side surfaces. The mounting system consists of a tool holder, a clamp, a clamp screw, a support plate, a support plate screw and a spring. This mounting system has increased rigidity compared to the other systems considered. This mounting system is the first-choice solution for rough machining. The main drawback of this mounting system is its high price compared to other mounting systems.

Fig. 8. Mounting system D. Extra stiff clamp.

Figure 9 shows a mounting system with a wedge-type strap from the top. A plate with a hole is positioned on one support and two side surfaces. The RPP is simultaneously pressed in the receptacle of the tool body along the support and side surfaces. The mounting system usually consists of a tool holder, a wedge-type strap, a screw of the wedge-type strap, a support plate, a screw, and a pin. A drawback of this design is its complexity in production and operation.

Fig. 9. Mounting system M. Clamping with a wedge-type strap from the top.

Figure 10 shows a mounting system with the attachment of a lever to a hole. A plate is positioned in the tool body on one support and two side surfaces with clamping on side surfaces only. The mounting system consists of a holder, a boot, a rod, and a support plate. However, there is no clamping on the support surface of the RPP in these designs, which deteriorates the reliability and rigidity of the attachment. Production of a tool holder for this type of attachment is the most labour-intensive job of the reviewed fastening systems. Figure 11 shows a mounting system with screw retainment of the plate. A plate is positioned on one support and side surfaces with clamping on the same surfaces. The mounting system consists of a holder and a fastening screw. A disadvantage of this design is small clamping force and the need for RPP production with high precision. The system with plate screw retainment is the least labour-intensive and has a minimum number of fasteners. This mounting system is also most commonly used for tangentially positioned plates. We choose this mounting system.

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Fig. 10. Mounting system P. Clamping with a lever to a hole.

Fig. 11. Mounting system S. Fastening the plate with a screw.

It should be noted that RPP must have a toroidal-shaped hole in order to use the chosen fixing method. The standard profile of the hole for fastening with M3.5 screw is shown in Fig. 12.

Fig. 12. Hole profile.

The standard hole in the plate shapes in question, Fig. 5, has a simple cylindrical shape. However, replacement of pins forming the hole in these molds is not laborintensive but will be a necessary condition for using the fixing method chosen.

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2.4 Coefficient of Volume Compactability Let us review a criterion of the volume compactability coefficient in order to optimize design solutions. The volume compactability coefficient K s is equal to the relationship between the number of main cutting edges of the plate Z and the workpiece volume V (1) Z (1) Ks = V This criterion enables the calculation of the utilization efficiency of tool materials for RPP. The greater the K s value, the more efficiently the tool materials are utilised. Based on the geometric values of the groove profile and allowances for grinding of base surfaces, we accept the thickness of the RPP workpiece as equal to 3.5 mm. Table. 1 shows the volume compactability coefficient for the plates in question with the hole shown in Fig. 12. Table 1. Evaluating the plates based on the volume compactability coefficient. Plate shape SNMA

TNMA

CNMA

Z

4

3

2

V, [mm3 ]

495.40

661.50

504.00

K s, [1/mm3 ]

0.0081

0.0045

0.0040

2.5 Labour Intensity in Plate Production The labour intensity in plate production is one of the key factors affecting the final cost of RPP. Grinding processes account for the major part of the labour intensity. To compare the selected plate shapes and take a final decision on selection, a criterion of plate production complexity is suggested. Since factories and tool shops manufacturing tools have different machine pools, it is not advisable to estimate the labour intensity based on production time. It is proposed to estimate the labour intensity in terms of the volume of the ground material required to produce a single cutting edge. Thus, it is proposed to calculate the labour intensity using the formula (2). V − V1 (2) Z where V is a workpiece volume prior to grinding, V 1 is RPP volume, Z is the number of main cutting edges of the plate. Table. 2 shows an estimated labour intensity in the production of plates in question with the hole shown in Fig. 12. The lower the T v value, the less labour-intensive is the production of the plate. Tv =

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Table 2. Evaluating the plates based on the criterion. Plate shape SNMA

TNMA CNMA

Z

4

3

V, [mm3 ]

495.40

661.50 504.00

2

V 1 , [mm3 ] 371.7

640.2

447.2

T v , [mm3 ] 30.925

7.1

28.4

3 Choosing the RPP Design The criteria reviewed may not uniquely determine the final design of the RPP. In this case, through consistent application of criteria, we get two possible close versions of RPP designs (production from a square shape SNMA 120408 or a triangular shape TNMA 220408). The final decision on choosing the shape of the plate depends on the amount of equipment at the specific production facility and cost of raw materials. The volume compactability coefficient prevails in cases where a powerful grinding equipment with a rigid process system is in place. Equipment to generate large amounts of material in one complete cycle will perform profile grinding over the same period of time on different plate shapes. A plate with a higher volume compactability coefficient will be a preferred option as the workpiece of a smaller volume would be cheaper. The criterion of labor intensity prevails in cases where the rigidity of the process system of the grinding machine is relatively low. In this case, the cost of 1 machine hour will be more critical for the final plate cost. Therefore, it is necessary to choose the least labour-intensive option to reduce the final cost of the plate. Following the analysis, an RPP made of a TNMA plate was proposed which was selected based on the prevailing criteria of labour intensity. Figure 13 shows the model of the developed prefabricated cutter.

Fig. 13. Model of the developed composite cutter.

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4 Conclusion Criteria for determining the design of shaped groove RPP were proposed. The models of the tool holder and RPP have been developed to ensure processing of a given profile. The suggested criteria allow us to define the most efficient design solution in each particular case and may be employed in various industries.

References 1. Zubkov NN (2020) Novel method of single-pass threading by cutter. In: Proceedings of the 5th international conference on industrial engineering (ICIE 2019). ICIE 2019, vol 2. Lecture Notes Mechanical Engineering. Springer, pp 973–982. https://doi.org/10.1007/978-3-03022063-1_103 2. Zubkov NN, Bityutskaya YuL (2018) Simulation of the deformational cutting and the geometric parameters of pin structures to analyze the thermohydraulic characteristics of heat-removal plates 13:1202–1207. https://doi.org/10.1134/S003602951813027X 3. Zubkov N, Poptsov V, Vasiliev S, Batako ADL (2018) Steel case hardening using deformational cutting. J Manufac Sci Eng. Trans Am Soc Mech Eng 6:8. https://doi.org/10.1115/1. 4039382 4. Zubkov NN, Vasil’ev SG, Poptsov VV (2017) New method of quench surface turning. Solid State Phenom 265:696–701 5. Zubkov NN, Ovchinnikov AI, Vasil’ev SG (2016) Tool–workpiece interaction in deformational cutting. Russ Eng Res 3:209–212 6. Petrushin SI, Proskokov AV (2010) Theory of constrained cutting: Chip formation with a developed plastic-deformation zone. Russ Eng Res 30:45–50 7. Kabaldin YuG, Kuzmishina AM (2016) Kvantovo-mekhanicheskoe modelirovanie deformatsii I razrushenia srezaemogo sloya pri rezanii (Quantum-mechanical deformation simulation and destruction of the cutting layer during cutting). Vestnik mashinostroeniya, Moscow 8. Grubyi SV (2014) Optimizatsiia protsessa mekhanicheskoi obrabotki i upravlenie rezhimnymi parametrami (Optimization of the machining process and control regime parameters). Optimizatsiia protsessa mekhanicheskoi obrabotki i upravlenie rezhimnymi parametrami, Moscow 9. Grubyi SV (2018) Calculation of the cutting forces when processing plastic materials with a wide range of thicknesses of the cutting layer. https://doi.org/10.18698/0536-1044-2018-23-10 10. Chaevskiy PA (2019) Optimizaciya konstrukcii sbornoj proreznoj frezy (Optimization of the design of the combined slotting mill) Budushchee mashinostroeniya Rossii.: tezisy dokl. Mezhdunarodnoj konf, Moscow 11. Grubyi SV, Chaevskiy PA (2020) Improving efficiency of machining of grooves on shafts of increased hardness structural steel. In: Proceedings of the 5th international conferenceon industrial engineering (ICIE 2019), Lecture Notes in Mechanical Engineering , vol 2. Springer, pp 921–929. https://doi.org/10.1007/978-3-030-22063-1_98 12. Artamonov EV, Pomigalova TE, Uteshev MH (2011) Raschet i proektirovanie smennyh rezhushchih plastin i sbornyh instrumentov (Calculation and design of removable cutting plates and prefabricated tools), TyumGNGU, Tyumen’ 13. Mikhailov MI (2016) Eksperimental’noe issledovanie vliyaniya sistem krepleniya rezhushchih plastin na zhestkost’ sbornyh rezcov (Experimental study of the effect of cutting plate mounting systems on the stiffness of precast cutters). Mekhanika mashin, mekhanizmov i materialov, Minsk

Mathematical Modeling of Cutting Process Output Parameters for Production Technological Preparation and Adaptive Control of Turning and Milling in Digital Production Systems A. R. Ingemansson(B) Volgograd State Technical University, 28, Lenin Avenue, Volgograd 400005, Russia [email protected]

Abstract. It is pointed out that the implementation of digital production systems (DPS) in mechanical engineering is the science-intensive solution for technological providing of stabile output of the machined surface finish and working performance of cutting instruments. On the basis of usage of modern CNC machinetools’ capabilities, the adaptive control (AC) of cutting modes is suggested. The up-to-date scientific problem of the development of mathematical models, which describe the influence of machining modes and parameters on the functional and output parameters of turning and milling, for the further implementation in technological preparation of production (TPP) and AC of cutting process in DPS was described. Typical materials for workpieces, cutting instruments, modes and parameters of turning and milling were determined. Experimental investigations were carried out and mathematical models were developed. For the convenient usage of models and for easy calculations at the stages of TPP and for AC of automated CNC machine-tools, mathematical models were presented as calculation formulas. On the basis of the analysis of developed mathematical models, the patterns of formation of machined surface roughness and cutting force, i.e., tool load, from points of the theory of cutting process and temperature-deformational patterns of high-speed plastic deformation were determined. Keywords: Digital production · Technological preparation · Adaptive control · Cutting process · Mathematical models · Surface roughness · Cutting force

1 Introduction The up-to-date direction of the increase of efficiency of the technological process of machining is the development of science-intensive solutions for technological providing of stable output of machined surface finish and working performance of cutting instrument. From the point of implementation of “Industry 4.0” concept in the mechanical engineering industry, this problem possesses a special value for digital production systems © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_123

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(DPS)––production systems, which is based on the integration of modern computing technologies, science-intensive equipment and technologies [1–4].

2 Relevance On the basis of implementation of modern CNC machine-tools capabilities [5], the adaptive control (AC) [6–8] of cutting modes is suggested. Modern CNC machine-tools allow to obtain information about the current spindle drive-motor power or torque and realize monitoring and automated maintenance on the basis of information about drive-motor load. Underlined parameters of load are directly depended upon main (tangential) cutting force––Pz (Ft). The adaptive control of the machining process is reasonably to realize through the cutting force value in aim to get desired results of machining––surface roughness and surface integrity and cutting tool life. Feed rate is the reasonable maintenance parameter, because the adaptive feed control is available in modern CNC machine tools. Besides this, feed factor possesses the most significant influence on the machined surface roughness and significant influence on tool life. However, there exists lack of complex methodologies, mathematical models, and software for maintenance of surface finish and tool life, based upon the underlined functions. Development of principles and mathematical models for adaptive control of the cutting process in DPS is the up-to-date scientific trend.

3 Setting of the Problem The target of the presented research is the development and justification of mathematical models, which describe the influence of machining modes and parameters on the functional and output parameters of turning and milling, for the further implementation in technological preparation of production (TPP) and AC of cutting process in DPS.

4 The Theoretical Part In the materials of the presented research, the arithmetic mean value Ra, mean roughness spacing Sm are the characteristics of output parameters of machining and tool load, which is expressed via cutting force Pz (Ft) is the characteristic of the functional parameter of machining. Due to the methodic of cutting modes assign, which is based on reference books and technological regulations [1, 9–14], the depth of cutting for preliminary turning and milling assigned to the value of 2 mm, for finish turning and milling–0.5 mm. Carbon and alloyed steels (“P” group) and stainless steels (“M” group) according to the international ISO standard been used as machined materials, which is widely spread in mechanical engineering industry. 40X steel GOST 4543-2016 (41Cr4 ISO, 5140 (H) AISI) is selected as a typical representative of carbon and alloyed steels and 20X13 steel GOST 5949-2018 (X20Cr13 ISO, 416 AISI) is selected as a typical representative of

Mathematical Modeling of Cutting Process Output Parameters

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stainless steels. Heat treatment modes in experimental investigations for three levels of variation of Brinell hardness HB factor for machined material have been assigned. The widely used and universal indexable inserts for NC turning operations are the rhombic inserts with the 80° angle between the side and end cutting edges (“C” form, according to ISO 1832-1991). Most widely spread indexable inserts in semi-finish and finish turning are inserts with nose radius 0.8 mm. Hereby, CNMG 120408 indexable inserts according to ISO 1832-1991 were assigned. Most widely spread and universal tools for NC milling are the end mills, which allow producing face milling, peripheral milling, shoulder milling, holes and slots machining, profile and plunger milling [14]. End mills with cylindrical shank and cemented carbide indexable inserts have been assigned as a typical representative of this kind of tools. Body of end mill: ST20-FCM20093-110, diameter of cutting part: 20 mm (“Big Daishowa”, Japan) [13]. Climb, nonsymmetric shoulder milling been used as a typical operation. Indexable inserts with nose radius 0.4 mm, as most versatile for semi-finish and finish milling has been used. In this research, thermal conductivity λ has been used as the factor, which represents the properties of tool material and shows a significant influence on temperaturedeformational, functional, and output parameters of cutting process. Besides this, values of thermal conductivity are available in reference books and in earlier suggested practical recommendations [15]. Following cemented carbides were selected according to the assigned tool and workpiece materials and modes of machining processes [15]. CVD-coated NC3215 indexable inserts, non-coated H01 inserts and non-coated cermet CN2500 (for preliminary turning) and CN1500 (for finish turning) were assigned for machining of carbon and alloyed steels (“P” group). CVD-coated NC5330 indexable inserts, non-coated H01 inserts and non-coated cermet CN2500 (for preliminary turning) and CN1500 (for finish turning) were used for machining of stainless steels (“M” group) (all listed inserts are “Korloy”, South Korea) [12]. PVD-coated ACP200, ACP300 and ACZ350S inserts (“Big Daishowa” (“Sumitomo”), Japan) were assigned for milling of “P” and “M” group steels [13]. Range of variations of factors of cutting speed and feed for preliminary and finish machining were assigned according to traditional methodology and reference books [1, 9–14]. Dry machining was performed. Turning operations were performed on CNC turning center, milling operations––on horizontal-spindle machining center (MC). Development of mathematical models was based on the results of multilevel fullfactor experiments. Minimal volume of the statistic sample for modeling obeys to dependency “Eq. 1”. kmin = 3n = 34 = 81

(1)

k min —minimal quantity of experimental combinations in full-factor experiments; n— quantity of factors. Comparison of obtained mathematical models by estimating their errors shows the advantage of power function models. For the convenient usage of models and for easy calculations at the stages of TPP and for AC of automated NC machine tools, mathematical models were presented as formulas, which are listed in Tables 1 and 2.

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Table 1. Mathematical models for TPP and AC of turning and milling operations with carbon and alloyed steels workpieces Type of machining

Calculation parameter

Calculation formula

Number of formula

Ra, µm

Ra = 130.7 × s1.18 × v−0.09 × λ0.02 × HB−0.36  1  1.18 Ra So = −0.09 0.02 −0.36

(2)

(4)

So (F), mm/rev

Sm = 0.57 × s0.94 × v0.01 × λ−0.06 × HB0.15  1  0.94 Sm So = 0.01 −0.06 0.15

Pz (Ft), N

Pz = 16501.7 × s0.72 × v−0.17 × λ0.006 × HB0.12 (6)

Ra, µm

Ra = 4520.9 × s1.08 × v−0.32 × λ0.31 × HB−1  1  1.08 Ra So = −0.32 0.31 −1

(7)

Sm = 1.65 × s0.87 × v−0.13 × λ0.11 × HB−0.03  1  0.87 Sm So = −0.13 0.11 −0.03

(9)

Pz (Ft), N

Pz = 1227438.3 × s0.22 × v−1.25 × λ0.02 × HB−0.004

(11)

Ra, µm

Ra = 7.13 × Sz 0.8 × v−0.21 × λ0.39 × HB−0.06 1  0.8 Ra Sz = −0.21 0.39 −0.06

(12)

(14)

Sz (F), mm/tooth

Sm = 5.96 × Sz 0.85 × v0.13 × λ−0.26 × HB−0.14  1  0.85 Sm Sz = 0.13 −0.26 −0.14

Pz (Ft), N

Pz = 4316.8 × Sz 0.2 × v−0.13 × λ0.04 × HB0.1

(16)

Ra, µm

Ra = 11.44 × Sz 0.84 × v−0.1 × λ0.09 × HB−0.02

(17)

Turning Preliminary

So (F), mm/rev Sm, mm

Finish

So (F), mm/rev Sm, mm So (F), mm/rev

130.7×v

0.57×v

×λ

×λ

1.65×v

(5)

×HB

×λ

4520.9×v

(3)

×HB

×λ

(8)

×HB

(10)

×HB

Milling Preliminary

Sz (F), mm/tooth Sm, mm

Finish

Sz (F), mm/tooth

7.13×v

5.96×v

Sz =



×λ

×λ

(13)

×HB

(15)

×HB

Ra 11.44×v −0.1 ×λ0.09 ×HB−0.02



1 0.84

(18)

Sz (F), mm/tooth

Sm = 0.27 × Sz 0.9 × v0.04 × λ−0.29 × HB0.52 1  0.9 Sm Sz = 0.04 −0.29 0.52

Pz (Ft), N

Pz = 10658.6 × Sz 0.1 × v−0.45 × λ0.19 × HB0.02 (21)

Sm, mm

0.27×v

×λ

(19) (20)

×HB

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Table 2. Mathematical models for TPP and AC of turning and milling operations with stainless steel workpieces Type of machining

Calculation parameter

Calculation formula

Number of formula

Ra, µm

Ra = 24.9 × s1.15 × v0.15 × λ−0.07 × HB−0.21  1  1.15 Ra So = 0.15 −0.07 −0.21

(22)

(24)

So (F), mm/rev

Sm = 0.76 × s0.88 × v−0.01 × λ−0.03 × HB0.1  1  0.88 Sm So = −0.01 −0.03 0.1

Pz (Ft), N

Pz = 134662.5 × s0.72 × v−0.57 × λ0.02 × HB0.04 (26)

Ra, µm

Ra = 20.4 × s1.4 × v−0.02 × λ0.01 × HB−0.04 1  1.4 Ra So = −0.02 0.01 −0.04

(27)

Sm = 1.16 × s0.91 × v−0.04 × λ0.1 × HB−0.04  1  0.91 Sm So = −0.04 0.1 −0.04

(29)

Pz (Ft), N

Pz = 1884646.9 × s0.14 × v−1.13 × λ−0.01 × HB−0.24

(31)

Ra, µm

Ra = 5.5 × Sz 0.51 × v−0.05 × λ0.53 × HB−0.43  1  0.51 Ra Sz = −0.05 0.53 −0.43

(32)

(34)

Sz (F), mm/tooth

Sm = 32.56 × Sz 1.04 × v0.01 × λ0.77 × HB−1.01  1  1.04 Sm Sz = 0.01 0.77 −1.01

Pz (Ft), N

Pz = 9891.1 × Sz 0.19 × v−0.22 × λ0.04 × HB0.03

(36)

Ra, µm

Ra = 4.7 × Sz 0.72 × v−0.02 × λ0.18 × HB−0.13

(37)

Turning Preliminary

So (F), mm/rev Sm, mm

Finish

So (F), mm/rev Sm, mm So (F), mm/rev

24.9×v

0.76×v

20.4×v

1.16×v

×λ

×λ

×λ

×λ

(23)

×HB

(25)

×HB

(28)

×HB

(30)

×HB

Milling Preliminary

Sz (F), mm/tooth Sm, mm

Finish

Sz (F), mm/tooth

5.5×v

32.56×v

Sz =



×λ

×λ

(33)

×HB

(35)

×HB

Ra 4.7×v −0.02 ×λ0.18 ×HB−0.13



1 0.72

(38)

Sz (F), mm/tooth

Sm = 14.72 × Sz 1.08 × v−0.32 × λ−0.17 × HB0.12 (39)  1  (40) 1.08 Sm Sz = −0.32 −0.17 0.12

Pz (Ft), N

Pz = 36536.2 × Sz 0.22 × v−0.55 × λ0.04 × HB0.03 (41)

Sm, mm

14.72×v

×λ

×HB

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The calculation formulas developed for modes and conditions of turning and milling, which listed in Table 3. Table 3. Modes and conditions for the implementation of developed formulas Type of machining (depth of cut)

Factor

Preliminary (t (ap) = 2 mm)

So (F), mm/rev

Finish (t (ap) = 0.5 mm)

Range

Turning

Factor

Range

HB of the workpiece material

0.09–0.15

Steel 40X HB 230–370 Steel 20X13 HB 190–300

Milling 0.3–0.5

Sz (F), mm/tooth

v (s), m/min

60–120

v (s), m/min

λ tool, Wt/m K

11–51

λ tool, Wt/m K

37.1–55.3

So (F), mm/rev

0.08–0.25

Sz (F), mm/tooth

0.06–0.12

v (s), m/min

100–200

λ tool, Wt/m K

11–51

60–120

v (s), m/min

100–200

λ tool, Wt/m K

37.1–55.3

5 Practical Significance Patterns of formation of machined surface roughness and cutting force, i.e. tool load, were formulated according to the analysis from the points of temperature-deformational patterns of cutting process [16]. Values of coefficients of degree in mathematical models for calculation of arithmetic mean value Ra for preliminary and finish turning and milling show that the feed rate influences more than other factors on the formation of machined surface roughness (formulas (2), (7), (12), (17), (22), (27, (32), (37)). Roughness increases with the increase of feed rate that corresponds with the patterns of surface roughness formation [10, 17]. The influence of cutting speed in turning process depends on the type of workpiece material. When turning a 40X steel, as a typical representative of carbon and alloyed steels, machined surface roughness decreases (formulas (2), (7)) with the increase of cutting speed. This trend corresponds with the increase of deformation speed and temperature in the cutting zone, and, respectively, easier metal flow in contact interaction zone (tool–chip) and improvement of conditions of formation of the machined surface. The influence of thermal conductivity of tool material in turning process also depends on the type of workpiece material. When turning 40X steel machined surface roughness Ra also increases (formulas (2), (7)) with the increase of thermal conductivity of tool material. This trend corresponds with an increase of heat flow from cutting zone due to the increase of thermal conductivity of tool material. This promotes the increase of the area of plastic contact of contact plastic deformations (CPD) zone (tool–chip interface), increase of cutting force and deterioration of conditions for the formation of the machined surface. With the increase of hardness of workpiece material, the value of arithmetic mean value Ra decreases (formulas (2), (7), (22), (27)) in turning and milling, which correspond with the patterns of cutting process ([10, 11, 16, 18] et al.).

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The influence of cutting speed and thermal conductivity of tool material on the value of arithmetic mean value Ra in turning process of stainless steels reflects features of the cutting process for such materials. With the increase of cutting speed in preliminary turning of 20X13 steel, the machined surface roughness also increases (formula (22)). Besides this, the increase of thermal conductivity of tool material leads to a decrease of Ra parameter value (formula (22)). These aspects are linked with the thermo-physical patterns of stainless steel cutting— high-frequency plastic deformation instability [16, 19]. The influence of cutting speed, thermal conductivity and hardness of workpiece material on the value of arithmetic mean value Ra in milling operations possesses its own features. Against the turning process [20], the influence of high-frequency plastic deformation instability in the machining process of stainless steels has a smaller influence in milling than in turning due to the short period of contact of every single cutting edge of milling tool in the chip formation process. The increase of cutting speed in preliminary and finish milling of carbon and alloyed steels and stainless steels promotes the decrease of Ra value (formulas (12), (17), (32), (37)). With the increase of thermal conductivity of tool material, machined surface roughness Ra also increases (formulas (12), (17), (32), (37)) in milling. Such influence of the increase of thermal conductivity of tool material corresponds with the increase of heat flow from cutting zone as it pointed before in the text. Mean roughness spacing Sm generally depends upon the feed rate [10] in edge cutting (formulas (4), (9), (14), (19), (24), (29), (34), (39)). Obtained mathematical models for cutting force Pz (Ft) calculation in turning and milling describe under-listed features of the machining process. With the increase of feed rate the thickness of the removed layer, stress level in deformation zone, dimensions of areas of plastic- and full-contact of CPD zone also increase, and, respectively, cutting force grows up (formulas (6), (11), (16), (21), (26), (31), (36), (41)). The increase of cutting speed promotes the decrease of cutting force (formulas (6), (11), (16), (21), (26), (31), (36), (41)). For example, in turning process, such influence corresponds with the increase of heat production, decrease of contact tangent stress level in CPD zone, the increase of share angle, decrease of areas of plastic- and full-contact of CPD zone. Thermal conductivity of tool material possesses not a significant influence on cutting force level in the investigated range of factors values. Increase of hardness of workpiece material promotes the increase of cutting force in preliminary turning (formulas (6), (16)). In finish turning reverse trend takes place– –the increase of hardness of workpiece material promotes the decrease of cutting force (formulas (11), (21)). This linked with the domination of the influence of heat production in the cutting zone on the cutting force level. In interrupted cutting (milling), the increase of stresses in cutting zone dominates over the intensity of heat production due to the short period of contact of every single cutting edge of milling tool in the chip formation process against the turning process.

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That is why the cutting force grows up a little with the increase of hardness of workpiece material in milling process (formulas (26), (31), (36), (41)).

6 Conclusions Developed calculation formulas allow to determine the values of arithmetic mean value Ra and mean roughness spacing Sm of machined surface, feed rate, and cutting forces in turning and milling. Formulas are intended for TPP and AC of automated NC equipment in DPS for metalworking. Listed mathematical models describe the patterns of formation of functional and output parameters of the cutting process. The analysis of developed mathematical models for TPP and AC of cutting process for modern automated CNC machine tools showed the patterns of formation of machined surface roughness and cutting force, i.e., tool load, from points of the theory of cutting process and temperaturedeformational patterns of high-speed plastic deformation.

References 1. Suslov AG et al (2019) Spravochnik tekhnologa (Reference book of the technologist). In: Suslov AG (ed). Innovacionnoe mashinostroenie. Moscow 2. Chang P (2017) Targeting “Industrie 4.0” . The Challenger 9:2–3 3. Ingemansson AR (2019) The development of informational-executive cyber-physical systems in materials production and metalworking. Innovative Technol Eng Design Competitive Prod 973:200–205. https://doi.org/10.1007/978-3-0357-3267-2 4. Ingemansson AR (2019) Characteristics, composition, mechanism function and modern aspects of implementation of digital production systems in mechanical engineering industry. In: Proceedings of the 5th international conference on industrial engineering 2:1167–1174. https://doi.org/10.1007/978-3-030-22063-1 5. Chang P (2018) AI case study. Breakthrough 10:12–15 6. Prasad BS, Prasad DS, Sandeep A et al (2013) Condition monitoring of CNC machining using adaptive control. Int J Autom Comput 10:202–209. https://doi.org/10.1007/s11633013-0713-1 7. Cus F, Zuperl U, Kiker E et al (2006) Adaptive controller design for feedrate maximization of machining process. J Achievements Mater Manuf Eng 17:237–240 8. Zuperl U, Cus F, Milfelner M (2005) Fuzzy control strategy for an adaptive force control in end-milling. J Mater Process Technol 164–165:1472–1478. https://doi.org/10.1016/j.jmatpr otec.2005.02/143 9. Dalskiy AM et al (2001) Spravochnik tekhnologa-mashinostroitelya. V 2 t. T. 2 (Reference book of the technologist. In 2 vol. Vol. 2). 5th ed. In: Dalskiy AM (ed). Mashinostroenie-1, Moscow 10. Suslov AG, Dalskiy AM (2002) Nauchnie osnovy technologii mashinostroeniya (Science basis of mechanical engineering technology). Mashinostroenie, Moscow 11. Gurevitch JL, Gorokhov MV, Zakharov VI et al (1986) Rezhimi rezaniya trudnoobrabativaemyh materialov: spravochnik (Cutting modes for hard-machined materials: reference book), 2nd edn. Mashinostroenie, Moscow 12. Korloy (2017) Metal cutting tools: catalogue. Korloy, South Korea 13. Daishowa B (2016) High precision toolholders: catalogue. Big Daishowa Seiki, Japan 14. Coromant S (2010) Machining work manual: guide. Elanders, Sweden

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15. Ingemansson AR, Bondarev AA (2019) The definition of thermal conductivity of cemented carbide cutting tools with multilayer wear-resistant coatings. Obrabotka metallov tekhnologia, oborudovanie, instrumenty (Metal working and material science) 3:97–105. https://doi.org/ 10.17212/1994-6309-2019-21.3-97-105 16. Talantov NV (1992) Fizicheskie osnovy protsessa rezaniya, iznashivaniya i razrusheniya instrumenta (Physical fundamentals of cutting, wear and destruction of the tool). Mashinostroenie, Moscow 17. Kalpakjian S, Schmid SR (2010) Manufacturing engineering and technology. Prentice Hall, USA 18. Makarov AD (1976) Optimizaciya protsessov rezaniya (Optimization of cutting processes). Mashinostroenie, Moscow 19. Lipatov AA (1987) Zakonomernosti protsessa rezaniya visokolegirovannyh stalei i puti povyshenia rabotosposobnosti tverdosplavnogo instrumenta (Highly-alloyed steels cutting process patterns and directions to increase efficiency of cemented carbide tools). Dissertation, Volgograd Polytechnical Institute 20. Solodkov VA (2018) Fizicheskie osnovy kontaktnih protsessov pri prerivistom rezanii (Physical fundamentals of contact processes in interrupted cutting). Volgogradskiy Gosudarstvenniy Tehnicheskiy Universitet, Volgograd

Study of Caprolon Turning Using Cutting Fluid O. Erenkov(B) , I. Lopushanskii, and D. Yavorskii Pacific National University, 136, Tikhookeanskaya street, Khabarovsk 680035, Russia [email protected]

Abstract. The article presents the results of experimental studies of caprolon turning using cutting fluid. The paper scientifically substantiates the use of water emulsion with the repellent addition during caprolon turning as a cutting fluid. Based on this, a new method for turning caprolon blanks was developed and patented. An experimentally established fact is that caprolon water absorption capacity is reduced when it is turned with the feeding of potassium palmitate water emulsion into the cutting zone. In this case, caprolon turning by means of traditional way leads to water absorption process activation. It has been experimentally proved that caprolon turning with the feeding of potassium palmitate water emulsion into the cutting zone provides better machined surface of the parts compared to the traditional method of turning. This is evidenced by the more uniform deviation profile treated surface and numerical values of the roughness parameters. The results of microstructural studies of caprolon chips are presented. It has been experimentally established that turning caprolon using an aqueous emulsion of potassium palmitate promotes the formation of continuous drainage chips. Turning caprolon in the traditional way leads to the formation of joint chips. Keywords: Caprolon · Turning · Cutting fluid · Water absorption · Cutting zone · Roughness

1 Introduction The characteristic feature of polymeric composite materials is their tendency to absorb moisture. This property is manifested due to the material structure heterogeneity and the presence of surface and interior cracks with various sizes in the volume of the material [1–3]. These cracks’ appearance is due to the features of the polymeric composite materials manufacturing process. The parts and products dimensions change and the physical and mechanical characteristics reducing are the consequences of the moisture absorption effect implementation which negatively affects the range of operational properties. The fact of the polymeric composite materials water absorption degree increasing after workpiece mechanical processing was established at previous studies [4–6]. Also, the significant intensification of polymeric composite materials’ water absorption process is significantly increased when the cutting fluids are used during the blanks turning.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_124

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At the same time, polymeric composite materials have low heat resistance which is 160–300 ºC. When these temperatures are exceeded, the material surface layer is melted and burns form on it. Such effects certainly reduce the treated surface quality of the part. Thus to ensure the high-quality machined surface of the polymeric composite materials part, it is necessary to reduce the temperature in the cutting zone during processing. However, the use of known cutting fluids for this purpose is considered impractical due to the above reason and, therefore polymeric composite materials are currently machined without the cutting lubricants using [7–10]. The technical solutions development aimed to resolve this contradiction is urgent, scientific, and practical. The task solution will ensure the required quality of parts and products made from polymeric composite materials while increasing the processing process productivity. The aim of this work is to experimentally verify the effectiveness of the new method for turning blanks from caprolon using cutting lubricants.

2 New Method Description This paper presents the original method for turning blanks made of caprolon and the method of technical essence is protected by a patent for the invention [11]. The technical problem to which the invention is directed is to improve the quality and productivity of the workpiece turning and ensure the required physical and mechanical properties of parts and products. This problem is solved by means of cutting fluid in the form of water-repellent emulsion stream supplying to the cutting zone at caprolon turning. The example of the method implementation. The caprolon blank is fixed in a lathe in a known manner. Then the workpiece is turned with a cutting tool and the cutting fluid simultaneously is fed into the cutting zone. The organosilicon liquids, water paraffin emulsion, asphalting-water-hydrocarbon emulsions, microwax water emulsions, sodium and potassium water emulsions of fatty acids salts can be used as water-repellent emulsion. The work of cutting is converted into thermal energy when caprolon is turned. The thermal energy significant part is absorbed by the tool cutting edges. Such effect leads to the cutting edges intense heating and consequently to its wear [12, 13]. Wear on the cutting edges provides roughness increase and formation of various surface defects on the treated caprolon surface. The receipt of the hydrophobizator emulsion to the cutting zone during caprolon turning will reduce the heating temperature of the workpiece surface layer, the forming chips and the cutting tool working edges. As a result, the degree of the cutting tool wear is reduced and the machined surface quality is improved as well as the processing accuracy by reducing the moisture absorption of caprolon from the emulsion and ambient air. This parameter is reduced due to the presence of the hydrophobic component in the emulsion. The presence of water-repellent additives in the emulsion ensures the hydrophobicity of the treated caprolon surface, which does not allow caprolon to absorb moisture from the emulsion and from the air surrounding the cutting zone. Due to this effect, the stability of physical and mechanical characteristics and the accuracy of the product

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linear dimensions are ensured. The cause of the defects formation in the form of surface and internal cracks is also eliminated.

3 Methods of Experimental Research Caprolon was chosen as the test material. This thermoplastic polymer material is widely used in various industries for the manufacture of a wide range of parts for various service purposes. Turning of experimental specimens was carried in a universal turning-screw cutting lathe 16K20F3S47. The geometric parameters and materials of the cutting tool, and also the cutting and feed rates were adopted on the basis of previous studies [14] and kept constant during this series of experiments. Component surface roughness was monitored by means of a TR 200 profilometer. As input parameters for surface roughness according to Russian standard 2789-73, the average deviations were selected for profile Ra , height of profile unevenness for ten points Rz , greatest height of profile unevenness Rmax , average step of profile unevenness S m . In addition, in accordance with the International standard ISO 4288-2014, the following surface roughness parameters were determined: distance from the tip of the greatest projection of the profile to the central line Rp ; distance from the bottom of the greatest depression of the profile to the central line Rv ; profile asymmetry Rsk . According to conditions of ISO 4288-2014, the profile with favorable values of parameter Rsk has clear high peaks, which differ from the average value. A surface with negative values of parameter Rsk has clear deep depressions in a smooth profile plateau. In less clear cases, parameter Rsk approaches zero. If Rsk > 1.5, then this means that the component surface does not have a simple shape, and it is probably impossible to characterize surface layer quality adequately according to parameters Ra and Rz . The component Pz of the cutting force in turning is measured by means of an SV1AK3 force sensor attached to the cutter. The results are displayed on the LCD screen of a DN-10 indicator [15]. The study of caprolon chips was carried out on a Primo Star electron microscope. In this work, we studied the parameters of caprolon samples water absorption in accordance with the requirements of Russian standard 4650-80. Such information is very useful since it allows estimates the advisability of caprolon blanks turning with cutting lubricants in the form of water-repellent emulsion. The water emulsion of palmitic acid potassium salt or potassium palmitate was used as cutting fluid in the form of water-repellent emulsion.

4 Results of Experimental Studies The profilograms of the processed surface are successfully used for profiling and operational quality control of the turning process [16, 17]. The profilograms of the caprolontreated surface for two cases of turning: without cutting lubricant and using cutting lubricant are presented in Fig. 1. The comparative analysis of these profilograms shows that the option of caprolon blanks turning with using cutting fluid, Fig. 1b is more preferable compared to the options for caprolon conventional turning without cutting fluid (Fig. 1a).

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This is evidenced by a more uniform deviation of the machined surface depressions and protrusions profile and the values of the roughness parameters, summarized in Table 1.

Fig. 1. Profilograms of the caprolon parts machined surfaces: a turning without cutting fluid; b turning with cutting fluid.

Table 1. The results of the study of the surface roughness of caprolon. Type of turning

The roughness parameters of the treated surface, µm Ra

Turning without cutting 8.39 fluid Turning with cutting fluid

4.92

Rz

Rmax Rp

Rv

Sm

Rsk

16.68 29.01 9.32 13.69 0.38 −0.17 8.70 10.75 5.52

8.23 1.27 −0.57

The analysis of the studied roughness parameters numerical values, (Table 1), confirms the fact of providing the better caprolon-treated surface in the case of turning blanks using cutting fluid. This is evidenced by the nature of the change in the controlled roughness parameters. So, the parameter Ra decreases by 1.7 times; the parameter Rz decreases by 1.9 times; the parameter Rmax decreases by 2.7 times. The remaining roughness parameters also have lower values compared to the turning option without the use of cutting fluid. Such effects convincingly indicate increasing in the treated surface quality in the case of the water emulsion of palmitic acid potassium salt using during turning. Microphotographs of caprolon chips obtained under various turning conditions (Fig. 2a, b) are experimental confirmation of the foregoing. The traditional caprolon turning without using a cutting lubricant leads to the articular chips formation (Fig. 2a). The formation of articular chips with increasing depth of cutting indicates deterioration in the conditions of chip formation and to increase in the energy intensity of the cutting process. The increase in the size of the chip individual elements occurs as a result

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of the compression stresses rising during turning. This leads to decreasing the quality indicators of the machined surface.

Fig. 2. Caprolon chips: a turning without cutting fluid; b turning with cutting fluid.

The caprolon turning with feeding into the cutting zone the potassium palmitate contributes to the continuous drainage chips formation (Fig. 2b). The formation of discharge chips with constant cross-sectional sizes along the entire length indicates the stability of the technological system when machining caprolon by turning [18, 19]. In turn, the stability of the processing process ensures the processed surface quality which is confirmed by the experimental data shown in Fig. 1 and Table 1. Table 2 summarizes the results of the cutting force component Pz study during caprolon turning while the depth of cut ranged from 1 to 6 mm. Table 2. The results of the cutting force component Pz study at caprolon turning. Type of turning

Cutting force component Pz , N Cutting depth, mm 1.0

2.0

3.0

4.0

5.0

6.0

Turning without cutting fluid

225

236

249

265

280

303

Turning with cutting fluid

198

206

223

244

261

289

Analysis of experimental data (Table 2) shows a steady tendency to increase cutting forces with of cutting depth rising. This tendency is manifested both when turning caprolon without potassium palmitate and when turning with potassium palmitate. Wherein the application of potassium palmitate provides the cutting force reduction over the cutting depth values entire range. In turn, the cutting force decrease leads to the appearance of such positive effects as the cutting speed increasing during turning and accordingly productivity of the entire processing process as well as a decrease in the power parameters of the process. The effect of the cutting force increasing with cutting depth rising is explained by the deformed material volume increasing during turning. This volume increasing occurs due to an increase in the cutting edges contact length with the material being processed [20].

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Table 3 summarizes the results of the caprolon water absorption study for various conditions of the workpieces’ external surface. Table 3. The results of the caprolon water absorption study. The investigated parameter

Sample surface condition Original

After turning without cutting fluid

After turning with cutting fluid

The average mass of absorbed water, mg

32.4

33.5

30.6

The average mass value of the absorbed water per unit surface area of the sample, mg/cm2

1.24

1.38

1.16

The average value of the mass fraction of water absorbed by the sample, %

0.57

0.46

0.41

Analysis of the experimental data summarized in Table 3 allows us to conclude that turning without the use of the water emulsion of palmitic acid potassium salt leads to the activation of the caprolon water absorption process. This effect is due to the material capillarity increase when the workpiece surface layer is removed. The degree of the water absorption process activity depends on the active area of the material involved in water absorption. The material active area depends on the values of the roughness parameters. Thus the higher the surface roughness of caprolon the more intensive the process of water absorption. This explains the fact caprolon water absorption capacity is reduced in case of turning with the water emulsion of palmitic acid potassium salt. The experimental data shown in Table 1 confirm this effect as the caprolon turning with the water emulsion of palmitic acid potassium salt provides a lower roughness of the treated surface. Wherein the intensity of caprolon moisture absorption after turning with the water emulsion of palmitic acid potassium salt is lower than that of the original, untreated workpiece. This is evidenced by the values of all the water absorption parameters studied in this work for the original material (Table 3). This fact is explained by the hydrophobic ability of the water emulsion of palmitic acid potassium salt used as a cutting lubricant for caprolon turning.

5 Conclusions It is scientifically substantiated the use of water emulsion with the repellent addition during caprolon turning as a cutting lubricant fluid. On this basis, the new method for turning caprolon blanks was developed and patented.

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An experimentally established fact is caprolon water absorption capacity is reduced in case of its turning with the feeding of potassium palmitate water emulsion into the cutting zone. In this case, caprolon turning by means of traditional way leads to activation of the water absorption process. It has been experimentally proved that caprolon turning with the feeding of potassium palmitate water emulsion into the cutting zone provides better machined surface of the parts in comparison with the traditional method of turning. This is evidenced by more uniform deviation profile treated surface, numerical values of the roughness parameters and the nature of the chip formation process. Acknowledgements. The reported study was funded by RFBR according to the research project № 20-08-00039.

References 1. Bartenev GV, Zuev YuS (1994) Strength and Disintegration of highly elastic materials. Chemistry, Moscow 2. Manin VN, Gromov AN (1980) Physicochemical stability of polymers in operational conditions. Chemistry, Leningrad 3. Arzamasov BN (2001) Material science: textbook for university students. Publishing House of MVTU, Moscow 4. Ratner SB, Yartsev VP (1982) Physical mechanics of plastics. Nauka, Moscow 5. Askadsky AA (1983) Chemical structure and physical properties of polymers. Chemistry, Moscow 6. Poduraev VN (1974) Cutting of hard-to-handle materials. Higher School, Moscow 7. Stepanov AA (1988) Cutting by high-strength composite materials. Engineering, Leningrad 8. Davim JP (2013) Nontraditional machining processes: research advances. Springer Science & Business Media, New York 9. Ahmad J (2009) Machining of polymer composites. Springer Science & Business Media, New York 10. Hong H, Tsa H (2012) Advanced analysis of nontraditional machining. Springer, New York 11. Erenkov OY (2017) The method of from caprolon billets turning. Russ Fed Pat 2612283, 3 March 2017 12. Kudinov VA (1967) Dynamics of machine tools. Mechanical Engineering, Moscow 13. Kabaldin YuG, Oleinikov AI, Shpilev AM et al (2000) Mathematical modeling of selforganizing processes in technological systems of cutting processing. Dalnauka, Vladivostok 14. Erenkov OYu (2015) Combined methods for turning polymer composite materials. Pacific National University, Khabarovsk 15. Erenkov OYu, Vereshchagina AS, Kravchenko EG et al (2016) Machining polymer workpieces on a lathe after preliminary surface deformation. Russ Eng Res 36:376–378 16. Suslov AG, Dalsky AG (2002) Scientific foundations of engineering technology. Mechanical Engineering, Moscow 17. Dornfeld DA, Lee D (2008) Precision manufacturing. Springer, New York 18. Ivakhnenko AG, Kuts VV (2013) Predesign studies of metal cutting systems. South-Western State University, Kursk 19. Kabaldin YuG, Shpilev AM (1998) Self-organizing processes in technological systems for machining diagnostics and control. Dalnauka, Vladivostok 20. Erenkov OYu, Faleeva EV, Erenkov SO (2012) Studies of the influence of cutting parameters on the type of chips during the turning of polymeric materials. Bull Mech Eng 9:68–70

Modeling and Optimization of Tools for Machining Helical Grooves A. A. Troshin1 , A. V. Kochetkov2 , and O. V. Zakharov1(B) 1 Yuri Gagarin State Technical University of Saratov, 77, Politechnicheskaya Street, Saratov

410054, Russia [email protected] 2 Perm National Research Polytechnic University, 29, Komsomol Pr., Perm 614990, Russia

Abstract. Helical grooves are the main element of end mills and drills. Processing a helical groove is a laborious, expensive, and technologically complex process. Currently, most commonly used disc tools are milling tools and grinding wheels. The profile of the tool is chosen simple. In this case, the problem of optimizing the size of the tool and its installation parameters is solved to obtain the best approximation to the given profile of the helical groove. The first drawback of this approach will be the uneven working conditions of different sections of the tool profile. The second drawback is the insufficiently high accuracy of the calculation, due to both the fundamental impossibility of obtaining an accurate profile and optimization errors. Therefore, the article proposes an accurate calculation of the profile of the tool for a given profile of the helical groove and the relative position parameters on the machine. A numerical method for calculating a profile that does not use differential geometry is considered. The advantage of the novel method is the guaranteed absence of cutting with an arbitrarily complex profile. The problem of determining the boundaries of the tool profile is also solved. The profile of the tool is also optimized depending on three parameters of its installation relative to the part (crossing angle, shortest center distance, and adjustment axial displacement). To test the algorithm, experiments were carried out to model the profile and its optimization. Some examples are presented in the article to illustrate the developed numerical algorithm. Keywords: Optimization · Disc tool · Helical groove · Complex profile · Milling tool · Numerical method

1 Introduction Helical grooves are the main element of end mills, drills, and rotors [1–6]. Processing a helical groove is a laborious, expensive, and technologically challenging process. The use of new complex profiles of helical grooves and increased accuracy requirements require improved calculation methods. Currently, the most frequently used for processing are disk tools such as milling cutters and grinding wheels [7–11]. The profile of the tool is © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_125

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chosen simply in the form of a cylinder, cone, torus, or combinations thereof. In this case, the problem of optimizing the dimensions of the tool and its installation parameters is solved to obtain the best approximation to the given profile of the helical groove [12– 17]. The solution of the problem can be carried out by methods of differential geometry [18–21], numerical methods [22–28], application of well-known CAD/CAE programs [29–32]. With the undoubted practical feasibility of the considered approach, it has drawbacks. The first drawback will be the uneven working conditions of different sections of the tool profile. The second drawback is the insufficiently high accuracy of the calculation, due to both the fundamental impossibility of obtaining an accurate profile and optimization errors. Therefore, the article considers the task of calculating the exact profile of a tool for a given profile of a helical groove and relative position parameters on the machine. Such a problem is more complicated and in the general case cannot be solved by differential geometry methods. A numerical method for calculating the profile is developed. The profile is modeled by a small set of reference points, which, by means of approximation, are increased by tens to hundreds of times. The advantage of the author’s method is the guaranteed absence of cutting with an arbitrarily complex profile. The developed method involves the processing of both traditional three-axis milling machines and 5-axis machining centers.

2 Mathematical Model For an analytical description, we use the coordinate processing scheme (Fig. 1). The Cartesian orthogonal coordinate system XYZ is connected to the helical groove in such a way that its profile is known in the plane Z = 0. The coordinate system X 1 Y 1 Z 1 is connected to the disk tool and correlated with the XYZ system using three settings: the shortest center distance A, the angle λ of the cross, and the adjustment axial displacement L. For convenience, the initial profile of the helical groove is set by reference points with coordinates x i , yi (i = 1, …, n), the number n of which determines the accuracy of the calculations. With a manual assignment, you can limit yourself to only 5–10 reference points (Fig. 2). To increase the accuracy of the calculation, the approximation of the obtained profile by a cubic spline is used to obtain the number of points 10–100 times greater than the initial number. The equations of the ith helix lying on the helical groove are ⎫ X = xi cos ϕ − yi sin ϕ; ⎬ (1) Y = xi sin ϕ + yi cos ϕ; ⎭ Z = ±pϕ, where p is the helix parameter (“ + ” corresponds to the right helix, “−” to the left); ϕ—angle of helical movement. Equations (1), when i is changed from 1 to n, describe a family of helical lines formed by the profile reference points. The helix lines defined by Eqs. (1) in the system X 1 Y 1 Z 1

Modeling and Optimization of Tools for Machining Helical Grooves

Fig. 1. Coordinate processing scheme.

Fig. 2. Specification of the helical groove profile.

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of a disk tool are transformed according to the formula: ⎫ X1 = −X sin λ + Z cos λ + L; ⎬ Y1 = −Y + A; ⎭ Z1 = X cos λ + Z sin λ.

(2)

The following numerical algorithm is used to calculate the instrument profile (Fig. 3). The initial data will be a family of helical lines in the coordinate system of a disk tool described by Equations (1) and (2). Dissect the desired tool surface with the system of planes Z 1 = C j (j = 1, …, m) and in each of the planes we find the minimum radius Rj min for the set of intersection points with i-helix lines. To do this, first solve the last equation of system (2) for all i-helix lines. After substituting expressions (1) into Eqs. (2), we obtain the transcendental equation for ϕ:

Fig. 3. The algorithm for calculating the tool profile.

f (ϕ) = (xi cos ϕ − yi sin ϕ)cosλ ± pϕ sin λ − Cj = 0

(3)

Substitute the obtained value of ϕ from Eq. (3) into the first and second equations of system (2) and find the coordinates X 1 and Y 1 of the points at which the helical lines intersected with the plane Z 1 = C j . In Fig. 1, these points form a contact line ab. If we construct all the projections of the intersection points in the axial plane and then the envelope to them, we get the picture in Fig. 4.

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Fig. 4. The construction of the envelope profile.

To calculate the radius Rj min of the tool surface in the plane Z 1 = C j , find the shortest distance from the axis of the disk tool (point 01) to the points found on the curve ab:   Rj min = min{Rj } = min X12 + Y12 . j

Having considered all the values j = (1, …, m), obtain the C − C profile of the surface of the disk tool in cylindrical coordinates Z 1 R1 , where Z 1 = C j , R1 = Rj min (Fig. 5).

Fig. 5. The surface of the disk tool.

The presented numerical algorithm does not use the differential characteristics of surfaces (tangent or normal). Therefore, the profile of the tool is determined unambiguously, and additional analysis of the obtained results or the solution of the inverse problem is not required. An important advantage of the considered numerical algorithm is the guaranteed absence of profile trimming during processing with the resulting disk tool.

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3 Simulation To implement the developed numerical algorithm, a program in MATLAB was prepared. The algorithm for calculating the profile of a disk tool additionally takes into account a number of aspects (see Fig. 3): (1) approximation of the profile of a helical groove to increase the number of reference points, (2) determination of the boundaries of the tool, (3) optimization of the profile of the tool. The second aspect is the definition of the boundaries of the disk tool required to set the C j range when calculating the profile. In general, it should be noted that one part of the tool processes the helical groove, the other only removes the allowance. The boundaries of the C − C profile can be calculated in different ways. One of the simplest and most reliable is to establish the applicate of the points of intersection of the 1st and nth helical lines with the axial plane of the tool, which have a minimum radius (Fig. 6). The point applicates are found in the third Eq. (2) when the angle ϕ in Eqs. (1) changes in the range ± 45°. If the profile point of the helical groove lies on a part of the surface facing the tool feed side, then its contact at this point does not end. Therefore, this part of the profile is supplemented by a straight line segment for technological reasons.

Fig. 6. Scheme defining tool boundaries.

The resulting tool profile may be technologically unsatisfactory. However, it can be significantly improved by changing the installation parameters of the tool relative to the part with a helical groove. The profile which is (1) has the smallest height, (2) has the smallest curvature should be considered the best. Numerical experiments showed that the profile of the instrument due to optimization can change the depth by 2–5 times and the curvature by 2–3 times. In this case, the sign of curvature may change (the profile becomes concave or convex). Some examples of the influence of the setup parameters on the tool profile are shown in Fig. 7. An analysis of these examples and the results of other calculations showed the following. The center distance to a lesser extent affects the profile, an increase in the parameter A leads to a slight decrease in the profile height, the curvature changes little. The center distance to a first approximation determines the maximum radius of the tool. Therefore, it should be assigned the largest possible.

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Fig. 7. Modeling the tool profile: a—crossing angle λ, b—adjustment offset L, c—shortest center distance A.

Changing the cross angle has the greatest effect on the form of the tool profile. This changes the width of the tool. Adjustment offset also affects the tool profile. However, the degree of change in the profile of the tool is highly dependent on the form of the profile and its initial location.

4 Conclusion A numerical algorithm is developed without using differential geometry to calculate the profile of a disk tool for machining a helical groove. The algorithm is implemented in a program in the MATLAB language. The correctness of the calculation was evaluated using various test cases and a comparative analysis with practical results. The advantage of the new method is the guaranteed absence of cutting with an arbitrarily complex profile.

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References 1. Litvin FL, Fuentes A (2004) Gear geometry and applied theory. Cambridge University Press, Cambridge 2. Wei J, Zhang Qi, Zhe Zhu Xu, Lyu SK (2010) Study on precision grinding of screw rotors using CBN wheel. Int J Precis Eng Manuf 11:651–658 3. Petukhov YuE, Domnin PV (2011) Shaping in machining a screw surfaces. Rusian Eng Res 31:1013–1015 4. Li G, Sun J, Li J (2014) Process modeling of end mill groove machining based on Boolean method. Int J Adv Manuf Technol 75:959–966 5. Teodor V, P˘aunoiu V, Berbinschi S, Baroiu N, Oancea N (2015) The metod of “In-plane generating trajectories” for tools which generate by enveloping—application in CATIA. J Mach Eng 15:69–80 6. Ren L, Wang S, Yi L, Sun S (2016) An accurate method for five-axis flute grinding in cylindricalend-mills using standard 1V1/1A1 grinding wheels. Precision Eng 43:387–394 7. Li G, Zhou H, Jing X, Tian G, Li L (2017) An intelligent wheel position searching algorithm for cutting tool grooves with diverse machining precision requirements. Int J Mach Tools Manuf 122:149–160 8. Liu Z, Tang Q, Liu N, Liang P, Liu W (2019) A Novel optimization design method of form grinding wheel for screw rotor. Appl Sci 9:5079 9. Nosov N, Bobrovskij S, Levitskih O, Khaimovich A, Kanatnikov N, Metel A, Zaides S (2019) Study of defects of the surface of rolls of rolling bearings under grinding. IOP Conf Se: Mater Sci Eng 537:032032 10. Shchurova AV (2017) Modeling the turbine rotor journal restoration located on cylindrical surface of the supporting bearer. Procedia Eng 206:1142–1147 11. Bolotov MA, Pechenin VA, Ruzanov NV (2016) Uncertainties in measuring the compressorblade profile in a gas-turbine engine. Russ Eng Res 36:1058–1065 12. Metel A, Zaides S, Bobrovskij N, Dak Fong F, Levitskih O, Quang LH, Lukyanov A (2019) Evaluation of microgeometry of cylindrical parts after cross-rolling in smooth plates. IOP Conf Ser Earth Environ Sci 315:062027 13. Pechenin VA, Bolotov MA, Rusanov NV (2014) Method of evaluation of profile form and shaped surfaces with application of wavelets. Res J Appl Sci 9:820–824 14. Fomin AA, Gusev VG, Timerbaev NF (2019) Providing of surfaces’ geometry at the design stage of profile milling operation of off-grade workpiece. Lecture notes in mechanical engineering. In: Proceedings 2019 of the 5th international conference on industrial engineering, pp 865–873 15. Grechnikov FV, Rezchikov AF, Zakharov OV (2018) Iterative method of adjusting the radius of the spherical probe of mobile coordinate-measuring machines when monitoring a rotation surface. Meas Tech 61:347–352 16. Ruzanov NV, Bolotov MA, Pechenin VA (2014) Development of compensation procedure for systematic errors of coordinate measuring machines with standard tooling. Res J Appl Sci 9:1082–1086 17. Telegin VV, Kozlov AM, Kirichek AV (2018) Solid modeling in autodesk inventor at initial stage of training of specialists in field mechanical engineering. In: Proceedings 2018 of the 4th international conference on industrial engineering. Lecture notes in mechanical engineering, pp 1241–1247 18. Pechenin VA, Bolotov MA (2016) Basing error in coordinate measurements of cylindrical gears. Russ Eng Res 36:630–634 19. Fomin AA, Gusev VG, Sattarova ZG (2018) Geometrical errors of surfaces milled with convex and concave profile tools. Solid State Phenom 284:281–288

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20. Lobanov DV, Arkhipov PV, Yanyushkin AS, Skeeba VY (2016) Research of influence electric conditions combined electrodiamond processing by on specific consumption of wheel. IOP Conf Mater Sci Eng. 142:012081 21. Zakharov OV, Balaev AF, Kochetkov AV (2017) Modeling optimal path of touch sensor of coordinate measuring machine based on traveling salesman problem solution. Procedia Eng 206:1458–1463 22. Bokhoeva LA, Rogov VE, Chermoshentseva AS, Lobanov DV (2016) Stability and process of destruction of compressed plate of layered composite materials with defects. IOP Conf Mater Sci Eng 142:012077 23. Fomin AA (2013) Kinematics of surface formation in milling. Russ Eng Res 33:660–662 24. Yalovoy OA, Zakharov OV, Kochetkov AV (2015) The centerless measurement of roundness with optimal adjustment. IOP Conf Ser Mater Sci Eng 93:012024 25. Korolev AA, Kochetkov AV, Zakharov OV (2018) Optimization of control points number at coordinate measurements based on the monte-carlo method. J Phys Conf Ser 944:012061 26. Lin C-J, Lin C-H (2019) An adaptive-group-based differential evolution algorithm for inspecting machined workpiece path planning. Int J Adv Manuf Technol 105:2647–2657 27. Zakharov OV, Kochetkov AV, Bobrovskij NM, Bobrovskij IN, Melnikov PA (2016) Analysis of stationary means of measurement filters with optimum sensitivity. In: Proceedings 2016 international conference on actual problems of electronic instrument engineering, pp 241–244 28. Liu Z, Tang Q, Liu N, Song J (2019) A profile error compensation method in precision grinding of screw rotors. Int J Adv Manuf Technol 100:2557–2567 29. Li G, Zhou H, Jing X, Tian G, Li L (2018) Modeling of integral cutting tool grooves using envelope theory and numerical methods. Int J Adv Manuf Technol 98:579–591 30. Brzhozovskii BM, Zakharov OV, Kochetkov AV (2014) Numerical shaping of a disk tool for the machining of helical surfaces. Russ Eng Res 34:740–742 31. Wasif M, Iqbal SA, Ahmed A, Tufail M, Rababah M (2019) Optimization of simplified grinding wheel geometry for the accurate generation of end-mill cutters using the five-axis CNC grinding process. Int J Adv Manuf Technol 105:4325–4344 32. Li G (2017) A new algorithm to solve the grinding wheel profile for end mill groove machining. Int J Adv Manuf Technol 90:775–784

Increase in Accuracy of Calculation of Cut Thickness Parameters at Profile Milling A. A. Fomin1(B) , R. G. Safin2 , and N. M. Terekhin2 1 Vladimir State University, 87, Gorky Street, Vladimir 600000, Russia

[email protected] 2 Kazan National Research Technological University, 68, K. Marx Street, Kazan 420015, Russia

Abstract. Machining of materials is characterized by a continuous increase in productivity, which is reached by the increase in the cutting modes and decrease in auxiliary time for the performance of technological operations. At design calculations of machining operations of steels, cast irons, other strong and solid metals and alloys, the authors developed and used the mathematical models of parameters of the cut thickness, which are received at certain assumptions, which decrease an accuracy of calculations of the maximum thickness, area, and volume of the cut thickness. Alongside with this, there is a large number of the materials (wood, plastic, etc.) which have a smaller mechanical durability in comparison with metals and are processed by turning, milling at much higher cutting modes. The processing of the specified materials is carried out at rather low cutting modes, and therefore errors of calculation of parameters of the cut thickness are made by no more, than one percent, which is quite admissible. The use of the known models of the cut thickness in design procedures of machining of wood, etc., leads to increasing of calculation errors by (10–17)%, which reduces the efficiency of the designed equipment during their subsequent operation. In this regard, there is a need for the development of some new mathematical models, which provide more exact calculations of parameters of the cut thickness and are not limited by the cutting modes. In the future, the importance of such models will only increase. The developed models considerably increase the accuracy of design calculations of machining operations, and they can be used for cylindrical and profile milling of workpieces at high cutting modes. Keywords: Milling · Cut thickness · Mathematical model · Calculation error · Cutting mode

1 Introduction The indicators of the cut thickness at machining of the substandard workpieces, which are characterized by a significant change of an allowance and hardness of the surface layer, define the mechanism of material removal [1–9], vibration level of a technological system [10–13], conditions of contact between cutting tool and workpiece, the firmness © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_126

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of tool and also the quality parameters of the processed surfaces [14–18]. The cut thickness determined also a productivity of technological operation, geometrical accuracy of processed surfaces (roughness, waviness, a deviation of a relative positioning of the surfaces) [8, 17, 19–25]. Besides, the values of the cut thickness parameters are necessary for the calculation of a cutting force, power of electric motors of the main movement of the cutting tool and working feed of workpiece [26–32], and therefore the calculation accuracy of the parameters of cutting layer is extremely important. At justification of technical characteristics of processing equipment, geometrical and physic-mechanical indicators of details and quality, the important part is assigned to mathematical modeling and computer optimization of machining processes [33–40].

2 The Reason of Quite Low Accuracy of the Known Formulas for Calculation of Cut Thickness at Machining So far parameters of the cut thickness are calculated by use of mathematical models, which of determining an assumption was accepted: an arch of movement trajectory of the cutting edge was replaced by a straight line, what led to an error of calculation of parameters of the cut thickness. At small working feeds of the cutting tool or the processed workpieces, the error of calculation of the cut thickness for the known models is no more than one percent, what quite meets the requirements of design accuracy. Milling of materials with the small physic-mechanical characteristics (hardness, durability, etc.) is implemented at the higher feeds of a cutting tool. When milling wood, working feeds are appointed in ten times more than when processing metals, which leads to a decrease in accuracy of calculation for the known models.

3 Influence of Workpiece Feed on Calculation Error of the Maximum Values of the Cut Thickness Now at design calculations of wood milling, the model of the maximum thickness of the cut thickness is used in the form: amax ≈ Sz sin ϕ,

(1)

where Sz —feed on mill tooth; ϕ—an exit angle of the cutter. Model (1) does not consider a profile of a shaped mill, is approximate, and an increase in feed leads to calculation errors (Fig. 1). In modern woodworking the machine tools, providing milling of wood with working feeds to 350 m per minute [11] are known. Calculations with an application of approximate model (1) show that at workpiece feed of 350 m/min a calculation error of the maximum values of thickness, area, and volume of cutting material is 17%. At further increase in feed, the calculation errors increase, which calls into question expediency of use of approximate models at the design of highly productive milling processes. Told confirms the need of development of mathematical models of the cut

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Fig. 1. Influence of working feed of workpiece on calculation errors of the maximum values of the cut thickness by using the known formulas.

thickness, which provide high- calculation precision of milling processes of wood and are not limited by the cutting modes. Let’s consider the scheme of thickness formation of the cut thickness amax during two adjacent elementary cuts by the teeth of a shaped mill (Fig. 2). After the turn of a shaped mill on one tooth, its center is moved in direction of axis X (system X O2 Y ) on a distance, equal to feed on tooth Sz . Traces of adjacent cuts O3 O6 i O4 O6 with radius Ri form the distance, which is equal to the maximum thickness of the cutting material amax = O3 O4 at the exit of teeth from a contact with the processed material. The mathematical formula of the maximum thickness of cutting material for the concave cutting profile of a shaped mill is developed:

Fig. 2. The scheme of thickness formation of the cut thickness αmax during two adjacent elementary cuts by the teeth of a shaped mill

 zi )) + Rmin = Rrk (1 − cos(arcsin Rrk    

2  2  vs  R 1 − cos arcsin zi + Rmin + 2π rk  R ωZ rk − 

amax

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4π vs − ωZ

    

zi + Rmin t − t 2 , 2 Rrk 1 − cos arcsin Rrk

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(2)

where Rrk —radius of cutting profile of a mill; zi —distance between the cross section and geometrical center of a mill; Rmin —minimum radius of a mill; vs —working feed of workpiece; ω—angular speed of a mill; z—number of mill teeth; t—cutting depth. Model (2) describes the change of the maximum thickness of the cut as milling mode elements (t, vs , ω) and parameters of a profile mill (Rrk , Rmin , zi , and z). Model is universal and can be used for cylindrical and profile milling and is not limited to cutting modes. From (2) follows that the value  amax is the variable function, depending in (2) turns into zero, what on distance zi . At zi = 0, three members cos arcsin Rzrki leads to an extremely maximum value of thickness of the cut thickness, which arises in the cross plane of symmetry of a shaped mill and is determined at the concave cutting contour (profile) of a shaped mill by a formula:   v 2 vs  s amax = Rmin − R2min + −2 2Rmin t − t 2 , (3) nZ nZ where n—frequency of rotation of a mill. The area of the cut thickness in the longitudinal workpiece section at zi = 0 is determined by a formula:     zi Fsl = Sz (t − k ) = Sz t + Rrk cos arcsin Rrk  

2  3    zi 10 π vs 2 ) + Rmin + Rrk − + Rmin + Rrk (4) − [−Rrk cos arcsin Rrk 60Zω where k —height of roughness of the processed surface, which is formed as a result of crossing of two adjacent elementary cuts by the radius Ri (Fig. 3). The roughness 1–4 has a height k , whose value when milling wood changes ranging from tens of micrometers to the tenth shares of millimeter depending on the cutting mode, and therefore it is possible to assume that this factor has no significant effect on calculation accuracy. However, as shown in experiments, despite small size, the factor k has a notable impact on results of calculation, which is explained by their large number (thousands) of the processed product surface. Point 5 is situated from the mills center O at distance of 0.5 Sz and is located in plane 2–5, where height k accepts the maximum value. In the known formulas of area of the cut thickness, the factor k is absent. The material volume, which is removed by a single tooth, is equal to   B , (5) Vsl = 2Fsl Rrk arcsin 2Rrk where B—is mill height. The adequacy of models (2)–(5) was estimated experimentally, at the same time the divergence of the design and experimental data made (0,1 −0, 3) % for the milling

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Fig. 3. Height of the roughness, formed on the processed surface as a result of crossing of two adjacent elementary cuts by mill teeth.

modes: mill radius R = 40 mm, cutting depth t = 5 mm, working feed of workpiece Sz = 0, 5 mm/tooth. 2. R = 50 mm, t = 15 mm, Sz = 1, 5 mm/tooth. 3. R = 65 mm, t = 25 mm, Sz = 2, 5 mm/tooth. The developed models (2)–(5) are checked for adequacy by their use when developing technology and the equipment for profile milling of substandard workpieces—the peripheral segments, which are formed when cutting logs and also products of stem wood. The equipment has a system of automatic control of cutting power, whose values are determined by the specified models. Comparison of calculated and experimental values of force characteristics and cutting capacities showed their good coincidence not only in laboratory, but also under production conditions. The analysis of models showed that at profile milling in the cross plane of symmetry of a shaped mill (Fig. 4a) with a concave profile a contact length of a cutting tooth with the processed material is more, than in the plane of each end face, as on the front, and the back surface of the cutting wedge (Fig. 4b, c). Width of the sickle on the front surface in the cross plane of symmetry was 1.1 mm, and on the back surface—0.9 mm, and the area of contact on the front surface of tooth is 19.5% more than on back surface.

Fig. 4. The mill tooth coated with blue paint before processing (a), change of the area of tooth contact with workpiece on a front (b), and back (c) surface.

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At profile milling by a mill with the convex cutting profile the situation changes: in the cross plane of symmetry of mill a width of the sickle is less than on both end faces, but the ratio of width of contact on the front and back surfaces of the cutting tooth remains the same. Thus, models (2)–(5) provide high precision of design calculations of technological operation, are not limited to a framework of the cutting modes, and are applicable for productive cylindrical and profile milling of workpieces. The obtained experimental data confirmed the theoretical provision that in the neighborhood of the cross plane of symmetry of a shaped mill with a concave profile arises a big cutting force and a cut thickness than in the neighborhood of end faces. Big width of the area of contact on the front and back surface of the cutting wedge in the neighborhood of the cross plane of symmetry of a mill testifies to this.

4 Conclusion 1. In design calculations of machining operations of steels, cast irons, solid alloys are developed and used mathematical formulas for determining parameters of the cut thickness, which are received at assumptions, which reduce the accuracy of calculation of the maximum thickness, the area, and volume of the cutting material and, therefore, force and power characteristics of the designed equipment. Processing of the specified materials is carried out at rather low cutting modes, therefore errors of calculation of parameters of the cut thickness make no more, than one percent, that is quite admissible. 2. There is a large amount of the materials (wood, plastic, etc.), which are characterized considerably by smaller mechanical durability in comparison with metals, and processed at much higher cutting modes, which causes an increase in errors of calculation to (10–17)%, reduces the quality of design procedures and efficiency of the designed equipment. 3. In this regard, new mathematical formulas for calculation of the cut thickness indicators are developed. Formulas are universal, provide exact calculations of cutting forces and cutting power, and are independent of cutting modes, which is very important. They are checked for adequacy during tests of the machine tool for milling of wood and can be used at design of technological operations of machining of wood.

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30. Nekrasov RY, Tempel YA, Putilova US (2018) Precision CNC machining and ways to achieve it. MATEC Web Conf ICMTMTE 224:30 31. Grechnikov FV, Rezchikov AF, Zakharov OV (2018) Iterative method of adjusting the radius of the spherical probe of mobile coordinate-measuring machines when monitoring a rotation surface. Meas Tech 61:347–352 32. Yemelyanov V, Tochilkina T, Vasilieva E, Nedelkin A, Shved E (2018) Computer diagnostics of the torpedo ladle cars. AIP Conf Proc 2034:020008. https://doi.org/10.1063/1.5067351 33. Yemelyanov VA (2014) Intelligent information technology of visual information processing for metals diagnostics. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu 4:66–73 34. Konovalov S, Chen X, Sarychev V et al (2017) Mathematical modeling of the concentrated energy flow effect on metallic materials. Metals 7(1) 35. Nekrasov RY, Tempel YA, Tempel OA, Soloviev IV, Starikov AI (2017) Numerical studies to determine spatial deviations of a workpiece that occur when machining on CNC machines. MATEC Web Conf ICMTMTE. 129:7 36. Nekrasov RY, Tempel YA, Starikov AI, Proskuryakov NA (2018) Fuzzy controllers in the adaptive control system of a CNC Lathe. Russ Eng Res 38(3):220–222. https://doi.org/10. 3103/S1068798X18030188 37. Sharkov OV, Koryagin SI, Velikanov NL (2016) Design models for shaping of tooth profile of external fine-module ratchet teeth. IOP Conf Ser Mater Sci Eng 124:012165. https://doi. org/10.1088/1757-899X/124/1/012165 38. Sharkov OV, Koryagin SI, Velikanov NL (2018) Shaping cutter original profile for fine-module ratchet teeth cutting. IOP Conf Ser Mater Sci Eng 327:042102. https://doi.org/10.1088/1757899X/327/4/042102 39. Gromov VE, Kormyshev VE, Glezer AM et al (2018) Microstructure and wear properties of Hardox 450 steel surface modified by Fe–C–Cr–Nb–W powder wire surfacing and electron beam treatment. IOP Conf Ser Mater Sci Eng 411(1) 40. Lashkov VA et al (2016) Modeling of a reduction zone of the gasifier installation IOP Conf Ser Mater Sci Eng 124:012111. https://doi.org/10.1088/1757-899X/124/1/012111

Mathematical Modeling of Energy Characteristics at Profile Milling of Substandard Workpieces A. A. Fomin1(B) , R. V. Yudin2 , and D. G. Riabushkin3 1 Vladimir State University, 87, Gorky street, Vladimir 600000, Russia

[email protected] 2 Voronezh State University of Forestry and Technologies Named After G.F. Morozov, 8,

Timiryazev Street, Voronezh 394087, Russia 3 Kazan National Research Technological University, 68, K. Marx Street, Kazan 420015, Russia

Abstract. The article presents the changing of the workload on the system MFTW (machine, fixture, tool, and workpiece) in the process of profile milling of workpieces, characterized by a permanent positive and negative change of the removable over-measure along the entire length of the treated surface. The mathematical dependences of the main and radial components of the cutting force, as well as the cutting power as a function of the increment of the over-measure, the elements of the profile milling regime, and the geometrical characteristics of the cutting tool are obtained, on the basis of which the modeling of the profile milling process was carried out. The scientific information, obtained as a result of modeling, is the basis for the qualitative design of the technological operation of profile milling of articles, characterized by a permanent change of the removable over-measure. The obtained models can be used for assigning cutting regimes at profile milling of sub-standard workpiece, which provides high geometric accuracy of the processed surfaces. Keywords: Profile milling · Workpiece · Single cut · Cutting speed · Changing over-measure · Cutting force · Cutting power

1 Introduction In the manufacturing process of preparations by methods of casting and stamping, the used equipment can wear out more intensively in one direction, as a result of which on the preparations a constantly increased or decreased over-measure is formed. This variable over-measure must be removed at a subsequent machining operation. In the woodworking industry at cutting of the logs the peripheral segments, coated by bark, remain [1–5]. The ends of peripheral segments, due to different diameters of the base and the top of the log, have a different thickness, and therefore the over-measure of these

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_127

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segments, permanently is changed in one direction, along the entire length of the workpiece. Peripheral segments in woodworking enterprises are formed in large numbers, are not used for their intended purpose: their are burned or, at best, they are reprocessed into a technological chain. Therefore, mechanical processing of peripheral segments, in order to obtain high-quality wood products, represents an important scientific and economic task [6–15]. The peripheral segments have a significant length (from 2 to 6 m). In the same time, a standard allows a relative increment of the over-measure in 10 mm on a length of 1 m, what leads to a significant increase in the over-measure, removable at the end of the processing of the long workpiece. A permanent positive or negative increment of the over-measure is called a runout, which causes an increase of the workload in the technological system and a significant increase in the vibration level of its elements, what negatively affects on the profile milling process [16–20]. So, at profile milling of the workpiece from oak with a positive increment of overmeasure 10 mm per 1 m of the length, the cutting power reaches 60 kW, what causes considerable elastic deformations of the elements of the technological system, a decreasing of the quality of the treated surfaces, and also overloading and possible breakdown of the machine’s executive organs [21–27]. To eliminate such extreme situations, schemes, methods of profile milling of workpieces with heterogeneous properties were analyzed, technological equipment with automatic control was developed. In this connection, information about the nature of the change of the workload and its numerical values in a function of the elements of the cutting regime and of the processing time is very important. Elimination of extreme situations during the processing of unstable workpieces is possible on the basis of mathematical models, connecting the energy characteristics of profile milling (components of cutting force and milling power) with the independent input factors, characterizing the workpieces, the cutting regime, and the cutting tool [28–33]. Known models of cutting force and effective power provide satisfactory calculation results for cylindrical milling at low cutting regimes and a relatively even distribution of the over-measure along the length of the workpiece. At high speeds of the working feed of the workpiece, the error of calculations for these models increases significantly, as a result of which the above models are unsuitable for profile milling, since they do not take into account the curvature of the cutting teeth of the profile tool, the significantly longer length of its contact with the workpiece, etc. In famous works, the profile milling of musical instrument parts from hornbeam wood was investigated, refined models of the parameters of the layer being cut are given for convex and concave tool’s teeth. The dependencies of the cutting force in the function of the feed to the tooth and the contact angle for milling hornbeam are determined. Recommended feed per tooth 1.0 … 1.2 mm and a cutting angle of 70°…°75°, which provide minimal energy costs for processing. Known dependencies are not applicable to profile milling of long and wide curvilinear convex and concave surfaces with shaped cutting tools [34–43]. The issues of profile milling of wood workpieces with knottiness, stochastic over-measure change and of hardness, lack of developed technological bases are not considered, as a result

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of which the recommendations, contained in well-known works are not applicable to high-performance processing of large sawmill waste [44–52]. Thus, the development of adequate mathematical models of cutting power, the main and radial components of the cutting force, applicable for the development of automated equipment and efficient processes for the profile milling of stem wood and large sawmill waste is in high demand nowadays.

2 The Time of a Single Cut in the Profile Milling of a Workpiece with a Runout and the Geometric Interpretation of the Main Component of the Cutting Force The change in the external load on the technological system takes place in time, so for the mathematical description it is necessary to have, first of all, the time of a single cut of the workpiece (cut by the tooth of the tool). The rate of increase in the over-measure to be taken depends on the amount of runout of the workpiece, which determines, along with the profile milling mode, the time of a single cut performed by one tooth of the cutter. By the time of the single cut τ E is meant the time of passing of one cutting blade of the cutter the angle of contact with the workpiece. When the workpiece is milled without a runout, the time τ E is constant from the beginning to the end of the workpiece machining, and when milling the workpiece with the runout τ E increases continuously with a positive increment of the over-measure and decreases with its negative increment. In the function of the cutting mode, the parameters of the shaped cutter, the time of a single cut for milling the workpiece without a runout are determined by the formula:    t0 /ω (1) τε = 2 arcsin 2Ri where t 0 is the initial cutting depth, defined by the machining regime; Ri , ω, respectively, the current value of the radius and the angular velocity of the profile mill. The time of a single cut, when milling a workpiece with a runout, is.  t0 ± vs τε tgβsb τsb1 = 2(arcsin )/ω (2) 2Ri where vs is a feed of the workpiece; β sb is the average statistical angle characterizing the value of the runout of the workpiece. The plus sign, minus sign in the formula (2) are used, respectively, when removing the over-measure of the workpiece with a positive and negative increment. The time increment of the second, third, ith unit cut caused by the runout of the workpiece with a positive increment of the over-measure is determined by the equalities: τsb2 = 2τsb1 ; τsb3 = 3τsb1 ; τsbi = i · τsb1 where i is the current number of a single cut.

(3)

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With a negative increment of the over-measure, expression (3) looks like τsb2 = 0.5τsb1 ; τsb3 = 0.33(3)τsb1 ; τsbi = τsb1 · i−1

(4)

It follows from (3) and (4) that when milling a workpiece with a positive increment of the over-measure, there is an increase in the time τ sbi , the main component of the cutting force, and a decrease in the rest time τ otd (in the absence of cutting) occurring in each elementary cutting cycle. Increasing the workload on the technological system causes additional elastic movements of its elements, which negatively affects the geometric accuracy of the machined surfaces of the product. When milling a workpiece with a negative increment in the over-measure, the time τ sbi and the main component of the cutting force are reduced, and the rest time τ otd increases, which contributes to a more complete resilient recovery of the technological system. Expressions (3) and (4) are necessary to determine the peak and average values of the elementary principal and radial components of the cutting force.

3 Graphic Interpretation of the Main Component of the Cutting Force When Milling a Workpiece with a Positive Increment of the Over-Measure With the passage of time τ, the number i of unit cuts increases. The peak value of the main component Pz of the cutting force when machining a workpiece with a positive increment of the over-measure increases from Pz max to Pzsbmax (Fig. 1, vertical dashed lines 1–4).

Fig. 1. Change of the main component Pz of the cutting force during profile milling of the workpiece with a positive increment of the over-measure.

During the turning time τ otd of the profile cutter by one turn, the increment of this force is Pzsb , and its total modulus reaches the value: Pzsbmax = Pz max + dPzsb

(5)

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The time of the elementary cutting cycle with a positive increment of the overmeasure is τz = τε + τsb1 τotd

(6)

The time of the elementary cutting cycle τ z and the machine time of a single cut τ E in the processing of wood without a runout are constants for the given cutting conditions and the characteristics of the cutting tool. The increase in the time of elementary cutting τ sbi during the processing of the workpiece with the runout + β sb continuously increases, which leads to a progressive decrease in the rest time of τ otd , and, consequently, the time of elastic restoration of the technological system. The latter circumstance leads to a decrease in the level of vibration of the technological system, but an increase in the over-measure due to the runout of + β sb leads to an increase in the cutting force and elastic deformation of the workpiece under the action of this force. Therefore, two factors affect the shaping process of the surface being treated: a progressive increase in the elastic deformations of the workpiece due to the increase in the cutting force and a reduction in the level of vibration of the technological system due to a reduction in the time of elastic restoration of the workpiece.

4 Graphical Interpretation of the Main Component of the Cutting Force When Milling a Workpiece with a Negative Increment of the Over-Measure During milling a workpiece with a negative increment of the over-measure (–β sb ), the cutting depth, the angle of contact (E1 + E2 )•i, and the thickness of the cut-off layer (Fig. 2) decrease, therefore, from the position of ensuring high geometric accuracy of the treated surface, it is advisable to direct the workpieces to a zone of cutting with the vertex end. In addition, the direction of the workpiece by the vertex end simplifies its orientation in the initial stage of processing. The time of the elementary cutting cycle with a negative increment of the overmeasure is τr = τε −τsb1 + τotd

(7)

Reducing the machine time of a single cut in the general structure τ z , typical for milling a workpiece with a negative increment of the over-measure, causes an increase in the rest time τ otd . Taking into account the prevailing influence of the elastic deformations of the workpiece on the shaping process, it can be stated that in the profile milling of the workpiece with a negative increment of the over-measure, the higher geometric accuracy of the machined surfaces of the product will be provided.

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Fig. 2. Change of force Pz at profile milling of a workpiece with a negative increment of the over-measure.

5 Models of the Main, Radial Components of the Cutting Force and the Power of Profile Milling of the Workpiece with a Runout The main component Pz of the cutting force is related to the cutting power Pr by the formula: Pz =

Pr v

(8)

where v is the average value of cutting speed. The radial component of the cutting force Py = mPz = m

Pr v

(9)

where m is a coefficient, which is a function of the initial conditions of cutting: the sharpness of the blade, the average thickness of the cut layer, and the cutting angle. It follows from (8) and (9) that the main Pz and radial Py components of the cutting force are determined, if the profile milling capacity Pr is known. Cutting power at profile milling with a positive and negative increment of an allowance of workpiece is determined respectively by formulas:     Kt · apop (t + vs τ · tgβsb ) Rmax − Rmin B arcsin (10) vs Pr = 30 1 − cos αmax 2Rpκ     Kt · apop (t + vs τ · tg(π − βsb )) Rmax − Rmin B Pr = arcsin (11) vs 30 1 − cos αmax 2Rpκ where K t is the tabular value of the specific work of cutting; apop = ap •aw •ar •aδ •av is the common correction factor; ap , aw , ar , aδ , av are the correction factor for the species, wood moisture, blunting of the cutting blades, cutting angle, and cutting speed; t is the depth of cut; vs is a minute feed of the workpiece; τ is the current milling time; β sb

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is the average statistical angle characterizing the amount of runout of the workpiece; Rmax , Rmin , respectively, maximum and minimum radius of a shaped mill; αmax is a half of the central corner, corresponding to length of a profile of a shaped mill; Rrk , B is the radius of the cutting profile and the height of the profile cutter, respectively. Minute feed of the workpiece and radius of the cutting profile of a shaped mill are defined, respectively, by formulas: vs = 10−3 Sz zn

(12)

Rrk = (Rmax − Rmin )(1 − cosαmax )−1

(13)

where Sz is a feed on mill tooth; z, n is the number of teeth and frequency of a mill rotation. In this connection, the mathematical models of cutting power at the profile milling of the workpiece with the positive and negative increment of the over-measure are found, respectively:   · apop (t + 10−3 Sz znτ · tgβsb ) B Sz znRrk arcsin Pr = 10 3 2Rrk   −3 Kt · apop (t + 10 Sz znτ · tg(π − βsb )) B Sz znRrk arcsin Pr = 10−4 3 2Rrk −4 Kt

(14) (15)

On the basis of (9)–(15), modeling of cutting power in the program Advanced Grapher environment is carried out and schedules (Fig. 3) of influence of height (a) and radius of a mill profile (b) on cutting power are constructed. The width at cylindrical milling is equal to height B of a tool, and cutting power is described by straight lines 1–3 (Fig. 3a), which relate to the processing of a pine, a birch, and of an oak, respectively. At profile milling a contact length of a tool with the workpiece increases, which causes an increase of cutting power according to dotted curves 4–6. In formulas (10), (11), (14), (15) of cutting power enter the expression arcsin(B/2Rrk ) containing the inverse trigonometrical function of a sine. In argument of this function, there is a height B—the positive number not equal to zero. The argument of function arcsin(B/2Rrk ) accepts zero value at Rrk = ∞, and value π/2—at Rrk = 0.5B. If the radius Rrk = ∞, then profile milling turns into cylindrical at which the cutting profile of a mill is outlined in a straight line. At Rrk = 0.5B, the cutting profile of a shaped mill represents a semi-circumference length π Rrk . In other words, the profile of a mill represents a semi-circle with the central corner a radian. Intermediate positions of a profile of a mill (from a semi-circle to a straight line) are characterized by the fact, that at increase Rrk , beginning from 0.5B, the center of a mill profile is removed on infinitely long distance Rrk = ∞. The physical sense of such change of radius Rrk from a position of milling process of wood is, which at Rrk = 0.5B there is a deformation of the processed wood most, while at Rrk = ∞ wood experiences the minimum deformation. The described influence of a factor arcsin(B/2Rrk ) on the process of milling confirms the schedule (Fig. 3b), where the cutting power decreases at an increase in radius Rrk . Results of modeling demonstrate that at profile milling of

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Fig. 3. a Influence of height and b of a profile radius of a shaped mill on the cutting power.

workpieces values of forces and cutting power are more than at cylindrical. This fact is explained not only with the bigger length of contact of the profile tool with workpiece but also with the bigger dispersion of the processed material, on which the expense of additional energy is required. The formulas (8), (9) relate the forces Pz , Py with the cutting power Pr and formulas (10), (11), (14), (15) relate the cutting power Pr with the independent factors, characterizing the mill (z,Rrk , B), the cutting regime (S z , n, t), the current time τ, the runout of the workpiece (β sb ), and also species, wood moisture, blunting of the cutting blades, cutting angle, etc. (K t , apop ). On the basis of these data are carried out schedules of influence of a cutting speed and radius of mill profile on the main component Pz of a cutting force (Fig. 4) at: vs = 20 m/ min, t = 15 mm, Rrk = 100 mm, B = 100 mm, v = 50 m/s.

Fig. 4. a Influence of a cutting speed, b of radius of mill profile on main component of cutting force for wood from: 1—pine; 2—birch; 3—oak.

At the constant cutting power increase in cutting speed causes reduction of the main component Pz of cutting force (Fig. 4a). Increase in profile radius Rrk causes reduction of force Pz (Fig. 4b), that is connected with the approach of profile milling to cylindrical, for which it is less energy cost of removal of an allowance. Schedules of dependences of a radial component Py on independent factors of profile milling are similar to schedules for the main component Pz . The main Pz and the radial Py components of the cutting force during cylindrical milling of the workpiece without running are constant and depend from the exit angle (from the angle of contact). At the end of each single cut, the main component Pz of the cutting force became equal Pz max and during subsequent cuts it does not change (we do not take into account the wear of the cutting tool). The time τ E of a single cut is also a constant value. It is possible to postpone not only the current time on X axis, but also

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the exit angle or the length passing by the cutting wedge along the contact arc of the cutter with the workpiece. The path of the cutting wedge along the contact arc at profile milling is equal: lki = Ri (ε1 + ε2 )i = vi τεi

(16)

where vi = ωRi —is the current cutting speed, which at milling changes along the cutter profile from ωRmin to ωRmax . In the calculation, the averaged over the arc of the contact and over the circumference, the components Pza , Pya , Pzc , and Pyc are used. The main component of the cutting force, averaged over the contact arc, is determined by formula: Pza = 0.5Pz max

(17)

where Pz max = Pzu bamax = Pzu bSz sin(ε1 + ε2 )i ; Pzu is the specific cutting force, N/mm2 ; b is the length of the profile cutter; amax —is the maximum thickness of the layer to be cut, a variable value, that depends on the current cutter radius and milling regime; B is the height of the mlll; S z is the feed of the workpiece to the tooth cutter; (11 + 12 )i is the current contact angle, which varies along the height of the profile milling cutter at profile milling. The main component of the cutting force, averaged over the circumference, is determined by formula: Pzc = Pza

z 2π

(18)

where z is the number of mill’s teeth. The radial component, averaged over the circumference, is determined by the formula: z (19) Pyc = Pya 2π When milling the workpiece with a positive increment of the over-measure, there is an increase in the cutting depth with each passage of cutting plate of the contact zone, and, consequently, an increase in the thickness of the removable layer. With an increase in the thickness of the layer being cut in all cases of cutting, the steady cutting process becomes unsteady. The quality of the treated surface is deteriorating. When milling a workpiece with a negative increment of the over-measure (−βsb ), the cutting depth, a contact angle (E1 + E2 ), and a layer thickness are decreasing, and therefore from the standpoint of ensuring of high geometric accuracy of the surface, it is advisable to direct the workpieces in the cutting zone by the vertex end. In addition, the direction by a vertex end simplifies orientation of the workpiece in the initial stage of processing. Thus, based on the obtained mathematical dependencies under known conditions of profile milling it is possible to determine the energy characteristics of the profile milling of substandard workpieces. The calculated values of the cutting power Pr and of the main component Pz of the cutting force are used for determining of the drive power of the main movement of machine and feed movement of the substandard workpiece.

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The radial component Py of the cutting force is used for calculating the elastic deformations of elements of technological system and the expected geometric accuracy of the processed surfaces.

6 Conclusion 1. In the process of cutting logs, due to different values of the diameter at the base and top of the log, remain the peripheral segments with over-measure, which is permanently varied on the length of the workpiece. Machining of peripheral segments with such over-measure leads to significant increasing of the workload, ignoring of which leads to loss of precision of the treated surfaces and to overloading executive bodies of the technological system. 2. Unresonant work of the technological system, intended for profile milling of workpieces with unstable geometrical and physical–mechanical properties, is possible on the basis of adequate mathematical models, which connect the energy characteristics with independent factors of profile milling process. 3. The time characteristics of the elementary cut are determined, mathematical models are obtained to determine the main, radial component of the cutting force, as well as the profile milling power of the workpieces with runout as a function of the cutting mode elements, the characteristics of the shaped cutter and the workpiece. These models are necessary for the qualitative design of the technological operation of profile milling of workpieces with permanently changing over-measure. 4. The calculated values of the cutting power and of the main component of the cutting force are used for determining the drive power of the main movement of machine and feed movement of the substandard workpiece. The radial component of the cutting force is used for calculating the elastic deformations of elements of technological system and the expected geometric accuracy of the processed surfaces.

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Regression Modeling of Machining Processes Yu. L. Tchigirinsky(B) , N. V. Chigirinskaya, and Z. S. Tikhonova Volgograd State Technical University, 28, Lenin’s Av., Volgograd 400005, Russia [email protected]

Abstract. According to the experimental studies of force patterns and patterns of the formation of microgeometry of the surface layer, a comparative analysis of various methods for constructing multifactor, in the general case non-linear, regression models of machining processes are carried out. Estimates of the modeling error are determined for various methods of initial data normalization, in particular, the relative error and the standard quadratic error of the model. For each multivariate model, according to the value of the F-criterion, the probability value is calculated, considered as a threshold for the adequacy of the model. The same value was established as a confidence probability determining the significance of the factors under consideration. It is shown that obtaining nonlinear dependencies is possible only as a result of preliminary processing of the results of statistical tests, and the smallest relative error and the highest reliability of modeling is obtained as a result of preliminary normalization of the initial data in accordance with the rules of the “Italian cube”. Keywords: Multivariate model · Standardization · Centering · Additive model · Multiplicative model · Relative error · Model adequacy · Cutting force · Thermophysical properties

1 Introduction Multivariate regression modeling is the most common means of statistical processing and analysis of experimental data. The most complete theory of regression analysis and theory of the experiment developed [1–8] for linear models and power polynomials. This approach is explained, first of all, by the fact that the tools of statistical and, in particular, regression analysis are most often used to model socioeconomic [9] processes––the accuracy of the resulting models in these fields of science is considered sufficient. The processes taking place in technical and technological systems are more complex, therefore, when conducting research in the field of cutting theory and mechanical engineering technology, models [9–11] are considered not only linear (1), but, as a rule, power-law (2), and exponential (3) mathematical dependencies. Linear models belong to the class of additive, and power and exponential ones belong to the class of

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_128

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multiplicative dependencies. R = a0 +

n 

aj j

(1)

j=1

R = a0 ·

n 

a

j j

(2)

j=1

R = a0 ·

n 

j

aj

(3)

j=1

where R

Dependent variable or response function representing the result of the simulated process; Fj Independent variable representing a certain factor determining the process conditions; a0 Regression constant; aj Regression coefficient “Fj to R”, reflecting the degree of influence of the corresponding independent variable on the response function. It should be noted that researchers quite often consider the concepts of multiple regression analysis and multi-factorial design of an experiment as synonymous. However, we believe that regression analysis is a set of mathematical methods used to build and evaluate the reliability of models, and the design of an experiment is only one of the possible ways of organizing a study, which, subject to fairly strict restrictions, reduces the complexity of experiments. In this paper, we will not go into details of the statistical modeling methodology. We only say that the regression model, to a certain extent reflecting the quantitative relations between independent and dependent variables, does not in any way reflect and, moreover, does not determine internal patterns. In most cases, the construction of a regression model is reduced to choosing the specification of the model (1, 2, or 3), calculating the regression coefficients, and estimating the error of the constructed model. The choice of model specification is determined, as a rule, by generally accepted, in this field of knowledge, ideas about the process being modeled––representations that are most often based on empirical knowledge.

2 Methods of Measurement and Evaluation of Surface Microrelief In the term of this proceeding, we believe that. 1. The number of experiments, determined in accordance with the specification of the model, is sufficient for the correct calculation of the regression coefficients; 2. Explanatory variables are mutually independent in pairs;

Regression Modeling of Machining Processes

1103

3. Explanatory variables represent the controlled factors of the simulated process. Let us consider (Fig. 1) three possible approaches to determining the parameters of the regression model.

Fig. 1. Preparation for calculating model parameters

• Without source data processing. To calculate the regression coefficients, the values of the independent and dependent variables obtained as a result of direct observations are used. The values of the response function and explanatory variables are dimensional quantities, since they are obtained as a result of direct observations. Because of this, transcendental mathematical transformations, for example, logarithm, of these values are unacceptable from a mathematical point of view. Therefore, the construction of a multiplicative model using the standard means of table processors is impossible, since it is impossible to convert a nonlinear mathematical model to a linear form. • Standardization and centering of the source data. The values of the variables measured during direct observations are centered relative to the mathematical expectation and are expressed in fractions of the standard deviation (4).

Yi =

Ri −R σ(R) ;

Xji =

ji −j σ(j )

.

(4)

To calculate the parameters of the regression model, dimensionless (4) normalized quantities are used, for which transcendental mathematical transformations are applicable and, therefore, it is possible to reduce the multiplicative models to a linear [9,

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10] form. However, it should be borne in mind that as a result of centering, nonpositive normalized values are necessarily obtained, for which the logarithm operation is not applicable. For the correct transformation of power and exponential models to a linear form, an additional linear transformation of a standardized coordinate system is necessary. The construction of a regression model of any of the specifications mentioned above (1..3) is possible using standard means of a table processor, provided that all the above transformations are performed. Note that the regression models constructed in this way can only be used as calculated dependencies. A comparative assessment of the degree of influence of each of the factors on the result of the process is incorrect, since the intervals of variation of various factors after normalization also differ. • Normalization. The values of the variables are reduced to a single range of normalized quantities by means of transformation (5).

Yi = 2 ·

ji − min Ri − Rmin j − 1; Xji = 2 · max − 1. Rmax − Rmin j − min j

(5)

To calculate the regression coefficients, normalized values of the initial data are used, which are dimensionless and comparable in scale factor; therefore, the model allows the comparison of independent variables in terms of the degree of influence on the response function. To formation nonlinear models, it is necessary to normalize.       ji ln ln Ri Rmin min j  −1  Yi = 2 ·  = 2 · − 1; X (6) ji   max  ln Rmax Rmin min ln ji  j

   ln Ri Rmin ji − min j  = 2 · −1 Yi = 2 ·  − 1; X ji  max − min R  max ln j j Rmin

(7)

Since, as a result of normalization (5..7), the coordinate space is transformed, the normalized model is linear, regardless of the original (1..3) specification. To calculate the parameters of the linear model, you can use regular means of spreadsheets.

3 Technique of Contactless Evaluation Microrelief Parameters As an illustration of the provisions formulated above, we will conduct a comparative analysis of the results of regression modeling (Table 1) of the turning the steels (US marking) 1020, 3020, 4130 [12]. The cutting force radial component Py is considered as a function of response. Factors determining the value of the response function: cutting speed V (90; 135; 180 m/min), feed rate S (0.083; 0.166; 0.256 mm/rev), cutting depth t (0.5; 0.6; 0.7 mm) and the thermal conductivity of the tool material λ (11, 27, 50 W m−1

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Table 1. Variable intervals №

Cutting depth, mm

Cutting speed, m/min

Feed rate, mm/rev

Thermal conductivity coefficient, W m−1 K−1

Radial cutting force Py , N

1

2

3

4

R

1

0.5

90

0.083

11

302

2

0.5

90

0.083

27

326

36

0.7

90

0.256

50

657

37

0.7

135

0.083

11

287

80

1

180

0.256

27

519

81

1

180

0.256

50

551

…

…

K−1 ) The study of the process was carried out using methods of full-factor experiment type 34 [9, 10]. The following tables (Tables 2, 3) show the data characterizing the regression models obtained using various methods of normalizing the initial values. We should note that standardization and centering as a way of preliminary processing of the initial data allows us to obtain only the additive model (1) as a result, since to construct the multiplicative (2, 3) models, it is necessary to linearize the source coordinate space of the experimental design. For this, it is necessary to carry out, sequentially, standardization and centering of each source value, and then the logarithm of the centered quantities. For source values not exceeding the corresponding average value (ij ≤ j ; Ri ≤ R), the logarithm operation cannot be performed. Linear dependences were obtained as a result of normalization of the initial models (1..3) in accordance with expressions (4..7) and data (Table 2). The regression coefficients aj are determined in accordance with the statistical significance verified by Student’s t-criterion [1–3, 9, 10] for a confidence probability (α) set at a level no less than the model adequacy (Table 3). The adequacy of the model is calculated by the value of Fisher’s F-criterion [1–3]. Data analysis (Table 3) shows that the full use of simulation results is possible when constructing a model based on previously normalized (5..7) data, since in this case the Gauss–Markov conditions with respect to orthogonal and rotatable experimental designs are observed. Speaking about the full use of the model, we mean the ability not only to predict the expected results of the process, but also to compare factors by the degree of influence on the response function and, thereby, select factors for a more “subtle” study of the physical laws of the process under study. For example, we can talk about a fairly reliable selection of significant independent factors, since the regression coefficient

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Model specification

Function Explanatory variables of response  2 1

Method to source data preparing 3

4

[0.083; 0.256]

[11; 50] –

function

factors

Without preparing Linear

[208; 807]

[0.5; 1.0]

[90; 180]

–

Standardization and centering [−1,22; + 1.22]

Linear

[−2.44; +2.44]

[−1.22; [−1.22; [−1.22; (4) + 1.22] + 1.22] +1.22]

Power-law

[error; + [error; + 0.96] 0.46]

[error; +0.47]

Exponential

[error; + [−1.22; + 0.96] 1.22]

[−1.22; [−1.22; [−1.22; (4), then +1.22] +1.22] +1.22] Ln (Y )

Linear

[−1; +1] [−1; +1]

[−1; + 1]

[−1; + 1]

[−1; + 1]

Power-law

[−1; +1] [−1; + 1]

[−1; + 1]

[−1; + 1]

[−1; + (6) 1]

Exponential

[−1; +1] [−1; +1]

[−1; + 1]

[−1; + 1]

[−1; + 1]

[error; +0.38]

[error; +0.34]

(4), then Ln (Y )

(4), then Ln (Xj) (4)

Normalization (5)

(7)

of the normalized model a0 , reflecting the influence of randomness, in multiplicative models is significantly (4…9 times) less than the coefficients for factors X 1 … X 4 . Similar studies of multivariate regression modeling methods were carried out to study the patterns of formation of microgeometric characteristics of the treated surface during turning with preliminary plastic deformation [13–16] of steels and physical and mechanical characteristics, the so-called “defective layer” during face milling of steels and non-ferrous alloys [17, 18].

4 Conclusion 1. In the absence of preliminary preparation of the initial data––rationing of any kind– –it is possible to obtain only multivariate regression models only in the form of polynomials of the first degree. Moreover, the adequacy of the models, estimated by the F-criterion, is close to zero, and the relative modeling error exceeds 100%. 2. The standardization and centering of the source data can significantly increase the reliability and adequacy of the resulting additive models that are acceptable in the study of relatively simple processes. The construction of nonlinear multiplicative models based on standardized and centered source data is impossible.

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Table 3. Simulation results Model specification

Regression coefficients a0

a1

a2

a3

a4

Relative error

Adequacy

Without preparing source values Linear

436.8

572.8

2.9

2406.6 11.9 390.1%

0.0000

Standardization and centering—normalized model coefficients Y (X 1 , …, X 4 ) Linear

−0.53

0.47

−0.45 0.71

0.27

16.8%

0.7512

Normalization—normalized model coefficients Y(X 1 , …, X 4 ) −0.29

0.34

Power-law

0.03

0.27

−0.28 0.40

0.13

Exponential

0.03

0.25

−0.29 0.40

0.12

Linear

−0.22 0.44

0.20

Normalization—real-scale model coefficients R(F1 , …, F4 ) Linear

−34.1

366

−1.3

1506

3.1

12.09% 0.9900

Power-law

8695

0.46

−0.48 0.48

0.1

5.95% 0.9999

Exponential

231

1.82

0.99 20,6

1

5.88% 0.9999

3. Normalization of the initial data according to the rules (5…7) allows you to build regression models of any of the most commonly used specifications––both additive and multiplicative. At the same time, a sufficiently high modeling accuracy is ensured with a substantial adequacy of the models. 4. To simulate the processes of mechanical processing of metals, multiplicative–– power or exponential––mathematical dependencies should be used, providing a significantly lower relative calculation error compared to linear ones.

References 1. Fisher RA (1971) The design of experiments (9th ed). Macmillan 2. Fisher RA (1922) The goodness of fit of regression formulae, and the distribution of regression coefficients. J Roy Stat Soc 85(4):597–612. https://doi.org/10.2307/2341124 3. Fisher RA (1954) Statistical methods for research workers, Twelfth. Oliver and Boyd, Edinburgh 4. Freedman DA (2009) Statistical models: theory and practice. Cambridge University Press 5. Kristal MG, Gorelova AY. Handling the results of planning an extreme experiment: Student’s book, Volgograd State Technical University, Volgograd 6. Hiks CR (1967) Fundamental concepts in the design of experiments. Moscow. (In Russian) 7. Montgomery D (2013) Design and analysis of experiments, 8th edn. Wiley , Hoboken, NJ 8. Grigoriev YD (2015) Optimal experiment planning methods: linear models: student’s book. “Lan” Publishing, St. Petersburg 9. Chigirinskaya NV, Tchigirinsky JuL, Gorobtsov AS (2015) Experiment planning in technical and economical tasks: Student’s book. Volgograd State Technical University, Volgograd

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10. Chigirinskaya NV, Tchigirinsky JuL, Gorobtso AS (2019) Modeling non-periodic stochastic processes: student’s book. Volgograd State Technical University, Volgograd 11. Ingemansson AR (2020) Development of mathematical models for technological preparation of production and adaptive control for turning and milling in digital production systems. Met Working Mater Sci 22(1):27–40. https://doi.org/10.17212/1994-6309-2020-22.1-27-40 12. Nesterenko P, Tchigirinsky J, Nesterenko E (2020) Analysis of influence of strains of technological system elements on machining accuracy under turning of non-rigid shafts based between centers. In: Radionov AA et al (eds) Proceedings of the 5th international conference on industrial engineering (ICIE 2019), Springer Nature Switzerland AG, Cham, pp 1193–1201. https://doi.org/10.1007/978-3-030-22063-1 13. Ingemansson A, Zaitseva N, Tchigirinsky J, Krainev D (2012) Mathematical model of the formation of the surface roughness during turning with advanced plastic deformation of corrosion-resistant steels. Metalloobrabotka 1:11–15 14. Polyanchikov YN, Tchigirinsky JL, Krainev DV, Ingemansson AR, Zaitseva NG, Razdrogin AV (2008) Volgograd state technical university. Calculation the mean deviation of the assessed profile of the machined surface during turning after prior plastic deformation and traditional turning. Certificate of state registration of a computer program 2012611474 15. Tikhonova Z, Frolov E, Krainev D, Plotnikov A (2019) Experimental research method when developing a mathematical model for calculating cutting speed in the course of turning steels with a coated tool. In: Bratan S (ed) MATEC web of conferences, vol 298. In: International conference on modern trends in manufacturing technologies and equipment: mechanical engineering and materials science (ICMTMTE 2019), p 8.https://doi.org/10.1051/matecconf/201 929800134 16. Krainev D, Bondarev A, Tikhonova Z (2020) Mathematical apparatus for predicting cutting tool life in turning process after prior plastic deformation. In: Radionov AA et al (eds) Proceedings of the 5th international conference on industrial engineering (ICIE 2019), Springer Nature Switzerland AG, Cham, pp 1107–1114. https://doi.org/10.1007/978-3-030-22063-1 17. Tchigirinsky J, Trong NQ, Firsov I (2019) Formation of the properties of the surface layer during multi-stage milling. In: Suslov A, Lysak V, Chigirinskiy J et al (eds) Materials science forum, vol. 973, IX International science and technology conference on engineering—innovation technology in engineering: from design to production of competitive products, pp 115–119. https://doi.org/10.4028/www.scientific.net/MSF.973.115 18. Tchigirinsky J, Trong NQ (2017) Influence of technological factors of blade processing on the forming of the defect layer. In: Bratan S et al (eds) MATEC web of conferences, vol. 129. In: International conference on modern trends in manufacturing technologies and equipment (ICMTMTE 2017), p 4. https://doi.org/10.1051/matecconf/201712901020

Research into the Influence of the Planetary Ball Mill Rotation Frequency on the Limiting Value of the Specific Surface Area of the WC and Co Nanopowders Caused by the Coalescence or Hardening of Particles M. Dvornik(B) and E. Mikhailenko Institute for Material Studies FEB RAS, 153, Tikhookeanskaya str, Khabarovsk 680042, Russia [email protected]

Abstract. The study of milling kinetics of WC and Co at various frequencies is made. The reduction in the rate of the specific surface area (SSA), growth detected for cobalt and WC particles due to their coalescence at the highest frequency of rotation of the mill (400 rpm). The growth of the WC powder surface at the minimum mill speed (150 rpm) is limited due to particle hardening. Increasing the frequency to 250 rpm allows for the increase in the limit value of the specific surface to the maximum. A further increase in the frequency to a maximum value (400 rpm) leads to a decrease in the limiting value due to the acceleration of the coalescence of particles. The work also shows the presence of a restriction on the growth of the WC/WC surface area at the maximum frequency of rotation of the mill. Keywords: Coalescence of particles · Hardening of particles · Grain boundary

1 Introduction Milling in planetary ball mills and other high-energy mills is a simple and effective method to obtain nanostructured powders, which are widely used in powder metallurgy. Nanostructured WC–Co hard alloys derived from such powders have high hardness and wear resistance due to the extremely small diameter of the WC grains [1, 2]. Many papers exist on the production of nanostructured WC, WC–Co, and other powders by high-energy milling in planetary mills [3–9]. To obtain a nanostructured powder with an average WC crystallite diameter of about 10 nm from which nanostructured hard alloy is made, it is necessary to grind the initial powder within 10 to 72 h [10, 11]. The high time and energy costs are one of the drawbacks of the method in the preparation of any nanostructured powders. The problem of optimizing the process of obtaining nanosized powders with extremely high dispersity in a planetary ball mill is common to all powder © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_129

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metallurgy. Researchers have done a lot of work aimed at streamlining the process and reducing the time and energy costs of the milling process for various powders [12–14]. Slowed SSA growth can occur due to agglomeration, coalescence [9, 15, 16] or hardening of grains and particles [6]. Coalescence and hardening have a significant impact on the size of the obtained particles and grains during long-term milling when the particle strength and the coalescence rate reach significant values. To reduce strength, manufacturers use surfactants. To combat coalescence, the temperature is reduced [17]. The milling rate increases with increasing frequency and energy of collisions of grinding media. Collision energy affects the probability of particle destruction in the powder layer. The collision energy affects the pressure and temperature in the layer of powder particles, on which the particle coalescence rate depends. The main parameter affecting the energy and frequency is the rotational speed of the mill. For these reasons, the influence of the frequency on the limiting value of the specific surface area remains unclear. The work aims to study the influence of the mill rotation frequency on the value of the limiting value of the specific surface area.

2 Experiment The milling was performed in a Retsch PM-400 planetary ball mill. WC powder samples were milled for 2400…76,800 s and Co powder samples were milled for 600…19,200 s. The frequencies of rotation for the disc and vials (ν) were 150, 250, and 400 rpm. Each vial contained 10 balls with a mass of 600 g and 60 g of powder. This ball to powder ratio (10:1) facilitates the high milling rate and high density of the impact energy. The temperature of the vial (T vial ) was measured during milling using a thermocouple specially installed in the surface of the vial. The power consumption was measured by the electricity supply metre (Pe ). The SSAs of the powders (S WC and S Co ) were determined using the Brunauer–Emmett–Teller (BET) gas adsorption method using Sorbi № 4.1. The SSA of powders determined using the BET method was recalculated in the m2 /m3 unit for direct comparison of materials with different densities. The densities of Co and WC powders were 8.9 g/cm3 and 15.6 g/cm3 , respectively. The morphology and structure of the particles were examined using an EVO 40 scanning electron microscope.

3 Results and Discussions The graphs (Fig. 1a), suggest that with an increase in the mill rotation frequency in the milling process of WC and Co powders, an accelerating increase in power consumption (Pe ) is observed, which is satisfactorily described by a cubic parabola. The observed increase in energy consumption should lead to an increase in energy volume and frequency of impacts, (Fig. 1b), which is efficiently described by a cubic parabola. The values obtained ranged from 300 to 400 K, which is consistent with other results obtained under similar conditions [18, 19]. An increase in temperature with an increase in the mill’s rotational speed provides the prospects for accelerating the coalescence process. The initial cobalt powder consists of elongated particles (Fig. 2a), which SSA is about 107 m2 /m3 (Sauter mean diameter is about 613 nm). The dependences of cobalt

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Fig. 1. The power consumption of the mill (a) and temperature of the vials (b) on the rotation frequency during milling of WC powder () and Co powder (▲).

SSA on milling time at all frequencies (Fig. 3a), are effectively described by a first-order kinetic equation. At the lowest frequency of the mill’s rotation (150 rpm), an increase in the SSA of the particles is observed with an initial velocity of 3700 m2 /(m3 s). The observed decrease in the surface growth rate is relatively slow. SSA at the same time tends to be 108 m2 /m3 (Sauter mean diameter about 60 nm). As the frequency increases to 250 rpm, the surface growth rate increases to 12,000 m2 /(m3 s). The growth of SSA stops relatively quickly, reaching 4 × 107 m2 /m3 (Sauter mean diameter is about 150 nm). The photographs indicate that the particles obtained at the maximum milling time (19,200 s) at 150 rpm (Fig. 2b) and 250 rpm (Fig. 2c), have diameters from 0.5 to 5 µm and a complex shape resulting from deformation. This decrease of the limiting SSA under an increase in the mill rotation frequency can be explained by the particle coalescence under increased temperature. A further increase in the mill speed (400 rpm) leads to a change in the direction of the process. Instead of an increasing SSA, its decrease is observed, which can be explained only by accelerating the coalescence of particles. The prevalence of coalescence over destruction does not allow the initial milling speed to be set at a frequency of 400 rpm. The photograph (Fig. 2d) shows that the particles obtained with a diameter of about 20 microns consist of coalesced initial particles. The initial WC powder consists of rounded particles (Fig. 2e) which SSA is about 3 × 106 m2 /m3 (Sauter mean diameter is about 2.2 µm). At the lowest rotation frequency ( = 150 rpm), the surface growth rate (3800 m2 /(m3 s)) and the SSA limit value (1.0 × 108 m2 /m3 ) (Sauter mean diameter about 60 nm) were the smallest. The milling of kinetic WC powders is effectively described by a first-order kinetic equation, similar to cobalt powders (Fig. 3b). If for Co, the limiting SSA at 150 rpm is maximal, then for WC it is minimal. Increasing the speed to  = 250 rpm leads to an increase in the SSA growth rate to 6500 m2 /(m3 s) and its SSA limiting value to 2.2 × 108 m2 /m3 (Sauter mean diameter about 27 nm). With further increase in the frequency to  = 250 rpm, the growth rate of SSA increases to the maximum value (k WC = 26,700 m2 /(m3 s)) and lim = 1.1 × 108 m2 /m3 (Sauter mean diameter about its limiting value decreases to SWC 55 nm). All milled WC powders consist of agglomerates with a diameter of 10–20 µm in which individual particles with a diameter of less than 100 nm can be seen (Fig. 2 f, g). The surface growth rate of WC and Co powders (Fig. 4a), depends on the cube of the mill rotation frequency [14]. This corresponds to the collision model currently in

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Fig. 2. Initial Co powder (a), Co powders milled during 19,200 s at 150 rpm (b) 250 rpm (c) and 400 rpm (d), initial WC powder (e), the milled WC powders during 76,800 s at 150 rpm(f), 250 rpm (g), and 400 rpm (h).

Fig. 3. The SSA milling kinetic of the Co (a) and WC (b) powders milling under various rotating frequencies 150 (˛), 250 (▲) and 400 (×) rpm.

use [20, 21]. Since the energy consumption depends on the cube of the mill rotation frequency too we can conclude the surface growth rate linearly depends on the power consumption. That is in accordance with Rittinger’s Kinetics. Only one point does not fit into this pattern for Co at 400 rpm. This is due to the fact that SSA growth does not observed at 400 rpm. When the rate of coalescence is higher than the milling rate throughout the process, it is impossible to determine the milling rate. The dependences of the limiting values to which the SSAs tend during milling on the frequency of rotation of the mill were found to be different for powders Co and WC. The limiting SSA value of Co decreases linearly with increasing mill speed which can only be explained by acceleration of coalescence. The SSA WC limit increases with increase in frequency from 150 to 250 rpm. This indicates that particle hardening is the principal limiting factor in this range. As the mill speed increases from 250 to 400 rpm, the SSA

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Fig. 4. Dependence of the growth rate of SSA of particles (a), dependences of calculated maximal values of SSA from rotation frequencies for WC () and Co (˛) particles.

WC limit value decreases, which can be explained by accelerating the coalescence of particles. Consequently, despite the high melting point and heat resistance, nanosized WC particles at the maximum milling speed are subject to coalescence. The results indicate that if it is necessary to obtain the maximum SSA of the powder due to milling in a planetary ball mill, it is necessary to consider the processes of hardening and coalescence of particles. Reducing the frequency of rotation of the planetary ball mill allows one to limit the coalescence of particles. Increasing the frequency of rotation of the mill allows the destruction of hardening particles by increasing the impact energy. If coalescence and hardening of particles able to occur during milling, it is necessary to search for the optimum frequency of rotation of the mill which will allow the achievement of the maximum possible SSA powder. Knowing the mechanisms preventing the growth of the SSA, it is possible to optimize the milling process by changing the mill’s rotations frequency during the milling process. For instance, increasing the mill speed to the maximum value (400 rpm), at the initial milling stage will allow the increase of the milling speed of WC powder to the maximum value. Subsequent reduction of the mill’s rotational speed after SSA particles to 250 rpm will prevent deceleration of the milling and allow WC to reach highest SSA (6.5 × 108 m2 /m3 ) (Sauter mean diameter about 27 nm).

4 Conclusion It has been defined that, the growth of the SSA of cobalt particles is limited by coalescence during planetary ball milling. The limiting SSA value of cobalt powder is decreasing from 108 m2 /m3 to 106 m2 /m3 with increasing mill rotation frequency from 150 to 400 rpm. At the maximum frequency of rotation of a planetary ball mill (400 rpm), a decrease in the SSA of Co particles occurs instead of increase because of coalescence, which is confirmed by the formation of big particles with diameter up to 30 µm. The limitation of the growth of the SSA of hard WC particles (150 rpm), is explained by the lack of impact energy for the destruction of the hardened particles. Increasing the frequency of the mill’s rotation to 250 rpm leads to an increase in the limit value due to an increase in the impact energy. With an increase in the mill’s rotation frequency to 400 rpm, the limiting value of the SSA of WC particles decreases due to the coalescence of particles with an increase in temperature.

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References 1. Fang ZZ, Wang X, Taegong R, Hwang KS, Sohn HY (2009) Synthesis, sintering, and mechanical properties of nanocrystalline cemented tungsten carbide—a review. Int J Refract Met Hard Mater 27:288–299. https://doi.org/10.1016/j.ijrmhm.2008.07.011 2. Saito H, Iwabuchi A, Shimizu T (2006) Effects of Co content and WC grain size on wear of WC cemented carbide. Wear 261:126–132. https://doi.org/10.1016/j.wear.2005.09.034 3. Zhang FL, Zhu M, Wang CY (2008) Parameters optimization in the planetary ball milling of nanostructured tungsten carbide/cobalt powder. Int J Refract Met Hard Mater 26:329–333. https://doi.org/10.1016/j.ijrmhm.2007.08.005 4. Hewitt SA, Laoui T, Kibble KK (2009) Effect of milling temperature on the synthesis and consolidation of nanocomposite WC–10 Co powders. Int J Refract Met Hard Mater 27:66–73 5. Hewitt SA, Kibble KA (2009) Effects of ball milling time on the synthesis and consolidation of nanostructured WC–Co composites. Int J Refract Met & Hard Mater 27:937–948 6. Gusev AI, Kurlov AS (2008) Production of nanocrystalline powders by high-energy ball milling: model and experiment. Nanotechnology 19:265302–265308. https://doi.org/10.1088/ 0957-4484/19/26/265302 7. Zhang FL, Wang CY, Zhu M (2003) Nanostructured WC/Co composite powder prepared by high energy ball milling. Scripta Mater 49:1123–1128 8. In-Jin S, Byung-Ryang K, Jung-Mann D, Yoon J-K, Kee-Do W (2010) Properties of nanostructured tungsten carbide and their rapid consolidation by pulsed current activated sintering. Phys Scr 139:014043–1–14044. https://doi.org/10.1088/0031-8949/2010/T139/014043 9. Dvornik MI, Zaytsev AV (2013) Research of surfaces and interfaces increasing during planetary ball milling of nanostructured tungsten carbide/cobalt powder. Int J Refract Met Hard Mater 36:271–277. https://doi.org/10.1016/j.ijrmhm.2012.10.004 10. Al-Aqeeli N (2015) Characterization of nano-cemented carbides Co-doped with vanadium and chromium carbides. Powder Technol 273:47–53. https://doi.org/10.1016/j.powtec.2014. 12.032 11. Al-Aqeeli N, Mohammad K, Laoui T, Saheb N (2015) The effect of variable binder content and sintering temperature on the mechanical properties of WC–Co–VC/Cr3C2. Nanocomposites. Mater Manuf Process 30:31–37. https://doi.org/10.1080/10426914.2014.930894 12. Ghayour H, Abdellahi M, Bahmanpour M (2016) Optimization of the high energy ballmilling: Modeling and parametric study. Powder Technol 291:7–13. https://doi.org/10.1016/ j.powtec.2015.12.004 13. Shashanka R, Chaira D (2015) Optimization of milling parameters for the synthesis of nanostructured duplex and ferritic stainless steel powders by high energy planetary milling. Powder Technol 278:35–45 14. Gotor FJ, Achimovicova M, Real C, Balaz P (2013) Influence of the milling parameters on the mechanical work intensity in planetary mills. Powder Technol 233:1–7. https://doi.org/ 10.1016/j.powtec.2012.08.031 15. Fadda S, Cincotti A, Concas A, Pisu M, Cao G (2009) Modelling breakage and agglomeration during fine dry grinding in ball milling devices. Powder Technol 194:207–216. https://doi. org/10.1016/j.powtec.2009.04.009 16. Pedro LG, Tino AAA, Juliano BS (2015) The onset of particle agglomeration during the dry ultrafine grinding of limestone in a planetary ball mill. Powder Technol 284:122–129 17. Gerasimov KB, Boldyrev VV (1996) On mechanism of new phases formation during mechanical alloying of Ag-Cu, Al-Ge and Fe-Sn systems. Mater Res Bull 31:1297–1305 18. Kleiv RA (2009) A simple heatsink for planetary mills. Miner Eng 22:516–518. https://doi. org/10.1016/j.mineng.2009.01.003

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19. Chaira D, Mishra BK, Sangal S (2007) Synthesis and characterization of silicon carbide by reaction milling in a dual-drive planetary mill. Mater Sci Eng A 460–461:111–120 20. Iasonna A, Magini M (1996) Power measurements during mechanical milling. An experimental way to investigate the energy transfer phenomena. Acta Mater 44:1109–1117 21. Khoa HX, Bae S, Bae S, Kim B-W, Kim JS (2014) Planetary ball mill process in aspect of milling energy. J Kor Powd Me Inst 21:155–164. https://doi.org/10.4150/KPMI.2014.21. 2.155

Analytical Simulation of Relations Between Cutting Force and Elastic Distortion of Process System During Plane Grinding P. Pereverzev(B) and S. Yudin South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, Russia [email protected]

Abstract. About 30% of finishing operations for tempered steel parts in contemporary machine engineering is plane grinding with wheel periphery (PGWP). This operation is done by computerized numerical control (CNC) machine tools. The performance management for plane grinding operations is done by incremental changing of programmatic feed rates using controlling software during each part grinding cycle. However, contemporary machine production establishments still face problems associated with the lack of AWCS systems and regulatory references for the selection of optimized cutting modes for PGWP operations performed by CNC machine tools. Therefore, the actual production lacks full automation of controlling software for plane grinding CNC tools, and the incremental feed change cycles are defined manually, thus reducing the grinding rates in order to keep the set quality of surface processing. This problem occurs due to the absence of a set of mathematical models that would allow automated planning for optimized feed cycles and other cutting modes maintaining the quality of surface finish when processing part batches under unstable grinding conditions and taking into consideration various processing requirements and restrictions associated with machines, grinding tools, workpieces, and processing organization conditions. This article deals with the development of a mathematical model for the calculation of feed cycles, elastic distortions of a process system, programmatic, and actual feed in a wide variation range for numerous processing factors. Keywords: Plane grinding with wheel periphery · Relations between cutting forces and processing parameters

1 Introduction About 30% of finishing operations for tempered steel parts in contemporary machine engineering is plane grinding with wheel periphery (PGWP). This operation is done by computerized numerical control (CNC) machine tools. The performance management for plane grinding operations is done by incremental changing of programmatic feed

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_130

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rates using controlling software during each part’s grinding cycle. However, contemporary machine production establishments still face problems associated with the lack of AWCS systems and regulatory references for the selection of optimized cutting modes for PGWP operations performed by CNC machine tools. Therefore, the actual production lacks full automation of controlling software for plane grinding CNC tools, and the incremental feed change cycles are defined manually, thus reducing the grinding rates in order to keep the set quality of surface processing. This problem occurs due to the absence of a set of mathematical models that would allow automated planning for optimized feed cycles and other cutting modes maintaining the quality of surface finish when processing part batches under unstable grinding conditions and taking into consideration various processing requirements and restrictions associated with machines, grinding tools, workpieces, and processing organization conditions. One of the key tasks to solve the problem is the development of a mathematical model that would establish the relationship of the cutting force and the processing mode (axial and radial feed, wheel and workpiece movement rates), as well as basic processing parameters (wheel specifications and its bluntness index, the geometrical parameters of the contact area of the wheel and the workpiece, physical and mechanical characteristics of the processed metal, etc.) [1–3], and take into consideration the following features of the processes taking place during PGWP operations done by CNC tools: 1. The processing is controlled simultaneously by incremental axial and radial feed cycles and workpiece plate feed; 2. A standard PGWP cycle consists of the direct and the reverse stroke; each stroke includes the cutting-in stage to the value of radial feed (cutting-in only takes place in the initial cross-section of the processed surface, thus leading to selecting another processing modes for other cross-sections); 3. Instable grinding conditions due to various grinding scenarios and the alternating contact area between the wheel and the workpiece; 4. Varying conditions during the grinding of the surfaces increase the instability of grinding conditions and lead to various processing inaccuracies in certain crosssections.

2 Analytical Simulation of the Relations Between the Cutting Force and the Elastic Distortion of a Process System During Plane Grinding Due to the presence of elastic movements in the processing system and the inertance of displaced masses (the plane and the workpiece), the actual feed Δt f with the incremental shift of programmatic feed Δt p , changes smoothly and is not equal to the programmatic feed increments values. Thus, the programmatic feed Δt p , cannot be used to calculate the basic time T O [4–6]. The actual feed Δt f by the end of a cycle stage is conditionally equal to the programmatic feed Δt p , though it is possible that in some cycles the actual feed cannot reach the programmatic value [7–11]. Figure 1 shows the graphs of programmatic and actual feeds for a two-stage automated cycle. The programmatic feed for the first stage

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is shown in the bold line and Δt p = 0.02 mm. The graph chart shows that the actual feed Δt f per each stage stroke approaches the programmatic value, but it is only reached at stroke 40. Then the second stage begins where Δt p = 0.005 mm and Δt f continues approaching the programmatic value until the end of the second stage of the cycle. The presence of clearances in the drive train of the machine tool and the elastic flexibility of processing system units leads to the discrepancies between the actual radial feed and programmatic values.

Fig. 1. Feed graphs for two-stage PGWP cycle with double stroke.

Therefore, the removal of metal during the grinding operation in a processing system (PS) shall be done while taking into consideration the flexibility γ and elastic distortion y of the PS that bind the actual feed Δt f , the programmatic feed t p , and various processing parameters (physical and mechanical properties of the processed material, workpiece diameter, etc.). Let us look at a schematic representation of programmatic Δt p and average actual Δt f feeds in an automated two-stage grinding cycle for a hypothetical, fully flattened workpiece. In order to create a mathematical model for the relationships between elastic distortions and technological parameters, we will use the known empirical interrelations [12–17], while considering the specific features of PGWP. To this end, we shall draw  a graph of accumulated feeds (Fig. 2), and mark the dimension chain on it, where tpz,i is the accumulated programmatic feed, tpz,i isthe programmatic feed per 1 stroke, ttz,i  isthe processing tension, tfz,i−1 is the accumulated actual feed, tfz,i is the actual feed per 1 stroke, z is the stage, i is the stroke. In order to establish the regularities in actual feed changes within the processing cycle, we shall look at the design diagram of the relationships between the programmatic and actual feeds with elastic distortions of the PS. The graph shows the values of accumulated programmatic and actual feeds for the i-th stroke of the z-th stage along the reference axes, calculated as sums of the corresponding feeds for every wheel stroke. Let us find the actual feed for the i-th stroke of the z-th stage using a restricted dimension contour. The restricted dimension contour for a cycle with direct stroke (DS) and reverse

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Fig. 2. Standard feed graph for two-stage PGWP cycle with double stroke.

stroke (RS) when both are operational looks the following way (Fig. 3a and 3b, bold line):

Fig. 3. Feed accumulation bar graph for two-stage PGWP cycle with double stroke and dimension chain.

RS DS tpDS + yz,i−1 = tfDS + yz,i z,i z,i

(1)

DS RS + yz,i−1 = tfRS + yz,i tpRS z,i z,i

(2)

The analysis of Eqs. (1–2) and works [1, 7, 18], shows that the current value of the actual radial feed is in direct relationship to the elastic distortion delta between the current and the previous stroke. Thus, we can produce the following universal mathematical notation: tpz,i + yz,i−1 = tfz,i + yz,i

(3)

One stroke makes evident the relationship between the programmatic and actual feeds via the elastic movements (elastic releases of the machine-device-tool-part system) yfz,i ,

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i.e., it is basically the difference between the programmatic and actual feeds at the current operational stroke: yfz,i = γ Pyfz,i

(4)

The accumulated programmatic feed is the sum of processing tension and the accumulated actual feed for i-th stroke of z-th cycle stage. The equation looks as follows: tpz,i = ttz,i + tfz,i−1

(5)

The processing tension ttz,i , in its turn, is the sum of elastic movements per stroke and the accumulated programmatic feed. The equation looks as follows: ttz,i = yz,i +  tfz,i

(6)

DS(RS)

is the programmatic value of the radial feed for the direct (reverse) stroke where tpz,i DS(RS) in mm/dx.str.; yz,i is the elastic distortion of the wheel axis for the direct (reverse) DS(RS)

stroke; tfz,i is the actual radial feed for the direct (reverse) stroke in mm. Equations (4–6) above lead us to the following pars: ttz,i = yz,i + tfz,i = tpz,i − tfz,i−1

(7)

ttz,i = γ Pyz,i + tfz,i = tpz,i − tfz,i−1

(8)

From [1], we know how to calculate Py using the average actual feed per stroke  Py = κ1 tfme + κ2 tfme (9) z,i z,i where K 1 and K 2 are the constituents of Eq. 9. They used for the simpler and more apparent representation of the equation from [19], and they look, respectively, as follows: κ1 = Vp B

σi εi tgβ Vκ κ2 = B

σi √ D 3

In order to establish the correlation, it is necessary to use this equation because the average actual feed, in this case, equals the actual feed per stroke. Thus, by introducing expression Eq. 8, into Eq. 9, we can get this  K1 · tfme + K2 · tfme + tfme = tpz,i − tfz,i−1 (10) z,i z,i z,i Then it is necessary to group the variables using mathematic transformations for the further expression of the average actual feed taking into consideration the elastic movements of the processing system during the processing. For the sake of convenience,

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let us move all the components to one side and make them equal to zero. Then let us group and factor out Eq. 10, to get Eq. 11     2  4(γ K1 + 1) tfz,i−1 − tpz,i γ K2 −γ K 2 me + tfz,i = − (11) 2(γ K1 + 1) 2(γ K1 + 1) 4(γ K1 + 1)2  Having solved the equation relative to tfme , we receive the following equation of z,i the relationship between the feeds, elastic distortions, and processing parameters: ⎛ tfme z,i

−γ K2 =⎝ + 2(γ K1 + 1)

 

γ K2 2(γ K1 + 1)

2

⎞2 tfz,i−1 − tpz,i ⎠ − γ K1 + 1

(12)

The calculation using Eq. 12, starts with the first stroke of the cycle. For the first stroke it is tfz,i−1 = 0, for the second, it is tfz,i−1 = tfme , etc. 1,1 Thus, we have established the correlation between the actual feed, elastic distortions, and technological parameters of Plane grinding with wheel periphery for double operating stroke.

3 Practical Significance, Proposals and Implementation Results, Experimental Results The comparison and adequacy analysis was performed using experimental data [20], received during plane grinding. During the workpiece processing, the following parameters were used: wheel: 500 × 20 × 203 25A BM1 12K5; material: 1045 steel; cutting mode: V w = 35 mps; B = 20 mm; t = 1 mm; V p = 400 mm/min. In order to compare the calculated and experimental data, we built a graph shown in Fig. 4, where experimental data are marked as open circles and calculated data are filled circles and a line. The comparison of the received and experimental data shows that the difference between them is no greater than 10% which confirms the adequacy of the developed analytical model of relations between cutting forces and technological parameters during the Plane grinding with wheel periphery.

4 Conclusions Based on work performed, we may draw the following conclusions: 1. The relevance of metal removal modeling in automated cycles of Plane grinding with wheel periphery performed by CNC machine tools is stipulated by the absence of automated planning systems, regulatory references and cycle planning methods satisfying the requirements of modern automated production. 2. The analytical model presented solves the problem of automated PGWP cycle planning and calculation by calculating the actual feeds and cutting forces for the cycle and grinding conditions giving.

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Fig. 4. Comparison graph for calculated and experimental data: a dependence of Py on the graininess of the wheel; b dependence of Py on thehardness of the wheel; c dependence of Py on the structure of the wheel.

3. The proposed calculation methods for automated cycles is based on the establishment of correlations between fundamental regularities of metal flow mechanics in the cutting area, cutting force model, PGWP kinematics, cutting modes, elastic distortions of the processing system associated with the programmatic and actual feeds, which allows the calculation of cycle parameters in a wide variation range of processing factors.

References 1. Pereverzev PP, Popova AV (2013) Analytical simulation of the relations between the cutting force and the basic processing parameters during internal grinding. Metalloobrabotka 621:24– 30 2. Pereverzev PP (2012) Modelling and optimizing controlling software for automated machine production. Bull South Ural State Univ. Ser Mech Eng Ind 621:152–157 3. Pereverzev PP (2012) Modelling processing restrictions during the optimization of automated grinding cycles. Bull South Ural State Univ Ser Mech Eng Ind 621:165–168 4. Akintseva A, Prokhorov A, Omelchenko S (2020a) Methodology for designing optimal internal grinding cycles resistant to varying processing conditions. IOP Conf Ser Mater Sci Eng 709:033004. https://doi.org/10.1088/1757-899X/709/3/033004 5. Akintseva A, Prokhorov A, Omelchenko S (2020b) Modelling of correlation of actual and program feeds in the automatic cycle. IOP Conf Ser Mate Sci Eng 709:033003. https://doi. org/10.1088/1757-899X/709/3/033003 6. Korchak SN (1973) Theoretical bases of processing parameter impact on the efficiency improvement of steel part grinding. Dissertation, South Ural State University of Chelyabinsk

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7. Korchak SN (1974) Steel part grinding efficiency by S. N. Korchak. Mashinostroyeniye. Moscow 8. Akintseva AA (2018) Productivity increase internal sanding optimization feed management cycles. Dissertation, South Ural State University of Chelyabinsk 9. Ardashev DV (2007) Cutting modes for works performed on manual and semi-automated grinding and finishing machines. ATOKSO, Chelyabinsk 10. Maslov YN (1951) The theoretical bases of metal grinding. Mashgiz, Moscow 11. Lur’e GB (1969) Metal grinding. Mashinostroyeniye, Moscow 12. Tergan VS (1969) Plane grinding. VysshayaShkola, Moscow 13. Tergan VS (1975) A young grinder’s reference book on plane grinding. Moscow VysshayaShkola, Moscow 14. Rowe WB, Ebbrell S (2004) Morgan MN. Process requirements for cost-effective precision grinding. CIRP Ann 53 (1):255–258.https://doi.org/10.1016/S0007-8506(07)60692-1 15. LiuYM YangTY, HeZ LiJY (2018) Analytical modeling of grinding process in rail profile correction considering grinding pattern. J Arch Civ Mech Eng 18:17–32. https://doi.org/10. 1016/j.acme.2017.10.009 16. Rowe WB (2013) Principles of modern grinding technology, 2nd edn. Elsevier, Liverpool 17. Gao S, Yang C, Xu J, Fu Y, Su H, Ding W (2017) Optimization for internal traverse grinding of valves based on wheel deflection. Int J Adv Manuf Technol 92:1105–1112. https://doi.org/ 10.1007/s00170-017-0210-8 18. Shipulin LV (2013) Improving the methods of operation planing for plane grinding with wheel periphery based on complex simulation modeling. Dissertation, South Ural State University of Chelyabinsk 19. Yudin S, Smolyanoy K, Pereverzev P (2020) Generalized cutting force model for grinding. IOP Conf Ser Mater Sci Eng 709:033005. https://doi.org/10.1088/1757-899X/709/3/033005 20. Nikolayenko AA (1998) Modelling and calculating high-efficiency automated cycles of plane creep profile grinding for CNC machine tools. Dissertation, South Ural State University of Chelyabinsk

Study of “Burr” Defect Cases in the Bolt Production S. A. Kurguzov, M. V. Nalimova(B) , and A. A. Kalchenko Nosov Magnitogorsk State Technical University, Lenin Ave., 38, Magnitogorsk 455000, Russia [email protected]

Abstract. The paper presents studies conducted to determine the causes of the burr defect in the bolt production. This defect occurs when trimming the hexagon of the bolt head. This operation is performed at the last stamping position of the multi-position automatic press. To determine the causes of the “burr” the authors have developed a device that allows determining the current efforts, the magnitude of absolute deformation, as well as obtaining samples to study the process. The experiments showed that U-shaped tears on the workpiece are formed in the region of the edge angles when trimming the bolt head. They bend to form a burr after the impact of the ejector and the separation of the splinter from the bolt head. The cutting force at the initial stage increases intensively and when the metal flow is stabilizing during the splinter formation, it changes insignificantly. Furthermore, when the sheared metal which formed the splinter is deposited between the movable and fixed matrices, the force is increasing sharply. The formation and size of the burr is proportional to the cutting edge wear and the cut allowance size, i.e., the diameter of the workpiece head. Bolts have an eccentric (up to 0.5 mm) head before trimming. To reduce efforts when edges are cutting and decrease the “burr” defect size, it is necessary to increase the front angle of the movable matrix, reduce the bolt workpiece head size and the roughness of the working surface. Keywords: Bolt · Bolt head · Cutter punch · Burr · Splinter · Trimming · Force

1 Introduction Product quality improvement is one of the urgent problems today in all industries. In the manufacture of bolts, the requirements of the standard [1], are not always complied with due to the occurrence of a burr defect [2–10]. The burr for bolts of execution 1 and also often for bolts of execution 2 [1], protrudes above the supporting surface of the product head which leads to damage to the fixed part surface and possibly damage to the coating applied to this surface during operation. In the future, such damage worsens the corrosion resistance of the entire product. Thereby the aim of this study is to determine the causes of the burr defect and possible suggestions for its prevention.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_131

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2 Model Development The “burr” defect (Fig. 1), is formed during the technological transition of trimming the bolt hex head with a trimming punch. This transition is performed at the last stamping position of the multi-position automatic press (Fig. 2). The workpiece 4 is set by the transfer mechanism opposite the hole of the matrix 2 then by the movement of the slider and attached edged punch 1 it enters the hole of the matrix (the transfer mechanism leaves the working space). Cutting of the edges is performed when the supporting surface of the bolt head is in contact with the surface of the fixed matrix. This transition is accompanied by cutting chips in the form of a ring with a hexagonal hole. At the moment of contact of the cut metal ring with the surface of the fixed matrix, it begins to additionally deform (to flatten and broaden in the radial direction). The cutter punch stops at a certain distance “h”. At this moment the ejector “B” strikes the end face of the bolt blank and the flask is separated from the bolt head and the bolt blank is pushed through the cutting punch into the conveying pipe to perform the last operation which is rolling the thread [10–15].

Fig. 1. Burr.

Fig. 2. Schematic diagram of the bolt edges trimming.

To determine the causes of the “burr” a device has been developed that allows to determine the current force, the magnitude of absolute deformation, as well as to produce undeformed samples to study the process of the cut flash deformation. The device consists

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of a hollow guide cylinder in the form of the hardened pipe with a high-quality bore. Cylindrical pistons are inserted into the hole at both ends. The upper piston is used to fasten the deforming tool (trimming punch) and the lower piston is used to install a fixed matrix with the bolt blank (test fixed using a dial indicator with an accuracy of 0.01 mm. The device is mounted on a tensile testing machine which creates the necessary displacements and efforts when conducting experiments. The dependence of the force change on the movement of the cutter punch during the cutting of the head was fixed using a recording device of a tensile testing machine. Blanks with uncut heads from one batch were used as samples. To increase the reliability of the results, a series of experiments were carried out according to 3–5 experiments with further statistical processing. The experiments showed that U-shaped tears on the workpiece are formed in the region of the edge angles when trimming the bolt head (Fig. 3). As can be seen from Fig. 3, these tears are formed at a small distance from the cutting surface. Then, after the impact of the ejector and separation of the splinter from the bolt head, the part of the metal (Fig. 4, left), is bent which is between the tear and the angle (Fig. 4, right).

Fig. 3. a Rupture of metal when trimming the bolt head (front angle 0°); b Rupture of metal when trimming the bolt head (front angle 23°).

Fig. 4. Burr defect pattern.

The measurement of the force P required for trimming the bolt head shows that with the increasing front angle from 0 to 23°, the dimensions of tears are decreasing, as well as the total working force (Fig. 5). From the graphs (Fig. 5), it can be seen that the cutting force P (path from 0 to 0.7 mm) increases intensively and when the metal flow is stabilizing during the splinter formation, it changes insignificantly. Furthermore, when the sheared metal which formed

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Fig. 5. a Cutting force P (front angle punch 0°); b Cutting force P (front angle punch 23°).

the cloud is deposited between the movable and fixed matrices, the force P is increasing sharply. And further, when the sheared metal which formed the splinter is deposited between the movable and fixed matrices, the force again increases sharply. The dashed lines in Fig. 5, show the lines after approximation. The graphs presented in Fig. 5 are described by the formula obtained by Excel program, kN.   0.13l 3 − 1.5l 2 + 6.8l − 5.2 (1) P = 10 cos(2γ ) where l—the cutting path, mm; γ —the front angle, degree. The study of incompletely deformed samples showed that tears are formed at a path of 1.75–2.0 mm for matrices with a front angle of 0° and at a path of 2.0–2.2 mm for matrices with a front angle of 23°. The tears, that formed when cutting the edges, are crumpled with a bend and form a burr later, in the process of cutting (when pushing through the moving matrix of the bolt) (Fig. 6). The burr size depends on the sharpness of the cut punch cutting edge. The sharp edge of the tool leads to the formation of a microburr (Fig. 6b). A significant burr is formed as a result of the rounding of the movable punch cutting edge due to wear. In spite of this, the wear doesn’t reach a critical value and the size of the bolt head is within acceptable limits. The wear of the working area of the cut punch is determined by the size of the bolt cut head, i.e., by tool wear on the back surface. However, the cutting edge of the cutter punch wears out earlier. It becomes dull and a rounding is formed (Fig. 6). This rounding reduces the possibility of cutting the tear and increases the probability of its plastic deformation with transformation into a burr. Sample analysis around the perimeter of the hex head also showed that the formation of discontinuities is associated with the size of the cut allowance, i.e., with the diameter of the planted head. The smaller diameter the greater tear magnitude. This relation was found due to the unevenness of the cut layer along the perimeter of the bolt head due to its eccentricity with respect to the rod. In order to study this phenomenon, five samples of bolt blanks with a shaped head were made from three bolt-heading automatic machines before the transition to the hexagon formation. These samples were measured to determine the magnitude of the head eccentricity. A prism with an angle at the apex of 90° and a tripod with a dial indicator equipped with a flat measuring tip was used. A bolt blank was placed at the top of the prism, which was subsequently rotated and

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Fig. 6. a A diagram of the tear formation before the bolt is ejected through the cutting punch; b Cutting of the tear with a sharp cutting punch with the formation of micro-burr and chips; c The burr formation with a cut punch with a rounded cutting edge due to wear.

eccentricity was measured. Based on the measurements, a typical eccentricity histogram (Fig. 7a), was described for bolts with a shaft length of 40 mm. Using this method, we also checked the eccentricity of the head on bolts with an already formed hexagon (Fig. 7b). The eccentricity of the formed head was determined along the faces. This made it possible to determine the complex effect of the misalignment of the cut punch in relation to the fixed matrix and the gap between the hole of the fixed die and the body of the bolt blank.

Fig. 7. Eccentricity histogram of the M6 bolt head; a Before the formation of the hexagon; b For a hex head.

Analysis of the histograms showed that all bolts have an eccentric head before trimming and the eccentricity is mainly in the range of 0.2–0.5 mm. Even the smallest eccentricity leads to the fact that the formation of a burr doesn’t occur on all the vertices of the bolt head. It should be noted also that the gap between the fixed matrix and the bolt

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shaft is 0.15–0.25 mm. Therefore, arithmetic addition of eccentricity and displacement of the bolt rod (gap) during operation occurs. Then the actual displacement of the head will be 0.3–0.7 mm. As a result, there will be a high probability of occurrence of tears and the formation of burrs along the vertices of the hexagon. Wear and rounding of the cutting edge of the sheathing contribute to this phenomenon, despite on the fact that dimensional wear doesn’t exceed the permissible value (the size of the turnkey bolt head doesn’t exceed the tolerance field) [16–20]. The study of the flake surface in contact with the movable punch showed that the direction of the roughness formed by finishing grinding the tool front surface also affects the tears size. It has been unequivocally established that the smaller the angle between the direction of the metal flow (the metal flows radially relative to the axis of the bolt) during trimming and the longitudinal direction of the roughness elements, the smaller the size of the tears or they don’t form. This indicates that one of the factors leading to the formation of a burr defect is the shear stress value in the surface layer of the workpiece metal in contact with the tool.

3 Conclusions Thus, in order to reduce efforts when cutting edges and reduce the burr defect, it is necessary to increase the front angle of the sheathing, increase the size of the bolt workpiece head and reduce the roughness of the working surface. It should be noted that increasing the size of the head is undesirable for two reasons such as this will lead to an increase in cutting forces and metal consumption. Therefore, it is necessary to change the geometric parameters of the tools, namely moving and stationary matrices so that the defect “burr” is not formed or had an allowable size. One of the options for wear reduction is changing stress–strain state of the metal tool surface layer [2, 3], and using surface-plastic deformation [4], which additionally smooths the roughness on the tool front surface and changes their size and direction.

References 1. State standard of the USSR 1759.2-82 Bolts, screws and studs. Surface defects and methods of control 2. Volkov AA, Kurguzov SA, Sidorenko VV (2009) The formation of a given surface roughness and hardening of parts when smoothing. Forging and stamping production. Process Mater Pressure 10:16–20 3. Kurguzov SA, Sidorenko VV, Volkov AA, Kurguzov VA (2009) The formation of residual stresses in the surface of a hardened steel tool during ironing. Vestnik Nosov Magnitogorsk State Techn Univ 1(25):52–55 4. Nosov AD, Kurguzov SA, Noskov EP, Kanaev DP, Kurguzov VA (2009) Device for finishing of the forming tool working surface. RU Patent 83022 5. Kadoshnikov VI, Reshetnikova ES, Reshetnikov LV (2008) Tool design for the production of high-quality flangeless bolt-free stamping bolts. Forging and stamping production. Process Mater Pressure 5:23–25 6. Semikhatsky SA, Kuznetsova AI, Semashko VV (2009) Improving the technology of preparing metal for cold stamping terminal bolts. Model Dev OMD Process 1:207–210

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7. Reshetnikova ES, Kadoshnikov VI (2014) Study of the multi-transition process of volumetric stamping of flange bolts. Forging and stamping production. Process Mater Pressure 8:18–20 8. Semashko VV (2012) Modeling of stamping processes for fasteners with rectangular heads in order to improve the manufacturing technology and design of the tool. Dissertation, Nosov Magnitogorsk State Technical University 9. Belan AK, Belan OA (2018) Modeling and development of technology for the cold forming process of progressive types of fasteners. Theory Technol Metall Prod 2(25):27–32 10. Reshetnikova ES, Usataya DYu, Usataya TV (2016) Computer graphics in design of process of cold forging bolts with flange. Eng Online Electron Sci J 4(2):60–63. https://journals.ipubl.ru/index.php/IndEng/article/view/1347 11. Kadoshnikov VI, Reshetnikova ES, Reshetnikov LV, Kochukov SV (2008) Improving the tool and mathematical modeling of the process of forming the heads of flange bolts. Vestnik Nosov Magnitogorsk State Tech Univ 2(22):52–56 12. Kadoshnikov VI, Reshetnikova ES, Tkachenko TG (2008) Application of the variational principle of mechanics in the design of new designs of flange bolts. Forging and stamping production. Process Mater Pressure 8:39–41 13. Gurov VD, Kuznetsova AI (2007) Low-waste hex head bolt technology. Forging and stamping production. Process Mater Pressure 7:24–28 14. Golubchik EM, Kuznetsova AS, Rubin GSh, Gun GS, Dyya H (2016) Application of the model and principles of technological adaptation of quality indicators in the production processes of hardware products. Vestnik Nosov Magnitogorsk State Tech Univ 14(1):101–108 15. Shubin IG, Kurkin AA, Bazykov AR, Stolyarov FA (2019) Study of the process of cold stamping blanks hexagonal nuts increased height. Ferrous metallurgy. Bull Sci Tech Econ Inf 75(8):979–985 16. Trukhin VV (2007) Study of wear of the cutting tool. Vestnik Kuzbass State Tech Univ 2(60):103–105 17. Zheleznov GS (2006) The effect of cutting tool wear and cutting depth on its real geometry. STIN 11:9–12 18. Shashok AV, Kutyshkin AV, Frolov EA, Kozhemyako IV (2011) Prediction of adhesive wear on a blade cutting tool. Metal Process (Technol, Equip, Tools) 1(50):23–26 19. Bezyazychny VF, Nepomiluev VV, Sutyagin AN (2007) Using the theory of similarity in the study of wear of a cutting tool. Friction Lubr Mach Mech 6:25–28 20. Kozochkin MP, Allenov DG (2015) Study of the influence of wear of the tool cutting edge on the deformation of the surface layer of the part. Bull MSTU Stankin 4(35):22–29

Reflection and Refraction Features of Sound Waves at Oblique Incidence on the Interface “Porous Medium–Gas” L. F. Sitdikova(B) and I. K. Gimaltdinov Ufa State Petroleum Technological University, 1, st. Cosmonauts, Ufa 450062, Russia [email protected]

Abstract. The article studies the reflection and refraction of sound waves passing through the “porous medium–gas” interface with oblique incidence from the side of the porous medium. Based on the analysis of the obtained analytical solutions, in the case of an oblique incidence of a “slow” wave at the interface from the side of the porous medium for a certain frequency range at angles of incidence exceeding a certain critical value, the general internal reflection (without reflection) is realized. This is due to the fact that the speed of the “slow” wave for a certain frequency range is less than the speed of sound waves in the gas surrounding the porous medium. In addition, it was found that the porous layer has certain wave properties, possibly slightly weak from the point of view of conventional waveguides. Keywords: Porous medium · Sound wave · Reflection and transmission coefficients · Total internal reflection

1 Introduction The study of the propagation of sound waves when passing through porous partitions, as well as their effect on obstacles covered by a porous layer, is of significant scientific and practical interest in connection with the wide distribution of porous materials in nature, modern technologies, and industry. This is also associated with the tasks of acoustic sounding of porous formations. Here are some works on the dynamics of sound waves in porous media and the features of the passage of the boundaries of inhomogeneity by waves [1–21]. In [7, 8], wave processes in moist, saturated with a vapor–gas mixture porous media were studied, taking into account interfacial forces of interaction, heat and mass transfer between the skeleton of a porous medium, a liquid, and a vapor–gas mixture. Dispersion expressions are obtained for cases of saturation of a porous medium with a vapor–gas mixture, steam, or gas. A study of the processes of reflection of sound waves through a porous medium in the case of their oblique incidence is presented in [10]. The study is presented for © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_132

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the boundary “gas–porous medium”, when the wave is incident from the gas side onto the porous medium. It is shown that with an increase in the angle of incidence, the transmission coefficient decreases. The features of the propagation of an acoustic wave into a porous layer and reflection from an obstacle were studied in [11]. This work also compared the calculated data with the experimental data regarding the passage of a pulse through a porous plate immersed in water. In [12], the reflection and transmission of plane waves incident at an angle to the interface between two porous half-spaces saturated with various liquids was studied. The dependence of the amplitude transmission and reflection coefficients on the angle of incidence is obtained. A method for determining the acoustic characteristics of a gas-saturated jet medium from the results of reflection of ultrasonic waves from the boundaries of a porous layer with a rigid skeleton with oblique incidence, proposed in [17, 18]. The method allows you to determine the coefficient of tortuosity and the characteristic viscosity and temperature length of the porous medium.

2 Basic Equations Let a sound wave propagating through a porous medium saturated with gas act on a flat surface, which is the boundary between the porous medium and the surrounding gas. Moreover, the gas surrounding the porous medium and the gas in the pores are one and the same. We assume that the boundaries are “open”: that is, the gas contained in the pores located directly at the boundary is in contact with the “free” gas surrounding the porous medium. The linearized form of the equation describing the motion in a porous medium [7–10] ∂υg ∂ρg ∂ρs ∂υs + ρg0 = 0, + ρs0 = 0, ∂t ∂x ∂t ∂x ∂υg ∂pg ρg0 = −αg0 − F, F = Fm + Fμ + FB , ∂t ∂x a03 , αg0 + αs0 = 1, αg0 = (a0 + b0 ) ∂pg ∂υg ∂σ ∗ ∂υs + ρs0 = s − , ρg0 ∂t ∂t  ∂x ∂x  ∂υg ∂υs 1 Fm = ηm αg0 αs0 ρg0 − , 2 ∂t ∂t   9 Fμ = ημ αg0 αs0 μg υg − υs a0−2 , 2 t   dτ ∂  2 0 υg − υs √ FB = 6ηB αg0 αs0 a0 πρg μg , ∂τ t−τ −∞

σs∗ = αs0 (σs0 + pg ), ∂ε 1 ∂σs σs ∂ε ∂υs  0 = + , = , pg = ρg0 BTg . ∂t Es ∂t μs ∂t ∂t

(1)

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Here ρj , ρj0 , υj , pj , αj —volume average and phase average density, speed, pressure, volumetric contents. Subscript j = g, s corresponds to the parameters of gas (gas) and the skeleton of the porous medium (skelton). pg is the gas phase pressure, αs and αg are volume contents of the solid and the gas phases, Fm is the virtual mass caused by the inertial interaction of the phases, Fμ isan analog of the Stokes viscous friction force, FB is an analog of the Basset force showing up at high frequencies because of the nonstationarity of the viscous boundary layer near the interface with the solid phase, σs∗ is the reduced stress, σs is the stress in the skeleton, μg is the dynamic viscosity of the gas. The additional subscript (0) denotes the parameters corresponding to the unperturbed state, and parameters without this subscript correspond to a small perturbation from the equilibrium value; the superscript (0) corresponds to the ideal value of a parameter. Parameters related to the micro-coordinate are marked with a dash. Using the mesh scheme [7] (Fig. 1), we describe the temperature inhomogeneities. Let us take the gas-saturated porous medium as a system of spherical gas bubbles surrounded by the skeleton material. In describing the process of heat transfer in the saturated porous medium, we assume that the length of the considered waves is much greater than the pore sizes. Let us assume, as the characteristic sizes of the medium, the mean pore radius a0 and the mean half-thickness of the pore walls b0 .

Fig. 1. Cell of the porous medium.

Thus, at each macroscopic point defined by the x coordinate, we introduce a typical cell consisting of a gas bubble and a skeleton falling at it. Inside the cell, there is a distribution of microparameters, namely the gas temperature Tj (t, x, r) and density ρj0 (t, x, r) where r—is a microcoordinate measured from the center of the cell. The temperature distribution in the cell of a porous medium is obtained on the basis of the system of heat conduction equations:  ∂Tg ∂Tg ∂pg 0 −2 ∂ 2 = λg r , (0 < r ≤ a0 ) ρg0 cg r + ∂t ∂t ∂r ∂t 0 ρs0 cs

∂Ts ∂ 2T  = λs 2s .(a0 < r < a0 + b0 ) ∂t ∂r

(2)

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where λj and cj —are the hect conductivity and the specific heat capacity coefficient at a constant pressure, respectively (j = g, s). The boundary conditions for system (2), have the form 

∂Tg ∂Ts = λg ; (r = a0 ) ∂r ∂r  ∂Tg ∂T  = 0, (r = 0). s = 0(r = a0 + b0 ) ∂r ∂r

Tg = Ts , λs

(3)

Solutions of Eqs. (1)–(3), are defined in the form of damped waves ρj0 , υj , pj , aj ∼ = Aj exp[i(Kx − ωt)], Tj = Tj (r) exp[i(Kx − ωt)], K = k + iδ, j = g, s.

(4)

where Aj (r) is the amplitude value, ω is the circular frequency, K is the complex wave number, and δ is the damping coefficient. It is known that in a porous medium there are two types of longitudinal waves, “fast” and “slow”, due to different compressibilities of the porous skeleton and the fluid saturating it [7, 10]. After a series of transformations, we obtain the dispersion relation, on the basis of which one can analyze the propagation of waves in a dispersion medium [13–15].

3 Border Conditions Indicate within which program or grant the work or sponsors was carried out. If there is no such link, delete this text field. Let a wave be incident on the “porous medium–gas” interface. We assume that, as in the case of ordinary single-phase media, reflected from the boundary and refracted waves are plane harmonic waves [16]. Then, in the zone of the porous medium, small perturbations represent the sum of two harmonic waves, and in the gas zone, one harmonic wave. The perturbations corresponding to the incident, reflected, and refracted waves are provided with upper symbols (0), (r), and (t). Then the pressure continuity condition at the interface can be written as pg(0) + pg(r) = pg(t) ,

(5)

(t)

where pg pressure disturbance in the gas region. We also write the condition of continuity of the normal velocity components. for a “slow” wave

 (0) (r) (t) (t) αg0 υg(0) cos θb + υg(r) cos θb = υeg cos θb for a “fast” wave

 (t) αs0 υs(0) cos θa(0) + υs(r) cos θa(r) = υes cos θa(t)

(6)

(7)

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(t) (t) where υeg and υes is perturbations of the velocity of the gas surrounding the porous medium due to refraction of the “slow” and “fast” waves at the “porous medium–gas” interface, respectively. θn(0) , θn(r) , θn(t) is, respectively, the angles of incidence, reflection, and refraction, where . The condition for the equality of forces acting per unit surface area, i.e., we write the equality of total stresses in the form



 (8) −αs0 σs(0) + σs(r) + αg0 pg(0) + pg(r) = pe(t) ,

where pe(t) is the total perturbation of the pressure in the gas surrounding the porous medium due to the passage of perturbations along the skeleton and gas from the porous medium into the gas region. The x axis is directed vertically downward to the gas side, and the y axis is directed so that the wave vector is parallel to the xoy coordinate plane. Since the “fast” wave when passing through the “porous medium–gas” boundary is reflected as from the free surface due to the large difference in acoustic impedances (that is, the perturbation practically does not pass through the gas region), we will consider the process of transmission and reflection only “slow” wave. After appropriate calculations and transformations, for the boundary “porous medium–gas” we obtain the following reflection and transmission coefficients: N(b) =

D(b) − 1 2D(b) , M(b) = , D(b) + 1 D(b) + 1

(9)

where D(b) =

0 C ρe0 e 0 ω ρg0

Kb +

iαg0 χV ω2 (1 + χT ) Ka Cg−2

 1 + iαs0 χV +

iαg0 χV Kb Ka

−1

cos θb(0) (t)

cos θb

.

4 Calculation Results Suppose that in pores and outside the porous medium the gas is air. The porous material was rubber, saturated with air (sponge). For numerical calculation, the phase parameters are taken at medium temperature 300 K. Figure 2 shows the frequency dependences of the phase velocity and the damping coefficient of the slow wave (solid lines) and the fast wave (dashed lines). It is seen that the velocity of the fast wave is higher than that of the slow wave. −1 Noteworthily,  the fast wave velocity is constant for frequencies ω ≥ 10 s and reaches a value Cs =

0 . The slow wave velocity increases with frequency. For frequencies Es /ρs0  0 is also attained. The “slow” wave attenuation ω ≥ 105 s−1 a value Cg = γ p0 /ρg0 coefficient is greater than the “fast” wave attenuation coefficient over the entire frequency range.

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Fig. 2. Dependence a phase velocity C p and b attenuation coefficient δ “slow” (solid lines) and “fast” (with dashed lines) waves of frequency ω. System parameters: αg = 0, 8, α0 = 10−3 m.

It was shown in [2], that due to the large difference in acoustic resistances, the perturbation amplitude in the gas surrounding the porous medium due to the refraction of the “fast” wave at the “porous medium–gas” interface is negligible, the “fast” wave does not pass into the gas region at passing the boundary “porous medium–gas”. Since for a certain frequency range, the speed of the “slow” wave is slower than the speed of sound in the gas surrounding the porous medium, total internal reflection can occur when the “slow” wave obliquely falls on the porous medium–gas interface [16]. The dependences of the real and imaginary parts of the angle of refraction, as well as the cosine of this angle for the “slow” wave, on the angle of incidence, are shown in Fig. 3.

Fig. 3. The influence (a) of the angle of incidence on the real and imaginary parts of the angle of refraction and (b) the cosine of the angle of refraction for the “slow” (solid lines) waves for the “porous medium–gas” interface.

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The presence of the imaginary part of the angle of refraction is due to the fact that the incident wave in the porous medium is damped. In this case, the real part of the angle (0) (0) has the usual geometric meaning. At θb ≥ 63◦ at ω = 103 s−1 i θb ≥ 34◦ at ω = (t) 10 s−1 angle of refraction θb ≥ 90◦ . In this case, the imaginary part prevails for the (t) cosine of the angle of refraction. For these angles of refraction (θb ≥ 90◦ ) in air, the wave remains a damped traveling wave, but for it, the characteristic damping distance of the wave amplitude will be much lower than the wavelength. That is, a monotonous exponential decrease in the wave amplitude in the direction perpendicular to the interface will be valid. And thereby, a complete internal reflection will be realized [16]. Thus, when a “slow” wave falls on the “porous medium–gas” boundary at angles exceeding a certain critical value, which depends on the sound frequency, the full reflection condition is realized. Figure 4 shows the dependences of the moduli and arguments of the reflection and transmission coefficients at the “porous medium–gas” interface on the frequency for a “slow” wave. Line 1 corresponds to normal incidence, and line 2 corresponds to incidence at an angle of 30° to the “porous medium–gas” interface.

Fig. 4. Modulus and argument (a) of reflection and (b) transmission coefficients (solid line— modulus, dashed line—argument) at the “porous medium—gas” interface for a “slow” wave. Line 1 corresponds to the normal incidence, line 2—at an angle of 30°. Other parameters are the same as in Fig. 2.

It can be seen from Fig. 4, that the modulus of the transmission coefficient in the case of oblique incidence is less than in the case of normal incidence. That is, for an oblique incidence of a “slow” wave, the porous medium becomes even more acoustically soft. This means that in this case, the “slow” wave passes through the “porous medium–gas” interface less than during normal incidence. We note that in the case of a wave incident on the “porous medium–gas” boundary at (0) an angle θb = 30◦ in the frequency range 0 ≤ ω ≤ 10 s−1 the reflection and transmission coefficients are equal −1 and 0, respectively, i.e., for this frequency range, total internal reflection is realized.

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Figure 5 shows the dependences of the moduli and arguments of the reflection and transmission coefficients at the “porous medium–gas” interface on the angle of incidence for “slow” waves.

Fig. 5. Modulus and argument a of reflection and b transmission coefficients (solid line—modulus, dashed line—argument) at the “porous medium—gas” interface for a “slow” wave. Lines 1 and 2 correspond—ω = 10s−1 i 103 s−1 . The remaining parameters are the same as in Fig. 2.

It can be seen from Fig. 5, that the reflection modulus increases with increasing angle of incidence to a certain critical angle, and then becomes equal to 1, while the transmission modulus becomes equal to 0, i.e., full reflection occurs from the “porous medium–gas” interface. Therefore, it can be argued that the porous layer has some waveguide properties, maybe a little weak from the point of view of conventional waveguides.

5 Conclusion The problem of the oblique incidence of a “slow” wave at the “porous medium–gas” interface has been solved. It is shown that when a “slow” wave is incident from the side of a porous medium for a certain frequency range at angles of incidence exceeding a certain critical value, total internal reflection is realized. This is due to the fact that the speed of the “slow” wave for this frequency range is less than the speed of sound waves in the gas surrounding the porous medium. It is established that the porous layer has the properties of a sound channel. Acknowledgements. The reported study was funded by RFBR, project number 19-31-60015.

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References 1. Biot MA (1956) Theory of propagation of elastic waves in fluid-saturated porous solid. Part I. Low frequency range. J Acoust Soc Amer 28(2):168–178 2. Biot MA (1956) Theory of propagation of elastic waves in fluid-saturated porous solid. Part II. Higher frequency range. J Acoust Soc Amer 28(2):179–191 3. Frenkel YaI (1944) On the theory of seismic and seismoelectric phenomena in moist soil. Izv. USSR Acad Sci ser. Geo Geophys 8(4):134–149 4. Stoll RD, Kan T-K (1981) Reflection of acoustic waves at a water-sediment interface. J Acoust Soc Amer 70(1):149–156 5. Belhocine F, Derible S, Franklin H (2007) Transition term method for the analysis of the reflected and the transmitted acoustic signals from water-saturated porous plates. J Acoust Soc Amer 122(3):1518–1526 6. Gubaidullin AA, Britan A, Dudko DN (2003) Air shock wave interaction with an obstacle covered by porous material. Shock Waves 13(1):41–48 7. Gimaltdinov IK, Dmitriev VL, Sitdikova LF (2014) Dynamics of sound waves in porous media saturated with a vapour–gas mixture. High Temp 52(4):545–553 8. Gimaltdinov IK, Dmitriev VL, Sitdikova LF (2013) On the evolution of sound waves in the wet porous media. Basic Res 10:2198–2202 9. Shagapov VSh, Khusainov IG, Dmitriev VL (2004a) Propagation of linear waves in porous media saturated with gas taking into account interphase heat transfer. Appl Mech Tech Phys 45(4):114–120 10. Gimaltdinov IK, Levina TM, Sitdikova LF, Dmitriev VL, Khabeev NS, Wanqing S (2017) Reflection of acoustic waves from a porous material at oblique incidence. J Eng Phys Thermophys 90(5):1043–1052 11. Gubaidullin AA, Boldyreva OY, Dudko DN (2009) Interaction of acoustic waves with porous layer. Thermophys Aeromech 16(3):429–443 12. Kumar R, Kumar S, Miglani A (2011) Refl ection and passage of plane waves between two different fl uids saturating porous half-spaces. Mekh Tekh Fiz 5:115–126 13. Nigmatulin RI (1987a) The dynamics of the multiphase media. Nauka, Moscow 14. Nigmatulin RI (1987b) The dynamics of multiphase media: part 1. Nauka, Moscow 15. Shagapov VSh, Khusainov IG, Dmitriev VL (2004b) Propagation of linear waves in gassaturated porous media with allowance for interphase heat transfer. J Appl Mech Tech Phys 45(4):552–557 16. Lependin LF (1987) Acoustics. Graduate School, Moscow 17. Fellah ZEA, Berger S, Lauriks W et al (2003) Measuring the porosity and the tortuosity of porous materials via reflected waves at oblique incidence. J Acoust Soc Am 113(5):2424–2433 18. Fellah ZEA, Depollier C, Berger S, Lauriks W, Trompette P, Chapelon J-Y (2003) Determination of transport parameters in air-saturated porous materials via reflected ultrasonic waves. J Acoust Soc Am 114(5):2561–2569 19. Kutushev AG, Rodionov SP (2000) Interaction of weak shock waves with a powder layer environment. Combust Explosion Phys 36(3):131–140 20. Lukin SV, Gubaidullin AA, Urmancheev SF (2006) Patterns of reflection of pressure waves from hard surfaces coated with a porous layer. Oil Gas Bus 4:35–40 21. Feuillade C (1996) The attenuation and dispersion of sound in water containing multiply interacting bubbles. J Acoust Soc Am 99:3412–3430

Forced Cooling Modeling in Grinding N. V. Lishchenko1 , V. P. Larshin2(B) , and I. V. Marchuk3 1 Odessa National Academy of Food Technologies, 112, Kanatna Street, Odessa 65039, Ukraine 2 Odessa National Polytechnic University, 1, Shevchenko Avenue, Odessa 65044, Ukraine

[email protected] 3 Lutsk National Technical University, 75, Lvivska Street, Lutsk 43018, Ukraine

Abstract. A mathematical model is developed for a grinding temperature cycle, invariant to the machining material properties and grinding modes with the managed dimensionless parameters of forced cooling, taking into account the heat exchange and grinding fluid temperature. The influence of these parameters on the dimensionless and dimensional grinding temperature is investigated. A grinding temperature cycle mathematical model includes the heating and cooling stages with and without grinding fluid application. The influence of the grinding fluid temperature and the heat transfer coefficient on the grinding temperature is established. Comparative studies of one- and two-dimensional solutions of the heat conduction differential equation that take into account the forced cooling during grinding have been carried out. The difference in the results of calculating the dimensionless temperature by the solutions of one- and two-dimensional mathematical models does not exceed 4.5–10.6%. The comparison of the two models is performed for the Peclet number with the value of more than 4 which just takes place in contemporary profile grinding. Keywords: Grinding temperature · Modeling · Heat conduction · Heat exchange

1 Introduction Grinding is one of the most common methods of machine parts finishing because of providing the necessary parts of dimensional accuracy, as well as surface finish and integrity. One of the factors limiting the grinding operations is the temperature in the contact zone between a grinding wheel and a workpiece being ground. Exceeding the permissible level of this temperature leads to the appearance of grinding burns and microcracks. Therefore, the task of monitoring the grinding temperature with high operation productivity on CNC machines is relevance for modern grinding technology. The solution to this problem will allow the development of computer subsystems for monitoring and diagnosing the state of the grinding system, as well as managing this operation.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_133

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2 Literature Review One of the factors that reduce the grinding temperature is the use of effective forced cooling which have a complex effect on the grinding process due to cooling, lubricating, and washing effects [1]. To date, the effect of forced cooling has not yet been fully investigated and the heat process in grinding is difficult to model mathematically. As a rule, the most objective data are obtained using the finite element method (FEM) or finite difference method (FDM). Such studies were performed in [2–6]. However, these methods require a considerable investment of time and for this reason cannot be used in the computer subsystems software both on production and production preparing stages. In this regard, taking into account the factor of forced cooling in analytical models of the temperature field in determining the grinding temperature is a reserve for improving the performance of CNC grinding machines. In [7–12], the grinding designing, monitoring and diagnosing computer subsystems were proposed for improving the efficiency of grinding operations on CNC machines. The mathematical software of these computer subsystems makes it possible optimizing grinding operations and adapting the grinding system to higher grinding productivity, including taking into account the influence of forced cooling on the grinding temperature. However, the mechanism for accounting the cooling factor in these works is not fully disclosed. In the following research works [13–15], the heat transfer into abrasive grain, grinding fluid, and workpiece are separated by introducing local heat transfer coefficients, and the separate models are coupled accounting the temperature both at the workpiece-fluid and the workpiece-grain interfaces. The model was further extended to account for the variation of the heat fluxes along the grinding contact zone in the down grinding with large Peclet number. In [6, 16, 17], it is made a review of the literature on the inclusion of cooling in grinding. These papers illustrate how important is expanding our knowledge about coolant supply into the grinding zone. Coolant types composition, nozzle design, and coolant flow rate can influence considerably on grinding productivity, workpiece quality, and tool wear. The closest work on both the technical essence and the result obtained are the papers [18, 19] using a two-dimensional solution of heat conduction differential equation with a moving strip heat source. A possible way to solve this complexity problem is to use Jaeger’s idea of close agreement between temperature fields from moving and unmoving heat sources, provided that the Peclet number is more than 5 [20] and (in accordance with our research) even 4 [21]. In this case, it becomes possible to sequentially (as this actually happens in grinding) consider the heating and cooling stages for the case of temperature propagation along one coordinate which is perpendicular to the surface being ground. It becomes possible to use the solution published in [21], to find the grinding temperature under the forced cooling [22]. This is even truer when one considers the current trend of high-speed grinding [23].

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3 Research Methodology Due to the complexity of the solution obtained, work [18] proposed a way to simplify it. According to this work, a heat exchange scheme for flat grinding is represented as follows. Over the flat surface of a semi-infinite body, which can be either thermallyinsulated (Fig. 1a) or washed by a coolant (Fig. 1b), a strip heat source moves along and in the positive direction of the z-axis and is infinitely long in the direction of the y-axis. The heat flux q over the entire surface of the moving contact is assumed uniform and constant, i.e., q = const. The temperature of the grinding fluid and the initial temperature of the semi-infinite body are assumed to be zero. The coordinate system is referenced to the moving heat source (Fig. 1). The corresponding solutions of the two-dimensional heat conduction differential equation for determining the dimensionless temperature have the following forms [18]. 1. Without cooling (Fig. 1a) Z+H 

1 (X , Z) =

exp(−ξ )K0

  X 2 + ξ 2 dξ

(1)

Z−H

Fig. 1. Thermal scheme of a strip heat source without (a) and with (b) forced cooling when the grinding fluid enters the surface even under the heat source.

2. With cooling over the entire surface, except for the contact zone (approximate solution) ⎡ Z+H    1 2 (X , Z) = ×⎣ exp(−ξ )K0 X 2 + ξ 2 − H 1 − 2Hβ π (Z)dZ Z−H  −β

−H Z+H

exp(βX − ξ )

Z−H



∞

 exp(−βX )K0 ( X 2 + ξ 2 dX dξ . (2)

X

3. With cooling over the entire surface including the contact zone (Fig. 1b).

Forced Cooling Modeling in Grinding

Z+H    2qa 3 (X , Z) = exp(−ξ )K0 X 2 + ξ 2 π λV Z−H ⎧   ⎫ ∞ ⎪ ⎪ 2 2 ⎪ exp(−βX )K0 X + ξ dX ⎪ ⎪ ⎪ ⎨ ⎬ X  dξ. × 1 − β exp(βX ) ⎪ ⎪ K0 X 2 + ξ 2 ⎪ ⎪ ⎪ ⎪ ⎩ ⎭

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(3)

In Eqs. (1–3), the following notations are used: X, Z are the dimensionless or relative coordinates which correspond to dimensional ones x, z in m; H is the dimensionless heat source half width (Peclet number) which correspond to the dimensional one h in m; K0 (s) stands for the zeroth-order modified Bessel function of the second kind. αh h Vz Vh 2a α Bi Here X = Vx 2a , Z = 2a , H = 2a , β = V λ = H , Bi = λ . Besides, h is the half width of the heat source, in m (Fig. 1); β is the dimensionless complex characterizing the efficiency of heat transfer; αh is the heat transfer coefficient, W/(m2 °C); Bi is the Biot number; a and λ are the thermal diffusivity in m2 /s and thermal conductivity in W/(m °C) of the workpiece material, respectively; V is the heat source velocity, m/s; To obtain temperature in degrees Celsius, Eqs. (1–3) need to be multiplied by the factor characterizing the actual conditions of the grinding. This factor is measured in 2 degrees Celsius and equal to π2qa λV , where q in W/m . For example, according to Eqs. (1– 3), the corresponding calculations are made with the following data: H = 5, a = 5·10–6 m2 /s, λ = 25.54 W/(m °C), α h = 36,000 W/(m2 °C), V = 3 m/min or 0.05 m/s, and αh 2·5·10−6 36000 β = 2a V λ = 5·10−2 25.54 = 0.282. 1 depends For the example under consideration, the multiplier k = H 1− 2Hβ π

−H

(Z)dZ

on the multiplication the β/π by the average integral value of the temperature under H 1 the source 2H (Z)dZ. It is found that under the above conditions we have k = −H

1.5. It follows that, compared with cooling over the entire surface including the contact zone, the lack of the cooling in the contact zone leads to an increase in temperature by half (1.5 times increase). Therefore, the entering of cooling into the contact zone significantly (38%) reduces the maximum grinding temperature. This is a significant reserve for increasing the grinding productivity. If coolant does not fall into the cutting zone then the effect of cooling on the maximum temperature in the contact zone is not significant (4%). In the theoretical calculations, the contact zone is represented in the form of a moving strip heat source A1 (Fig. 2a) [20]. It is known that with H more than 5 the maximum temperature can be determined by a one-dimensional solution [21]. In this solution, the heat source velocity V is replaced by the time of its impact, i.e.τH = 2hVH (Fig. 2b, c). This solution is valid for an unlimited surface A2 (Fig. 2b) and for a bounded surface site A3 .

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Fig. 2. Moving zone A1 a, unmoving A2 b, and A3 c zones in which the heat flux q acts at the stage of heating.

The temperature field at the heating stage in dimensionless form is described by a mathematical dependence which is a solution of a one-dimensional differential equation of heat conduction [21], i.e.  X H (X , HH ) = 2π HH · ierfc √ + 0 (4) 2 HH 2

where H = V4a τ is the dimensionless coordinate, 0 ≤ H ≤ HH ; τ is the action time of the unmoving heat source (heating time of the surface to be ground, 0 ≤ τ ≤ τH ) in s; 0 is the initial workpiece dimensionless temperature. To determine the temperature at the cooling stage which follows immediately after heating, with the initial conditions obtained during the heating stage, the following equation for the dimensionless grinding temperature was obtained on the basis of transforming the equation published in [22], i.e.          ∞  1 X − X 2 X + X 2 exp − √ + exp − √ C (X , HH , HC ) = √ 2 π HC 2 HC 2 HC 0    Bi 2 Bi Bi  × exp HC + (X + X ) − HH HH HH   X + X Bi  ·erfc √ × f (X  )dX  HC + HH 2 HC   ⎡ 2 4a HC X V2 √ exp − 2 H −H ⎢ C Bi ⎢ √ + ⎣ HH π(HC − H ) 0

  2 Bi  Bi Bi − HC − H + exp X HH HH HH   X Bi  × erfc √ + HC − H · a (HC )dH . HH 2 HC − H Here (see Eq. 4).  f (X  ) = 2π HH ierfc

X + 0 √ 2 · HH

(5)

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In Eqs. (4) and (5), the following designations are used: HH = (V 2 /4a)τH ; τ = 2h/V are the Peclet number and the maximum heating time at the heating stage in s, HC = (V 2 /4a)tC is the equivalent of some spatial coordinate Z  which is proportional to the actual cooling time 0 ≤ τ ≤ t; t is the cooling time in s; (HC ) the starting dimensionless temperature of the grinding fluid, which can vary even over the cooling time interval H, 0 ≤ H ≤ HC . Thus, the set of Eqs. (4) and (5), describes the stages of heating and cooling in their natural sequence, i.e., just as this happens in the real grinding operation. To obtain the dimensional temperature in the stages of heating and cooling, the expressions (4) and (5), must be multiplied by the factor π2qa λV commonly accepted in the grinding thermophysics.

4 Results The obtained one-dimensional mathematical model with two Eqs. (4) and (5), was compared with a similar two-dimensional model with Eq. (2), analyzed above which contains one equation both for heating and cooling stages. Equation (2) is obtained under the boundary conditions of the third kind, but with a number of assumptions that allow us to take into account the non-homogeneous (discontinuous) boundary conditions of the real problem [18]. Thus, a one-dimensional mathematical model containing two Eqs. (4) and (5), differs only in the absence of a coordinate Z in the direction of which the strip heat source moves at a velocity V. Comparative studies of one- and two-dimensional mathematical models according to Eqs. (4) and (5), on the one hand, and Eq. (2), on the other hand, were performed with the following input data: a = 5 × 10−6 m2 /s; λ = 25.54 W/(m °C); α h = 36,000 W/m2 °C; V = 3 m/min (0.05 m/s); hH = 1 mm (half width of the contact); HH = Vh 2a = 5; −3

−6

αh 2×5×10 36000 Bi = αλh h = 36000×1×10 = 1.41; k = 1.54; β = 2a 25.54 V λ = 5×10−2 25.54 = 0.282 (or the same β = Bi/HH = 1.41/5 = 0.282). The dimensionless coordinate along the depth of the surface layer in Eq. (2), was taken equal to X = 0, X = 1, X = 3 (Fig. 3). It is seen that the temperature fields for the one- and two-dimensional models are similar in heating and cooling stages. At the heating stage (+1 ≥ Z/HH ≥ −1), as the magnitude X increases the dimensionless temperature  decreases. In the area of stable cooling, i.e., in the interval of −4 ≥ Z/HH ≥ −5, on the contrary, as the magnitude X increases the dimensionless temperature  increases. However, according to a one-dimensional solution (dashed lines in Fig. 3), the temperature at the cooling stage throughout the investigated range X is lower (dashed lines are below the level of the corresponding continuous lines).

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Fig. 3. Grinding temperature in a two-dimensional coordinate system of a moving source (continuous lines) and in a one-dimensional coordinate system of a unmoving equivalent source (dashed lines).

Taking into account that during grinding the most dangerous are high temperatures in the range of −0.5 ≥ Z/HH ≥ −1.5 (the trailing edge of the source), we can conclude that the results of the grinding temperature calculation are closely related, to wit: in the interval of the argument −0.5 ≥ Z/HH ≥ −1.5 the difference in the calculation results does not exceed 4.5–10.6%. It is known that for an overwhelming number of grinding schemes, the change interval for the Peclet number HH is 20 ≥ HH ≥ 4 [21] and even HH ≥ 20 [23]. Moreover, the difference between the one-dimensional and two-dimensional models increases as the value HH approaches the lower value of this interval, i.e. at HH = 4 [21]. Thus, the comparison of two solutions in an unfavorable situation, e.g. at H = HH = 5 is methodologically justified since in the interval of HH ≥ 5 the difference in the calculations will be less than indicated. The trend of contemporary grinding technology is the transition to high [10] and super-high [23] speeds. Consequently, the lawfulness of using a one-dimensional solution increases and the difference in the results of the grinding temperature determination decreases in terms of one- and two-dimensional solutions.

5 Conclusions 1. One-dimensional mathematical model containing two Eqs. (4) and (5), describes the dimensionless grinding temperature at the heating and cooling stages of the surface to be ground, taking into account the forced cooling of this surface at the cooling stage, in accordance with the solution of the one-dimensional differential equation of heat conduction. A distinctive feature of this grinding temperature model is the account of not only the intensity of heat exchange Bi, but also the dimensionless temperature of the cooling medium which in general can be varied in the interval of unlimited dimensionless cooling time.

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2. An equation for determining the temperature of grinding over time and depth of the surface layer at the forced cooling stage is established. It allows determining the effect of the constant and variable temperature of the grinding fluid on the temperature field in grinding. 3. A single mathematical model of the temperature cycle of grinding which contains the stages of heating and cooling under the boundary conditions of the second and third kinds, respectively, was developed. This allowed eliminating the contradiction characteristic of the two-dimensional model of the temperature field when the boundary conditions of the second and third kinds simultaneously operated at the heating stage. 4. The influence of forced cooling on the grinding temperature and its distribution in the depth of the surface layer is investigated. It is confirmed that during the cooling stage, the temperature in the deep layers of the material may exceed the temperature of the above layers, i.e., there is a change in the direction of the heat flux which affects the nature of the structural-and-phase transformations of the material of the surface layer. 5. A more functional mathematical model of the grinding temperature cycle is developed which allows studying the dimensionless temperature field in the heating and cooling stages taking into account the effect of forced cooling surface to be ground. 6. The degree of influence of forced cooling is characterized also by the grinding liquid temperature and the factor β, which is equal to the ratio of Biot (Bi) and Peclet (HH ) numbers. 7. A comparative study of one-dimensional and two-dimensional mathematical models of a dimensionless temperature field with a dimensionless heating time H = HH = 5 has been made; their qualitative and quantitative correspondence is established in the range of the most dangerous temperatures on the trailing edge of the heat source, i.e., at −1.5 ≤ Z/HH ≤ −0.5 and with a steady cooling process, i.e., at −5 ≤ Z/HH ≤ −4. For example, it was found that in the interval of the most significant temperatures, i.e., at −1.5 ≤ Z/HH ≤ −0.5 the difference in the results of calculating the dimensionless temperature by the equations of the one- and twodimensional mathematical models does not exceed 4.5–10.6%. The comparison of the two models is performed in an unfavorable situation, when HH = 5 since it is known that the difference in the results of the calculation of temperature by the equations of the one- and two-dimensional mathematical models, in other equal conditions, increases with decreasing HH in the interval of 5 ≤ HH ≤ 20 and even more so in the interval of 20 < HH . 8. When the heat transfer coefficient is in the interval of 0 ≤ αH ≤ 100 (a vacuum— 0, an air—10, an oil lubricant—100), the effect of the temperature of the cooling medium on the grinding temperature (with the account of only the cooling effect) is not significant and it can be neglected. 9. The developed grinding cycle temperature mathematical model which takes into account forced cooling can be used to optimize the design of macro- and microslotted grinding wheels because entering the forced cooling into the contact zone will significantly (about 38%) reduce the maximum grinding temperature. In addition, there is an opportunity to develop embedded computer subsystems for grinding operation designing, its monitoring and diagnosing for CNC machines.

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References 1. Lavine AS (1988) A simple model for convective cooling during the grinding process. J Eng Ind 110(1):1–6. https://doi.org/10.1115/1.3187837 2. Shen B, Shih AJ, Xiao G (2011) A heat transfer model based on finite difference method for grinding. J Manuf Sci Eng 133(3):031001-1–031001-10. https://doi.org/10.1115/1.4003947 3. Li J, Li JCM (2005) Temperature distribution in workpiece during scratching and grinding. Mater Sci Eng A 409:108–119. https://doi.org/10.1016/j.msea.2005.07.057 4. Biermann D, Schneider M (1997) Modeling and simulation of workpiece temperature in grinding by finite element analysis. Mach Sci Technol 1(2):173–183. https://doi.org/10.1080/ 10940349708945645 5. Westkamper E, Hoffmeister H-W, Weber T (1996) Grinding process simulation with FEM. Prod Eng Res Devel 111(2):45–48 6. Lin B, Morgan MN, Chen XW, Wang YK (2009) Study on the convection heat transfer coefficient of coolant and the maximum temperature in the grinding process. Int J Adv Manuf Technol 42(11–12):1175–1186. https://doi.org/10.1007/s00170-008-1668-1 7. Larshin V, Lishchenko N (2018a) Gear grinding system adapting to higher CNC grinder throughput. MATEC Web Conf 226:04033. https://doi.org/10.1051/matecconf/201 822604033 8. Larshin V, Lishchenko N (2019) Adaptive profile gear grinding boosts productivity of this operation on the CNC machine tools. In: Lecture notes in mechanical engineering. Springer, Cham, pp 79–88. https://doi.org/10.1007/978-3-319-93587-4_9 9. Larshin V, Lishchenko N (2018b) Research methodology for grinding systems. Russ Eng Res 38(9):712–713. https://doi.org/10.3103/S1068798X18090204 10. Lishchenko NV, Larshin VP (2019) Profile gear grinding temperature determination. In: Proceedings of the 4th international conference on industrial engineering ICIE 2018. Lecture notes in mechanical engineering. Springer, Cham, pp 1723–1730. https://doi.org/10.1007/ 978-3-319-95630-5_185 11. Lishchenko NV, Larshin VP (2020) Temperature field analysis in grinding. In: Lecture notes in mechanical engineering. Springer, Cham, pp 199–208. https://doi.org/10.1007/978-3-03022365-6_20 12. Lishchenko NV, Larshin VP (2020) Gear-grinding temperature modeling and simulation. In: Lecture notes in mechanical engineering. Springer, Cham, pp 199–208. https://doi.org/10. 1007/978-3-030-22063-1_32 13. Lavine AS, Jen TC (1991) Thermal aspects of grinding. Heat transfer to workpiece, wheel, and fluid. J Heat Transfer 113(2):296–303. https://doi.org/10.1016/S0007-8506(07)62002-2 14. Lavine AS, Jen TC (1991) Coupled heat transfer to workpiece, wheel, and fluid in grinding, and the occurrence of workpiece burn. Int J Heat Mass Transfer 34(4–5):983–992. https:// doi.org/10.1016/0017-9310(91)90009-4 15. Jen TC, Lavine AS (1995) A variable heat flux model of heat transfer in grinding: model development. J Heat Transf 117(2):473–478. https://doi.org/10.1115/1.2822546 16. Brinksmeier E, Aurich JC, Govekar E, Heinzel C, Hoffmeister H-W, Klocke F, Peters J, Rentsch R, Stephenson DJ, Uhlmann E, Weinert K, Wittmann M (2006) Advances in modeling and simulation of grinding processes. Annals CIRP 55(2):667–696. https://doi.org/10.1016/ j.cirp.2006.10.003 17. Brinksmeier E, Heinzel C, Wittmann M (1999) Friction, cooling and lubrication in grinding. Annals ClRP 48(21):581–598. https://doi.org/10.1016/S0007-8506(07)63236-3 18. Sipaylov VA (1978) Teplovye protsessy pri shlifovanii i upravlenie kachestvompoverkhnosti (Thermal processes during grinding and surface quality control). Mashinostroenie, Moscow

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Theory of Energy Conservation as the Basis for the Design of Wire Drawing L. V. Radionova(B) , R. A. Lisovsky, and V. D. Lezin South Ural State University, 76, Lenin prospekt, Chelyabinsk 454080, Russia [email protected]

Abstract. The article provides a methodology for calculating the energy efficiency of the wire drawing process. It is established that an increase in mechanical properties can lead to a decrease in the unhomogeneity of deformation over the cross section of wire. It has been determined that for the formation of mechanical properties and the retention of the ductility margin of the wire, the drawing sequence must be constructed with the maximum degrees of deformation that are maximum permissible under the condition of continuous drawing, the minimum angle of die, and ensuring a low coefficient of friction. It is important to increase the energy efficiency of the process when constructing resource-saving drawing sequences. The calculation of the power spent on shaping and overcoming the friction forces in the deformation zone showed that the efficiency of the drawing process increases with an increase of an elementary degree of deformation, a decrease in the working angle of the die and the value of the friction coefficient. The analysis of a typical drawing sequence from the point of view of these principles revealed that the resource-saving effect is achieved by using monolithic dies with a working angle of 8°. In this case, the sequence should be consistent with the remaining parameters of the deformation zone (an elementary degree of deformation and a coefficient of friction provided by the quality of preparation of the billet surface and the applied process lubricant). Keywords: Wire drawing · Monolithic die · Drawing die · Degree of deformation · Coefficient of friction

1 Introduction The energy theory of rolling is based on the fundamental laws of energy conservation and minimum energy. It is widely used as a method of scientific research and solving problems of the theory of metal forming [1]. Wire drawing in monolithic die is one of the metals forming types, which at first glance seems very simple and quite easy to implement. However, this is a misconception. It is a rather complicated task to obtain a stable process of wire drawing from various steel grades. The process requires high total deformations and the speeds that modern mills © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_134

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provide today. Many researchers of drawing carry out a large number of experimental and theoretical studies to solve this problem [2–5]. It is necessary to take into account several features of the process for constructing a drawing sequence. At first, the drawing should be continuous. The resistance to rupture of the metal limits the front pulling force carrying out the process of wire plastic deformation. In the practice of wire drawing, it is customary to have a safety factor of 1.4–1.5 [6], which is defined as σtui (1) γi = σdrawi where tensile strength of the wire, MPa; σtui σdrawi drawing stress, MPa. Finished wire must meet the requirements of All Union State standard or specification in terms of geometric parameters and mechanical characteristics. Obtaining the required mechanical properties of the wire is directly related to the diameter of the finished wire. Metal hardening is connected with the total deformation ratio. However, different grades of steel and alloys harden differently, moreover, even with the same total degree of deformation; the mechanical properties depend on the type of drawing sequence. They can be uniform, decreasing or increasing. Recently, there have appeared works in which it is recommended to construct a drawing sequence based on the principle of reducing the unhomogeneity of deformation along the wire cross section during drawing [7–9]. As the research results [10] show, the wire obtained along such sequences has an increased ductility resource and can be deformed with large total reductions. Thereby it is providing an increased tensile limit while maintaining its plastic properties. Wire with enhanced mechanical properties is more competitive in the hardware market. However, in addition to a high level of mechanical properties, an equally important indicator of competitiveness is its cost price, which is the sum of the cost of the billet and the costs of its shaping process, i.e., drawing. Therefore, it is necessary to be guided not only by obtaining the required geometric dimensions and a complex of mechanical properties, but also by the costs that allowed them to be provided when constructing resource-saving drawing routes. Therefore, it is necessary to be guided not only by obtaining the required geometric dimensions and a complex of mechanical properties, but also by the costs that allowed them to be provided when constructing resource-saving drawing sequences. Costs consist primarily of electricity consumption for the drawing process, and secondly-of tool consumption, process lubrication, intermediate heat treatments to restore ductility, etc. At present, to analyze the energy-power parameters of the drawing process, two fundamentally different calculation methods are used [11]. The first is based on compliance with the plasticity of the billet under the balance of forces in the deformation zone [12]. The second is based on the balance of power of external and internal forces on the process of plastic deformation of a metal [1, 13, 14].

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The aim of the work is to develop a method for calculating resource-saving wire drawing sequences based on the energy theory of the power balance, of external and internal forces spent on the plastic deformation process. That provides a high level of mechanical properties of the finished wire.

2 Energy Theory of the Drawing Process The power of electrical energy Peng is converted by an electric motor into mechanical energy Neng and supplied to the drum of a drawing mill by a gearbox. This energy is spent on overcoming the following forces (Fig. 1). • The force that carries out the main plastic deformation—the shape changes of the wire; • The force spent to overcome the friction between the wire and the surface of the working part of the die; • The force that overcomes the counter-tension of the wire.

Fig. 1. Energy diagram.

Pel , Peng , Pmech , Pad electric, magnetic, mechanical, and other (additional) losses in the drive electric motor; mechanical losses in the kinematic line of the drawing sequence; nmech power supplied to the deformation zone; Ndz contact friction power; Nfr elastic force; Nel.f. power of additional plastic deformation force; Na.p.d. power force to overcome the counter-tension; NQ power spent on change of shape. Nel.f.

Theory of Energy Conservation as the Basis

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The power balance of the drawing process can be determined on the principle of energy conservation and written in the equation N − NQ = Nsh + Nel.f. + Nfr + Na.d. + Nothers

(2)

where N NQ Nsh Nel.f. Nfr Na.d. Nothers

power supplied to the deformation zone by a pulling force T through the head end of the wire; power supplied to the deformation zone by countertension Q through the bottom end of the wire; the power spent on shaping (drawing) the metal; power spent on elastic deformation of the wire in the drawing die; power of sliding frictional forces on the contact surface of the metal being machined with the draw die (both conical and calibrating parts); the power spent on the creation of additional deformations (shifts) due to the shape of the drawing die channel; other types of powers (to change the kinetic energy of the processed wire, etc.).

The power of additional deformations and other types of power are neglected due to their insignificant value in further discussions. The power supplied to the deformation zone by pulling force and back-pull can be defined as. NT = T · V exit ; NQ = Q · V entr = Q ·

V exit μ

(3)

where entr

μ = SS exit S entr , S exit T Q V entr , V exit

elongation ratio; the cross section of the treated metal at the deformation zone entrance and at the exit from it, mm2 ; front pulling force, N; back-pull force, N; the speed of the wire at the entrance to the deformation zone and exit from it, m/s.

The power Ns carrying out the main plastic deformation is called the power of pure deformation and can be determined from the Fink formula [15], written for the work of pure deformation Ash = σs · θd.v. where σs

flow limit of wrought metal, MPa;

(4)

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θd.v. the amount of displaced volume, defined as

din2

θd.v. = θ · ln

(5)

df2

where ln

2 din df2

din , df θ

integral degree of reduction measure; wire diameter before and after the draw die, respectively, mm; the volume of metal machined over time t, m3;

θ=

π · df2 4

· Lw =

π · df2 4

· Vdexit · t

(6)

Lw —length of wire machined over time t, m. Substituting (5) and (6), into (4), taking into account that Ash = Nsh · t, power of forming is defined as Nsh = σs ·

π · df2 4

· Vdexit · ln

din2 df2

(7)

Similarly, the power spent on elastic deformation in the die can be found from the equation  σ  dθ σ dAel.d. el el = σel · ln = σel · ln + 1 · S entr · V entr (8) +1 · Nel.d. = dt dt E Power Nfr spent on overcoming the friction forces on the contact surface in the deformation zone can be found by summing the values of the elementary powers  NfrI , allocated on the elementary sections of the contact surface of the working part of the drawing die and the power spent on overcoming the friction forces on the contact surface of the finishing part Nfr.f.  Nfr =  NfrI + Nfr.f. (9) I

The surface of the working part of the die with a conical profile (Fig. 2), must be divided into elementary cylinders, each of which will have a radius r1 , width l1 and area S1 . The basis for calculating the friction force is the Coulomb—Amonton law for calculating the specific friction force τ τ = f · σn where

(10)

Theory of Energy Conservation as the Basis

f σn

1155

coefficient of friction on the contact surface (assumed constant over the entire length of the deformation zone); normal stress, MPa.

Fig. 2. To the calculation of the power spent on overcoming friction.

The change in the friction force that occurs in the elementary section can be defined as  FfrI = τ · S = f · σn · 2 · π · rI ·  lI

(11)

Then the power of this force can be found from the equation  NfrI = FfrI · VI

(12)

where VI —wire speed on the die surface in I section, whose projection on the axis of movement of the wire (Fig. 2), is determined by the trigonometric relation. vI = VI · cos α

(13)

where α—half-angle of drawing die. This speed can be determined from the equations written for drawing the wire from the beginning of the deformation zone to this section. μI =

d2 vIx = in2 entr Vd dI

(14)

as vI =

din2 dI2

· Vdentr

(15)

Then, in a consideration of (13) and (15), the speed of the wire along the drawing die surface is defined as VI =

din2 · Vdentr dI2 · cos α

(16)

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or taking into account that (Fig. 2) dI = din − 2 · sin α ·  lI

(17)

din2 · Vdentr VI =  2 din − 2 · sin α ·  lI · cos α

(18)

as

here  lI —die surface length from start up to I sections including.  lI =

I 

 lJ

(19)

J =1

Substituting (11), (18), and (19) into (12), after simple transformations, we obtain df2 · Vdexit  NfrI = π · f · σs ·  lI ·   I  din − 2 · sin α ·  lJ · cos α

(20)

J =1

The power of the friction forces in the finishing part of the die can be determined as Nfr.f. = Ffr.f. · Vdexit = τ · Sf · Vdexit = f · σs · π · df · lf · Vdexit

(21)

whereNfr —length of finishing part of the die. The power spent on overcoming the friction forces can be determined by the equation ⎡ ⎤ ⎢ d ⎥   lI ⎢ f ⎥ + ·lf ⎥ Nfr = π · f · σs · df · Vdexit · ⎢ ·   I ⎣ cos α ⎦  I din − 2 · sin α ·  lJ

(22)

J =1

The efficiency for the drawing process can be defined as. sh Efficiency = NfrN+N · 100%. sh

3 Configuration Drawing Sequences Providing High Mechanical Properties of the Wire The drawing sequence should be constructed from the condition for increasing the mechanical properties of the wire by reducing the uneven deformation along the cross section of the wire [16]   1 − arctg(tgα + f ) 2 (23) ε =1− 1 + arctg(tgα + f )

Theory of Energy Conservation as the Basis

where ε =

2 din —degree dI2

1157

of deformation.

Compression should be selected from the following conditions to obtain compressive stresses in the surface layer  ε 1−

1 − arctg(tgα + f ) 1 + arctg(tgα + f )

2 (25)

The graphs (Fig. 3), constructed according to relation (23), can be used for preliminary selection of the unit strain with possible changes in the die angle and the value of the friction coefficient.

Fig. 3. Values of an elementary degree of deformation providing uniform deformation over the cross section of the wire, depending on friction coefficient f and half-angel of drawing die α.

As follows from Fig. 3, in order to obtain a uniform cross section of the wire, single reductions should be quite high, of the order of 35–45%. It is convenient to use graphs similar to those shown in Fig. 4, to select the required value of a reduction per die, providing a certain nature of the residual stresses in the wire according to the relations (23) and (25).

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Fig. 4. The nature of the residual stresses in the surface layer depending on the technological parameters

The presence of tensile stresses in the surface layer of the wire is the cause of alligatoring and cracking [17, 18]. Studies [10] were carried out to experimentally confirm the possibility of improving the mechanical properties and quality of the wire due to the formation of the type of residual stresses during the drawing process. During those studies a billet with a diameter of 5.5 mm (steel grade 70, σrs = 1150 MPa) was stretched under laboratory conditions on a single drawing mill with the same compression under the condition of the formation of “tensile”, “close to zero”, and “compressive” stresses in the surface layer of the wire (Table 1). Table 1. The formation of the type of residual stress depending on the parameters of the deformation zone during drawing Sample Number

Wire diameter before drawing din , mm

Wire diameter after drawing df , mm

Elementary degree of deformation ε, %

Angle of die 2α,◦

Type of residual axial stresses on the wire surface

1

5,50

4,50

33

10

Stretching

2

5,50

4,50

33

8

Close to zero

3

5,50

4,50

33

6

Compressive

The experiment was supplemented by wire drawing to a diameter of 3.00 mm along the sequences. 33%

33%

33%

33%

33%

33%

33%

33%

33%

Sample 1—5,50 −→ 4,50 −→ 3,70 −→ 3,00 (2α = 10◦ ); Sample 2—5,50 −→ 4,50 −→ 3,70 −→ 3,00 (2α = 10◦ ); Sample 3—5,50 −→ 4,50 −→ 3,70 −→ 3,00 (2α = 10◦ ).

Theory of Energy Conservation as the Basis

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The laboratory experimental wire with a diameter of 3.00 mm was tested for breaking, torsion and bending. The results of mechanical tests are presented in Table 2. Table 2. Mechanical properties of steel wire grade 70 with a 3.00 mm diameter Sample Number

Tensile strength σtu , MPa

Flow limit σ0.2 , MPa

Percentage Relative of reduction, elongation, δ ψ % %

Number of torsions, m

Number of bends, n

1

1640

1425

2.5

56

40

18

2

1635

1390

3.0

60

43

20

3

1645

1435

3.5

64

48

26

The level of crack resistance of a material cannot be estimated only by the values of anyone characteristic—strength or ductility (σtu , σ0.2 , δ,ψ) [19]. It is determined by the value of the specific strain energy, for the calculation of which all of the above parameters are necessary simultaneously. Wire obtained in sequence 5.5 33%

33%

33%

−→ 4.5 −→ 3.7 −→ 3.0 (2α = 6◦ ), (sample No. 3), in the presence of compressive stresses in the surface layer, has increased crack resistance (Table 3), as the calculation results are shown in following work [20]. Table 3. Values of criteria for the initiation Kcn and propagation of cracks Kcp Sample Number

The nucleation criterion Kcn

The propagation criterion Kcp

1

0.8947

0.6710

2

1.0132

0.7599

3

1.1169

0.8377

The crack nucleation criterion quantitatively determines the ability of a material to resist cracking during deformation (the higher Kcn , the higher the crack resistance of the material). The crack propagation criterion quantitatively determines the ability of a material to resist the free movement of cracks upon deformation under conditions of reaching a critical stress state (the higher Kcp , the less crack propagation in the material). The drawing sequence must be constructed with the maximum degree of deformation allowed by condition (1), the minimum drag angle, and while ensuring a low coefficient of friction, as a result for the formation of mechanical properties and preservation of the ductility margin of the wire. However, the question arises: how will such technological parameters affect the energy efficiency of the drawing process.

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4 Principles of Building Resource-Saving Wire Drawing Sequences The calculation of the power spent on shaping (7) and overcoming the friction forces in the deformation zone (22) showed (Tables 4, 5 and 6), that the efficiency of the drawing process increases with an increase in the elementary degree of deformation, a decrease of drawing angle and the value of the friction coefficient. Table 4. The results of calculating the efficiency of the wire drawing process depending on the value of a elementary degree of deformation No Billet Wire Elementary Half-angle Coefficient diameter diameter degree of of die α, ° of friction, d0 , mm d1 , mm deformation f ε, %

Power to overcome friction Nfr , Watt

Forming Efficiency Nsh power Nfr +Nsh , Nsh , % Watt

1

5.5

5.07

15

4

0.03

10,866

9204

45.9

2

5.5

4.92

20

4

0.03

10,271

11,864

53.6

3

5.5

4.76

25

4

0.03

9655

14,400

59.9

4

5.5

4.60

30

4

0.03

9057

16,630

64.7

5

5.5

4.43

35

4

0.03

8443

18,674

68.9

Table 5 The results of calculating the efficiency of the wire drawing process, depending on the size of the drawing die half-angle No Billet Wire Elementary Half-angle Coefficient diameter diameter degree of of die α, ° of friction, d0 , mm d1 , mm deformation f ε, %

Power to overcome friction Nfr , Watt

Forming Efficiency Nsh power Nfr +Nsh , Nsh , % Watt

1

5.5

4.79

24

3

0.03

9545

13,948

2

5.5

4.79

24

4

0.03

9769

13,948

58.8

3

5.5

4.79

24

5

0.03

10,010

13,948

58.2

4

5.5

4.79

24

6

0.03

10,273

13,948

57.6

5

5.5

4.79

24

7

0.03

10,559

13,948

56.9

59.4

The efficiency of the drawing process increases with an increase of the elementary degree of deformation, if the parameters of the deformation zone are selected according to relation (23), and at a constant value of the friction coefficient for all considered cases. However, it was found that the friction coefficient substantially depends on the drawing die angle in [21]. The experimentally obtained data show [22], that only with a change in the drawing die angle the friction coefficient can change from 0.05 to 0.03. The maximum efficiency of the process is observed at a die angle of 8° and a single degree of deformation of 33%, taking into account the change in the friction coefficient depending on the working angle of the die (Table 7). This is due to the fact that the friction coefficient decreases with a decreasing drawing angle. Such a dependence was

Theory of Energy Conservation as the Basis

1161

Table 6 The results of calculating the efficiency of the wire drawing process, depending on the value of the friction coefficient No Billet Wire Elementary Half-angle Coefficient diameter diameter degree of of die α, ° of friction, d0 , mm d1 , mm deformation f ε, %

Power to overcome friction Nfr , Watt

Forming Efficiency Nsh power Nfr +Nsh , Nsh , % Watt

1

5.5

4.76

25

4

0,03

9655

14,400

59.9

2

5.5

4.76

25

4

0,04

12,873

14,400

52.8

3

5.5

4.76

25

4

0,05

16,091

14,400

47.2

4

5.5

4.76

25

4

0,06

19,309

14,400

42.7

recorded by us earlier [10], in experimental studies, similar data were obtained by foreign scientists [23]. Table 7 The results of the efficiency of the wire drawing process taking into account the coefficient of friction № Billet Wire Elementary Half-angle Coefficient diameter diameter degree of of die α, ° of friction, d0 , mm d1 , mm deformation f ε, %

Power to overcome friction Nfr , Watt

Forming Efficiency Nsh power Nfr +Nsh , Nsh , % Watt

1

5.5

4.7

28

3

0.03

9213

15,272

2

5.5

4.5

33

4

0.03

8694

17,873

67.3

3

5.5

4.4

37

5

0.04

11,388

19,001

62.5

4

5.5

4.2

42

6

0.05

13,391

20,922

60.1

62.4

5 Conclusion Calculation formulas for determining the power spent on the drawing process in a monolithic drawing die are obtained. Those equations based on the development of the energy method for solving technological problems of metal forming. That fact that it is necessary to be guided by two principles when designing resourcesaving wire drawing sequences is described in this article. The first is to obtain a highquality wire. It can be achieved by reducing the unevenness of deformation along the cross section of the wire and the formation of compressive stresses on the surface of the wire. This can be obtained by coordinating an elementary degree of deformation, the drawing angle of the die and the coefficient of friction. The second is the reduction in the power consumed for drawing and increasing the efficiency of the process, due to the choice of energy-saving technological parameters of the drawing process. It is obvious that the efficiency of the drawing process increases with an increase in the elementary degree of deformation.

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The analysis of a typical drawing sequence from the point of view of these principles showed that the resource-saving effect is achieved by using monolithic dies with a drawing angle of 8°. The sequence should be consistent with the other parameters of the deformation zone (a single degree of deformation and the coefficient of friction provided by the quality of preparation of the surface of the billet and the applied process lubricant).

References 1. Vydrin VN (1960) Dynamics of rolling mills. Metallurgizdat, Sverdlovsk 2. Kharitonov VA, Zyuzin VI, Belan AK (2003) Resource saving in wire production. NMSTU, Magnitogorsk 3. Krasilnikov LA, Lysenko AG (1987) Wire drawer: teaching medium. Metallurgy, Moscow 4. Perlin IL, Yermanok MZ (1971) Drawing theory, 2nd edn. Metallurgy, Moscow 5. Kulesha VA, Klekovkina NA, Belalov HN et al (1999) High quality wire production: multiauthored monograph. Beloretsk 6. Rudskoy AI, Lunev VA, Shaboldo OP (2011) Drawing: teaching medium, Publishing House of Polytechnic University 7. Radionova LV, Ivanov VA, Shatalov VS (2014) Investigation of the monolithic drawing die working angle influence on the stress-strain state of the wire in the deformation zone. Eng Online Electron Sci J 61:21–25 8. Guryanov GN (2010) The calculating method the of the drawing die working cone optimal angle for drawing a round solid profile. Metall Min Ind 58–60 9. Lin J, Liu Y, Farrugia D et al (2005) Development of dislocation based-unified material model for simulating microstructure evolution in multipass hot rolling. Phil Mag 4523:1967–1987 10. Kharitonov VA, Radionova LV (2008) Designing resource-saving technologies for the production of high-strength carbon wire based on modeling: a monograph. NMSTU, Magnitogorsk 11. Kolmogorov VL (1986) Mechanics of metal forming. Metallurgy, Moscow 12. Rubio EM, Camacho AM, Sevilla L, Sebastián MA (2005) Calculation of the forward tension in drawing processes. J Mater Process Technol A 784:551–557 13. Dobrov IV (2016) Development of an energy method for the power parameters of a strip drawing process calculating in a monolithic drawing die. Univ Proc Nonferrous Metall 82:58– 66 14. Radionov AA, Radionova LV (2008) Energy approach to the study of the counter-tension effect on the process of drawing. Izvestiya. Ferrous Metall 9–22 15. Gun GYa, (1980) Theoretical foundations of metal forming (plasticity theory). Metallurgy, Moscow 16. Radionova LV (2014) Analytical studies of the technological parameters influence on the strain rate during high-speed wire drawing. Eng Online Electron Sci J 81:28–33 17. Zaydes SA (1992) Residual stresses and quality of calibrated metal. Publishing House of Irkutsk University, Irkutsk 18. YaD V, Piskarev VD (1989) Residual stress control in metals and alloys. Metallurgy, Moscow 19. Baron AA, Gavlich DS, Bahracheva YS (2003) Specific energy of plastic deformation as a measure of structural materials crack resistance. Metals 85–90 20. Kharitonov VA, Zyuzin VI, Radionova LV, Rol’shchikov LD (2002) Method for the production of high-strength carbon steel wire with increased plastic properties. In: Interuniversity collection of scientific treatises—NMSTU, Magnitogorsk, pp 41–45 21. Radionova LV, Kharitonov VA, Zyuzin VI, Rol’shchikov LD (2001) New technological lubricants for steel wire drawing. Steel Trans 49–50

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22. Kharitonov VA, Zyuzin VI, Radionova LV, Rol’shchikov LD (2001) New technological lubricants and power parameters for drawing steel wire. Ferrous Metall 38–39 23. Muskalski Z, Wiewiórowska S (2011) The theoretical analysis of wire drawing process or hydrodynamic friction conditions. Metall Min Ind 74–78

Accuracy Assessment of Setting Pressure Change Speed in Aircraft Control Systems of Air-Speed Flight Parameters A. Markov(B) Baltic State Technical University “VOENMEH” Named After. D.F. Ustinov, b. 1, 1st Krasnoarmeyskaya str, St. Petersburg 190005, Russia [email protected]

Abstract. The purpose of this article is to develop an algorithm for setting the speed of air pressure change used in control systems of air-speed flight parameters (CSASFP) of aircrafts, and to assess setting speed accuracy. Research methods include theories of automatic control and system modeling, as well as the basic laws and provisions of gas dynamics. Results of studies of the processes of airflow with constant pressure drops through the throttling sections of CSASFP were used to develop a mathematical model of a pressure regulator that implements an algorithm for setting the pressure change speed, the main parameters of gasdynamic processes occurring in a closed volume in which the pressure change speed is set are established. Dependencies are established to assess the accuracy of setting air pressure change speed. Experimental studies of the process of setting the air pressure change speed in a closed volume were carried out, which confirmed the accuracy of the proposed algorithm. The algorithm for setting air pressure change speed in a closed volume is calculated and can be used to solve problems of designing CSASFP in which modern control methods can be implemented. Keywords: Pressure measurement · Absolute pressure · Pressure setting · Automated control · Pressure change · Pressure control

1 Introduction Development of aircrafts for various purposes determines the change in the requirements for metrological assurance of devices for monitoring air-speed flight parameters, namely, systems for monitoring air-speed flight parameters (CSASFP) [1–6]. CSASFP are created on the basis of systems for automatic absolute air pressure setting, containing a control unit (CU) that implements control functions of the pneumatic part, an absolute air pressure sensor (AAPS), pneumatic throttles (PT), pneumatic regulators of constant pressure differential (PRCPD), high pressure sources (HPS) and low pressure sources (LPS), and receiver (R) where air pressure is set (Fig. 1). When conducting quality control of aviation devices, in particular, vertical speed meters, it is required to set the speed © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_135

Accuracy Assessment of Setting Pressure Change Speed

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of pressure change. Therefore, modern CSASFP should contain algorithms that provide setting not only specific values of air pressure (stabilization mode), but also the speed of change [7, 8].

Fig. 1. SCASFP structure.

2 Development of an Algorithm for Setting Air Pressure Change Speed and Setting Speed Accuracy Assessment In a pneumatic system, it is quite difficult to ensure a pressure change according to any arbitrary law that would be maintained with high accuracy [9, 10]. The reason for this lies in the compressibility of the air. By regulating the speed of pressure change, we mean a change close to uniform. Experience shows that, despite a number of difficulties, with the right choice of controller parameters and speed control tools, the uniformity and smoothness of the increase (decrease) in pressure will be sufficient for the control work. In addition, it is quite often possible not to take into account the nature of the change in speed (within specified accuracy), but it is only important to maintain the specified control time, i.e., average speed. “Equation 1” describing proportional-integral-differentiating (PID) regulator has the form u(k) = u(k − 1) + q0 e(k) + q1 e(k − 1) + q2 e(k − 2)

(1)

where e(k) = ps.cur. (k) − pcur. (k), e(k − 1) = ps.cur. (k1) − pcur. (k − 1), e(k − 2) = ps.cur. (k − 2) − pcur. (k − 2), ps.cur. —set current pressure value, pcur. —current pressure value, u(k)—control signal. Setting the speed of pressure change ps.cur. is carried out by calculating the pressure trajectory in time ps.cur. (t) according to “Eq. 2” ps.cur. (k) = pcur. (k − 1) + ps.cur. T0 where T 0 is the step of discrete setting of the speed of pressure change.

(2)

1166

A. Markov

In case of a computation time limit, it is possible to decrease the frequency of determining the setting signal due to missing (advancing) a certain number of quantization steps (1 k, 2 k, 3 k, etc.), but in this case, the smoothness of the curve pcur. (t) may change due to changes in the increment step of the setting signal. In accordance with the above, an algorithm has been developed for discrete speed of pressure change setting (Fig. 2).

Fig. 2. The algorithm for discrete setting the speed of pressure change.

In the general case, the resulting error of the discrete speed setting is formed from methodical error; interpolation error; error caused by random noise; instrumental errors. By methodical error, we understand the error of the setting method—the difference between the average value of the speed at the interval of discreteness and the instant value of it at the moment (at the polling point).

Accuracy Assessment of Setting Pressure Change Speed

1167

By interpolation error, at discrete speed setting, we understand the methodical error between polling points (nodes). Both of these errors occur due to setting discreteness and can be combined under the common name of discreteness errors. Real automated systems of pressure setting in the mode of stabilization of pressure change speed operate under conditions when their input receives interference together with useful signal (as a rule, additive and multiplicative interference have the greatest impact). Electrical shielding must be used to reduce interference effects. Instrumental errors are caused by imperfections of technical means and individual links and elements of the CSASFP. They can be both systematic and random. Discreteness errors are of the most theoretical and practical interest. They mainly cause the selection of adjustment parameters, in particular the interval of discreteness, during device designing. “Equation 3”, describes methodical error δ m of discrete speed setting at the moment of time t i δM (ti ) =

pcur. (ti ) − pcur. (ti−1 )  − ps.cur. (ti ) t

(3)

which occurs due to the deviation of the average speed from the true value. In two essentially various cases of δ m it can be equal to zero or it is close to it: in the first case when speed is constant, i.e., p cur. (t) = 0, then δ m = 0 at all t values, and in the second case, when speed is changeable, i.e., p cur. (t) = 0, then δ m → 0 only at t → 0. To estimate the methodical error, it can be assumed that all other errors are absent. We consider pcur .(t) a smooth function of time, which at any point is spread into a Taylor row. Calculated average speed value is shown in “Eq. 4” pcur. (ti ) − pcur. (ti − t) pcur. (ti ) = t t

(4)

It is possible to consider an approximate value or to refer conditionally to such value of instantaneous speed at time points of t t i and t i − t. 1. At the moment t i methodical error is calculated using “Eq. 5” δM (ti ) =

pcur. (ti )  − ps.cur. (ti ) t

(5)

We spread out pcur .(t i − t) in the neighborhood of t i point into Taylor’s row. We limit ourselves to three members of the row and we get “Eq. 6” pcur. (ti − t) = pcur. (ti ) −

t  t  pcur. (ti ) + p (ν) 1! 2! cur.

(6)

where ν is a point between t i−1 and t i . Then we get “Eq. 7” pcur. (ti ) − pcur. (ti − t) t   − pcur. (ti ) = − pcur. (ν) t 2

(7)

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and therefore, “Eq. 8”      t    t |δM (ti )| = − pcur. (ν) ≤ maxpcur. (t) 2 2

(8)

2. It is similarly possible to estimate a methodical error at the time point of t i − t, i.e., at the beginning of a discretization interval in “Eq. 9”

   t |δM (ti − t)| ≤ maxpcur. (t) 2   ti−1 , ti

(9)

Thus, the estimates of the methodical errors of the discrete speed setting at the end and at the beginning of the discreteness interval are the same. Now we estimate the interpolation errors. Interpolation error occurs at discrete methods of setting the pressure change speed and is calculated using “Eq. 10”    |δint (t)| ≤ maxpcur. (t)t   ti−1 , ti (10) where t i−1 < t < t i . Considering the above, let us focus on the fundamental question—how to understand the set speed value? Different approaches are possible here. For example, a set speed value is its approximate value at some fixed point within a discreteness cycle at the end or in the middle. The selection of a fixed point depends on how the set speed values will be used in the future. In automatic control systems, it is permissible to assign the speed value to one of the extreme points. Experimental studies of pressure reproduction process were conducted on an experimental stand. Parameters q0 , q1 and q2 were calculated using parametric adjustment algorithms, which allowed obtaining regulator parameters close to optimal ones, which were corrected during accurate adjustment of CSASFP. The purpose of the experimental studies was to prove the appropriateness of using a parametrically optimized second-order control algorithm for a digital automatic pressure regulator with the required characteristics of the transient process of controlled pressure (in particular, the speed of air pressure change). As a result of the experimental studies, the real characteristics of the transient were taken from the frequency pressure sensor, some of which are shown in Figs. 3, 4, 5 and 6. The pressure values are given in periods of the frequency pressure sensor (ms), pressure numbers in (kPa) from the sensor calibration table are shown next for comparison.

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Fig. 3. Transient process oscillogram when the receiver is emptied at a constant speed (p = − 6 kPa/s).

Fig. 4. Transient process oscillogram of the area A.

The oscillogram (Fig. 3), shows a graph of the transient process of speed of pressure change during emptying of the receiver (the graph of the transient process during filling is not shown, since the nature of the transient process is identical), which allows to conclude that the pressure in the receiver changes with the set speed. On the oscillograms, characteristic areas A, B, and C. are highlighted. Area A (Fig. 4), shows the process of changing the pressure speed in the receiver. The instant value of the speed of pressure change is pulsating in nature, however, uniformity and smoothness of the increase (decrease) in pressure is ensured, that is, the average speed is maintained fairly

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Fig. 5. Transient process oscillogram of the area B.

Fig. 6. Transient process oscillogram of the area C.

accurately. Area B (Fig. 5), illustrates the process of transition of the control system from the speed setting mode to the stabilization mode. The transient process shown in Fig. 5, proves that the system has a sufficient margin of stability. Area C (Fig. 6), reflects the nature of the pressure stabilization process. The control system fulfills small random disturbances, this explains the outliers shown on the waveform.

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3 Conclusion The data of experimental studies allows judging the correct use of a parametrically optimized second-order pressure regulator when implementing the algorithm for discrete setting the speed of air pressure change for CSASFP. The algorithm for setting air pressure change speed in a closed volume is calculated and can be used to solve problems of designing CSASFP in which modern control methods can be implemented.

References 1. Markov AV (2014) Problems and ways of absolute pressure sensors quality control systems modernization. Age Qual 4:30–32 2. Markov AV (2015) Concept of measuring instruments of absolute pressure sensors quality control systems. Age Qual 1:34–35 3. Markov AV (2018a) Mathematical model of automated deadweight absolute pressure control system. Vestnik IrGTU 22(11):112–125 4. Pushkov SG, Lovitsky LL, Korsun ON (2018) Aero-dynamic errors of the aircraft static pressure measurement systems in sliding modes. Meas Tech 2:37–42 5. Pushkov SG, Gorshkova OYu, Korsun ON (2013) Mathematic models of in-flight measurements of speed and angle of attack in aircraft landing modes. Mech Autom Control 18:66–70 6. Korsun ON, Nikolaev SV, Pushkov SG (2016) Algorithm for estimating systematic errors in airspeed measurements, angles of attack and slip in flight tests. In: Proceedings of the Russian Academy of Sciences. The theory of control systems, vol 3, pp 118–12 7. Markov AV (2018) The concept of precision automated control systems for pressure sensors as a means of metrological support of aircrafts. In: Questions of defense technology. Series 16: Technical means of countering terrorism 9–10(123–124), pp 150–154 8. Markov AV (2018b) The concept of precision automated deadweight piston quality control systems for pressure sensors quality. Innov Educ 4:89–93 9. Mirskaya VA, Nazarevich DA, Ibavov NV (2017) Method of pressure measurement on an experimental installation for studying the complex of thermophysical properties of liquids and gases. Meas Tech 9:33–36 10. Mirskaya VA, Ibavov NV, Nazarevich DA (2016) Automated experimental installation for investigating the complex of thermophysical properties of liquids and gases. Thermophys Temp 54(2):237–242

Hydrodynamics of Flow in a Flat Slot with Boundary Change of Viscosity V. Sokolov(B) Volodymyr Dahl East Ukrainian National University, 59-a, Central Pr., Severodonetsk 93400, Ukraine [email protected]

Abstract. The laminar flow of viscous incompressible fluid in a flat slot is considered with allowance for the boundary change of viscosity near a solid surface. The model of the stepwise distribution of the dynamic viscosity over the cross section of the channel with its abrupt increase near the slot walls was adopted. In the general case, the different viscosity jumps near the solid surface are introduced into consideration. Also, the dimensions of the boundary layers, where the change of viscosity appears, are considered different. For the accepted dynamic viscosity distribution, integration of the equation for laminar fluid motion was performed. The dependences for calculating the velocity profile in a flat slot are obtained. The researches on the effect of viscosity jump on flow velocity have been conducted. The examples of calculating the velocity distribution along the height of a flat slot are presented. The flows with symmetric and asymmetrical distribution of dynamic viscosity are considered. Based on the obtained velocity distribution, dependences for calculating the flow rate in the flat slot were established. The researches of the influence on the flow rate in a slot of the parameters for the distribution of dynamic viscosity along the cross section of the channel have been conducted. The received result analysis showed that the boundary increase of the dynamic viscosity unambiguously leads to the drop of the throughflow capacity for the flow section. The boundaries of applicability of the traditional approach to calculating the laminar flow of viscous fluid in a flat slot are estimated. Keywords: Laminar flow · Flat slot · Dynamic viscosity · Flow velocity · Flow rate · Equation of motion

1 Introduction The fluid flow in a flat slot is of practical importance in connection with solving problems of sealing hydraulic devices and apparatuses [1–5]. This is due to the fact that the tightness of the connection of movable pairs of hydraulic devices and apparatuses is very often ensured by the providing of a guaranteed micron gap [6–10]. The traditional approach to calculating the flow in a flat slot assumes the constancy of the fluid dynamic viscosity over the cross section [11–15]. However, based on theoretical © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_136

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positions and experimental data of a number of authors [16, 17], near the solid-state boundary (up to several thousand angstroms, 1 Å = 10–4 µm = 10–10 m), the viscosity of mineral oils increases abruptly. Although the dimensions of the layers, where the viscosity deviates, are noticeably smaller than the magnitudes of the gaps (the sizes of the slots in the hydraulic apparatuses are of the order of 10–15 µm), there is undoubted interest in estimating the hydromechanical parameters of the flow, taking into account the noted effect.

2 Literature Review The fluid stream in the gaps of hydraulic devices and apparatuses for common operating conditions of hydraulic systems is laminar in nature and the flow is calculated based on known dependencies for flat, concentric and eccentric slots [11, 12, 18–21]. These dependences do not take into account the magnitude of the jump for the dynamic viscosity and the size of the layer, where its increase appears. The magnitude of the jump is influenced by the type of liquid, the material of the solid wall, temperature, etc. The researches of the properties for the boundary layers of liquids shows that these are layers where the liquid is in a particular phase state, characterized by a high degree of ordering of the molecules [16, 17]. One of the simplest consistent theories, which take into account the effects of near-wall flows, comes from a continuum model with internal rotation of non-point structural elements [22–24]. Despite the fact that the qualitative estimates for the boundary increase of viscosity near the solid surface are fairly well represented in the literature, there are no quantitative characteristics for estimating the hydromechanical parameters of the flow in a flat slot. The purpose of this paper is to research the hydrodynamics of the laminar flow for a viscous incompressible fluid in a flat slot with allowance for the boundary change for viscosity near a solid surface, to obtain dependencies for calculating the distribution of velocity and flow rate, and to analyze the change of throughflow capacity for the flow section.

3 Research of Flow in a Flat Slot with Boundary Change of Viscosity Consider the stationary flow in a flat slot formed by two parallel walls of unlimited width. Choosing the x-axis along the flow, the y-axis being perpendicular to the walls of the slot (Fig. 1), we write the equation of motion for incompressible fluid with the variable dynamic viscosity [11, 12].   ∂ ∂ux ∂p = μ (1) ∂x ∂y ∂y

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Fig. 1. The flow scheme in flat slot.

 where ux —velocity of the fluid flow; dp dx—pressure gradient; μ—dynamic viscosity. We assume that the walls forming the slot are made, in general, of different materials. This implies introducing into consideration various magnitudes of the viscosity jumps near the solid surface, as well as different sizes of the boundary layers where the change of viscosity appears. Therefore, the assignment of the next distribution for the dynamic viscosity over the slot height is not contradictorily consistent (Fig. 2a). ⎧ ⎨ μ0 + μ1 , y < δ1 ; (2) μ = μ0 , δ1 ≤ y ≤ δ − δ2 ; ⎩ μ0 + μ2 , y > δ − δ2 ;

Fig. 2. a The dimension distribution of the dynamic viscosity along the slot height; b the dimensionless distribution.

where δ—slot size; δ 1 , δ 2 —dimensions of the boundary layers at each of the slot walls, near which there is an increase of viscosity; μ0— dynamic viscosity in the main fluid flow outside the boundary layers; μ1 , μ2 —magnitude of the boundary viscosity jumps. To simplify the further mathematical transformations, we introduce the next dimensionless variables: dimensionless coordinates    (3) y = y δ; δ 1 = δ1 δ; δ 2 = δ2 δ; dimensionless viscosity and its jumps    μ = μ μ0 ; μ1 = μ1 μ0 ; μ2 = μ2 μ0 ;

(4)

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dimensionless velocity  pδ 2 δ 2 ∂p = ; u = ux V0 ; V0 = − 12μ0 ∂x 12μ0 l

(5)

where V 0 —average velocity in the traditional calculation of the flow in a flat slot; p—pressure differences across a slot; l—slot length [11, 12, 25–27]. Taking into account (3–5), Eq. (1) and distribution (2) take the next dimensionless form   ∂ux ∂ = −12; (6) μ ∂y ∂y ⎧ ⎨ 1 + μ1 , y < δ 1 : μ = 1, (7) δ1 ≤ y ≤ 1 − δ2 ; ⎩ 1 + μ2 , y > 1 − δ 2 . The dimensionless viscosity distribution (7) is shown in Fig. 2b To find the velocity distribution along the slot height, we allocate (Fig. 3) the three zones (0, 1, 2), which correspond to the constant viscosity values. Next, we integrate Eq. (6) for zones u1 (y) = −

6 y2 + C11 y + C12 ; 1 + μ1

u0 (y) = −6y2 + C01 y + C02 ; u2 (y) = −

6 y2 + C21 y + C22 ; 1 + μ2

(8) (9) (10)

where C11 , C12 , C01 , C02 , C21 , C22 —integration constants. To determine the integration constants, we consider the next boundary conditions u1 (0) = 0; u2 (1) = 0

(11)

and enter according to Fig. 3 still unknown speeds u∗1 = u1 (δ 1 ) = u0 (δ 1 ); u∗2 = u2 (1 − δ 2 ) = u0 (1 − δ 2 ).

(12)

Taking into account (11, 12), we obtain the values of the constants, after substitution of which into (8–10) we have  y 6 y δ 1 − y + u∗1 ; 1 + μ1 δ1

2   2 ∗ ∗ u − u + 6 δ − 1 − δ 2  1 1 2 2  u0 (y) = u∗1 + 6δ 1 − 6y2 + y − δ1 ; δ1 − 1 − δ2 u1 (y) =

(13)

(14)

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Fig. 3. To determine the velocity distribution in a flat slot.

u2 (y) =

 6 (1 − y) . (1 − y) δ 2 − 1 + y + u∗2 1 + μ2 δ2

(15)

Given that the functional expressions for the velocity must be continuous and smooth, to determine the velocities u∗1 , u∗2 , we use the conditions of equality of the derivatives of the velocity at the points of merging of the velocity profiles of different zones (Fig. 3) du1 du0 du2 du0 = ; = . (16) dy δ 1 dy δ 1 dy 1−δ 2 dy 1−δ 2 The dependencies (17) give the following equations:

2   2 u∗1 − u∗2 + 6 δ 1 − 1 − δ 2 u∗1 6δ 1  ; (17) − + = −12δ 1 + 1 + μ1 δ1 δ1 − 1 − δ2

2   2 ∗ ∗ u1 − u2 + 6 δ 1 − 1 − δ 2  6δ 2 12(1 − y) u∗2  − . (18) + − = −12 1 − δ 2 + 1 + μ2 1 + μ2 δ2 δ1 − 1 − δ2 Solving together (17) and (18), we obtain 3

2

2

u∗1 =

 6δ 1 μ1 − 6δ 1 μ1 6δ δ μ − 1 2 2 + 6δ 1 1 − δ 1 ; 1 + μ1 1 + μ2

u∗2 =

 6δ 2 μ2 − 6δ 2 μ2 6δ δ μ − 1 2 1 + 6δ 2 1 − δ 2 . 1 + μ2 1 + μ1

3

2

(19)

2

Substituting (19, 20) into (13–15), we have

 2 2 δ 2 μ2 δ 1 μ1 − 2δ 1 μ1 − y u1 (y) = 6y 1 − + ; 1 + μ2 1 + μ1

(20)

(21)

Hydrodynamics of Flow in a Flat Slot with Boundary

 2 2 2 δ 1 μ1 δ 2 μ2 6δ 1 μ1 u0 (y) = − + 6y 1 − y + − ; 1 + μ1 1 + μ1 1 + μ2

 2 2 y + δ 2 μ2 − 2δ 2 μ2 + μ2 δ 1 μ1 u2 (y) = 6(1 − y) − . 1 + μ2 1 + μ1

1177

(22)

(23)

The dependences (21–23) give the complete distribution of the dimensionless velocity over the slot height. The examples of the velocity profiles calculated according to these dependences for the case δ 2 = 2δ 1 and μ1 = 1, μ2 = 2 are shown in Fig. 4. As can be seen, the flow velocity is less than the velocity determined by the traditional calculation. Also, there is a noticeable shift in the maximum value of the rate from the slot center with the uneven distribution of viscosity.

Fig. 4. The velocity distribution in flat slot.

We introduce the dimensionless fluid flow rate in a flat slot δ Q=

Q = Q0

ux (y)dy

0

V0 δ

;

(24)

where Q—actual flow rate in the slot; Q0 —flow rate in the slot according to the traditional calculation. This expression shows that the value Q is the ratio between the value of the flow rate, determined considering the jump-like boundary change of the viscosity, and the flow rate, determined by the traditional calculation. The value Q can also be considered as the drop of the throughflow capacity for the flat slot. Given (3, 5) and also considering zones according to Fig. 3, instead of (24) we have δ 1

1 Q=

ux (y)dy = 0

1−δ  2

u1 (y)dy + 0

1

u0 (y)dy + δ1

1−δ 2

u2 (y)dy.

(25)

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Substituting (21–23) into (25), we obtain the next expression for determining the drop of the throughflow capacity for the flow section of the flat slot. 2 3 − 2δ 1

Q = 1 − μ1 δ 1

1 + μ1

2

− μ2 δ 2

(26)

It should be noted that for μ1 , μ2 → 0 or δ 1 , δ 2 → 0, expression (26) gives Q = 1, i.e. there is an explicit limit to the traditional calculation of the flow of viscous incompressible fluid in a flat slot. The more detailed analysis of the effect of an abrupt increase of viscosity can be made if we consider the flow in the flat gap between the walls of similar materials. For this condition, we have one value of the boundary zone size and the magnitude of the boundary viscosity jump δ = δ 1 = δ 2 ; μ = μ1 = μ2 .

(27)

Due to the symmetry of the velocity distribution appearing in this case, the dependences (21–23) are written for half of the slot height ⎧

 ⎨ 6y 1 − 2δμ+y , 0 ≤ y < δ; 1+μ (28) u(y) = ⎩ 6y(1 − y) − 6μδ 2 , δ ≤ y ≤ 0, 5. 1+μ Examples of calculating the velocity distributions at μ = 1 for various values δ are shown in Fig. 5.

Fig. 5. The velocity semi-profile in a flat slot between the walls of similar materials.

On the basis of (27), we obtain the next expression for determining the drop of the throughflow capacity for the flow section of the flat slot Q = 1 − 2μδ

2 3 − 2δ

1+μ

.

(29)

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The examples of the calculation of the dependence for the drop of the throughflow capacity for the flow section from the boundary zone size at various values of the viscosity jump are shown in Fig. 6a. The examples of the calculation of the dependence for the drop of the throughflow capacity for the flow section from the viscosity boundary jump at various values of the boundary zone size are shown in Fig. 6b. The received result analysis shows that the boundary increase of the dynamic viscosity unambiguously leads to the drop of the throughflow capacity for the flow section of the flat slot. It can also be considered that the drop of the flow rate is no more than 5% at δ < 0.1 and μ < 4, and known dependencies are quite applicable for the design of technological systems [1, 28–30]. It is interesting to note the following. A similar model of flow with allowance for the jump-like boundary increase of the viscosity can also be constructed for the cylindrical channel with radius r 0 . Denote δ—boundary zone size near the wall, where the viscosity increases, and  δ = δ r0 . (30)

Fig. 6. The drop of the throughflow capacity depending on a the boundary zone size with increased viscosity; b the viscosity jump.

If we perform conversions like (10–29) in the cylindrical coordinate system, we get the next expression for the drop of the throughflow capacity for the cylindrical channel  2 2−δ . Q = 1 − μδ 1+μ 2

(31)

4 Conclusions Thus, the laminar flow of viscous incompressible fluid in a flat slot is considered with allowance for the boundary change of viscosity near a solid surface. The model of the stepwise distribution of the dynamic viscosity over the cross section of the channel

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with its abrupt increase near the slot walls was adopted. In the general case, the different viscosity jumps near the solid surface are introduced into consideration. Also, the dimensions of the boundary layers, where the change of viscosity appears, are considered different. For the accepted dynamic viscosity distribution, integration of the equation for the laminar fluid motion was performed. The dependences for calculating the velocity profile in a flat slot are obtained. The researches on the effect of viscosity jump on flow velocity have been conducted. The examples of calculating the velocity distribution along the height of a flat slot are presented. The flows with symmetric and asymmetrical distribution of dynamic viscosity are considered. Based on the obtained velocity distribution, dependences for calculating the flow rate in a flat slot were established. The researches of the influence on the flow rate in a slot of the parameters for the distribution of dynamic viscosity along the cross section of the channel have been conducted. The received result analysis showed that the boundary increase of the dynamic viscosity unambiguously leads to the drop of the throughflow capacity for the flow section of the flat slot. The boundaries of applicability of the traditional approach to calculating the laminar flow of viscous fluid in a flat slot are estimated. So, at δ < 0.1 and μ < 4 the drop of the flow rate is no more than 5%, which makes it possible to use known dependencies to calculate the flow.

References 1. Navrotskiy K (1991) Theory and designing hydro- and pneumodrives. Machinery Engineering, Moscow 2. Fedorovich V, Mitsyk A (2014) Mathematical simulation of kinematics of vibrating boiling granular medium at treatment in the oscillating reservoir. Key Eng Mater 581:456–461. https:// doi.org/10.4028/www.scientific.net/KEM.581.456 3. Sveshnikov V (2007) Hydrodrives in modern mechanical engineering. Hydraul Pneumatic 28:10–16 4. Kundrák J, Mitsyk A, Fedorovich V, Morgan M, Markopoulos A (2019) The use of the kinetic theory of gases to simulate the physical situations on the surface of autonomously moving parts during multi-energy vibration processing. Materials 12(19):3054. https://doi. org/10.3390/ma12193054 5. Popov D (1987) Dynamics and regulation hydro-and pneumatic systems. Machinery Engineering, Moscow 6. Sveshnikov V (2008) Hydrodrives of tools. Machinery Engineering, Moscow 7. Shevchenko S, Muhovaty A, Krol O (2016) Geometric aspects of modifications of tapered roller. Proc Eng 150:1107–1112. https://doi.org/10.1016/j.proeng.2016.07.221 8. Popov D (2005) Mechanics of hydro- and pneumodrives. MGTU, Moscow 9. Shevchenko S, Muhovaty A, Krol O (2017) Gear clutch with modified tooth profiles. Proc Eng 206:979–984. https://doi.org/10.1016/j.proeng.2017.10.581 10. Krol O (2019) Parametric modeling of gear cutting tools. In: Advances in manufacturing II. Lecture Notes in Mechanical Engineering 4:3–11. Springer, Cham. https://doi.org/10.1007/ 978-3-030-16943-5_1 11. Emtsev B (1987) Technical hydromechanics. Machinery Engineering, Moscow 12. Loytsyanskiy L (1987) Mechanics of a liquid and gas. Science, Moscow

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13. Sokolov V (2019) Diffusion of circular source in the channels of ventilation systems. In: advances in engineering research and application. ICERA 2018. Lecture Notes in Networks and Systems 63:278–283. Springer, Cham. https://doi.org/10.1007/978-3-030-04792-4_37 14. Sokolov V (2020) Transfer functions for shearing stress in nonstationary fluid friction. In: Proceedings of the 5th international conference on industrial engineering (ICIE 2019). Lecture Notes in Mechanical Engineering 1:707–715. https://doi.org/10.1007/978-3-030-22041-9_76 15. Popov D (1982) Non-stationary hydromechanical processes. Machinery Engineering, Moscow 16. Deryagin B, Churaev N, Muller V (1983) Surface forces. Science, Moscow 17. Deryagin B, Churaev N (1984) Wetting films. Science, Moscow 18. Sokolov V, Krol O, Baturin Y (2019) Dynamics research and automatic control of technological equipment with electrohydraulic drive. In: 2019 International Russian automation conference (RusAutoCon). IEEE. https://doi.org/10.1109/RUSAUTOCON.2019.8867652 19. Sokolov V, Krol O, Stepanova O (2018) Automatic control system for electrohydraulic drive of production equipment. In: 2018 International Russian automation conference. IEEE. https:// doi.org/10.1109/RUSAUTOCON.2018.8501609 20. Sokolov V, Krol O, Stepanova O (2020) Choice of correcting link for electrohydraulic servo drive of technological equipment. In: Advances in design, simulation and manufacturing II. DSMIE 2019. Lecture Notes in Mechanical Engineering. Springer, Cham, pp 702–710. https://doi.org/10.1007/978-3-030-22365-6_70 21. Sokolov V, Krol O, Stepanova O (2019) Nonlinear simulation of electrohydraulic drive for technological equipment. J Phys Conf Ser 1278:012003. https://doi.org/10.1088/1742-6596/ 1278/1/012003 22. Bondarenko N, Nerpin S (1972) The ratio between the shear strength of liquids in the volume and limited layers. In: Surface forces in thin films and disperse systems. Science, Moscow 23. Listrov A (1967) About viscous fluid model with an asymmetric stress tensor. Appl Math Mech 31(1):112–115 24. Cosserat E, Cosserat F (1909) Theoretically deformable bodies. Herman, Paris 25. Sokolova Y, Azarenko N (2014) The synthesis of system of automatic control of equipment for machining materials with hydraulic drive. Eastern-Euro J Enterp Technol 2/2(68):56–60 26. Rogovyi A (2018) Energy performances of the vortex chamber supercharger. Energy 163:52– 60. https://doi.org/10.1016/j.energy.2018.08.075 27. Sokolova Y, Tavanyuk T, Greshnoy D (2011) Linear modeling of the electrohydraulic watching drive. TEKA. Commission of motorization and energetics in agriculture XIB:167–176 28. Pavlenko I, Trojanowska J, Ivanov V, Liaposhchenko O (2019) Scientific and methodological approach for the identification of mathematical models of mechanical systems by using artificial neural networks. In: Innovation, engineering and entrepreneurship. HELIX 2018. Lecture Notes in Electrical Engineering 505:299–306. https://doi.org/10.1007/978-3-31991334-6_41 29. Shevchenko S, Muhovaty A, Krol O (2020) Gear transmission with conic Axoid on parallel axes. In: Proceedings of the 5th international conference on industrial engineering (ICIE 2019). Lecture Notes in Mechanical Engineering 1:1–10. https://doi.org/10.1007/978-3-03022041-9_1 30. Fesenko A, Basova Y, Ivanov V, Ivanova M, Yevsiukova F, Gasanov M (2019) Increasing of equipment efficiency by intensification of technological processes. Periodica Polytech Mech Eng 63(1):67–73. https://doi.org/10.1007/978-3-030-04792-4_37

Increased Measurement Accuracy of Average Velocity for Turbulent Flows in Channels of Ventilation Systems V. Sokolov(B) Volodymyr Dahl East Ukrainian National University, 59-a, Central Pr., Severodonetsk 93400, Ukraine [email protected]

Abstract. The turbulent gas-air flow in cylindrical channels of industrial ventilation systems is considered. The incompressible viscous fluid model has been adopted to describe the flow. It is shown that the measurement accuracy of the average velocity is determined by the sensor location in the flow section of the channel. The velocity distribution in the channels is represented by power dependence. The experimental data of the exponent in the velocity distribution along the radius of the circular cylindrical pipe are used. The approximation of the experimental exponent by analytical dependence was performed, which allows determining the radius of the average velocity depending on the Reynolds number. The recommendations for increasing the accuracy of measuring the average speed in the circular cylindrical channel are formulated. The empirical dependence was used to determine the radius of maximum velocity in the ring-shaped cylindrical channel. This dependence allowed us to establish algorithmic expressions for the two radii of the average velocity in the ring-shaped channel. It is shown that the radii of the average velocity practically do not depend on the Reynolds number and essentially depend on the dimensionless form parameter determined by the ratio of the radii for the inner and outer surfaces of the channel. It is recommended that of the two radii of the average velocity in the ring-shaped cylindrical channel, the greater one will be used, where, due to the smaller radial velocity gradient, the sensor installation error for the measurement accuracy is less pronounced. Keywords: Ventilation systems · Turbulent flow · Reynolds number · Flow velocity · Radius of the average velocity

1 Introduction The integral part of any industrial enterprise is engineering and technical facilities such as ventilation systems that provide the required sanitary and technical standards in production buildings, labor safety and compliance with technological processes [1–3].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_137

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Special attention to ventilation systems is also paid as the main source of production waste emissions hazardous to human health and the environment, which are caused by the technological processes in the energy, chemical, mining, building and other branches of the economy. In this regard, to improve the ventilation systems, the actual task is to increase the reliability of monitoring the characteristics of air-gas emissions. The solution of this task will allow achieving the effect in the technical, economic, social and environmental aspects [4–6].

2 Literature Review One of the main parameters in the control of industrial emissions is their volume, which is determined by the flow rate in the channels of ventilation systems that are directly released. The flow rate is determined by the area of the channel cross section and the measured flow velocity. Methods and means of measuring speed are diverse [7–12], among which the hydrodynamic method using the Pitot or Pitot-Prandtl tube speed sensor is quite common [13–16]. The velocity sensor is installed on the length of at least 20 hydraulic diameters for the channel from the inlet [17–20], so as to have the formed velocity profile in the control section. The accuracy of flow rate measurement significantly depends on the location of the sensor over the channel cross section, since the flow velocity is unevenly distributed over the cross section. In addition, the distribution of velocity depends on the Reynolds number [7, 13, 14], i.e. from the itself average velocity or flow rate. And, if for circular cylindrical channels there are recommendations for the location of speed sensors at developed turbulent flow [7, 14, 18], then for the ring-shaped channels such information is missing in the literature. At the same time, the ring-shaped cylindrical channels are fairly common in industrial ventilation systems, in particular, in the ventilation systems of power units for nuclear stations. The purpose of this paper is to obtain analytical dependencies for determining the radii of the average velocity for turbulent flows in the circular and ring-shaped cylindrical channels of ventilation systems, to develop recommendations for increasing the accuracy of measuring the average velocity.

3 Determination of the Radii of the Average Velocity for Turbulent Flows in the Circular and Ring-Shaped Cylindrical Channels of Ventilation Systems The gas-air flow in the circular and ring-shaped cylindrical channels of ventilation systems at speeds up to 70 m/s and the Reynolds numbers Re > 104 is permissible to be considered in the framework of the model of incompressible viscous fluid [21, 22]. For turbulent flow in the circular cylindrical pipe, the velocity distribution can be represented by the following power dependence [13, 17]:   r n u (n + 1)(n + 1) 1− = , (1) V0 2 R0

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where V 0 —average flow velocity; n—exponent depending on the Reynolds number (for example, n = 1/7 for Re = 105 , the so-called 7th exponent law); r—radius of arbitrary point, measured from the axis of the pipe; R0 —radius of the pipe. Reynolds number Re =

V0 d , ν

(2)

where ν—coefficient of kinematic viscosity [23, 24]. Dimensionless velocity deviation from the average u =

u − V0 u = − 1. V0 V0

(3)

In view of (1), the expression for the dimensionless deviation of velocity from the average value will look like   r n (n + 1)(n + 2) 1− u = − 1. (4) 2 R0 Figure 1 shows the distribution of the modulus for the dimensionless velocity deviation from the average value over the dimensionless radius, calculated according to (4) with n = 1/7 (Re = 105 ). As you can see, on the axis |u| = 0.2245, i.e. the measurement error of the average flow velocity when installing the sensor in the center of the pipe will be 22.45%. Therefore, to increase the accuracy of measuring the average velocity, the velocity sensor should be installed at a radius corresponding to the average velocity value. The radius value of the average velocity is obtained by substituting into (1) the equalities u = V0  1   n 2 ∗ r = R0 1 − . (5) (n + 1)(n + 2) To determine the radius of the average velocity for arbitrary Reynolds numbers, we use the experimental data [17] of the values of the exponent in the velocity distribution (1) along the pipe radius. The values of n for series of the Reynolds numbers Re are presented in Table 1.

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Fig. 1. The distribution of the modulus for the dimensionless velocity deviation from the average value over dimensionless pipe radius.

Table 1. The values of the exponent in the velocity distribution. Re 4.103 2.3.104 105 1.1.106 3.2.106 n

1/6

1/6.6

1/7 1/8.8

1/10

The tabular data is approximated by the least square’s method by the following dependency: n = 0.252 − 2.29 · 10−2 lg Re.

(6)

The calculated dependence (6) is compared with the experimental values of n in Fig. 2.

Fig. 2. The comparison of the calculated dependence for the exponent with experimental data.

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Taking into account the approximation dependence (6), it is possible to establish the relationship between the radius of the average velocity and the Reynolds number for a circular cylindrical channel. However, as the calculations show, the radius of the average velocity is almost independent of the Reynolds number and has a value ≈0.76R0 in the range Re = 105 ÷ 106 , which works for industrial ventilation systems. The velocity distribution in the ring-shaped cylindrical channel will also be represented by power dependence ⎧

n ⎨ r−R1 , R1 ≤ r ≤ rm ; u rm −R1

n (7) = ⎩ R2 −r , rm ≤ r ≤ R2 ; Vm R2 −rm where V m ––maximum velocity; R1 , R2 —radii of the inner and outer surfaces of the channel; r m —radius of the maximum velocity. For the maximum velocity radius, we use the following empirical dependence [25]: rm − R1 = R2 − rm



R1 R2

0,343 .

(8)

Since the average velocity in the ring-shaped cylindrical channel V0 = and flow rate

R2 Q = 2π

Q ,  2 π R2 − R21 ⎛

⎜ urdr = 2π ⎝

R1

rm

R1

(9)

R2 urdr +

⎞ ⎟ urdr ⎠,

(10)

rm

then taking into account (7) we get V0 R1 + R2 + nrm 2 = . Vm R1 + R2 (n + 1)(n + 2)

(11)

Based on (11), we transform the dependence (7) to the form ⎧

n ⎨ r−R1 , R1 ≤ r ≤ rm ; R1 + R2 u (n + 1)(n + 2) r −R = × m 1 n V0 2 R1 + R2 + nrm ⎩ R2 −r , rm ≤ r ≤ R2 . R2 −rm

(12)

Substituting the equality u = V 0 here, we establish expressions for the two radii of the average velocity  r1∗ = R1 + (rm − R1 )

2 R1 + R2 + nrm R1 + R2 (n + 1)(n + 2)

1 n

;

(13)

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r2∗



2 R1 + R2 + nrm = R2 − (r2 − rm ) R1 + R2 (n + 1)(n + 2)

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1 n

.

(14)

Consider for the ring-shaped cylindrical channel the dimensionless shape parameter R1 R2

(15)

r1∗ ∗ r∗ rm ; r2 = 2 ; rm = . R2 R2 R2

(16)

ξ= and the dimensionless radii r ∗1 =

Then according to (13) and (14), we have r ∗1 = 1 + (r m − ξ )



r ∗2 = 1 − (1 − r m )



2 1 + ξ + nr m 1+ξ (n + 1)(n + 2) 2 1 + ξ + nr m 1+ξ (n + 1)(n + 2)

1 n

;

(17)

.

(18)

1 n

and based on (8) rm =

ξ + ξ 0.343 . 1 + ξ 0.343

(19)

Figure 3 shows the dependences of the dimensionless radii of the average velocity r ∗1 and r ∗2 from the dimensionless channel form parameter ξ, calculated according to (17) and (18) taking into account (19) for n = 1/7. As can be seen, the radii of the average velocity essentially depend on the ratio of the radii of the inner and outer surfaces of the channel. A rough estimate for the influence of the Reynolds number on the radii of the average velocity can be made on the basis of the approximation dependence (6). However, the calculations show that in the range of Reynolds numbers, which works for industrial ventilation systems, the values of the radii of the average velocity do not change significantly, as in the case of the circular cylindrical channel. It should also be noted that in practice [26–30], of the two average radii of velocity in the ring-shaped cylindrical channel, the greater one should be recommended, where, due to the smaller radial velocity gradient, the sensor installation error for the measurement accuracy is less pronounced.

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Fig. 3. The dimensionless radii of the average velocity in the ring-shaped cylindrical channel.

4 Conclusions Thus, the turbulent gas-air flow in cylindrical channels of industrial ventilation systems is considered. The incompressible viscous fluid model has been adopted to describe the flow. It is shown that the measurement accuracy of the average velocity is determined by the sensor location in the flow section of the channel. The velocity distribution in the channels is represented by power dependence. The experimental data of the exponent in the velocity distribution along the radius of the circular cylindrical pipe are used. The approximation of the experimental exponent by analytical dependence was performed, which allows determining the radius of the average velocity depending on the Reynolds number. The calculations showed that the radius of the average velocity is almost independent of the Reynolds number and has a value ≈0.76R0 in the range of the Reynolds numbers Re = 105 ÷ 106 , which works for industrial ventilation systems. The empirical dependence was used to determine the radius of maximum speed in the ring-shaped cylindrical channel. This dependence allowed us to establish algorithmic expressions for the two radii of the average velocity in the ring-shaped channel. It is shown that the radii of the average velocity practically do not depend on the Reynolds number and essentially depend on the dimensionless form parameter determined by the ratio of the radii for the inner and outer surfaces of the channel. It is recommended that of the two radii of the average velocity in the ring-shaped cylindrical channel, the greater one will be used, where, due to the smaller radial velocity gradient, the sensor installation error for the measurement accuracy is less pronounced.

References 1. Svistunov V, Pushnyakov N (2007) Heating, ventilation and air conditioning facilities of the agro-industrial complex and utilities. St. Petersburg 2. Becker A (2005) Ventilation systems. Euroclimate, Moscow

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3. Sokolov V, Krol O, Stepanova O (2018) Automatic control system for electrohydraulic drive of production equipment. In: 2018 International Russian automation conference. IEEE. https:// doi.org/10.1109/RUSAUTOCON.2018.8501609 4. Elinsky I (1989) Ventilation and heating of electroplating shops of machine-building enterprises. Machinery Engineering, Moscow 5. Ananyev V (2001) Ventilation and air conditioning systems. Euroclimate, Moscow 6. Sokolov V, Krol O, Baturin Y (2019) Dynamics research and automatic control of technological equipment with electrohydraulic drive. In: 2019 International Russian automation conference (RusAutoCon). IEEE. https://doi.org/10.1109/RUSAUTOCON.2019.8867652 7. Loytsyansky L (1987) Mechanics of a liquid and gas. Science, Moscow 8. Popov D (1982) Non-stationary hydromechanical processes. Machinery Engineering, Moscow 9. Sokolov V (2019) Diffusion of circular source in the channels of ventilation systems. Advances in engineering research and application. ICERA 2018. Lecture Notes in Networks and Systems 63:278–283. https://doi.org/10.1007/978-3-030-04792-4_37 10. Andriychuk N et al (2008) Hydraulics and hydropneumatic drives. VEUNU, Lugansk 11. Popov D (2005) Mechanics of hydro- and pneumodrives. MGTU, Moscow 12. Popov D (1987) Dynamics and regulation hydro-and pneumatic systems. Machinery Engineering, Moscow 13. Emtsev B (1987) Technical hydromechanics. Machinery Engineering, Moscow 14. Povh I (1974) Aerodynamic experiment in mechanical engineering. Machinery Engineering, Leningrad 15. Sokolov V, Krol O, Stepanova O (2019) Nonlinear simulation of electrohydraulic drive for technological equipment. J Phys Conf Ser 1278:012003. https://doi.org/10.1088/1742-6596/ 1278/1/012003 16. Kovalenko A et al (1998) Fundamentals of technical mechanics of liquids and gases. EUSU, Lugansk 17. Schlichting G (1974) Theory of the boundary layer. Science, Moscow 18. Pavlenko I, Trojanowska J, Ivanov V, Liaposhchenko O (2019) Scientific and methodological approach for the identification of mathematical models of mechanical systems by using artificial neural networks. In: Innovation, engineering and entrepreneurship. Lecture Notes in Electrical Engineering. 505:299–306. https://doi.org/10.1007/978-3-319-91334-6_41 19. Andriychuk N et al (2005) Thermodynamics for civil engineers. VEUNU, Lugansk 20. Hintze I (1963) Turbulence. Science, Moscow 21. Nedopekin F et al (2010) Fundamentals of continuum mechanics. VEUNU, Lugansk 22. Gusetsova Y et al (2005) Ventilation systems: modeling, optimization. VEUNU, Lugansk 23. Andriychuk N et al (2009) Aerohydromechanics. VEUNU, Lugansk 24. Sokolov V (2020) Transfer functions for shearing stress in nonstationary fluid friction. In: Proceedings of the 5th international conference on industrial engineering (ICIE 2019). Lecture Notes in Mechanical Engineering 1:707–715. https://doi.org/10.1007/978-3-030-22041-9_76 25. Kays W, Leung E (1963) Heat transfer in annular passages - hydrodynamically developed turbulent flow with arbitrarily prescribed heat flux. Heat Mass Transfer 6:537–557 26. Shevchenko S, Muhovaty A, Krol O (2016) Geometric aspects of modifications of tapered roller. Proc Eng 150:1107–1112. https://doi.org/10.1016/j.proeng.2016.07.221 27. Shevchenko S, Muhovaty A, Krol O (2017) Gear clutch with modified tooth profiles. Proc Eng 206:979–984. https://doi.org/10.1016/j.proeng.2017.10.581 28. Sokolov V, Krol O, Stepanova O (2020) Choice of correcting link for electrohydraulic servo drive of technological equipment. In: Advances in design, simulation and manufacturing II. DSMIE 2019. Lecture Notes in Mechanical Engineering, Springer, Cham, pp 702–710. https://doi.org/10.1007/978-3-030-22365-6_70

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29. Krol O (2019) Parametric modeling of gear cutting tools. In: Advances in manufacturing II. Lecture Notes in Mechanical Engineering 4:3–11. https://doi.org/10.1007/978-3-030-169 43-5_1 30. Shevchenko S, Muhovaty A, Krol O (2020) Gear Transmission with Conic Axoid on Parallel Axes. In: Proceedings of the 5th international conference on industrial engineering (ICIE 2019). Lecture Notes in Mechanical Engineering 1:1–10. https://doi.org/10.1007/978-3-03022041-9_1

Actuation Control System of a Hydraulic Machine Drive Locking Device N. A. Fomenko(B) , S. V. Aleksikov, and S. G. Artemova Volgograd State Technical Universit, 1, Akademicheskaya Str., Volgograd 400074, Russia [email protected]

Abstract. Special and general ground machines including those intended for road-construction, industrial, forestry, agricultural, land-reclamation, etc. works are equipped with a hydraulic drive of working attachments. During the technological operations, the hydraulic drive of working attachments ensures an increase in the speed and evenness of positioning control of the machine and the working attachments, optimizes the force action on the working attachments, facilitates operator’s work, enhances machine performance and reduces operating costs. Destruction of high-pressure hoses and the unauthorized discharge of hydraulic fluid into the atmosphere should be considered as the weak points of the hydraulic system of machines. Therefore, the work aimed at optimizing the working pressure and the physicochemical properties of hydraulic fluid as well as at creating technical means of hydraulic drive protection has been performed. Attempts have been made to use environmentally compatible hydraulic fluids, which do not contribute to environmental pollution when machines are operated. Works, which are focused on the improvement of flexible high-pressure hoses, metal pipelines and their hinged connections as well as the methods and systems of pipeline protection are in progress. It has been found out that flexible high-pressure hoses or pipeline protection methods do not solve the problem of environmental protection against discharges of hydraulic fluid into the atmosphere to the full degree. The use of organic hydraulic fluids increases the operating self-cost, and the optimization of the working pressure in a hydraulic system reduces machine performance. Keywords: Hydraulic drive · High-pressure hose · Hydraulic fluid · Locking device · Contact pair · Contact plate · Electrical circuit

1 Introduction Alternating-sign dynamic loads exceeding the permissible ones appear in hydraulic drives of modern machines at the boundary of the optimal working pressure. They lead to the destructions of hoses, unauthorized discharge of hydraulic fluid into the atmosphere, increased operating costs and reduced environmental safety.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_138

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A feasibility study has been carried out to analyze the use of environmentally compatible hydraulic fluids of vegetable origin, braided and wound reinforcement design, gastype envelope of high-pressure hoses, metal pipelines with hinged connections, reduced working pressure in hydraulic systems as well as of advanced methods of hydraulic drive protection against the unauthorized discharge of hydraulic fluid into the atmosphere. It has been revealed that the considered engineering solutions do not eliminate the reasons causing the unauthorized discharge of hydraulic fluid into the atmosphere to the full degree, and do not ensure the ecological safety of the environment. Design of an actuation control system of a locking device is suggested which allows for both retaining the functionality of the protection system of the hydraulic drive and providing high operational reliability of the hydraulic drive complemented by a reduction in operating costs.

2 Topicality, Scientific Significance of the Issue with a Brief Overview of the Literature The studies [1, 2] show that in the case of enhancement of hydraulic drive capacity by means of an increase in the working pressure and the use of various protection methods, a possibility of unauthorized discharge of hydraulic fluid into the atmosphere resulting in environmental pollution still remains. Therefore, the elimination of negative consequences of hydraulic fluid discharge into the environment is considered a topical task. The scientific significance of the engineering solution lies in the fact that the authors have developed and patented an actuation control system of a locking device of a hydraulic drive equipped with an electric controller of its operation process, warning light and sound signals intended for reporting to the operator on a failure in the hydraulic drive and for an automatical shutoff in the damaged hydraulic line.

3 Task Statement Based on the drawbacks of the existing methods and devices of hydraulic drive protection, to develop an engineering solution for the elimination of the given disadvantageous features.

4 Theoretical Part The operating process of machines equipped with a positive-displacement hydraulic drive is accompanied by explicit dynamic loads [3–9] when technological processes are in progress. Alternative-sign loading mode appears upon multiple switchover of the power flow of the hydraulic fluid. Dynamic loads in high-pressure hoses result in

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their destruction and unauthorized discharge of hydraulic fluid into the atmosphere. Enhancement of machine performance by means of an increase in the capacity and nominal working pressure in the hydraulic system also lead to fatigue destruction of high-pressure hoses and unauthorized discharge of hydraulic fluid into the atmosphere. Reducing the working pressure up to 20 MPa, i.e. limiting its growth beyond the boundaries of the nominal value is one of the main activities aimed at diminishing the dynamic loads in high-pressure hoses. Improvement of pipelines is another trend to enhance the reliability of hydraulic drive protection [10]. The use of flexible high-pressure hoses of either a braided or a wound reinforcement design does not always ensure their durability under cyclic loads and specified nominal pressure; it does not guarantee the reliability. In hoses with a gas-type envelope, the cyclic loads on the inner wall decrease, though the probability of destruction of the inner wall of the envelope cannot be excluded [11]. There exist several methods of protection of a hydraulic machine drive [12–24]. When actuated, a float-type protection system placed inside a hydraulic tank leads to hydraulic fluid loss up to 10 L, while a pneumo-electrical protection system results in the losses up to 8 L. In the works [19], a reduction in the loss up to 0.5, …1.2 L was achieved, and the authors’ works [20, 21] demonstrate a method of hydraulic drive protection classified as a hydraulic-mechanical one in which the actuation of a locking device reduces the loss to 0.17 L. However, in all the three cases under consideration, the loss increases due to the absence of an automatical fluid shutoff system and a warning signal indicating a hydraulic drive failure. Therefore, the problem of loss reduction in the case of the actuation of the hydraulic drive protection system remains relevant.

5 Practical Relevance, Suggestions and Results of Implementation, Results of Experimental Investigations. The suggested engineering solution (Figs. 1 and 2) [25] is of practical significance. Modeling of the experimental research allows revealing a considerable advantage when compared to earlier developments. Without sacrificing the functionality, the suggested system of hydraulic drive protection provides an enhanced operational reliability and environmental safety of the use of machines equipped with a hydraulic drive. The system of hydraulic drive protection comprises a hydraulic tank 1, a pump 2, a delivery hydraulic line 3, a drain line 4 leading to the hydraulic tank, a flow control valve 5, a hydraulic prime mover 6, a locking device 7, and electrical circuit diagram 8 of the warning signal to indicate the locking device actuation and to shut off the hydraulic fluid supply into the damaged hydraulic line.

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Fig. 1. Actuation control system of locking device of hydraulic drive. 1—tank, 2—pump, 3— delivery hydraulic line, 4—drain line leading to the hydraulic tank, 5—flow control valve, 6— hydraulic prime mover, 7—locking device, 8—electrical circuit diagram, 9, 20—case, 10–12— fitting pipes, 13—plug, 14—plunger, 15—groove, 16— radial bores, 17—fixed stop, 18—axial channel, 19, 22—spring, 21—rod, 23—blind, 24—shutoff mechanism, 25—pressure reducing valve.

The locking device 7 comprises a case 9, an inlet fitting pipe 10, an outlet fitting pipe 11, a drain fitting pipe 12, a plug 13, a plunger 14 with a ring-type groove 15 and radial bores 16 located on its external surface at the distance equal to the full travel f of the plunger 14 from the vertical axis of the drain fitting pipe 12. The contact surface of the fixed stop 17 of the plug 13 is located at the distance equal to the full travel f of the plunger 14 from the side end of the axial bore 18 of the plunger 14. The plunger 14 is kept in the initial position by the spring 19 located between the side end of the plunger 14 and the side end of the plug 13.

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Fig. 2. Electrical circuit of the actuation control system of locking device of hydraulic drive. 24—shutoff mechanism, AB—accumulator battery, WK—switch, K1, K2—contacts to switch on the elements of the electrical circuit, LS—warning light, ZS—warning sound signal.

Chambers A, B and C are interconnected by means of the axial channel 18 which is covered by the fixed stop 17. Inside the through-hole of the plug 13, the case 20 is installed at the one side while at the other side, the rod 21 is installed which is springloaded with the spring 22 and equipped with a collar at the distance f from the side end of the plunger 14. A contact plate is placed at the side end of the rod 21, and a contact pair is placed at the side end of the blind located in the case 20; this contact pair closes the contacts K1 and K2 of the electrical circuit 8 the gap h between which is equal to the extending part of the rod 21. The electrical circuit 8 consists of on-board power source AB, contacts K1 and K2 to switch the warning light and sound signals and the shutoff mechanism of the hydraulic fluid supply. When the protection system is under working conditions, the hydraulic fluid pressure in the chambers A and B is equal and close to the atmospheric one. In this case, the plunger 14 is kept in the extreme left position by the spring 19. When the flow control valve 5 is switched on, the pressure in the chambers A and B increases to the nominal one. In the case if the hoses are torn, the hydraulic fluid pressure in the outlet chamber B decreases immediately due to the pressure difference in the chambers A and B, the plunger 14 surmounts the resistance of the spring 19, the axial channel 18 is covered by the fixed stop 17 and the fluid flow is delivered through the chamber D of the drain fitting pipe 12 to the hydraulic tank. Simultaneously, compressing the spring 22, the plunger 14 moves the rod 21 to the distance h and closes the contact pair of the electrical circuit. As a result, the warning light and sound signals inform the operator on an unauthorized discharge of hydraulic fluid into the atmosphere and the hydraulic fluid supply to the

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damaged line is automatically shut off with the help of the solenoid coil of the control valve 24.

6 Conclusion Without sacrificing the hydraulic drive functionality, the loss of hydraulic fluid is reduced, and high operational reliability and ecological safety of the environment are ensured due to the actuation control of the locking device of the hydraulic drive protection system.

References 1. Fomenko VN (2000) Development of hydraulic drive protection systems of mechanisms of mounted machines, traction and special transport vehicles. Thesis for the scientific degree of Candidate of Technical Sciences, Volgograd 2. Fomenko NA (2002) Improving the performance characteristics of hydraulic systems in machine-tractor aggregates. Thesis for the scientific degree of Candidate of Technical Sciences, Volgograd 3. Pyndak VI, Strokov VL, Lapynin YuG et al (1999) Reducing dynamic loads in hydraulically driven cyclic machines. Nauka-proizvodstvu, Mashinostroenie, Moscow, p 10 4. Fedyakin VI, Shevchuk VP et al (2001) Evaluation of reliability indices of hydraulic system of machine-tractor aggregate. In: Issues of land husbandry in market economy conditions: Proceedings of international scientific and practical conference, Volgograd 5. Burlachenko OV, Serdobintsev YuP, Skhirtladze AA (2010) Enhancing the quality of technological equipment operation (monograph). TNT Publ, Stary Oskol, pp 398–410 6. Fomenko NA, Tyrnov YuA (2013) Investigation of the performance capability of hydraulic system hoses of machine-tractor aggregates. In: Enhancing the efficiency of resources use in agriproducts production—new technologies and new-generation equipment for crop growing and animal husbandry: college of scientific articles of XVII internship scientific practice conference, 24–25 Sept 2013, R. V. Pershin Publishing, Tambov, pp 146–149 7. Fomenko NA, Bogdanov VI, Aleksikov SV et al (2014) Resource-saving hydraulic system of construction equipment. In: College of scientific articles based on the proceedings of the internship scientific practice conference, Published at Saratov State Technical University, Saratov, pp 221–224 8. Fomenko NA, Bogdanov VI, Burlachenko OV, Aleksikov SV (2015) Reducing the energy of hydraulic shock in the locking device of hydraulic system for construction and road-building machines. Internet-Vestnik VolgGASU 1(37) 9. Fomenko NA, Bogdanov VI, Sapozhkova NV (2014) Ways of improvement of a hydraulic actuator of traction vehicles. Vestnik VolgGASU. Bull Volgograd State Univ Architec Civ Eng. Ser Constr Architec 36(55):218–222 10. Fomenko NA, Aleksikov SV, Bogdanov VI, Sapozhkova NV (2014) Pipeline of the hydraulic system of road construction machines. Bull Sci Edu Dev 3:115–117 11. Fomenko NA, Bogdanov VI, Fomenko VN High-pressure pipeline. Patent No. 2511926 C2 Russian Federation MPK F 15 B 20/00 12. Fomenko NA, Bogdanov VI, Burlachenko OV, Aleksikov SV (2015) Reliability improvement of the locking structure of the protection system of hydraulic gear of construction and road cars (scientific article). Bull Volgograd State Univ Architec Civ Eng. Ser Constr Architec 41(60):169–180

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13. Fomenko NA, Bogdanov VI, Burlachenko OV, Aleksikov SV (2015) Relief valve of protection system of hydraulic drive of a machine (scientific article). Bull Volgograd State Univ Architec Civ Eng. Ser Constr Architec 42(61):163–173 14. Fomenko NA, Dubinsky SV, Golobuta GI, Lyshko GP Hydraulic drive protection system. Patent SU1813937A1F15B20/00 15. Fomenko NA, Perelmiter VI, Fomenko VN Hydraulic drive protection system. Patent RU15763U17F15B21/00 16. Fomenko VN, Perelmiter VI, Fomenko NA, Shevchuk VP Hydraulic system. Patent RU 15764 U1 7 F 15 B 21/00 17. Shevchuk VP, Bobkov YuK et al (1991) Method of hydraulic drive protection. Inventor’s certificate 1661483 USSR, Bulletin 25 18. Manuylov VYu, Ershov OB, Kurmambayev AE (1991) System of hydraulic drive protection. Inventor’s certificate 1605046 USSR, Bulletin 41 19. Fomenko NA, Bogdanov VI, Burlachenko OV et al System of hydraulic drive protection. Patent 2549754 C1 Russian Federation MPK F 15 B 20/00 20. Fomenko NA, Bogdanov VI, Burlachenko OV et al System of hydraulic drive protection. Patent 2571240 RU C1 F 15 B 20/00 21. Fomenko NA, Burlachenko OV, Aleksikov SV, Fomenko VN System of hydraulic drive protection. Patent RU 2 583 195 C1 F 15 B 20/00 22. Perelmiter VI Hydraulic system. Patent SU 1822471 A3 F 15B20/00 23. Gadzhiev BA, Kirsh BA (1990) Device for eliminating of leakages. Inventor’s certificate 1576770 USSR, Bulletin 25 24. Shevchuk VP, Bobkov YuK et al (1991) Method of protecting hydraulic system. Inventor’s certificate 1661483 USSR, Bulletin 25 25. Fomenko NA, Bogdanov VI, Burlachenko OV et al System of hydraulic drive protection. Patent 2556835 C1 Russian Federation MPK F 15 B 20/00

Re-engineering of Equipment to Feed the Melting Furnace with Aluminum Charge A. V. Nefedov1(B) , V. V. Svichkar1 , and O. N. Chicheneva2 1 Novotroitsk Branch of the Federal State Autonomous Educational Institution of Higher Education “National Research Technological University “MISiS”, 8, Frunze St., Novotroitsk 462359, Russia [email protected] 2 Federal State Autonomous Educational Institution of Higher Education “National Research Technological University “MISiS”, 4, Leninsky Prospekt, Moscow 119049, Russia

Abstract. To increase operational reliability and reduce maintenance costs of the equipment, intended to feed melting furnace with aluminum charge, replacing the electromechanical chain hoist drive with a hydraulic one is proposed to lift and overturn a charging bin. A hydraulic hoist system integrated with a hydraulic system of the furnace was developed. The main hydraulic system elements were chosen, including a single-acting multistage telescopic hydraulic cylinder to lift the bin and double-acting hydraulic cylinders to overturn it. Due to the development of a hydraulically driven furnace feeder, the bin lifting and overturning scheme was simplified, and energy costs and the maintenance burden were reduced. Replacing the electromechanical drive with a hydraulic one increases the operational reliability of feeding the furnace with charge materials. The calculations show that the implementation of design solutions does not require large capital expenditures and as a result of the measures proposed, the production cost will be reduced by 0.02%; the payback period of the investment project proposed will not exceed 4 months. Keywords: Foundry · Melting furnace · Feeder · Hydraulic circuit · Multistage telescopic single-acting hydraulic cylinder · Double-acting hydraulic cylinder

1 Introduction Currently, metallurgical enterprises pay great attention to upgrading available equipment, introducing new advanced technologies, fully automated control over the metallurgical processes using high-performance computer systems, and improving the arrangement of labor and the skills of working personnel. One of the important issues of the metallurgical industry is increasing equipment reliability, which is solved by modernizing or replacing obsolete equipment [1–11]. The article discusses the re-engineering of a skip hoist to feed a furnace of foundry complexes of the RIFAR CJSC. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_139

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RIFAR is a domestic manufacturer of a new series of high-quality bimetallic and aluminum sectional radiators. They are well operated in Russia and CIS countries both in autonomous heating systems for private houses and collective heating systems for cottage villages as well as in central heating systems for multistory structures and buildings. The RIFAR radiators have proven themselves in various Russian regions and CIS countries. The high reliability of radiators ensures their long-term operability and allows creating comfortable heat with any functional heating system [12, 13].

2 The RIFAR CJSC Casting and Melting Complex The casting and melting complex LPK–01 is designed to produce shaped castings from aluminum alloys by injection molding and is a combination of equipment in which all components perform interconnected process operations in a certain sequence to produce castings of radiator sections by injection molding. The number of equipment items to perform a single operation may vary depending on the given capacity of the casting and melting complex. Thus, the number of melting furnaces depends on the required amount of melt; the number of holding vessels and die-casting machines (DCMs) depends on the total capacity of the casting and melting complex and the DCM capacity. The number of casting ladles, ladle heating devices, and ladle trucks depends on the number of operating DCMs. The casting and melting complex consists of two groups of equipment: melting group equipment intended for smelting and preparing the melt for casting, and casting group equipment designed to produce shaped castings from the melt by injection molding. The casting and melting complex equipment is arranged in the production premise in such a way as to ensure the sequence of all process operations, the optimal routes of transporting casting ladle to the complex elements, as well as the ease of operation, maintenance, and repair of equipment [14]. The casting section comprises an Italian-made MTX-300 gas-fired melting furnace, in which the aluminum smelting and casting take place. High-quality aluminum alloy by Russian manufacturers, steady maintenance of constant temperature, and strictly dosed amount of metal allow minimizing the production wastes. To produce the melt, the aluminum ingots AK12M2 according to GOST 1583–93 should be used. The furnace is fed with ingots and secondary wastes (gates and burrs) using an automated skip hoist, on the pins of which a charging car is placed. To achieve maximum furnace efficiency, the order and schedule of feeding charge materials provided for by regulatory documents should be strictly observed [14, 15]. The MTX-300 model melting furnace is a furnace with a strong steel shell, the bath of which is lined with state-of-the-art fireproof materials. The MTX-300 furnace body is mounted on a support platform and is equipped with a tilting mechanism intended to discharge the melt. The tilting mechanism is designed using hydraulic cylinders, which incline the furnace to the required angle by operator command and thereby allow the melt to be discharged into the casting ladle for transportation. As a charge, aluminum ingots and foundry wastes (gates, burrs, defective castings, and products) are used. These wastes should be collected in special containers, sorted out by size, and returned to the MTX-300 furnaces as part of the charge. Thus, a closed process of using charge materials in melt production is ensured.

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3 Equipment to Feed the Melting Furnace with Aluminum Charge The charge is fed into the furnace by a feeder, which is a machine equipped with a hoist, on the pins of which a charging car (bin) is placed. The hoist is moved along the guides by an electromechanical drive consisting of a gear motor and a chain gear. The amount of charge loaded into the bin is controlled by an electronic overload protection system, which stops the machine operation when the permissible amount of the loaded charge is exceeded. The bin rises and pours the charge into the furnace filling zone from the top through the furnace feeding hole, which opens using a hydraulic drive. The lifting mechanism of the feeder is equipped with a protective shutter with position sensors, the combination of signals of which prevents the machine operation when the shutter is raised, thereby ensuring safe working conditions for personnel. On the furnace, a chain hoist is installed. The main hoist elements are steel structure with guide rails, a bin, a traction chain, a motor, and a gearbox. The guide rails are arranged vertically and at the end of the path, they are curved to ensure the overturn and discharge of the bin. The maximum load capacity indicated in the technical datasheet is 500 kg. The hoisting speed is 0.05 m/s. The bin is lifted by a traction chain, which in turn is driven by a drive shaft powered by the motor through a two-stage cylindrical gearbox. The hoist is loaded using a forklift. The bin with aluminum ingots is transported and placed on the seat. Then, it is lifted, and aluminum is discharged directly into the furnace shaft. The hoist is equipped with a lot of wearing details, therefore, the regular shutdown of the equipment for repair and maintenance is required. Scheduled maintenance of the skip requires at least 8 h per week, excluding unscheduled repairs. Scheduled maintenance includes lubrication of the traction chain, the rail track, and bearings, and keeping the oil level in the gearbox. In the course of skip operation, the traction chain is extended and should be timely replaced. Otherwise, the traction chain may break, and the skip would fall.

4 Re-engineering of Equipment to Feed the Melting Furnace with Aluminum Charge Since the available equipment intended to feed the melting furnace with aluminum charge requires frequent shutdowns for maintenance and repair, its upgrading has been proposed. To reduce downtime and energy costs, replacing the chain hoist drive with a hydraulic one by dismantling the old hoisting system and installing hydraulic cylinders to lift and overturn the bin has been proposed. To do this, the steel structure should be changed without affecting its bearing part; the guide rails should only be replaced and fasteners for the hydraulic cylinders installed. Analysis of the hydraulic circuit of the furnace indicated the possibility of integrating the hydraulic hoist circuit into it (Fig. 1). The upgraded hoist operating principle is as follows [16, 17]. The power fluid from tank 1 is sucked by pump 4 and fed to hydraulic distributor 10, then to telescopic hydraulic cylinder 15; when the upper position is reached, discharge

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valve 13 opens and the fluid is fed through flow divider 17 to hydraulic cylinders of overturn 16. In the neutral position of distributor sections, the power fluid passes a small circuit through an additional hydraulic distributor 3 without performing useful work, is cleaned in filter 2, and discharged into tank 1.

Fig. 1. Hydraulic Skip Hoist Circuit Combined with the Hydraulic MTX-3000 Furnace Circuit: 1—hydraulic tank; 2—filter; 3—distributor; 4—hydraulic pump; 5—motor; 6—check valve; 7— safety valve; 8—pressure gage; 9—hydraulic distributors of the furnace; 10—hydraulic distributor of the skip hoist; 11—throttle; 12—double hydraulic lock; 13—discharge valve; 14—pressure gage; 15—telescopic hydraulic cylinder; 16—overturn hydraulic cylinders; 17—flow divider; 18—double hydraulic lock of the MTX-3000 furnace; 19—furnace throttle; 20—furnace hydraulic cylinders.

When any of the consumers is turned on, the fluid performs useful work passing through check valve 6 and turned on distributor 3. In the hydraulic system, a safety valve 7 is provided, which opens allowing fluid to bypass consumers when the rated operating pressure is exceeded. The charge is fed into the furnace by a feeder, on the pins of which a charging car (bin) is placed. The hoist is moved along the guides by a hydraulic drive consisting of a telescopic hydraulic cylinder and two overturn hydraulic cylinders. The charging bin rises and pours the charge into the furnace filling zone from the top through the furnace feeding hole, which opens using a hydraulic drive. A three-dimensional model of the furnace feeder with a hydraulic drive is shown in Fig. 2, and the principle of its operation is shown in Fig. 3.

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Fig. 2. Three-dimensional model of the furnace feeder with a hydraulic drive: 1—steel structure, 2—box, 3—guide roller, 4—the box base, 5—hydraulic cylinder.

Fig. 3. Skip hoist with a hydraulic drive operation scheme: a—starting position; b—lifting the bin; c—overturning the bin.

A single-acting multistage telescopic hydraulic cylinder (THC) is used to raise the bin. It is intended to ensure lifting and holding of the bin at a height of 4.5 m, as well as to feed the charge into the furnace. Lifting is carried out by supplying fluid to the

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workspace of the THC through a hydraulic distributor; a double hydraulic lock is used as protection against falling. Lowering is performed by gravity by switching the valve to the position opposite to lifting. The power fluid is returned to the tank through the throttle. In order to raise the bin, it is necessary to use a single-acting multi stage telescopic hydraulic cylinder of GL–19. MT1.175.150.130.110.5180.MP5.A. A type with a maximum rod stroke of 5180 mm [18, 19] has been chosen. In the extended state the hydraulic cylinder has 4 sections, which have the following length l i , external Di : and internal diameter d i : l 1 = 1300 mm, D1 = 130 mm, d 1 = 90 mm; l2 = 1300 mm, D2 = 220 mm, d 2 = 190 mm; l 3 = 1300 mm, D3 = 290 mm, d 3 = 260 mm; l4 = 1300 mm, D4 = 360 mm, d 4 = 330 mm. Technical specifications of the hoist: capacity, kg/h

1500–2000

feeder weight, kg

2500

load capacity, kg

500

the box lifting height, m

4.5

hydraulic system pressure, MPa

12

To estimate the economic efficiency of implementing the hydraulic drive hoist, a capital expenditure estimate has been drawn up, based on which it has been determined that the amount of capital investments is about 300 thousand rubles. The main economic effect expected from the implementation of the technical solutions proposed is associated with a reduction in power consumption. Prior to the upgrade, the company spent 2.1 million rubles to power. The upgrade proposed will reduce these costs by 920 thousand rubles that will favorably affect the company’s economy, considering the increase in power prices. As a result, the cost of one battery section reduces by about 0.1 rubles (0.02%), which ensures a significant economic effect at a production output of 11.5 million pieces. The costs of implementing the skip hoist with a hydraulic drive will pay off in 116 days from the start of the implemented equipment operation. These indicators prove the economic efficiency of the project developed.

5 Conclusion The design of a skip hoist to feed the furnace of the RIFAR CJSC casting complex has been developed, which has reduced power and operating costs. A skip hoist hydraulic system integrated with a hydraulic system of furnace has been developed. The main hydraulic system elements have been chosen, including a single-acting multistage telescopic hydraulic cylinder to lift the skip and double-acting hydraulic cylinders to overturn it. Calculations show that the implementation of design solutions does not require large capital expenditures and as a result of the measures proposed, the production cost will be reduced by 0.02%; the payback period of the investment project proposed will not exceed 4 months.

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References 1. Mazhirin E, Chichenev N, Zadorozhnyi V (2008) Modernizing the track units of the 2800 thick-sheet Mill at OAO Ural’skaya Stal. Steel Trans 38(12):1048–1050 2. Mazhirin E, Chichenev N, Zadorozhnyi V (2009) Extending the life of disk cutters for thick strip. Steel Trans 39(1):84–85 3. Zhiltsov A, Vishnevskiy D, Kozachishen V et al (2018) development of an algorithm and a computer program to calculate the equipment reliability and production risk in the metallurgical industry. Ferrous Metals 11:27–33 4. Gorbatyuk S, Kochanov A (2012) Method and equipment for mechanically strengthening the surface of rolling-mill rolls. Metallurgist 56(3–4):279–283 5. Chichenev N (2015) Import-replacing re-engineering of the drive of the rollers in the intermediate roller table of a continuous bloom caster. Metallurgist 58(9–10):892–895 6. Gorbatyuk S, Morozova I, Naumova M (2017) development of the working model of production reindustrialization of die steel heat treatment. Izv. Vysshikh Uchebnykh Zavedenij. Chernaya Metallurgiya 60(5):410–415 7. Eron’ko S, Gorbatyuk S, Oshovskaya E et al (2017) Development of automatic system of gasdynamic cut-off of slag for converter with rotating vessel shell. Izvestiya Vysshikh Uchebnykh Zavedenij. Chernaya Metallurgiya 60(11):863–869 8. Chichenev N (2018) Reengineering of the slab-centering unit of a roughing mill stand. Metallurgist 62(7–8):701–706 9. Gorbatyuk S, Zarapin A, Chichenev N (2018) Retrofit of vibrating screen of Catoca mining company (Angola). Min Inf Anal Bull 1:143–149 10. Gorbatyuk S, Zarapin A, Chichenev N (2018) Reengineering of spiral classifier of Catoca mining company (Angola) (2018) Min Inf Anal Bull 2018(2):215–221 11. Bardovskiy A, Gorbatyuk S, Keropyan A et al (2018) Assessing parameters of the accelerator disk of a centrifugal mill taking into account features of particle motion on the disk surface. J Friction Wear 39(4):326–329 12. https://exemer.ru/article/kompaniya-rifar-rifar_-rossiya.html. Accessed 6 Jan 2019 13. https://dspace.susu.ru/xmlui/bitstream/handle/0001.74/9748/2016_544_ibatullinaos.pdf? isAllowed=y&sequence=1. Accessed 6 Jan 2019 14. Kalyadin N, Mikaev S, Fisenko S (2017) Casting and melting complex datasheet. Gay, RIFAR, p 42 15. Pen’kov A, Kalyadin N, Mikaev S et al (2017) LKP–01 operating manual. RIFAR, Gay, p 136 16. Vdovin K, Mysik V, Tochilkin V et al (2016) Designing steelmaking workshops/textbook for universities. MSTU G.I. Nosov, Magnitogorsk, p 505 17. Nazemtsev A, Rybalchenko D (2007) Pneumatic and hydraulic drives and systems. In 2 Parts. Part 2. Hydraulic drives and systems: textbook. FORUM, Moscow, p 304 18. Model Range of Telescopic Cylinders with MT1+MP5 Fastening. Hydrolast (2019) https:// www.gidrolast.ru/produktsiya/gidrotsilindry/teleskopicheskie-gidrotsilindry/kreplenie-mt1 –mp5/teleskopicheskie-gidrotsilindry-gidrolast. Accessed 9 Jan 2019 19. Hydraulic Cylinders of HC Series. SUET (2019). https://www.suet-hydravlica.ru/catalogue/ hydraulic_cylinder/brand_GC.htm. Accessed 9 Jan 2019

Comprehensive Diagnostics of the State of Metallurgical Equipment S. N. Rednikov1(B) , E. N. Akhmedyanova1 , and D. M. Zakirov2 1 South Ural State University, 76 Lenin Avenue, Chelyabinsk 454080, Russia

[email protected] 2 State Aviation Technical University, 12, K. Marx str., Ufa 450008, Russia

Abstract. One of the ways to reduce production costs in the metallurgical industry is the organization of equipment maintenance according to its technical condition. Evaluation of the state of the equipment is possible by various methods, but one of the promising is the method of control of thermal fields of devices. The method of monitoring equipment temperature fields is not new and is often used in the diagnosis of metallurgical equipment. In more complex cases, when the body has a composite structure or inside the object there is a movement of liquid or gaseous media, a simple analysis of the external thermal fields is clearly not enough. With the known geometry of the installation, the initial temperature distribution, the dependence of the thermal conductivity of the material, the working medium and the known heat transfer coefficients at the boundaries of the shells, it is possible to determine the temperature fields in the apparatus at any time. A simplified method of calculation is proposed. Keywords: Sensors · Hydraulic · Vibrio diagnostic · Thermal equipment · Working fluids · Diagnostic measures · Emergency situation

1 Introduction A feature of the current state of metallurgical enterprises is a sufficiently high saturation of the old equipment, as the equipment were created more than 30 years ago and were designed taking into account long-term operation with timely maintenance and repair cycles (at a number of enterprises the share of this equipment is more than 60% [1, 2], and modern equipment designed over the past 5–10 years by foreign companies, and the features of the operation of this equipment at the enterprises of Russia by designers as a rule, were not taken into account [3]). Under these conditions, particularly acute issues of improving production efficiency by reducing the cost of repairs and maintenance of equipment while reducing downtime and reducing production costs. Equally important is the task of reducing accidents and possible harm to the environment.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_140

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2 Problem Analysis of major accidents shows that for the metallurgical industry, severe accidents associated with metal spills, accidents associated with long-term maintenance-free operation, non-compliance of materials with installation errors are more common [4–6]. These are the factors whose harmful effects can be significantly reduced with proper organization of diagnostic maintenance and repair [7]. No less urgent task is to optimize the supply of spare parts for metallurgical equipment. The formation of a fleet of spare parts only on the basis of the analysis of failure statistics is not always possible and appropriate; the method of expert evaluation is also not effective in the presence of fundamentally new equipment used in production [8]. One of the most effective methods in this regard is the method of assessing residual life by monitoring the diagnosed parameters of the system [9]. The importance of monitoring the condition of equipment by non-destructive testing and diagnostics has long been recognized by a vast majority of metallurgical enterprises [9, 10]. But the traditional division of responsibilities between the various services of the enterprise engaged in the repair and maintenance of technological equipment or elements of this equipment often complicates the process of assessing the real state of the object. In addition, it is not always advisable to equip each service with its own diagnostic kit of expensive equipment. One of the universal methods of monitoring the condition of metallurgical equipment is thermal imaging control (see Figs. 1 and 2). Its basis is the registration of temperature fields and heat fluxes by scanning the thermal imaging system.

Fig. 1. Detecting the defect.

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Fig. 2. a Thermogram; b current signal from an electromagnet distributor for intensive abrasive wear.

3 Solution Approach The method of monitoring equipment temperature fields is not new [11] and is often used in the diagnosis of metallurgical equipment. For relatively simple cases, such as duct condition monitoring, and for the quality of the protective lining, this is enough. Thermal imaging diagnostics are usually carried out in two stages, the first stage is obtaining temperature fields. The second processing of temperature fields and analysis of anomalies and defects. The second stage is the most important part and requires high qualification. At the second stage, the interpretation of images, determination of object temperatures and analysis of the causes of temperature deviation from the norm are carried out. To do this, determine the temperature of objects based on the results of thermal imaging and compare with standard temperatures or thermal fields, determine the cause of losses and temperature deviations from the norm. In more complex cases, when the body has a composite structure or inside the object, when there is a movement of liquid or gaseous media, a simple analysis of the external thermal fields is clearly not enough. Knowing the geometry of the installation, the initial temperature distribution and the dependence of the thermal conductivity of the material, the working environment, given that there is a process of heat transfer through a multilayer wall with a known thermal conductivity of materials of all layers, with known heat transfer coefficients at the boundaries of the outer and inner shells, it is possible to determine the temperature fields in the apparatus and the internal volume of the medium at any time. This approach makes it quite easy to determine the temperature fields, to obtain the values of the temperature change of the liquid medium at the boundary of the inner surface of the body, both at the stage of stabilization and when the liquid moves in a particular zone of the system. In addition, the problem of determining the amount of heat passing through the wall zone is solved simultaneously. The disadvantage of this approach is a high delay, determined by the rate of heat transfer in the material, in addition, the approach requires high accuracy of temperature determination, not less than tenths of a degree, to estimate the temperature of the medium to be studied with accuracy to a degree. The solution of two- and three-dimensional heat conduction equations by modern computing systems has been repeatedly described in [1, 8–10]. For an axisymmetric problem, a solution in a cylindrical coordinate system is often sufficient. The system of equations in this case

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can be presented in the classical version: (1 − s)ρk ck

 2  ∂ t ∂tk 1 ∂t = αv (T − t) + λe + ∂τ ∂R2 R ∂R (−s)ucg

∂T = αv (T − t) ∂x

(1) (2)

boundary condition τ = 0; t = t(x, R) ∂t = 0; T = Tg ∂R ∂t =0 x = H; ∂x R = 0;

R = R; k(t − tb ) = λe

∂t ∂R

where: αv —given heat transfer coefficient; s—parameter of the direction of heat flow; ρk ck —density and heat capacity of the material; λe—thermal conductivity of the material; cg —heat capacity of the gas at the border; k—heat transfer coefficient to the environment; R,Rn —respectively, current and external radii; H —height; t—material temperature; u—coolant velocity; tb —ambient temperature; T ,Tg —coolant temperature at the border; τ —time.

4 System of Current Diagnostics The creation of systems for continuous non-contact diagnostics and monitoring of the state of the intermediate ladle and power drive units is a very urgent task [11]. Since hydraulic systems are often used as drives, while the conditions of their operation are significantly different from those adopted in the general machine-building practice [12, 13], the development of methods for their diagnostics is actual [14]. Hydraulic resistance of the unit is checked usually only once at normal temperature [15]. Before testing and after testing, the rubbing parts of the spool are subjected to micro-measurement. The difference in measurements makes it possible to judge its wear and tear. This approach requires expensive equipment and significant time-consuming costs. At the same time, any change in the state of the sleeve pair—the slide valve—causes a change and forces on the electromagnetic system [16]. Fixing the change in force is quite possible by evaluating the current signal on the electromagnet of the distributor when it is turned on (see Figs. 2 and 3). As a rule, the increase in the force of friction of the spool of the hydraulic distributor is connected. • With the action of high pressure in the lines of force created by the pressure source and resulting in an increase in the concentration of wear particles in the gaps of the spools;

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• Effects of the forces of dry friction of the spool on the body at the time of its failure [17]; • Residual magnetization of the armature of the electromechanical converter in the magnetic fields of the control electromagnets. By fixing and analyzing the current signals from the electromagnets of the valves, the authors of the work were able in a number of cases to determine the causes of the failures of the aggregates.

Fig. 3. Regular work of the distributor.

5 Method of Solution The problem is solved by iteration. If the problem is formulated as a problem of determining the residual thickness of the insulation layer, then at a known intensity of heat transfer and known conditions of heat removal, the calculation is made before determining the temperature on the outer surface of the wall; in contrast to the actual temperature of the object, the thickness of the insulation is adjusted and the calculation is repeated until the required accuracy is achieved. If the solution of the equation of heat conductivity in itself does not cause complexity, then the determination of the intensity of heat transfer to a wall from the heat carrier in case of movement of the liquid medium in the presence of phase transitions or the two-phase environment represents the very actual problem. The used empirical methods of calculation give the accuracy of determining the intensity of heat transfer in the range of 15–20%, which does not provide the required accuracy [18]. Thermal control methods increase the efficiency of use is possible due to the integration of the temperature field control system on the surface of the device and calculation complexes for finding the temperature distribution in the volume of the object under study. This will allow estimating the condition of metallurgical equipment elements with minimum cost and high reliability. The proposed method of non-contact diagnostics of electrohydraulic distributors of drive systems of a stopper is highly visible and reproducible and can be used as one

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of the methods of preliminary diagnostics. The combination with television methods makes it possible to significantly increase the reliability of predicting the state of the hydraulic actuators of the intermediate ladle stopper. The use of combined diagnostic methods allowed not only to reduce by 30–70% the time of troubleshooting, but also allowed to increase the accuracy of failure forecasts.

References 1. Brovman MJ (2007) Nepreryvnaja razlivka metallov (Continuous casting of metals). Izdatel’stvo Jekomet, p 484 2. Kashheev ID (2004) Svojstva i primenenie ogneuporov. Teplotehnik, Moscow, Spravochnoe izdanie (Properties and application of refractories), p 352 3. Kazancev EI (1975) Promyshlennye pechi. Spravochnoe rukovodstvo dlja raschetov i proektirovanija (Industrial furnaces. Reference guide for calculation and design). Moscow, p 368 4. Krivandin VA, Filimonov Ju P (1986) Teorija konstrukcii i raschety metallurgicheskih pechej (Theory of construction and calculations of metallurgical furnaces) “Metallurgija”, Moscow, p 479 5. Lisienko VG, Lobanov VI, Kitaev BI (1995) Teplofizika metallurgicheskih processov (Thermophysics of metallurgical processes). Moscow, p 240 6. Mastrjukov BS (1978) Teorija, konstrukcii i raschety metallurgicheskih pechej. Tom 2. Raschety metallurgicheskih pechej (Theory, designs and calculations of metallurgical furnaces, vol 2. Calculations of metallurgical furnaces). Moscow, p 272 7. Plahtin VD (1983) Nadezhnost, remont i montazh metallurgicheskih mashin (Reliability, repair and installation of metallurgical machines). Moscow, p 415 8. Smirnov AN, Piljushenko VL, Minaev AA, et al (2002) Processy nepreryvnoj razlivki Monografija (Continuous casting processes). Doneck, p 536 9. Grebenik VM, Ivanchenko FK, Pavlenko BA et al (1991) Mehanicheskoe oborudovanie metallurgicheskih zavodov. Mehanicheskoe oborudovanie konverternyh i martenovskih cehov (Mechanical equipment of metallurgical plants. Mechanical equipment of converter and open hearth shops). Kiev, p 287 10. Pavlova GA (2011) Statisticheskij analiz avarij i travmatizma na metallurgicheskih predprijatijah (Statistical analysis of accidents and injuries at metallurgical plants) Internet-zhurnal “Tehnologii tehnosfernoj bezopasnosti". https://ipb.mos.ru/ttb. Accessed 10 Jan 2020 11. Alekseeva TV, Babanskaja VD, Bashta TM et al (1989) Tehnicheskaja diagnostika gidravlicheskih privodov (Technical diagnostics of hydraulic actuators). Moscow, p 264 12. Bataev VA (2007) Metody strukturnogo analiza materialov i kontrolja kachestva detalej (Methods of structural analysis of materials and quality control of parts). Moscow, p 224 13. Zedginidze IG (1976) Planirovanie jeksperimenta pri issledovanii mnogokomponentnyh system (Planning an experiment in the study of multicomponent systems). Moscow, p 390 14. Sherkunov VG, Rednikov SN, Vlasov AE et al (2016) Matematicheskoe modelirovanie processov nanesenija gal’vanicheskih pokrytij pri razlichnyh skorostnyh rezhimah (Mathematical modeling of galvanic coating deposition processes at different speed modes). Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im. G. I. Nosova 14(2):101–106 15. Rednikov SN, Muromcev NN (2011) Opredelenie temperatury issleduemoj sredy pri vysokih davlenijah (Determination of the temperature of the medium under study at high pressures). Izvestija Samarskogo Nauchnogo Centra Rossijskoj Akademii Nauk 13(1–3):620–622

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16. Rednikov SN, Rahmatullin BB (2012) Metodika jekspress diagnostiki uzlov gidravlicheskih system (The method of express diagnostics of hydraulic system units). Dinamika mashin i rabochih processov: sbornik dokladov Vserossijskoj nauchno-tehnicheskoj konferencii. Izdvo JuUrGU, Cheljabinsk, p 267 17. Fominyh AV, Chinjaev IR, Shanaurin AL et al (2016) Truboprovodnaja armatura kak osnova sistem passivnoj zashhity (Pipe fittings as the basis of passive protection systems). Armaturostroenie 4:58–63 18. Rednikov SN, Zakirov DM, Platov SI et al (2018) Complex diagnostics of metallurgical equipment. Magnitogorsk, p 75

Research of a Mathematical Model of a Pneumatic Actuator with Energy Recovery A. N. Sirotenko(B) and S. A. Partko Don State Technical University, 1, Gagarin area, Rostov-on-Don 344000, Russia [email protected]

Abstract. An energy-saving pneumatic drive with energy recovery is considered in the paper. Energy is recovered into some additional volume during the output link braking by counterpressure. A mathematical model of the pneumatic drive dynamic processes is considered. The output link motion equation and the dependence of pressure in the pneumatic motor chambers during the counterpressure braking are given. The initial additional volume parameters are dwelt upon. Further, the authors provide a pneumatic circuit diagram of a pneumatic drive with the recovery of braking energy into an additional volume. To ensure operating flexibility, the initial additional volume parameters can be preset. The possibility of using recovered energy when reversing the output link motion is schematically implemented. The mathematical model is investigated for stability. The Jacobi matrix of an autonomous nonlinear system of equations is constructed, the characteristic equation is obtained, and practical testing is conducted. Keywords: Pneumatic drive · Recovery · Counterpressure · Mathematical model · Dynamics · Stability

1 Introduction Pneumatic drives are widely used in various industries. This is due to the operational simplicity and accessibility of the power medium. However, the issue of energy saving in pneumatic drives remains relevant [1, 2], which has led to a wide range of ways to reduce their energy costs [3–6]. The technique of braking the inertial output link by counterpressure with the recovery of the compressed air energy into the exhaust chamber is of greatest interest [1, 3, 7]. The technique allows accumulating the compressed air energy during braking and using it in a further operation cycle. However, a significant volume of air in the pneumatic motor chambers, its compressibility, and instability of characteristics complicate the design calculations and, ultimately, limit the speed that negatively affects the response [3]. In addition, the output link rebound is inevitable, which complicates the positioner and requires the introduction of special built-in and external braking devices to ensure a fixed stop and end-of-stroke dwell [3, 8–10].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_141

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The Research Objective is to propose a hardware design of a technique that allows adjusting the recovery parameters during counterpressure braking and a mathematical model describing the dynamic characteristics of a pneumatic drive. 1.1 The Main Part of the Research To increase the operating flexibility of the equipment and expand the braking force regulation range during counterpressure braking, an additional volume has been connected to the exhaust chamber with preset initial parameters—pressure and additional volume (Fig. 1). The pneumatic drive operates as follows: before starting, all the elements are in the positions shown in the diagram. The initial pressure values in the rod and piston ends of the pneumatic cylinder (PC) are equal to the main and atmospheric pressure, respectively. The command to start motion is sent via the channel by switching D3 control valve spool to the extreme left position; the compressed air from the main is supplied through D4 end valve spool and switches D5 pilot of D1 control valve to maximum up position. D1 valve spool will move to the extreme right position starting acceleration of the output link of the pneumatic cylinder. Acceleration continues until D7 travel control valve trips giving a command to start braking the actuator. D1 valve spool will move to the “neutral” position and the piston and rod ends of the pneumatic cylinder PC will be cut off from the main and the atmosphere, respectively. D5 pilot and D1 valve spools will return to their original positions, and D10 pilot spool will take its maximum up position and switch D2 valve spool to the extreme left position. The brake chamber of the pneumatic cylinder PC will be connected to the additional volume AV with preset initial parameters. From this moment, braking starts with the recovery of the compressed air energy into the additional volume. The initial additional volume parameters (pressure and volume) and the point of switch to braking have been chosen to stop the pneumatic cylinder PC rod in the given point. At this moment, the output link kinetic energy will be converted into the potential energy of the air compressed in the brake chamber and the additional volume. The pressure difference between the pneumatic cylinder PC rod and piston chambers will cause the reverse motion of its output link. The motion lasts until all recovered energy is used. Then, D8 travel valve will trip and the additional volume will be disconnected from the rod chamber of the pneumatic cylinder PC by switching D10, D6, and D11 control pilots to the respective maximum up and down positions. D2 valve spool will switch to the extreme left position and connect the additional volume AV chamber with the pressure reducing valve RV, through which it will be filled from the main until the initial pressure setting is reached. D1 valve spool will move to the extreme right position and connect the rod end of the pneumatic cylinder with the main and the piston end with the atmosphere. The motion will continue until D4 end valve trips. Then, the cycle repeats. By varying the initial additional volume parameters—pressure and volume—we achieve their balanced combination to ensure maximum response and reduce the power consumption of the pneumatic drive without changing the position of D7 and D8 end

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valves. This increases the technological capabilities of the equipment when reconfiguring the other operating modes. ⎧  2 ⎪ mn ddt 2x = pp · Fn − P0 − pb · Fb (1.1)  ⎪ ⎪ k   ⎪ ⎪  ⎪ n ⎨ pp = xx01 +x · p (1.2) pn  +x 02 

 ⎞k ⎛ (1) 1 1  ⎪ (s+x02 −x)(pbn ) k +h (pak ) k  ⎪ ⎪ ⎪ ⎠ (1.3)  ⎪ ⎪p = ⎝ (s+x02 +h−x) ⎩ 

Fig. 1. Pneumatic drive with energy recovery, principal circuit.

The large and varying volumes of air do not allow a simplified solution to the issue of calculating the braking parameters and require the use of numerical integration techniques [7, 11, 12]. The mathematical model describing the dynamic characteristics of a pneumatic drive consists of two parts. The first one describes the acceleration of the pneumatic drive output link and is known [7]. The second system (1) describes the pneumatic drive dynamics during the counterpressure braking, considering the initial additional volume parameters [13, 14]. The volumes of the brake and piston chambers of the pneumatic drive have finite values and therefore, changing pressure in them can be described by the equations of thermodynamics: pressure change in the discharge chamber (1.2); pressure change in the brake chamber (1.3). Only the equation of motion (1.1.) remains in the differential form: here, mn is the reduced mass of the moving parts, kg; F n , F b are effective piston and rod areas of the pneumatic cylinder, respectively,

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m2 ; pa , pp , pb are the values of absolute pressure in the atmosphere and the working and exhaust ends of the pneumatic cylinder, Pa; pak is the absolute initial additional volume pressure, Pa; p is the absolute current pressure in the additional volume already connected to the exhaust end of the pneumatic cylinder, Pa; x is the current stroke of the piston in the pneumatic motor, m; s is the maximum piston stroke, m; x 01 , x 02 are the “passive volume” values reduced to the working areas of the piston and rod ends of the pneumatic cylinder, m; t is the time of stroke, s; P0 is the friction force, N; k is the adiabatic exponent; pbn , ppn are the initial pressure values during braking in the exhaust and discharge chambers of the pneumatic cylinder, respectively, Pa; x n is the coordinate of switching to braking, m; and h is the geometric additional volume reduced to the effective rod area of the pneumatic cylinder, m. The adequacy of the mathematical model provided has been confirmed by the characteristic coincidence of dynamic dependences and Fisher’s Exact Test [15]. Let us evaluate the stability of the system of Eqs. (1) describing the work process of the pneumatic drive braking. We transform the equation of the pneumatic cylinder piston motion (1.1) by the following substitutions and replacements: x1 = x01 ; x2 = x02 ; A = (x1 + xn )k × ppn C=

−P0 Fn −Fb ;B = ;E = ; mn + kB mn mn

1 −kb ; PG = (pbn ) k ; N = (s + x2 ) × PG; mn 1

M = h × (pak ) k ; PP = s + x2 + h After substituting these changes made into the equation of pneumatic cylinder output link motion (1.1), we obtain the system of equations: ⎧ ⎨ dx = y; dt k  (2) (N −PG×x+M ) A ⎩ dy = B × sign y + C × y + E × + (x +x) k; dt PP−x 1

We equate the right-hand sides of the resulting system (2) to zero and after the transformation, construct the Jacobi matrix of an autonomous nonlinear system of equations:   k (N − PG × x + M )k−1 · (N + M − PG × PP) −A× × F = k ×E (PP − x)k+1 (x1 + x)k+1 If: y > 0, then, Δ = B + C. y < 0, then, Δ = –B + C. y = 0, then, Δ = C. If all the eigenvalues of the Jacobi matrix have negative real parts, the equilibrium state (x, y) of the autonomous nonlinear system is asymptotically stable according to Lyapunov at t → ∞ [16–18].

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Let us construct the characteristic equation: det|F − λ × 1|:  −λ k ×E×

(N −PG×x+M )k−1 ×(N +M −PG×PP) (PP−x)k+1

−A×

k (x1 +x)k+1

1



× ;  − λ

where 1 is the unit vector. The characteristic equation has the form: k −k ×E (x1 + x)k+1 (N − PG × x + M )k−1 × (N + M − PG × PP) × (PP − x)k+1

λ2 −  × λ + A ×

We denote z =A·

k (N − PG · x + M )k−1 · (N + M − PG · PP) − k · E · (x1 + x)k+1 (PP − x)k+1

Then:  = 2 − 4 · z. We denote the model parameters: 1 Fn −P0 −Fb ; B= ; E= ; PG = (pbn ) k ; mn mn mn 1 −kb N = PG · (s + x2 ); C = ; M = h · (pak ) k ; pp = s + x2 + h mn

A = (x1 + xmn )k · ppn ·

Considering the pneumatic system parameters [15], we obtain the numerical values of the model parameters: A = 2.33; B = −2.65; D = 0; E = −1.24 × 10−5 ; PG = 6.12 × 103 ; N = 3.06 × 103 ; M = 1.5 × 103 ; PP = 0.6 To determine the system equilibrium, we find the polynomial root f(x): f (x) = A × (PP−x)k + (x1 + x)k × (PP − x)k + E × (N + M −PG × x)k × (x1 + x)k Let us introduce the initial value of the polynomial root f(x): x = 0.01. The polynomial root search function has the form: r = root(f(x),x) = 0.38. The stability condition will take the form: (N + M − PG · PP) k − k · E · (N + M − PG · r)k − 1 · ; k+1 (x1 + r) (PP − r)k+1  = C 2 − 4 · zz;  ≺ 0;  = C;  = −2.94 · 10−3

zz = A ·

The system of equations is equilibrium and stable, since  < 0. The result obtained allows proceeding to a computational experiment to determine the balanced additional volume parameters [19–21].

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2 Conclusions A hardware design allowing the recovery of the compressed air energy during the pneumatic drive output link braking by counterpressure has been proposed. The solution considers the case of using a single-rod pneumatic cylinder when reversing its movement with a payload. Therefore, two travel control valves D7 and D8 have been introduced in the circuit. When reversing without a payload, e.g., in the case of a pusher pneumatic cylinder, the circuit is simplified. The ability to vary the initial additional volume parameters ensures operating flexibility and allows rationally solving the issues of response and energy saving in the pneumatic drive without reconfiguring the travel valve positions. The stability of the mathematical model of the proposed pneumatic drive dynamic processes has been confirmed, which allows using it in the general system of equations to describe and analyze the braking process dynamics and assess the recovery rate.

References 1. Yusop MY (2006) Energy Saving for Pneumatic Actuation using Dynamic Model Prediction. Cardiff University, Wally 2. Krytikov G, Strizhak M, Strizhak V (2017) The synthesis of structure and parameters of energy efficient pneumatic actuator Eastern-European. J. Enterp Technol 7(85):38–44 3. Filipov IB (1987) Deceleration Devices of Pneumatic Actuator. Machine-building, Leningrad 4. Blagojevic VA, Jankovic PL (2016) Advantages of restoring energy in the execution part of pneumatic system with semi-rotary actuator. Therm Sci 20(5):1599–1609 5. Al-Dakkan KA, Barth EJ, Goldfarb M (2006) Dynamic constraint-based energy-saving control of pneumatic servo systems. J Dyn Syst Meas Contr 128:655–662 6. Rahmat MF et al (2011) Review on modeling and controller design in pneumatic actuator control system. Int J Smart Sens Intell Syst 4(4):630–661 7. Hertz EV (1985) Dynamics of Pneumatic Systems of Machines. Machine-building, Moscow 8. Dao TA, Sidorenko VS, Dymochkin DD (2015) Study on positioning accuracy of automated pneumatic drive with an outer brake. Vestn Don State Tech Univ 15(4):46–53 9. Grishchenko VI, Kilina MS, Chernavskiy VA (2012) Positioning dynamics of drive gears with hydroabsorber. Vestn Don State Techn Univ 12(4):16–21 10. Obukhova, E.N., Grishchenko, V.I., Dolgov. G.A.: Formalization of Dynamic Model of Pneumatic Drive with Variable Structure. MATEC Web of Conferences, 02022. https://doi.org/10. 1051/matecconf/201822602022 (2018) 11. Sirotenko, A.N., Partko, S.A.: Calculation of Dynamic Parameters of Pneumatic Hydraulic Drive with Energy Recovery. Certificate of registration of the computer program, RUS 2018613130 RF, 10.01.2018 (2018) 12. Sirotenko, A.N., Partko, S.A.: Calculation of Dynamic Characteristics of PneumaticMechanical Drive. Certificate of registration of the computer program, RUS 2018663925 RF, 15.10.2018 (2018) 13. Sirotenko AN, Partko SA, Salloum W (2018) Effect of recuperative volume parameters on dynamic characteristics of pneumatic drive underbraking. Vestn Don State Techn Univ 18(4):379–384. https://doi.org/10.23947/1992-5980-2018-18-4-379-384 14. Sirotenko AN, Partko SA (2017a) Mathematical model of dynamic processes of pneumatic drive during braking by reverse pressure, with recovery of energy into additional volume. Sci Rev 21:67–74

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15. Sirotenko AN, Partko SA (2017b) Decrease in power inputs in pneumodrive weighing-andpacking machine. Int J Appl Eng Res 12(14):4599–4603 16. Demidovich BP (1967) Lectures on Mathematical Stability Theory. Science, Moscow 17. Stability by Liapunov’s direct metbod (1961) With Applications. Acad. press, Joseph La-Salle and Solomon Lefschetz, New York-London 18. Partko, S.A., Groshev, L.M., Sirotenko, A.N.: Finding Stable Region of Torsional Vibrations of Agro-industrial Rotary Cultivators. Proceedings of the 5th International Conference on Industrial Engineering (ICIE 2019). Lecture Notes in Mechanical Engineering. Springer International Publishing AG, (2019) 19. Sirotenko, A.N., Partko, S.A.: The influence of initial parameters of pneumatic accumulator on the dynamic characteristics of the actuator during braking back pressure. J. Phys. Conf. Ser. 1399(4), 044098(1–6) (2019) https://doi.org/10.1088/1742-6596/1399/4/044098 20. Sirotenko AN, Partko SA, Saed BA (2017) Dependence of energy-speed characteristics of pneumatic drive on initial parameters of additional volume under counterpressure braking. Vestn Don State Techn Univ 17(4):69–76. https://doi.org/10.23947/1992-5980-2017-17-469-76 21. Sirotenko, A.N., Partko, S.A., Voinash, S.A.: Research of Pneumodrive with Energy Recovery into Additional Volume. Proceedings of the 5th International Conference on Industrial Engineering (ICIE 2019), vol. II, pp. 1325–1333. Lecture Notes in Mechanical Engineering. Springer International Publishing AG (2019)

Adaptive Vibration Protection Systems for Pipelines K. V. Naigert1(B) and V. A. Tselischev2 1 South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, Russia

[email protected] 2 Ufa State Aviation Technical University, 12, K. Marx Street, Ufa 450008, Russia

Abstract. Vibration protection is required to preserve the integrity of pipeline systems and the homogeneity of the transported environment. The improving efficiency of mechanical energy dissipation needs an organization of feedback; it is possible through the workflow automation of vibration protection. Automation is technically difficult to implement. The mechanical systems and mechanical and hydraulic vibration damping devices use electromechanical transducers of electrical control signals, which are expensive and possess inertia of moving masses and low dynamic characteristics. Therefore, the implementation of magnetorheological and ferrofluid systems greatly simplifies the organization of automatic control; it allows engineers to create autonomous and adaptive vibration protection systems and preserves many advantages of hydraulic supports, but exceeds them in dynamic characteristics. The text describes the way of vibration protection by generating acoustic waves and oscillations in the antiphase mode to mechanical shock and vibration loads. The article presents two original patented designs that give the opportunity to realize damping and vibration damping protection by the antiphase mode. Numerical dependencies of frequency and phase characteristics of control signals are presented. These dependencies are required for generating regulatory acoustic waves and oscillations. An algorithm of the control signal generation and feedback organization in magnetorheological and ferrofluid vibration protection systems is proposed. A numerical experiment is carried out; the results confirm the effectiveness of vibration protection by way of generating regulatory acoustic waves and oscillations in the antiphase mode to shock waves and vibrations at mechanical loads on pipelines. Keywords: Automation vibration damping devices · Acoustic waves · Oscillations · Ferrofluid

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_142

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1 Introduction Automation of technological processes in petroleum, chemical, and pharmaceutical industries requires the creation of large-scale pipeline systems for various purposes. Pipelines need protection from mechanical loads; therefore, in many cases, it is advisable to implement vibration protection and vibration isolation of technological piping systems. The most common application problem is vibration protection, which is related to the oscillations of structures at high-speed fluid flow. In case of external mechanical loads on pipelines, vibration isolation is realized; it is highly relevant in seismic zones. It is obvious that the design and hardware/program implementation of their control depend on the purpose of vibration protection systems. In case of pipelines’ protection from their own vibrations, the use of presetting systems is possible. But vibration isolation needs adaptive supports with control in real time; consequently, adaptive vibration isolation and vibration protection systems must be developed [1–7].

2 Actuality of the Research The maintaining of technological objects’ integrity is an important applied and research task, but vibration isolation and vibration protection have more essential applications in the technological processes. For example, vibration protection of trunk pipelines prevents the falling out of paraffin fraction of oil, or vibration isolation and vibration protection of technological lines preserve molecules of the transported environment from mechanical destruction. The development of adaptive vibration protection systems for pipelines and improvement of control algorithms are relevant.

3 Statement of the Problem This research is dedicated to developing new design solutions and automated control algorithms for adaptive vibration protection systems for pipelines, which are able to optimize their workflows and to increase the efficiency of energy dissipation of mechanical loads.

4 Constructive Solution of the Problem Depending on the functional features of developed systems for vibration isolation and vibration protection, two original patented design solutions are proposed: an adaptive combined rheological damper (Patent RU 175,044) [8] and a ferrofluid active protection device for large-scale structures’ protection from resonant vibration (Patent RU 185,538) [9]. A distinctive feature of the workflow of the adaptive combined rheological damper is the creation of inhomogeneous distributed dissipative/rigidity properties of the working chamber; it is implemented by a cascade of electromagnets. Design features of the adaptive combined rheological damper, and methods of calculation of its performance, were previously published in the papers [8, 10–12]. The way to create a ferrofluid oscillator and methods of calculation of its geometric and functional parameters were

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published in [9, 13]. This way is based on the ferrofluid active vibration protection device design. An obvious advantage of magnetorheological and ferrofluid systems is the simple organization of regulation in real time and feedback, because the electrical control signals on the electromagnets do not require the transformation of electrical energy into other forms of energy. This simplifies the control and signal correction algorithms and makes magnetorheological and ferrofluid systems ideal for technological process automation.

5 Control Algorithm of Adaptive Vibration Protection Systems for Pipelines Control algorithms for adaptive vibration isolation and vibration protection systems primarily depend on the desired rate of mechanical energy dissipation. Most hydraulic and magnetorheological supports produce the viscous dissipation of mechanical energy, but it is obvious that the suppression of vibration and shock loads is possible to organize by the generation of control acoustic waves and oscillations in the volume of magnetorheological fluid and ferrofluid. In the developed designs of adaptive vibration isolation and vibration protection systems, several principles of suppressing vibrations are applied. The use of the adaptive combined rheological damper allows the damping by the creation of inhomogeneous distributed dissipative/rigidity properties of the working chamber and by the generation of acoustic waves in the antiphase mode to mechanical shock and vibration loads. Ferrofluid active vibration protection devices have preferred modes of operation; that is either generation of oscillations, which lead to an increase in the natural frequency of pipelines and to a shift of natural frequency of pipelines in relation to disturbing frequency, or the creation of oscillations with the ferrofluid oscillator, which coincide with damped frequencies, but are in the antiphase mode to them. The absence of mechanical moving elements in the similar devices and of inertial effects allows an increase in the speed of control signal processing and the reduction of accuracy errors to valid values. The formation of control and correction signals needs the creation of a numerical model of parametric characteristics of signals. The numerical model of inhomogeneous distributed dissipative/rigidity properties of the working chamber of the adaptive combined rheological damper is described. The propagation of control acoustic wave velocity in the volume of the magnetorheological chamber can be determined by expressions [14, 15]:   H 2 = Ha2 sh2 kx + sin2 (kz − ωt) , ρ

∂v 1 = −cf2 ∇ρ  + μ0 χ ∇H 2 + ∇ηv ∂t 2  ∂ρ  ηs  ∇(∇v), + ρ divv = 0, + ∇ ηv + 3 ∂t vz = vza cos[2(kz − ωt) + ϕvz ].

(1)

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The parameters are written as vza =

   ω Am ρ · k 

1/ 2 ω 2 2 2 2 2 cf − + 4ω bm k

,

Ha = B0 /μ0 (1 + χ )shkl, Am = μ0 χ Ha2 /4,    bm = ηv + 4 3 ηs /ρ, 2bm ω   2 , − ωk

 1 τn M (H ) τsh ηs = . + ηv + · γ˙v 4 1 + (τn τs HM (H ))/J

tgϕvz =

cf2

(2)

H —magnetic field strength, k—wave vector, cf —sound speed in the magnetorheological fluid, l—volume height of magnetorheological fluid in the working chamber, ϕvz —difference of phases, τsh —shear stress, J —moment of inertia, τn ; τs —relaxation times of non-magnetic and magnetic particles, γ˙v —velocity gradient, ηv —bulk viscosity, χ —magnetic susceptibility, x; z—coordinates, ω—frequency, t—time, μ0 — magnetic permeability, v—velocity, η—viscosity, M — magnetization, B0 —magnetic induction, ρ—density, ρ  —deviations from initial values. The numerical model of control signals of the ferrofluid active protection device for large-scale structures’ protection at resonant vibration takes the form as follows. Fluctuations of ferrofluid volume are calculated by [16–20] m¨z + ς z˙ + c(t)z = F sin ωt, z¨ + 2θ z˙ + ω2 z = Fr sin ωt,  c c F ,ω = . Fr = , θ = m 2m m

(3)

m—mass of volume, c—coefficient of proportionality, which is characterized by restoring force, z˙ —oscillating velocity of mass,¨z —oscillating acceleration of mass,ς — liquid friction coefficient,F—disturbing force. Displacement of the oscillator can be solved as: z = Fm sin(ωt + ϕ0 )

(4)

Fm —amplitude of disturbing force, ϕ0 —initial phase. Velocity of displacement of the oscillator is  π (5) vos = Fm ω cos(ωt + ϕ0 ) = Fm ω sin (ωt + ϕ0 ) + 2 Acceleration of displacement of the oscillator is: aos = −Fm ω2 sin(ωt + ϕ0 ) = Fm ω2 sin[(ωt + ϕ0 ) + π ]

(6)

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The frequency of the ferrofluid oscillator is formed by the frequency of a control signal on the windings of the electromagnetic control unit. The formation of correction signals is based on the scanning of vibration sensors. An algorithm of the formation of control and correction signals is proposed in Fig. 1.

Fig. 1. Algorithm of formation of control and correction signals in the magnetorheological and ferrofluid vibration protection devices.

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6 Sensor Installation and Error Estimate for Automated Control Systems In case of vibration isolation of pipelines, the piezoelectric vibration sensors are set on the supports; they register the acceleration of the plunger of a vibration isolation device. Vibration protection demands the tracking of pipelines’ acceleration, therefore, the piezoelectric vibration sensors are set on the protected area of a pipe. Temperature sensors are integrated into the working chambers. The dynamic measurements of parameters are carried out in accordance with the time intervals, which depend on the structural and functional features of sensors. Considering the large size of the damped object and the permissibility of small values of multidirectional displacements of the pipeline, high precision of vibration protection operation is not required. The high speed response to control signals in the magnetorheological and ferrofluid devices and their good dynamic characteristics (transients are less than 200 ms) allow the calculations of the control signal on the base of results of dynamic polling of vibration sensors. The electrical signal on the control units (electromagnets) does not require transformation, and the feedback signal of vibration sensors is an electrical signal too, therefore, the simple implementation of a control signal correction is possible; for example, the setting of the control signal during the correction is proportional to the change of the feedback signal. Regulation is performed by the modulation of current–voltage and frequency-amplitude characteristics of the control signal in relation to parameters of the feedback signal at the dynamic polling of vibration sensors.

7 Calculation Results The modeling of workflows of the adaptive combined rheological damper and ferrofluid active vibration protection device is carried out. Consider the case when the velocity of a shock wave and vibration load obey the sinusoidal law. A numerical experiment of shock and vibration loads’ suppression by regulatory acoustic wave and oscillations was realized in MATLAB, Figs. 2 and 3. The way of suppression of the shock wave propagation is organized by the generation of a regulatory acoustic wave in the antiphase mode to the shock wave, Fig. 2. The obtained resulting dependency illustrates the high efficiency of the proposed way of the shock wave suppression. Figure 3 presents the process of vibration damping (oscillation damping) by means of regulatory oscillations. Similar to the previous resulting dependency, the obtained resulting dependency confirms the appropriateness of the application of the antiphase mode. The results of the numerical experiment verify the ease of implementation and high efficiency of application of adaptive magnetorheological and ferrofluid devices in the automated vibration protection systems for pipelines and prove the feasibility of the use of the antiphase mode in the automated vibration protection systems.

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Fig. 2. Velocity characteristics of adaptive combined rheological damper: 1—shock wave, 2— regulatory acoustic wave, 3—resulting dependency.

Fig. 3. Displacement characteristics of ferrofluid active vibration protection device: 1—oscillations, 2—regulatory oscillations, 3—resulting dependency.

8 Novelty, Practical and Scientific Significance of Research Developed patented original designs of adaptive vibration protection devices for pipelines apply the effects of the distribution of dissipative/rigidity properties in the working chamber and ferrofluid oscillations for mechanical energy dissipation and resonance prevention [8, 9]. The control algorithm and numerical dependencies of control signals are proposed for the adaptive combined rheological damper and the ferrofluid active vibration protection device.

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9 Conclusions The presented ways of vibration protection of pipelines, their constructive implementation, and control algorithms are effective and provide high accuracy. The proposed adaptive vibration protection devices are able to work autonomously and to regulate the process of mechanical energy dissipation in real time. The use of these original devices greatly simplifies the automation process of vibration protection for pipelines in petroleum, chemical, and pharmaceutical industries. The results of the numerical experiment confirm the vibration and shock suppression efficiency of patented original adaptive vibration protection devices.

References 1. Burchenkov VN et al (2000) Magnitozhidkostnoye ustroystvo dlya gasheniya kolebaniy (Magnetorheological device for vibration damping). RU Patent. 2145394:10 2. Korchagin AB et al (2012) Reguliruyemyy magnitoreologicheskiy pnevmaticheskiy amortizator (Adjustable magnetorheological pneumatic damper). RU Patent. 2449188:27 3. Gusev EP, Plotnikov AM, Voevodov SYu (2003) Magnitoreologicheskiy amortizator (Magnetorheological shock absorber). RU Patent. 2232316:27 4. Kudryakov YuB et al (1998) Magnitoreologicheskiy vibrogasitel’ (Magnetorheological vibration damper). RU Patent. 2106551:10 5. Yamanin IA et al (2009) Dinamicheskiy gasitel (Dynamic absorber). RU Patent. 2354867:10 6. Mikhailov VP et al (2012) Magnitoreologicheskaya pozitsioniruyushchaya i vibroizoliruyushchaya sistema (Magneticoreological positioning and vibrational insulation system). RU Patent. 2443911:27 7. Gordeev BA et al (2015) Magnitoreologicheskiy amortizator (Magnetorheological damper). RU Patent. 2561610:27 8. Naigert KV, Tutynin VT (2017) Adaptivnyy kombinirovannyy reologicheskiy amortizator (The adaptive combined rheological damper). RU Patent. 175044:20 9. Naigert KV, Tutynin VT (2018) Magnitoreologicheskoye ustroystvo aktivnoy zashchity dlinnomernoy konstruktsii ot rezonansnoy vibratsii (MR device of active protection of large scale structures from resonant vibration). RU Patent. 185538:7 10. Naigert KV, Tselischev VA (2019) Reologicheskiye sistemy dempfirovaniya, primenyayushchiye kombinirovannyye i rotatsionnyye magnitoreologicheskiye tekhnologii (Combined and rotary magnetorheological fluid technologies in rheological damping systems). Bulletin of the South Ural State University. Ser. Mechan. Eng. Ind. 19(1):26–36 11. Naigert KV, Tselischev VA (2018) Raschet kharakteristik kombinirovannykh magnitoreologicheskikh opor s uchetom effektov magnitnoy levitatsii i osobennostey opredeleniya koeffitsiyentov ikh elementov (Calculation of characteristics of combined magnetorheological supports by taking into account the effects of magnetic levitation and peculiarities of the determining of coefficients of their elements). Science and technology. Materials XXXVIII all-Russian conference dedicated to the 75th anniversary SUSU. Russ. Acad. Sci. 1:125–137 12. Naigert, K.V., Tselischev, V.A.: Hardware Implementation of Automatic Control System for New Generation Magnetorheological Supports. Proceedings of the 4th International Conference on Industrial Engineering. ICIE 2018. Lecture Notes in Mechanical Engineering. Springer, pp 2219–2228 (2019) 13. Naigert, K.V., Tselischev, V.A.: Methodology and Constructive Implementation of Active Vibration Protection of Large Scale Structures. Proceedings of the 5th International Conference on Industrial Engineering. ICIE 2019. Lecture Notes in Mechanical Engineering, vol. II, Springer, pp 1305–1313 (2019)

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14. Polunin VM (2012) Akusticheskiye Svoystva Nanodispersnykh Magnitnykh Zhidkostey (Acoustic Properties of Nanodispersed Magnetic Fluids). Publishing house Fizmatlit, Moscow 15. Takeketi S, Tikazumi S (1993) Magnitnyye Zhidkosti (Magnetic fluids). Mir, Moscow 16. Inman DJ (2001) Engineering Vibration. Prentice Hall, New Jersey 17. Thompson WT (1996) Theory of Vibrations. Nelson Thornes Ltd., Oxford 18. Tongue B (2001) Principles of Vibration. University Press, Oxford 19. Fan H, Gao F (2014) Asymptotic stability of solutions to elastic systems with structural damping. Electro. J. Differ. Equ. 245:1–9 20. Fan H, Li Y (2014) Analyticity and exponential stability of semigroups for the elastic systems with structural damping in banach spaces. J. Math. Anal. Appl. 410:316–322

Hybrid Hydraulic Systems in Technological Processes K. V. Naigert1(B) and V. A. Tselischev2 1 South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, Russia

[email protected] 2 Ufa State Aviation Technical University, 12, K. Marx Street, Ufa 450008, Russia

Abstract. Technological improvement of the production process, increasing the energy efficiency, and cost reduction are impossible without the automation of technological processes. The use of classic hydraulic control devices in technological systems for the petroleum and chemical industries is limited by the design features and instability of materials in aggressive environments. Therefore, the development of new hybrid hydraulic technologies for the control of flow characteristics in hydraulic systems is very relevant. The text presents an original patented design of a hybrid hydraulic device with ferrofluid control elements, which allows mixing and dosing of a liquid environment. The design without moving mechanical parts greatly simplifies the device maintenance and permits to use the polymeric materials and composites as construction materials, inert to aggressive environments. The proposed design of a hybrid hydraulic device with ferrofluid control elements can be integrated into the existing technological systems. The article represents a numerical model of ferrofluid control elements’ dynamics. A control algorithm for the original hybrid hydraulic device—a mixing and dosing system with ferrofluid control elements—is described and realized as a program code. Variants of control signals of ferrofluid control elements and an algorithm of their synchronization/desynchronization are presented. Graphic dependencies of control signals are obtained as a result of numerical simulation; they illustrate excellent dynamic performance of ferrofluid control elements and the ease of implementation of automation of the developed design of a hybrid hydraulic device. Keywords: Hybrid hydraulic device · Ferrofluid control element · Automation of technological processes

1 Introduction The automation of technological processes of the petroleum and chemical industries requires the use of the equipment, which is resistant to aggressive environments; therefore, its design involves minimizing the number of mechanical moving parts, simplifying geometry, and using inert materials or protective compounds on surfaces of flow parts. In © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_143

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technological lines of the petrochemical industry, the jet hydraulic equipment is widely used. The jet hydraulic equipment demands the creation of active flows for organization of its performance, as well as pressure sources, which contain mechanical moving parts. Jet hydraulic automation systems have many advantages, provided high-purity inert working environments are used. It is obvious that the application of active flows of aggressive environments in the petroleum and chemical industries is possible through the use of special-purpose blade machines as a source of pressure. The petrochemical industry imposes similar requirements for blade machines as for the jet hydraulic equipment. This leads to a high cost of technological equipment and to difficulties in its manufacture, maintenance, and operation. Therefore, it is necessary to create an alternative class of technological equipment for the petroleum and chemical industries [1–8].

2 Actuality of the Research The improving automation of technological processes of the petroleum and chemical industries is an important applied task and requires the increase in the number of original design solutions and development of calculation methods for their designs, which are based on generally accepted and widely available theoretical terms. The creation of hybrid hydraulic devices with a fundamentally new class of control elements, their implementation in existing technological lines, and research on the features of the workflow of hybrid hydraulic devices are relevant.

3 Statement of the Problem The research is dedicated to the creation of a hybrid hydraulic device, which excludes mechanical moving parts and is able to carry out a combination of widely used technological operations in the petroleum and chemical industries. A control algorithm for the proposed hybrid hydraulic device design and a numerical model for assessing the dynamics of its workflow need to be developed.

4 Constructive Solution of the Problem Application of the proposed design (Patent RU 2,639,906) allows the installation of a mixing and dosing system with the ferrofluid control elements, Fig. 1, in the existing pipe network [9]. The spherical volume of ferrofluid is transformed by external magnetic fields and acquires an elliptical shape; the ferrofluid volume is stretched in the parallel direction to the magnetic field strength and compressed in the perpendicular direction to the magnetic field strength [10]. The calculation method of a mixing and dosing system with ferrofluid control elements is described in the previous publications [9, 11, 12].

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Fig. 1. Mixing and dosing system with the ferrofluid control elements: 1—housing, 2—supply channels with components, 3—elastic annular element, 4—ferrofluid chamber, 5—operating cavity, 6, 7, 8—ferrofluid control elements, 9, 10, 11, 12—annular control electromagnets, 13—pressure channel with mixture, 14—fastening element, 15—technological line with mixture, H—magnetic field strength.

5 Calculation of Dynamics of Ferrofluid Control Elements The spherical shape of a small volume of ferrofluid is more preferable; it is associated with capillary effects in fluids. The directional external magnetic fields create the pressure difference on the symmetry axes of the spherical volume of ferrofluid and lead to the spherical volume transformation to an elliptical shape and compensation of pressure inhomogeneity inside the volume of ferrofluid by increasing surface curvature and growing capillary pressure. The shape of the volume of ferrofluid in the external magnetic fields by a minimum of magnetic energy depends on [10]     E = Eg + umag + ES , ES = 2π γ ab 1 k + arcsin 1 e ,

  a 2 2 k = b, e = a −b a, Eg = ρagV . (1) umag —magnetic energy,γ —coefficient of surface tension,a; b—axis,e—ellipsoid eccentricity, V —volume of ferrofluid control element, g—gravity acceleration, ρ— density which will take the form: ρ=

τn M (H ) 1 η∗ ∗ ,η = η + · . ϑ 4 1 + (τn τs HM (H ))/J

(2)

J —moment of inertia, τn ; τs —relaxation times (non-magnetic and magnetic particles), M —magnetization, H —magnetic field strength, η—viscosity of ferrofluid, ϑ—kinematic viscosity. The energy of ferrofluid can be calculated by  H  M H  dH  (3) umag = −V 0

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Relaxation times of ferrofluids are extremely short, therefore, the dynamics of hybrid hydraulic devices depends on the dynamics of electromagnetic control units; therefore, consideration of the dynamics of the control element—electromagnet—is necessary. The dynamics of control of the circuit of the electromagnet is written as [13, 14] dIy Ly · + Iy = Uy , Iy = Im sin ωt. Ry + Rb dt

(4)

Ly —winding inductance of electromagnet,Ry —active resistance of electromagnet, Rb —resistance of output stage of amplifier, Uy —voltage, Iy —current,Im —current amplitude, ω—frequency, t—time.

6 Control Algorithm for Mixing and Dosing System with Ferrofluid Control Elements and Its Realization as Program Code The performance of a hybrid hydraulic device needs optimization of sequence and duration characteristics of control signals of electromagnets, because the increasing pressure in the working chamber is realized by the ferrofluid control chamber at the moment of the simultaneous shutdown of electromagnets 9, 11, 12 and activation of electromagnet 10. Initial overpressure in the working chamber is formed by the simultaneous shutdown of electromagnet 9 and activation of electromagnets 11, 12 or activation of one electromagnet of electromagnets 11, 12. The supply of the mixture is carried out by the simultaneous activation of electromagnet 9 and shutdown of electromagnets 11, 12 and may be accompanied by the activation of electromagnet 10. The switching intervals of electromagnets are calculated on the base of volumes of components, volume of the mixture, pressure in the channels, viscosity of components, dispersion of components, and required homogeneity of the mixture. The initial overpressure in the working chamber is corrected by adjusting the pressure in the supply channels. For automation of the workflow, the control signals of bipolar transistor switches (NPN) of annular control electromagnets are set as follows. The control signal of annular control electromagnets 11, 12 (ferrofluid control elements in the supply channels 2) is set by the sinusoidal law: Im = 1.5; w = 5; t = 0:0.001:1; f = 0; I = Im.*sin(w.*t + f); L = 0.5; Ry = 50; Rb = 5; U = 12; f = @(t,I)(U-I)./(L./(Ry + Rb)). The control signal of annular control electromagnet 9 (ferrofluid control element in the pressure channel 13) is set by the sinusoidal law too:

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Im = 1.5; w = 5; t = 0:0.001:1; f = pi; I = Im.*sin(w.*t + f); L = 0.5; Ry = 50; Rb = 5; U = 12; f = @(t,I)(U-I)./(L./(Ry + Rb)). For annular control electromagnet 10 (ferrofluid control chamber), a rectangular control signal with a required duration and periodicity characteristics of impulses is realized: tao = 0.2; eps = 0.0005; etl = 1e1; w = 0.6; Im = 1.5; f = pi/6; t = (0:eps:etl); d = (0:w:etl) + tao/2 + f; x = Im.*pulstran(t, d, @rectpuls, tao).

7 Calculation of Required Flow Rate Characteristics in Working Channels In accordance with the characteristics of a control signal, the geometric parameters of ferrofluid control elements and flow rate in the working channels can be calculated. The pressure in the supply channels is regulated. The pressure at the section of the mixture supply channel with closed ferrofluid control element 8 is considered equal to atmospheric pressure. The flow rate at ferrofluid control elements 6, 7 are described as [15–20] Q6 =

p6 π d6 δ63 p7 π d7 δ73 , p = p − p , Q = , p7 = p2R − p5 . 6 2L 7 5 2μl6 · 105 2μl7 · 105

(5)

p2L —pressure in the supply channel L, p2R —pressure in the supply channel R, p5 —pressure in the working chamber at electromagnet 10 shutdown. The flow rate at ferrofluid control element 8 is calculated by Q8 =

p8 π d8 δ83 , p8 = p13 − p15 , p8 = pt5 − p15 , p5 ≈ p13 . 2μm l8 · 105

(6)

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δ6 ; δ7 ; δ8 —radial clearances between channels and ferrofluid control elements 6, 7, 8, p6 ; p7 ; p8 —pressure drops on ferrofluid control elements 6, 7, 8, d6 ; d7 ; d8 —diameters of ferrofluid control elements 6, 7, 8, μ—viscosity of environment, μm —viscosity of mixture, l6 ; l7 ; l8 —lengths of ferrofluid control elements 6, 7, 8, p13 —pressure in the channel with mixture, p15 —pressure in the technological line with mixture. Pressure in the working chamber at electromagnet 10 activation is 

H

pt5 = pf 5 + p4 , p4 = const − ρgz +

 M H  dH  .

(7)

0

z—coordinate. Initial pressure in the working chamber 5 is

2 vf25 − v2L v2 pf 5 = p2L − hf 5 − h2L + γm + γm ξ , 2g 2g

2 vf25 − v2R v2 pf 5 = p2R − hf 5 − h2R + γm ξ. γm + 2g 2g

(8)

γm —specific gravity, hf 5 − h2L ; hf 5 − h2R —differences in the heights of centers of gravity on the control sections, vf 5 ; v2R ; v2L —velocity, ξ —drag coefficient. On the base of the above equations and geometric parameters of ferrofluid control elements in the external magnetic fields, the required flow rates at obtained radial clearances are calculated and correlated to the opening time of ferrofluid control elements and to the frequency of their opening.

8 Calculation Results The graphic dependencies of control signals of electromagnets are shown in Figs. 2 and 3. Signals for ferrofluid control elements are represented on curve 1 (supply channels) and curve 2 (pressure channel). The positive parts of sinusoidal input signals open bipolar transistor switches (NPN) of ferrofluid control elements in the channels, Fig. 2. Bipolar transistor switch (NPN) of the electromagnet of the ferrofluid chamber has a positive square wave control signal. Simultaneous signal modulation of control electromagnets allows out-of-sync mode by opening/closing of ferrofluid control elements in the supply and pressure channels, synchronization of pressure increase in the ferrofluid chamber with the moment of closing of ferrofluid control elements in the supply channels, and synchronization of the opening of the ferrofluid control element in the pressure channel with a signal delay, Fig. 3. Continuous positive square wave signal of the control electromagnet of the ferrofluid chamber in the absence of control signals of ferrofluid control elements (at the closing of supply and pressure channels) permits the pulse pressure increase in the working area and mixing components.

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Fig. 2. Control signals of annular electromagnets: 1—ferrofluid control elements in the supply channels, 2—ferrofluid control element in the pressure channel.

Fig. 3. Control signals of annular electromagnets: 1—ferrofluid control elements in the supply channels, 2—ferrofluid control element in the pressure channel, 3—ferrofluid chamber. Dosing components’ and dosing mixture modes.

9 Novelty, Practical and Scientific Significance of Research The workflow of the developed patented design of a hybrid hydraulic device is realized by ferrofluid effects, which allow mixing of environments by changes in the electromagnetic component of the pressure of the ferrofluid chamber and dosing of environments and the mixture by the transformation of the spherical ferrofluid volume to an elliptical shape in the external magnetic fields [9]. A control algorithm for the original hybrid hydraulic device design and its realization as a program code in MATLAB scripting language are

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presented. The proposed calculation method of the hybrid hydraulic device parameters is applicable to optimize the performance of the original design of a mixing and dosing system with the ferrofluid control elements for the rationalization of the control signals at the operation of the device.

10 Conclusions The proposed original hybrid hydraulic device design is easily integrated into automated process lines and is capable of performing many technological operations: dosing of components, dosing of the mixture, and mixing of components. The developed control algorithm and its realization as a program code allow a fully automated workflow of a hybrid hydraulic device with ferrofluid control elements. Ferrofluid control elements permit simplification of flow rate control implementation of a hybrid hydraulic device and increase of control accuracy and raise of speed of response to a control signal. Hybrid hydraulic devices have simple geometry and are less prone to the erosion of flow parts; consequently, flow rate characteristics are stable during exploitation. Hybrid hydraulic devices possess high efficiency, reliability, and potential for further development.

References 1. Rosenfeldt, H. et al.: Pressure motor for electro-rheological fluids. US Patent 6116144, 05 June (2001) 2. Durward, R.: Method and apparatus for enhancing fluid velocities in pipelines. US Patent 2004/0247451, (09 Dec 2004) 3. Ciocanel, C., Islam, N.: Integrated electro-magnetohydrodynamic micropumps and methods for pumping fluids. US Patent 2011/0037325, (17 Feb 2011) 4. Proselkov YuM, Pakhlian IA (2012) Gidroezhektornyy smesitel (The hydro ejector mixer). RU Patent 2442686:20 5. Daub, M., Steigert, J.: Cartridge, centrifuge and method. US Patent 9399214, (26 July 2016) 6. Eckert, C.E.: Method for molten metal treatment. US Patent 5462580, (31 Oct 1995) 7. Vlasov, A.V.: Uprugoobolochechnyye magnitozhidkostnyye elementy sistem upravleniya (Elastic shell ferrofluid elements of control systems) Publishing house BIBiU, Balakovo (2011) 8. Vlasov AV (2010) Elektrogidravlicheskoye Magnitozhidkostnoye Reguliruyushcheye Ustroystvo (Electro-hydraulic ferrofluid regulating device). Publishing house BIBiU, Balakovo 9. Naigert KV, Tutynin VT (2017) Smesitel’-dozator s magnitozhidkostnymi upravlyayushchimi elementami (The mixing and dosing system with the ferrofluid control elements). RU Patent 2639906:25 10. Takeketi S, Tikazumi S (1993) Magnitnyye Zhidkosti (Magnetic fluids). Mir, Moscow 11. Naigert, K.V., Tselischev, V.A.: New Generation Magnetorheological, Magnetodynamic, and Ferrofluid Control Devices with Nonstationary Electromagnetic Fields. Proceedings of the 4th International Conference on Industrial Engineering. ICIE 2018. Lecture Notes in Mechanical Engineering. Springer, pp 1375–1384 (2019) 12. Naigert KV, Tselischev VA (2018) Osobennosti rascheta rabochikh parametrov gibridnykh gidravlicheskikh sistem s magnitozhidkostnymi upravlyayushchimi elementami (Calculating performance parameters of hybrid hydraulic systems with ferrofluid control elements) Bulletin of the South Ural State University. Ser. Mechanical Engineering Industry 18(4):38–47

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13. Landau LD, Lifshitz EM (1993) Electrodynamics of Continuous Media. ButterworthHeinemann, Oxford 14. Landau LD, Lifshitz EM (1995) The Classical Theory of Fields. Butterworth-Heinemann, Oxford 15. Kramarenko EY et al (2015) Magnetic and viscoelastic response of elastomers with hard magnetic filler. Smart Mater. Struct. 24:1–11 16. Stepanov GV et al (2012) Magnetorheological and deformation properties of magnetically controlled elastomer with hard magnetic filler. J. Magn. Magn. Mater. 324:3448–3451 17. Dorfmann A, Ogden RW (2004) Nonlinear magnetoelastic deformations. Q. J. Mech. Appl. Math. 57(4):599–622 18. Bustamante R et al (2008) On variational formulations in nonlinear magnetoelastostatics. Math. Mech. Solids. 13:725–745 19. Filipcsei G, Zrínyi M (2010) Magnetodeformation effects and the swelling of ferrogels in a uniform magnetic field. J. Phys. Condens. Matter. 22:276001 20. Bustamante R et al (2007) A nonlinear magnetoelastic tube under extension and inflation in an axial magnetic field: numerical solution. J. Eng. Math. 59:139–153

Determination of the Main Structural Parameters of the Device for Creating a Two-Layer Annular Flow L. A. Ilina(B) , M. S. Krasnodubrovsky, and N. A. Dukov Volgograd State Technical University, 28, Lenin Avenue, 400005 Volgograd, Russia [email protected]

Abstract. Creation of a stable annular flow will reduce pressure losses in the operation of hydraulic systems and the transportation of liquids via pipelines. Developing the design of a device to create a stable annular flow is an urgent task. Determination of the design parameters of the device based on the proposed methodology for liquids with different rheological characteristics will allow manufacturing devices for creating a stable annular flow in pipelines in various technological processes for many industries. Based on the obtained parameters, a device for creating a wall annular flow was developed and used in a pilot installation. The experimental studies of the two-layer annular flow stability were carried out using the example of a model viscous fluid (vegetable oil) with a wall gas layer. The experimental studies have shown the ability of the structure to reduce hydraulic resistance during transportation of high-viscosity media inside a round pipe. Thus, the developed methodology for determining the structural parameters of the device for creating an annular flow makes it possible to select such device parameters providing a flow of close to the optimal amount of low-viscosity liquid (gas) supplied to the annular space to create a stable annular flow. Keywords: Hydraulic resistance · Wall layer · High-viscosity fluid · Annular flow · Structural dimension

1 Introduction The development of structures for creating a stable flow of high-viscosity fluids in the low-viscosity gas ring layer during transportation in industrial and transport pipelines is currently an urgent task. Creating a stable two-layer annular flow will reduce hydraulic resistance and, as a result, reduce energy consumption for transportation of high-viscosity fluids via pipelines [1–3]. Annular flow stability problems and methods for solving them were considered in [4–7]. At present, quite a few fundamental structures are presented for creating a two-layer annular flow [6–11]. In this case, a low-viscosity wall layer is formed both due to the © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_144

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supply of a low-viscosity liquid or gas and due to a change in the aggregate state of the transported fluid in the wall layer. The theoretical foundations of a two-layer annular flow in a pipeline are considered in many scientific works [3, 6, 7, 12–14]. Studies show that the most important conditions for creating a stable annular flow with a given position of a low-viscosity ring are the method and conditions for introducing liquid or gas into the annular layer [2, 6, 15], which confirms the relevance of developing methods and devices for such transportation of fluids. The aim of this work is to develop a methodology for determining the main structural parameters of a device for creating a two-layer annular flow.

2 Theoretical Basis for the Design of a Device for Creating an Annular Flow A condition for a stable two-layer annular flow [6, 14] is the equality of velocities at the phase boundary of the laminar flow of the main high-viscosity fluid and the wall low-viscosity fluid or gas (Fig. 1).

Fig. 1. Curves of tangent stresses τ and velocities V 1 , V for annular two-layer flow of nonNewtonian and viscous fluids in a pipe [6].

A condition for achieving equal velocities and shear stresses at the phase boundary at the time of creating such two-layer annular flow is the use of a structure for supplying gas to the wall layer, which makes it possible to form an annular flow with the corresponding radius of the phase boundary, taking into account the rheological characteristics of the transported fluid. In experimental works [16–18], to create an annular flow, the devices used had an annular gap through which gas was supplied to create a wall gas layer. In this case, the gas flow rate was controlled by changing the pressure of the supplied gas, and the dimensions of the annular gap itself were chosen regardless of the physical characteristics of the transported fluid. The task is to determine the dimensions of the annular gap for the supply of gas or low-viscosity fluid to create a stable two-layer annular flow ensuring equal velocities and shear stresses at the phase boundary.

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3 Methodology for Determining the Structural Dimensions of the Device to Create a Stable Annular Flow To determine the main structural dimensions of the device (Fig. 2), it is proposed to use the following calculation procedure: Bulleted lists may be included and should look like this: • The flow rate of a low-viscosity fluid is determined by known methods for calculating Newtonian viscous fluid [12], a viscous power-law fluid [14], a fluid with an arbitrary rheological curve [13], or based on the obtained equation for predicting the flow of a high-viscosity fluid in a ring of a low-viscosity fluid (gas) [19]; • The boundary condition for the calculation is the maintenance of the laminar flow regime of the main and wall fluid (criterion Re < 2300); • Define the estimated internal diameter of the pipeline [20]:  4·Q (1) def = 3600 · π · ω0 • Based on the result, choose the closest larger outer diameter, taking into account the wall thickness, from a standard series of pipeline diameters; • The outer diameter for the fluid flow will be equal to the inner diameter of the gas ring, df = dg . Since, at the initial time, the fluid occupies the entire cross section of the pipe, it is necessary to reduce df . Then, the outer diameter of the gas ring will be determined from the relation dg > df . • Determine the equivalent diameter of the gas stream deg :   π  π · Dg2 − · dg2 / π · Dg + π · dg = Dg − dg , (2) deg = 4 · 4 4 • Determine the Reynolds number for the gas flow, while the velocity is selected from the condition of equality of velocities at the gas–liquid phase boundary [21]: Reg =

ωg · deg · ρg , μg

(3)

• where ωg is gas velocity in the pipe, m3 /s; ρg is pumped gas density, kg/m3 ; • μg is pumped gas viscosity, Pa · s. • Determine the thickness of the wall layer of gas: δg =

deg , 2

(4)

• where δg is thickness of the wall gas layer, m • The length of the distribution sleeve is determined from the following ratio: lg = dg · 1, 5

(5)

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Fig. 2. Scheme of the device for creating a stable two-layer annular flow in the pipeline 1 is device housing; 2 is sleeve.

• Determine the diameter of unions and branch pipes for supplying gas knowing gas flow rate and velocity according to the formula:  4 · Qg dgp = , (6) 3600 · π · ωg • where dgp is internal diameter of the gas supply valve, m Determine the diameter of nozzles for supplying gas to the distribution sleeve:  π 2 /n · dgp , (7) dgn = 2 · 4 π where n is number of gas nozzles. The developed technique makes it possible to determine the main structural dimensions of the device depending on the physical properties of the main transported and auxiliary wall fluid or gas.

4 Experimental Evaluation of the Effectiveness of the Device to Create a Two-Layer Annular Flow • To conduct experimental studies of the stability of a two-layer annular flow, the pilot installation for creating an annular flow was upgraded [16, 17]. • The setup is shown in Fig. 3 and comprises the primaryse-fluid feed tank 1 mounted on the stand 2 and connected to the receiving tank 5 in the reservoir 6 via the spacer 12 of the thin-walled steel pipe 4. Gas is supplied to the wall-adjacent layer by the compressor 7. Compressor equipment includes the pressure gauge 9, the air-feed tap

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8, the tap-equipped pipe 10, the gas meter 11, and the wall-adjacent annular layer generator 12; this equipment is connected to the pipe 4 to generate a wall-adjacent annular gas layer. The pipe 4 is mounted horizontally to the reservoir 6 and is held in place by the holder 13. • When conducting experimental studies, an upgraded device was used to create an annular gas layer, made taking into account the proposed methodology for determining the main structural parameters. • The experimental technique is similar to that presented in [17].

Fig. 3. Experimental setup layout 1 is the feed tank; 2 is the stand; 3 and 10 are taps; 4 is the pipe; 5 is the receiving tank; 6 is the reservoir; 7 is the compressor; 8 is the tap; 9 is the pressure gauge; 11 is the gas meter; 12 is the wall-adjacent annular layer generator; 13 is the holder.

4.1 Objects of Study and Their Characteristics As the main fluid vegetable oil was chosen, the characteristics of which are given in Table 1. Table 1. Characteristics of refined sunflower oil [22] Indicator

Value

Kinematic viscosity, m2 /s, at 200 C 60.6 · 10−6 Dinamic viscosity, Pa · s, at 200 C 0.055 Congelation temperature, 0 C

−18

Density, kg/m3 , at 200 C

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To create a wall annular gas layer, air was used, the characteristics of which are given in Table 2. Table 2. Ambient air Indicator

Value

Dinamic viscosity, Pa · s, at 200 C 0.018 · 10−3 Density, kg/m3 , at 200 C 1.184

5 Analysis of the Results of Experimental Studies The results of experimental studies of the dependence of the flow rate of the main fluid (vegetable oil) Qf , on the flow rate of the auxiliary medium (air) Qg , used as an annular wall layer, are presented in the graphical form in Fig. 4.

Fig. 4. Dependence of the flow rate of the main fluid (vegetable oil) Qf on the gas flow rate Qg.

Compare the results obtained in the course of the experiment in this work with the results presented in [18]. An analysis of the obtained experimental data, its comparison with the results obtained earlier shows that replacing the device for creating a twolayer annular flow with a device made using the proposed method for calculating the structural dimensions made it possible to increase the throughput of the pipeline for the same working fluids (vegetable oil–atmospheric air) from 10 to 30%. Thus, we can talk about the effectiveness of the proposed methodology for determining the main structural parameters of the device to create a two-layer annular flow, increasing the throughput of the pipeline by reducing hydraulic resistance by 30%.

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References 1. Charles, M.E., Redberge, P.J.: The reduction of pressure gradients in oil pipelines by the addition of water. Canad. J. Chem. Eng. aprile (1967) 2. Mastobayev BN, Shammazov AM, Movsumzade EM (2002) Khimicheskiye sredstva i tekhnologii v truboprovodnom transporte nefti (Chemical Agents and Technologies for Oil Transport by Pipelines). Khimiya, Moscow, p 296 3. Ilina, L.A., Golovanchikov, A.B., Ilin, A.V., Vasilyeva, E.V.: Snizheniye gidravlicheskogo soprotivleniya pri dvukhsloynom koltsevom techenii vysokovyazkoy zhidkosti v truboprovode (Hydraulic-Resistance Reduction by Two-Layer Annular Flow of High-Viscosity Fluids in Pipelines), Izvestia VSTU. Series: Rheology, Processes, and Devices in Chemistry. Iss. 7: Inter-University Proceedings 1(128), 114–117 (2014) 4. Russell TWF, Hodgson GW, Govier GW (1959) Horizontal pipeline flow of mixtures of oil and water. Canad. J. Chem. Eng. 2:34–36 5. Poesio P, Strazza D, Sotgia G (2009) Very-viscous-oil/water/air flow through horizontal pipes: pressure drop measurement and prediction. Chem. Eng. Sci. 64(6):1136–1142 6. Golovanchikov AB, Ilin AV, Ilina LA (2007) Teoreticheskiye osnovy techeniya zhidkostey v truboprovode s malovyazkim pogranichnym sloyem (Theory Behind Fluid Flow in Pipelines with Low-Viscosity Boundary Layers). Volgograd, VSTU, p 108 7. Golovanchikov AB, Vasilyeva EV, Ilina LA (2017) Granichnaya ustoychivost geterofaznykh zhidkostey na makro- i mikrourovnyakh(Marginal Stability of Heterophase Lluids at Macroand Micro-Levels). Volgograd, VSTU, p 131 8. Golovanchikov, A.B., Vasiliev, E.V., Dulkina, N.A., Murzenkov, D.S., Polskaya, N.N., Ilina, L.A.: Method of moving viscous petroleum products and fluids. Pat. RF 2542647, Volgograd State Technical University (2015) 9. Golovanchikov, A.B., Vasiliev, E.V., Dulkina, N.A., Khritova, E.V., Polskaya, N.N., Ilina, L.A.: Device for reducing hydraulic losses in the pipeline. P. m. RF 120165, Volgograd State Technical University (2012) 10. Golovanchikov, A.B., Vasiliev, E.V., Dulkina, N.A., Khritova, E.V., Volman, A.N.: Device for reducing hydraulic losses in the pipeline. P. m. RF 114494, Volgograd State Technical University (2012) 11. Golovanchikov, A.B., Dulkina, N.A., Khritova, E.V., Vasilieva, E.V., Pavlov, D.A.: Device for reducing hydraulic losses in the pipeline, P. m. RF 114493, Volgograd State Technical University (2012) 12. Golovanchikov AB, Ilina LA, Ilin AV, Dulkina NA, Dulkin AB (2006) Transportation of oil and petroleum products with a gas boundary layer. Oil Gas Technol. 4:10–14 13. Golovanchikov, A.B., Ilin, A.V., Ilina, L.A.: Model dvukhsloynogo koltsevogo techeniya vyazkoy zhidkosti s proizvolnoy reologicheskoy krivoy s malovyazkim pristennym sloyem v trube (Two-Layer Annular-Flow Model for a Viscous Fluid with an Arbitrary Rheological Curve and a Low-Viscosity Wall-Adjacent Layer). Izvestia VSTU. Series: Rheology, Processes, and Devices in Chemistry. Iss. 5: Inter-University Proceedings 1, 12–14 (2012) 14. Golovanchikov, A.B., Ilin, A.V., Ilina, L.A.: Techeniye v trube nenyutonovskoy zhidkosti s malovyazkim pogranichnym sloyem (Non-Newtonian Fluid: Pipe Flow with a Low-Viscosity Boundary Layer). Izvestia VSTU. Series: Conceptual Design in Education, Engineering, and Technology: Inter-University Proceedings 1(5), 19–21 (2004) 15. Skripnikov, YuV.: Vliyaniye malovyazkogo pristennogo sloya na ustoychivost techeniya v krugloy trube (How Low-Viscosity Wall-Adjacent Layer Affects Round-Pipe Flow Stability). In: Sovershenstvovaniye sistem upravleniya i ekspluatatsii magistralnogo transporta, Ufa, VNIISPT neft (1988)

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16. Ilin AV, Kareva GN, Vasilyeva EV, Ilina LA, Golovanchikov AB (2013) Eksperimentalnye issledovaniya ustoychivosti techeniya nefteproduktov v trube s pristennym zhidkim (gazovym) sloyem(Experimental Research of Petroleum-Product Flow Stability in Pipes with Wall-Adjacent Fluid (Gas) Layers). Tekhnologii Nefti I Gaza 5:36–41 17. Ilina, L., Goncharov, N., Shagarova, A.: Experimental Research on Reducing Hydraulic Resistance When Transporting High-Viscosity Fluids by Pipeline. In: Proceedings of the 5th International Conference on Industrial Engineering (ICIE 2019), Springer Nature Switzerland, pp 1369–1376 (2019). https://doi.org/10.1007/978-3-030-22063-1 18. Krasnodubrovsky, M.S., Dukov, N.A.: Experimental study of the flow of a viscous nonNewtonian fluid with a wall annular gas layer. XXIII Regional Conference of Young Researchers of the Volgograd Region, 11–14 December 2018, Volgograd State Tech. University, Volgograd, pp 22–24 (2018) 19. Ilina, L., Vasilyev, P., Krasnodubrovsky, M.: Finding Flow of Non-Newtonian Fluids in Circular Pipe with Wall-Adjacent Gas Layer. In: Radionov, A.A. et al. (eds.), Proceedings of the 5th International Conference on Industrial Engineering (ICIE 2019), Lecture Notes in Mechanical Engineering—LNME, pp 1395–1403. (2019) https://doi.org/10.1007/978-3-030-22063-1 20. Pavlov KF, Romankov PG, Noskov AA (2006) Primery i zadachi po kursu protsessov i apparatov khimicheskoy tekhnologii (Examples and Problems for the Course in Chemical Processes and Devices), 13th edn. AlianS, Moscow, p 575 21. Kasatkin AG (1971) Osnovnye Protsessy i Apparaty Khimicheskoy Tekhnologii (Basic Processes and Devices in Chemical Technology). Khimiya, Moscow, p 784 22. Plesovskikh VA, Bezdenezhnykh AA (2001) Physico-chemical and Thermophysical Properties of Substances and Materials in Soap and Cosmetic Industries: Reference Information Collection. Pishchepromizdat, Moscow, p 138

Positional Hydraulic Drive of Rotary Dividing Gears with Increased Speed and Exactitude V. S. Sidorenko(B) , D. A. Korotych, and S. P. Prikhodko Don State Technical University, 1, Gagarin Square, Rostov-on-Don 344002, Russia [email protected]

Abstract. The paper offers a generalized technical solution for a multistructural positional hydraulic drive with internal hydromechanical links in an original control loop of the gyrating distributor and various actuation devices (the hydrolock, a hydromechanical brake). The spill method fixes overflow performances of the gyrating distributor, their empirical approximations. The research of generalizations in a mathematical model of the offered drive gear, experimental research of its various structural realizations have established fixed influence of kinematic and power performances of a drive gear on the duration and the precision of the positioning process is applicable to the rotary dividing gear of the machine tool coordinate table. The paper provides recommendations for the structurally parametrical control of a high-speed positional hydraulic drive to be executed in engineering practice. Keywords: Hydraulic drive · Position gear · High-speed actuator · The distributor

1 Problem Statement The development of industrial production is continuously linked with the intensification technological and working processes of the atomized complexes of the equipment. It leads to increase of requirements to kinematic, power, power performances of systems of the drive gears that serve the working and adjusting movements of target gears. In these conditions of perfecting operating and searching new circuit design decisions allows to improve essentially indexes of quality and efficiency of the operative equipment (capacity, exactitude, reliability). Auxiliary and adjusting movements, being positional, occupy to 30% of a piece run time. Abbreviation of their duration at specified accuracy is a subject of a problem of optimum speed and demand corresponding means of support [1–6]. The decision of a problem of optimum speed is successful in case of sufficient on amount and exactitude of execution of coordinates ϕp1 , ϕp2 , ϕp3 (Fig. 1) a positional cycle.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_145

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Fig. 1. The positional cycle.

1.1 Main Part At such approach, it is possible to organize the structurally parametrical control of the stated positional cycle that most completely answering to principles of optimum control [7–9]. The technical decision of a considered problem is presented in Fig. 2 for a rotary coordinate table equipped with a high-speed positional hydraulic drive. The control plant is intended for angle positioning of preform at drilling of a considerable quantity of holes in details of type a flange, covers and others [10–13]. The power head loop of a drive gear is realized by a throttle hydraulic drive with a steered draining an among choke + a back-pressure valve. The HM hydraulic motor ensures control U1 of power performance U1 = MHM −

1 qHM (p1 − p2 ) 2π

(1)

and structure I (p1 − p2 )—control of a pressure p1 and draining p2 . In structure II control of pressure p1 realizes gyrating distributor GD at which combination of working doors a pressure line incorporates to draining. The hydraulically controlled brake HCB realizes structure III and controls U3. The head loop of structurally parametrical control of a drive gear consists of the gyrating distributor GD, integrating internal kinematic and hydraulic links. The set angle migrations of a circular table of rotary coordinate table are ensured with gyrating distributor GD kinematically linked with its turning movement thus, for half of turnover of a rotary disk angle migration of a circular table makes 15 degrees. Within discrete equal to 15 degrees the coordinate is set by the angular displacement of a feeder dial from the step-by-step drive SM, controlled by a programmable controller

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Fig. 2. The technical decision.

PLC. The hydraulic link of a head loop of control is realized by the pipe duct parallel to a hydromotor pressure line HM. Constructive circuit GD is presented in Fig. 3. At rotation of a rotary disk 4 diametrically opposite windows are serially combined with the slots in the liners 3, generate on an exit the pulsing pressure registered by the pressure control device PS and PLC. The amplitude characterizes pressure p1 in the pressure head cavity, the frequency ϕ—amount angle discrete the spinning distributor. The logical—computing block PLC shapes control action for control switching in coordinates, ensuring preplanned sequence execution. In Fig. 4 are presented overflow performances of a flowing part of the gyrating distributor at combination of working doors in a point of positioning C (Fig. 1).[14–18].

2 Result Results of mathematical, experimental simulation of process of positioning of structure of a drive gear I, II, II + III are presented in Fig. 5 and in Table 1. In Fig. 5 are presented dependences of run-down of the shaft of the hydromotor HM from the rate, fixed on the stand-model of an offered drive gear for considered structures I, II, IV.

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Fig. 3. Face GD with the fixed feeder dial 1—the cage, 2—a cover, 3—the liner, 4—a rotary disk, 5—the supply port.

It is fixed: • Essential influence of rate of positioning on run-down that speaks increase in kinematic energy of gyrating masses. Ek =

Im ω 2 2

(2)

dispersed at braking. So, for all structures run-down is augmented in 1,3–1,5 times at change of rate within 5 … 15 rad/s. • Under equal conditions magnitude of run-down in many respects depends on drive gear structure. The best result is ensured with the combined structure IV. • In the table are presented the results of computing and natural experiments, for structures I and II at sufficing qualitative and quantitative coincidence of main specifications of the identical process of positioning, the adequacy of the generalized mathematical sample piece and the reliability of the received values proves to be true.

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Fig. 4. Dynamic account performances face RD.

3 Output • For abbreviation of duration and heightening of exactitude of positioning the combined structures which are powering up internal and external brake arrangements (in Fig. 5 structure IV = II (p1 ) + III (FT 3 )) are effective. • Structurally parametrical control of the positional hydraulic drive by a combination or structure change at execution of positional cycles it is reached by abbreviation of duration and heightening of exactitude of coordinate migrations. • The use of internal hydromechanical links in a head loop of control with a drive gear and PLC ensure stable in time and space switching of control actions in points ϕp1 . . . ϕp3 raising quality of positioning.

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Fig. 5. Influence of rate on exactitude of positioning.

Table 1. Results computer (CE) and natural (NE) experiments. tn (s)

tT (s)

T (s)

 ϕB (rad)

ωp (rad/s)

Model

CE

0.139

0.431

0.5696

−0.0287

47.49

1MPD

FE

0.313

0.210

0.523

−0,031

48.2

Stand

CE

0.03

0.07

0.4

0.5

0.0062

14

1MPD

FE

0.05

0.075

0.36

0.485

0.0058

14.1

Stand

No structures II I (P1,P2)

tn —an actuation device switching time, tT —a braking time, T—positioning time,  ϕB — exactitude of positioning, ωp —rate of positioning

References 1. Sidorenko VS, Grishchenko VI, Rakulenko SV, Poleshkin MS (2017) Adaptive hydraulic variable displacement supply technological machine tool. Bul. Don State Techn Univ 2(89):88–98 2. Grishchenko, V.I., Sidorenko, V.S.: Mathematical model of pneumatic hydraulic drive for positioning of process equipment actuators. Works of the VIII International Scientific and

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3.

4.

5. 6. 7.

8.

9.

10.

11.

12.

13. 14. 15.

16.

17.

18.

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Technical Conference on Technological Systems Dynamics, Don. State Techn. Un-t. 3, 52–57 (2009) Sidorenko, V.S., Grishchenko, V.I.: Synthesis pneumatic positioning systems, high speed and accuracy. Hydropnevmosystems mobile and technological machines: Sat. Rep. intern. Scientific and Technical. conf., is dedicated. 25th anniversary of the department and gidropnevmoavtomatiki. National Technical University Publ., Minsk, pp 209–215 (2010) Sidorenko, V.S., Poleshkin, M.S., Dymochkin, D.D.: The Problem of Optimal Operation Speed of Positional Hydromechanical Drive Systems. Procedia Engineering (ICIE-2017) Elsevier 206, 347–353 (2017) Poleshkin MS, Sidorenko VS (2012a) Unsteady hydromechanical flow characteristics of the valve operator. Bul. Don State Techn. Univ. 12(6):93–102 Grishchenko VI, Sidorenko VS, Dymochkin DD (2012) Modeling positioning adjusting movement of fluid drive. Indus. Hydraulics Pneumatics 1(35):50–55 Grishchenko, V.I., Rakulenko, S.V., Poleshkin, M.S.: Amplitude-frequency method of control of a mobile drilling machine hydraulic drive with a dependent tool advance. Proceedings of the 4th International Conference on Industrial Engineering (ICIE 2018) Springer. Lecture Notes in Mechanical Engineering, pp 331–339 (2018) Poleshkin MS, Sidorenko VS, Rakulenko SV (2017) A study of the position of hydraulic drive with automatic hydraulic control circuit. Procedia Engineering (ILAC-2017). Elsevier 206:340–346 Al-Kudah, A.M., Sidorenko, V.S., Grishchenko V.I.: Simulation process rotary positioning mechanisms of automatic handling equipment devices with hydraulic communication lines. Bul. of the Don State Techn. Univ. 4(39), 191–201 (2008) Sidorenko, V.S., Poleshkin, M.S., Rakulenko, S.V.: Dynamics of hydromechanical system of production machine with an adaptive tool feed drive. Bul. of the Samara Univ., Aerospace engine., Technol. Prod. Technol. 1, 162–175 (2017) Sidorenko, V.S., Rakulenko, S.V., Poleshkin, M.S., Grishchenko, V.I.: Modeling of the hydraulic system dependent feed mobile rig tool. Hydraulic machines, hydraulic and gidropnevmoavtomatiki. Current state and prospects of development: Proceedings of the IX International Scientific and Technical Conference - June 9–10. Publishing House of the Polytechnic, St. Petersburg, pp 365–375 (2016) Grishchenko VI, Sidorenko VS (2009) Simulation process of positioning actuators of process equipment of fluid discrete device with pneumatic communication lines. Bul. Don State Techn. Univ. 9(S2):81–89 Sidorenko, V.S.: Synthesis hydro positioning metalworking equipment devices. D. t. N thesis. Don State Technical University, Rostov-on-Don (2001) Poleshkin MS, Sidorenko VS (2012b) Unsteady hydromechanical flow characteristics of the valve operator. Bulletin of the Don State Technical University 12(6):93–102 Poleshkin, M.S., Sidorenko, V.S.: Mathematical modeling automatically controlled positioner hydraulic drive mechanisms main machine hydraulic circuit with a high efficiency control. Eng. Gazette Don 3(21), (2012) Dolgov, G.A., Sidorenko, V.S., Grishchenko, V.I.: Positioner pneumatic control characteristics of pipe fittings ehnergosilovyh installations. Youth Science and Technology Bulletin, MSTU, NE Bauman. Publ., (9) (2016) Gryshchenko, V.I., Kozhukhova, A.V., Dolgov, G.A., Dymochkin, D.D.: Mathematical modeling of the drive rotor position of pipe fittings. Social Science and Humanity №3. The collection includes the 5th The International Conference “Social Science and Humanity” by SCIEURO in London, 23–29 September 2016, p 23–34 (2016) Radin, V.V.: Drive of farm vehicles, vol. 7: Farm vehicles: theory, calculation, design, use. Zernograd, Azovochernomorskaya State Agroengineering Academy 7(1), 512 (2013)

The Calculation of Pneumatic Actuator Pipelines D. D. Dymochkin(B) , D. A. Korotych, and A. N. Kharchenko Don State Technical University, 1, Gagarin Square, 344002 Rostov-on-Don, Russia [email protected]

Abstract. The physical properties of compressed air and the peculiarities of its behavior make the analytical calculation of pneumatic drives quite difficult, requiring high qualification of the staff performing it. Therefore, companies that produce pneumatic automation offer simplified calculation techniques. They are based on the fact that a number of assumptions are made to simplify the selection of pneumatic equipment, and the necessary parameters of the drive operation are then provided by adjusting the throttles and dampers of pneumatic cylinders (or external damping devices). This approach does not always lead to an optimal solution in terms of cost and weight-dimensional characteristics, but allows for a significant reduction in the time for design and the requirements to the qualification of the designer. Existing nomograms are intended for calculation of the main pipelines. Pipelines connecting cylinders and distributors are much smaller in length, but have a smaller diameter, so they also require responsible calculation. Incorrect diameter selection can cause complete loss of drive functionality. Keywords: Pipelines calculation · Pneumatic pipelines · Pneumatic actuator · Pneumatic equipment

1 Problem Statement In order to simplify calculations, companies offer reference tables [1], graphs, nomograms [2], which reduce the number of calculations required by formulas. One step where formulas still have to be used is to calculate the inner diameter of the pipeline, which determines the magnitude of the compressed air pressure loss. Error in calculations even for one type of size can lead to complete inactivity of the drive. For example, with a compressed air flow rate of 1500 nl/min through a 5-m long line with an inner diameter of 10 mm, the losses will be about 1 bar and through an 8-mm inner diameter line about 5 bar (Fig. 1). Accurate analytical calculation of pressure losses in the pipeline is also a rather complex analytical task, which requires taking into account thermodynamic processes [4, 5], so various nomograms have been developed to simplify calculations [6–8]. In Russia, the nomogram presented in Fig. 2, as well as its modifications, was the most widespread. It is recommended by both Russian and European authors [2, 7–11] and is widely represented in the Russian segment of the Internet. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_146

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Fig. 1. Flow characteristics of tube 12/10 a and 10/8 b [3].

Fig. 2. The nomogram for calculation of pipe ducts [2].

The remaining nomograms were not widely distributed for various reasons. According to the authors, this is due to the following factors:

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• Nomogram presented in [6] does not fully reflect modern nomenclature of internal diameters of pipelines for pneumatic drives; with its help, it is not very convenient to solve the inverse problem (determination of the permissible internal diameter of the pipeline at the specified permissible pressure difference); • Nomogram [8] is relatively complex and requires 8 steps; • Sources [6, 8] are produced in Russia in relatively small circulation, so modern specialists in the field of pneumatic drives may simply not know about the existence of these nomograms. The disadvantages of the nomogram shown in Fig. 2 include the need for additional builds, as well as the fact that the internal diameter scale has a minimum value of 20 mm or ½ inches. Thus, the nomogram allows to perform calculation of main pipelines, but is limited in application for calculation of pipelines of pneumatic drives and systems installed directly on equipment.

2 Main Part The following simplified formula [8, 11] is proposed for analytical calculation by European manufacturers: D5 = A · Q1,85 · L · (P · P)−1

(1)

where D—is the inner diameter of the pipeline; Q—is compressed air flow rate; L— is length of pipeline (or equivalent length taking into account local resistances); P— is absolute pressure at the pipeline inlet (supply pressure); P—is the pressure loss (difference) in the pipeline; A—is the coefficient which numerical value depends on the chosen dimension of D, Q, L, P, and P. Russian sources suggest the following formulas [5]: • for steel pipelines D5 = A1 · Q2 · L · (P · P)−1

(2)

D4,75 = A2 · Q1,75 · L · (P · P)−1

(3)

• for polyethylene pipes

where A1 and A2 are coefficients depending on pipeline material (steel or polyethylene), pipeline pressure level (low—up to 0.05 bar; medium—0.05… 3 bar; high—3… 12 bar) and kinematic viscosity of transported gas under normal conditions. Besides, P means average absolute gas pressure in the main line. Thus, the smaller the pressure loss, the closer the averaged pressure is to the feed pressure and the smaller the calculation error.

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Preliminary analysis of formulas (1)–(3) shows that on the basis of them it is possible to build simpler nomograms, which will allow to carry out calculation in 3–4 steps. For this purpose (1) we will present in the form:    D = f 3 Q, f 2 L, f 1(P, P) (4) For creation of the nomogram we build at first the schedule of F1 = f1 (P, ΔP) (Fig. 3). To the right of it, we plot F2 = f2 (f1, L) and turn diagonally so that the scales f1 are near. Naturally, the limits of change f1 on both graphs should be the same. Then below the second graph, we plot D = f3 (f2, Q). Change limits f2 must also be the same on the second and third schedule. Consistently moving according to schedules to a scale of D (explanations are provided on Fig. 3) we receive the decision from ΔP scale concerning D. For expansion of range of change of variables and obtaining linear dependences it is necessary to build schedules in logarithmic scale. 1. 2. 3. 4.

Step 1—we draw a vertical line from the value set P to supply pressure P; Step 2—we draw a horizontal line to a given length L; Step 3—we draw a vertical line to a given flow Q; Step 4—we draw a horizontal line to the diameter scale.

Fig. 3. Construction of nomogram by formulas (1)–(3).

If the function lines are well positioned, you can combine three graphs into one to produce a more compact chart. To do this, you can choose a different sequence of obtaining f1-f3 functions, flip or reflect graphs in pairs. For the nomogram to be convenient and widely distributed, it must meet the following requirements:

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• be relatively simple and allow to solve the problem in a minimum number of steps (preferably without additional builds); • allow to solve direct and reverse task; • be numbered in units and ranges used in pneumatic actuators. For installation of pneumatic drives, a plastic tube is used more often, with a range of internal diameters of 2… 16 mm [1]. Therefore, the inner diameter must be substituted in [mm]. Nominal flow rates of pneumatic devices are generally specified in [nl/min] and range from units to several thousand nl/min [1]. Pipeline lengths for complex automatic production lines can be several tens of meters, but with a length of more than 20 m you can use the nomogram in Fig. 2. Operating pressures in the pneumatic actuator are within 10 bar. When calculated, the power pressure set by the regulator is more often set to multiples of 1 (less often −0.5) bar. Pressure loss shall not exceed one bar. For these dimensions, formula (1) is D5 = 0, 23 · Q1,85 · L · (P · P)−1

(5)

where D—[mm]; Q—[nl/min]; L—[m]; ΔP—[bar]; Considering also that they are more often operated not by absolute pressure, but by overpressure, on the basis of preliminary analysis of function graphs for their convenient integration into one formula (1) we will present the following form: 0,54  Q = D5 · L−1 · 4, 35 · (Pizb + 1) · P

(6)

where Pizb overpressure at pipeline inlet (supply pressure), bar. At the same time we accept the following sequence of functions: f 1 = 4, 35 · (Pizb + 1) · P

(7)

f 2 = f 1 · L−1

(8)

Q = (f 2 · D5 )0,54

(9)

Turning the graphs of functions f1 and f2 (around the horizontal axis) and combining three graphs into one, we get the nomogram shown in Fig. 4. A binary logarithm is selected for f1 values and a decimal logarithm for other variables to obtain a logarithmic scale.

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Fig. 4. The nomogram constructed by formula (6).

To solve a direct task, consider the following example: To determine pipeline diameter L = 8 m on which the maximum flow of compressed air is Q = 300 nl/min with a supply pressure of Pizb = 4 bars that pressure losses of ΔP did not exceed 0.3 bars. The task is solved in the following order: • Step 1: from the specified maximum permissible pressure drop we conduct vertical straight line 1 to the line of the specified excess supply pressure. • Step 2: from the resulting point, we draw a horizontal straight 2 to a sloped line that defines the length of the pipeline. • Step 3: from the obtained point we draw a vertical straight line 3 to the intersection with the maximum flow line. The resulting point is between the inner diameters of the pipeline 8 and 10 mm (approximately 8.3… 8.5 mm). Therefore, it is necessary to select a pipeline with an internal diameter of 10 mm. Calculation by formula (5) gives value D = 8,6 mm. To solve the reverse problem, consider the following example:

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Determine pressure drop in line length L = 6 m with internal diameter of 12 mm, by which compressed air flow rate is Q = 2000 nl/min at supply pressure Pizb = 7 bar. The task is solved in the following order: • Step 1: find the point, where the specified flow rate intersects with the specified diameter, from which we draw a vertical straight 4 to the intersection with a sloped line of the specified length. • Step 2: from the obtained point we draw a horizontal straight line 5 to the intersection with the line of the specified supply pressure. • Step 3: from the obtained point we draw a vertical straight line 6 to determine the pressure difference. In our case, we get a value between 0.9 and 1 bar (approximately 0.92… 0.94 bar). The calculation gives a value of 0.89 bar by formula 5. Deviations are caused by errors in the construction of lines 1–6. Thus, the obtained nomogram allows to solve quite quickly both the task of selecting the minimum permissible diameter of the pipeline and the task of calculating pressure losses at the specified parameters of the pipeline. At the same time, it is worth noting some of its shortcomings: • the nomogram is heavily loaded with crossing lines, especially in the central part, so it is desirable to use it in a color image; • the nomogram is not understood purely intuitively, in order to solve the problem correctly, it is necessary to know exactly the correct sequence of actions (steps). Let us present formula (5) as P = 0, 23 · D−5 · Q1,85 · L · P −1

(10)

It can be seen from this that the pressure loss is directly proportional to the length of the pipeline. You can try to simplify the nomogram by taking L = 1 and determine the losses per unit length of the pipeline as in [6]. For this purpose, the formula (6) is conveniently represented as f 1 = 4, 35 · (Pizb + 1) · P = D−5 · Q1,85

(11)

The nomogram constructed by this formula is shown in Fig. 5. Let us show the use of the nomogram on the previous examples. In the first example, the pressure drop per unit length of the pipeline should not exceed 0.038 bar. From this value, we conduct horizontal straight line 1 to intersection with supply pressure line P = 4 bars. From the obtained point we draw vertical straight line 2 to the specified flow rate. The resulting point, as before, lies between diameters 8 and 10 mm. Therefore, we select a pipeline with an internal diameter of D = 10 mm. For the second example, we draw the vertical line 3 from the point where the specified flow rate intersects the line of the specified internal diameter to the supply pressure line. Further, we draw a horizontal straight line 4 and we define that pressure difference on

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Fig. 5. Nomogram constructed by formula (11).

1 m of the pipeline ΔP ≈ 0.15 bars. Then the pressure loss over the entire length is about 0.9 bar. Finally, you can obtain a graph family, as shown in Fig. 1, for each pipeline diameter at a certain supply pressure by introducing a supply pressure correction factor. You can also enter an internal diameter correction factor and obtain a typical graph for all diameters that differs only by the range of the cost scale. Such graphs are shown in Fig. 6. For example, point A corresponds to various characteristics: • pressure difference ΔP = 0,3 bars for the pipeline long L = 3 m and with an internal diameter of D = 4 mm at expense Q = 75 nl/min and pressure supply of Pizb = 6 bar;

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• pressure difference 0.191 bar at Pizb = 10 bar, D = 12 mm, Q = 1500 nl/min at the same pipeline length; • ΔP = 0.525 bar at Pizb = 3 bars, D = 8 mm and Q = 500 nl/min. For ease of drawing the nomogram, the values were rounded, in determining the flow rates, depending on the internal diameters of the pipeline. The maximum rounding error was 5.6% at D = 2 mm. As the diameter increases, the error decreases and at D = 16 mm is 0.03%.

Fig. 6. Typical diagrams of pressure losses in pipelines.

References 1. Pneumatic equipment. Large catalog. Version 8.8 (2016). https://catalog.camozzi.ru/#!d90 g02s20p01. Accessed 20 Nov 2019 2. Pneumatics for all. From the Theoretical Foundations to Practical Skills (2016). https://did. camozzi.ru/. Accessed 20 Nov 2019 3. Flow characteristics of pneumatic tubes (2019) https://www.aircrafter.ru/index.php?option= com_content&view=article&id=66&Itemid=76. Accessed 20 Nov 2019 4. Hertz EV, Kreynin GV (1975) Calculation of Pneumatic Actuators. Reference manual, Mechanical Engineering, Moscow p, p 272 5. Kudryavtsev AI, Pyatidveryi AP, Novik AM (1968) Choice, Calculation and Maintenance of the Equipment Pneumatic Actuators and Control Systems of Machines, Presses and Other Machines (industry guidance material). NIIMash, Moscow, p 94 6. Burlakov OA, Litvinov VN (1986) Engineering Calculations in the Development of Pneumatic and Hydraulic Actuators. NIINavtoprom, Moscow, Overview, p 51 7. Hesse, S.: The compressed air as an energy carrier. SV Suliga, DP “Festo”, p. 124 (2004) 8. Nazemtsev, A.S.: Hydraulic and pneumatic systems. Part 1: Pneumatic actuators and means of automation: manual. FORUM, Moscow, p. 240 (2004)

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9. Energy-efficient compressed air system. Practical recommendations for improving the efficiency of production. The International Finance Corporation. (2009) 10. Pnevmotehnika. Basic theory and practical advice (2018). https://www.kaeser.com/int-ru/ser vis/prakticheskie-znaniya/rukovodstvo-po-kompressornoy-tekhnike/. Accessed 20 Nov 2019 11. TECE. Technical information (2015). https://www.tece.com/ru/servis/tekhnicheskaya-inform aciya/teceflex-tekhnicheskaya-informaciya. Accessed 20 Nov 2019

Mathematical Model of Hydraulic Shock Absorber with Feedback V. I. Grishchenko(B) , M. S. Kilina, and G. A. Dolgov Don State Technical University, 1, Gagarin square, 344000 Rostov-on-Don, Russia [email protected]

Abstract. In the given paper the original design of the hydraulic shock absorber with feedback is considered, the developed mathematical model of the given design is presented. As a result of mathematical modeling graphs of the associations of process parameters of braking from time are received. From the received outcomes of mathematical modeling it is possible to draw conclusions on that as the feedback presence allows one to ensure safe stopping mobile parts of cars and process equipment mechanisms and carry out unaccented braking of mobile parts of the process equipment at a maximum mass of 400 kg. The developed mathematical model has allowed one to estimate such parameters of the hydraulic shock absorber with feedback, such as: pressure modifications in a concavity of the hydroshock-absorber, a modification of the piston velocity of the hydroshock-absorber, a modification of a velocity of a mobile element of the valve, a modification of transition of the piston of the hydroshock-absorber, a modification of transition mobile a valve. Keywords: Mathematical model · Hydraulic shock absorber · Process equipment · External brake

1 Introduction Heightening of power and heightening of capacity of the process equipment one of the most actual problems now. Increase in the rate of mobile parts of the equipment one of the conditions, allowing to augment capacity of the technological car. Frequently, mobile elements possess considerable masses and rates that does inconvenient process of unaccented braking. For the abbreviation of a work cycle time of the process equipment it is required to ensure not only a minimum air-cutting time and a tap, but also stopping time. At projection of drive gears it is necessary to pay attention to execution of transients at movement of elements of drive gears and, in particular on process of braking [1–3]. For braking of mobile parts of the process equipment exist series of known modes of braking 9. One of the most simple modes—application of external brake arrangements. The simple equipment as, for example, rubber bumpers and twisted springs cannot be suitable everywhere since promote effect of reflexive reflecting: the big kinetic energy absorbed by this equipment during blow is again transferred on topmozimoe a body and © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_147

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promotes that to uncontrollable blow which can lead to damage zatopmaivaemogo bodies. It is possible to consider as the most interesting external brake arrangements liquid or hydraulic shock absorbers. This equipment works by a principle of change of kinetic energy on thermal with the subsequent radiation of thermal energy in atmosphere. The movement operating on the bucket of the absorber, squeezes a fluid in the absorber, forces it to leak through holes, and promotes its flash heat. Thermal energy is transferred on a cylinder body which radiates it in atmosphere.[4].

2 Mathematical Sample Piece One of interesting decisions is the hydraulic shock absorber with feedback (the patent for useful sample piece RU 168,453) (Fig. 1). The principal feature of the given hydroabsorber is self-adjustment possibility, at change of the affixed load that allows to improve performances of process of braking [5–9]. Performances of movement of mobile elements of the hydraulic shock absorber will allow to draw outputs on character of process of braking since at the moment of contact of a plunger and a mobile element of a drive gear the system can be considered as a unit. The mathematical sample piece of the hydraulic shock absorber is developed with series of assumptions: the sample piece of compressibility of a fluid with the concentrated parametres is accepted, i.e. it is considered that changes of pressure in the closed volumes of the hydraulic shock absorber occurs simultaneously in all points [10–16]. The equation of motion of the piston hydraulic shock is as follows: M

d 2 xv = (P1 · S1 − P3 · S3 + P2 · S2 − Fsp − Fg − Ffr − Fe ); dt 2

(1)

Fig. 1. Structure hydraulic shock feedback (utility model patent RU 168,453). 1 —absorber; 2—plunger; 3—the main cavity; 4—union nut; 5—a stopper; 6—cover; 7—flat; 8—a closed cavity; 9—the accumulator; 10—opening; 11—check valve; 12—locking ring; 13—strip; 14— Screw; 15—a valve body; 16—the delivery port; 17—valve cavity; 18—opening of the valve; 19—locking—a movable valve element; 20—opening damper valve; 21—spring; 22—piston of the valve; 23—feedback channel; 24—the cavity above the piston valve.

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where P1 —the pressure in the piston accumulator, Pa;P2 —the pressure on the valve end, Pa; P3 —pressure in the chamber of the safety valve, Pa;Ftr —a friction force which prevents the movement of the movable valve member, is assumed constant, N;Fsp —the force of the spring pressure on the movable valve element, N; Fe —damping force of the movable valve element, N; M —inhabitable weight value given to the piston of the hydraulic shock absorber, kg;t—time, s. P1 pressure change in the oral suspension: dp1 E = (Qa − Qth1 − Qv1 − Qtr ) · ; dt Wa

(2)

Qa = Va · Sa ;

(3)

 Qv1 = Sv1 ·

2 · (P1 − P2 ) · sign(P1 − P2 ); ρ Sv1 = k · xv1 ;

(4) (5)

where: Qa —flow into the main cavity of the shock absorber; Qv1 —hydraulic valve flow equation;Sv1 —the valve opening area;Wa —the amount of oil in the piston chamber hydraulic shock, m3 ;E—the volume of fluid elastic modulus mN2 ; Qth1 —on the throttle 3

flow 1, ms . Changing pressure p2 ,p3 ,p4 in the valve cavities: dp2 E = (−Qo.v1 + Qv1 − Qth2 ) · ; dt W2

(6)

dp3 E = (Qo.v1 + Qp ) · ; dt W3

(7)

dp4 E = (Qpot.tr − Qpis ) · ; dt W4

(8)

where: p4 —the pressure in the cavity supravalvular, Pa; Qv1 —flow safety valve, Qth2 —expenditure on the throttle 2, ms3 . The change in pressure in the accumulator cancer hydraulic damper: dpac E = (Qth1 − Qac ) · ; dt W4

m3 s ;

(9)

where: pac —the pressure in the accumulator damper, Pa; Equations of motion of the movable elements of the hydraulic shock absorber with feedback: M

d 2 xpis = P4 · Spis − P3 · Spis − Fsp − Ffr − Fe ; dt 2

(10)

Mathematical Model of Hydraulic Shock Absorber with Feedback

M

d 2 xa = F − P1 · Sa − Ffr − Fe ; dt 2

1265

(11)

Changes in oil volume in the piston chamber of the hydraulic shock absorber: Wa = xa · Sa + Wo.a

(12)

where: Sa —flow area of the valve section, m2 ;xa —amount of displacement of the piston hydraulic shock,m; In equations:x—movement of the piston hydraulic shock;t—time;y—movement of the movable valve member. In order to solve the mathematical model used Runge–Kutta method. To calculate   introduce the following numerical data: The initial rate of hydraulic shock rod dx dt = m 0.4 s ; the mass of moving parts in the constant pressure force constant friction force hydraulic shock absorber hole M = 400 kg; piston diameter D = 0.032m; gas volume in the accumulator at Wat = 25 · 10−6 m3 ; an initial pressure of the initial gas pressure in the accumulator Pac.o = 100000Pa; polytropic index n = 1.2; reduced modulus of elasticity E = 109 mN2 ; of the piston stroke hydraulic shock xmax = 0.06m; diameter of the valve Dk = 0.003m;F = 40000N ; Ft = 100N ; at finish taper movable valve element of the local density α = 90◦ ; of the fluid resistance coefficient ρ = 885 mkg3 ; mace movable ζ = 2.2; valve member m = 0.02kg; diameter of the movable valve member Dnk = 0.017m; from sludge valve spring compression (initial) F0 = 20N ; diameter of the valve spring. c1 = 5440 Nm ; stiffness throttle hole (with small steady movement speed)D0 = 0.003m; of the initial compression F0 = 7N ; force of the spring c2 = 720 Nm ; constant hole diameter of the spring damper member in the movable valve DD = 0.01m [17–23].

3 Results of Mathematical Simulation As a result of holding of mathematical experiment graphs of some dependencies of parameters are received the hydraulic shock absorber with feedback (Figs. 2, 3, 4, 5, 6, and 7). On a drawing (Fig. 3) is visible pressure jump in an absorber cavity, it occurs at the expense of hydroabsorber hard braking, in an instant from 0.7 and to 1.1 s. After pressure it is stabilized. During saltus time, pressure does not exceed an allowable pressure in the hydroabsorber.

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Fig. 2. The dependence of the rate of change of the parameters of the time.

Fig. 3. Dependence of pressure change in the cavity hydraulic shock.

From the graph (Fig. 4) it is obviously visible that in an initial instant the bucket possesses in the certain rate, braking process occurs to a small saltus. Further rate of a mobile element is stabilized. On a drawing of dependence of rate of movement of a mobile element of the valve of the hydraulic shock absorber with feedback (Fig. 5) it is visible that in an initial instant the bucket possesses in the certain rate, braking process occurs to a small saltus, further rate of movement is stabilized. On a drawing (Fig. 6) is visible a saltus of rate, but for 0,75 with there is a stabilization of rate. The further movement occurs to the fixed rate. In a following drawing (Fig. 7) dependence of position (migration) of a mobile element of the valve of migration on time is presented.

Mathematical Model of Hydraulic Shock Absorber with Feedback

Fig. 5. Dependence of the change speed of the movable valve member.

Fig. 6. Dependence of change of movement of the piston hydraulic shock.

Fig. 7. Dependence of the movement of the movable valve member.

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Fig. 4. Dependence of the rate of change of the piston hydraulic shock.

4 Conclusion As a result of holding of the mathematical experiment, the received graphs allow to evaluate parameters of operation of the absorber with feedback at braking of mobile parts of the process equipment in mass 400kg. From the received graphs it is possible to draw an output that the offered construction of the hydraulic shock absorber allows to ensure an optimum combination of rate of braking and dynamic indexes of the process equipment, and also influence of power and kinematic performances on process of positioning is fixed.[24–32].

References 1. Poleshkin MS, Al-Kudah AM, Grishchenko VI, Sidorenko VS (2008) Structural and parametric control pnevmogidromehanicheskim positioning device, in the book: Hydraulic machines, hydraulic and gidropnevmoavtomatiki abstracts of the XII International Scientific Conference of students and graduate students. The Ministry of Education and Science, Moscow Power Engineering Institute (Technical University), Moscow State Technical University, Bauman, Moscow, 2008, pp 22–23 2. Sidorenko VS, Grishchenko VI, Rakulenko SV, Poleshkin MS (2017) Adaptive hydraulic drive with delivery tool-feed control of production machine. Vestnik of Don State Technical University 17(2):88–98 (In Russ.). https://doi.org/10.23947/1992-5980-2017-17-2-88-98 3. Grishchenko VI, Sidorenko VS, Dymochkin DD (2012) Positioning modeling adjusting movement of fluid drive. Industrial Hydraulics and Pneumatics 1(35):50–55 4. Kilina MS (2013) Improving the Efficiency of Installation Motion Drives with Hydraulic Shock Absorbers. Uch. St. kand. Techn. sciences. DSTU, Rostov on don, Abstract on the job, p 17 5. Sidorenko VS, Poleshkin MS (2010) Structural and parametric control of hydromechanical machines positioners mechanisms. In the collection hydropnevmosystems mobile and technological machines International scientific-technical conference “hydropnevmosystems mobile and technological machines” dedicated to the 25th anniversary of the Department “gidropnevmoavtomatiki and Hydro”, Belarusian National Technical University pp 221–227 6. Sidorenko VS (2001) Synthesis Hydro Positioning Metalworking Equipment Devices. Dissertation, Rostov on Don

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7. Kilina MS, Grishchenko VI, Kozhukhova AV, Nevzorova MY (2017) The Hydraulic Shock Absorber. A Utility Model Patent RU 168453, Application number 2016119753, 23.05.2016 8. Poleshkin MS, Sidorenko VS (2012a) Mathematical modeling of the automated positioning of hydraulic drive mechanisms target machines with hydraulic control circuit improved efficiency. Eng. Gazette Don 3(21):283–293 9. Tsuhanova EA (1963) Calculation of braking devices hydraulic drive automatic machines and lines for a given law braking. Advanced science and technology and production experience. GOSINTI, 20-63-531 10. Sidorenko VS, Poleshkin MS, Rakulenko SV (2017) Dynamics of hydromechanical system of the machine tool with an adaptive tool feed drive. Bul. Samara Univ. Aerosp. Eng. Technol. Eng. 16(1):162–175 11. Sidorenko VS, Grishchenko VI, Rakulenko SV, Poleshkin MS (2017b) Adaptive hydraulic variable displacement supply technological machine tool. Bul. Don State Techn. Univ. 17(2):88–99 12. Sidorenko VS, Poleshkin MS, Dymochkin DD (2017) The problem of optimal operation speed of positional hydromechanical drive systems. Procedia Engineering (ICIE-two thousand and seventeen) Elsevier 206:347–353 13. Sidorenko VS, Rakulenko SV, Poleshkin MS, Grishchenko VI (2016) Modeling of the hydraulic system dependent feed mobile rig tool. Hydraulic machines, hydraulic and gidropnevmoavtomatiki. In: Current state and prospects of development: Proceedings of the IX International Scientific and Technical Conference—June 9–10. St. Petersburg: Publishing House of the Polytechnic, University Press, pp 365–375 14. Grishchenko VI (2008) Simulation of the process of positioning of rotary-dividing mechanisms of automatic process equipment with devices with hydraulic communication lines. Vestnik of Don State Technical University. 8, 4(39) 15. Grishchenko VI (2012) Modeling ranking process pneumohydraulic actuator adjusting movements. Promyslova gidravlika i pneumatics 1(35) 16. Poleshkin MS, Sidorenko VS, Rakulenko SV (2017) Research of Automated Positional Hydrodrive with Hydraulic Control Circuit. Procedia Engineering (ICIE-two thousand and seventeen) Elsevier, pp 340–346 17. Grishchenko VI, Rakulenko SV, Poleshkin MS (2018) Amplitude-frequency method of control of a mobile drilling machine hydraulic drive with a dependent tool advance. In: Proceedings of the 4th International Conference on Industrial Engineering (ICIE 2018), Springer, Lecture Notes in Mechanical Engineering, pp 331–339 18. Grishchenko VI (2010) Increase in accuracy of the high-speed pneumohydraulic drive of mechanisms of machine. Dissertation, Don State Technical University, Rostov on Don, p 161 19. Tumakov AA, Grishchenko VI, Kozhukhova AV (2017) Mathematical modeling of the sensor tilt membrane type. Procedia Eng 206:421–426. https://doi.org/10.1016/j.proeng.2017. 10.495 20. Gryshchenko VI, Kozhukhova AV, Dolgov GA, Dymochkin DD (2016) Mathematical modeling of the drive rotor position of pipe fittings. Social Science and Humanity, The collection includes the 5th The International Conference “Social Science and Humanity” by SCIEURO in London, vol. 3, pp 23–34 21. Dolgov GA, Sidorenko VS, Grishchenko VI (2016) Positioner Pneumatic Control Characteristics of Pipe Fittings Energosilovyh Installations. MSTU. NE Bauman. Publ, Youth Science and Technology Bulletin, p 9 22. Obukhova EN, Grishchenko VI, Dolgov GA (2018) Formalization of dynamic model of pneumatic drive with variable structure. MATEC Web of Conferences. XIV International Scientific-Technical Conference “Dynamic of Technical Systems”, Rostov on Don, vol 226

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23. Grishchenko VI, Sidorenko VS (2009) Simulation of the process of positioning actuators of the process equipment pneumohydraulic discrete device with pneumatic communication lines, Vestnik of Don State Technical University. T. 9. № S2. P. 81–89 24. Sidorenko VS, Grishchenko VI (2010) Synthesis pneumatic positioning systems, high speed and accuracy. Hydropnevmosystems mobile and technological machines: Sat. Rep. intern. Scientific and Technical. conf., is dedicated. 25th anniversary of the department and gidropnevmoavtomatiki”, Minsk, National Technical University Publ., pp 209–215 25. Al-Kudah AM, Sidorenko VS, Grishchenko VI (2008) Simulation process rotary positioning mechanisms of automatic handling equipment devices with hydraulic communication lines. Vestnik of Don State Technical University, Rostov on Don, vol 8. number 4 (39), pp 191–201 26. Poleshkin MS, Al-Kudah AM, Grishchenko VI, Sidorenko VS (2008) Identification workflows omni brake device. Hydraulic machines, hydraulic and gidropnevmoavtomatiki: Meas. rep. XII Intern. scientific and engineering. Conf. undergraduate and graduate students, pp 54–55 27. Poleshkin MS, Sidorenko VS (2012) Mathematical modeling of the automated positioning of hydraulic drive mechanisms targeted machines with hydraulic control circuit improved efficiency. Engineering Bulletin Don 3 28. Poleshkin MS, Sidorenko VS (2012b) Transient characteristic hydromechanical control devices running part of the valve type. Vestn DonSTU 9:93–102 29. Grishchenko VI, Sidorenko VS (2009) Mathematical model of pneumatic hydraulic drive for positioning of process equipment actuators / Works of the VIII International Scientific and Technical Conference on Technological Systems Dynamics / Don. State technical. Un-t. Rostov n/D: DGTU. vol 3. pp 52–57 30. Grishchenko VI, Kilina MS, Chernavskii VA (2012) Dynamic positioning actuators with hydraulic shock absorbers / Vestnik of Don State Technical University 4(65):16–21 31. Sidorenko VS, Grishchenko VI, Rakulenko SV, Poleshkin MS, Dymochkin DD (2019) Study on oil pilot circuit of adaptive hydraulic drive of tool advance in mobile drilling machine. Vestnik of Don State Technical University 19(1):13–23. https://doi.org/10.23947/1992-59802019-19-1-13-23 32. Grishchenko VI, Tumakov AA, Poleshkin MS, Kilina MS, Dymochkin DD (2019) Modeling of automatic leveling system steep mobile machine with a hydraulic tilt sensor. Omsk Sci. Bul. 2(164):11–17

Making up Model for Forced Cathode Cooling of Casing Powerful Aluminum Electrolyzer with Prebaked Anodes I. A. Sysoev(B) Irkutsk National Research Technical University, 83 Lermontov Street, Irkutsk 664074, Russia [email protected]

Abstract. The technology of aluminum electrolysis is permanently improved in the direction of increasing the unit power of electrolyzers. The leading aluminum companies over the world try to exploit powerful electrolyzers with roasted anodes operating at current intensities higher than 300 kA because their application improves the ecological and economic efficiency of new plants. The elevation of the current strength aimed at increasing the productivity of electrolyzers is often restricted by the negative consequences of thermal load influence. To get a stable technology of electrolysis when the power is increased, it is necessary to guarantee the possibility of efficient heat removal from the structural elements. We present the materials on the development and verification of the mathematical model of electrolyzers with a base level of current strength equal to 300 kA. The power parameters of electrolyzers are obtained for the current strength elevated up to 330 kA. Keywords: Aluminum · Electrolyzer · Modeling · Temperature · Current strength · Voltage · Cathode · Anode

1 Introduction Currently, there are tougher requirements for energy and resource saving, in connection with the problem of increasing energy deficit. This is due to the fact that the pace of development of large cities exceeds previously founded: developing social services, housing, and industrial production. At the same time, aluminum plants are among the largest energy consumers with a low changing schedule load and a high degree of depending on the source of electricity and its cost [1–4]. Aluminum electrolysis technology is continuously improved in the direction of increasing the unit capacity of electrolytic cells. Thus, in order to produce 1 ton of aluminum by the Héroult– Hall method, it is necessary to spend (13.2–16.0) 103 kW*h of electric energy depending on the type of electrolyzer [5–8]. The leading aluminum companies in the world tend to operate powerful electrolyzers working at the high current strength (300–500 kA), since their use improves the cost-effectiveness of new plants due to lower specific capital and operating © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_148

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costs [9–12]. In view of the current trends of development of powerful electrolyzers with roasted anodes and current intensities of 300 and 500 kA in Russia and the prospects of reconstruction and modernization of operating production facilities, it is relevant to solve the structural and technological problems both in the stage of design and in the course of improvement of this technology [13–16].

2 Setting of the Problem For the analysis of the energy efficiency of electrolyzer, it is customary to use the method of determination of the power balance. In the electrolysis of cryolite aluminous melts, the electric current is simultaneously used in the electrochemical processes and to keep the electrolyte in the melted state, which creates a certain relationship between the thermal and electric components of the energy balance. In the general form, the energy balance is given by the formula [17] Wel = Htot + Qh , where Wel is the income of heat caused by the electricity, kW·h; Htot is the increment of enthalpy in the electrolytic reactions, kW; Qh are the heat losses into the environment, kW. The classical procedure of evaluation of the power balance of electrolyzers taking into account the temperatures of the process and the environment is fairly completely presented in the works [17, 18]. It is known that the heat balance of the powerful aluminum electrolytic provides the removing of the significant amount of heat. Therefore, special attention in the calculations by increasing the amperage of 350 kA should be paid to the intensification of heat transfer from the cathode casing. One way of solving this problem is the use of forced air flow sides of the cathode casing in the middle and upper zone of the compressed air. One of the effective tools for improving the design of aluminum electrolytic cell is the use of numerical simulation [19, 20]. To solve the posed problems of evaluation of the energy parameters of electrolyzers, we used the ANSYS computing system. In the construction of numerical models, we used fi le-tasks or the so-called macros. These are text files specially developed for the specific structure and the type of problems with the use of the APDL command language. In the development of a fi le-task for the threedimensional model of aluminum electrolyzer with roasted anodes, we applied the method of construction of a three-dimensional model of electrolyzer combining the numerical analysis of the energy state of electrolyzer with elements of the classical method.The model allows us to study the direct and indirect effects of changing the power mode of variation of any parameter (current, pole distance (PD), the chemical composition of the electrolyte) and to consider the impact of each factor separately. Presented numerical models of electric and thermal state can be used for preliminary comparative analysis of the effectiveness of structures cathode linings powerful aluminum electrolyzers with stepwise increasing of the current.

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3 The Results of Experiments To determine the effect of forced cooling of the shell of middle and upper zones of the cathode casing on the heat transfer coefficient value (from the casing to the environment) has developed a special numerical model of hydrodynamics and heat transfer in the space for performing calculations in ANSYS-CFX system. The calculations were made when setting the excess pressure and air velocity at the inlet nozzles of forced cooling of the cathode casing. Calculation results when you change the input parameters of the cathode cooling system are given in Tables 1 and 2 and in Fig. 1. Table 1. Calculation results in case of changing excess air pressure at the inlet nozzles of the system. № Pin.ex., atm/Pa Vin ,

Vout , m/s

m/s 1

qconv , W/m2

qrad , W/m2

qtotal , W/m2

αconv , W/(m2 •K) min–max

T, °C

αeff , W/(m2 •K)

0

0.19

0.79

1150.2 4430.0

5258.9

0.7–5.1

225.5

23.3

2a 0

0.19

0.75

641.7 1819.2

2233.8

0.7–4.6

139.5

16.0

3b 0

0.19

0.72

265.1

1149.5

0.4–4.0

66.3

5.8

948.4

4

0.0125 1266.6

43.9

10.3

13,733.5 4429.7 18,045.4

3.5–51.6

266.2

67.8

5

0.025 2533.1

62.3

14.6

17,719.7 4429.7 22,031.4

4.6–66.4

266.8

82.6

6

0.05 5066.3

88.1

20.7

22,936.3 4429.8 27,248.6

6.0–85.9

267.0 102.0

7

0.1 10,132

124.8

29.4

29,763.7 4429.9 34,076.5

7.7–111.5 266.9 127.7

8

1 101,325

395.8

93.5

72,244

4430.4 76,557

17.6–271.7 265.9 281.8

a It is decreased emission contribution by reducing the heat-wall temperature of 300 to 200 °C; b It is decreased emission contribution by reducing the heat-wall temperature of 300 to 100 °C.

Table 2. The results of calculations with the change of reference air speed in the system inlet nozzles. No Vin , Pin.ex., Pa Vout , m/s m/s 1

0.0 −0.05

qconv , W/m2

qrad , W/m2

qtotal , W/m2

0.79 1149.5

4430.0 5258.2

α conv , T, W/(m2 •K) °C min–max 0,7–5,1

α eff , W/(m2 •K)

225.4 23.3

2

20.0 54

4.8

7949.9

4429.9 12,262.2 1,9–30,0

264.9 46.3

3

40.0 212

9.5

13,017.7 4429.6 17,327.6 3,3–48,9

266.2 65.1

4

70.0 635

16.8

19,598.7 4429.7 23,909.2 5,2–73,7

265.9 89.9

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Fig. 1. The results of the calculation of heat transfer when using forced cooling of the middle and upper zones of the cathode casing at a pressure in the inlet nozzles 0.0125 atm. a speed–vector; b speed–current line; c convective heat flux; d radiative heat flux; e total heat flux; f heat transfer coefficient.

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where Pin.ex. —inlet excess pressure in the cooling system, atm; Vin —maximum airspeed inlet to the system, m/s; Vout —maximum airspeed outlet from the system, m/c; qconv — convective heat flux on the shell of the upper and middle zones of the cathode casing, W/m2 ; qrad —radiative heat flux on the shell of the upper and middle zones of the cathode casing, W/m2 ; qtotal —total heat flow (convection + radiation) on the shell of the upper and middle zones of the cathode casing, W/m2 ; α conv —the coefficient of thermal heat flow on the shell of the upper and middle zones of the cathode casing, W/(m2 •K); T = qconv /αconv —determinative temperature difference, °C; αeff = qtotal /T—the maximum value of the effective heat transfer coefficient (allows for convection and radiation), W/(m2 •K). In the calculations of forced cooling system it is studied the effect of emitting on the alpha eff., the change in pressure and speed at the input to the system on the values of alpha conv., alpha eff. Analysis of the data shows that at blowing speed of 20 m/c the maximum value of the effective heat transfer coefficient of the middle and upper zone of the shell cathode casing increases in about 2 times while increasing the speed to 40 and 70 m/c—increases, respectively, in 3 and 4 times.

4 Conclusions Analysis of the data based on the conducted electrical and thermal calculations allows us to do the following conclusions: Blowout sides of the cathode casing in the middle and upper zone of compressed air leads to a significant reduction of 70–100 °C temperatures on smooth surfaces of the cathode casing relative to the base case. Thus, the use of forced cooling of the upper and middle zones of the cathode casing by blowing compressed air positively affects at the temperature of the shell casing and the required thickness of the skull. When the current load on the electrolyzer to minimize the effects of excessive heat load on the tub, it is advisable to use measures to intensify heat cathode housing.

References 1. Bogdanov JuV, Zelberg BI, Knizhnik AV, Kondratyev VV, Grigoryev VG (2009) Industrial testings of pilot electrolyzers with roasted anodes during current increase from 300 up to 330 ka. Tsvetnye Metally 2:47–50 2. Noghko SI, Turusov SN, Nikitin VI (2006) Technological approach to managing the power parameters of electrolyzer. Tsvetnye Metally 8:85–87 3. Sysoev, I.A., Ershov, V.A., Kondrat’ev, V.V.: Method of controlling the energy balance of electrolytic cells for aluminum production. Metallurgist 59(3), (2015) 4. Shakhrai SG, Korostovenko VV, Gron VA, Kondrat’ev VV, Belyanin AV (2014) Improving the energy efficiency of a top-worked electrolysis cell. Metallurgist 58(1–2):138–140 5. Bogdanov JuV, Grigoryev VG, Knizhnik AV, Kondratyev VV, Chalykh VI (2009) Simulation of power and magnetic hydrodynamic parameters of electrolysis with roasted anodes for 300 ka current up to 330 ka current. Tsvetnye Metally 2:42–46

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6. Shakhray SG, Kondratiev VV, Belyanin AV, Nikolaev VN, Gron VA (2015) Cooling of the anode gases of aluminum reduction cells in alumina-heating heat exchangers. Metallurgist 59(1–2):126–129 7. Shahray SG, Skuratov AP, Kondratyev VV, Ershov VA (2016) Heat recovery of anode gases of aluminium elecrtolyzer. Tsvetnye Metally 2(878):52–56 8. Ershov VA, Kondratiev VV, Sysoev IA, Mekhnin AO (2013) Extraction of carbon nanoparticles from fluorinated alumina during aluminum production. Metallurgist 56(11–12):952–956 9. Kondratiev VV, Ivanov NA, Bogdanov YV, Ershov VA, Mekhnin AO (2012) Research and development of a nanoinoculated cast iron composition for aluminum electrolyser anode stubs. Metallurgist 56(1–2):59–63 10. Petrovskaya VN, Kondratiev VV (2012) Gas-hydrodynamic nature of the anode effect. Metallurgist 56(3–4):215–221 11. Kondrat’ev VV, Nikolaev VN, Rzhechitskii EP, Kornyakov MV, Afanas’ev AD (2014) Technological solutions for saving energy and reducing the capital intensity of gas-removal and gas-cleaning systems at aluminum factories. Metallurgist 57(9–10):779–782 12. Shahray SG, Belyanin AV, Kondratev VV, Lapaev II (2014) Decreasing of ohmic loss of stress at gas-containing elcectrolyte layer in electrolytic cell with self-baking anode. Tsvetnye Metally 8(860):46–49 13. Kondratev VV, Ershov VA, Shahray SG, Ivanov NA (2015) Preliminary heating of calcined anode. Tsvetnye Metally 1(865):54–56 14. Ershov VA, Sysoev IA, Kondratiev VV, Bogdanov YuV, Kamagantsev VG (2012) Controlling the concentration of alumina in the electrolyte during the production of aluminum. Metallurgist 55(11–12):859–864 15. Ershov VA, Sysoev IA, Kondrat’ev VV (2013) Determination of aluminum oxide concentration in molten cryolite-alumina. Metallurgist 57(3–4):346–351 16. Shakhrai SG, Budnik EV, Kondratiev VV (2013) Effect of deposits in the sub-bell space of s-8 and s-8bm electrolysis cells on the environmental indices of the electrolysis operation. Metallurgist 56(9–10):700–704 17. Vetyukov MM, Tsyplakov AM, Shkol’nikov SN, (1987) Electrometallurgy of Aluminum and Magnesium. Metallurgiya, Moscow 18. Galevskii GV, Mintsis MYa, Sirazutdinov GA (2010) Aluminum Metallurgy: A Handbook of Technological and Design-Basis Measurements and Numerical Analyses. Sib. State Industrial Univ, Novokuznetsk 19. Karvats’kyi AYa, Dudnikov PI, Leleka SV, Zhuchenko AI (2005) Application of the method of boundary elements to the solution of three-dimensional problems of heat conduction. Nauk. Visti NTUU KPI 5:5–13 20. Arkhipov, GV.: Mathematical modeling of aluminum reduction cells in the Russian Aluminum Company. Light Metals, pp. 473–478 (2004)

Heat System for Rigid Wedge Valves A. A. Bazarov(B) , N. V. Bondareva, and A. A. Navasardyan Samara State Technical University, 244 St. Molodogvardeyskaya, Samara 443100, Russia [email protected]

Abstract. The authors consider the problems of electromagnetic, thermal, and hydraulic processes during heating of the valve with liquid to eliminate jamming. This effect is characteristic of rigid wedge valves with a decrease in ambient temperature. Heating the valve body is used to eliminate jamming. The use of induction heaters allows for local heating with a specified intensity. This heating method does not require a tight fit of the heater to the valve body. The power and location of heart source are determined taking into account the limitations of the maximum value of the liquid temperature. Overheating can lead to vaporization and increased pressure. The analysis of convective flow in the inside cavity of valve body showed the mixing processes near lower surface of wedge are less intense and limited by a small volume. The movement of fluid at the side walls occurs along the entire height of the valve body. This difference leads to local overheating of liquid in the lower areas. In designing of the induction heater, the localization of heating zones is provided. This is necessary to prevent eddy currents in the areas of the housing where overheating is dangerous. In the design of the inductor, the cup-shaped magnetic core is made of ferrite to reduce the magnetic dispersion field and increase power factor. The lateral protrusions of the magnetic core limit the area with eddy currents. Keywords: Valve · Rigid wedge · Thermal–hydraulic processes · Induction heating

1 Introduction The flow of pumped liquids and gases is controlled by means of locking elements, one of which is a wedge valve. It is used as a locking construction and is not intended for flow control. Wedge valves are considered to be the most reliable type of shut-off valves. The application field of the wedge valves is pipelines with different working environments. The contact surfaces of the valve body (seat) are located at a slight angle to each other. The gate has the shape of a wedge, which in the closed position fits tightly between the contact surfaces. There are several types of steel wedge gate valves [1]. Good tightness is provided in valves with a unit-cast, solid wedge, but with a significant decrease in the ambient temperature, jamming is possible [2]. This problem is solved in valves with a composite double-disk locking element or rubberized wedge. Valves with a rigid wedge © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_149

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are in operation despite the advantages of construction with a composite or rubberized wedge. The rigid wedge provides reliable tightness of the locking element. This is achieved by high-precision processing of the wedge and seat surfaces of the body [2, 3]. Figure 1 shows a simplified design of the valve with a rigid wedge. The sealing surfaces are surfaced with high-alloy steel, which allows to provide the specified tightness during operation for a long time. The valve body is made of A732 (2A) steel.

Fig. 1. Valve section: 1—body; 2—wedge; 3—cover; 4—rod; 5—cavity under the cover; 6— lower cavity.

A tight fit of the wedge with the body is provided when creating a significant force. For this motors, power from 0.025 kW to 7.5 kW are used with a nominal diameter of 50 mm to 1200 mm. The valve drive contains a reducer that reduces the rotation speed and increases the torque. All this leads to an increase in the forces created when lifting the wedge, which can lead to a break in the rod (spindle) when it is jammed [4].

2 Problem Statement Deformations of the body and components of the valve when the temperature changes occur due to differences in physical properties and geometric non-symmetry disproportionately. Many papers have been devoted to the problems of reliable operation of valves and jamming [2–9]. The paper deals with the improvement of calculation methods [6, 9], analysis of the causes of destruction [7], modeling of deformation processes [10, 11], and improvement of operational characteristics [12]. To explain this problem, an analysis was made of the processes of deformation of valves with different body designs [10]. The reason for the occurrence of significant compressive forces in the lower part of the wedge is revealed. This phenomenon occurs in valves, where the body is narrowed at the bottom. In valves with a cylindrical body shape,

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there are no deformations that can lead to jamming during cooling. Theoretically, it is possible to create a system for monitoring the status of the valve. For this, it is necessary to apply short-term control actions to the electric drive for opening and subsequent closing when changing external conditions, so that the stress in the valve is always at an acceptable level. A similar approach is realized in the rig [13]. In practice, using a steam generator to heat the valves requires manual labor and time to transport the equipment to the location. It is more convenient to use electric heating. Induction heating is more preferable than resistive heating due to the complex shape of the lower part of the body. When calculating the parameters of the induction heater, power, dimensions, and location, it is necessary to take into account the limitations on the maximum temperature of the liquid inside the valve body. Liquid temperature depends on thermophysical characteristics and convective processes. When designing a heater, it is necessary to develop electromagnetic, thermal, and hydraulic models of the valve—liquid system, make the calculations, and determine parameters.

3 Development of Mathematical Models A lot of work is devoted to determining the parameters of thermal deformation processes in the design of the valve construction [10–15]. Induction heating systems are used for a long time, and compete with other types of heating with great success. High temperature and high frequency of the supply voltage significantly limit the use of magnetic conductors in the manufacture of inductors. This has a negative effect on the energy characteristics of induction heating devices, mainly due to the large scattering fields of the magnetic field. Lately the use of magnetic conductors made of new materials, such as magnetodielectrics, has expanded. This has a positive effect on managing the distribution of the magnetic field and internal heat sources in the load. The proposed work is aimed at expanding the capabilities of induction devices through the use of magnetic cores. The ultimate goal of this solution is to increase the manageability of the process of forming internal sources. The peculiarity of the problems under consideration is the complexity of the mathematical apparatus and the significant resource intensity of calculations [16–21]. Simulation of thermal processes is less resource-intensive. This procedure significantly complicates the calculation, given the increase in the size of the source vectors and stiffness matrices when integrating electromagnetic and thermal problems. It is much more economical and faster to identify the trajectory of current flow and determine the power of heat generation, and then transfer it to the heat model. Of course, it is not profitable to do this with a one-time solution or with a two-dimensional model. Induction heating systems usually use an increased voltage frequency, which together with a low power factor causes an increase in voltage and power losses in the grid. The solution of the problem of an induction system designing should be focused on achieving the following indicators: minimum weight of the equipment complex, maximum autonomy from engineering systems, and high precision of temperature control [5]. The main reason for the jamming of valves with a rigid wedge was identified by studying the deformation processes in the valve, which occur when the ambient temperature decreases [10]. The narrowing of the body in the lower part leads to the appearance

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of forces directed along the horizontal axis of the valve. In the upper part of the wedge, the forces are directed to stretch, and in the lower part to compress. The tensile forces are not large enough to form a visible gap, but the compressive forces are sufficient to prevent the valve actuator from jamming or breaking the rod. To eliminate the phenomenon of jamming in this situation, you need to warm up the valve. Heat flows in different areas are caused by thermal conductivity and convection processes in the liquid, so the complex design of the valve does not allow to act selectively on individual elements. Studies of thermal and hydraulic processes are necessary to determine the effective design of the heater [22]. The use of industrial frequency currents allows the use of charged iron as the material for the magnetic core, but for disk inductor constructions, the absence of electrical conductivity in one direction is not enough. Therefore, the use of ferrites is more advantageous for the magnetic core. Two inductors for heating the vertical part of the body are made in the form of multiturn coils located in an annular slot. The use of numerical calculation methods makes it possible to obtain effective heating systems for bodies of complex shapes [23, 24]. Elcut and Comsol software packages are used for designing an induction heater, which allow calculations of electromagnetic and thermal processes [19–21]. To provide the flux closure and currents when changing the direction of motion and to describe the electromagnetic field, a set of vector magnetic potential A and electric scalar potential V is used.   ∇ ×A + σ ∇V = J e , (1) jωσ A + ∇ × μ0 μr   (2) −∇ jωσ A + σ ∇V − J e = 0, →

→

→

→ → →

∂ ∂ j ∂ + ∂z where ∇—nabla, ∇ = ∂x i + ∂y k , where i , j , k —unit vectors along the axes x, y, z, respectively, μ0 , μr —vacuum magnetic permeability, and i relative magnetic permeability of the media. The zero equality of the potential combination on a surface far from the structure is used as boundary conditions.

A = 0; V = 0.

(3)

A three-dimensional region is used to describe thermal processes. The equation of thermal conductivity with internal heat sources has the form, ρCP

∂T + ∇ · (−k∇T ) = Q − ρCP u · ∇T , ∂t

(4)

where ρ—material density, k—coefficient of conductivity, T —temperature, Q—specific heat input, and u—vector of the displacement velocity. The speed of movement is provided for the liquid filling the body. Convective heat transfer in the formula is used as boundary conditions on surfaces, k

∂T = α(T − Text ), ∂n

(5)

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where n—normal line in relation to the surface under consideration. The condition of thermal insulation is set on the line of symmetry. ∂T = 0. (6) k ∂n The initial temperature value is assumed to be equal to the ambient temperature T0 = Text = 253 K. The fluid velocity is determined in the application for calculating hydraulic processes and imported into the thermal model.  T (7) u= uv . The coefficient of conductivity k = 0,11 W /(m · K), density ρ = 880 kg/m3 , and heat capacity CP = 1700J /(kg · K). Icpolzovano ypavnenie Have-Ctokca dl necimaemo idkocti dl modelipovani gidpavliqeckix ppoceccov.

  (8) ρ(u · ∇)u = ∇ · −pI + η ∇u + (∇u)T + F, ∇ · u = 0,

(9)

where coefficient of dynamic viscosity η = 0.005 Pa · s. The vertical component of the lift force is set for the formation of convective fluid transfer flows, Fy = −9.81 · (880 − 0.6 · (T − 253)),

(10)

Fy = −g · (ρ − kV · (T − T0 )), where kV = 0.6 kg/(m3 K)—coefficient of decrease in fluid density due to temperature increase. The zero velocity on the line corresponding to the wall is set as the boundary conditions. u = 0.

(11)

The velocity is set as a scalar value in the sections of axial symmetry Uw and the condition prescribes n · u = 0, u · t = Uw

(12)

  where t—vector value t = −nx, ny . Thus, the boundary condition is written.    n · u = 0, t · −pI + η ∇u + (∇u)T n = 0.(13). The simulation of hydraulic processes in this problem has features related to heating and the complex shape of the internal cavity of the valve. This makes calculation difficult, pacqet [25]. Thus, a complex of mathematical model has been formed for two- and threedimensional formulations, which allows one to calculate electromagnetic and thermal processes when studying the properties of an induction heater with a magnetic core.

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4 Calculation of the Heating System Parameters Heat sources are provided in the lower part of the body under the wedge, in the vertical part of the section, from the base to the horizontal center line. The simulation of thermal processes without taking into account hydraulic processes was carried out on a three-dimensional model. One inductor is located in the lower part of the body and two inductors in the vertical part at a height not exceeding the point of the center line of the valve. A temperature control system that limits the maximum value is implemented in the simulation. The required heat dissipation capacity in each zone was determined when calculating the thermal processes. The power of the lower inductor is 2 kW, for vertical ones 1 kW. The total power is 4 kW. The considered approach to solving the heating problem has a large error in calculations due to the lack of hydraulic processes. The complexity of the design, the size of the design area, and the combination of solid and liquid media make it difficult to use a three-dimensional thermohydraulic model. A two-dimensional model for a liquid medium is used to study the processes of convective heat transfer. The heat input is specified with the boundary conditions of the third order. The heat transfer coefficient α is taken to be 500. This allows us to correctly approximate the actual process of heat transfer from the metal wall to the liquid. In the actual heating process, the wall temperature increases and it becomes liquid. In the actual heating process, the wall temperature increases and the liquid warms up simultaneously. Taking into account the duration of the heating process of the valve body walls, to speed up the calculation, the wall temperature is assumed to be 100 °C. The temperature and velocity distributions for time points 2 s and 12 shown in Fig. 2 illustrate the rapid formation of a convective fluid flow. The flow of liquid leads to the rise of a thin layer along the outer surface, followed by lowering along the surface of the wedge. The small thickness of the liquid layer in the lower part does not allow the formation of large vortices. At time 12 s, a large number of small moving vortices are formed in the entire volume. Because of this, the density of the heat flux into the liquid from the wall is unstable (Table 1). At the time of 10 s, there is some stabilization of the heat exchange process and the movement of the liquid. After that, the density of the lower section flow q2 changes within 3%, and for the upper section q1 —5%. The maximum velocity of the liquid near the wall increases to 4 sm/s. This leads to the fact that the density of the heat flux from the wall in comparison with the transfer of heat to a stationary fluid is more than 10 times. As can be seen from Table 1, the density of the heat flux q3 absorbed by the wedge is only 24–34 W/m, which is much less than the flux absorbed by the liquid. The results obtained show that heat transfer to the “seat-wedge” joint is more efficient due to convective flows in the liquid when the maximum value of the wall temperature is limited. Much of the heat is absorbed by the upper layers of the liquid above the wedge. Therefore, the heating of the wedge is a long process, taking into account only the convective heat transfer. The calculated value of the heater power can be determined based on the heat flux density and the area of the side and bottom surfaces of the housing that are available for placing induction heaters. Based on the values of the surface area of the base and the vertical surface fragment and the heat flux densities, the heat output values in the load

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Fig. 2. Temperature and velocity distributions of the liquid in the valve in the wedge subspace: a—at time 2 c; b—at time 12 c. Table 1. Heat flux density from the walls t, s

4

6

q1 , W/m 1009 875

8

10

11

12

14

16

18

823

799

806

819

841

839

855

q2 , W/m 1988 2115 2238 2239 2220 2277 2232 2171 2170 q3 , W/m 10

4

5

23

18

24

27

26

34

are 800 W and 2 × 100 W. Previously, the obtained power values are sufficient to heat the valve, with a nominal diameter of 150 mm and taking into account oil filling, by 20 degrees for 1800s.

5 Determination of Inductor Parameters Determining the parameters of inductors for heating the lower cup-shaped surface and the sector of the front cylindrical surface is performed using two-dimensional models, in which some assumptions provide an acceptable error. The appearance of the first inductor is shown in Fig. 3. The multilayer coil on the lower side is bounded by a magnetic core that reduces the scattering fields and serves as a support construction. Two versions of the inductor are considered: without cooling when using industrial frequency voltage and with cooling when using high frequency. At a frequency of 50 Hz, the limitation is the temperature of the inductor. Increasing the number of layers increases

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Fig. 3. Inductor for the lower surface of the valve body.

the magnetic field strength and power in the load. Each additional layer reduces the efficiency and worsens the heat exchange conditions of the coil with the environment. As a result, due to the current density restriction, the power value in the load is obtained P2 = 500 W instead of the required 800 W. The coil contains 135 turns of copper splint with a cross section of 1, 5 × 3 mm2 . The inductor current is 45 A and the voltage is 220 V. The power factor is 0.278 and the efficiency is 0.927. The higher frequency option is more attractive for the reliability of the inductor, since the required power in the load is provided without overheating the conductors. However, the need to use a semiconductor frequency converter and an inductor cooling system reduces the reliability of the heating system. This is not acceptable for maintenance-free installations. The use of a profiled tube with sides equal to 10 mm is provided as the conductors of the inductor coil. Based on the results of the calculations (Table 2), a step-down transformer is required for matching with the frequency converter. Table 2. Parameters of inductors at different current frequencies. F, Hz

2400 4000 10,000 20,000

I, A

195

155

104

75

U, V

27

31

43

54

P2 , W

781

801

814

780

Pind , W 387

365

203

Pind , W

1188 1154 1017

142 922

In general, the high-frequency heater is inferior to the low frequency due to the cost and complex implementation. The inductor for heating the sector of the vertical front surface of the valve body has a design with one annular slot in the magnetic core. A multi-turn coil, having the shape of a rectangle, is located in the magnetic core. When the load power is increased to 200 W, the voltage is 220 V, the current is 71 A, the number of turns is 51, and the

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conductor cross section is 10 mm2 . The size of the inner window filled with a core is 10 × 10 mm. Studies have shown that without a central core, the characteristics of the inductor deteriorate dramatically.

6 Conclusion The development of an induction heating system for individual sections of the valve body allows you to solve an important problem to eliminate jamming and provides operational management of pipelines with petroleum products. Studies of electromagnetic, thermal, and hydraulic processes in the system “inductor-valve body-oil” allowed us to determine the parameters of induction heaters and the location of temperature sensors that guarantee trouble-proof operation. Acknowledgements. Work on the article was supported by the Russian Federal Property Fund (project no. 19-06-00212).

References 1. Shegelman, I.R., Vasilyev, A.S., Shchukin, P.O.: Zadvizhka zapornaya dlya truboprovoda (Gate valve for the pipeline) Nauka i biznes: puti razvitiya. Izdatelstvo: Fond razvitiya nauki i kultury 8(50), 36–38 (2015) 2. Podrezova IS, Shutova LV, YuYe U, Pugacheva OYu, Yelzhov YuN (2014) Analiz prichin zaklinivaniya i obryvov shtokov truboprovodnoy elektroprivodnoy armatury (Analysis of the causes of jamming and breaks in the rods of electric pipeline valves). Globalnaya Yadernaya Bezopasnost 4(13):32–37 3. Zhuk, D.I., Gaffanov, R.F., Shchenyatskiy, A.V.: Analiz vliyaniya mekhanicheskikh vozdeystviy na uplotnitelnye poverkhosti zaporno-reguliruyushchey armatury (Analysis of the influence of mechanical stresses on the sealing surfaces of shut-off and control valves). Vestnik IZhGTU imeni M.T. Kalashnikova. Izdatelstvo: Izhevskiy gosudarstvennyy tekhnicheskiy universitet im. M.T. Kalashnikova 19(2), 27–29 (2016) 4. Kakuzin VB et al (2008) Problimy nastroyki elektroprivodov zadvizhek (Problems of setting up electric actuators of valves). Armaturostroenie 4(55):74–76 5. YeI B (1966) Posadki s natyagom v mashinostoenii: Spravochnoe posobie (Fixing tight in mechanical engineering). Mashinostroenie, Moscow, p 168 6. Kuznetsova, N.V.: Truboprovodnaya armatura. Konstruirovanie i raschet zadvizhek stalnykh klinovyhk (Pipe fittings. Design and calculation of wedge gate valves). Izdatelstvo Sputnik, Moscow, p. 175 (2010) 7. Muratayev, F.I.: Issledovanie razrusheniya litogo korpusa zadvizhki magistralnogo nefteprovoda (Investigation of the destruction of the molten body of the valve of the main oil pipeline) Professionalnye kommunikacii v nauchnoy srede—factor obespecheniya kachestva issledovaniy. Sbornik materialov Vserossiyskoy nauchno-prakticheskoy konferentsii. Izdatelstvo “Pero”, Moscow, pp. 27–32 (2017) 8. Zakirnichnaya MM, Kulsharipov IM (2016) Osobennosti rascheta resursa bezopasnoy ekspluatatsii klinovykh zadvizhek s uchetom rabochikh parametrov v tekhnologicheskikh truboprovodakh (Features of calculating the resource for the safe operation of wedge gate valves, taking into account operating parameters in process pipelines). Neftegazovoe Delo 14(4):121–125

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9. Zhukovskiy VK, Gokhman AR (2009) Svyaz koefficienta lineynogo temperaturnogo rasshireniya s ostatochnymi napryazheniyami (The relationship of the coefficient of linear thermal expansion with residual stresses). Gurnal Tekhnicheskoy Fiziki 79(4):90–96 10. Bazarov AA, Bondareva NV, Navasardyan AA (2019) Modelirovanie protsessov deformatsii v zadvizhke (Modeling of deformation processes in a valve) “EurasiaScience” XXV Mezhdunarodnaya nauchno-prakticheskaya konferentsiya. Nauchno-izdatelskiy tsentr “Aktualnost RF” . Sbornik Statey. Chast I:69–72 11. Barbotko MA (2018) Chislennoe modelirovanie termicheskikh napryazheniy i deformatsiy v tsilindre s upruguplasticheskoy obolochkoy i vyazkouprugim zapolnitelem (Numerical simulation of thermal stresses and strains in a cylinder with an elastoplastic shell and a viscoelastic filler). Vestn. Ingenernoy Shkoly Dalnevostochnogo Federalnogo Universiteta 4(37):16–23 12. Mayskiy RA, Chernova AYu (2014) Vozmozhnosti programmnykh kompleksov na osnove metoda konechnykh elementov pri otsenke rabotodosobnogo sostoyaniya elementov truboprovodnoy armatury (Possibilities of software systems based on the finite element method in assessing the operational state of pipeline fittings). Informatsionnye Tekhnologii. Problemy I Resheniya 1–2:47–49 13. Ma W, Ma F (2016) Modeling and experimental study on drilling rig anti-jamming valve with BP neural network. Eng. Rev. 36(2):99–106 14. Sathishkumar S, Hemanathan R, Gopinath R, Dilipkumar D (2017) Design and analysis of gate valve body and seat ring. Int. J. Mechan. Eng. Technol. 8(3):131–141 15. Glukhov, V.I., Shalay, V.V., Grinevich, V.A., Panin, YuN.: Geometricheskoe modelorovanie detaley klinovogo zatvora dlya obespecheniya germetichnosti zadvizhek (Geometrical modeling of wedge gate parts to ensure valve tightness) Tekhnika i tekhnologiya neftekhimicheskogo i neftegazgvogo proizvodstva. Materialy 8-y mezhdunarodnoy nauchno-tekhnicheskoy konferentsii. Omskiy gosudarstvennyy tekhnicheskyy universitet, pp. 193–194 (2018) 16. Zenkevich O (1975) Metod konechnykh elementov v tekhnike (Finite Element Method in Engineering). Mir, Moscow, p 541 17. Khalifa M, Barka N, Brousseau J, Bocher P (2019) Optimization of the edge effect of 4340 steel specimen heated by induction process with flux concentrators using finite element axis-symmetric simulation and experimental validation. Int. J. Adv. Manuf. Technol. 104(9–12):4549–4557 18. Alferov, B.I., Steshenkova, N.A.: Primenenie MKE dlya resheniya teplovoy i deformatsionnoy zadach rascheta svarochnykh deformatsiy sudovykh korpusnykh konstruktsiy (FEM for solving thermal and deformation problems of calculation of welding deformations of ship hull structures). Trudy TsNII im. akad. A.N. Krylova 56(340), 147–162 (2010) 19. Nemkov VS, Demidovich VB (1988) Teoriya I raschet ustroystv induktsionnogo nagreva (Theory and Calculation of Induction Heating Devices). Energoatomizdat, Leningrad, p 280 20. Kuvaldin AB (2005) Matematicheskie modeli dlya issledovaniya elektromagnitnogo polya v ferromagnitnykh sredakh (Mathematical models for the study of electromagnetic fields in ferromagnetic environment). Elektrichestvo 11:56–61 21. Gnatov AV, Argun Shch V, Chaplygin EA, Sabokar OS (2015) Induktsionnyy nagrev ferromagnetikov ploskim krugovym mnogovitkovym solenoidom (Induction heating of ferromagnets with a flat circular multi-turn solenoid). Vestn. Kharkovskogo Natsionalnogo Avtomobilno-Djrozhnogo Universiteta 70:113–118 22. Hinov, N., Petkov, T., Ibrishimov, H.: Modeling of the thermal and electromagnetic processes in the induction water heating system. 28th International Scientific Conference Electronics, ET 2019—Proceedings, Sozopol, Bulgaria, pp. 12–14 (2019) 23. Mannanov, E., Galunin, S., Yermekova, M., Nikanorov, A., Nacke, B.: Numerical simulation, investigation and development of induction systems for heating of disks with complex profile. Proceedings of the 2019 IEEE Conference of Russian Young Researchers in Electrical and

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Mathematical Modeling of Gas Transportation System Using Graph Theory K. Syzrantseva(B) , V. Rumyantsev, and M. Alfyorova Tyumen Industrial University, 38, Volodarskiy Street, Tyumen 625000, Russia [email protected]

Abstract. The article describes building a high-precision model of a gas transportation system based on the graph theory, which allows achieving optimal functioning of pipeline networks under normal operation conditions and in emergencies. The issues of mathematical description of gas transportation system initial information uncertainty and algorithms designed for searching optimal routes have been analyzed. The choice of the Floyd algorithm for finding the shortest path between any two graph vertices has been substantiated. The algorithm software implementation has been considered in detail. The software module structure, implemented in MATLAB, performing mathematical modeling and optimization of gas transportation system operation conditions has been given. During the implementation of the source environment, an open system of inclusion of graph theory methods to determine the shortest path from one node of the modeled diagram to another has been formed. The developed software has been illustrated by an example of finding the shortest path of the directed graph designed for a fragment of the process flow diagram of OOO “Gazprom Pererabotka.” Keywords: Mathematical modeling · Gas system · Graph theory · Floyd algorithm · Optimal path · Computer simulation · MATLAB

1 Introduction Currently, strict requirements are specified to the certainty of determining pipeline systems’ functioning parameters in the sectors of the fuel and energy complex, so it is necessary to ensure high accuracy of modeling gas transformation systems (GTS) [1–3]. However, when modeling, they often have to use imprecise information about the state and characteristics of pipelines [4–6]; as a result, there is a need to perform optimization calculations in order to plan gas transportation system operation modes [7]. During the pipelines operation, hydraulic resistance coefficients vary due to hydrates and condensate formation as well as sludge deposition in the pipe cavity. Over time, the pipeline strength characteristics [8–10] worsen resulting in a decrease in the maximum allowable gas pressure to reduce the probability of pipeline failure [9, 11, 12]. Using the modern method of building a mathematical model applying the graph theory, it is © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_150

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possible to build a high-precision model of a gas transportation system, which allows to achieve optimal functioning of pipeline networks under normal operation condition and in emergencies [13–15]. Up to date, there are complex pumping technologies with a possibility of multiple connections of incoming and outgoing trunk pipelines between tank farms, which are located on the same technological site. At such facilities, it is difficult to determine quickly all possible connections between flow sources and receivers, depending on the state of the shut-off valves. The graph theory [16–18] is an adequate apparatus for modeling complex gas condensate transportation technological structures for the purpose of subsequent high-precision flow processing and industrial process control.

2 Theoretical Part In control systems, industrial process modeling software complexes are used to perform process flow calculations and solve other dispatching problems. In these complexes, gas transport technological workflows are presented in the form of computational objects and schemes in the solution of process flow problems [18, 19]. The choice of algorithms and computational procedures for solving the corresponding process flow problems largely depend on this presentation. The GTS design scheme of any topology can be represented by a graph whose edges are the computational objects (Fig. 1a). Numerical identifiers are assigned to all the computational objects. Figure 1b shows the diagram of information chains of objects of the computational scheme. The efficiency of calculations is determined based on a number of criteria; in this case, the dominant criterion is provision of minimal energy consumption and in an emergency operating condition, it is minimization of losses [7, 20]. These cases are particular options for solving the optimization problem with a transfer of a number of criteria into restrictions. However, in the general case, these criteria can be ranked according to different principles, and classical methods of multi-criteria optimization can be used to solve this problem [5, 21]. Floyd algorithm [22–24] was chosen to solve the problems with which high-precision calculations can be performed, since it is effective for finding all shortest paths in dense oriented graphs when there are a large number of edge pairs between vertex pairs. Dijkstra algorithm [23] is not suitable for this task due to the large constant factor and the inability to work with dense graphs while Floyd algorithm will allow an optimal control of industrial processes both under normal operation conditions and in an emergency.

3 Mathematical Description of Floyd Algorithm Floyd method is directly based on the fact that in a graph with positive edge weights, every non-elementary (containing more than one edge) shortest path consists of other shortest paths. This algorithm is more general than Dijkstra algorithm because it finds the shortest paths between any two vertices of the graph [23, 25]. Floyd algorithm uses matrix A of nxn size, in which the lengths of the shortest paths are calculated. Element A[i, j] is equal to the distance from vertex i to vertex j, which has a finite value if there is an edge (i, j), and, otherwise, is equal to infinity.

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Fig. 1. a Model optimal control of GTS; b diagram of chains of objects of the computational scheme.

In accordance with Floyd algorithm, it is necessary to build a succession of matrices:    (k)  C (k) = Cij , (k = 0, 1, 2, . . . , n),    (0)  where C (0) = Cij  is a matrix of graph weights (0) Cij

     v ; , v w vi , vj , arc weight i j   = ∞, with no arc vi , vj ,

(1)

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(k)

and Cij (k = 1, 2, ...n) is the length of the shortest path from vertex vi to vertex vj , all the intermediate vertices of which are contained in a set of v1 , v2 , ..., vk , i.e., are contained in the first k vertices. It is evident that Cijn is the unknown distance between vertices and vj . Matrices C (k−1) and C (k) are bound by the following recurrence formula:  (k) (k−1) (k−1) (k−1) . (2) Cij = min Cij , Cik + Ckj We consider the shortest [vi , vj ] path P with intermediate vertices from set v1 , v2 , ..., vk . Two cases are possible: either vertex vk enters this path or not. (k) (k−1) If vertex vk does not enter path P, then, as it is easily seen that Cij = Cij . If vertex vk enters path P, then, breaking this path into the paths from vi to vk and from vk to vj , we get two new paths, all the intermediate vertices of which enter set v1 , v2 , ..., vk−1 v1 , v2 , . . . , vk−1 . Since any sub-path of the shortest path is itself the shortest path between the corresponding vertices, this is a truly proved equality. Equality 2 makes it easy to find the distances between all pairs of vertices: it is (0) (1) (n) necessary to consistently calculate values Cij , Cij , ..., Cij for all pairs of vertices and (n)

take into account that the distance from vi to vj is equal to Cij . (1)

(0)

The algorithm below assumes that Cij = 0 and Cij = ∞ if the arc (vi , vj ) is missing. The nonnegativity of the weights of arcs is not assumed, but it is assumed that there are no contours of negative length in the graph. The algorithm uses a twodimensional array Pred of size [1..n, 1..n]. Pred [i, j] is equal to the number of the vertex, which is the last but one in the shortest [vi , vj ] path (the last vertex in such a path is vertex vi ). If Pred [i, j] = k, then looking at the value of Pred [i, k], we get the next vertex in the [vj , vi ] path. Thus, moving from element to element of the Pred array it is easy to build a path for any pair of vertices. Below is an algorithm for calculating distances between all pairs of vertices.    (0)  Entry: Graph G = (V , E, c), given by the matrix of weights C (0) = Cij  of n order. Exit: Distance dij for all pairs vi , vj ∈ V , matrix Pred, in which Pred [i, j] is equal to the number of the last but one vertex in the shortest [vi , vj ] path. The software implementation of the algorithm is given in Fig. 2.

4 Software Implementation of an Algorithm for Building a Directed Graph (Digraph) The described algorithm for obtaining a digraph with Floyd method was implemented in the MATLAB software environment as a function and placed in the Graph Theory Toolbox. Stage 1. Validation of the input data is performed. This is done using the grValidation function included into the Graph Theory Toolbox. If the weights of vertices are not specified by the user, it is necessary to set them as single ones (the path with the minimum number of vertices will be found).

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Fig. 2. Software implementation of floyd algorithm.

Stage 2. Duplication of vertices. The vertices of the original digraph have numbers from 1 to n. We assign these numbers to the first vertices of each pair (vertex v11 in Fig. 2). The second vertex of each pair (V12 in Fig. 3) will get a number, which is n greater than the first one. New n of the arcs connect the vertices of each pair; only these arcs will have weight.

Fig. 3. Duplication of graph vertices.

Stage 3. Search for all digraph bases and cobases, combining the vertices in them and computing the number of vertices in the resulting sets S and T (Fig. 4a). To find bases and cobases, functions grBase and grCoBase from package Graph Theory Toolbox are used. Stage 4. Complement of the resulting digraph with two more vertices: a common source S0 and a common drain t0 , as shown in Fig. 4b. Building arcs from S0 to all vertices S and from all vertices T to t0 .

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Fig. 4. a Combining the vertices; b adding the initial and final vertices.

Stage 5. To obtain the digraph with weighted arcs, it is necessary to solve an ordinary problem of the shortest path and get the result: vertex numbers and the total weight of the path (or the number of vertices). The grShortPath function is available in the Graph Theory Toolbox.

5 Computer Modeling of Gas Transportation System Facility Management As an example, we consider modeling of the facilities of an actual gas transportation system of OOO “Gazprom Pererabotka,” the work of which is laid out in the operating procedure of the enterprise (TP-6400-20,806-07-2013) [26], and their technological connections are presented in the form of a graph. The graph nodes represent the places where connections of the modeling objects can converge [19, 23]. Because the graph is determined by either its adjacencies or its incidences, this information can be conveniently represented in a matrix form. For computer processing, the matrix form is transformed into a list of weighted arcs of the directed graph [25]. This form of data organization provides advantages that allow data optimization for an implementation of the following algorithms: visualization of the pipeline structures

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topology, determination of the flow blockage threat, and obtaining the pipeline system operation parameters required to determine the optimal strategy for managing the industrial processes of product transportation. We regard a fragment of the process flow diagram of OOO “Gazprom Pererabotka” (Fig. 5). Applying the method of describing the process flow as a directed graph, we obtain the following object graph (Fig. 7).

Fig. 5. Fragment of the tank farm process flow diagram.

In this figure, vertices 1A…6A indicate receiving tanks P-1201/1A…6A in the workflow diagram (Fig. 5). The properties of these vertices are binding to an actual reservoir and a type of the vertex (reservoir). Vertices with designations 1A/1…6A/5 are gate valves, which correspond to the numbers in Fig. 6. The properties of these vertices are correspondence to an actual gate valve and a type of the vertex (gate valve).

Fig. 6. Directed graph of a process flow fragment.

Vertices with the letter U designate technological pipelines that act as binding elements of the graph vertices in accordance with the operating procedure of the facility. This graph is directed, which makes it possible to represent the backpressure valves of technological pipelines. The graph processing has been implemented in the MATLAB software environment, since it is characterized by maximum speed of searching connections between the vertices and minimum amount of RAM used.

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To minimize the use of RAM, it is necessary to minimize the graph by reducing the vertices starting with the letter U, and leaving the connectivity of the control subjects unchanged. This will reduce the number of iterations during the cycle of searching for a reach stack. As a result of the program operation, we obtain a built original digraph. The shortest route along the given path, obtained as a result of testing the developed program, is shown in Fig. 7.

Fig. 7. The result of finding the digraph shortest path.

6 Conclusion The proposed mathematical models and the graph theory methods, as well as their software implementation allow obtaining higher technological dispatching solutions, facilitating the reduction of energy costs for gas transportation. Process flow diagrams of a gas transportation system, presented in the form of a directed graph, as well as algorithms for finding optimal paths between their vertices, are effective for processing information at the automated workplace of an operator or a scheduler. This, in turn, allows improving the perception of the obtained information by visualizing a gas condensate flow, as well as determining the locked sections of the gas pipeline (by assessing the reach from technological pipelines).

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Diagnostics of a Pressure Transmitter Based on Output Signal Noise Characteristics E. S. Tugova(B) , D. D. Salov, and O. Yu. Bushuev South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, Russia [email protected]

Abstract. This paper describes an experimental investigation to develop diagnostics for a common fault mode for an industrial pressure transmitter. Within the transmitter housing, a silicone oil is used to transmit pressure from the isolation diaphragm to the internal transducer. The fault mode entails oil loss through leakage, induced by fatigue or cracking. In collaboration with the manufacturer, faulty transmitters have been engineered with known and controlled leak volumes, so that the signal behavior during incremental liquid leakage can be characterized. It is shown that the amount of liquid in the measuring channel of the pressure transducer directly affects the statistical and frequency characteristics of the output noise. Faulty behavior includes such symptoms as inability to follow the applied input pressure transients and minimum values of signal standard deviation constant with pressure. The experimental work and analysis has been limited by the fixed noise characteristics of the current test rig, and further work with known and controllable process noise is required. Keywords: Fault detection · Diagnosis · Pressure sensor · Self-validation · Signal processing

1 Introduction Pressure transmitters, whether measuring absolute, gage, or differential pressure, are the most widely used sensors in the process industries. Verifying that the measurement data is correct is an essential part of ensuring process safety and efficiency. Therefore, methods and algorithms for checking the diagnostic state of the sensor are required. The development of intelligent instrument with local diagnostic capability led to the concept of the self-validating (SEVA) sensor, proposed by Henry and Clarke [1] and metrological self-check by Taymanov [2]. A SEVA sensor performs the following tasks: • Detecting the most common and/or important faults modes; • Correcting each measurement value for the influence of any fault mode; and • Assessing the quality of the final measurement (with or without a fault being present).

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_151

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SEVA and related concepts have been codified in both UK [3] and Russian [4] standards. A survey of recent developments in multifunctional sensors, including sensor validation, is given in [5]. A key requirement for the development of self-validating instrumentation is the creation of “realistic” fault modes so that detection strategies based on internal signals can be derived. Where a fault mode leads ultimately to complete loss of measurement function, there is particular interest in capturing the transient behavior that is indicative of the condition so that maintenance action can be taken ahead of measurement failure. The contribution of this paper is the development and analysis of a realistic set of intermediate set of faulty conditions for an important class of pressure transmitter failures, where this has been achieved in close collaboration with the transducer manufacturer. This collaboration assists in ensuring that the fault mode creation is realistic and controlled, while the resulting analysis and fault detection strategies may, if successfully completed, lead directly to implementation in industrial products.

2 A Pressure Transmitter and Its Fault Modes According to [6], the main reason for failure in pressure transducers is damage to the diaphragm due to hydraulic shock or sudden pressure pulsations. Hydraulic shock produces microfractures. Microcracks and corrosive environments lead to pitting on the isolating diaphragm. Degradation of the diaphragm may lead to leaking of the silicone oil from the channel. Ignoring the width of the channel and the surface tension of the filling oil, the movement of the oil inside the channel can be described by the equation of the fluid in a pipe [7]: pl

dxd d 2 xd + p2 = p1 + Fpl dt 2 dt

(1)

where xd is the fluid movement, ρ is the fluid density, l is channel length, F is the coefficient of friction for the fluid in the channel, p1 is the pressure at the start of the channel (at the isolating diaphragm to the external process), and p2 is pressure at the end of the channel (at the pressure sensor) on Fig. 1. If there is no pressure in front of the isolation diaphragm, then the pressure outside and inside the fill fluid passageway is equal and the system is in balance. When the input pressure is applied to the isolation diaphragm, it causes a response in output electrical signal. If the integrity of the fill fluid passageway is lost due to a fault, then assuming the silicone oil in the channel is incompressible, several consequences may arise as given below: • Oil will flow out, and the volume of the cavity will decrease due to stable deformation of the diaphragm; • The volume of the cavity will not change, and the leaked oil will be replaced with another fluid or gas.

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Fig. 1. Diagrammatic view of a pressure sensor assembly [8].

This research considers the second option, and assumes that the cavity volume becomes filled with a gas–liquid mixture. The compressibility of this gas–liquid mixture results in a change in the measurement characteristics of the sensor. Any subsequent increase in the process pressure will lead to a deformation of the isolation diaphragm. However, a portion of the transmitted energy will be used to compress the gas–liquid mixture, so that the deformation of the isolation diaphragm is reduced. The specific strain values depend on many factors. However, it is very likely that there will be reduced or even zero mechanical connection between applied pressure and pressure sensor. Figure 2 shows the diagrammatic view of a pressure transducer, consisting of an isolation diaphragm with stiffness C1 , where the input process pressure P1 is applied and a channel is filled with silicone oil to transfer pressure from the isolation diaphragm to a pressure sensor with corresponding pressure P2 and stiffness C2 . Adjacent to the pressure sensor is a tensometric transducer or capacitive cell, at the output of which the initial pressure is converted into an electrical signal. Our basic hypothesis is that the statistical characteristics in time and frequency domains depend on the condition of the transmitter. This was described in former studies. Hashemian [9, 10] explores the effect of impulse line clogging for pressure transducers, investigating how the response time depends on the condition of the sensing line. The technique exploits pressure fluctuations inherent in the external industrial process to perform noise analysis, assuming the following conditions are true: • The dynamics of the transducer are linear; • There is noise in the process. For a good quantitative analysis, additional conditions must be met [9, 10]:

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Fig. 2. Diagrammatic view of a pressure transducer: a normal case; b faulty case.

• Process fluctuations should be broadband (the bandwidth should be wider than that of the transducer); • Process fluctuations must be powerful enough to cause measurable disturbances in the output signal; • Noise at the input and output of the transducer is Gaussian (normal); and • The spectrum of the process should not have significant resonances. The noise analysis method consists of the following steps: (a) recording the sensor output signal; (b) subtracting the DC component; and (c) amplifying, filtering, digitizing, and analyzing the signal in order to estimate the sensor time response. For the assessment, data are collected within 1 h. The time response is determined by the spectral power density of the output signal. Also, in the calculations, the noise probability density is determined and the hypothesis of normality is checked. Rosemount researchers developed the statistical process monitoring (SPM) algorithm [11], which uses statistical analysis methods to determine the condition of process equipment using sensor readings. In [7], it was found that a decrease in the stiffness of the diaphragm of a pressure transducer leads to a reduction in the frequency of the resonance peak of the power spectral density. A similar effect may be due to the presence of air bubbles in the impulse line [12]. When liquid flows out, the characteristics of the sensor become non-linear, the standard deviation of noise decreases, and the asymmetry of the distribution of the noise amplitude increases [12]. At the same time, liquid leakage most likely does not affect the resonance peaks of spectral density [13]. Overall, the literature [7, 9–16] suggests that signal noise analysis can lead to useful diagnostics. A limitation is that previous work is either based on theoretical calculations, or restricted to capacitive [7, 9–13] or piezoresistive [14–16] pressure sensor technology as the research focus. For strain gage pressure sensors, diagnostics can be based on physical redundancy [17]. Despite these limitations, based on similar mechanical processes in capacitive and strain gage pressure sensors, it can be argued that when the internal cavity liquid leaks

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as a result of material damage, the characteristic of the sensor output becomes nonlinear, the standard deviation of noise decreases, and skewness of the noise distribution increases [13].

3 Experiment and Results The challenge was to develop a more complete understanding of the fault modes and the corresponding symptoms in the output signal of a pressure transmitter. Former studies suggest list of symptoms of a malfunction when filling oil leaks: • A sustained drift; • An abruptly decreasing drift (for high range gage); • A change in process noise including amplitude variations or asymmetric noise distributions; • Slow response to, or inability to follow, planned or unplanned plant transients; and • Non-linearity of the transfer function. Russian pressure transmitter supplier manufactured 16 pressure transducers where the fill liquid was carefully controlled to simulate various stages of liquid loss, with air replacing fill fluid: • • • • • • • •

Three non-faulty transducers (100% liquid fill); One faulty transducer (94% liquid fill); Two faulty transducers (89% liquid fill); Two faulty transducers (87% liquid fill); Two faulty transducers (84% liquid fill); Two faulty transducers (83% liquid fill); Two faulty transducers (76% liquid fill); and Two faulty transducers (53% liquid fill).

To provide a meaningful analysis of signal properties, it is necessary that the experimental rig introduces noise. We used a rig in which it is possible to create and maintain static pressure. The rig consists of a circulation pump, a control valve, a flow meter (FE), and a reference pressure transmitter (PE) (Fig. 3). The system generates static pressure of 15 to 500 kPa, which matches the measurement range of the sensors.

Fig. 3. Experimental facility.

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To process signals from a pressure transmitter and extract diagnostic information, the following analysis was developed (Fig. 4). ADC codes are filtered, the trend (moving average) is subtracted, and statistical and frequency characteristics are estimated. The standard deviation (STD) and the skewness of the noise distribution are used as the time-domain characteristics, while the noise power spectral density (PSD) is used to characterize frequency-domain behavior. Based on the value of the characteristics, diagnostic conclusions are drawn.

Fig. 4. The algorithm for processing output signals from the pressure transmitter.

At the beginning of the experiment, it is necessary to check the effect of the fault on signal variance. To do this, compare the statistical and frequency characteristics of normal transmitters with faulty transmitters. Sampling frequency of ADC is 22 Hz. For each pressure setpoint, 20,000 conversions were taken, and statistical characteristics were calculated for every 1000 samples. Note that in the following plots the range shown is mean ± 2 * std range of pressure transmitter output. Liquid loss results in a reduction in standard deviation (STD) of the output ADC codes (an example at 50 kPa is shown in Fig. 5). A significant reduction in standard deviation is observed under identical conditions for transmitters with different volumes of liquid loss. These results suggest that statistical characteristics can act as diagnostic parameters for detecting change in technical condition of a pressure transmitter.

Fig. 5. Standard deviation of noise of an output signal from normal and faulty pressure sensors.

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Experimental results show that • Non-faulty modules are linear and STD depends on pressure (Fig. 6);

Fig. 6. Static characteristics a and STD b for normal sensors.

• The module with 94% fill oil is similar to 100%; • Modules with 87% fill oil or less show faulty behavior (Fig. 7); and

Fig. 7. ADC codes of modules with 94% and 83–87% fill oil.

• Modules with 89% show a transition from normal to faulty behavior (Fig. 8). Faulty behavior includes such symptoms as inability to follow the applied input pressure transients and minimum values of signal STD that is constant with pressure. The assumption that the loss of liquid will lead to a change in the power spectrum is confirmed. Typical results are shown in Fig. 9, where it can be seen that the frequency characteristics changed in faulty case.

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Fig. 8. STD of signal noise for sensor with 94% liquid fill and sensors with 89% liquid fill.

Fig. 9. Power spectrum of output signals from normal and faulty pressure transmitters.

A limitation of both the standard deviation and frequency analysis approaches is that they are dependent on the characteristics of the underlying process noise—a change in process operation may result in a corresponding change in statistical properties leading potentially to a false diagnosis.

4 Discussion and Conclusions This paper has provided first results in a promising new approach to developing pressure transmitter diagnostics, through the carefully controlled introduction of faults by the transmitter manufacturer. In the case of silicone oil loss, a series of transmitters with

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various stages of failure have been prepared, each of which has undergone identical testing in order to determine the resulting signal characteristic changes. The research showed that, as hypothesized, the amount of liquid in the measuring channel of the pressure transducer directly affects the statistical and frequency characteristics of the output noise. However, the experimental work and analysis has been limited by the (fixed) noise characteristics of the current test rig. In future work, we will. • Introduce more graduated fault conditions into additional transducers, in order to obtain a better understanding of the evolution of the statistical properties of the signal with increasing fluid loss; • Develop a new test stand allowing the introduction of wideband noise, to facilitate a more flexible analysis of the frequency-domain effects of liquid loss; • Develop new experimental procedures to provide controlled degradation of the transducer structure (e.g., via fatigue) and this will complement the analysis of controlled liquid leakage; and • Develop improved models of failure mechanisms and corresponding signal characteristics.

Acknowledgements. The team thanks “METRAN IG,” as well as the Aerospace Department of South Ural State University for support and the provision of equipment for conducting experiments.

References 1. Henry MP, Clarke DW (1993) The Self-validating Sensor: Rationale, Definitions and Examples. Control Eng Practice 1(4):585–610 2. Taymanov RE, Sapozhnikova KV (2010) Metrological Selfcheck and Evolution of Metrology. Measurement 43(7):869–877 3. BSI (2005) Specification for data quality metrics for industrial measurement and control systems, BS7986:2005. British Standards Institute, 389, Chiswick High Rd London W4 4AL. BSI (2005). “Specification for data quality metrics for industrial measurement and control systems”, BS7986:2005. British Standards Institute, 389, Chiswick High Rd London W4 4AL. BSI (2005) Specification for data quality metrics for industrial measurement and control systems. BS7986:2005. British Standards Institute, 389 4. GOST R 8.615, Amended (2008) State system for ensuring uniformity of measurements. Measurement of quantity of oil and petroleum gas extracted from subsoil. General metrological and technical requirements. Federal Agency for technical regulation and metrology (in Russian) 5. Deb MB, Roy JK, Recent PS (2019) Advances in Multifunctional Sensing Technology on a Perspective of Multi-Sensor System: A Review. IEEE Sens J 19(4):1204–1214 6. Bushuev OYu, Semenov AS, Chernavskiy AO et al (2012) Detecting changes in the condition of a pressure transducer by analysing its output signal. 20th IMEKO World Congress 1:190– 193 7. Blazquez J, Ballestrin J (1995) Pressure transmitter surveillance: the dominant real pole case. Prog Nucl Energy 29(3):290–303

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8. Strei DM, Willcox CR, Petersen BT et al (2019) In-line process fluid pressure transmitter for high pressure application. US Patent 10209154 B2, Feb 2019 9. Hashemian HM, Mitchell DW, Fain RE et al (1993) Long Term Performance and Aging Characteristics of Nuclear Plants Pressure Transmitters. In: Nuclear Regulatory Commission NUREG/CR-5851 10. Hashemian HM (2011) Measurement of Dynamic Temperatures and Pressures in Nuclear Power Plants. Electronic Thesis and Dissertation Repository 11. Wehrs D (2006) Detection of Plugged Impulse Lines Using Statistical Process Monitoring Technology. Emerson Process Management. https://www.spartancontrols.com/~/media/res ources/rosemount/t/374_rosemount_technical.pdf. Accessed 13 Mar 2020 12. Barbero J, Vela BJ, O, (2000) Bubbles in the sensing line of nuclear power plant pressure transmitters: the shift of spectrum resonances. Nucl Eng Des 199:327–334 13. García-Berrocal A, Chicharro JM, Blázquez J et al (2004) Non-linear noise analysis from a capacitive pressure transmitter. Mechanical Syst Signal Process 18:187–197 14. Hoa Phan LP, Suchaneck G, Gerlach G (2002) Investigation of dynamic disturbance quantities in piezoresistive silicon sensors. Microelectron Reliab 42:1819–1822 15. Szentpáli B, Ádám M, Mohácsy T (2005) Noise in piezoresistive Si pressure sensors. Proc SPIE 5846:169–179 16. Jevtic MM, Smiljani MA (2008) Diagnostic of silicon piezoresistive pressure sensors by low frequency noise measurements. Sens Actuators 144:267–274 17. Henry M, Bushuev OY, Salov D (2018) Sensor validation via ultrasonic signal processing analysis. Global Smart Indus Conf. https://doi.org/10.1109/GloSIC.2018.8570158

Environmental Issues of the Railway Transport and Solutions Thereto A. V. Muratov and V. V. Lyashenko(B) Samara State Transport University, 2V, Svobody Ulitsa, Samara 43066, Russia [email protected]

Abstract. The article is dedicated to the issue of reducing emissions of harmful substances by the railway transport. According to the Russian national strategy of toughening harmful emission limits in railway transportation, autonomous traction equipment is the main source of environmental problems associated with emissions of harmful substances and a major threat to the environmental safety of Russia. The article provides the primary ways to improve ecological compliance of use of autonomous locomotives to resolve the environmental issues in the sphere of railway transportation. The authors concluded on the basis of results of completed studies and computing experiments, as well as of calculations of the total harmfulness of autonomous equipment exhausts that the most promising means to resolve environmental issues are such alcohols as methanol and ethanol. Keywords: Environmental safety · Emissions of harmful substances · Limits for ˇ emissions of harmful substances · Power equipment · Railway transport · CME3 diesel locomotives · Alternative fuel types

1 Introduction The expected results of the primary spheres of the National Environmental Protection Strategy of the Russian Federation for 2012–2020 include the need in developing and implementing environmentally effective innovative technologies to ensure reduction of specific emission parameters and discharge of harmful substances (contaminants) [1]. The issue of reduction of emissions of harmful substances is especially urgent in the sphere of railway transport. RHzD, OJSC, is one of the major consumers of electric power and diesel fuel; their shares in the consumption of these fuel types are 4.6 and 9%, respectively. At the same time, use of power resources is directly associated with environmental problems such as depletion of natural resources (resource supply), airborne emissions of harmful substances, the ozone layer issue (reduction of emissions of greenhouse gases), the smog issue in larger cities, etc. That is why the urgency of the issues related to the improvement of efficiency of power resources by RZhD, OJSC, as well as to the reduction of negative consequences of their use for the environment is beyond any doubt. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_152

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To identify the most environmentally threating objects of railway transport, let us review the consumers of fuel and power resources within RZhD, OJSC, in more detail. According to the holding’s official information, the autonomous traction equipment is by definition the largest consumer of power resources. Ca. 85% of the diesel fuel, i.e., 70.5% of public expenditures on power resources for the primary activity, is used for haulage of trains. The main unit of the traction equipment is a diesel locomotive that employs heat power equipment. Heat power equipment use is accompanied by large emissions of toxic substances.

2 Problem Statement Despite the strategy of toughening limits for harmful substances emitted by the power equipment used in the railway transport and currently manufactured consistently implemented by the government, the average age of the autonomous traction equipment consisting primarily of shunting and mainline diesel locomotives and, therefore, of its power equipment is more than 25 years. They were produced in compliance with GOST standard 24,585–81 regulating and limiting contaminant emission rates. If we compare the contaminant emission limits for the power equipment widely used in the railway transport in Russia with the current limits for new power equipment, we see that the requirements have been significantly toughened in terms of emissions of carbon oxides (CO) (reduction by 75%, i.e., from 10 to 1.5 g/kW*h) and nitrogen oxides (NOx ) (reduction by 85%, i.e., from 29 to 7.4 g/kW*h). We may therefore conclude that most currently used diesel locomotive power equipment units are characterized by large emissions of harmful substances in significant excess of the current requirements. This makes diesel locomotives the main threat to environmental safety in the sphere of railway transport in Russia. Furthermore, the problem is aggravated by low quality of fuel, oils, and GOST standards (in comparison with EURO standards), absence of regional limits for emissions of toxic components with exhaust gases, shortage of ecological monitoring devices and of other due equipment, etc. The legislation still lacks provisions to stimulate development and implementation of low-toxic power equipment, means to reduce exhaust gas toxicity, and of other environmentally friendly types of fuel and oil of required quality. There are still no efficient legal and economic factors to force users of natural resources to bear responsibility for excessive airborne contaminant emissions. The currently available production capacity for maintenance and repairs does not conform to current requirements, including in the sphere of power equipment exhaust gas toxicity diagnosis and control. The issue of ensuring environmental safety of the autonomous traction equipment is especially urgent for larger cities (where locomotive depots, stations, and large plants are located), where mostly shunting diesel locomotives are used, i.e., the emission rate of toxic substances is high. On this basis the article describes ways to resolve the issues associated with improveˇ ment of ecological compliance of shunting CME3 diesel locomotives that are especially

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frequently used at many industrial plants and constitute the main type of shunting diesel locomotives in RZhD, OJSC—ca. 60% of all the diesel locomotives in Russia. The composition of exhaust gases of diesel engines used in locomotives depends primarily on the type of used fuel, oil, organization of maintenance, and repair (just like in other power equipment types). Fuel’s toxicity refers to the performance properties characterizing the impact of the fuel itself and of the combustion and degradation products on people and the environment.

3 Research Questions Monitoring and control of performance factors, such as diesel engine operation modes, diesel engine’s technical condition, environmental factors, engine oil quality, burning oil consumption, and quality of the used fuel possess significant potential for improving environmental parameters [2, 3]. To reduce exhaust gas toxicity, non-traditional fuel types (light oil and alternative fuels, gas fuels) may also be used, hydrogen may be delivered into cylinders of diesel locomotive power equipment units; furthermore, various fuel and engine oil additives may be used [4–6]. That is why the scope of this study includes the use of various fuel types, engine oil additives, as well as of systems to ensure the use thereof in diesel locomotive power equipment units. The search for environmentally friendly fuels for railway transport makes numerous researchers look for the most promising combinations and new fuel types. The analysis of current trends in the use of various engine oils in diesel locomotive power equipment units helped to classify them as follows. The most widely considered is the potential for using liquefied petroleum gas (LPG), liquefied and compressed natural gases (LNG and CNG, respectively) as the engine fuel for autonomous traction equipment [6–8]. The possibility of implementing effective and low-toxic operating processes in diesel locomotive power equipment units when gaseous or liquefied hydrogen is used as a fuel or a fuel component in carburation or injection has already been proven [9–11]. Methanol and ethanol (oxygen-bearing fuels) are still considered the main alternative transport fuels. Feature-wise, these fuels are a better match for positive ignition engines; however, they may be used in diesel engines, too [12, 13]. The aforementioned fuels are rightfully considered the best alternative to the diesel fuel used in diesel locomotives; however, as has been mentioned above, most diesel locomotives are outdated, which is why it is not reasonable to significantly change their design in terms of cost-effectiveness. Therefore, the most practicable and effective way to resolve the issue of improving ecological compliance of diesel locomotive power equipment units is the use of combined fuel types, i.e., the fuels made of a mixture of an alternative fuel type and the diesel fuel. This way to resolve this issue is rather promising, because when the diesel fuel is diluted to 70–95% with additives, the design of power equipment units of used diesel locomotives does not have to be changed much.

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4 Theoretical Section Let us now analyze results of the experimental studies conducted in the conditions of ˇ real use of CME3 diesel locomotives and of calculation/mathematical studies using simulation software suites [14, 15]. The analysis was dedicated to studying rates of toxic exhaust gas substances (nitrogen ˇ oxides (NOx ) and carbon oxides (CO)) and smoke opacity N during operation of a CME3 diesel locomotive power equipment unit in different modes using a multicomponent fuel and resulted in the following data (Table 1). ˇ Table 1 Mode of operation of the CME3 diesel locomotive power equipment unit ˇ Mode of operation of the CME3 diesel locomotive power equipment unit. Effective power Ne (kW)

Fuel components

Diesel fuel

70%—diesel fuel, 30%—LPG (C3 H8 )

0 (idle)

100

250

550

850 (nominal mode)

NOx , g/nm3

0.7

1.35

1.75

2.4

2.6

CO, g/nm3

0.45

0.95

1.25

1.6

1.8

N (%)

28

26

23

21

17

NOx , g/nm3

0.65

1.3

1.55

2.3

2.5

CO, g/nm3

0.35

0.4

0.6

1.2

1.4

N (%)

25

22

21

19

16

0.6

1.25

1.45

2.2

2.4

90%—diesel fuel, NOx , g/nm3 10%—LNG (CH4 ) CO, g/nm3

0.35

0.5

0.8

1.4

1.5

N (%)

21

23

22

18

15.5

95%—diesel fuel, 5%—hydrogen (H2 )

NOx , g/nm3

0.65

1.11

1.53

2.1

2.4

96%—diesel fuel, 4%—alcohol (CH3 OH)

CO, g/nm3

1.1

1.2

1.5

1.6

1.7

N (%)

20

12

9

6

3

NOx, g/nm3

0.95

1.15

1.6

2.3

2.75

CO, g/nm3

0.25

0.4

0.9

1.7

2.5

N (%)

30

21

12

20

25

The results of analysis and computation experiments provided in Table 1 demonstrate that substitution of the diesel fuel with natural gas promoting the largest reduction of carbon oxide (CO) emissions and of smoke opacity D, and an insignificant increase in nitrogen oxide (NOx ) emissions (within the acceptable range) is the most promising solution rather simple to implement. An insignificant increase in NOx when the diesel fuel is substituted with natural gas is observed due to the increase in caloric efficiency of the natural gas vehicle fuel.

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Currently, various additives for engine oils or for engine fuels used in heat engines have become widely used [14, 16]. Let us review results of the studies of effectiveness of use of metal-cladding additives in terms of ecological compliance conducted at a locomotive repair shop and at a research laboratory. The results demonstrate that carbon oxide (CO) emissions decrease by 8–10%, nitrogen oxide (NOx ) emissions increase by 7–10%, and smoke opacity D decreases by 6–9% ˇ on the average after 6 h of a CME3 diesel locomotive’s diesel engine running-in at the nominal mode using modified M-14B2 engine oil at a load test station with environmental control depending on the principal controller’s position.

5 Findings It is reasonable to consider aggregate nuisance value E of exhaust gases (conditional g/kg of fuel) when analyzing effectiveness of the aforementioned ways to improve environmental safety of equipment units and heterogeneity of the obtained results for different toxic substances emitted during operation. It is known that the largest gross airborne emissions of diesel engines in the conditions of use include soot, nitrogen oxides, carbon oxides, and hydrocarbons. These substances have the following aggressiveness factors normalized by CO (Aco = 1): Atq = 41.1, A NOx = 41.1 i A CH = 3.16. The aggregate nuisance value E of exhaust gases determines the impact of the whole spectrum of harmful substances on engine’s environmental parameters [13]. Conditional g/kg of fuel are determined as follows: E = SAi ei , where Ai —relative substance aggressiveness, ei —specific emission of chemical components (g/kg of fuel) in engine exhaust gases.

6 Conclusion According to results of the conducted studies and calculations of the aggregate nuisance value of equipment exhaust gases, methyl and ethyl alcohols are the most promising in terms of environmental safety. Furthermore, alcohols may be used as additives to the diesel fuel, the more so since the design does not have to be changed if their share in a fuel does not exceed 10%. As for gaseous fuels, hydrogen is unparalleled; its use in transport is accompanied by only insignificant NOx emissions. However, there is a range of difficulties associated with its extreme combustibility and high cost. The methane-bearing natural gas shall be considered the most promising gaseous fuel for heat engines used in railway transport; it improves almost all the environmental parameters except for nitrogen oxide (NOx ) emissions.

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References 1. National Environmental Protection Program of the Russian Federation for 2012–2020 2. Nosyrev DI, Skachkova EA, Rosliakov AD (2006) Emissions of harmful substances by locomotive power equipment units: a monograph. Marshrut, p 248 3. Skachkova EA (2007) Ways to reduce emissions of harmful substances by diesel locomotive engines: a monograph. Samara, SamGAPS, p 110 4. Markov VA, Kozlov SI (2000) Fuel delivery of multifuel and gas diesel engines. Publishing Office of the Bauman Moscow State Technical University, Moscow p, p 296 5. Markov VA, Bashirov RM, Gabitov II (2002) Toxicity of diesel engine exhaust gases. 2nd issue (updated and revised). Publishing Office of the Bauman Moscow State Technical University, Moscow, p 376 6. Nosyrev DI, Starikova AG, Muratov AV, Mishkin AA (2006) The impact of hydrogen-bearing gas additives on the rates of harmful substances emitted by diesel locomotive engines. News of the Samara Research Center of the Russian Academy of Sciences. Special issue “Current railway transport issues”. Samara Research Center of the Russian Academy of Sciences, Samara, pp 239–241 7. Nosyrev DI, Muratov AV (2007) Evaluation of the impact of propane additives on the harmful substances emitted by shunting diesel locomotive engines. News of the Samara Research Center of the Russian Academy of Sciences. Special issue “Prospects and areas for transport system development”. Samara Research Center of the Russian Academy of Sciences, Samara, pp 123–125 8. Kurmanova LS (2017) Improvement of diesel locomotive efficiency by the use of natural gas vehicle fuels. Transsiberian Railway News 3(31):22–31 9. Kavtaradze RZ (2011) Thermophysical processes in diesel engines converted to natural gas and hydrogen. Publishing Office of the Bauman Moscow State Technical University, Moscow, p 238 10. Nosyrev DI, Muratov AV, Petukhov SA (2014) Prospects and problems of using hydrogen in locomotive power equipment units: a monograph. Samara, SamGUPS, p 112 11. Mishkin AA, Muratov AV, Nosyrev DI (2006) Effectiveness of hydrogen use in internal combustion engines. From Student Research Days: a compilation of research papers of students and Ph.D. candidates, SamGUPS, Samara, pp 55–56 12. Markov VA, Vallejo Maldonado PR, Biriukov VV (2015) Alcohol-based fuels for diesel engines. News of Institutions of Higher Education. Mech Eng 11:39–52 13. Bulygin II (2006) Fundamentals of simulation of intracylinder processes and toxicity of diesel locomotive engines: a doctoral thesis (05.04.02). Rostov-on-Don, p 328 14. Diesel-RK software suite. https://www.diesel-rk.bmstu.ru 15. Bulygin LV, YatsenkoOV, Zhigulin IN, Ladosh EN (2002) Calculation of the energyecological parameters of the internal combustion engine “ENGINE". Certificate of official registration of the computer program No. 2002610605 . Priority of 11 March 2002, Bull. 3 16. Prosvirov IE, Nosyrev DI, Muratov AV, Petukhov SA (2012) Innovative power-saving technologies for locomotives: a monograph. Samara, SamGUPS, p 123

Disposal of Spent Coolant by Dynamic Membrane D. D. Fazullin(B) , G. V. Mavrin, and L. I. Fazullina Kazan Federal University, 68/19 (1/18), Prospect Mira, Naberezhnye Chelny 423800, Tatarstan, Russia [email protected]

Abstract. Coolants are used in metalworking processes to reduce friction, cooling, and chip removal. As a result of the use of coolant, spent emulsions are formed, which are more toxic than the original emulsion. The methods of purification of coolant containing wastewater, currently used at local treatment facilities of enterprises, do not provide a reduction in the concentration of basic pollutants to established standards, which causes significant environmental pollution. Currently, membrane methods are often used to separate spent emulsions. For ultrafiltration of spent emulsions, a dynamic membrane with an external polystyrene film and on a semipermeable basis of hydrophilic PTFE was obtained. According to the results of scanning electron microscopy, after applying a dynamic film, the membrane surface is coated with spherical polystyrene microparticles, in which particles with a size of 0.1 µm predominate and particles with sizes from 0.4 to 1.5 µm are found, which is confirmed by data from a study of the particle size of a polystyrene suspension. A high retention ability of the PTFE-PSd dynamic membrane for oil products was revealed: more than 94% at a specific productivity of 410 dm3 /m2 h and a working pressure of 7 bar, which is no worse than the performance of a commercial UPM-100 ultrafiltration membrane. Keywords: Petroleum products · Oil · Emulsion · Purification · Utilization · Ultrafiltration · Dynamic membrane · Polystyrene

1 Introduction Improving the processes of metal cutting is of great importance for modern engineering, the development of which requires the use of a large amount of coolant. Coolant removes chips, reduces friction, reduces wear and heat, acting simultaneously as a cooler and lubricant. They significantly affect the productivity and accuracy of processing and the quality of the surfaces of the parts, removing heat and thus preventing local cold welding of the tool with the workpiece. As a result of exposure to coolant at high temperatures, impurities, and the multiplication of microorganisms, the emulsion loses its properties: the hydrogen index, light, odor, density decrease, which requires replacing the spent emulsion with a fresh © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_153

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portion of coolant. As a result, there is a need for disposal of spent coolant, which is an urgent problem for the machine-building complex, where the volume of formation of spent coolant is 10–60 m3 /day, the concentration of oil products in which reaches up to 100 g/dm3 . As a result of the use of coolant, wastewater is contaminated with emulsified oil products (NP), surface-active substances (surfactants), and heavy metals [1]. The proportion of oily wastewater at large industrial enterprises amounts to 70% of the total plant runoff. Admission to biological treatment facilities of poorly treated sewage leads to the death of micro-flora and, further, to pollution of water bodies, which causes a change in the physical, chemical, and biological properties and characteristics of the natural habitat, and disrupts the course of natural biological processes. Also during the transformation of NPs, even more toxic compounds with carcinogenic and mutagenic properties that are resistant to microbiological cleavage can be formed. The methods of purification of coolant containing wastewater, currently used at local treatment facilities of enterprises, do not provide a reduction in the concentration of basic pollutants to established requirements that allow the use of purified water for repreparation of solutions, or for other industries, or discharged into an industrial sewage system, which causes significant environmental pollution. At present, membrane methods are often used to filter spent emulsions, which have a high retention capacity for pollutants [2–4]. Microfiltration and ultrafiltration membranes with pore sizes ranging from 0.1 µm to 0.005 µm are often used to treat wastewater containing hydrocarbons. As a result of the membrane separation process, a filtrate is formed—purified water and a concentrate—pollutants (suspended particles, colloids, petroleum products, fats, and surfactants). Of all the varieties of membrane elements, semipermeable composite films have priority when separating an oil-in-water emulsion. So while reducing the permeability of the membrane elements, you can replace the top layer of polystyrene with a new one, which will restore the original performance. By applying different particle sizes of the applied polymer or by obtaining many composite layers, the desired pore size of the membranes can be established. Depending on the physicochemical properties of the material of the dynamic layer, different wettability and surface roughness of the membranes can be obtained [5]. In the work, a dynamic element filter was used to decompose a dispersed system of the oil-in-water type. The advantages of a dynamic membrane are the possibility of replacing the surface layer in case of contamination of the membrane with oil, solid particles trapped as a result of the filtration process, and the application of a new separation layer [6–12]. To protect and increase the life of the membrane from oil pollution in [13], dynamic layers of TiO2 and SnO2 were applied to the membrane surface. Tightly bound hydrated layers protect the membrane surface from the adhesion of crude oil, which was revealed in the study of the ultrafiltration of a dispersed oil-in-water system. The authors of [14] obtained a dynamic titanium carbide layer (about 30 nm thick), which was deposited on a substrate of porous polyethersulfone (PES). The membrane showed high resistance to contamination and high efficiency in the removal of petroleum products from a dispersed system of the type “oil in water.” The high degree of removal of oil products from the emulsion by a semipermeable membrane is due to the low adhesion of oil particles

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to the surface, as well as the regular laying of a 2D plate structure. To improve the surface morphology, wettability, and antifouling properties of the membrane, bentonite was applied to the surface of a polyvinyl chloride substrate [15]. The membrane was used for ultrafiltration of a dispersed system of the oil-in-water type with high salinity. After applying the dynamic layer, the specific productivity of the membrane increased, and the degree of removal of oil products ranged from 92.5 to 97%, depending on the salinity of the aqueous phase. The study [16] obtained flat polyurethane membranes synthesized on a substrate made of polyethersulfone (PES) with the application of polyvinylpyrrolidone (PVP) in a solution of N.N-dimethylacetamide. The effectiveness of the membranes was evaluated using a model oil-in-water emulsion. In the course of the experiments, the filtrate flow and the concentrate discharge in percent were determined for various operating conditions. To reduce the phenomenon of concentration polarization, the authors subjected the membrane to ultrasonic treatment. The authors found a decrease in particle size of the dispersed phase of the emulsion when exposed to high power ultrasound, which led to a decrease in the separation efficiency of the emulsion. A higher efficiency of ultrafiltration of an oil-in-water emulsion is achieved with periodic exposure to a membrane by ultrasound than with continuous use of ultrasound. In [17], the authors obtained a dynamic membrane, the surface layer of which consists of polystyrene-maleic anhydride (PSMA) and polyethyleneimine (PEI). Various materials were used as the substrate: microfiltration membrane made of polyvinylidene fluoride (PVDF), cotton fabric, nylon mesh, and stainless steel mesh. A layer of PSMA particles contained in the suspension is initially applied to the substrate, and then a layer of PEI particles is applied. As a result, the surface layer of the membrane acquires super-hydrophilic and super-oleophobic properties, and also increases the resistance of the membrane to contamination and exposure to acidic and alkaline media. The authors propose to use the obtained membranes for the separation of oil-in-water emulsions. Earlier, we obtained ultrafiltration membranes consisting of one and several dynamic layers of polystyrene particles deposited on a polymer base of nylon [18]. After applying a dynamic film, an increase in the contact angle of the membrane with a drop of distilled water from 45° to 106° was revealed. The degree of removal of petroleum products from the model dispersed system of the oil-in-water type was 93–96% with a specific permeability of 803 dm3 /m2 h. To stabilize the dynamic polystyrene layer, the membrane was subjected to heat treatment and microwave radiation [19, 20]. As a result of processing the membrane, stabilization of the dynamic layer is achieved, and the specific productivity after backwashing does not increase. Also, after processing, a decrease in surface roughness and an increase in the hydrophilicity of the nylon-PS membrane were found. As a result of thermal and microwave processing of the membrane, the surface layer is compacted, which leads to an increase in the degree of removal of petroleum products from 96 to 99%, with a slight decrease in specific productivity. In this work, in order to increase the membrane resistance to aggressive media and increase the mechanical strength, dynamic membranes with a surface polystyrene film based on porous hydrophilic polytetrafluoroethylene (PTFE) are obtained.

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2 Methods This work describes the parameters of the process of ultrafiltration of wastewater-oil emulsions with a composite membrane polytetrafluoroethylene-polystyrene (PTFEgPS) and a commercial membrane made of UPM-100 polysulfonamide. To obtain a composite dynamic membrane, hydrophilic polytetrafluoroethylene (PTFE) was chosen as the basis, which has high heat resistance, flexible and elastic, surpasses all known synthetic materials in its chemical resistance, and is an inert material. The surface layer of the ultrafiltration membrane was obtained from polystyrene (PS) particles present in the suspension, the sizes of which lie in the range 54-351 nm. PS particles from the suspension to the surface of the PTFE substrate were transferred by filtering the suspension through a semipermeable substrate. To stabilize the surface layer of PS particles, the composite membrane was subjected to heat treatment at a temperature of 30°C for 2 h. The content of PS in the filter element was determined by the gravimetric method using an analytical balance. Using the analyzer of the Nano Brook Omni brand, the sizes of some PSs in an equilibrium state in a 0.5% suspension of an aqueous solution of acetone were determined by dynamic light scattering. The distribution ranges of PS particle sizes in an aqueous acetone solution according to the signal intensity of the device and the number of particles are shown in Fig. 1.

Fig. 1. Ranges and main peaks corresponding to the particle sizes of PS present in an aqueous solution of acetone.

Commercial UPF-100 ultrafiltration membrane manufactured by Vladipor CJSC is a porous polymer film based on the Sulfon-4T aromatic polysulfonamide on substrates: non-woven lavsan and polypropylene. The characteristics of the UPM-100 membrane are presented in Table 1. Micrographs of the membrane surface were obtained by scanning electron microscopy using a LEO-1430 VP microscope. Membrane samples were tested under high vacuum. As the main indicators of the ultrafiltration process, we considered the specific permeability and the degree of removal of oil products, determined by the change in the oil

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D. D. Fazullin et al. Table 1. Characteristics of the ultrafiltration membrane UPM-100.

Membrane brand

UPM-100

Operating pressure, MPa

Distilled water productivity, dm3 /m2 h

Holding capacity,% of raw milk

hemoglobin (64500D)

0.1

840

95

97

content after membrane separation of spent coolant and in the filtrate of the membranes. The mass content of oil products in the coolant sample and the filtrate was measured by the IR spectrometric method using a KN-3 concentrator. The specific productivity of the membranes was calculated as the ratio of the amount of permeate formed to the active area of the membrane and the time of the baromembrane separation process in terms of dm3 /m2 h. The ultrafiltration process was subjected to the spent 3% water-oil coolant of the Isanol VPS-2 brand. The hydrocarbon content in the spent coolant is more than 33 g/dm3 . Experimental studies of ultrafiltration processes were carried out on a laboratory membrane unit using the obtained composite and commercial membranes. The initial liquid containing suspended particles, emulsified oil products, and surfactants as impurities is pumped to the membrane module by a pump. Under the action of working pressure, the flow is divided into two parts: a filtrate partially purified from contaminants, which is collected in a receiving tank, and a concentrate, which is constantly returned to the original tank. In the process, there is a gradual concentration of impurities to the maximum possible values. The pressure was recorded by a manometer. In the process of ultrafiltration, the maximum pressure was 7 bar, at a temperature of spent coolant which is 24.5°C.

3 The Results of the Study of the Properties and Parameters of Ultrafiltration with a Composite Membrane PTFEg-PSd According to Fig. 1, according to the signal intensity 0.5%, the PS suspension is a polydisperse system with a particle size distribution in the ranges 54.6–74.9 nm and 185–269 nm, and the signal intensity over particles with a size of 54.6–74.9 nm is less than 6%, the main share in intensity corresponds to a particle size of 185–269 nm. By the number of particles, PS particles were identified only in the range 54.6–74.9 nm, which corresponds to a 100% content; therefore, the number of particles with sizes of 185–269 nm is insignificant. The ξ potential of a 0.5% suspension of PS in one acetone solution was −15.4 mV. The content of PS in the surface layer of the membrane after applying the dynamic layer of particles established by the gravimetric method is presented in Table 2. After applying PS particles by filtration from a 0.5% suspension onto a hydrophilic PTFE base, a PTFE-PSD composite membrane with a PS content of 4.2% (mass) was obtained.

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Table 2. The proportion of PS in the mass of the composite dynamic membrane PTFEg-PSd. Membrane name

Initial Mass membranes, g

Polystyrene content, g

Polystyrene content,% (by weight)

PTFEg-PSd

0.1439

0.006

4.2

The change in the surface structure of the membranes after applying the dynamic PS layer was studied using the electron microscopy method, the results of which are shown in Fig. 2.

Fig. 2. Electron micrographs of membranes: a an initial membrane of hydrophilic PTFE; b dynamic membrane PTFEg-PSd (increase in 4000 times).

According to Fig. 2, the surface of the initial membrane of hydrophilic PTFE is smooth, and there are pores with sizes from 0.17 to 0.8 µm. After applying a dynamic layer, the membrane surface is coated with PS particles of a spherical shape, in which particles with a size of 0.1 µm prevail and particles with sizes from 0.4 to 1.5 µm are found. (Figure 2b), which is confirmed by data from a study of the particle size of PS suspension. Subsequently, a study was conducted on the process of ultrafiltration of spent coolant during which the specific productivity of the membranes was established, and the results of the study are given in Table 3. As a result of applying a layer of polystyrene to the base surface of a semipermeable PTFE film, an 18-fold decrease in membrane permeability was revealed due to the formation of a composite layer on the surface and in the pores of the polymer base from PS particles. The specific productivity of the dynamic membrane for spent emulsion and distilled water exceeds the performance of the UPM-100 commercial ultrafiltration membrane by 1.4 times and 1.2 times, respectively. In the process of ultrafiltration of the spent emulsion, the specific productivity of the membranes decreases sharply, in connection with this, the working pressure of the separation process was increased to 7 bar. The results of the detention of petroleum products by ultrafiltration from spent coolant are described in Table 4.

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Table 3. The specific permeability of the composite and commercial ultrafiltration membrane. Membrane

Polystyrene content, % (by Specific capacity of membranes, dm3 /m2 ·h weight) for distilled water for spent 3% coolant (pressure 3.5 bar) (pressure 7 bar)

PTFEg

–

PTFEg-PSd UPM-100

17546

6967

4.2

944

410

–

809

292

Table 4. Retention capacity of ultrafiltration membranes for oil products from spent coolant. Membrane

PTFEg

Concentration of oil products, g/dm3 Original

Permeate

33.4

17.4

Retention capacity,%

Standard *, g/dm3

47.9

0.01

PTFEg-PSd

1.87

94.4

UPM -100

6.75

79.8

* Wastewater quality standards in accordance with Decree of the Government of the Russian Federation N 644 “On approval of the Rules for cold water supply and sanitation”

In the spent coolant, the concentration of oil products is more than 33 g/dm3 , which exceeds the standard for water disposal by 3340 times. After the ultrafiltration process, the concentration of oil products in the membrane permeates decreases, but the requirements of the standard are not satisfied. So, the hydrocarbon content after microfiltration with a PTFE membrane decreased 1.9 times, after ultrafiltration with a PTFE-PSD composite membrane it decreased 18 times, and after filtration with a commercial UPM-100 membrane it decreased 5 times. The calculated retention capacity of the PTFE microfiltration membrane for petroleum products was not more than 48%, and after applying a dynamic polystyrene layer, the retention capacity increased to 94.4%, which is 14.6% higher than the retention capacity of the UPM-100 commercial ultrafiltration membrane. To achieve an acceptable concentration in terms of hydrocarbon content, it is necessary to carry out repeated ultrafiltration, or after-treatment of the aqueous phase of spent coolant by nanofiltration.

4 Conclusion For ultrafiltration of spent emulsions, a dynamic membrane with a thin coating of polystyrene and based on hydrophilic PTFE was obtained. The mass content of polystyrene in the membrane was 4.1%. According to the results of scanning electron microscopy, after applying a dynamic layer, the surface of the membrane is coated with spherical polystyrene particles, in which particles with a size of 0.1 µm predominate and particles with sizes from 0.4 to 1.5 µm are found, which are confirmed by the study

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of particle size of a polystyrene suspension. The specific productivity of the dynamic membrane for distilled water and spent coolant with an oil content of 33 g/dm3 was determined. A high retention ability of the PTFE-PSd dynamic membrane for petroleum products was revealed: more than 94% with a specific productivity of 410 dm3 /m2 •h and a working pressure of 7 bar. During ultrafiltration of spent coolant, the UPM-100 commercial membrane showed lower efficiency: the oil-retention membrane was 80%, with a specific productivity of 292 dm3 /m2 •h and a pressure of 7 bar. Although the concentration of oil products in the ultrafiltrate of the spent coolant exceeds the requirements for discharging wastewater into the sewage system, it is recommended to use a dynamic membrane in water treatment processes from emulsified petroleum products and for the disposal of spent coolant with subsequent post-treatment by repeated ultrafiltration or nanofiltration. The resulting filtrate can be used to re-prepare a fresh portion of coolant. The spent coolant concentrate consisting mainly of oil products, fatty acids, and surfactants can be used as heating oil, after preliminary removal of moisture. Acknowledgements. The studies were supported by a grant from the President of the Russian Federation (grant number: MK-1107.2019.8).

References 1. Fazullin DD, Mavrin GV, Sokolov MP (2015) Utilization of waste lubricating-cooling fluids by membrane methods. Chem Technol Fuels Oils 51:93–98. https://doi.org/10.1007/s10553015-0579-8 2. Fazullin DD, Mavrin GV, Shaikhiev IG et al (2016) Separation of oil products from aqueous emulsion sewage using a modified nylon–polyaniline membrane. Pet Chem 56:454–458. https://doi.org/10.1134/S0965544116050054 3. Fazullin DD, Mavrin GV (2015) Effect of the pH of emulsion on ultrafiltration of oil products and nonionic surfactants. Pet Chem 57:969–973. https://doi.org/10.1134/S09655441170 90043 4. Fazullin DD, Mavrin GV (2017) Separation of water-oil emulsions with a dynamic membrane of gelatin on a nylon substrate. Int J Green Pharm 11:S823–S826 5. Fazullin DD, Mavrin GV (2019) Formation and properties of a dynamic ultrafiltration membrane. IOP Conf Series: Earth Environ Sci 288:012082. https://doi.org/10.1088/1755-1315/ 288/1/012082 6. Shao Senlin, Liu Yang, Shi Danting et al (2019) Control of organic and surfactant fouling using dynamic membranes in the separation of oil-in-water emulsions. J Colloid Interface Sci 560:787–794. https://doi.org/10.1016/j.jcis.2019.11.013 7. Liu Mingming, Li Jing, Guo Zhiguang (2016) Polyaniline coated membranes for effective separation of oil-in-water emulsions. J Colloid Interface Sci 467:261–270. https://doi.org/10. 1016/j.jcis.2016.01.024 8. Yan L et al (2006) Effect of nano-sized Al2O3-particle addition on PVDF ultrafiltration membrane performance. J Membr Sci 276:162–167. https://doi.org/10.1016/j.memsci.2005. 09.044 9. Lind ML et al (2009) Effect of mobile cation on zeolite-polyamide thin film nanocomposite membranes. J Mater Res 24:1624–1630. https://doi.org/10.1557/jmr.2009.0189 10. Zhang Feng et al (2013) Sol–gel preparation of PAA-g-PVDF/TiO2 nanocomposite hollow fiber membranes with extremely high water flux and improved anti fouling property. J Membr Sci 432:25–32. https://doi.org/10.1016/j.memsci.2012.12.041

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11. He Yang, Hong Jun Ming (2011) Advanced materials and processes: ADME 2011. Adv Mater Res 311–313:1818–1821. https://doi.org/10.4028/www.scientific.net/AMR.311-313.1818 12. Fazullin DD, Mavrin GV, Shaikhiev IG (2017) Modified PTFE–PANI membranes for the recovery of oil products from aqueous oil emulsions. Pet Chem 57:165 13. Yang HC, Xie YS, Chan H et al (2018) Crude-oil-repellent membranes by atomic layer deposition: oxide interface engineering. ACS Nano 12:8678–8685. https://doi.org/10.1021/ acsnano.8b04632 14. Li ZK, Liu Y et al (2019) Ultra-thin titanium carbide (MXene) sheet membranes for highefficient oil/water emulsions separation. J Membr Sci 592:UNSP 117361. https://doi.org/10. 1016/j.memsci.2019.117361 15. Ahmad Tausif, Guria Chandan, Mandal Ajay (2018) Synthesis, characterization and performance studies of mixed-matrix poly(vinyl chloride)-bentonite ultrafiltration membrane for the treatment of saline oily wastewater. Process Saf Environ Prot 116:703–717. https://doi. org/10.1016/j.psep.2018.03.033 16. Agi A, Junin R, Yahya A et al (2018) Comparative study of continuous and intermittent ultrasonic ultrafiltration membrane for treatment of synthetic produced water containing emulsion. Chem Eng Process-Process Intensification 132:137–147. https://doi.org/10.1016/j.cep.2018. 08.016 17. Zhang GW, Jia XY, Xing JL et al (2019) A facile and fast approach to coat various substrates with poly(styrene-co-maleic anhydride) and polyethyleneimine for oil. Water Sep Ind Eng Chem Res 58:19475–19485. https://doi.org/10.1021/acs.iecr.9b03465 18. Fazullin DD, Mavrin GV, Shaikhiev IG et al (2018) ultrafiltration of oil-in-water emulsions with a dynamic nylon-polystyrene membrane. Pet Chem 58:145–151. https://doi.org/10.1134/ S0965544117130047 19. Fazullin DD, Mavrin GV, Shaikhiev IG et al (2019) Stabilization of the dynamic layer of the membraneby microwave radiation. Membr Membr Technol 1:1–6. https://doi.org/10.1134/ S2517751619010025 20. Qing Weihua, Shi Xiaonan, Zhang Weidong (2018) Solvent-thermal induced roughening: a novel and versatile method to prepare superhydrophobic membranes. J Membr Sci 564:456– 472. https://doi.org/10.1016/j.memsci.2018.07.035

Effectiveness of the Plasma Neutralization Technology for Supertoxicants S. V. Anakhov1(B) , A. V. Matushkin2 , and Yu A. Pyckin3 1 Russian State Vocational Professional University, 11, Mashinostroiteley, Yekaterinburg

620012, Russia [email protected] 2 Ural Federal University, 19, Mira Str, Yekaterinburg 620078, Russia 3 Ural State Forest Engineering University, 37, Siberian Tract, Yekaterinburg 620038, Russia

Abstract. The plasma neutralization technology for the products of thermal waste processing—supertoxicants (polychlorinated dibenzodioxines, dibenzofurans, biphenyls, etc.)—is investigated. The problem of supertoxicants formation in the process of thermal processing for household and industrial waste of different composition is identified. To solve this problem, we propose the use of plasma generators in environmental technologies, in which due to the high-energy plasma effect on substances of different phase compositions, their deep decomposition (plasma incineration—”burning”) occurs. Known methods of thermal neutralization of dioxins are considered. Temperature approximations of the decomposition time for dioxins in the temperature range of plasma heating are found. Efficiency criteria of plasma heating and neutralization are introduced. The modernized design of the plasma torch for utilization of gaseous waste of supertoxicants processing is offered. The gas-dynamic parameters of the air-plasma flow in the process of thermal heating by a plasma jet are determined by the methods of mathematical modeling. Efficiency of the considered technology of plasma incineration is proved. Keywords: Plasmatron · Design · Efficiency · Environmental safety · Recycling · Ecological safety · Decontamination · Incineration · Plasma torch

1 Introduction One of the problems currently facing developers of environmental technologies is the formation of supertoxicants (polychlorinated dibenzodioxides, dibenzofurans, biphenyls, etc.) in the process of thermal waste processing. One solution to this problem is the use of plasma torches for these purposes [1], in which due to the high-energy plasma effect on substances of different phase compositions, their deep decomposition occurs—plasma incineration (“burning”) [2]. The introduction of plasma torches at the afterburning stage of gaseous products of hazardous waste processing is rational. Similar technologies using DC arc plasma torches were proposed by the authors earlier [3–6]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_154

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To assess the effectiveness of such methods, dioxins were selected, which are formed as by-products in pulp and paper, chemical, metallurgical, waste processing, and other industries (especially chlorine and bromine) [7]. In addition, they are formed in the process of high-temperature incineration of waste together with fuel in furnaces of stationary or mobile type. It is possible to reduce the content of dioxins in the exhaust gases by means of activated carbon [8] injected into the bag filter, or by installing special layer filters used, for example, in Hitachi Zosen Inova installations, which are currently being introduced in Russia [9]. At the same time, however, there is a problem of disposal of contaminated activated carbon. For this reason, it is widely accepted that the mandatory element of furnaces for waste burning is the afterburning chamber, necessary for the complete destruction of dioxins.

2 Technique of Researches According to the results of recent studies [10], we can conclude that for the purpose of preventing the formation of dioxins in the combustion zone should adhere to the following process parameters: temperature above 1150–1300 K, the residence time of the waste in the combustion zone at least two seconds, and 6% excess oxygen in the gas mixture; in the cooling zone, the temperature range is 500–800 K and a residence time is not exceeding 1 s. Based on a small amount of known information on hightemperature neutralization of dioxins [11] (at temperatures of 15,000 and 50,000), the authors made approximations of the temperature dependence of the required time of their decomposition. The search for approximation dependencies was carried out on the basis of the Arrhenius equation for the reaction rate constant: k = k0 · e−E/RT ,

(1)

where k o and E depend on the nature of the reagents and E is the activation energy. Since the decomposition time and the reaction rate are inversely proportional, the search was carried out using equations of two types (with a constant and temperaturedependent pre-exponential factor): t = t0 · e−E/RT ,

(2)

t = t0 (T ) · e−E/RT .

(3)

As a result, two equations were obtained: t = 1.28 · 10−5 · e18/T ,

(4)

7.2 · 10−5 21.7/T ·e , T 3/2

(5)

t=

where [t] = sec, [T ] = thousand K, with an activation energy E = 150÷180 kJ. On the basis of the obtained equations, the following estimates of the required time for their decomposition were made (Table 1).

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Table 1. Temperature dependence of the decomposition time for dioxins (estimation) T, thousand K

1.5

2

t, msec by 2000 100 Eq. (4)

2.5

3

3.5 4

20

5

2

by 2000 1300 110 20 5 Eq. (5)

4.5 5

5.5

1.2 0.7 0.5 0.3 2

0.9 0.5 0.3

Since in the process of plasma heating, the volume of the gas mixture passing through the mixing chamber of the plasma torch warms up unevenly (at different temperatures and at different times), it makes sense to introduce universal criteria for the efficiency of the decomposition for dioxins. It is obvious that both the temperature and the heating time increase in efficiency, and also taking into account the activation mechanism of decomposition reactions, the following criteria were derived on the basis of the obtained approximating dependences: RT · ln(t/t10 ) > E,

(6)

RT · ln(T 3/2 · t/t20 ) > E.

(7)

The following expressions can be used as numerical criteria for evaluating effectiveness: C1 = T · ln(t/t10 ), C1 > 18,

(8)

C2 = T · ln(T 3/2 t/t20 ), C2 > 21.7

(9)

where [t] = sec, [T ] = thousand K, t10 = 12.8 µsec, t20 = 72 µsec. Since there are no reliable data on the decomposition time of dioxins in the entire studied temperature range, it is advisable to use not the data of Table 1, but both the proposed criteria C1 and C2 when evaluating the heating efficiency. It is obvious that the technology of plasma afterburning of gaseous wastes proposed by the authors should, at a minimum, provide the required time of the gas flow of hazardous wastes at the appropriate temperature set by heating the mixing chamber (MC) of the utilized and plasma-forming gas flows by plasma arc (jet). Similar technology (Fig. 1a), as is known [12], was developed on the basis of a patented model of an arc plasma torch [13] with its subsequent modernization for neutralization of toxic vaporgas flows of different compositions and phase states. The plasma jet is formed in the MC by the interaction of the plasma arc excited and burning between the cathode and the anode of the nozzle unit of the plasma torch, with the vortex flow of the plasma-forming gas (PFG) and its subsequent blowing into the MC due to the high kinetic energy of the PFG flow (Fig. 1b). The new design of plasma torch is characterized by the presence of a mixing chamber (MC), in which the mixing and heating of the flows of the tangentially supplied toxic vapor-gas mixture and PFG flow pre-swirled with the help of a gas-vortex

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stabilization system are provided. The nozzles for supplying the secondary (recycled) flow are located on the replaceable part of the plasma torch, or can be carried out beyond it and located under the nozzle section at any angle to the axis of the plasma jet (Fig. 1a).

Fig. 1. The plasma torch for the hazardous waste neutralization: a calculation model, b experimental model.

The estimation of efficiency for heating of a gas-air mixture in MC was made by calculation of gas-dynamic parameters in the application FlowWorks of the SolidWorks software with variable value of a grid discretization. Gas-dynamic modeling was carried out at the mass flow rate of the PFG 0,011 kg/s and the diameter of the inlet hole in MC 4 mm (typical for the effective gas-vortex stabilization of the arc plasma torch). The calculation of temperatures in the MC was carried out on several rectilinear trajectories (lines) of different distances from the axis of the chamber (Fig. 2a) at the characteristic airplasma arc (jet) temperature of 7000 K. As the calculations showed, the main flow of the utilized gas moves in the MC along a spiral trajectory (Fig. 2b), and therefore estimates of the kinematic parameters were made along the characteristic spiral line. In accordance with the velocity distribution in the mixing chamber, the parameters of the spiral line along which the recycled gas flow predominantly moves were selected: diameter—5 cm, pitch—8.5 cm, and length of one spiral—20 cm. Since the spiral nature of the gas flow calculation of the rectilinear trajectory leads to strong oscillations of parameters along the line of motion, also used the calculation of the average cross-section of the MC temperatures and velocities.

Fig. 2. Calculation of gas-dynamic parameters in the plasma torch system: a trajectory calculation of speed and temperature in the MC; b temperature distribution.

In the initial calculations, the technological scheme was analyzed with the supply of the secondary flow of the utilized gas through two axisymmetrically arranged nozzles at angles of 10° , 20° , and 30° to the axis of the plasma jet with a length of 90 mm,

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with a mass flow rate of 0.005 kg/s for each tube. Geometry of MC: length not less 150 mm, the angle of primary parts disclosure—20º, disclosure on the rest part of MC: for cylindrical—00, for confusor—5°. The results of the gas-dynamic parameter (temperature, speed, and heating times) calculations for the utilized gas in various areas of cylindrical- and confusor-type MC showed that heating occurs at average temperatures 1500–4000 K and average speeds in 50–100 m/s at typical heating times 2–5 ms. In the confusor type, the heating time increases by 1.5–2 times depending on the trajectory, with the greatest increase occurring near the walls of the MC. The latest results correlate with the orders of magnitude of the decomposition time for dioxins at such temperatures (Table 1) and indicates the possibility of using the method of plasma afterburning of hazardous waste processing. At the next stage, the upgraded constructive scheme was considered. Supply of the utilized gas in this scheme is on a tangent to a stream of PFG by four channels (diameter 4 mm) located perpendicularly to an axis of MC at distance of 11 mm from a nozzle unit (Fig. 1a). This scheme was chosen in order to assess the efficiency of the technology at a higher productivity (increasing the volume of recycled gas). For comparative analysis, we selected comparable process parameters: the consumption of PFG—0.005 kg/s, the consumption of gas utilized by channel—0,004 kg/s, and the temperature of the airplasma arc—7000 K. In order to ensure effectiveness, it was reviewed by two options of heating: by « short » plasma jet with a length of 90 mm (similarly to the previously discussed technologies) and « long » plasma arc of 170 mm. It is obvious that the latest version requires twice as big power supply of power source for plasma arc. Geometry of such MC: length not less 170 mm, the angle of primary parts disclosure—20°, and disclosure on the rest part of MC—0° (cylindrical configuration).

3 Results of Research and Their Discussion When calculating along the spiral trajectory, significantly smaller oscillations of gasdynamic parameters were observed, which confirms the preferential distribution and nature of the movement of the disposed gas in the MC. In the approximation of the spiral trajectories, the evaluation of the heating time shows a twofold increase for the most remote from the axis trajectories, and about half the rise in average temperature along the path, which for the recyclable gas flow is 3–5,5 thousand K (Fig. 3a). The analysis of the presented results allows us to conclude that the increase in the length of the plasma jet in the MC leads to an increase in the gas velocity (Fig. 3b), which naturally affects the reduction of heating time (Fig. 4a). However, the average temperature of the gas everywhere in MC increases by about 500 K (Fig. 4b), resulting in the efficiency of dioxins decomposition which is 30–40% higher (according to criteria C1 and C2). Similar conclusions can be made in the analysis of gas-dynamic parameters and heating temperatures, made along the spiral, which, as noted earlier, corresponds to the movement of the recycled gas in the MC. Comparison with the previously obtained results [12] also demonstrates the advantages of the upgraded technology. Figure 5 shows the results of the calculation of linear trajectories which shows an increase of 13% (when heated by a jet of 170 mm) and 35% (with a comparable length of the jet of 90 mm) heating time at comparable heating

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Fig. 3. Distribution of calculated parameters in the MC of plasma torch: a temperature along the spiral trajectory (plasma jet length 170 mm); b velocity along rectilinear trajectories in MC under heating by short (90 mm) and long (170 mm) plasma jet.

Fig. 4. Distribution of calculated parameters along rectilinear trajectories in MC of plasma torch under heating by short (90 mm) and long (170 mm) plasma jet: a heating time; b temperature.

temperatures. Process efficiency estimates made according to the introduced criteria, C1 and C2 (Fig. 6), talk about increasing efficiency for upgraded technology. Evaluation by criterion C1 shows the efficiency of the process both when heated by a short (90 mm) and long (170 mm) plasma jet. More stringent requirements (simultaneous implementation of criteria C1 and C2) clearly determine the need for a long (170 mm) plasma jet for neutralization of dioxins. It should be noted that the calculations made along the spiral trajectory demonstrate the maximum values of the process efficiency (Figs. 5 and 6). It is obvious that the further direction of the considered technology improvement should become its constructive optimization according to integral criteria of neutralization efficiency and profitability. In this regard, the following parameters should be considered: the consumption of gas flows, the angles of the supply for utilized gas, the geometry of MC, and the power supply of source power, providing plasma jets of required length in the MC. It is also advisable to provide a quenching chamber before the emission of gases into the atmosphere when designing the neutralization technology.

4 Conclusions The results of the analysis presented in this paper indicate the validity of this neutralization method on the example of one of the most dangerous supertoxicant—dioxin. This technology, as noted earlier [12], has significant advantages over the known technologies

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Fig. 5. The average values of time and temperature for different designs of MC.

Fig. 6. Criteria of the heating efficiency for different designs of the MC.

of high-temperature combustion and waste disposal due to the speed and efficiency of the process. However, the development and analysis of this eco-technology should be continued in order to find the optimal parameters for its application. Acknowledgements. The work is executed at support of RFBR grant 19-08-0019.

References 1. Cherednichenko V, Anshakov A, Kuzmin M (2011) Plasma electrotechnological installations. NGTU, Novosibirsk 2. Chernets I et al (2011) Development of high-power plasma reformer and power supply for large scale applications. In: 20th international symposium on plasma chemistry. 24–29 July 2011 3. Anakhov S, Pyckin Yu (2012) Ecological designing: strategy and technologies. LAP LAMBERT Academic Publishingb Saarbrucken 4. Anakhov S, Pyckin Yu, Shakurov S (2014) System principles in the decision of ecological safety problems with application of plasma technologies. Ecol Ind Russia 1:4–9 5. Fridman A (2008) Plasma chemistry. Cambridge University Press, Cambridge 6. Anakhov S (2014) Principles and methods of design in electroplasma and welding technologies. RSVPU, Ekaterinburg 7. Gumerova G, Gogol E, Vasilev A (2014) New approach to qualitative and quantitative determination of dioxins. Proceedings of Samara Scientific Center of RAS 1(6):1717–1719 8. Ladygin K (2014) On the issue of preliminary assessment and methods for reducing the content of dioxins in the waste gases of thermal-oxidative treatment of medical waste. Sci J NIU ITMO 2:14–15

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9. Leontyev L (2019) Prospects for solid waste disposal in Russia. Proceedings of the congress “TEHNOGEN-2019”. UrO RAS, Ekaterinburg, p 18–24 10. Petrov V, Trubachev A (2012) Neutralization of organochlorine industrial waste without formation of dioxins. Bulletin of Udmurt University. Phys Chem Ser 3:64–68 11. Disinfection technologies. Electronic resource. http://www.seu.ru/cci/lib/books/dioksiny/8/ 02.htm 12. Anakhov S, Pyckin Yu, Matushkin A (2019) Modeling of the plasma incineration technology of waste utilization and neutralization. Technosphere Saf 1:129–141 13. Pykin Y, Anakhov S, Shakurov S (2007) Plasmatron. RF Patent 67909, 22 May 2007

State of the Nickel Alloy Surface Layer After Grinding with a Minimum Quantity Lubrication A. P. Mitrofanov(B) , A. A. Isaeva, and V. A. Nosenko Volzhsky Polytechnic Institute (Branch) of VSTU, 42a Engels Street, Volzhsky, Volgograd Region 404121, Russia [email protected]

Abstract. Modern trends in mechanical engineering are associated with the introduction of green technologies, in particular the use of a minimum quantity lubrication (MQL) in abrasive processing operations. However, due to the low cooling capacity of this technology, the use of cold air (CAMQL) is used increasingly often. This article summarizes the results of comparative tests of the application of this technology, using soy oil as a lubricant. The properties of the surface layer of a nickel alloy obtained after grinding have been studied using electron microscopy, X-ray diffraction analysis, and evaluation of the electron yield by the Kelvin probe method. It was found that when using CAMQL, there is a decrease in oxidative and adhesive processes, while the level of micro-stresses in the surface layer is reduced twice. The results obtained indicate an improvement in the quality of the surface layer when grinding a nickel alloy with CAMQL. Keywords: Grinding · Minimum quantity lubrication · Cold air · Soybean oil · Surface morphology · Electronic work function · EDS subsurface layer

1 Introduction Quite a significant issue, from the point of view of environment, is the use of cooling mixtures (coolants) in mechanical engineering. In this regard, recently there has been considerable interest in the study of grinding technology with a minimum quantity of lubrication (MQL), which is fed to the cutting zone of the air-lubricating medium. There are significant advantages of using MQL in comparison with the use of traditional coolant, such as reduced consumption of special liquids, reduced environmental pollution, lower cost, and low requirements for the equipment of the working area [1]. However, in the process of abrasive processing, where high contact temperatures are observed, the use of MQL in its usual representation is not always effective in comparison with the coolant application. In order to reduce the heat load during grinding, the authors [2, 3] used additional cooling of the cutting zone with cryogenic media (liquid nitrogen, CO2). The complexity of the design of the supply and storage of cryogenic media creates problems for the further development of this direction. In article [4], it is © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_155

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proposed to cool the contact interaction zone using a vortex tube (based on the vortex effect). This method is quite simple to implement, but its effectiveness without the use of lubrication is not so high. In the development of this direction, the authors of studies [5, 6] investigate the technology of supplying cold air with minimum quantity lubrication (CAMQL) by using a vortex tube. In study [6], mineral oil is used, which somewhat contradicts the concept of environmentally-friendly grinding. Vegetable oil has excellent biodegradability, meets the requirements for the properties of lubrication, and has great potential for use in MQL [7–10]. The main focus of the existing publications is the study of operational parameters of the abrasive treatment process using MQL or CAMQL technology. At the same time, it is of particular interest to obtain the properties of the surface layer, which have a significant impact on the further behavior of the treated surface. Thus, the purpose of this article is to study the properties of a thin surface layer as the most informative source that reflects the processes occurring as a result of contact interaction.

2 Research Methods For experimental research, a Smart-B1224III CHEVALIER model CNC surface grinder was used. Characteristics of the 25AF100I10V abrasive tool are Grinding mode: wheel speed v = 35 m/s; table feed speed vs = 6 m/min; feed to a depth t—0.01 mm/stroke. The value of the allowance removed in one experiment—0.5 mm, the number of parallel experiments—3. Analysis of the existing publications on the application of MQL and CAMQL feeding technology in the grinding process shows that the dosing mode of the lubricant, depending on the processing conditions, in most cases varies in the range from 20 to 100 ml/h [4–7]. In our research, we stopped at the mode of 30 ml/h. AIRRUS CE 250-V135 compressor was used to supply air to the air cooling system. As part of the concept of minimal environmental impact, vegetable oil is proposed as a lubricant. In articles [11, 12], the possibility of using three types of vegetable oils: corn, mustard, and soy as a lubricating medium is proposed. According to the results of operational tests, it was found that soy oil is more effective. The supply of the cold air with minimum quantity lubrication (CAMQL) is implemented through the synthesis of the MQL unit (Spraymat700 model, manufactured by Steidle Germany) and the vortex tube. The peculiarity of the vortex tube is the regulation of the ratio of the cold air temperature to the flow value. In our studies, the flow rate was 12 m3 /h, at the corresponding air temperature of −5°C. The choice of the flow rate was based on the results of research summarized in article [6, 13]. Schematically, the experimental setup is shown in Fig. 1. Using the capabilities of 3D printing, a nozzle was manufactured to implement the CAMQL technology (Fig. 1), in which the MQL feed nozzle is located in the center of the tip with a circular cross-section. The inclination angle of the nozzle relative to the workpiece is 15°. The heat-resistant alloy HN45MVTYUBR, which is an analogue of one of the most popular nickel alloy Inconel 718 in the world, was selected as the processed material. suchlike materials are used to make critical parts of aircraft and chemical engineering industry, working at high temperatures. Having excellent technical characteristics, this alloy is very difficult to process by cutting, including grinding. For experimental studies,

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Fig. 1. Experimental setup: 1—Spraymat700 lubrication system; 2—nozzle; 3—compressor; 4— vortex tube; 5—hot air outlet; 6—workpiece; 7—supply of cold air; 8—oil supply pipe.

samples of 75 × 35 × 7 mm were prepared, which were heat-treated according to standard technology, resulting in their hardness of 37 HRC. Heat-treated samples were fixed in a vise and heaved before conducting experiments. The study of the surface morphology of the treated samples was carried out using a two-beam electron scanning microscope Versa 3D LoVac at an accelerating voltage U = 20 kV. In order to assess the changes in the near-surface layer, a cross-section was formed by ion etching. Using the integrated system of micro-X-ray-spectral energy dispersion analysis EDAX Apollo X, the elemental composition of the surface layer with a high degree of localization was determined. The contact potential difference (CPD) was measured using the Solver PRO atomic force microscope (manufactured by NT–MDT) using the Kelvin Probe method. The method used is based on a two-pass method. In the first stroke, the surface relief of the sample is determined using the intermittent contact method (cantilever vibrations are excited mechanically). In the second stroke, this relief is tracked when passing over the sample at some height to determine the surface electric potential ϕ(x). A conductive cantilever (CSG10/Au) coated with gold was used for the research. X-ray structural analysis of the characteristics of the thin structure of the nickel alloy after grinding was carried out on the X-ray diffractometer Bruker D8 Advance. The methodology included the imaging of lines 111 and 222. Their analysis, which included determining the half-width and center of gravity of the line, was carried out using Diffrac.EVA (version 4.2.1). The dimensions of the coherent scattering regions, the relative micro-deformation of the lattice, and the level of micro-stresses (type II) were determined by the approximation method using the broadening of lines 111 and 222. According to the data on the position of the gravity center of line 222, taking into account the quadratic shape, the lattice period was determined for the cubic syngony.

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The experiments were performed under normal conditions in the Bregg–Brentano geometry using CuKα radiation. Alignment and positioning of the sample surface was performed using a laser guidance system. The survey was conducted in the range of angles 2θ, corresponding to lines 111 and 222 of the alloy, with a scanning step of 0,01° and an exposure time of τ = 1 s. Before carrying out all these tests, to remove contamination from the surface, the samples were cleaned in ethanol using an ultrasonic bath (power of 50 W, duration of 3 min).

3 Results and Discussion Characteristics of the properties of the treated material surface layer depend on many factors, including a significant impact on the mechanical, physical, and chemical transformations that accompany the process of abrasive treatment. When grinding using MQL technology, traces of adhesive interaction are observed (Fig. 2a). A better and smoother surface is obtained after grinding with CAMQL technology (Fig. 2b), which indicates a reduction in adverse events during contact interaction in the process of abrasive treatment.

Fig. 2. SEM images of the worn surface: a MQL; b CAMQL.

In the course of surface layer studies, a cross-section was formed by ion etching. After grinding with MQL technology, there is a significant transformation of the thin surface layer to a depth of about 1 micron (Fig. 3a), on the contrary, the sample obtained by using CAMQL technology has a sufficiently smooth surface layer (Fig. 3b). Elemental analysis of the cross-section of the samples shows that directly on the surface treated with MQL technology (Fig. 3c), there is a significant amount of oxygen-almost 2%, while the sample grinded using CAMQL technology almost lacks oxygen on the surface, by which quantity gradually increases in depth, but does not exceed 0.5% (Fig. 3d). It is also worth noting that the surface layer of the sample obtained using MQL technology is saturated with molybdenum atoms, while the sample grinded using CAMQL technology is saturated with niobium atoms. In article [14], it is stated that with increasing oxidation temperature of the Inconel 718 nickel alloy, the oxidation rate, the thickness of the external scale, and the internal

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Fig. 3. SEM images and EDS spectra of the subsurface layer of post-grinding: a MQL; b CAMQL.

oxidation zone are increased. During the oxidation process, a layer of Cr2O3 is formed with the formation of TiO2 on the surface itself [14, 15], and the amount of TiO2 increases with the increasing temperature [14]. Increasing the concentration of Nb (Fig. 3d) is consistent with the results of study [14, 15], where the formation of the intermetallic phase of Ni3Nb at the oxide–alloy interface due to the diffusion of Nb atoms is noted. Thus, we can assume that the mechanisms of oxidation are similar. In general, the results obtained confirm the effectiveness of the cooling function of the CAMQL technology. One of the fundamental parameters of the surface layer energy state is the electronic work function (EWF), which is determined by the difference between the minimum energy required to move the electron from the volume of a solid body and the Fermi energy. Knowledge of the EWF actual value makes it possible to determine the surface energy of metals and other solids with great accuracy, and thus to track the change in the state of their surface layers. Numerous studies have shown that the EWF function is inextricably linked to many mechanical properties of metals [16–18]. For example, the modulus of elasticity of pure metals correlates with the ratio of the sixth degree with the work function [17]. Y. Zhou, J. Q. Lu, and co-authors have experimentally proved the effect of EWF deformation: elastic deformations cause EWF growth, and in the area of plastic deformation, the output work decreases [19]. The function of the work affects the adhesion activity of the surface, hence the effect on friction, tribological processes, etc. [20].

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Therefore, the EWF function can be used to predict and evaluate the mechanical properties of metals. In addition, knowledge of the general EWF provides additional information about the surface layers of materials, which will allow to manage the adaptation of materials and their properties. We know an expression in the form (1), which binds the EWF of the test sample, through the CPD value measured by the Kelvin probe method [21]: ϕ=−

W1 − W2 e

(1)

where ϕ is the CPD value, W 1 is the EWF of the sample, W 2 is the EWF of the probe material, and e is the electron charge. Taking into account that the EWF of the probe W 2 is a constant value during measurements, the spatial distribution of the CPD ϕ over the sample surface has a similar tendency to the distribution of the EWF values of the sample W 1 surface. The results of measurement of the surface obtained after grinding using MQL technology show that there is a fairly contrasting micro-relief with characteristic risks from abrasive grains and the CPD varies in the range from 0 to 150 mV with a maximum number of values of about 50 mV (Fig. 4a), i.e. the sample EWF is close to the value of the probe EWF. The probe is covered with a film of gold, the EWF of which is 5.1 eV [22].

Fig. 4. Contact potential difference of post-grinding: a MQL; b CAMQL.

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The use of CAMQL technology provides a more uniform micro-relief of the sample, a shift to the positive area of the CPD with a maximum value in the region of 125 mV (Fig. 4b). Thus, the surface EWF increases in the range from 0.05 to 0.1 eV. The difference in the EWF values of the studied samples may be in the oxidation mechanism described above. If we take into account the hypothesis that with an increase in the grinding temperature on the treated surface, the amount of titanium oxide TiO2, which has a lower EWF value (4.7 eV), increases, the overall EWF level of the surface should reduce. In addition, in article [20], the study of friction processes proved that surfaces with higher EWF values better retain lubrication and form stable tribo-films with a low friction coefficient. Thus, the results of the EWF evaluation study show a more favorable state of the surface obtained after grinding with CAMQL technology. X-ray structural analysis of the characteristics of the nickel alloy thin structure after grinding showed that the samples under study are in a single-phase polycrystalline state. Only structural lines are present on diffractograms. Diffraction reflections of metastable phases were not detected. According to the results of research, it was found that the samples have a highly developed thin structure with a small size of the coherent scattering region (CSR), and in absolute values, the CSR values are almost identical and are in the range of 470–480 Å. After grinding with CAMQL technology, the micro-stress level on the surface is 2 times lower (155 MPa instead of 308 MPa), while the CSR is equal.

4 Conclusions The results of the study of the surface layer acquired properties show that the use of CAMQL technology in comparison with the use of MQL alone provides a qualitative improvement in the condition of the treated surface, expressed through a reduction in oxidative and adhesive processes. The cooling effect of CAMQL technology also has a positive effect on the level of micro-stresses, significantly reducing them. Thus, it can be assumed that the use of CAMQL technology will help to improve the performance of processed products by improving the quality of their surfaces. Acknowledgements. The reported study was funded by RFBR according to the research project № 18-38-00597 “The study of the process of an extreme contact interaction of solids under the conditions of the presence of a minimum amount of refrigerant distributed in a cooled air stream”.

References 1. Lee PA (2015) Study on Thermal Characteristics of Micro-Scale Grinding Process Using Nanofluid Minimum Quantity Lubrication (MQL). Int J Precis Eng Manuf 16:1899–1909. https://doi.org/10.1007/s12541-015-0247-2 2. García E, Méresse D, Pombo I, Dubar M, Sánchez J (2016) Role of frozen lubricant film on tribological behaviour and wear mechanisms in grinding. Int J Adv Manuf Technol 82:1017– 1027. https://doi.org/10.1007/s00170-015-7397-3 3. Reddy PP, Ghosh A (2016) Some critical issues in cryo-grinding by a vitrified bonded alumina wheel using liquid nitrogen jet. J Mater Process Technol 339:329–337. https://doi.org/10. 1016/j.jmatprotec.2015.09.040

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4. Nguyen T (2003) An assessment of the applicability of cold air and oil mist in surface grinding. J Mater Process Technol 140:224–230. https://doi.org/10.1016/S0924-0136(03)00714 5. Choi HZ, Lee SW, Jeong HD (2002) The cooling effects of compressed cold air in cylindrical grinding with alumina and CBN wheels. J Mater Process Technol 127:155–158. https://doi. org/10.1016/S0924-0136(02)00117-6 6. Saberi A, Parsa H, Ashrafijou M, Rabiei F (2016) Improvement of surface grinding process performance of CK45 soft steel by minimum quantity lubrication (MQL) technique using compressed cold air jet from vortex tube. J Cleaner Prod 131:728–738. https://doi.org/10. 1016/j.jclepro.2016.04.10411 7. Guo SM, Li C et al (2017) Experimental evaluation of the lubrication performance of mixtures of castor oil with other vegetable oils in MQL grinding of nickel-based alloy. J Clean Prod 140:1060–1076. https://doi.org/10.1016/j.jclepro.2016.10.073 8. Dogra M, Sharma VS, Dureja JS, Gill SS (2018) Environment-friendly technological advancements to enhance the sustainability in surface grinding—a review. J Cleaner Prod 197:218–231. https://doi.org/10.1016/j.jclepro.2018.05.280 9. Jia DZ, Li CH (2017) Specific energy and surface roughness of minimum quantity lubrication grinding Ni-based alloy with mixed vegetable oil-based nanofluids. Precis Eng J Int Soc Precis Eng Nanotechnol 50:48–62. https://doi.org/10.1016/j.precisioneng.2017.05.012 10. Mao KQ, Zhang LC (2006) The effect of compressed cold air and vegetable oil on the subsurface residual stress of ground tool steel. J Mater Process Technol 178:9–13. https://doi. org/10.1016/j.jmatprotec.2005.05.013 11. Krutikova AA, Mitrofanov AP, Parsheva KA (2019) Application of technology for supply of minimum lubricant amount in cooled air flow during heat-resistant alloy grinding. Tekhnologiya Metallov 8:9–15. https://doi.org/10.31044/1684-2499-2019-8-0-9-15 12. Mitrofanov A, Nosenko V (2019) Investigation of the technology of microdosed supply of lubricant compositions with nanoparticles during grinding of heat-resistant ni-based with additional air cooling. Obrabotka Metallov-Metal Working and Material Science 21:6–18. https://doi.org/10.17212/1994-6309-2019-21.4-6-18 13. Zhang J, Li C et al (2018) Temperature field model and experimental verification on cryogenic air nanofluid minimum quantity lubrication grinding. Int J Adv Manuf Technol 97:209–228. https://doi.org/10.1007/s00170-018-1936-7 14. Al-hatab KA, Al-bukhaiti MA, Krupp U, Kantehm M (2011) Cyclic oxidation be-havior of IN 718 superalloy in air at high temperatures. Oxid Met 75:209–228. https://doi.org/10.1007/ s11085-010-9230-6 15. Delaunay F, Berthier C, Lenglet M, Lameille JM (2000) SEM-EDS and XPS studies of the high temperature oxidation behaviour of Inconel 718. Mikrochim Acta 132:337–343. https:// doi.org/10.1007/s006040050027 16. Li W (2006) Influences of tensile strain and strain rate on the electron work function of metals and alloys. Scripta Mater 54:921–924. https://doi.org/10.1016/j.scriptamat.2005.10.064 17. Hua G, Li D (2011) Generic relation between the electron work function and Young’s modulus of metals. Appl Phys Lett 99(4):041907. https://doi.org/10.1063/1.3614475 18. Lu H (2016) Electron work function – a promising guiding parameter for material design. Sci Rep 6:1–11. https://doi.org/10.1038/srep24366 19. Zhou Y, Lu JQ, Qin WG (2009) Change in the electronic work function under different loading conditions. Mater Chem Phys 118:12–14. https://doi.org/10.1016/j.matchemphys. 2009.07.062

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20. Shiyi L, Hao L, Li DY (2015) The relationship between the electron work function and friction behavior of passive alloys under different conditions. Appl Surf Sci 351:316–319. https://doi. org/10.1016/j.apsusc.2015.05.125 21. Melitz W, Shen J, Kummel AC, Lee S (2011) Kelvin probe force microscopy and its application. Surf Sci Rep 66:1–27. https://doi.org/10.1016/j.surfrep.2010.10.001 22. Wang J, Wang SQ (2014) Surface energy and work function of fcc and bcc crystals: Density functional study. Surf Sci 630:216–224. https://doi.org/10.1016/j.susc.2014.08.017

Comparative Analysis of the Performance of Oscillating and Propeller Stirrers L. A. Ilina(B) , A. A. Shagarova, and I. O. Goncharov Volgograd State Technical University, 28, Lenin Avenue, Volgograd 400005, Russia [email protected]

Abstract. The paper considers available modern designs of stirring devices, and their application in various industrial processes has been considered. The operating principle has been considered for a new design of an oscillating stirrer to obtain high-viscosity structural and non-Newtonian solutions, suspensions, and emulsions. An experimental unit has been developed to estimate the energy efficiency of the new oscillating stirrer design. Based on the previously developed technique, experimental studies have been performed to estimate the efficiency of using high-speed propeller stirrer and oscillating ones by evaluating the stability of emulsions (industrial oil-water) obtained with various stirring devices. The analysis of the effect of the high-speed and oscillating stirrers’ structural and kinematic characteristics on the intensity and efficiency of mixing liquid heterogeneous systems has been performed. The experimental study results have shown that using an oscillating stirrer is more than 20 times more efficient compared to a high-speed propeller one, while it is increasing the power costs by only 25– 30%. Using new energy-efficient stirrers in the designed and existing industries would decrease the mixing duration by several times, while obtaining emulsions with desired properties at an overall reduction in power consumption per unit of output. Keywords: Mixing · Resonance · High-speed stirrer · Oscillating stirrer · Intensity of mixing · Efficiency of mixing

1 Introduction Mixing media is widely used in various industries to obtain homogeneous solutions, emulsions, and suspensions. Mixing is an effective way to intensify hydrodynamic as well as heat and mass transfer processes [1–3]. Solving the issue of reducing power consumption in the production of stable, high-viscosity structural and non-Newtonian solutions, suspensions, and emulsions is an urgent task when designing new and retrofitting existing processes in engineering, metallurgy, energy, chemical, petrochemical, and other industries, as well as environmental processes of liquid waste processing, which include mixing. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_156

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The mixing techniques and device designs depend on the source media properties and the requirements for the finished product [4]. Preparing solutions, emulsions, and suspensions in engineering, chemical, petrochemical, and other industries is most often performed using mechanical stirrers rotating in a vessel [4, 5]. Mixing is characterized by efficiency and intensity [5–7]. In this case, efficiency means the uniform distribution of concentrations throughout the volume of liquid. Intensity means the power consumed per unit of the mixed liquid volume. An increase in intensity, as a rule, leads to an increase in energy costs but not always in the mixing efficiency. When choosing the stirrer design, the main task is not only retaining the mixing efficiency but also developing energy-efficient stirrer designs that may reduce power consumption during the stirrer operation. An advanced direction in mixing liquid media is the development and use of a new generation of equipment, which increases turbulence and circulation of flows while reducing power consumption and mixing time [7]. Considerable attention is paid to mixing modes, as this is one of the defining moments to increase the process efficiency [4, 8]. Currently, a wide range of combined and resonance stirrer designs have been proposed, which allow obtaining stable emulsions using energy-efficient stirrer designs [9– 13]. These stirrer designs operate based on the resonance phenomenon, which increases the efficiency of mixing media at the micro- and macro-levels but negatively affects the integrity of equipment designs due to the resonance effect that has been detected during experimental studies [14–16]. Thus, developing the designs of stirring devices operating in a mode close to resonance but not achieving a resonance effect, while increasing the mixing efficiency at the micro- and macro-levels is an urgent task, which, if solved, allows finding the energy-efficient stirring equipment operating modes close to optimal to obtain stable emulsions. The work objective is to estimate the effect of the high-speed and oscillating stirrers’ structural and kinematic characteristics on the intensity and efficiency of mixing based on experimental studies.

2 The Stirring Device Design and Operating Mode An analysis of new designs of stirrers operating based on the resonance effect principles and previous experimental studies has shown [14, 16] that to increase the mixing intensity, it makes sense to operate a combined stirrer in the effective mode as shown in Fig. 1. Presumably, such an operating mode of oscillating stirrer would allow a significant increase in the mixing efficiency without entering the resonance oscillation mode, while retaining or slightly increasing the power consumption. Let us consider the operating principle of a combined stirrer built based on the prototype in a similar mode [13]. The main difference between the experimental unit and the prototype is the absence of radial distributing plates, which allows avoiding a

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Fig. 1. The effective stirrer operating mode.

resonance phenomenon, while maintaining intensive turbulence of the mixed media due to the simultaneous rotation and oscillation of the stirrer design elements. The stirrer design [13] is shown in Fig. 2. The description of the prototype stirrer operating principle indicates that using this stirrer design in devices with baffle plates is effective. In this case, when the coil spring ends pass near the baffle plates, the rotating resistance increases due to the hydraulic wedge effect. Stirrers consisting of coil springs bend in the stirrer rotation plane, after which return to their original position. The circular oscillations of the spring coils contribute even more to the generation of micro-vortices in the liquid mixed intensifying the mixing itself, reducing the required time, and, therefore, increasing productivity [13]. To reduce the resonance effect likelihood, it has been decided to refuse from baffle plates in the experimental unit. Such a change in the stirrer design simultaneously facilitates the further unit operation when working with high-viscosity media, as it allows avoiding a need to additionally clean the plates contaminated.

3 Experimental Unit Based on the design proposed, a prototype oscillating stirrer has been built. Experimental studies have been performed based on the ES-8300D stirring device having several replaceable shafts, on which a high-speed propeller stirrer and the developed oscillating one have been installed. The stirring device ES-8300D consists of an engine block with a three-jaw chuck and a control unit (Fig. 3). The lower part of the engine block comprises a sliding bearing with a shaft, on which a three-jaw chuck 5 is fixed. The motor shaft torque is transmitted to the stirrer through a system of two metal bushings and a rubber clutch. Three-jaw chuck 5 allows fixing stirrers with a shaft diameter of 1–8 mm.

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Fig. 2. The oscillating stirrer design [13]: 1—case; 2—removable cover; 3—motor; 4—gear; 5—shaft; 6—stirrer; 7, 8, 10, 11—tubes; 9—jacket; 12—supports.

4 The Study Objects and Their Characteristics As test fluids, almost immiscible water and industrial oil I-40A in a ratio of 1:1 have been used. The finished mixing product is an emulsion. The characteristics of the test fluids are given in Tables 1 and 2. It is worth noting that using an industrial oil in this experiment was a conscious choice, since earlier experimental studies were performed with vegetable oil and water as test fluids and the stability of the emulsions obtained was up to 200 h, which complicated the research, therefore, choosing industrial oil and water reduced the experiment time. During the experiments, the stability of the emulsions obtained has been studied at the operation of the high-speed propeller and oscillating stirrers.

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Fig. 3. Experimental unit: a—high-speed propeller stirrer; b—oscillating stirrer. 1—multimeter; 2—ammeter connecting electric circuit breakers; 3—motor control unit with a digital indicator of the stirrer rotation speed; 4—motor; 5—three-jaw chuck; 6—cylindrical vessel with a medium mixed; 7—propeller stirrer; 8—coil spring; 9—holder.

Table 1. Industrial oil I-40A characteristics [17] Indicators

Value

Kinematic viscosity, mm2 /s, at 20°C

61

Pour point, °C

−15

Density, kg/m3 , at 20°C

900

Table 2. Water characteristics [18]. Indicators

Value

Kinematic viscosity, mm2 /s, at 20°C

1.006

Freezing point, °C

0

Density, kg/m3 , at 20°C

998

5 Analysis of the Experimental Study Results The most important stirrer characteristics that can be the basis for their comparative evaluation are the mixing efficiency and intensity [6, 19, 20]. Obtaining a stable emulsion depends on the mixing intensity and time. The Reynolds criterion can be used as a parameter characterizing the mixing intensity. Re =

ρ · n · dm2 , μ

(1)

where ρ is the emulsion density, kg/m3 ; n is the stirrer rotation speed, s−1 ; μ is the dynamic viscosity coefficient, Pa•s; d m is the stirrer diameter, m.

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The stirrer power criterion KN : KN =

N , ρ · n3 · dm5

(2)

where N is the stirrer power consumption, W. An integral characteristic of the mixing intensity in the device is the intensity coefficient determined by the formula (3): N , V

I=

(3)

where V is the mixed liquid volume, m3 To estimate the mixing efficiency, a mixing efficiency coefficient has been introduced, which is determined by the formula (4): E=

τobt , τref

(4)

where τobt —is the studied emulsion breakdown time, s; τref —is the reference emulsion breakdown time, s. For the experiment, the 10 min reference emulsion breakdown time has been adopted. The experimental results have been averaged over three parameters. In the course of the experimental studies, the emulsion breakdown time has been recorded (Table 3). Table 3. Experimental Data for the Mixing Volume V = 2000 ml. Rotation speed, rpm

Current I, A·10−3 Propeller stirrer

Oscillating stirrer

Propeller stirrer

Oscillating stirrer

600

55

215

0,66

0,7

0,77

7,16

7,4

7,63

800

60

305

0,79

0,75

0,69

18,05

18,3

18,67

1000

90

375

2,18

2,25

2,31

23,59

24

24,29

Emulsion breakdown time τ, min

Based on the experimental study results, the dependencies of the relative efficiency and mixing intensity coefficient values on the stirrer rotation speed have been plotted (Fig. 4). An analysis of the graphical dependencies shows that the oscillating stirrer efficiency coefficient increases from 7.5 to 25 times as compared to the propeller one. When using an oscillating stirrer, the mixing intensity increases by 25% maximum compared to the propeller one. Obviously, the technological effect, which in this case is the emulsion stability increases many times when using an oscillating stirrer that allows reducing the equipment operating time to achieve the specified quality indicators of the product obtained.

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Fig. 4. Dependence of the efficiency a and intensity b coefficients on the stirrer rotation speed.

Thus, we can talk about a significant reduction in the mixing power consumption due to the use of an oscillating stirrer, which provides the required technological effect for a shorter period. Oscillating stirrers can be used in the machine-building, chemical, and petrochemical processes. The oscillating stirrer is easy to install both on newly designed devices and operating ones, when retrofitted.

References 1. Strenk F (1975) Mixing and equipment with stirrers. Chemistry, Leningrad, Moscow 2. Mersmann AB (2010) World congress III chemical engineering Tokyo, 21–25 Sept 2010, vol 3, p 23 3. Borisov GS (1991) Basic processes and apparatuses of chemical technology. Chemistry, Moscow 4. Nagata S (1975) Mixing. Tokyo Halsted Press Book, Principles and Application 5. Barabash VM, Begichev VI, Belevitskaya MA et al (2007) Issues and trends in the development of the theory and practice of mixing liquid media. Theor Basis Chem Technol 41(2):140 6. Braginsky LN, Begachev VI, Barabash VM (1984) Mixing in liquid media: physical fundamentals and engineering analysis methods. Chemistry, Leningrad 7. Balmont SD, Guyumdzhyan PP, Balmont TM (2010) The degree and intensity as the main parameters of mixing liquid and heterogeneous media. Modern high technologies: Coll. Sc. Papers. Ivanovo state technical university, Ivanovo, no 1, p 48 8. Shagarova AA, Golovanchikov AB, Korzhova MV (2012) Determining the optimal operating mode of stirrers during emulsification. Mathematical methods in engineering and technology—MMTT–25. Coll. Proc. 25th Int Scientific Conf. In 10 vol. V. 7. Section 11, Volgograd, 29–31 May 2012, p 106–107 9. Golovanchikov AB, Vorotneva SB, Dulkina NA et al (2015) Stirrer. P.m. 154488 Russian Federation, IPC B01F7/24. Volgograd State Technical University 10. Golovanchikov AB, Vasiliev PS, Ilina LA et al (2017) Stirrer. P.m. 169417 Russian Federation, IPC B01F7/18. Volgograd State Technical University

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11. Golovanchikov AB, Shandybina IM et al (2017) Stirrer. P.m. 171021 Russian Federation, IPC B01F7. Volgograd State Technical University 12. Golovanchikov AB, Aristova YuV, Fomenkov SA et al (2017) Stirring device for a stirrer. P. m. 171493 Russian Federation, IPC B01F7/22, B01F11/00. Volgograd State Technical University 13. Golovanchikov AB, Prokhorenko NA, Cherikova KV et al (2018) Stirrer. P. m. 177043 Russian Federation, IPC B01F7/24. Volgograd State Technical University 14. Lysko YuA, Ilina LA, Bykov NS (2017) Experimental studies of mixing using stirrers with a resonance effect. Technologies and Equipment for the Chemical, Biotechnological, and Food Industries: Proc. 10th All-Russian Sc.-Pract. Conf. Students, Post-grad. Students, and Young Scientists with International Participation, Biysk, 24–26 May 2017, p 249–254 15. Lysko YuA, Ilina LA, Golovanchikov AB (2016) Resonance effect as a method to intensify mixing. Creative Youth to Russia: 9th Region. Sc.-Pract. Student Conf. Abstracts, In 2 v. V. 1. VSTU, KTI (branch) VSTU, 27–28 April 2016, Volgograd, p 76 16. Bykov NS, Goncharov IO, Belyakov IA (2019) Experimental study of mixing heterophase media using a combined stirrer. 24th Regional Conference of Young Scientists and Researchers of the Volgograd Region: Coll. Proc. Conf. Committee for Education, Science, and Youth Policy of the Volgograd Region, State Budgetary Institution of the Volgograd Region Center of Youth Policy, Volgograd State Technical University, Volgograd, p 13–14 17. Anisimov IG, Badyshtova KM, Bnatov SA et al (1999) Reference Book: Fuels, Lubricants, and Technical Fluids. Assortment and Application. Ed. 2nd rev. and add. Publishing Center Tekhinform, Moscow 18. Pavlov KF, Romankov PG, Noskov AA (2006) Examples and tasks on the course of processes and apparatus of chemical technology, 13th edn. Stereotype, AllianS, Moscow 19. Shagarova AA, Dorokhina TB, Danilicheva MV (2014) Experimental studies of the effect of structural and kinematic characteristics of high-speed and combined stirrers on the mixing intensity and efficiency. News of Volgograd State Technical University. Series “Rheology, Processes and Apparatuses of Chemical Technology”. Vol. 7: Interuniversity Coll. Sc. Papers/ Volgograd STU 1 (128):14–19 20. Shagarova AA, Ilina LA (2019) Evaluating Energy efficiency of high-speed and hybrid stirrers. Fibre Chem 51(4):300–302

Environmental Aspects of Trucks Transition to Alternative Type of Fuel A. G. Vozmilov1(B) , R. Yu. Ilimbetov1 , and D. V. Astafev1,2 1 South Ural State University, 76, Lenin Ave, Chelyabinsk 454080, Russia

[email protected] 2 South Ural State Agrarian University, 75, Lenin Ave, Chelyabinsk 454080, Russia

Abstract. The article considers the analysis of the environmental situation in the world where the source of pollution is road transport. All the leading countries of the world are interested in improving the environmental situation. The prospects of the transition from a traditional type of fuel to a more environmentally friendly one for vehicles, operating on internal combustion engines, are considered. Possible prospects of computer modeling in the field of mechanical engineering are considered. The description of the AVL Cruise program is presented, in which all the technical characteristics of vehicles are introduced, driving cycles are selected, the necessary corrective changes are made to the existing structures of units and assemblies, to simulate the process of car movement under given conditions. The comparative results of modeling the movement of the KAMAZ automobile along the driving cycle using various types of fuel are presented. The conclusions explain the results of comparative modeling in the AVL Cruise program in terms of the environmentally and economically viable type of fuel. Keywords: Modeling · Car · Methane · Ecology · Gas · Engine · Fuel · Environmental pollution

1 Introduction In the modern world, vehicles occupy a leading place in the global economy and everyday life of a person, satisfying his needs. However, the operation of vehicles (land, air, and sea) also entails negative consequences affecting the state of the environment, which is constantly increasing with an increase in their number [1–3]. Today in the world there is an acute question of environmental safety. One of these problems is air pollution, where cars are one of the main sources [4]. In this regard, today special attention is paid to the environmental performance of modern cars, which use new technical solutions to increase their environmental and economic performance [5–8].

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_157

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2 Problems of Environmental Pollution by Transport According to the WARD’S automobile magazine, in 2019 there are more than 1.2 billion cars on the planet, and by 2040, agency analysts predict an increase in cars by more than two times. Given the increase in motorization in the world, the question of environmental safety arises [7–9]. According to the results of environmental studies conducted by the International Energy Agency in 2019, CO2 emissions from enterprises producing electric energy are 44%, emissions from the share of manufacturing and construction industries—18%, and transport—16% (Fig. 1) [10, 11].

Fig. 1. The share of industries polluting the Earth’s atmosphere.

Analysis in Fig. 1 shows that transport is one of the three leaders in economic sectors polluting the Earth’s atmosphere [12–14]. Structural analysis only by the type of vehicles shows that land transport accounts for 75% of them 22%—for trucks, 43%—cars up to 3.5 tons, 6%—buses, and 2%— motorcycles (Fig. 2) [15]. According to the Kyoto Protocol, one of the priority areas in the world is work to reduce environmental pollution by emissions from industrial enterprises and transport [16, 17]. In order to reduce global CO2 emissions from the transport sector, the following solutions are proposed • the transition of vehicles running on diesel or gasoline fuel to a more environmentally friendly fuel—natural gas methane; • transition to a hybrid vehicle (internal combustion engine + electric motor); • replacement of internal combustion engine with a traction electric motor.

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Fig. 2. Structure of global CO2 emissions by vehicle type.

3 Computer Simulation of Truck Movement in the AVL CRUISE Program Today, computer technology provides not only the widest range of high-tech engineering calculations, but also their analysis, taking into account real operating conditions. Thus, even in the early stages of design, high-precision computer models of various technical solutions are created [18, 19]. Today, there are a large number of modern software products that allow you to simulate the processes of components and assemblies of cars. The specialized computer program “AVL CRUISE” [19–21] was selected as a simulation of the process of moving a truck on different types of fuel and with different types of transmission. As the object of modeling, one of the common types of trucks in the territory of the Russian Federation was chosen—this is KAMAZ-65115 with a 6 × 4 wheel formula. This car belongs to the category of combined road machines for cleaning the streets and carriageways from debris, dirt, and snow. In the AVL Cruise program, the following conditions for computer simulation of the KAMAZ vehicle were considered: • dependence of fuel consumption on its type in urban and mixed traffic cycles; • the dependence of the environmental performance of internal combustion engines when burning different types of fuel.

4 Structural Scheme for Computer Simulation of a Truck In order to proceed to full-fledged modeling in the “AVL CRUISE” program, it is necessary to assemble the corresponding structural scheme of the KAMAZ-65115 truck, consisting of a power unit, a transmission, and propulsion devices (Fig. 3) [21–23]. In each block of the structural scheme, the technical parameters of the components and assemblies of the car were introduced not only of the engine, transmission, or

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Fig. 3. Structural scheme of the truck KAMAZ – 65115

drive wheels, but also the physical properties of such technical fluids as oils, fuels, and antifreeze. Figure 4 shows the interface of the program for data entry for internal combustion engines [18–21].

Fig. 4. An example of the parameter input interface in the AVL Cruse program. 1—type of fuel; 2—type of air supply to the combustion chamber; 3—engine volume; 4—engine temperature; 5— number of cylinders; 6—the number of ticks in the engine; 7—single turns; 8—maximum engine speed; 9—inertial moment of the engine; 10—calorific value; 11—fuel density; 12—residual fuel volume; 13—minimum engine speed at which fuel is supplied; 14—maximum engine speed at which the fuel supply is turned off.

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5 The Results of Modeling the Movement of a Car on Diesel and Gas Engine Fuel Comparative results of modeling the fuel consumption of a KAMAZ automobile in urban and combined driving cycles are presented in Figs. 5 and 6.

Fig. 5. Car fuel consumption in the urban cycle of the UDC indicated in blue: a diesel fuel; b gas engine fuel—methane.

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Fig. 6. Car fuel consumption in the NEDC combined driving cycle is indicated in blue: a diesel fuel; b gas engine fuel—methane.

Computer simulation results show that when the car moves 100 km along the track, the fuel consumption in the urban driving cycle compared with the mixed one is increased by 16.89% for diesel fuel and 9.15% for gas engine. Compared to diesel, gas engine fuel consumption is 29.72 higher for mixed and 21.14% for urban driving cycles (Fig. 7a). Economic calculations, according to the results of computer modeling, show that costs in the urban cycle of movement, compared to mixed, increase by 8.42% for diesel

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Fig. 7. Indicators of consumption and costs for diesel and gas engine fuel: a fuel consumption from the cycle of movement and type of fuel; b the price of fuel consumption per 100 km of track, depending on the driving cycle and type of fuel.

fuel, respectively, for gas-powered—7.76%. Despite the fact that the consumption of motor gas compared to diesel is 20–30% higher, however, its price is 250–300% lower. Analyzing Fig. 7b it can be seen that from an economic point of view, the operation of a vehicle with gas engine fuel is much more profitable than with diesel, an average of 252.6% or 861 rubles per 100 km.

6 The Results of Modeling the Environmental Performance of ICE on Different Types of Fuel The simulation results show that when a car is powered by gas engine fuel in an urban cycle, the amount of harmful carbon monoxide CO emitted into the atmosphere will decrease by 8 times, nitrogen oxides NOx by 2 times, soot by 2,000 times, and the smoke content of HC will decrease by more than 10 times (Fig. 8). If the environmental indicators of diesel fuel, such as CO, NOx, HC, and soot Soot, are taken as 100%, then the environmental indicators of gas engine fuel against diesel are reduced by an average of 62.7% (Fig. 9). Thus, the results of simulation modeling of the movement of a KAMAZ-65115 truck confirm the relevance of using gas motor fuel instead of diesel on all types of vehicles. Further work on the modeling of the movement of a KAMAZ-65115 truck suggests the study of its work on a hybrid and electromechanical transmission, with the aim of determining the most environmentally friendly structural design of the vehicle.

7 Conclusion Thanks to modern computer simulation products, with the help of which it is possible to perform studies taking into account real operating conditions, it was possible to determine the effective type of fuel for vehicles running on internal combustion engines. Today, for a combination of factors, gas engine fuel appears to be the most promising substitute for diesel fuel due to lower cost and lower prices compared to other types of fuel by more than 250%. The environmental aspect, as a negative environmental impact factor, for motor gas is significantly lower than for traditional diesel fuel by more than 60%.

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Fig. 8. Graphs of emissions of toxic substances during fuel combustion in the urban cycle of movement: a diesel fuel; b gas engine fuel—methane.

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Fig. 9. Emission of toxic substances during fuel combustion in the urban cycle of movement

References 1. Sysoeva S (2009) Fuel economy, efficiency, ecology-attributes of new cars, engines and systems. Compon Technol 95:29–36 2. Igor Levitin (2011) Transport and environment: a national approach. Transp Russ Fed 6(37):4– 5 3. Vozmilov AG, Ilimbetov RY, Astapenko AM (2013) Relevance of application of the combined power installation in trucks. In: Achievements of science-agro-industrial production Materials of the LII international scientific and technical conference, p 60–65 4. Ilimbetov RY, Astapenko MA, Bakanov AV (2013) History of the development of hybrid trucks. In: SUSU science materials of the 65th scientific conference, p 7–10 5. Ilimbetov RY, Astapenko MA, Popov VV (2013) Application of hybrid systems in trucks. experience of foreign countries. In: SUSU science materials of the 65th scientific conference, p 15–18 6. Ilimbetov RYu, Solomin EV, Astapenko MA, Bakanov AV (2013) Application of Electromechanical transmission in trucks to improve environmental performance. Int Sci J Altern Energy Ecol 5–1(125):88–93 7. Ilimbetov RYu, Astapenko MA (2013) Development of the layout scheme of a combined power plant for a truck with improved environmental indicators. Bulletin of the South Ural state University. Series: Mechanical Engineering 13(1):72–79 8. Battalkhanov AA (2015) Methane on transport. Problems, challenges and prospects for the development of compressed natural gas markets 9. Belyaev SV, Davydkov GA (2010) Problems and prospects of using gas-engine fuels, p 16 10. Veselov VN, Veselova YuA, Vishnyakova MYu (2010) Use of natural gas as a method of ecologization of automobile transport, p 33 11. Abagnale C, Cameretti MC, De Simio L, Gambino M, Iannaccone S, Tuccillo R (2014) Numerical simulation and experimental test of dual fuel operated diesel engines. Appl Therm Eng 65(1–2):403–417

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12. Hegab A, La Rocca A, Shayler P (2017) Towards keeping diesel fuel supply and demand in balance: Dual-fueling of diesel engines with natural gas. Renew Sustain Energy Rev 70:666– 697 13. Bhave A, Kraft M, Montorsi L, Mauss F (2004) Modeling a Dual-fueled Multi-cylinder HCCI Engine Using a PDF based engine cycle simulator. SAE Technical Papers 2004-01-0561 14. Korkmaz M, Ritter D, Jochim B, Abel D, Pitsch H (2019) Effects of injection strategy on performance and emissions metrics in a diesel/methane dual-fuel single-cylinder compression ignition engine. Int J Engine Res 15. Mariani A, Unich A, Minale M (2018) Combustion of hydrogen enriched methane and biogases containing hydrogen in a controlled auto-ignition engine. Appl Sci (Switzerland) 8(12):2667 16. Guo H, Liko B, Luque L, Littlejohns J (2018) Combustion performance and unburned hydrocarbon emissions of a natural gas-diesel dual fuel engine at a low load condition. J Eng Gas Turbines Power 140(11):112801 17. Alaya M, Ennetta R, Said R (2018) Numerical investigation of the effect of hydrogen addition on methane flame velocity and pollutant emissions using several detailed reaction mechanisms. Emission Control Sci Technol 4(4):321–329 18. Hutter R, De Libero L, Elbert P, Onder CH (2018) Catalytic oxidation of methane in the exhaust gas aftertreatment of a lean-burn natural gas engine. Chem Eng J 349:156–167 19. Ilimbetov RYu, Popov VV, Vozmilov AG (2015) Comparative analysis of “NGTU-electro” electric car movement processes modeling in MATLAB SIMULINK and AVL CRUISE software. Proced Eng 129:879–885 20. Ilimbetov RYu, Popov VV (2015) Results of modeling the electromechanical transmission of a KAMAZ truck. In: SUSU science materials of the 67th scientific conference. Ministry of education and science of the Russian Federation; South Ural state University, p 84–90 21. Ilimbetov RYu, Dernov VV (2014) Computer simulation of the electromechanical transmission of the Ural-4320 truck. In the collection: SUSU science materials of the 66th scientific conference, p 241–247 22. Ilimbetov RYu, Popov VV, Bakanov AV, Kirpichnikov IV (2014) Computer modeling of passenger car movement processes with sequential combined power plant. Bulletin of the Chelyabinsk state Agroengineering Academy 70:71–77 23. Ilimbetov RY, Astapenko MA, Dernov VV (2013) Morphological analysis of electromechanical transmissions of trucks. In: SUSU science materials of the 65th scientific conference, p 11–14

Analysis of Experience of Actual Operation of Gas Turbine Units Capstone C1000. Issues of Concern and Methods for Problem-Solving A. S. Rychkova(B) , V. Y. Sokolov, and S. A. Naumov Orenburg State University, 13, Prospekt Pobedy, Orenburg 460000, Russia [email protected]

Abstract. Capstone microturbines represent modern equipment for autonomous heat supply to the consumers. They combine excellent technical and operational characteristics. Unsurpassed consumer properties and careful study of all elements with the use of innovative technologies of Capstone Turbine Corporation, protected by more than 100 patents, make it possible to distinguish microturbines into a separate class of power generating equipment. Microturbines ideally meet the needs of modern distributed energy and the needs of enterprises in various sectors of the economy. Over the last few years, the microturbines Capstone found wide application in the following areas: organization of autonomous energy supply of industrial enterprises, utilities, remote villages, radio relay stations, shopping and office centers, and many other objects. In this paper, the authors have analyzed the experience of actual operation of Capstone C1000 gas turbine electric units (hereinafter referred to as GTEA) with a capacity of 1000 kW. The main problems that occurred during the operation of GTEA data are also summarized. The authors present methods for solving these problems that have already been tested and proven, as well as those that are under trial operation. Keywords: Capstone turbine · Gas turbine · Fault

1 General Information In this work, we analyzed the experience of actual operation of gas turbine electric power units (hereinafter GTPU) with a capacity of 1000 KW. The main problems that arose during the operation of GTEA data are summarized. Problem-solving methods are presented both tested and proven and under pilot operation. GPTU Capstone C1000 is a cluster of 5 microturbine units (hereinafter MTU) of Capstone C200 with a capacity of 200 KW each operating on gas fuel [1–8]. 4 types of gas can be used as a fuel: • High-pressure natural gas (HPNG); • Low-pressure natural gas (LPNG); © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_158

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• High-pressure (anaerobic) landfill gas; • High-pressure industrial propane. MTU C200 is a turbine engine on air bearings with a three-phase two-pole generator installed on the rotor shaft with variable speed from 20,000 to 60,000 rpm. GPTU Capstone C1000 can work in three operating modes: • Parallel to external grid (grid connect mode); • Standalone (Standalone mode); • Combined (Dual mode). Physical form of GTPU as well as MTU are showed in Fig. 1.

Fig. 1. Appearance of GPTU Capstone C1000 and MTU C200.

2 Analysis of Operational Experience A feature of GTPU is the possibility of combining up to 10 units into a single cluster MultyPack. An analysis of the experience of a cluster of 4GTPU (20 MTU units) operating on high-pressure natural gas in a standalone mode, with a total capacity of 4 MW for the period from 2015 up to October 2019 inclusive is given below. Key moments of GPTU Capstone C1000 operating can be divided into three enlarged groups:

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1. Technical features of equipment Capstone C1000. 2. Failures, failures of spare parts and separate units, emergency situations, and software errors occurring during operation. 3. Pricing for spare parts, consumables, and service maintenance in Russian Federation. In the group of technical features, we have identified some design and technical solutions of GPTU Capstone C1000 which influence operation process, forcing maintenance staff to readjust the operation of the energy complex to these features [9–10]. Such features include • A need to maintain several additional MTU as a « hot reserve » to ensure stable operation of GTPU, especially with an abruptly variable load. Selection of MTU quantity to provide “rotary reserve” is a set as approximate value of maximum change of electric power demand taking into account GTPU auxiliaries. Selection of MTU quantity to provide “rotary reserve” is set as approximate value of maximum change of electric power demand taking into account GTEA auxiliary needs (battery charge). It entails additional gas fuel consumption and equipment damping. The number of MTU in the “hot reserve” depends directly on the state of the electric batteries (hereinafter EB). • Dependence of stable operation of GTPU on state and quality of batteries. There are 960 hermitic lead-oxide batteries in 4 × GTPU, 48 units in each MTU. • Higher sensitivity of MTU relay protection to other network relay protection. Impossibility to perform selectivity adjustment, as the MTU cut-off response time is faster than the network switching devices. • Impossibility to switch on power transformers in the network without complete disconnection of all GTPU, as the transformer magnetization is perceived by the machine as a short circuit in the network, after which it resets the load. • Insistence to grounding. It is important that the grounding in the entire network is performed through the TNS system for GTPU. The presence of other grounding systems in the network causes unstable operation of turbines up to stops. Thus, the actual operation of GTPU is different from that declared by the manufacturer Capstone Inc. in terms of reliability, economy, and simplicity of equipment.

3 MTU Malfunctions But the most significant problems encountered during the operation of the units were numerous emergency stops both of the units as a whole and of individual MTUs. The reasons for such stops were failures of individual spare parts and MTU nodes, software failures, and communication errors [11–13]. The reasons for emergency stops can be divided into several groups as shown in Fig. 2. 1. Failures of a “hot” part. These are failures related to MTU elements, where fuel is burned, as well as to the fuel supply system, from the failure of nozzles, deformation

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Fig. 2. MTU malfunctions.

2.

3.

4.

5.

of ignitors, to the passage of combustion chambers and jamming of the rotor part (Power Head). Regular combustion chamber outburst is the most significant problem in GTPU operation, which is still in the solution stage. This problem will be discussed separately below. Failures related to EB. Due to the fact that in standalone mode the EB starts microturbines, stops them and compensates for short-term power increase in the network, the main types of failures are premature failure, or battery discharge due to power increase in the network. As a rule, both failures are related to incorrect selection of MTU quantity for “hot” reserve or to incorrect selection of EB brand. Software failures (hereinafter software)—are all software malfunctions. It is not possible to solve this problem without contacting the company developer, as equipment manufacturers categorically do not allow consumers to source software codes. Experience of operation has shown that it is necessary to completely reinstall software and firmware on all MTU for stable operation of GTPU at least once a year. Loss of communication within MTU and between MTU in the cluster. To operate in standalone mode, one of the LTU in the cluster at the software level is assigned as master, the rest as slave. Master MTU takes over the load first, distributing it to slave MTU. Loss of communication between MTU leads to shutdown of the unit by reloading, loss of communication inside MTU leads to its shutdown, which also leads to shutdown of the whole unit in the future. Failures related to controls. This type of failures includes all types of failures of MTU control boards and other elements of power electronics, what is called “iron” failures. Statistics on failure groups for the period under analysis are shown in Fig. 3.

Figure 3 shows that it is the hot part that causes the most failures. Second failures are software failures, then there are failures of EB, control elements, and loss of communication. Other faults are emergency stops caused by GTPU relay protection actuation due to short circuits in the network. These are the cases when the operation of the relay protection of the turbines occurs faster than the operation of the switching devices. Figure 4 shows the general statistics of MTU emergency stops as part of GTPU Capstone C1000 by year.

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Fig. 3. Statistics on fault groups.

Fig. 4. General statistics of MTU failures.

The figure shows that the peak of emergency stops is in 2016. Deformations and outburst of combustion chambers of MTU began to diagnose for the first time in the same period. By this moment, GTPU had been in operation for 4 years (operation began in 2012). General view of the burnout chamber is shown in Fig. 5.

4 The Problem of Burnout of the Combustion Chamber We want to focus on the problem of combustion chambers burnout, as today it does not have a final solution.

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Fig. 5. General view of the burnout chamber.

Declared by the manufacturer service life of combustion chambers before replacement is 20,000 motor hours, but the first outages appeared at operating time of 8087, which is more than half less than they declared. Performed analysis of operating conditions of GTPU and characteristics of used gas fuel showed that units are operated in full compliance with requirements of manufacturer. Gas fuel quality also corresponds to manufacturer’s requirements [15]. At that combustion chamber burnout was detected at different operating hours of motor chambers, not at every MTU. So we drew conclusion either about design failure of MTU or about use of different grades of metal in the manufacture of combustion chambers and to assign these faults accordingly to guarantee claim. Thus, our company appealed to the official dealer Capstone Inc. in Russia to replace combustion chambers on warranty. The official dealer did not recognize this case as warranty and offered to get new combustion chambers that failed. Cost of one combustion chamber at dealer price was about 14,000 $. Nowadays this price in Russia is 36,000$. It should be noted that despite the fact that Capstone Corporation has not officially recognized combustion chamber burnout as a result of structural shortcomings, all turbines produced after 2015 have combustion chambers of modified (reworked) design. Due to the high price of combustion chambers, we decided to repair them. During 2017, the organization carrying out maintenance of GTEA searched the plants ready to repair chambers, as well as selection of metal for such repair [14, 16–20].

5 Repair of Combustion Chambers The only organization that was ready to repair combustion chambers was one of the aircraft factories in the territory of the Republic of Belarus. Chambers repaired by this plant are shown in Figs. 6. There were also certain problems with the selection of metal for combustion chambers. At initial stages, the repaired chambers were repeatedly burned 100–300 h of operating time. This has increased over time and now the repaired combustion chambers are currently operating more than 10,000 motor hours. In addition, ceramic spraying

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Fig. 6. Repaired combustion chambers.

was applied to one of the repaired chambers as an experiment, and now it is in pilot operation. It should be noted that two MTUs are currently operating on original cameras and have an operating time of more than 20,000 motor hours. At present, we have already repaired 32 combustion chambers. Statistics of combustion chambers failure by motor hours operating time are given in Table 1. Table 1. Statistics of combustion chamber failures by operating hours. Unit’s name

GTPU № 1

Cameras operating time at the moment of burnout

Total operating time, motor hours

Note

MTU C200 A

–

–

–

–

20,704

Original chamber

MTU C200 B

12,287

–

–

–

18,879

MTU C200 C

16,078

–

–

–

20,022

MTU C200 D

13,121

13,242

14,571

18,578

19,962

MTU C200 E

18,578

–

–

–

19,824 (continued)

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Table 1. (continued) Unit’s name

Cameras operating time at the moment of burnout

Total operating time, motor hours

Note

Original chamber

GTPU № 1

MTU C200 A

–

GTPU № 2

MTU C200 A

11,444

14,588

MTU C200 B

8087

9390

GTPU № 3

GTPU № 4

–

–

–

20,704

17,614

–

20,053

–

–

17,700

MTU C200 C

–

–

–

–

1278

MTU C200 D

–

–

–

–

22,558

MTU C200 E

8567

–

–

–

20,636

MTU C200 A

16,054

–

–

–

19,737

MTU C200 B

9377

12,802

18,328

MTU C200 C

13,656

–

–

–

18,566

MTU C200 D

10,424

–

–

–

18,253

MTU C200 E

9472

9754

17,448

–

18,757

MTU C200 A

10,867

11,207

12,827

19,203

20,429

MTU C200 B

9736

–

–

–

22,086

MTU C200 C

16,121

–

–

–

18,580

MTU C200 D

11,149

16,888

–

–

17,694

MTU C200 E

20,454

–

–

–

20,714

9488

9942

MTU is faulty Original chamber

6 Results Summing up the analysis, it can be said that the experience of actual operation of GTEA Capstone C1000 showed a number of differences between the operation of the unit and the declared producer company. There are some shortcomings and features of units described in this article. Moreover, GTEA operating is complicated by the distributor’s unwillingness to cooperate to correct defects and the high price of consumables and spare parts. However, GTEA has a rather potential power generating plant and, if it properly developed, may well occupy a decent niche for autonomous power supply for small enterprises or villages, which is especially relevant for energy companies located isolated from the EEC of the Russian Federation.

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References 1. Perelshtein BH (2008) New energy system. KGTU im. A. N, Tupoleva, Kazan p, p 203 2. Rumyantsev MYu, Sigachev SI, Berilov AV, Gribin VG, Serkov SA (2015) High-speed turbogenerators for autonomous systems of small distributed power engineering. Ind Power Eng 5:20–25 3. Gockner L, Heinrici M, Wilkening M (2010) Major upgrade turns up heat at Simmering. Mod Power Syst 30(10):25–30 4. Gragger JV, Giuliani H, Kral C, Bauml T, Kapeller H, Pirker F (2006) The Smart Electric Drives Library—powerful models for fast simulations of electric drives. The 5th international modelica conference, p 571–577 5. Hashemi F, Ghadimi N, Salehi M, Ghadimi R (2012) Modelling and simulation of mucroturbine as distributed generation and present a new method for islanding detection. Energy Procedia 14:87–93 6. Ray D, McMichael D (1982) Heat pumps: TRANS. Energoizdat, Moscow, p 224 7. Moore MJ (ed) (2002) Micro-turbine generators. Professional Engineering, Printed in the USA 8. Shlyakhin PN (19740 Steam and gas turbines. Textbook for technical schools. Ed.2-e, Rev. and additional. “Energy”, Moscow, Berlin 9. Moore MJ (2002) Micro-turbine generators. Professional engineering, Printed in the USA, p 263 10. Gas turbine electric units S 600, S 800, S 1000. Operating manual, BPCE.400024.00 re, BPC group, 2010. J. Clerk Maxwell, A treatise on electricity and magnetism, vol. 2, 3rd edn. Clarendon, Oxford, 1892, p 68–73 11. Troubleshooting guide for Capstone microturbine units model C200/C1000 (Troubleshooting Guide), BPC group, 2011, K. Elissa 12. A multi-variable multi-objective methodology for experimental data and thermodynamic analysis validation. https://reader.elsevier.com/reader/sd/pii/S1359431117332751 13. Biogas upgrading and liquefaction in an anaerobic digester plant. https://www.sciencedirect. com/science/article/pii/S1876610218304491 14. Energy, economic and environmental (3E) analysis of a micro gas turbine employed for onsite combined heat and power production. https://www.sciencedirect.com/science/article/pii/ S0378778809002151 15. Incorporating available micro gas turbines and fuel cell: Matching considerations and performance evaluation. https://www.sciencedirect.com/science/article/abs/pii/S03062619120 07325 16. STC “Microturbine technologies” Review and state of development of modern low-power gas turbine plants. http://stc-mtt.ru/publication 17. Capstone microturbines product catalog, P0212 CAP115, 2010 Capstone Turbine Corporation, p 4 18. Chizhma SN (2014) Improvement of methods and means of quality control of electric power and power components in electric power plants systems with traction load. Dissertation, Omsk, p 367 19. Suresh C Gupta, Douglas R Burnham, J Michael Teets, Teets JW (2005) Method and apparatus for compensating output voltage fluctuations of turbine/alternator on common shaft, US 6909199 B2, Application number US10/678,509, 21 June 2005 20. Besedin SN (2009) Autonomous gas turbine installations of low power. Scientific and Technical Vedomosti SPbGPU 4–1(89):153–166

Folding Wind Turbines with Vertical Axis of Rotation as Way to Ensure Safe Operation in Emergency Situations A. Miroshnichenko, A. Kulganatov(B) , and E. Sirotkin South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, Russia [email protected]

Abstract. The development trend of renewable energy in the world is gaining more and more popularity. Among all renewable energy sources, wind energy is the most developing. But this direction has several technical drawbacks. The main one is the occurrence of emergency situations, which subsequently leads to costly repairs or failure of the wind power installation. The article presents an analysis of emergency situations in wind power plants. In view of the fact that accidents in wind turbines lead not only to the repair of expensive power equipment, but also, in 20% of cases, to the installation failure the authors proposed the option of using unique folding rotors to ensure the safety of wind turbines. The Solidworks software package built a three-dimensional model of a folding installation. The authors also analyzed existing domestic developments in the field of folding wind turbines. Further, based on the design of the rotor, the generated power at the rated wind speed is calculated. Keywords: Renewable energy sources · Wind energy · Vertical axis wind turbines · Folding rotors

1 Introduction The consumption and cost of electric energy is increasing in every country, and Russia is no exception in this case. It is known that the fossil fuels are being depleted and the environmental problem is causing increasing concern. An acute shortage of energy is experienced by many farmers, gardeners, shift workers, geologists, and stock farmers in many countries of the world, isolated from central energy systems. Power outages due to natural factors, problems with insolvency, and simply theft of power cables are becoming commonplace. The problem is exacerbated by the fact that many high-voltage power lines have a high degree of deterioration and require repair or complete replacement of live, insulating, and supporting elements. Short-term power outages are perceived as a small but real problem [1]. In this regard, interest in renewable clean energy sources is constantly increasing such as the solar, wind, and geothermal energy. Partial or full replacement of traditional © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_159

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energy sources by renewable energy sources allows not only to drastically reduce the extraction of fossil resources, but also to change the principles of energy production in general [2]. Under certain conditions and government support, in a few decades, the production of electricity from renewable sources can develop in many variations with the implementation in different climatic and geographical conditions, which already today in the experience of several countries allows us to consider renewable energy sources at the level of state energy balances as direct competition to traditional approaches [3]. One of the fastest-growing areas in green energy is wind energy. The world’s wind power reached 600 GW by the end of 2018. 53.9 GW was added during 2018. Over the past 5 years, the increase in power amounted to more than 38% [4]. In the article, we will consider the concept of creating a unique folding vertically axial wind power plant.

2 Ensuring the Safety of Wind Turbines One of the key factors in the long-term operation of wind generators is ensuring the safety of their work, as well as preventing the occurrence of emergency situations that can lead to a complete failure of the installation. Given the global trend in the use of wind turbines, it is known that at high wind speeds there is a high probability of destruction of the blades and overheating of the generator. In addition, at a high rotor speed, vibrations can occur that have a negative effect on the functioning of all elements of a wind turbine, in particular moving parts—bearings, rotor components, and elements of brake devices. To prevent the occurrence of these negative factors, it is necessary to equip wind turbines control systems or reduce the load on the generator [5]. Accidents in the operation of wind turbines can be caused by various reasons: adverse weather conditions, errors in the control system, production defects, etc. Statistics show that approximately 20% of the total number of wind turbines during their operation had an emergency with a further failure of the wind turbine. This accident rate is quite high and shows that modern methods of accident prevention do not always work efficiently. Also note that the most emergency class is small wind turbines (up to 10 kW) [6]. The first option, in which a standard control system is unable to prevent an emergency, is overheating of the generator windings. It can be caused by various reasons: excessive electrical load, defective assembly, etc. But, regardless of the reason, the braking of the generator will be impossible to apply if its windings are overheated or completely disabled [7]. The second option, in which the wind turbine control system is technically impossible to prevent an accident, is a significant increase in wind speed. When calculating wind turbines, it is impossible to state exactly what the maximum possible wind speed will occur at its place of work. There are maps of wind potentials of regions with an indication of the percentage in the repeatability of wind speed. Values of hurricane wind speeds (more than 15 m/s on the Beaufort scale) are single for a long period of time, i.e. may be fractions of a percent, but they cannot be completely excluded. At significant steadystate wind speeds, the control system will not be able to control the rotor speed due to the fact that the generator will operate in an overloaded mode and will quickly fail. In this case, the only possible option could be a complete stop of the wind wheel with the subsequent closure of the generator windings. However, existing control systems cannot fully guarantee the complete stop of the rotor in case of significant wind loads [8].

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Also, in some cases, mechanical brake systems may be relevant. However, it is problematic to predict the life of the brake mechanical systems. With one use, the pads can become worthless and will not provide a braking effect when repeated adverse weather conditions occur, which will entail the failure of the wind turbine [9]. Thus, based on the above arguments, we can conclude that ensuring the safe operation of wind turbines is one of the most relevant in modern wind energy. The failure of the control system, mechanical brake systems will entail enormous financial losses, including those spent on ensuring the safe operation of wind turbines. The design proposed by the developers can solve the problem of the accident rate of vertically axial wind power plants. In our case, the rotor will be damaged and the rotation of the wind turbine stops [10]. From the formula for the generated power of wind turbines [11], it can be seen that one of the parameters affecting power generation is the area swept by the rotor. In the case of vertical orientation of the rotor, the area will be the projection of the rotor on a vertical plane and will look like a rectangle. The width of the rectangle will be equal to the diameter of the rotor, and the height will be the sum of the length of the blade (blades with a multi-level arrangement) [12]. P = cp ρV 3 S/2

(1)

ρ

Density of air passing through the rotor (1,2041 kg/m3 in dry air at temperature 20°C and atmospheric pressure 101,325 kPa), kg/m3 ; V Wind speed in front of the rotor, m/s; M Mass of air passing through the rotor in 1 s, kg; S Rotor swept area, m2. The formula shows that the generated power is directly proportional to the area swept by the rotor. With increasing wind speed, it is possible to reduce the rotor area and thereby reduce generation, which will prevent overheating of the generator windings [13]. On the other hand, with increasing wind speed, additional kinetic energy of air mass movement arises, which, according to the law of conservation of energy, will be transferred to the rotor, which will cause an increase in the rotor speed (without taking into account losses) [14]. Ek.wind = Ek.rotor

(2)

Ek.wind = m · V 2 /2

(3)

Ek.rotor = J · ω2 /2

(4)

where

The moment of rotor inertia is J =

n  i=1

mi · ri2

(5)

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Then 2 2 m · Vwind /2 = m · r 2 · ωr.rotor /2

(6)

Analyzing this equality, we can conclude that with an increase in wind speed, in order to prevent a wind turbine accident, i.e. to prevent an increase in the angular speed of the rotor rotation, its radius decreases [15]. In other words, with an increase in wind speed and the absence of mechanical brake systems, in order to prevent the failure of a wind turbine, it is possible to reduce the radius, i.e. make it “folding”.

3 Components of a Folding Rotor The elements of the folding rotor must meet the safety requirements during operation, and also have sufficient strength. The main elements of the rotor will be central labor, ring, blades (upper and lower), jet thrust, double thrust, short thrust, and staples. Thus, the power plant will be two-level, which will reduce the starting wind speed and increase the total power generation from wind turbines [16]. The central pipe with a wall thickness of 3.75 cm (an internal diameter of 60 cm) is located vertically and has slots for moving rings with brackets in them. In Fig. 1, these sections are not shown to reduce the congestion of the drawing. The outer diameter of the pipe coincides with the inner diameter of the ring. The brackets protruding from the inner side of the ring will move freely in the slots of the rings, and by acting on them, the ring will be set in motion. The rotation of the ring around its axis is not provided.

Fig. 1. Interaction of rods with a ring and a pipe.

Elements that are intermediate between the ring and the pipe will be a traction system. Traction will be driven when the ring moves up and down the pipe. We agree that for the correct assembly, the connection of the brackets to the rods will be on the right side of the rod or on the left side of the bracket. Connect the rods with the ring as follows. Description of the lower tier (in Fig. 2 on the left): two jet rods are fastened with pins to the brackets of the movable ring, which are located in parallel. The double rod is attached with a pin to a single bracket. The short rod is fastened with a pin to the center of the double rod, the other end also with a pin to the bracket welded at the top of the

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pipe. Thus, when the ring moves up and down, the angle between the rods and the pipe changes from 0 to 90 degrees. Description of the upper tier (on the right): two jet rods are connected through studs to brackets welded into the upper part of the pipe. The distance between the brackets is 20 cm. The double rod is connected to the bracket welded into the pipe, which is located at a distance of 40 cm from the upper edge of the pipe. The short link connects to the central part of the double link, the other end connects via a pin to the bracket in the ring. Thus, a pipe with a ring and rods in the folded and unfolded states will have the form:

Fig. 2. a Linkage system with a raised ring, b Linkage system with a lowered ring.

In Fig. 3, the two upper and lower rods are moving in a horizontal plane along with the ring. For a three-blade installation, with a blade spacing of 120 degrees, we obtain the following result. The final assembly step will be the installation of the blades. The blade has 3 fixed brackets, which will be connected with rods. The blade will have an aerodynamic profile and, therefore, the wind turbine will be classified as highly efficient. In wind energy, there is a tacit distribution of all vertically axial wind turbines into highly efficient and low efficient. The first includes wind turbines with blades having an aerodynamic profile, i.e. that operate on the principle of lifting force. The second group includes wind turbines, the principle of operation of which is based on the difference in moments (rotors of the Savonius type) as shown in Fig. 4[17]. As a result, in the folded and unfolded state, the wind turbine will look like as shown in (Fig. 5). We note again that the specially marked yellow ring does not rotate relative to the pipe; it only moves up and down. In this case, the whole pipe will rotate, which will be attached to the mast through a beare system.

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Fig. 3. Traction system with a movable ring and a central pipe.

Fig. 4. General view of the folding rotor.

4 Calculation of Generated Power Based on the geometric dimensions of the developed rotor, we will calculate its parameters. For vertically axial rotors, according to the formula, we obtain the area swept by

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Fig. 5. a rotor unfolded state, b rotor when folded.

the rotor [18]: S = D · H , m2

(7)

where D—rotor diameter; H—rotor height S = 5.1 · 4.83 = 24.36, m2

(8)

However, this area value is complete. It is necessary to find the value of the usable area, i.e. subtract the area of the central pipe S = 24.36 − 0, 675 · 2.65 = 24.36 − 1.79 = 22.57, m2

(9)

Aerodynamic power is the energy of the incident wind flow transmitted to the wind turbine rotor (wind wheel) in 1 s [19]: PA = (m · v2 )/2 = (ρ · V · v2 )/2 = (ρ · S · v · v2 )/2 = (ρ · S · v3 )/2, Wt

(10)

The calculation will be carried out at the nominal wind speed for most wind turbines—11 m/s PA = (1.2041 · 22.57 · 113 )/2 = 18.09, k Wt

(11)

The electric power of wind turbines PE is calculated through the aerodynamic power PA through the coefficient of utilization of wind energy ξ: PE = ξ · PA , Wt

(13)

Thus, the calculations showed that it is quite realistic to provide electric energy to the consumer using wind energy. Since the calculation was performed for the rated speed (11 m/s), the actual output at lower wind values will be lower [20]. However, under adverse weather conditions, an increase in wind force is possible and, thereby, an increase in the value of power generation.

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5 Conclusion The design of the folding vertical-axis wind power plant described in the article will allow solving the problem of accident rate and complete failure (destruction) of wind turbines. The developers do not fully guarantee 100% safety of such a wind turbine at significant wind speeds. However, the idea of such a rotor takes place when used later in mobile power complexes. Additionally, it is necessary to consider the issues of connecting the rotor to the mast, as well as the location of the electric generator in it. Work in this direction will be continued. Acknowledgements. The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0011, by RF President Scholarship for young scientists and postgraduate students (SP-71.2018.1).

References 1. Miroshnichenko A, Sirotkin E, Bodrova E (2019) On the possibility to solve the problems of electrical power supply to autonomous consumers by using renewable energy sources. Int Multi-Conf Ind Eng Mod Technol, FarEastCon 2019, 8934250 2. Tatarkin AI, Loginov VG (2015) Estimation of potential for natural resources and production in northern and Arctic areas: conditions and prospects for use. Stud Russ Econ Dev 26(1):22– 31 3. Bashmakov I (2009) Resource of energy efficiency in Russia: scale, costs, and benefits. Energy Effi 2(4):369–386 4. Aleskerov F, Demin S (2018) Modelling possible oil spills in the barents sea and their consequences. Springer Optim Appl 140:47–56 5. Sirotkin EA, Solomin EV, Gandzha SA, Kirpichnikova IM (2018) Backup mechanical brake system of the wind turbine. J Phys: Conf Ser 944(1):012109 6. Usynin YS, Sychev DA, Savosteenko NV (2017) Energy saving in pilger mill electric drives. Complete solution. Int J Power Electron Drive Syst 8(4):1673–1681 7. Panfilov AA (2018) Features of calculation schemes and methods for design of wind turbine foundations for arctic conditions. Int Ural Conf Green Energy, UralCon 8544376:122–126 8. Sirotkin E, Martyanov A, Ibrahim A (2018) Mathematical modeling of wind turbine brake system. Int Ural Conf Green Energy, UralCon 8544362:51–56 9. Fedchishin VG (1998) Folding wind turbine with a vertical axis of rotation. RF Patent 94024869, 1 Oct 1998 10. Ustinov NA, Dontsova MA, Zhuravleva VV (2015) Folding wind turbine of a mobile wind farm. Young Scientist 23–1(103):41–42 11. Andreev SA, Sudnik YuA, Vagin AV (2013) Small wind turbine. RF Patent 2013112159, 3 Feb 2013 12. Software CAD for modeling (2019) Dassault Systemes SolidWorks Corporation. https://www. solidworks.com/ru. Accessed 06 Dec 2019 13. Akimov AV, Bogdan AV et al (2017) A device for wireless inductive transmission of electricity from the fixed part of a vertical-axis wind power installation to a mobile one. RF Patent 2017143950:12 14. Kirpichnikova IM, Mart’Yanov AS, Solomin EV (2013) Simulation of a generator for a wind-power unit. Russian Electrical Engineering 84(10):577–580

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15. Kulganatov A, Ibrahim A, Miroshnichenko A (2020) Comparison of lifting mechanisms for raising wind wheel in mobile power complex based on renewable energy sources. Lecture Notes in Mechanical Engineering, p 1475–1482 16. Martyanov A, Martyanov N, Sirotkin E (2018) State observer for variable speed wind turbine. 2018 International ural conference on green energy, UralCon 2018, 8544344, p 97–100 17. Abbaticchio E, Sirotkin E, Miroshnichenko A (2019) Transmission of electric energy from wind power plants to the network: patent search. Int Multi-Conf Ind Eng Mod Technol, FarEastCon 2019, 8934250 18. Martyanov AS, Korobatov DV, Sirotkin EA (2016) Modeling of battery charging algorithms. 2nd International conference on industrial engineering, applications and manufacturing, ICIEAM 2016, 7911469 19. Datta R, Ranganathan VT (2003) A method of tracking the peak power points for a variable speed wind energy conversion system. IEEE Trans Energy Convers 18(1):163–168 20. Wang K, Hansen MOL, Moan T (2014) Dynamic analysis of a floating vertical axis wind turbine under emergency shutdown using hydrodynamic brake. Energy Procedia 53:56–69

New Type of Energy-Saving Oil Treatment Plant B. H. Gaitov, A. V. Samorodov, and V. A. Kim(B) Kuban State Technological University, 2A, Moskovskaya St, Krasnodar 350072, Russia [email protected]

Abstract. This paper dwells upon a novel energy-saving oil refinery. These promising energy—and resource-saving machines have been designed by the Department of Electrical Engineering and Machinery of FSBU Kuban State Technological University to refine oil; they are based on electromechanical energy converters of combined design, which are different from the common designs of centrifugal oil separators in the sense that the separator drum also functions as its effector where the oil is separated and the rotor of the asynchronous motor is hosted. The research team has analyzed Russian and international designs of centrifugal oil separators to find their cons and whether they had room for improvement. This paper proposes a novel oil separation method and presents designs to implement it. Energy-saving installations for oil treatment can also reduce energy costs for heating the separated product due to the use of heat in the drum and stator of the separator, so the oil heater will need to heat the oil by a smaller t. Keywords: Separator · Energy saving · Novelty · Oil refinery

1 Introduction The Department of Electrical Engineering and Machinery, Kuban State Technological University, has designed a promising resource- and energy-saving unit for oil refining; it is based on electromechanical energy converters of combined designed [1–7]. Before that the team reviewed and analyzed the existing oil separator designs [8– 19], which can be commonly defined as preheating separators, such a separator contains a reduction gear, making its weight, size, energy performance, costs, and reliability rather unfavorable. Separating oil in such a unit requires full-volume preheating, which consumes extra energy. Heating oil is many times more energy-intensive than powering a motor. Improving the oil refinery performance requires novel separators that could at least partially reduce energy consumption by lowering the energy intensity of preheating. Creating such a separator in fact means creating a novel type of energy-saving combined electromechanical energy converters for oil preparation. Such units must be based on a novel separation method. The oil separation method [20] shown in Fig. 1 comprises preheating crude oil, separating it, and then producing refined oil and the sediment. Crude oil is preheated to 58–66 °C. Then the oil passes through the compound-lined tubes that encircle the © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_160

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separator stator windings to be additionally heated by the heat emitted by the windings and magnetic cores of the separator motor stator. Then the end and the cylinder of the separator drum, which is also the rotor, heat the oil to 62–65 °C, a temperature necessary for further separation. Besides, the oil is also affected by the electromagnetic field of the axial and cylindrical parts of the motor stator. As a result, this method [20] intensifies the separation process while also making it less energy-intensive.

Fig. 1. Oil Separation method.

All of this means it is theoretically possible to create novel combined energy-saving electromechanical energy converters for oil treatment that not only separate the oil, gas, and water emulsion to further produce refined oil, gas, and water, but also preheat the separation product. This functional combination might reduce the energy costs of oil preparation in the heater. Oil could be heated at lower energy costs by using the heat emitted in the separator drum and stator to partially heat the oil in the drum such that the heater would have to heat the oil by lesser t.

2 Energy-Saving Oil Separation Units A known fluid separator [21] shown in Fig. 2 has an enclosure that contains the axial stator of a motor with windings, the frontal part of which is surrounded with compoundbound tubes for the fluid to be separated; the enclosure also contains a bearing-fixed rotor which serves as the separator drum and is made of a conductive nonmagnetic material that is rigidly connected to the shaft.

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Fig. 2. Fluid separator.

In [21], the motor stator is located under the lower end of the separator drum. This enables partial reuse of the drum-emitted heat to heat the separated fluid in the lower part of the drum above the end of the axial stator of the motor, as the drum is heated by eddy currents. However, the separated fluid stays in the lower part of the drum for a relatively short time. This means that the fluid to be separated is only heated by interfacing with the end of the drum for a short time. Besides, the positive effect the axial stator-generated electromagnetic field has on the fluid is also insignificant, as most of that field is scattered in the drum bottom as well as in a relatively small layer of the fluid to be separated. One significant drawback of the separator [21] is that there must be a large air gap between the magnetic core of the stator and the rotor drum of the separator, as having the axial stator alone means that the axial electromagnetic forces cause the drum to “go down” vertically, which destroys the bearing assembly and might result in the rotating drum rotor interfacing mechanically with the axial stator. Increasing that air gap will amplify the magnetic resistance, thus requiring stronger stator current (magnetizing current) to generate the necessary magnetic flux, i.e. necessitating larger winding crosssection and thus greater weight and size of the separator. Figure 3 shows a unit that is the closest one to the presented concept of a novel combined energy-saving electromechanical converter that a new separating motor could be based upon [22]. The unit has the enclosure 1, a motor stator assembled within it that

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consists of two parts (the cylinder 2–1, the axial part 2–2), and the winding 3 of the two stator parts; the tubes 4 go around the frontal parts of the winding and are lined with the compound 5; the separator drum 6 also serves as the motor rotor and is rigidly connected to the shaft 7; the unit also includes the oil heater 15 and the connecting tubes 16, 17. The shaft 7 is born by the bearing assembles 8 and 9. The separator drum 6 consists of the base 10 with a central tube, the separating trays 11, the lid 12, the tray holder 13, and the sealing ring 14. The connecting tube 16 connects the oil heater 15 to the inlet of the tubes 4, while the tube 17 connects the outlet of the tubes 4 to the insides of the separator drum 6.

Fig. 3. Oil separation unit.

Powering the winding 3 of the cylindrical part 2–1 and the axial part 2–2 of the stator will generate a rotating magnetic field that induces eddy currents in the drum 6, which is also the motor rotor. As the rotating magnetic field interacts with the one created by the eddy currents in the drum 6, there emerges a torque, which causes the drum 6 and the shaft 7 to rotate. The nontreated oil goes to the oil heater 15, where it is partially heated to a specific temperature. After the heater 15, the preheated oil goes to the inlet of the tubes 4 via the connecting tube 16. As it goes through the tubes 4, the oil is also heated by the heat emitted by the windings 4 and the magnetic cores in parts 2–1 and 2–2 of the stator. As the tubes 4 heat it, the oil cools down the magnetic cores and the

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winding 3 of both parts of the stator 2. As it exits the tubes 4, the connecting tube 17 carries that oil to the drum (unlaminated rotor) 6, where it goes through the central tube to the drum bottom, then to the channels of the tray holder 13. While in the drum bottom, the oil receives additional heating from the end and cylindrical parts of the drum 6, thus reaching the temperature necessary for further separation. While in the drum bottom, the oil is exposed to the electromagnetic field from both the axial part of the stator and its cylindrical counterpart, which improves the separation process. The process itself takes place in the separating trays 11. Separation products (including refined oil) then leave the drum. However, the unit described in [22] has a few drawbacks: its energy performance, weight, size, and reliability lack luster. The gravest shortcoming of the separator described in [22] is that it, as any electric machine with an axial magnetic core, has a significant axial electromagnetic force induced by the unavoidable attraction of the rotor drum to the axial magnetic core. This force destroys the bearings and results in their premature failure; besides, it might cause the rotating drum to interface mechanically with the axial magnetic core. Moreover, the drum rotation might cause its tilt with respect to the axial magnetic core due to a greater axial electromagnetic force. The implications here are the same. Either way, the separation unit becomes unreliable. To prevent the rotor drum from interfacing with the axial magnetic core, there must be a large air gap between the axial magnetic core (in the stator) and the rotor drum. Besides, a known [22] separator shows its rotor swinging, vibrating, and running out inside the cylindrical magnetic core. As a result, the drum might interface with the cylindrical magnetic core. This also makes the separator less reliable and necessitates a greater air gap between the rotor and the cylindrical magnetic core.

3 Separator Performance Improvement Proposal Increasing that air gap between the axial/cylindrical magnetic core and the rotor will amplify the magnetic resistance, thus requiring stronger stator current (magnetizing current) to generate the necessary magnetic flux, i.e. ecessitating larger winding crosssection and thus greater weight and size of the separator coupled with worse energy performance. Thus, the task on the agenda is to improve the separator design to enhance its reliability, energy performance, weight, and size. This can be done by reducing the air gap between the rotor base and the axial magnetic core; between the rotor sides and the cylindrical magnetic core. Reducing that gap will lower the energy consumption, allow using more lightweight stator windings in a smaller separator, while also minimizing the risk of the rotor-magnetic core interface. This is made attainable by the fact that the separator enclosure contains the motor stator and the rotor, which is also the separator drum, while the stator is rigidly connected to the enclosure and contains a cylindrical magnetic core whose slots hold the first winding, as well as an axial magnetic core whose slots bear the second winding; the stator has an external bandage ring with hemispheric cavities in its upper part. The first winding and the second winding are connected in series, their frontal parts encircled with the compound-lined tubes that cool down the stator and heat the product to be separated.

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The rotor (which is also the separator drum) is rigidly fixed onto the axle carried by the bearing assembles and has a package of separating trays, a tray holder, a sealing ring with a hole, a connecting pipe that links the rotor insides to the outlet of the stator-cooling, fluid-heating tubes, and a base with a central tube that has semicircular grooves that are used to place the rotor on nonferromagnetic balls so that it could rotate. Reducing the air gap between the rotor base, the axial magnetic core, and the cylindrical magnetic core can be done by making with hemispheric cavities in the upper part of the bandage ring to put nonferromagnetic balls in there, whereas the rotor base has semicircular grooves that are used to place the rotor on nonferromagnetic balls so that it could rotate. This prevents the rotor from “going down” vertically, which reduces the air gap between the rotor base and the axial magnetic core so that the gap could be set based on the energy performance of the separator (efficiency η and cos ϕ), i.e. effectively improve the energy performance of the separator. Preventing the rotor from going down vertically helps increase not only the air gap δ2 between the rotor base and the axial magnetic core, but also the air gap δ2 between the cylindrical magnetic core and the rotor walls that form the cylinder. Reducing the air gaps δ1 and δ2 to estimated values makes the rotor more “rigid”, i.e. reduces its vibration and swing with respect to the vertical axes, which effectively nullifies the chance of the rotor interfacing with either magnetic core. Reducing the air gaps to a permissible minimum in the electric machine that the combined separator actually (the separator drum also serves as the motor rotor) will also reduce the magnetizing current, enabling the use of lower weight stator windings in a smaller separator, effectively improving the weight and size of the unit as well as its energy performance. As the base of the rotor has semicircular grooves that are used to place the rotor on nonferromagnetic balls so that it could rotate, while the balls are in the hemispheric cavities of the upper part of the external bandage ring, the entire structure reduces both the vertical and the horizontal vibrations of the rotor. Thanks to this, the rotating rotor will not interface with the axial and cylindrical magnetic cores for a generally more robust design. Figure 4 shows a piece of the separate with its designed improved as proposed herein. The electric motor is assembled rigidly in the enclosure 1 and has the cylindrical magnetic core 2 whose slots hold the first winding 3, and the axial magnetic core 5 whose slots bear the second winding 10; it also has the external bandage ring 7. At the top of the bandage ring 7, there is a hemispheric cavity 11 that holds the nonferromagnetic balls 12. The first winding 3 and the second winding 10 are connected in series, their frontal parts are encircled with the tubes 8 to cool down the stator and to heat up the separated fluid; they are lined with the compound 9. The base of the rotor drum 4 has the semicircular groove 13 encircling it, which carries the rotor as it rotates on the nonferromagnetic balls 12. Above are the designs of separation units that effectively implement the novel oil separation concept, the distinctive feature of which is that the separator drum functions as the separator effector, i.e. it performs as the rotor while also containing the oil separation process. As there is no comprehensive theory behind constructing such converters, algorithmizing the calculation of structural and electromagnetic parameters for the separation motor is on the agenda.

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Fig. 4. Part of the combined separator view.

Acknowledgements. The research has been supported by the Russian Foundation for Basic Research as well as by the Krasnodar Krai administration under the Research Project No. 19-48-230010 p_a.

References 1. Kashin YaM, Kopelevich LE, Samorodov AV, Kim VA (2017) Experimental determination of parameters and characteristics of the oil separation unit of combined design. IOP Conference Series: Earth and Environmental Science, vol 194. https://doi.org/10.1088/1755-1315/194/8/ 082017 2. Kashin YM, Sharshak AA, Kopelevich LE, Badalyan AS (2018) Electromagnetic, Electromechanical and Thermal Transient Characteristics of an Asynchronous Motor with Variable Parameters. International Multi-Conference on Industrial Engineering and Modern Technologies, Vladivostok, p 1–6. https://doi.org/10.1109/fareastcon.2018.860251 3. Gaitov BH, YaM Kashin, Kopelevich LE, Samorodov AV, Kim VA (2019) Energosberegayushchaya ustanovka dlya separirovaniya nefti i opredeleniya eye parametrov (Energysaving plant for oil separation and analysis). Energy Saving and Water Treatment 4(120):58– 62 4. Gaitov BH, Kashin YaM, Kopelevich LE, Samorodov AV, Kim VA (2019) Razrabotka novogo vida energosberegayushchey ustanovki dlya pererabotki nefti (Development of a new type of energy-saving installation for oil refining). Bulletin of the Adyghe State University. Naturalmathematical and technical sciences 3(246):103–108 5. Kopelevich LE, Kim VA, Artenyan KZ (2019) Mathematical model for diagnosing rotor-drum of resource saving unit for oil refining, 2019 International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon), Vladivostok, Russia, p 1–5. https://doi. org/10.1109/fareastcon.2019.8933837

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6. Gaitov BH, Kim VA, Artenyan KZ (2019) Adjustment characteristics of resource saving unit for oil refining, International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon), Vladivostok, p 1–5. https://doi.org/10.1109/fareastcon.2019.893 4816 7. YaM Kashin, Kopelevich LE, Samorodov AV, Kim VA, Artenyan KZ (2019) Separator dlya pererabotki nefti sovmeshchennoy konstruktsii i yego temperaturnoye pole (Separator for oil processing of a complete construction and its temperature field). Scientific works of the Kuban State Technological University 5:86–99 8. Hurnasti L (2013) Centrifugal separator and method of separation. Russian Federation Patent 2480291, 27 April 2013 9. Thorvid P, Isaksson R, Moberg H, Heggmark K, Krook G (2016) Centrifugal separator and method of periodic release control. Russ Fed Pat 2577261:10 10. Stroucken K, Ridderstrole R, Montano J (2004) Separator. Russ Fed Pat 2233709:10 11. Borgström L, Hurnasti L (2010) Centrifugal separator and method of separation. Russ Fed Pat 2393024:27 12. Ternblom O, Eliasson T, Burmeister J, Pogen M, Stjernswärd P (2013) Gas-cleaning separator. Russ Fed Pat 2501592:20 13. Borgström L, Hurnasti L, Balback DJ, Childs DH, Kisior TE, Raid K (2016) Centrifugal separator with an inlet port. Russ Fed Pat 2588201:27 14. Starokozhev VA, Starokozhev AV, Starokozhev AV, Litvinov VA (2004) Sunloading liquid separator. Russ Fed Pat 2232644:20 15. Vilgot N (1994) Centrifugal separator. Russ Fede Pat 2010611, 15 April 1994 16. Campbell WR, Robinson FL, Perry BA, Schwiefert D (1994) Oil separator. US Patent 5316029A, 31 May 1994 17. Kouba GE (2004) Method for separating liquids in a separation system having a flow coalescing apparatus and separation apparatus. US Patent 6730236B2, 04 May 2004 18. Ghadiri M, Eow JS (2003) Separating components of liquid/liquid emulsion using electrostatic force. UK Patent 2377397A:15 19. Lewis AK, Maddock TM (2003) Separation of oil and water. WO Patent 2003000377A1, 03 January 2003 20. Kopelevich LE (2016) Method for separation of oil. Russ Fed Pat 2585636, 27 May 2016 21. Gaitov BH, Kopelevich LE, Pismenny VYa, Bykov YeA (1988) Fluid separator. USSR Patent 1427501:30 22. Kopelevich LE (2016) Plant for oil separation. Russ Fed Pat 2593626, 10 August 2016

Electric Heating of Non-conductive Dispersed Raw Materials in Activated Carbon Production V. Kushnir(B) , I. Koshkin, and S. Ibragimova A. Baitursynov Kostanay State University, 47, Baitursynov St, Kostanay 110000, Kazakhstan [email protected]

Abstract. This article about the electric heating is used for the realization of the new method of activated carbon production—effective sorbent. The mathematical interpretation of the energy transformation in the electro-technological process of producing activated carbon is presented. The mechanism of formation of electrical conductivity in the reactor is described. The energy balance of the process in the conditions of variable voltage and electric current in the reactor is compiled. The process power characteristics are shown. The temperature intervals, connected to the basic stages of transformation of a host material, are marked. The structure of particles of the activated carbon, received from grain materials, is submitted. The wide spectrum of the application of activated carbon in many adsorption processes is provided with their structure and activation in an electric field. The results of research testify to the expediency of development of the offered technology in wide scales. Keywords: Activated carbon · Absorption · Electro-technical equipment · Raw materials · Technological process · Energy-saving · Production

1 Introduction The urgency of the problem is acute in sorbents need for water treatment, gas, extraction of valuable substances in the manufacturing processes and the need to collect spilled on the surface of the water and hydrocarbons used for their production of resource and energy-saving technologies [1–3]. More than two billion people in the world live in conditions of permanent water scarcity that leads to “hydromigrations”. The plight of the water quality is observed in many regions of Kazakhstan [1, 2]. In the preparation of drinking water, many contaminants are not extracted mechanically, not neutralized during biological treatment and are not removed by settling and coagulation. This necessitates the introduction of technological scheme of water treatment sorption purification stage. Sorption processes have become the basis for many technologies implemented using various sorbents—silica gels, resins, zeolites, various forms of carbon materials. The most efficient and common sorbent is activated carbon which can be regenerated after use and reused [3]. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_161

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Activated carbon is widely used in many processes, including water and air purification, food and pharmaceutical industry, hydrometallurgy, with spills of petroleum products from the surface of bodies of water. Extent of use of activated carbon is constantly increasing, at the same time increasing its cost. Price is determined by the value of activated carbon raw material (coconut shells, wood, rare breeds, rare species of fossil coal), available volumes of which are very limited, and energy-intensive production technology with flue gas. In Kazakhstan, the need for activated carbon is provided by imports. The above determines the need for new, cheap, widely available raw materials and the creation of new energy-saving production processes to ensure minimal loss of feedstock, the ability to accurately monitor the progress of the process, uniform heating of the material being processed. Particularly important is the ability of the process in a controlled atmosphere of inert gases, water vapor, carbon dioxide in the medium or process gas, which can be achieved only by using electric heating. Called porous activated carbon material in powder or granules obtained from solid carbonaceous material—wood, walnut, coconut, sugar 600–950 °C synthetic resins at a temperature in the absence of oxygen and able to sorb different elements from liquids and gases. The high level of porosity makes activated carbon, “activated” and determines its sorption properties [4–6]. Decisive influence on the pore structure of activated carbons has the raw materials for their production. Activated carbons based on coconut shells are characterized by a greater proportion of microscopic pores, and activated carbons based on coal—the greater proportion of mesopores. A large proportion of macroscopic pores is characteristic of activated carbons based on wood [7, 8].

2 The Main Part We propose to use a variety of agricultural wastes derived from food, or directions made specifically grain cereal materials. Conversion of cheap raw materials in expensive activated carbon is an urgent task that can add to the profitability of agriculture substantial financial resources. Preparation of activated carbon and regeneration in modern technology is carried out in furnaces with fluidized bed, shaft, multi hearth, drum using different coolants—flue gases, vapors, and gases are produced. The disadvantages of these methods are high losses of raw materials and the finished product, capital intensity, material consumption, unsafe in terms of ecology, it is difficult to control, the heterogeneity of the material properties within a single party [9–11]. It is promising to obtain activated carbon with the use of electrical energy. In this regard, there is known method for producing activated carbon comprising a thermal treatment of raw materials in the reaction chamber with external heating, a method of producing activated carbon indirect electrical heating, followed by the transition to the direct electrical heating. The first method has a complicated flow chart that requires special power supplies. The disadvantage of the second method is the presence of heaters that have a limited life, working installation space loaded electrodes, which eliminates the possibility of mixing the material being processed [12, 13].

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The scientific and practical interest is the development of a new method of heating the activated carbon, which provides a complete and uniform treatment of the entire volume of the material in precisely controlled intervals, low energy consumption, and environmentally friendly process diagram using cheap, widely available raw materials, which contributes to an increase in charcoal production volumes and lower of its value [14, 15]. Characteristics of the test method are as follows. The non-conducting particulate raw material is the input to the process initiator—electrically conductive carbon—forming conductors between the electrodes located inside the layers of the heated volume. When passing through them the raw material is subjected to a current first indirectly heated by coal dispersed resistors and electrodes from massive, heated by the same current that flows through the dispersed conductors. After the raw material carbonization, its particles become electrically conductive, creating total volumetric conductivity and subjected to direct heat passing through it current by Joule–Lenz to the required temperature for the technology. In the process of heating the raw material is carbonized, the activation step takes place which, according to the literature, is in a temperature range of 890–950 °C. Compliance with the optimum electrical and temperature chart of the heating process is controlled by the testimony of electric devices, thermocouples and provides for the regulation of the current density in the bulk material and applying vibration pulses per processed volume. Formed in the process of heating the gases containing hydrocarbons are used to process the material in the activation period. After cooling and discharging the fine product fraction is separated from the main part of it to be used as seed layer for initiating the next batch of raw material heating process. Implementation of the method carried out by creating a physical model, which includes the preparation and loading of raw materials, process reactors, power supply, registration of the process parameters, upload the finished product, and the gas collection system (Fig. 1). The energy expended for technological process is written in the form:    t  1 1 1 (U1 + U1 ) · + E(T ) · l + 2 · IRel + (U2 + U2 ) · · f (γ · S · U ) dt. Q= 2 2 l 0

(1) where U a and U c —respectively—the anode and the cathode drop potential, resulting from the contact surface of the electrodes with a dispersion medium that has a complicated mechanism of electrical conductivity, V; E—linear potential gradient on the inter-electrode space of the reactor, filled with cages V/cm; l—the distance between the electrodes, cm; I—the reactor current, A; REL —non-linear active resistance of the electrode, depending on its temperature, Ohm. The conditions limiting the magnitude of current flowing through the voltage applied to the electrodes of the reactor is regulated at different stages of the process. At a constant distance between the electrodes is variable linear potential gradient E, depending on the physical properties of the cages.

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Fig. 1. The physical model of the process. The design of electro circuit reactor to produce activated carbon is shown in Fig. 2. PSA—a system of registration of process parameters; SAC— System of automatic power control; solid line—wire communication; dashed line—technological connection; ●—cranes.

E linear-gradient change when the experimental reactor operating in the range of 22–0.4 V/cm. As the warm layer overlying the start of his raw material layers are shifted conducting channel up the reactor. An important function of the electrode is the heat transport from the starting layer in the upper part of the reactor. The current density on the electrode varies between 0.4 A/mm2 and 0.238 × 10–2 A/mm2 . The maximum density occurs at the start of the process. The expenditure part of the energy conversion has the following composition: Q = Q1 + Q2 + Q3 + Q4 + Q5 + Q6 ,

(2)

where Q1 —the raw material of heating energy to the boiling point of water (T = T 0 ÷ 100 °C); Q2 —the energy spent on evaporation and removal of moisture (T = 100 ÷ 140 °C); Q3 —energy heating of the medium before the start of the hydrocarbon decomposition (T = 140 ÷ 450 °C); Q4 —the energy of the evaporation and removal of hydrocarbons (T = 450 ÷ 600 °C); Q5 —activation energy (T = 600 ÷ 950 °C); Q6 — heat loss to the environment through the liner and the reactor lid; early in the process minimum and maximum for activation stage. The values of thermal parameters Q1 ÷ Q5 contain recycled material and are characterized by common values—the weight of the G, heat capacity C, and the temperature differences, the respective heating levels. Energy losses to the environment through the thermal protection of the reactor and the reactor insulated cover Q6 defined.

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Fig. 2. Electro-technological reactor. 1—lining of the reactor; 2—electrodes; 3—current leads; 4—raw materials; 5—retractable pod; 6—tank for unloading the finished product; 7—refractory support; 8—thermocouple for temperature measurement in the working layer; 9—insulation; 10— the lid of the reactor; 11—thermocouple for measuring the temperature of the electrode; 12—the handle; 13—vapor pipe; 14—the starting layer.

The total energy process, taking into account the structure of (1) and (2) is represented as follows: tr  (U1 + U1 ) ·

Q=

   1 1 1 + E(T ) · l + 2 · IRel + (U2 + U2 ) · · f (γ · S · U ) dt 2 2 l

0

= Graw · C1 · (T − T0 ) + Gwater · Cwater · (T140 − T100 ) + Q3 + + Q4 + G · C600÷950 · (T950 − T600 ) + Q6 .

(3)

The above description of the process allows calculating the theoretical yield of the final product and the energy cost of its production. Depending on the load and the content of volatile components in the feed, the processing time in the heated reactor is from thirty to ninety minutes. The “energy yield” depends on the moisture content of raw materials and hydrocarbons. The indicator “weight yield” at standard humidity of 10 ÷ 15% and hydrocarbons content of decomposing is 67 ÷ 57, 29 ÷ 34%. For carrying out the process, it is necessary that the starting volume of the layer with a controlled height of the reactor has technically minimum area; resistance starter layer is compatible with the current flow starting at a higher voltage power source.

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Upon completion of the process of the production goes to the new process as its initiator—the starting layer. Therefore, in the reactor there is always some “dead” volume of the material. To ensure a high utilization rate of reactor volume and energy must be reduced to a minimum amount of material in the starting layer, and thus its height. The height of the starting layer l is defined as follows: l = R · Sc · γ ,

(4)

Rc —the starting layer resistance, Ohm; S c —square bottom of the reactor, which is blocked by filling layer in, CM2 ; γ —the conductivity of the layer, CM2 • CM2 . Under the influence of the static pressure, the number of contact points increases between the particles. Experimentally, the dependence of the starting resistance layer varying heights of pressure on him, produced by the SADC (Fig. 3).

Fig. 3. The effect of static load on resistance of starter layer.

The pressure generated by the SADC stabilizes the resistivity of the starting layer and can be considered as an organizing process parameter. Due to the pressure of the upper layers, the electrical conductivity occurs in the lower channel compacted layers, and then extends upward. This coincides with the direction of motion in the heated gaseous mass. The functions of the electrodes are the supply of electricity and heat to the cage, the stabilization of the temperature throughout the reactor space by conduction through the electrode body. The transverse dimensions of the electrode must ensure the overlap of the working volume of the reactor space. Cross-section’s size of the electrode is determined by   I 2 · ρ0 · (1 + αc · Tadd ) 



  3 , (5) a= δ 1 n · · K 2m · (m + 1) · Tenv − Traw + SQ+Q + λ K cool. lim T .f .

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I —the current of reactor, A; ρ0 —resistivity of the steel at a temperature of 0 °C, OM · M; α—temperature coefficient resistance of steel, grad–1 ; Ton —permissible steel temperature, °C; m = ab ; T env , T raw —ambient temperature (air) and raw materials °C; Q—heat flux carried through the side surface of the reactor lining, W; Q—energy losses of reactor in environment, W; S coollin —cross-sectional area of the reactor lining, m2 ; δ—lining thickness, m; λ—coefficient of the lining thermal conW W ductivity, m· ◦ ; KT .φ —reactor heat transfer lining coefficient, m2 ·◦ ; +—electrode’s heat W transfer coefficient, m2 ·◦ . The electrical resistance of cages, which is a parallel resistance of the resulting channel conductivity, decreases with increasing temperature, as shown in Fig. 4.

Fig. 4. Dependence of resistivity cages by temperature.

When raw materials are heated, its resistance decreases; this leads to a current increase up to values approaching the maximum allowable current of the power supply. During this period, power switching is performed at the lower voltage level of the reactor and maintaining the current within the limits. Tracing of process is shown in Fig. 5a. The process of carbon activation within 850 ÷ 950 °C is carried at the lower power level in the on–off control regime. Experimental characterization of the heating process is shown in Fig. 5b. As the graph shows, raw material and the electrode have the same temperature at the start of process. Subsequently, the electrode temperature rises and reaches 600 °C. At the same time the thermocouple is placed in the volume of the activated carbon, also shows the temperature increase, but its value reaches a desired level—850 ÷ 950 °C. Minimal electrode temperature is explained in the emissivity of the reactor lining, which generates heat loss value in (2). Activating coal with extracting at 850 ÷ 950 °C lasts 15–20 min. After unloading the activated carbon is cooled without air access.

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Fig. 5. a The tracing of carbon’s production process; b changing temperatures of electrode and raw materials during the process.

The resulting energy content of the process in the experiments ranges 0.403 ÷ 1.29 kW • h/kg depending on moisture content in the feed and decaying components. The internal structure of receiving activated carbons was studied using secondary electron photomicrography on energy dispersive spectrometry, mounted on electron probe microanalyzer and shown in the photographs (Fig. 6).

Fig. 6. Digital photography structure of activated carbon particles derived from wheat: a the outer shell (1:300 mkm); b a layer adjacent to the shell grains (1:500 mkm); c the central part (1:100 mkm).

3 Equations There is an entire spectrum of known pore’s types in the resulting charcoal: inner region has larger pores, the shell contains small and medium-sized pores, the transition regions have pores of different diameters. These coals match with the requirements of the sorbents used to solve various technological problems. At the same time, they are well moistened with oil products; possess buoyancy; environmentally friendly; useful for collecting oil spilled on a water surface. Water treatment with activated carbon results the reduce of total hardness from 10 to 7 mg/eq, a dry residue from 419 to 295 mg/dm3 at a rate of, respectively, 7 mg/eq to 1000 mg/dm3 .

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Similarly, after treatment with activated carbon there is a decrease in the water content of nickel, molybdenum, manganese, cobalt. Analysis of gold sorption data shows that all coal samples have characteristics at the level of “Norit” standard coal.

References 1. The UNDP project (2003) Use of renewable energy sources to supply drinking water to remote settlements in the economically disadvantaged region of Kazakhstan. Project No. KAZ/02 / M08/NP/71, 2003 2. Bolotov AV et al (2004) The method of heating the activated mass in the production and regeneration of dispersed activated carbons and a device for its implementation. In: Preliminary patent of the Republic of Kazakhstan 14189 KZ, 15 Apr 2004, Bull. 4 3. Habashi F (1997) Handbook of extractive metallurgy, vol 1–4. Wiley-VCH, pp 24–26 4. Narowska B, Kulazynski M, Lukaszewicz M, Burchacka E (2019) Use of activated carbons as catalyst supports for biodiesel production. Renew Energy 135:176–185 5. Heidari A, Khaki E, Younesi H, Lu HYR (2019) Evaluation of fast and slow pyrolysis methods for bio-oil and activated carbon production from eucalyptus wastes using a life cycle assessment approach. J Cleaner Product 241:118394 6. Kudratov AM (2006) Development of technology for the production of new types of adsorbents based on brown coal of the Angren field. Geotechnology 25 7. Zhylybaeva NK (2003) Morphology, structure and properties of carbonized sorbents based on apricot kernels. Dissertation, Almaty, p 108 8. Ozsin G, Kilic M, Apaydin-Varol E, Putun AE (2019) Chemically activated carbon production from agricultural waste of chickpea and its application for heavy metal adsorption: equilibrium, kinetic, and thermodynamic studies. Appl Water Sci 9(3):UNSP 56 9. Bolotov AV, Bolotov SA, Nogai VK, Leontieva NS (2002) A method of heating an activated mass in the production and regeneration of dispersed activated carbons and a device for its implementation. In: Decision on the grant of a preliminary patent for an invention according to application, No. 2002/1171, IPC7 C01B31/08 10. Bolotov AV, Bolotov SA (2007) Bolotov method of producing activated carbon and a device for its implementation. In: Preliminary patent of the Republic of Kazakhstan 18852, 15 Oct 2007, Bull. 10 11. Bolotov AV et al (2004) A method of producing activated carbon and a device for its implementation. In: Preliminary patent of the Republic of Kazakhstan 14190 KZ, 15 Apr 2004, Bull. 4 12. Saleem J, Bin Shahid U, Hijab M, Mackey H, McKay G (2019) Production and applications of activated carbons as adsorbents from olive stones. Biomass Convers Biorefinery 4:775–802 13. Tsai WT, Huang PC, Lin YQ (2019) Reusing cow manure for the production of activated carbon using potassium hydroxide (KOH) activation process and its liquid-phase adsorption. Processes 7(10):737 14. Kushnir V, Koshkin I, Benyukh O. (2017) Simulation of 6 (10) kV electrical networks for fault location. In: International conference on industrial engineering, applications and manufacturing, 19 Oct 2017, 80762792017 15. Bolotov AV, Mashkina SV (2008) Mathematical interpretation of electro energy transformations in the process of obtaining activated carbon. Bull Nat Eng Acad Repub Kaz 4:82–87

Biofuel Produced From Larch Dry Debarking Waste Yu.Ya. Simkin1(B) and S. A. Voinash2 1 Reshetnev Siberian State University of Science and Technology, 31, Krasnoyarsky Rabochy

Av., Krasnoyarsk 660037, Russia [email protected] 2 Novosibirsk State Agrarian University, 160, Dobrolyubova Str., Novosibirsk 630039, Russia

Abstract. Most of dry debarking waste in Siberia is formed from larch, the processing of which is difficult due to high humidity, polydispersity, low-mechanical strength. In this research work, briquettes have been obtained in a single-seated mold from large-tonnage waste dry debarked larch on the GSM-50 laboratory press without the use of binders and elevated temperatures. Briquettes have been pyrolyzed in a laboratory retort at a temperature of 500 °C, their internal structure and mechanical strength have been studied depending on the fractional composition and molding pressure. It has been revealed that small particles of dry debarking waste contained in the mixture of fractions have little effect on the mechanical strength of the briquettes; the coals obtained from briquettes under a pressing pressure of 100 MPa are not inferior in mechanical strength to charcoals from stem wood. The characteristics of briquettes and coals obtained from the dry debarks of Siberian larch are fit to be used as biofuels in domestic and industrial fuel plants, for heating residential and industrial buildings, for gas-generating plants that produce gases used in internal combustion engines, as well as for production electricity at a mini-CHP. Keywords: Waste debarking · Larch · Briquettes · Pyrolysis · Biofuel · Press molding

1 Introduction In woodworking and pulp and paper production, debarking waste is generated, the properties and quantity of which for many enterprises pose significant difficulties in disposal. The large tonnage of waste from dry debarking of larch is due to the fact that in Siberia larch accounts for 51.4% of all forest resources [1], and the bark in larch accounts for up to 25% of the total tree [2]. The total real resources of tree bark in Russia reaches 15–18 millions of cu.m. Considering that in the process of debarking logs part of the wood is removed along with the bark, the total waste of debarking of this wood species is produced in even larger volumes. Thus, with dry debarking on rotary machines, the content of wood fiber in the waste is on average 1.8%, with debarking on drum machines is up © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_162

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to 10.3%. After the stoppage in production of the Baikal Pulp and Paper Mill in 2008, where larch was the main raw material, 500,000 cu.m. of wood bark wastes accumulated on the shore of Lake Baikal [3]. A small amount of debarking waste is used as fuel in agriculture. Most of the wastes are transferred to waste landfills which lead to pollution of subsoil and open water with larch decomposition products and extractives. At the same time, debarking waste is an attractive type of raw material to use as fuel for domestic and industrial needs [4]. Special role in small power gains second generation biofuel had passed background work by molding of non-food remains of plants and wood. Compared to the feedstock, fuel molded into pellets or briquettes takes up a much smaller volume, practically does not dust in transportation and transshipment operations, can be stored for a long time, and easy-to-handle when use. Small-scale power plants operating on such biofuel have become widespread, providing heat and electricity to individual production facilities, medical facilities, private homes, technical installations, and utility rooms.

2 Characteristics of Larch Dry Debarking Wastes Dry bark differs little from wood in terms of composition of the combustible mass, the yield of volatile substances, and the combustion temperature. According to the lower calorific value, dry larch bark (21.87 MJ/kg) is not inferior to dry trunk wood (18.9 MJ/kg) [5]. Unlike coal and oil, the burning of bark does not produce harmful sulfur compounds that pollute the environment, and the remaining ash which contains a lot of calcium, potassium, and phosphorus is an effective fertilizer for agriculture. The industrial use of debarking waste is limited by a number of their properties: high humidity—an average of 65% of dry debarking, low-calorific value of wet bark, poor flowability, heterogeneity in size, low-mechanical strength: compressive strength along larch bark fibers—3.8 MPa larch wood—70.5 MPa [6]. The use of such waste in its original form in household and industrial devices of various types for burning fuel and in logistics is a significant challenge. From the analysis of the chemical composition, it follows that the larch bark differs significantly from wood in terms of the content of the components. So, lignin in the bark contains 40–50%, in wood much less 28–30%, cellulose, respectively, in the larch bark 25%, in the wood 40%, mineral components in the coniferous bark 2.1–2.4%, in wood 0.5–1.1% [7]. The bark also contains substances that are not found in wood. For example, suberin in the cortex contains 2.5–3.5%. In this regard, the chemical composition of debarking waste depends on the content of bark and wood. The presence in the bark of lignin, which has binding properties, in an amount 1.7 times greater than in wood, gives it an advantage in the processes of forming bulk materials. The greatest difficulties are caused by the particle size distribution and mechanical strength of the waste of dry debarking, which is determined by the anatomical structure of the bark, see Fig. 1a. On the left side of the picture shot with the electron microscope REM-100U clearly visible layers of elongated suberized cells of the fellema occupying the main space of the cross-section which are the main component of the bark and have thin fragile walls. In the phloem—bast part of the bark (see right part of the picture)—there are large

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Fig. 1. a Micrograph of a cross-section cut of Siberian larch bark, b briquettes produced from larch dry debarking wastes.

parenchymal cells which size reach 100–150 microns and occupy a significant volume of section cut. Between the parenchymal cells are separate rows of 4–12 in a row of small sieve cells with a cross-section size of 15–40 microns [8]. Stony cells along with bast fiber confer main mechanical strength to the bark. The presence within bark structure of large number of fragile cells provides low-mechanical strength of bark and debarking wastes. In this context, the way to increase mechanical strength of debarking wastes is to reduce the percentage by volume of suberized and sieve cells in original bark and thus increase the content of firm stone cells. Rational preparatory measures such as drying and briquetting can solve most of the problems related to the energy use of dry debarking waste materials [9, 10]. Bringing such wastes into a uniform-size lump material which is convenient for use and transportation and does not contain dust and foreign inclusions significantly increase their processing appeal and expand the possibilities of utilizing them as raw materials [11, 12]. First of all, load factor of vehicles and fuel equipment increases and the operating culture improves. High dispersiveness of wastes generated at pulp and paper enterprises during dry debarking can have a significant impact on the pressing process and the properties of the resulting briquettes [13, 14]. During research work, wastes of dry debarking of Siberian larch of Selenginsky pulp and cardboard plant were used. Fractions of original wastes of dry debarking were divided into several groups in Table 1. Table 1. Fractional composition of wastes resulted from dry debarking of Siberian larch timber at Selenginsky pulp and cardboard plant. No. of fractions Particle size, mm Content, % wt 1

Less than 1

10

2

From 1 to 5

15

3

From 5 to 10

57

4

From10 to 20

8

5

More than 20

10

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A significant part of the wastes (43%) accounts for fractions which differ in size from the main one (5–10 mm), which leads to polydispersity of debarking wastes. The proportions of fractions 1–5: 5–10: 10–20 mm is close to the ratio of 1:4: 0.5. A fraction of less than 20 mm can be considered as fit-for-technological processing, since it accounts for about 90% of the debarking wastes.

3 Biofuel Based on Briquettes Produced from Dry Debarking Wastes A grading fraction of size less than 20 mm was sorted out for briquetting. Prior to press molding, raw material was dried to a humidity of 10–14%. Briquettes made of dry debarking wastes were obtained with the pressing machine GSM-50 in a single-seated mold, see Fig. 1b. The increased content of lignin in the bark allows briquetting of larch debarking wastes at standard temperature without any binders, at a molding pressure of 60 MPA or higher. For most of serial briquetting pressing machines of stamp, roll, and extrusion types, usual molding pressure is 100 MPa [15–17]. The diameter of the produced briquettes is 37.5 mm and height is 18–25 mm. In addition to the bark, there are inclusions of wood fibers in the composition of produced briquettes. The lowest calorific value of briquettes is 20–21 MJ/kg. Content of the cut-off picture of the briquette, see Fig. 2a, shot with magnification of 500 times reflects that during molding there are significant changes of the anatomical structure (microstructure) of dry debarking wastes.

Fig. 2. a Micrograph of a cross-section cut of a briquette produced from Siberian larch debarking wastes; b pyrolyzed briquettes had been produced from larch dry debarking wastes.

Thus, it can be observed that stone cells remained after molding, as well as a continuous mass consisted of decomposed walls of mechanically fragile suberized, sieve, and large parenchymal cells, which are not visible on the picture. Such changes of the structure of debarking wastes during molding significantly change their properties: for example, the apparent density of larch bark with a humidity of 15% is on average 430 kg/cu.m. [2], and for briquettes produced from debarking wastes is 830–930 kg/cu.m. Remained stony cells while combustion are able to ensure penetration of gaseous oxidizing substances into the depth of the briquette and the withdrawal of combustion products from it.

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While fuel-bed firing and transportation of lumpy raw materials, their strength properties have a significant influence. The compressive strength of larch bark is 4.0 MPa [2]. The mechanical strength of the briquettes was determined by squeezing test sample with a GSM-50 pressing machine with a fixed load. The abrasive resistance (drum sample) was determined with the aid of standard practice [18]. The effect of the fractional composition of debarking waste on the strength of briquettes was also studied. For the purpose of briquetting a material with size of particles less than 20 mm was selected. Material of original wastes of dry debarking was divided into four groups: I (small) 0–5 mm, II (medium) 5–10 mm, III (large) 10–20 mm, IV-an undivided mixture of all groups I + II + III, (with ratio of 1:4:0.5 according to the results of studying the fractional composition is in Table 1. According to the data given in Table 2, briquettes obtained from debarking waste of a large fraction have the highest strength characteristics for abrasion and compression. Table 2. Influence of the fractional composition of debarking wastes to mechanical strength of briquettes produced from dry debarking wastes. Briquette characteristics

A type of fraction composition I

II

III

IV

Compressive strength, MPa

39

43

47

46

Abrasive resistance, %

80

86

91

87

Briquettes obtained from different fractions of debarking waste have different apparent density. So, for briquettes obtained from a coarse fraction at a compression pressure of 100 MPa, the apparent density is 920–940 kg/cu.m, from a middle fraction is 870–890 kg/cu.m, from a fine fraction is 830–845 kg/cu.m. The data of the strength dependence of debarking waste briquettes on the pressing pressure on abrasion and compression are presented in Table 3. Table 3. An influence of molding pressure to mechanical strength of briquettes produced dry debarking wastes. Briquette characteristics

Molding pressure, MPa 60

100

150

200

250

300

Compressive strength, MPa

31

47

50

52

53

54

Abrasive resistance, %

80

83

85

89

91

91

Results demonstrated that briquettes produced from debarking wastes in comparison with the original bark have a compressive strength of 8–14 times more, and in the same time density of briquettes is only 1.9–2.2 times higher than density of the bark. Such increase in strength in comparison with changes in density is explained by decreasing of

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the number of fragile cells (their decomposition) resulted from molding, the exposure of intermolecular bonding forces within briquettes, and the appearance of a large number of bonds during lignin plasticization. Briquettes produced from larch dry debarking wastes can be burned in domestic stoves and fireplaces, utilized for heating railway carriages and housing and utilities services, and utilized with gas-generating plants [19, 20]. Real opportunities for organizing practical preparation for incineration of dry larch debarking wastes are available in places where they are accumulated at Siberian pulp and paper production enterprises, sawmills, plywood manufactures, and at lower timber landings of timber enterprises.

4 Smokeless Biofuel Based on Briquettes Produced from Dry Debarking Wastes Metallurgical coke, charcoal, briquettes made with adhesive materials from charcoal and pre-heat-treated fossil coal contain almost no gum-forming components produced during combustion. The combustion of such-type of fuel even in household appliances occurs without generation of visible flue gases in opposite to combustion of wood or fossil coal. The released gases resulted from combustion of this fuel do not contain such harmful substances as Benzopyrene and soot. In order to obtain this fuel, briquettes produced from the wastes of Siberian larch dry debarking were pyrolized in a laboratory retort at a heating rate of 2 °C/min up to a temperature of 500 °C with subsequent exposure at this temperature for one hour. The yield of pyrolysis of briquettes produced from dry debarking is 29% of briquettes coals, 13% of resin, 21% of pyrolysis water, 22% of non-condensed gases, and 12% of physical moisture. The content of non-volatile carbon in pyrolyzed briquettes is 82.5%, volatile substances 12, and 5.5% of ash. Coals obtained from briquettes retain their original shape, see Fig. 2b. Their dimensions are height 12–17 mm, diameter 32.5 mm. It is close to dimensions of individual pieces of charcoal used in production sector which corresponds to the technology of layer processes for burning lumpy smokeless carbon fuel. The most fit-for-technological processing are pyrolysis briquettes made of dry debarking wastes under a molding pressure of 100 MPa where the acceptable squeezing pressure corresponds to the highest abrasive resistance in Table 4. Table 4. Molding pressure versus strength of pyrolyzed briquettes response characteristic. The strength of the briquettes

Molding pressure, MPa 60

100

150

200

250

300

Compressive strength, MPa

20

26

28

29

30

30

Abrasive resistance, %

87

88

86

82

78

73

In terms of mechanical strength, coal produced from dry debarking wastes briquettes exceeds characteristic of charcoal and as contrasted retains the same strength when squeezed in any direction. Thus, compressive strength along the length of the coal fiber

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of coal produced at a temperature of 500 °C made of larch wood is 7–10, and 4–6 MPa in radial direction [21]; for pyrolyzed briquettes in any direction—at the level of 20– 25 MPa. This circumstance makes it possible to use such fuel in fuel-bed firing methods in furnaces and gas generators. Calorific value of coals produced from briquettes is 27– 30 MJ/kg. The composition of combustion gases from the combustion of these coals does not differ from the composition of combustion gases which resulted from combustion of a charcoal. Briquettes from debarking waste and coal obtained from them are convenient for transportation and handling, and can be effectively used as biofuels in domestic and industrial layered combustion plants, and in heating residential and industrial buildings to generate fuel gas in gas generator plants used in engines internal combustion and when receiving electricity in a mini-CHP. Pyrolyzed briquettes from debarking waste are subject to storage along with charcoal, have an advantage over it due to their greater mechanical strength and can also be used as ecological fuel in the preparation of meat and fish dishes. It is recommended that the production and use of briquettes from the waste of dry debarking of larch and coal from them as biofuel be carried out according to the following scheme Fig. 3.

Fig. 3. Production and use of briquetted biofuels from the wastes of dry Siberian larch debarking.

5 Conclusion 1. In Siberia, the largest by weight and volume of dry debarking waste is formed from larch, the processing of which is difficult due to high humidity, polydispersity, and low mechanical strength. 2. Wastes from dry debarked larch fractions of less than 20 mm with a moisture content of 10–15% are briquetted without the use of binders and elevated temperatures at pressures of serial presses. 3. Small particles of dry debarking waste inside the fraction of less than 20 mm have a slight effect on the mechanical strength of the briquettes 4. During the briquetting of dry debarking waste, stony cells remain intact in the briquette structure, and the destruction and compaction of mechanically unstable sieve and parenchymal cortex cells leads to an increase in briquette density by 1.9–2.1 times and mechanical strength by 8–12 times.

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5. The mechanical strength of coals obtained from briquettes of dry debarking waste under a pressing pressure of 100 MPa exceeds the mechanical strength of charcoal from stem larch wood by compression 2.6–6.5 times, abrasion—1.4 times. 6. Briquettes from waste debarking and coal obtained from them, in comparison with the feedstock, are convenient for transportation and handling, can be effectively used as biofuels in domestic and industrial plants for layer burning, for heating residential and industrial buildings, for production in gas-generating fuel gas installations used in internal combustion engines and when generating electricity in a mini-CHP.

References 1. Antipenko TA, Bersneva LA, Vukolova IA et al (2003) Spravochnik lesnichego (Forester Handbook). In: Filipchuk AN (ed). VNIILM, Moscow 2. Zhitkov AV (1985) Utilizatsiya drevesnoy kory (Wood bark disposal). Lesn. prom-st’ , Moscow 3. K zasedaniyu Mezhvedomstvennoy komissii po voprosam okhrany ozera Baykal (By the meeting of the Interagency Commission for the Protection of Lake Baikal). https://www. geol.irk.ru/baikal/baikal/baikal_law. Accessed 24 Jan 2020 4. McKendry P (2002) Energy production from biomass, part 1: overview of biomass. Biores Technol 83:37–46 5. Borovikov AM, Ugolev BNm (1989) Spravochnik po drevesine (Handbook of wood). Lesn. prom-st’, Moscow 6. Golovkov SI, Koperin IF, Naydenov VI (1987) Utilizatsiya drevesnykh otkhodov dlya proizvodstva energii (Wood wastes utilization for energy production). Lesn. prom-st’ , Moscow 7. Tsyvin MM (1973) Ispol’zovaniye drevesnoy kory (The use of wood bark.). Lesn. prom-st’, Moscow 8. Fengel D, Vegener G (1988) Drevesina (khimiya, ul’trastruktura, reaktsii) (Wood (chemistry, ultrastructure, reactions)). In: Leonovicha AA (ed). Lesn. Prom-st’, Moscow 9. Lehtikangas P (2001) Quality properties of pelletised sawdust, logging residues and bark. Biomass Bioenerg 20:351–360 10. Suwinarti W, Amirta R, Yuliansyah (2018) Production of high-calorie energy briquettes from bark waste, plastic and oil. In: 1st international conference on tropical studies and its application (ICTROPS) IOP publishing IOP conference. Series: earth and environmental science, Mulawarman University. Indonesia, pp 1–6. https://doi.org/10.1088/1755-1315/144/ 1/012034 11. Hodolic J, Vukelic Dj, Agarski B et al (2007) Briquetting of biomass and environmental engineering. In: Proceedings—quality festival 2007—2. conference about quality of life: center for quality, faculty for mechanical engineering, Kragujevac,p p 8–11 12. Luengo CA, Felfli FF, Suarez JA et al (2005) Wood briquette torrefaction. Energy Sustain Dev IX(3). https://www.fac.uo.edu.cu/fim/files/2013/10/7-Wood-briquettes-torrefaction.pdf. Accessed 24 Jan 2020 13. Mitchual S, Frimpong-Mensah K, Darkwa N (2013) Effect of species, particle size and compacting pressure on relaxed density and compressive strength of fuel briquettes. Int J Energy Environ Eng 4:1–6 14. Myuller OD, Melekhov VI, Malygin VI (2015) Elastoplastic deformation of Fine_Grain Media. Russ Eng Res 35(12):911–918

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15. Krizan P, Vukelic D (2008) Shape of pressing chamber for wood biomass compacting. Int J Qual Res 2(3):193–197 16. Chaiyaomporn K, Chavalparit O (2010) Fuel pellets production from biodiesel waste. Environ Asia 3(1):103–110 17. Matus M, Krizan P (2012) Modularity of pressing tools for screw press production solid biofuels. Acta Polytech 52(3):71–76 18. GOST 21289–75 (1986) Brikety ugol’nyye. Metody opredeleniya mekhanicheskoy prochnosti. (Charcoal briquettes. Methods for determining mechanical strength). Izdatel’stvo standartov, Moscow 19. Arena U (2012) Process and technological aspects of municipal solid waste gasification. Review Waste Manag 32:625–639 20. Brandy S, Tam K, Leung G et al (2008) Zero waste biodiesel: using glycerin and biomass to create renewable energy UCR. Undergrad Res J II:5–11 21. Sorokina GI (1985) Svoystva i polucheniye uglerodistogo vosstanovitelya iz lesosechnykh otkhodov listvennitsy sibirskoy (Properties and production of carbonaceous reducing agent from logging waste of Siberian larch). Dissertation. Institute of Wood Chemistry, Academy of Sciences of the Latvian SSR, Riga, p 21

Improving the Technology of Wood Glued Materials Production S. Isaev, O. Erenkov(B) , and I. Galanina Pacific National University, 136, Tikhookeanskaya street, Khabarovsk 680035, Russia [email protected]

Abstract. The paper studies the wood parts gluing process using water-based adhesives modified by exposure to the microwave radiation electromagnetic field. The studies have been carried out on an experimental installation, and the processing of the adhesive solution has been carried out immediately after applying it to the surface of the wood billet. The experiment has proven that the preliminary non-thermal exposure to the electromagnetic field microwave radiation allows for the effective change in the supramolecular structure of the adhesive material polymer in the liquid phase, which provides compounds with increased adhesive and cohesive strength of the adhesive joint. The results of the analytical examination of the linear and branched polymers structures are presented and it is established that linear unbranched macromolecules can be densely packed into bundles forming a quasi-crystalline structure. The assumption is made that preliminary processing of the adhesive system with the electromagnetic field of microwave radiation will cause the polarization of its particles and the boundary layers of the adhesive joint which will affect its strength. Keywords: Gluing wood · Adhesives joint · Strength · Electromagnetic field · Microwave radiation · Exposure time

1 Introduction Currently, wood glued materials are actively used in mechanical engineering as a structural, self-lubricating, antifriction material. The use of wood-based adhesive products will reduce the mass of working machines components and details and the consumption of ferrous and non-ferrous metals. The thermoplastic and thermoset adhesives are used for the production of wood glued materials for engineering purposes. The chemical and physical properties of the adhesives directly affect the process and accordingly the operational strength of the final product. The directed improvement of properties by modifying resins and adhesives is currently gaining particular relevance as an effective way of influencing adhesives in order to produce high-quality wood glued materials that meet the technological, aesthetic, economic, and environmental requirements of the consumer market. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_163

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At present, various electro-physical methods are widely used to intensify the polymeric materials modification processes such as elastic vibrations of the sound and ultrasonic frequency ranges, vibration processing, high-frequency currents, laser, electronic, and ultraviolet radiation [1–9]. The scientific works dealing with the application of electro-physical methods of polymer materials processing have appeared at the last century end. These works present the studies of the non-thermal effects of microwave electromagnetic fields on adhesive polymer systems [10–15]. Its known microwave radiation has various applications in the production and modification of many materials [16–20]. The effect of microwave electromagnetic field on adhesive water-borne polymer systems was founded in the exploratory studies [21–24]. The fact of the compositions technological properties and operational characteristics change was proved in these works. The presented work is actually due to insufficient knowledge of the properties changes in the water-based adhesives modified by the electromagnetic fields of microwave radiation exposure and their application in gluing wood. The aim of the scientific work is to research the efficiency of the gluing wood process on the base of the electromagnetic field microwave radiation influence on water-borne adhesive compositions.

2 Physical Representations The above analytical analysis of the linear and branched polymers structures made it possible to establish that linear unbranched macromolecules can be densely packed into bundles, forming a quasi-crystalline structure. In addition, linear and branched macromolecules are able to form globules which are rolled into macromolecules tangles. The globules can be arranged with ordered packing of macromolecules in a condensed state if the diameters of the globules are small. This forms a certain supramolecular structure which can significantly affect the physical and mechanical properties of adhesive layers polymer films. The degree of exposure is depending on the size and level of macromolecules ordering. It has been revealed that a characteristic feature of polymers is the independent movement of chain sections consisting of a large number of monomer segments. However, internal rotation in polymer molecules is inhibited due to chemically unrelated atoms. This can be an interaction between atoms of the same chain (intermolecular interaction leading to the formation of coils) and an interaction between links atoms of neighboring coils (intermolecular interaction leading to the formation of aggregates and clusters). Thus to separate aggregates and clusters into globules an electromagnetic field should be applied to them with a frequency that will cause vibrational and rotational resonance in the links of macromolecules. The break of aggregates and clusters is the result of the electromagnetic field affect. The structure of the entire macromolecule as a whole weakly affects the vibration frequencies of characteristic groups. In this case, the groups of atoms that make up the

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molecule and contain light elements (such groups as –CH3 , –0H, –C=N, –C=0) absorb high-frequency radiation. Here, only the frequency is absorbed by the molecule the energy of which exactly corresponds to the differences between the binding energy two levels and as a result of which the resonance energy of this vibration does not increase monotonically but stepwise. The region of deformation vibrations of these bonds is determined by the range of 660 … 990 cm−1 , and the vibrations of the chain –C–C–C– correspond to a value of 575 cm−1 . It is known that the conversion factor of the transition from 1 cm−1 to 1 Hz is 3.33563 × 10−11 . Using this factor, it was determined that the region of macromolecules bonds deformational vibrations from the range of 660 … 990 cm−1 will correspond to 1979 … 2698 MHz. The industrial microwave installations are used for various materials and products processing technologies and have an electromagnetic field frequency of 2450 ± 50 MHz. Therefore, the use of the devices with an electromagnetic field oscillation frequency within 2450 MHz for irradiating the adhesive composition must be accompanied by absorption of electromagnetic waves by macromolecules. Such effect will cause stretching or bending of the corresponding bonds and, as a result, the destruction of aggregates and clusters into tangles of macromolecules. In this case, it can be assumed that the preliminary treatment of the adhesive system with the electromagnetic field of microwave radiation will cause the polarization of its particles and the adhesive joint boundary layers and such action will affect its strength.

3 Experiment The through-type installation was specially designed to study the influence of the microwave electromagnetic processing parameters on the adhesive bonding strength of samples made from solid wood [25, 26]. The installation design allows to processes the adhesive solution immediately after applying it on the wood billet surface. The glue based on polyvinyl acetate dispersion was used. The schematic diagram of the installation is shown in Fig. 1.

Fig. 1. Schematic diagram of the installation for glue electromagnetic processing by microwave radiation.

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The installation for applying and electromagnetic processing of a glue on the wood workpieces surface (Fig. 1) contains workpieces transporting mechanism 1, including a supply 2, receiving 3, and transporting 4, 5 belts. The adhesive supply unit of the installation contains the adhesive reservoir 6, the glue supplying pipeline 7, the applicator head 8, and the glue collector 9. Also, the glue microwave processing module 10 made in the form of a monoblock is included in the installation. The microwave energy source with adjustable radiation power and the microwave working chamber 11 are combined in the module 10. The conveyor belt 4 located after the head 8 is integrated into the working chamber 11 of the microwave module 10. The active infrared motion sensors 12 are installed at the inlet and outlet of the working chamber 11 of the microwave module 10. The evaluation was carried out for the cold bonding technology with polyvinyl acetate glue and for the hot bonding technology with urea–formaldehyde glue. To conduct experimental studies on the effect of electromagnetic processing by microwave radiation on the polyvinyl acetate dispersion adhesive solution the following values of the variable factors were adopted: • Processing time (t 1 )—3 … 9 s; • The duration of exposure in the press (t 2 )—10 … 30 min. The regression equation is obtained after the experimental data processing: τck = 4.31 − 0.36t1 + 0.0035t2 + 0.0361t12 + 0.0014t22 − 0.004t1 t2

(1)

Equation (1) adequately describes the dependence of the adhesive layer shearing strength of solid wood samples on the on varied factors.

4 Discussion To analyze the influence of the pressing mode controlled factors on the adhesive joint during shearing strength the dependencies shown in Figs. 2 and 3 are constructed on the basis of the regression Eq. (1). The graphical dependencies shown in Fig. 2 confirm the fact of intensively globules crushing when the Dorus MD 072 adhesive solution is treated with microwave radiation. This crushing process leads to creating of monoglobular layers with a denser molecular packing. In this case, the energy interaction between the globules is increased. Such effect leads to minimization of the adhesive layer thickness and consequently to increasing of the adhesive joint strength. The dependences characterizing the change in the adhesive gluing strength of wood depending on the microwave treatment duration for various periods of exposure under pressure are presented in Fig. 3. The presented data show that the electromagnetic modification of the adhesive applied on the wood billet reduces the exposure time under pressure in the press providing adhesive strength exceeding the requirements for adhesives of group D3 according to EN 204.

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Fig. 2. The dependence of the adhesive joint strength on the exposure time under pressure at various microwave processing durations: 1–3; 2–6; 3–9 s; 4—standard value according to EN 204 for D4.

Fig. 3. The dependence of the adhesive joint strength on the microwave treatment time for various pressing duration in press: 1–10; 2–20; 3–30 min; 4—standard value according to EN 204 for D4.

The joint analysis of the dependency graphs in Figs. 2 and 3 suggests that adhesive microwave processing during 3–5 s and the duration of exposure in the press for 25– 30 min ensures the bonding strength of wood blanks corresponding to the normative value for group adhesives D4 to EN 204. Experimental studies on the urea–formaldehyde glue processing by microwave electromagnetic field have made it possible to establish the fact that its gelation time is reduced at a temperature of 100 °C. At the same time, the viscosity of the glue working solution remains technologically suitable for four hours. Therefore, it can be argued that the use of glue treated by electromagnetic field microwave radiation will reduce the total duration of the exposure periods of the veneer package under pressure and thereby increase the productivity of the size press when gluing veneers. The value of the pressing pressure rational values when gluing larch veneer with glue treated by electromagnetic field microwave radiation is in the same range of values from 1.5 to 1.7 MPa. This pressure values are recommended by the existing technological conditions for the manufacture of softwood plywood. The using of glue treated by

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electromagnetic field microwave range can reduce the hot press cycle duration to 20% and increase size press performance. This is achieved by reducing the exposure time of a veneer package under pressure while ensuring the plywood necessary strength 1.18 MPa when shearing plywood along the adhesive layer.

5 Conclusion The preliminary non-thermal exposure of the electromagnetic field microwave radiation allows to effectively change the supramolecular structure of the adhesive material polymer in the liquid phase, which provides compounds with increased adhesive and cohesive strength of the adhesive joint. Acknowledgements. The reported study was funded by RFBR, project number 20-08-00039.

References 1. Gilman AB (2003) Exposure to low-temperature plasma as an effective method for modifying the surface of polymeric materials. High-Energy Chem 37(1):20–26 2. Kestelman VN (1980) Physical methods for the modification of polymeric materials. Chemistry, Moscow 3. Pobedinsky VS (2000) Activation of the processes of finishing textile materials with the energy of electromagnetic waves of the high, microwave and UV ranges. IHR RAS, Ivanovo 4. Kwo Han Kiu (2007) Study of adhesion properties of natural rubber, epoxidied natural rubber, and ethylene–propylene diene terpolymer–based adhesives: author’s abstract. Universiti Sains Malaysia 5. Piskarev VS (2010) Surface modification of polyfluoroolefin films in a DC glow discharge. Fundam Prob Radioelectron Instrum 10(1–2):274–279 6. Gilman AB (2014) Adhesion properties of polyfluoroolefin films modified in a direct current discharge. Adhes Sealants Technol 1:14–16 7. Piskarev MS (2008) Changes in the properties and structure of polyvinylidene fluoride films under the influence of a glowing low-frequency discharge and a direct current discharge. Fundam Prob Electron Instrum Making 126–129 8. Gilman AB (2008) Modification of polypropylene films in a direct current discharge. High Energy Chem 42(1):368–371 9. Piskarev MS (2007) The effect of a glow discharge on the surface properties of polyimide films based on aliphatic diamines. HighEnergy Chem 41(4):342–344 10. Kalganova SG (2009) Electrotechnology of non-thermal modification of polymeric materials in a microwave electromagnetic field. Saratov 11. Lavrentiev VA (2009) Influence of the microwave electromagnetic field on the physicomechanical properties of the epoxy compound. Saratov 12. Zavrazhin DO (2006) The influence of microwave radiation on the formation of a structure with improved physical and mechanical characteristics of modified polymer-carbon materials during solid-phase pressure treatment. Promising Mater 4:34–38 13. Estel L, Lebaudy Ph, Ledoux A (2004) Microwave assisted blow molding of polyethylene– terephthalate (PET) bottles. In: Proceedings of the fourth world congress on microwave and radio frequency applications, Austin, Texas

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14. Erenkov OYu, Igumnov PV, Nikishechkin VL (2010) Mechanical properties of polymer composites. Russ Eng Res 30(4):373–375 15. Erenkov OYu, Ivakhnenko AG, Radchenko MV (2013) Method for molding fiberglass objects based on polymer binder electrophysical treatment. Chem Pet Eng 49(5):346–350 16. Mehdizadeh M (2004) Microwave methods for detection and drying of residual water in polymers. In: Proceedings of the fourth world congress on microwave and radio frequency applications, Austin, Texas 17. Gunaratne RD, Day RJ (2004) Microwave and conventional mechanical & thermal analysis of the reactions in epoxy vinyl ester resins. In: Proceedings of the fourth world congress on microwave and radio frequency applications, Austin, Texas 18. Morozov GA (2011) Microwave processing of thermosetting and thermoplastic polymers. Phys Wave Processes Radio Eng Syst 14(3):114–121 19. Abakacheva EM (2010) Application of a microwave electromagnetic installation for the modification of polymer films and the study of their properties. Bashkir Chem J 17(5):79–81 20. Kuzeev IR (2011) Influence of electromagnetic waves of the microwave range on the adhesive ability of polymeric materials. Oil Gas Bus 6:452–457 21. Isaev SP, Shevchuk KA (2016) The influence of microwave processing on the structure of water-based adhesive films. Bulletin of the St. Petersburg Forest Acad 216:200–209 22. Isaev SP, Begunkova NO, Begunkov OI, Shevchuk KA (2018) Justification of the effectiveness of processing an aqueous adhesive solution Dorus FU 406 microwave radiation in the technology of gluing veneers. Syst Methods Technol 4(38):125–132 23. Isaev SP, Shevchuk KA (2015) Modernization of equipment for applying glue in the technology of gluing wood. Actual Prob Forest Complex 42:44–47 24. Isaev SP, Shevchuk KA (2016) Influence of the microwave electromagnetic field on the structure of adhesives used for gluing wood. In: Gedjo (ed) Russian forests: politics, industry, science, education, St. Petersburg 25. Shevchuk KA, Isaev SP (2015) Installation for applying glue to the surface of wood billets. Russian Patent 151359, 10 April 2015 26. Shevchuk KA, Isaev SP (2015) A unit for applying and electromagnetic processing of glue on the surface of wood billets. Russian Patent 154916, 10 Sept 2015

Hydropower Potential as a Resource for Improving the Water Management Situation in Crimea R. Y. Zakharov1(B) and N. E. Volkova2 1 V. I. Vernadsky Crimean Federal University, 4, Prospekt Vernadskogo, Simferopol 295007,

Russia [email protected] 2 Research Institute of Agriculture of Crimea, 150 Kievskaya str, Simferopol 295493, Russia

Abstract. Water storage facilities like any other technical constructions need timely maintenance, which, in turn, implies the need for allocation of the funds necessary to execute these activities. There are many ways to solve this problem, one of which is the use of hydropower potential. The paper analyzes the water management situation on the example of the Belogorsk reservoir, considers various feasible economic mechanisms for improving the efficiency of its management, and identifies the most optimal one. For the chosen water facility, it is the use of its hydropower potential. The development of the Belogorsk reservoir with hydropower equipment and the use of a regulated mode of operation at constant pressure will make it possible to recoup the investment in less than two years, and then to receive additional financial resources for the necessary operational measures at this water body. Keywords: Water reservoir · Power potential · Energy source · Water management · Optimization

1 Introduction Most of the water storage facilities on the territory of the Republic of Crimea were put into operation in 1960–1990 and currently require significant financial costs to maintain the required level of their technical reliability and favorable environmental situation both on the water bodies and on their adjacent territories [1, 2]. The problem of the efficiency improvement of water management facilities’ operation of this type was carried out by many researchers, among whom we would like to point out the following: Levit-Gurevich [3], Mudarisov and Mangazinova [4], Shabanova [5], Nikanorova and Dronin [6], Kokumbaeva [7], Fedorov and Maslikov [8], and many others. The results of their work are reflected in a number of publications [3–8], which show the economic, environmental, and technical aspects of solving this problem. The general conclusion reached by most of the studies conducted in this direction was that © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 A. A. Radionov and V. R. Gasiyarov (eds.), Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020), Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-3-030-54817-9_164

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the use of hydropower potential will increase the efficiency of operation of these water facilities. In the Crimean region, the possibility of using the hydropower resources of rivers was first investigated by D. I. Kocherin and M. V. Keller in the 1920s. The results of these works were reflected in the publications “White coal in Crimea” [9] and “Electrification of Crimea” [10], respectively. D. I. Kocherin was the first to give a large summary of the possibility of using the hydropower potential of Crimean rivers. In his article “White coal in Crimea” [9], he calculated power for 18 rivers in three versions: • Using water storage facilities for water runoff regulations; • Without regulations for winter water consumption; • Without regulations for summer water consumption in low-water season. D. I. Kocherin estimated that the total hydropower potential of these watercourses had amounted to about 3 million watts. In turn, M. V. Keller, speaking about the use of “white coal” in Crimea, noted in his article “Electrification of Crimea” that “… rivers and streams of Crimea, with all their low-water availability, can nevertheless produce, on average, an amount of energy far exceeding the expected demand. The main difficulty with hydropower-based resources is that the debit of the sources is very uneven, reaching 20–25% of average values in the driest years. Thus, the use of white coal is possible only if there is any other power reserve for covering energy shortages in dry years” [10]. Today the Crimean scientists continue their interest in this problem. Among the latest researches, we would like to commend the following works: Oliferov [11], Borovsky and Timchenko [12, 13], Zaharov and Pashkova [14, Zaharov 15], Gorbunova and Gorbunov [16], Vanieva and Abdieva [17], Timchenko et al. [18–20]. We would also like to focus on the work “Renewable Energy” of E. A. Bekirov. In his book, the author gives the following conclusions characterizing the energy potential of Crimean rivers: • The estimated hydropower potential of Crimea is 756 MWth, of which 30% are rivers, 53% are reservoirs, and the remaining 17% are small hydropower plants installed on pressure pipelines of water supply and sewage systems; • Rivers of the western part of the northern slope of the Crimean Mountains have the greatest potential for hydropower (the Kokozka, the Alma, the Kacha and Belbek rivers) [20]. It should be noticed that in the works mentioned above, the main emphasis was on assessing the hydropower potential and the possibility of using this renewable energy source in the Republic of Crimea to cover the needs of the population and sectors of the economy in this type of resource. However, little attention was given to the fact that the development of this direction at already existing water management facilities (reservoirs, ponds) can become a source of additional financial resources for their maintenance. In this regard, the goal of this work was formulated—to assess the possibility of improving the management efficiency of the existing water storage facilities of the Republic of Crimea, on the example of the Belogorsk reservoir, including through the use of their hydropower potential.

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2 Methods and Materials The methodology is based on the principles of systemic, statistical, and comparative analysis. The work was carried out in four stages. At the first stage, the information on the main characteristics of the Belogorsk hydroelectric complex was collected and analyzed (volume, pressure, location, source of filling, list of main water consumers, hydropower potential). At the second stage, a list of possible means of improving the management efficiency of water storage from an economic perspective is compiled, and the most appropriate way is selected among them. At the third stage, the changes in the pressureflow parameters were evaluated and, based on them, the hydraulic turbine was chosen and technological schemes were established. At the fourth stage, the most suitable scheme was identified according to the economic feasibility.

3 Results The Belogorsk reservoir is located on the river Biyuk-Karasu near the city of Belogorsk. This water management facility was commissioned in 1970. The water storage was built for irrigation purposes of Belogorsky, Nizhnegorsky, and Soviet districts of the Crimean region. However, after the external water source was cutoff in 2014, the accumulated runoff is transferred to the East of Crimea through the North Crimean Canal system to cover drinking and industrial needs. The water storage volume of the facility is 23.3 million m3 ; its mirror area—225 ha; length—4.6 km; maximum width—580 m; the maximum depth is 29 m. The earth-fill dam is 26 m high and 560.5 m long and is built from Aptian clays and has a crest width of 7 m. The hydroelectric complex includes a jumper, water intake, spillway, a bypass structures, and a bottom outlet. The spillway facility with a throughput ability of 53.0 m3 /s consists of a supply channel, a connecting channel, a spillway channel, and a discharge channel. The bypass facility, which is used for filling the Taigan reservoir, consists of a supply channel, a tubular bypass, a quick-flow tray, a discharge channel with a throughput ability of 20 m3 /s. The jumper is designed to prevent overflow of water from the Belogorsk reservoir into the Taigan reservoir [21, 22]. In economic terms, the management efficiency of water storage facilities can be improved by following: • • • •

Increase and optimization of the used potential of accumulated water volumes; Tariff increase for customers; Use for other purposes, including for recreational activities, fishing; boating, etc.; Use of energy potentials of these structures to generate electrical energy.

Consider each of the proposed methods on the example of the Belogorsk reservoir. The filling dynamics of this hydraulic system in 2014–2016 is shown in Fig. 1. From the analysis of Fig. 1, it is clearly seen that the average filling volume of the water storage was gradually reduced over the study period. It is not related to the water inflow decrease. The highest rates were recorded in 2015. The main reason is

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Fig. 1. The filling dynamics of Belogorsk reservoir in 2014–2016.

the rising expenditure component. Where once the reservoir was discharged during the growing season, now water is supplied year-round and a larger volume is taken. As a consequence, the reduction of the expenditure component can become necessary. In turn, it will affect the amount of financial resources received from the operation of these hydraulic structures. Therefore, it is not reasonable to talk now about the increase of the used potential of accumulated water volumes, because they are being used to their full. The Belogorsk branch of the State Budgetary Institution of “Crimean Water Management and Irrigation”, which is responsible for the hydroelectric complex mentioned above, can make adjustments to the water tariffs, but only for agricultural consumers who have concluded a water supply agreement. For other groups of water users, tariffs are set by organizations responsible for water treatment and water supply to consumers, if these tariffs are agreed on regional legal structures. The use of the Belogorsk hydroelectric complex for other purposes, including recreational activities, fishing, boating, can adversely affect the ecological status of water body and adjacent territories, therefore, the possible economic income from this type of activity, taking into account the costs of covering these negative processes, is likely to be insignificant. Based on significant pressures, as well as on the regular operation of the hydroelectric complex, the use of the energy potential of the Belogorsk reservoir (Table 1) for generating electric energy may become the most promising of mentioned methods to increase the efficiency of its operation. However, the feasibility of introducing this method directly depends on the results of the feasibility study. The main parameters, on the basis of which the type of hydraulic turbine for the Belogorsk reservoir was selected, are • Average monthly flow (maximum, minimum and average flow) over the study period (2014–2016)—3.2, 0.5, and 2.1 m3 /s, respectively; • Average monthly pressure (maximum, minimum and average pressure) over the study period (2014–2016)—26, 18, and 23 m, respectively.

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Table 1. Potential capacity of the Belogorsk reservoir. Month

Potential capacity of the Belogorsk reservoir (kW) 2014

2015

2016

January

476.6

902.8

455.7

February

1101.5

905.3

370.7

March

174.2

860.1

462.2

April

203.6

1384.8

455.2

May

694.1

827.0

285.4

June

553.6

1421.2

516.7

July

100.6

1018.8

608.1

15.3

798.8

543.8

342.3

667.6

402.9

August September October

477.8

281.1

262.0

November

176.2

158.1

0.2

December Annual average

89.5

188.1

0.0

367.1

784.5

363.6

Based on these technical characteristics, a hydraulic turbine of type RO30–RO30GM-65 was selected. The estimation of its electricity generation was carried out according to four options: • I—the number of hydraulic turbines—1 pc, the operating mode is constant, the pressure is 18 m, the flow rate is 0.5 m3 /s; • II—the number of hydraulic turbines—2 pcs, the operating mode is constant, the pressure is 18 m, the flow rate is 0.5 m3 /s; • III—the number of hydraulic turbines—1 pc, the operating mode is adjustable, the pressure is variable, assigned according to the monthly average data, taking into account that the maximum pressure of the hydraulic turbine (23 m) should not be exceeded, the flow rate is 0.5 m3 /s; • IV—the number of hydraulic turbines—1 pc, the operating mode is adjustable, the pressure is 18 m, the flow rate is 1.0 m3 /s for the period January–October and 0.5 m3 /s for the period November–December. As a result, the annual volume of electricity generation in the first option was 531,957 kWh, in the second and fourth options—975,012 kWh, in the third option—642,640 kWh. Figure 2 shows the results of a feasibility comparison of options. The analysis shows clearly that, in general, the improvement of the Belogorsky reservoir with the proposed hydropower equipment must be recouped in less than three years. The most cost-effective is option IV, which requires the installation of 1 hydraulic turbine and the

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adjustable operation mode. The result shows that of all the means of improving the management efficiency of Belogorsk reservoir mentioned above, the use of its hydropower potential is the most promising.

Fig. 2. The results of a feasibility comparison of options.

4 Conclusion Based on the research, the following conclusions can be made. • The increase of the anthropogenic load on water bodies in conjunction with natural and climatic features, as well as socio-economic characteristics may have an impact on the amount of financial means received from the operation of water storage facilities, therefore, when optimizing their operation, particular attention should be paid to the economic component, which is the basis for prompt inspections, repairs, and maintaining favorable environmental conditions in these water bodies and adjacent territories; • From an economic perspective, it is possible to increase the operation efficiency of water storage facilities using the following methods: increase of the used potential of accumulated volumes of water; tariff increases for consumers; use for recreational activities; using the energy potentials of these water facilities to generate electrical energy. The choice of the most appropriate of them or their combination should be carried out for each specific case; • Concerning the Belogorsk reservoir, the use of energy potential for generating electric energy is the most appropriate way to increase the efficiency of its operation; • The most cost-effective of the proposed technological schemes for Belogorsk hydroelectric complex is option IV (the number of hydraulic turbines—1 pc, the adjustable operating mode, the pressure—18 m, the flow rate—1.0 m3 /s for the period January–October and 0.5 m3 /s for the period November–December).

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Increased water stress, which is characteristic of the Republic of Crimea, includes the development and implementation of a list of measures aimed at improving the operation efficiency of water storage facilities, and primarily of reservoirs. From an economic perspective, the use of their energy potential for generating electricity can help strengthen the material basis and improve the environmental situation at the facility and surrounding areas. Concerning the Belogorsk hydroelectric complex, the installation of a hydraulic turbine and its operation in accordance with the fourth technological scheme will make it possible to pay back the invested funds in less than two years (most likely, the existing operating mode of the reservoir will not change over this period), and then get the pure profit.

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