Advances in Manufacturing II: Volume 4 - Mechanical Engineering [1st ed.] 978-3-030-16942-8;978-3-030-16943-5

Table of contents :
Front Matter ....Pages i-xviii
Front Matter ....Pages 1-1
Parametric Modeling of Gear Cutting Tools (Oleg Krol, Volodymyr Sokolov)....Pages 3-11
Verification of Machine Tool Set-Up Stability Using a Simplified Wolfram Language-Based Model (Andrzej Gessner, Paweł Łuszczewski, Krzysztof Starosta)....Pages 12-24
Balancing of a Wire Rope Hoist Using a Cam Mechanism (Jacek Buśkiewicz)....Pages 25-35
The Influence of Imperfections on the Strength and Stability of Cold-Formed Sigma Channels with Corrugated Flanges (Jakub Kasprzak, Piotr Paczos)....Pages 36-49
Fatigue Life of Auxetic Re-entrant Honeycomb Structure (Jakub Michalski, Tomasz Strek)....Pages 50-60
Experimental Investigations of Steel Welded Machine Tool Bodies Filled with Composite Material (Paweł Dunaj, Tomasz Okulik, Bartosz Powałka, Stefan Berczyński, Marcin Chodźko)....Pages 61-69
Loader Crane Modal Analysis Using Simplified Hydraulic Actuator Model (Paweł Dunaj, Beata Niesterowicz, Bartłomiej Szymczak)....Pages 70-80
Temperature Distribution in Workpiece During Flowdrill - Numerical Experiment Based on Meshless Methods (Anita Uscilowska)....Pages 81-95
Injection Moulding Simulation and Validation of Thin Wall Components for Precision Applications (Aminul Islam, Xiaoliu Li, Maja Wirska)....Pages 96-107
Problems of Flaking in Strengthening Shaft Burnishing (Stefan Dzionk, Bogdan Ścibiorski, Włodzimierz Przybylski)....Pages 108-121
Parametric Modeling of Transverse Layout for Machine Tool Gearboxes (Oleg Krol, Volodymyr Sokolov)....Pages 122-130
Front Matter ....Pages 131-131
Increasing of Lathe Equipment Efficiency by Application of Gang-Tool Holder (Magomediemin Gasanov, Alexey Kotliar, Yevheniia Basova, Maryna Ivanova, Olga Panamariova)....Pages 133-144
Fabrication of Biodegradable Mg Alloy Bone Scaffold Through Electrical Discharge µ-Drilling Route (Neeraj Ahuja, Kamal Kumar, Uma Batra, Sudhir Kumar Garg)....Pages 145-155
Possibility of Block Grouping of Magnetic Inspection Operations for Iron Impurities in Oils and Cutting Fluids (Alexander V. Sandulyak, Anna A. Sandulyak, Vera A. Ershova)....Pages 156-163
Construction of the Facility for Aluminium Alloys Electromagnetic Stirring During Casting (Piotr Mikolajczak, Jerzy Janiszewski, Jacek Jackowski)....Pages 164-175
The Influence of Technological Parameters on Cutting Force Components in Milling of Magnesium Alloys with PCD Tools and Prediction with Artificial Neural Networks (Ireneusz Zagórski, Monika Kulisz)....Pages 176-188
Investigations of Electronic Controller for Electrohydraulic Valve with DC and Stepper Motor (Dominik Rybarczyk)....Pages 189-200
Evaluation of Castings Surface Quality Made in 3D Printed Sand Moulds Using 3DP Technology (Paweł Szymański, Marcin Borowiak)....Pages 201-212
Impedance-Based PZT Transducer and Fuzzy Logic to Detect Damage in Multi-point Dressers (Pedro O. Junior, Doriana M. D’Addona, Felipe A. Alexandre, Rodrigo Ruzzi, Paulo R. Aguiar, Fabricio G. Baptista et al.)....Pages 213-222
Hybrid Numerical-Analytical Approach for Force Prediction in End Milling of 42CrMo4 Steel (Marek Madajewski, Szymon Wojciechowski, Natalia Znojkiewicz, Paweł Twardowski)....Pages 223-232
Analysis of the Pulsating Water Jet Maximum Erosive Effect on Stainless Steel (Dominika Lehocka, Jiri Klich, Jan Pitel, Lucie Krejci, Zdenek Storkan, Darina Duplakova et al.)....Pages 233-241
Comparison of the Weld Quality Created by Metal Active Gas and Shielded Metal Arc Welding (Darina Duplakova, Michal Hatala, Dusan Knezo, Frantisek Botko, Pavol Radic, Dusan Sutak)....Pages 242-256
Application of the Motion Capture System in the Biomechanical Analysis of the Injured Knee Joint (Jakub Otworowski, Tomasz Walczak, Adam Gramala, Jakub K. Grabski, Maurizio Tripi, Adam M. Pogorzała)....Pages 257-265
Hydrogen Embrittlement After Surface Treatments (Hana Hrdinová, Viktor Kreibich, Jan Kudláček, Jakub Horník)....Pages 266-275
Effect of Modification of Mono-crystalline Corundum Grinding Wheel on Cutting Forces in Grinding of Aluminum Alloy 7075 (Witold Habrat, Wojciech Skóra, Jolanta B. Królczyk, Stanisław Legutko)....Pages 276-286
Influence of Processing Parameters on Clamping Force During Injection Molding Process (Przemysław Poszwa, Paweł Brzęk, Ilya Gontarev)....Pages 287-299
Prediction of the Microhardness Characteristics, the Removable Material Volume for the Durability Period, Cutting Tools Durability and Processing Productivity Depending on the Grain Size of the Coating or Cutting Tool Base Material (Gennadiy Kostyuk)....Pages 300-316
Modelling and Analysis of Cutting Force Components in Turning Process of Commercially Pure Titanium Grade 2 (Witold Habrat, Monika Sala, Jolanta B. Królczyk, Angelos P. Markopoulos, Stanisław Legutko)....Pages 317-328
Surface Quality Analysis After Face Grinding of Ceramic Shafts Characterized by Various States of Sintering (Marcin Żółkoś, Roman Wdowik, R. M. Chandima Ratnayake, Witold Habrat, Janusz Świder)....Pages 329-341
Influence of the Most Important Elements of the Prosthesis on Biomechanics of the Human Gait After Amputation of the Lower Limb (Adam Gramala, Jakub Otworowski, Tomasz Walczak, Jakub K. Grabski, Adam M. Pogorzała)....Pages 342-356
Potential Studies of Waterjet Cavitation Peening on Surface Treatment, Fatigue and Residual Stress (P. Manoj Kumar, K. Balamurugan, M. Uthayakumar, S. Thirumalai Kumaran, Adam Slota, Jerzy Zajac)....Pages 357-373
Thermo-Mechanical Phenomena in Aluminum Alloy Casting During Cooling – Experimental Simulation (Jakub Hajkowski, Robert Sika, Mieczysław Hajkowski, Zenon Ignaszak, Paweł Popielarski)....Pages 374-383
Micro-machining and Process Optimization of Electrochemical Discharge Machining (ECDM) Process by GRA Method (Mohinder Pal Garg, Manpreet Singh, Sarbjit Singh)....Pages 384-392
Analysis of Material Removal Efficiency in Face Milling of Aluminum Alloy (János Kundrák, Viktor Molnár, Tamás Makkai, Tamás Dági)....Pages 393-404
The Examination of Cutting Force as Function of Depth of Cut in Cases with Constant and Changing Chip Cross Section (János Kundrák, Angelos P. Markopoulos, Nikolaos E. Karkalos, Tamás Makkai)....Pages 405-415
Methodology of Determination of Key Casting Process Parameters on DISA MATCH Automatic Moulding Line Affecting the Formation of Alloy-Mould Contact Defects (Robert Sika, Adam Jarczyński, Arkadiusz Kroma)....Pages 416-433
Numerical Modeling of MuCell® Injection Moulding Process (Jacek Nabiałek, Tomasz Jaruga)....Pages 434-447
Front Matter ....Pages 449-449
Comparative Experimental Investigation of Mechanical Properties and Adhesion of Low Temperature PVD Coated TiO2 Thin Films (Muhammad Ghufran, Ghulam Moeen Uddin, Awais Ahmad Khan, Hma Hussein, Khuram Khurshid, Syed Muhammad Arafat)....Pages 451-460
Frictional Properties of α-Nucleated Polypropylene-Based Composites Filled with Wood Flour (Olga Mysiukiewicz, Piotr Jabłoński, Radomir Majchrowski, Robert Śledzik, Tomasz Sterzyński)....Pages 461-472
Preparation and Characterization of the Injection Molded Polymer Composites Based on Natural/Synthetic Fiber Reinforcement (Jacek Andrzejewski, Marek Szostak)....Pages 473-484
Innovative Natural Yarn Manufactured from Waste (Sandra Heffernan)....Pages 485-494
Mechanical and Thermal Properties of Rotational Molded PE/Flax and PE/Hemp Composites (Marek Szostak, Natalia Tomaszewska, Ryszard Kozlowski)....Pages 495-506
Clay/EVA Copolymer Nanocomposite - Processing and Properties (Dagmar Měřínská, Vladimír Pata, Libuše Sýkorová, Oldřich Šuba)....Pages 507-517
Synthesis and Characterization of Bioceramic Oxide Coating on Zr-Ti-Cu-Ni-Be BMG by Electro Discharge Process (Abdul’Azeez Abdu Aliyu, Ahmad Majdi Abdul-Rani, Turnad Lenggo Ginta, Chander Prakash, Tadimalla Varaha Venkata Lakshmi Narasimha Rao, Eugen Axinte et al.)....Pages 518-531
Investigation of Alloy Composition and Sintering Parameters on the Corrosion Resistance and Microhardness of 316L Stainless Steel Alloy (Sadaqat Ali, Ahmad Majdi Abdul Rani, Khurram Altaf, Patthi Hussain, Chander Prakash, Sri Hastuty et al.)....Pages 532-541
The Impact of Long-Term Environmental Conditions on the Lifetime Prediction (S-N) of Biomaterial Used in Dentistry (Mateusz Wirwicki)....Pages 542-550
Influence of Residual Stress Induced in Steel Material on Eddy Currents Response Parameters (Frantisek Botko, Jozef Zajac, Andrej Czan, Svetlana Radchenko, Dominika Lehocka, Jan Duplak)....Pages 551-560
Determination of Dynamic Properties of a Steel Hollow Section Filled with Composite Mineral Casting (Tomasz Okulik, Paweł Dunaj, Marcin Chodźko, Krzysztof Marchelek, Bartosz Powałka)....Pages 561-571
Corrosion Resistance of Alternative Chemical Pre-treatments of Hot-Dip Galvanized Zinc Surface (Jakub Svoboda, Jan Kudláček, Viktor Kreibich, Stanislaw Legutko)....Pages 572-581
The Influence of Mixing Method and Mixing Parameters in Process of Preparation of Anti-static Coating Materials Containing Nanoparticles (Michal Zoubek, Jan Kudláček, Viktor Kreibich, Tomáš Jirout, Andrey Abramov)....Pages 582-590
Cleaning of Internal Surfaces (Jiří Kuchař, Viktor Kreibich)....Pages 591-600
Mechanical Properties and Structure of Reactive Rotationally Molded Polyurethane - Basalt Powder Composites (Mateusz Barczewski, Paulina Wojciechowska, Marek Szostak)....Pages 601-609
Manufacturing and Properties of Biodegradable Composites Based on Thermoplastic Starch/Polyethylene-Vinyl Alcohol and Silver Particles (Monika Knitter, Dorota Czarnecka-Komorowska, Natalia Czaja-Jagielska, Daria Szymanowska-Powałowska)....Pages 610-624
Manufacturing and Properties of Recycled Polyethylene Films with an Inorganic Filler by the Extrusion Blow Moulding Method (Dorota Czarnecka-Komorowska, Karolina Wiszumirska, Tomasz Garbacz)....Pages 625-638
Hybrid Epoxy Composites Reinforced with Flax Fiber and Basalt Fiber (Danuta Matykiewicz, Maciej Bogusławski)....Pages 639-650
Back Matter ....Pages 651-653

Citation preview

Lecture Notes in Mechanical Engineering

Bartosz Gapiński Marek Szostak Vitalii Ivanov Editors

Advances in Manufacturing II Volume 4 - Mechanical Engineering

Lecture Notes in Mechanical Engineering

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 in your country: China: Li Shen at [email protected] India: Dr. Akash Chakraborty 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. The books of the series are submitted for indexing to Web of Science.

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

Bartosz Gapiński Marek Szostak Vitalii Ivanov •

•

Editors

Advances in Manufacturing II Volume 4 - Mechanical Engineering

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Editors Bartosz Gapiński Institute of Mechanical Technology, Division of Metrology and Measurement Systems Poznan University of Technology Poznan, Poland

Marek Szostak Institute of Material’s Technology, Division of Polymer Processing Poznan University of Technology Poznan, Poland

Vitalii Ivanov Department of Manufacturing Engineering, Machines and Tools Sumy State University Sumy, Ukraine

ISSN 2195-4356 ISSN 2195-4364 (electronic) Lecture Notes in Mechanical Engineering ISBN 978-3-030-16942-8 ISBN 978-3-030-16943-5 (eBook) https://doi.org/10.1007/978-3-030-16943-5 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved 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

This volume of Lecture Notes in Mechanical Engineering contains selected papers presented at the sixth International Scientific-Technical Conference MANUFACTURING 2019, held in Poznan, Poland, on May 19–22, 2019. The conference was organized by the Faculty of Mechanical Engineering and Management, Poznan University of Technology, Poland, under the scientific auspices of the Committee on Machine Building and Committee on Production Engineering of the Polish Academy of Sciences. The aim of the conference was to present the latest achievements in mechanical engineering and to provide an occasion for discussion and exchange of views and opinions. The main conference topics were: • • • • •

quality engineering and management production engineering and management mechanical engineering metrology and measurement systems solutions for Industry 4.0.

The organizers received 293 contributions from 36 countries around the world. After a thorough peer review process, the committee accepted 167 papers for conference proceedings prepared by 491 authors from 23 countries (acceptance rate around 57%). Extended versions of selected best papers will be published in the following journals: Flexible Services and Manufacturing Journal, Research in Engineering Design, Management and Production Engineering Review and Archives of Mechanical Technology and Materials. The book Advances in Manufacturing II - Volume 4 - Mechanical Engineering will be devoted to widely understood issues regarding novelties in the field of machine manufacturing and constructing. A permanent urge to search for more effective manufacturing processes gives rise to continuous development, both in the constructing and manufacturing areas. In the book, you will find a discussion about problems concerning the following topics: constructing machine parts, mechatronic solutions, and modern drives. In the scope of manufacturing, we will present you with ideas on machine cutting, cutting tools, and precise processing v

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Preface

technology. Chipless technologies, such as founding, plastic forming, non-metal construction materials and composites, deserve equal attention. Finally, additive techniques are an indispensable aspect of modern manufacturing. We hope that this book will make a significant contribution to the development of this area of science and would be attractive to the industry. May 2019

Bartosz Gapiński Marek Szostak Vitalii Ivanov

Organization

Steering Committee General Chair Adam Hamrol

Poznan University of Technology, Poland

Chairs Olaf Ciszak Stanisław Legutko

Poznan University of Technology, Poland Poznan University of Technology, Poland

Scientific Committee Stanisław Adamczak, Poland Michal Balog, Slovakia Zbigniew Banaszak, Poland Myriam Elena Baron, Argentina Stefan Berczyński, Poland Johan Berglund, Sweden Wojciech Bonenberg, Poland Christopher A. Brown, USA Anna Burduk, Poland Somnath Chattopadhyaya, India Shin-Guang Chen, Taiwan Danut Chira, Romania Edward Chlebus, Poland Damir Ciglar, Croatia Marcela Contreras, Mexico Nadežda Cuboňová, Slovakia

Jens J. Dahlgaard, Sweden María de los Angeles Cervantes Rosas, Mexico Andrzej Demenko, Poland Magdalena Diering, Poland Ewa Dostatni, Poland Jan Duda, Poland Davor Dujak, Croatia Milan Edl, Czech Republic Sabahudin Ekinovic, Bosnia and Herzegovina Mosè Gallo, Italy Bartosz Gapiński, Poland Józef Gawlik, Poland Hans Georg Gemuenden, Norway Boštjan Gomišček, UEA

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Marta Grabowska, Poland Wit Grzesik, Poland Michal Hatala, Slovakia Sandra Heffernan, New Zealand Christoph Herrmann, Germany Ivan Hudec, Slovakia Vitalii Ivanov, Ukraine Andrzej Jardzioch, Poland Mieczyslaw Jurczyk, Poland Wojciech Kacalak, Poland Lyudmila Kalafatova, Ukraine Anna Karwasz, Poland Mourad Keddam, Algeria Sławomir Kłos, Poland Ryszard Knosala, Poland Janusz Kowal, Poland Drazan Kozak, Croatia Agnieszka Kujawińska, Poland Janos Kundrak, Hungary Maciej Kupczyk, Poland Ivan Kuric, Slovakia Oleksandr Liaposhchenko, Ukraine Piotr Łebkowski, Poland José Mendes Machado, Portugal Aleksandar Makedonski, Bulgaria Ilija Mamuzic, Croatia Krzysztof Marchelek, Poland Tadeusz Markowski, Poland Edison Perozo Martinez, Colombia Thomas Mathia, France Józef Matuszek, Poland Adam Mazurkiewicz, Poland Andrzej Milecki, Poland Mirosław Pajor, Poland Ivan Pavlenko, Ukraine Dragan Perakovic, Croatia

Organization

Alejandro Pereira Dominguez, Spain Marko Periša, Croatia Emilio Picasso, Argentina Jan Pitel, Slovakia Alla Polyanska, Ukraine Włodzimierz Przybylski, Poland Luis Paulo Reis, Portugal Álvaro Rocha, Portugal Rajkumar Roy, UK Iwan Samardzic, Croatia Krzysztof Santarek, Poland Jarosław Sęp, Poland Bożena Skołud, Poland Jerzy Sładek, Poland Roman Staniek, Poland Beata Starzyńska, Poland Tomasz Sterzyński, Poland Tomasz Stręk, Poland Antun Stoić, Croatia Manuel Francisco Suarez Barraza, Mexico Marek Szostak, Poland Rafał Talar, Poland Franciszek Tomaszewski, Poland María Estela Torres Jaquez, Mexico Justyna Trojanowska, Poland Stefan Trzcieliński, Poland Maria Leonilde R. Varela, Portugal Sachin D. Waigaonkar, India Edmund Weiss, Poland Michał Wieczorowski, Poland Ralf Woll, Germany Magdalena Wyrwicka, Poland Jozef Zajac, Slovakia Jan Żurek, Poland

Program Committee Available on http://manufacturing.put.poznan.pl/en/.

Organization

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Special Sessions Collaborative Manufacturing and Management in the Context of Industry 4.0 Special Session Organizing Committee Leonilde Varela Justyna Trojanowska Vijaya Kumar Manupati José Machado Eric Costa Sara Bragança

University of Minho, Portugal Poznan University of Technology, Poland Mechanical Engineering Department, NIT Warangal University of Minho, Portugal Solent University, UK Solent University, UK

Intelligent Manufacturing Systems Special Session Organizing Committee Ivan Pavlenko Sławomir Luściński

Sumy State University, Ukraine Kielce University of Technology, Poland

Tooling and Fixtures: Design, Optimization, Verification Special Session Organizing Committee Vitalii Ivanov Yiming Rong

Sumy State University, Ukraine Southern University of Science and Technology, China

Advanced Manufacturing Technologies Special Session Organizing Committee Jozef Jurko Michal Balog Tadeusz E. Zaborowski

TU Košice, Slovak Republic TU Košice, Slovak Republic TU Poznań, Poland

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Organization

The Changing Face of Production Engineering and Management in a Contemporary Business Landscape Special Session Organizing Committee Damjan Maletič

Matjaž Maletič

Tomaž Kern

University of Maribor, Faculty of Organizational Sciences, Enterprise engineering Laboratory, Slovenia University of Maribor, Faculty of Organizational Sciences, Enterprise engineering Laboratory, Slovenia University of Maribor, Faculty of Organizational Sciences, Enterprise engineering Laboratory, Slovenia

Enabling Tools and Education for Industry 4.0 Special Session Organizing Committee Dorota Stadnicka Dario Antonelli Katarzyna Antosz

Politechnika Rzeszowska, Poland Politecnico di Torino, Italy Politechnika Rzeszowska, Poland

Staff for the Industry of the Future Special Session Organizing Committee Magdalena Wyrwicka Anna Vaňová Maciej Szafrański Magdalena Graczyk-Kucharska

Poznan University of Technology, Poland Faculty of Economics, Matej Bel University, Slovakia Poznan University of Technology, Poland Poznan University of Technology, Poland

Advances in Manufacturing, Properties, and Surface Integrity of Construction Materials Special Session Organizing Committee Szymon Wojciechowski Grzegorz M. Królczyk Sergei Hloch

Poznan University of Technology, Poland Opole University of Technology, Poland Technical University of Kosice, Slovakia

Organization

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Materials Engineering Special Session Organizing Committee Monika Dobrzyńska-Mizera Monika Knitter Robert Sika Dariusz Bartkowski Waldemar Matysiak Anna Zawadzka

Poznan University of Technology, Poland Institute of Materials Technology, Poznan University of Technology, Poland Institute of Materials Technology, Poznan University of Technology, Poland Institute of Materials Technology, Poznan University of Technology, Poland Institute of Materials Technology, Poznan University of Technology, Poland Institute of Materials Technology, Poznan University of Technology, Poland

Advanced Mechanics of Systems, Materials and Structures Special Session Organizing Committee Hubert Jopek Paweł Fritzkowski Jakub Grabski Krzysztof Sowiński Agata Matuszewska

Institute of Applied Mechanics, Poznan University of Technology, Poland Institute of Applied Mechanics, Poznan University of Technology, Poland Institute of Applied Mechanics, Poznan University of Technology, Poland Institute of Applied Mechanics, Poznan University of Technology, Poland Institute of Applied Mechanics, Poznan University of Technology, Poland

Virtual and Augmented Reality in Manufacturing Special Session Organizing Committee Filip Górski Paweł Buń Damian Grajewski Jorge Martin-Gutierrez Letizia Neira Eduardo Gonzalez Mendivil

Poznan University of Technology, Poland Poznan University of Technology, Poland Poznan University of Technology, Poland Universidad de la Laguna, Spain Universidad Autónoma de Nuevo León, Mexico Tecnologico de Monterrey, Mexico

Contents

Construction Parametric Modeling of Gear Cutting Tools . . . . . . . . . . . . . . . . . . . . . Oleg Krol and Volodymyr Sokolov Verification of Machine Tool Set-Up Stability Using a Simplified Wolfram Language-Based Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Andrzej Gessner, Paweł Łuszczewski, and Krzysztof Starosta Balancing of a Wire Rope Hoist Using a Cam Mechanism . . . . . . . . . . Jacek Buśkiewicz The Influence of Imperfections on the Strength and Stability of Cold-Formed Sigma Channels with Corrugated Flanges . . . . . . . . . . Jakub Kasprzak and Piotr Paczos Fatigue Life of Auxetic Re-entrant Honeycomb Structure . . . . . . . . . . . Jakub Michalski and Tomasz Strek Experimental Investigations of Steel Welded Machine Tool Bodies Filled with Composite Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Paweł Dunaj, Tomasz Okulik, Bartosz Powałka, Stefan Berczyński, and Marcin Chodźko

3

12 25

36 50

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Loader Crane Modal Analysis Using Simplified Hydraulic Actuator Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Paweł Dunaj, Beata Niesterowicz, and Bartłomiej Szymczak

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Temperature Distribution in Workpiece During Flowdrill - Numerical Experiment Based on Meshless Methods . . . . . . . . . . . . . . . . . . . . . . . . Anita Uscilowska

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Injection Moulding Simulation and Validation of Thin Wall Components for Precision Applications . . . . . . . . . . . . . . . . . . . . . . . . . Aminul Islam, Xiaoliu Li, and Maja Wirska

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Contents

Problems of Flaking in Strengthening Shaft Burnishing . . . . . . . . . . . . . 108 Stefan Dzionk, Bogdan Ścibiorski, and Włodzimierz Przybylski Parametric Modeling of Transverse Layout for Machine Tool Gearboxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Oleg Krol and Volodymyr Sokolov Technology Increasing of Lathe Equipment Efficiency by Application of Gang-Tool Holder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Magomediemin Gasanov, Alexey Kotliar, Yevheniia Basova, Maryna Ivanova, and Olga Panamariova Fabrication of Biodegradable Mg Alloy Bone Scaffold Through Electrical Discharge µ-Drilling Route . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Neeraj Ahuja, Kamal Kumar, Uma Batra, and Sudhir Kumar Garg Possibility of Block Grouping of Magnetic Inspection Operations for Iron Impurities in Oils and Cutting Fluids . . . . . . . . . . . . . . . . . . . . 156 Alexander V. Sandulyak, Anna A. Sandulyak, and Vera A. Ershova Construction of the Facility for Aluminium Alloys Electromagnetic Stirring During Casting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 Piotr Mikolajczak, Jerzy Janiszewski, and Jacek Jackowski The Influence of Technological Parameters on Cutting Force Components in Milling of Magnesium Alloys with PCD Tools and Prediction with Artificial Neural Networks . . . . . . . . . . . . . . . . . . . 176 Ireneusz Zagórski and Monika Kulisz Investigations of Electronic Controller for Electrohydraulic Valve with DC and Stepper Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Dominik Rybarczyk Evaluation of Castings Surface Quality Made in 3D Printed Sand Moulds Using 3DP Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Paweł Szymański and Marcin Borowiak Impedance-Based PZT Transducer and Fuzzy Logic to Detect Damage in Multi-point Dressers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Pedro O. Junior, Doriana M. D’Addona, Felipe A. Alexandre, Rodrigo Ruzzi, Paulo R. Aguiar, Fabricio G. Baptista, and Eduardo C. Bianchi Hybrid Numerical-Analytical Approach for Force Prediction in End Milling of 42CrMo4 Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Marek Madajewski, Szymon Wojciechowski, Natalia Znojkiewicz, and Paweł Twardowski

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Analysis of the Pulsating Water Jet Maximum Erosive Effect on Stainless Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 Dominika Lehocka, Jiri Klich, Jan Pitel, Lucie Krejci, Zdenek Storkan, Darina Duplakova, Vladimira Schindlerova, and Ivana Sajdlerova Comparison of the Weld Quality Created by Metal Active Gas and Shielded Metal Arc Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 Darina Duplakova, Michal Hatala, Dusan Knezo, Frantisek Botko, Pavol Radic, and Dusan Sutak Application of the Motion Capture System in the Biomechanical Analysis of the Injured Knee Joint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Jakub Otworowski, Tomasz Walczak, Adam Gramala, Jakub K. Grabski, Maurizio Tripi, and Adam M. Pogorzała Hydrogen Embrittlement After Surface Treatments . . . . . . . . . . . . . . . . 266 Hana Hrdinová, Viktor Kreibich, Jan Kudláček, and Jakub Horník Effect of Modification of Mono-crystalline Corundum Grinding Wheel on Cutting Forces in Grinding of Aluminum Alloy 7075 . . . . . . . . . . . . 276 Witold Habrat, Wojciech Skóra, Jolanta B. Królczyk, and Stanisław Legutko Influence of Processing Parameters on Clamping Force During Injection Molding Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 Przemysław Poszwa, Paweł Brzęk, and Ilya Gontarev Prediction of the Microhardness Characteristics, the Removable Material Volume for the Durability Period, Cutting Tools Durability and Processing Productivity Depending on the Grain Size of the Coating or Cutting Tool Base Material . . . . . . . . . . . . . . . . . . . . 300 Gennadiy Kostyuk Modelling and Analysis of Cutting Force Components in Turning Process of Commercially Pure Titanium Grade 2 . . . . . . . . . . . . . . . . . 317 Witold Habrat, Monika Sala, Jolanta B. Królczyk, Angelos P. Markopoulos, and Stanisław Legutko Surface Quality Analysis After Face Grinding of Ceramic Shafts Characterized by Various States of Sintering . . . . . . . . . . . . . . . . . . . . . 329 Marcin Żółkoś, Roman Wdowik, R. M. Chandima Ratnayake, Witold Habrat, and Janusz Świder Influence of the Most Important Elements of the Prosthesis on Biomechanics of the Human Gait After Amputation of the Lower Limb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 Adam Gramala, Jakub Otworowski, Tomasz Walczak, Jakub K. Grabski, and Adam M. Pogorzała

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Potential Studies of Waterjet Cavitation Peening on Surface Treatment, Fatigue and Residual Stress . . . . . . . . . . . . . . . . . . . . . . . . . 357 P. Manoj Kumar, K. Balamurugan, M. Uthayakumar, S. Thirumalai Kumaran, Adam Slota, and Jerzy Zajac Thermo-Mechanical Phenomena in Aluminum Alloy Casting During Cooling – Experimental Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 Jakub Hajkowski, Robert Sika, Mieczysław Hajkowski, Zenon Ignaszak, and Paweł Popielarski Micro-machining and Process Optimization of Electrochemical Discharge Machining (ECDM) Process by GRA Method . . . . . . . . . . . . 384 Mohinder Pal Garg, Manpreet Singh, and Sarbjit Singh Analysis of Material Removal Efficiency in Face Milling of Aluminum Alloy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 János Kundrák, Viktor Molnár, Tamás Makkai, and Tamás Dági The Examination of Cutting Force as Function of Depth of Cut in Cases with Constant and Changing Chip Cross Section . . . . . . . . . . . 405 János Kundrák, Angelos P. Markopoulos, Nikolaos E. Karkalos, and Tamás Makkai Methodology of Determination of Key Casting Process Parameters on DISA MATCH Automatic Moulding Line Affecting the Formation of Alloy-Mould Contact Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 Robert Sika, Adam Jarczyński, and Arkadiusz Kroma Numerical Modeling of MuCell® Injection Moulding Process . . . . . . . . 434 Jacek Nabiałek and Tomasz Jaruga Materials Comparative Experimental Investigation of Mechanical Properties and Adhesion of Low Temperature PVD Coated TiO2 Thin Films . . . . 451 Muhammad Ghufran, Ghulam Moeen Uddin, Awais Ahmad Khan, Hma Hussein, Khuram Khurshid, and Syed Muhammad Arafat Frictional Properties of a-Nucleated Polypropylene-Based Composites Filled with Wood Flour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 Olga Mysiukiewicz, Piotr Jabłoński, Radomir Majchrowski, Robert Śledzik, and Tomasz Sterzyński Preparation and Characterization of the Injection Molded Polymer Composites Based on Natural/Synthetic Fiber Reinforcement . . . . . . . . 473 Jacek Andrzejewski and Marek Szostak Innovative Natural Yarn Manufactured from Waste . . . . . . . . . . . . . . . 485 Sandra Heffernan

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Mechanical and Thermal Properties of Rotational Molded PE/Flax and PE/Hemp Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 Marek Szostak, Natalia Tomaszewska, and Ryszard Kozlowski Clay/EVA Copolymer Nanocomposite - Processing and Properties . . . . 507 Dagmar Měřínská, Vladimír Pata, Libuše Sýkorová, and Oldřich Šuba Synthesis and Characterization of Bioceramic Oxide Coating on Zr-Ti-Cu-Ni-Be BMG by Electro Discharge Process . . . . . . . . . . . . . 518 Abdul’Azeez Abdu Aliyu, Ahmad Majdi Abdul-Rani, Turnad Lenggo Ginta, Chander Prakash, Tadimalla Varaha Venkata Lakshmi Narasimha Rao, Eugen Axinte, and Sadaqat Ali Investigation of Alloy Composition and Sintering Parameters on the Corrosion Resistance and Microhardness of 316L Stainless Steel Alloy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532 Sadaqat Ali, Ahmad Majdi Abdul Rani, Khurram Altaf, Patthi Hussain, Chander Prakash, Sri Hastuty, Tadimalla Varaha Venkata Lakshmi Narasimha Rao, Abdul’Azeez Abdu Aliyu, and Krishnan Subramaniam The Impact of Long-Term Environmental Conditions on the Lifetime Prediction (S-N) of Biomaterial Used in Dentistry . . . . . . . . . . . . . . . . . 542 Mateusz Wirwicki Influence of Residual Stress Induced in Steel Material on Eddy Currents Response Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551 Frantisek Botko, Jozef Zajac, Andrej Czan, Svetlana Radchenko, Dominika Lehocka, and Jan Duplak Determination of Dynamic Properties of a Steel Hollow Section Filled with Composite Mineral Casting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561 Tomasz Okulik, Paweł Dunaj, Marcin Chodźko, Krzysztof Marchelek, and Bartosz Powałka Corrosion Resistance of Alternative Chemical Pre-treatments of Hot-Dip Galvanized Zinc Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572 Jakub Svoboda, Jan Kudláček, Viktor Kreibich, and Stanislaw Legutko The Influence of Mixing Method and Mixing Parameters in Process of Preparation of Anti-static Coating Materials Containing Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582 Michal Zoubek, Jan Kudláček, Viktor Kreibich, Tomáš Jirout, and Andrey Abramov Cleaning of Internal Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591 Jiří Kuchař and Viktor Kreibich

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Mechanical Properties and Structure of Reactive Rotationally Molded Polyurethane - Basalt Powder Composites . . . . . . . . . . . . . . . . . . . . . . . 601 Mateusz Barczewski, Paulina Wojciechowska, and Marek Szostak Manufacturing and Properties of Biodegradable Composites Based on Thermoplastic Starch/Polyethylene-Vinyl Alcohol and Silver Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610 Monika Knitter, Dorota Czarnecka-Komorowska, Natalia Czaja-Jagielska, and Daria Szymanowska-Powałowska Manufacturing and Properties of Recycled Polyethylene Films with an Inorganic Filler by the Extrusion Blow Moulding Method . . . . 625 Dorota Czarnecka-Komorowska, Karolina Wiszumirska, and Tomasz Garbacz Hybrid Epoxy Composites Reinforced with Flax Fiber and Basalt Fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639 Danuta Matykiewicz and Maciej Bogusławski Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651

Construction

Parametric Modeling of Gear Cutting Tools Oleg Krol(&) and Volodymyr Sokolov Volodymyr Dahl East Ukrainian National University, 59-a Central Pr., Severodonetsk 93400, Ukraine [email protected]

Abstract. A toolkit of parametric modeling in the application to the tasks of designing and studying a gear-cutting tool operating according to the contour machining method and the generating method is proposed. Specialized programs for constructing parametrized profiles of a disk-type gear milling cutter and a gear-cutting hob for machining gear wheels and spline shafts have been developed. Construction procedures of specialized graphic primitives for modeling a rack contour, an involute and spline profile, and a transition curve of the milling tooth flank surface have been proposed. The program of parametric modeling introduces a method for verifying permissible variants of the nonworking part contours for the mill profile, by taking into account restrictions in the form of a message variable. The features of the parametric profiles interaction in the 2D-graphics editor APM Graph with the subsequent export to the 3D-editor APM Studio are considered. Three-dimensional solid models of disktype gear milling cutter and a gear-cutting hob in the APM Studio editor based on parameterized graphic primitives are built. The study of the stress-strain state of the tooth cutter by finite element method is performed. Keywords: Parametric modeling Tooth contour
3D model




Gear cutting tools




Graphic primitives




1 Introduction Modern metal-cutting tools and tool systems (TS) represent complex assembly structures, including tool storage, tool positioners, auxiliary and cutting tools. The ubiquitous transition to the multivariate design of TS and their components is associated with exceeding the normative terms for designing, and fulfilling a large amount of duplicate design activities. Similar problems arise when modeling the important properties of the cutting and auxiliary tools under study. The solution of these problems is associated with the creation of reference models and parametric modeling of graphical procedures that are flexibly set up to change the number and composition of the alternatives considered. The parametrized 3D models libraries, orientated for designing tooling of the Bridgeport DIN 69871 type, as a component of a three-axis milling machine TS are proposed in [1]. As an auxiliary tool used arbor ISO 230 series, which correspond to the equipment of small-sized machines (first and second dimension type). As part of the machine tooling system, there is disk tool storage with 14 tool positions. There is a problem of introducing the approach proposed by the author to machines of other © Springer Nature Switzerland AG 2019 B. Gapiński et al. (Eds.): Advances in Manufacturing II - Volume 4, LNME, pp. 3–11, 2019. https://doi.org/10.1007/978-3-030-16943-5_1

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dimension type, and, consequently, creating the corresponding sets of tool storages 3D models of and rigging for them. On the basis of the developed spindle assembly 3D model with a set of tooling for milling, new approaches that research the static rigidity field of the working space for a high-performance computerized CNC machine [2] is considerated. In the boundaries of this method, a parametric model of a shaping unit equipped with TS taking into account to six directional static rigidity for designing and evaluating its values in the scale of the machine working space has been created. The results for further discussions on the evaluation and reduction of processing errors under various loads are used. Work [3] is devoted to the development of methods for designing metal-cutting tools using parametric 3D modeling. For each type of cutting tool, a parametric prototype is created with the same type of image fragments, which differ only in size. As geometrical interrelations, the specified angles and distances between the planes of the cutting part of the tool surface and the planes of sketches of the model being created are exemplified by a boring tool. It should be noted that for a cutting tool complex profile, the description of the relationship between graphic objects is not limited to angles and distances. So for a disk-type gear milling cutter with a module up to 8 mm, a set of 8 cutters are used, intended for cutting wheels with a certain number of teeth [4, 5]. For cutters No. 1–5, the tooth contour is outlined by a type I profile (graphic primitive I) consisting of a circular arc, straight line and evolving. A profile of type II (graphic primitive II) is characterized by another combination – a straight line segment, an arc, and an involute (cutters No. 6–8). This complicates the parametric description procedure by introducing variables such as the cutter number, type of profile, etc. An analysis of the above work has shown that the questions of parametric models development and 3D modeling of tooling based on parametric models for machining gears have not found proper application. The specificity of the tool production objects for machining gears, which is associated with unification, a wide range of different types of cutting and auxiliary tools, makes it efficient to use the parameterization technology when creating models of TS component designs. In modern computer aided design systems, the presence of a parametric model is embedded in the ideology of the CAD system itself [6]. The existence of an object parametric description is the basis for the entire design process. Almost all systems, such as Autodesk Mechanical Desktop, Unigraphics, CATIA, I-DEAS, etc., use one universal parameterizer of the British company – D-CUBED. The parametrizer DCUBED, focused on 3D modeling, is ineffective in 2D drawing. The mathematics that successfully works on tens of profile lines in the 3D system sketcher can’t handle with thousands of interrelated elements of drawings. In the well-known T-FLEX CAD [7, 8], both directions were simultaneously developed and evaluated - parametric drawing and parametric solid modeling. One very useful use of parameterization is the creation of standard element libraries. The cost of creating a parameterization diagram pays off by reusing libraries. In the well-known APM WinMachine CAD/CAE system [9–11], the expensive adopted parametrizer is not used, but its own software is implemented to create the drawing and graphic parametric editor APM Graph, which can be used both as part of the system and independently. The parametric model created in this way can be inserted into a standard drawing as a parametric unit, which is effective in the process

Parametric Modeling of Gear Cutting Tools

5

of researching tooling. In those situations when there are a significant number of unified elements in a design that vary within a single product range, it is advisable to use a means of parameterizing these elements. The combination of parametric profiles in 2-D graphic editors with the subsequent export to the 3-D editor seems effective. Such a compromise version is constructively implemented in the well-known CAD APM “WinMachine” [10].

2 Research Problem The task of create a specialized software package for parametric modeling of a gearcutting tool is formulated in this article. The main emphasis will be directed on the construction of parameterized graphic primitives, on the basis of which the synthesis of the gear-cutting tool design is realized.

3 Results Parameterization of a gear-cutting tool using the APM WinMachine toolkit is aimed at creating a specialized set of the profile: rack contour, involute profile, form-relived tooth profile, etc. As is known, the profile and dimensions of the wheels teeth are determined by the basic rack profile and cutting contours [12, 13]. In the machine tool industry is often used a modified contour, which regulates the coefficient of the tooth addendum height ha0 (no more than 0.45) and the depth factor of the flank af . Such a contour ensures smooth conjugating of the teeth in the process of engagement [14–16]. When creating a parametric model, one should take into account the difference in the size values of the tooth addendum height ha (per size of the radial clearance in the gear); tooth thickness sn0 (increased by the amount of required backlash clearance) and the location of the flank (af and hf 0 ) on the root of tooth. In the APM Graph module, parametric models of the basic rack (Fig. 1a) contours and cutting (Fig. 1b) contours (Graphic primitive “Contour”) are built. Pno

rao

hfo hao

m

ho

Sno

rfo

af a

b

Fig. 1. Standard contour: a – basic rack profile; b – modified profile.

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For a wide range of cutting tools, a parametric model of the involute tooth profile is built. It is considered as a parameterized graphical primitive “Involute profile” (Fig. 2a) using the analytical relationships in the APM WinMachine syntax (Fig. 2b).

a

b

Fig. 2. Parametric model of the involute tooth profile: a – construction; b – analytical form in the APM Graph variables window.

When profiling tools using the contour machining method, along with the involute part, it is necessary to investigate the profile of the non-working and non-involute part of the cutter, which, in turn, depends on the number of teeth of the cutting twin wheels [17–19]. There is a known method for finding the point K defined by the radius Rk on the involute portion of the tooth profile, which is the boundary of the tooth active part profile that actually participates in the engagement. Consider the option when the radius of the base circle rb is either equal to the radius of the root circle Rf , or exceeds it by a small amount. In this case, the radius rb remains less than the radius Rk of the lower point of the wheel profile active part. In this case, the profile of the wheel tooth will be involute only for a distance from the addendum circle to the base circle. The segment from point K, bounded by a root circle with radius Rf , will be non-involute and will be described by a transition curve [20, 21]. In this case, a section of an elongated epicycloid (when two gears are engagement) or an elongated involute (when the wheel is rolling along the rack) is attached to point K. In Fig. 3 shows the tooth profile of a gear-cutting milling cutter with a transition curve based on a parametric model (the “Transition curve” graphic primitive).

Parametric Modeling of Gear Cutting Tools

a

7

b

Fig. 3. The profile of the tooth cutter: a – contour profile; b – transition curve in the form of an elongated epicycloid.

When machining straight spline shafts, their profile is formed as a result of the tool bending around the spline with tool cutting edges when rolling without sliding the centroids (base straight) of the workpiece [22–24]. When constructing the theoretical profile of the cutting edge of the cutter’s tooth (for machining straight-through spline shafts), a parametric model has been developed. It allows entering the “Splined profile” graphic primitive (Fig. 4).

a

b

Fig. 4. Splined tooth: a – profiling diagram; b – fragment of the parametric model.

For processing complex shaped surfaces according to the generating method, a widely used form-relived tooth profile, this gives a constant and identical profile during the entire period of its operation. In the APM Graph module, parametric models of single and double form-relived teeth profile of cutters, delineated by an Archimedean spiral, constructed as parametrized graphic primitives: “Single form-relived” and “Double form-relived” are built. In Fig. 5 shows a fragment of the program for the formation of a double formrelived tooth of a gear-cutting cutter (Fig. 5a) and the corresponding graphical plotting of the form-relived tool surfaces – single (Fig. 5b) and double (Fig. 5c).

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a

b

c

Fig. 5. The profile of the form-relived surface of the tool: a – fragment of the parameterization program; b – single form-relived; c – double form-relived.

4 Discussion The organization of a computer technology for creating tool systems is based on the formation of a complete electronic layout of a product, since it is the creation of threedimensional electronic models that are adequate to the actually designed product, which opens up possibilities for creating better products [17]. Three-dimensional modeling is necessary as a reliable, flexible and easy-to-use tool for optimizing the design process of a complex profile tool and, finally, combining CAD/CAM tasks in the same environment [18, 19]. In situations where a design has a significant number of unified elements that vary within a single product range, it is advisable to combine parametric profiles in a 2D graphics editor and then export to a 3D editor [10]. As an example, the involute profile (graphic primitive) of a tooth for disk-type gear milling cutter (Fig. 6a) is constructed in the 2D graphic editor APM Graph; a circular array is built in the same place (Fig. 6b). It array are exported to the 3D editor APM Studio [20]. Using 3D operations in APM Studio, a three-dimensional model of the tooth is formed using the graphic primitive “Double form-relived” (Fig. 6c) and the actual disk-type gear milling cutter presented in the gear cutting diagram.

Parametric Modeling of Gear Cutting Tools

a

b

c

9

d

Fig. 6. The combination of 2D- and 3D editors APM: a – involute contour of the tooth; b – circular array; c – 3D model fragment; d – 3D diagram of teeth cutting.

As an example, three-dimensional models of a gear rack are shown – a graphic primitive “Contour” (Fig. 7a), a form-relived tooth of a gear-cutting hob – a graphic primitive “Single gear-cutting hob” (Fig. 7b) and a gear-cutting hob cutter (Fig. 7c) are developed in the module APM Studio.

a

b

c

Fig. 7. 3D models: a – toothed rack; b – single form-relived tooth; c – gear-cutting hob cutter.

In the environment of the APM Studio module, a study of the stress-strain state of a gear-cutting hob cutter (Fig. 8a) was carried out and a finite element mesh was generated with a specific partitioning step (Fig. 8b). In the finite element analysis mode, the fixings are set (displacements along the X, Y, Z axes are fixed) and forces are applied (Fig. 8b). Within the environment of the APM Studio module, a static calculation of the structure was carried out [25, 26]. The results of static calculation can be visualized in graphic and numerical form (Fig. 8c, d). Analysis of the obtained results indicates the maximum deformation at the root tooth (Fig. 8c) and the maximum displacement at the tooth addendum (Fig. 8d), which corresponds to theoretical data.

a

b

c

d

Fig. 8. 3D modeling of a gear-cutting hob cutter: a – design; b – loading diagram; c – stress field; d – field of displacement.

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Thus, in the tasks of designing a gear-cutting tool, an approach based on a combination of procedures for creating parametric profiles in a 2D graphic editor with subsequent export to a 3D editor, creating and researching a three-dimensional model of the tool design seems promising [21, 27].

5 Conclusions 1. Specialized application programs for parametric modeling of a complex-profile gear cutting tool based on the CAD APM WinMachine syntax are developed. Parametric models of the basic rack contour, the involute profile and single- and double formrelived teeth of the gear-cutting milling cutters, working both by the contour machining method and by generation method, are proposed. Developed parametrization mechanism is aimed at express analysis of the designs study for gear-cutting tool based on the constructed parametric models are used. Moreover, each new version is synthesized only by changing a limited set of source data, which reduces the time for multivariate design and the search for a rational structure. 2. Graphic primitives of contours for complex-profile gear cutting tool have been developed. Significantly increases the productivity of the designer, giving him an alternative to standard graphic primitives (line segment, arc of a circle, etc.) is a consequence of the proposed graphic primitives using. This is one of the most effective ways to improve the technical level of design decisions. 3. The proposed approach provides for the verification of permissible variants of the cutter tooth contours by entering restrictions into the parameterization program in the form of a message variable. These variables reflect the position of the nonworking part of the tooth profile, with a positive distance of the transition curve from the elongated epicycloid. 4. The use of the CAD APM WinMachine parameterization toolkit makes the process of designing the gamma of a modern complex profile cutting tool a very effective procedure using the finite element analysis and solid modeling. In the environment of the APM Studio module, a three-dimensional model of a gear-cutting hob cutter was constructed and the stress-strain state of the working surface of the tooth was analyzed.

References 1. Afsharizand, B., Zhang, X., Newman, S.T., Nassehi, A.: Determination of accuracy over machine tool life cycle. In: Proceeding of the 47th CIRP Conference on Manufacturing Systems, vol. 17, pp. 760–765 (2014) 2. Gao, X., Li, B., Hong, J., Guo, J.: Stiffness modeling tools. Int. J. Adv. Manuf. Technol. 86 (5–8), 2093–2106 (2016) 3. Pritykin, F.N., Shmulenkova, E.E.: The main elements of CAD metal-cutting tools when using parametric 3D modeling. Omsk Scientific Herald, vol. 1, no. 107, pp. 278–282 (2012). (in Russian)

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4. Semenchenko, I.I., Matyushin, V.M., Sakharov, G.N.: Designing metal-cutting tools, Moscow (1963). (in Russian) 5. Rodin, P.R.: Fundamentals of cutting tools design, Moscow (1990). (in Russian) 6. Ushakov, D.: Who and why need direct modeling? Rev. Compet. Technol. 1(91), 31–42 (2012). Isicad.ru 7. Shustikov, I.: Parameterization in T-FLEX CAD 3D 8.0, CAD and graphics, vol. 10, pp. 56– 64 (2003). (in Russian) 8. Kirichek, A.V., Afonin, A.N.: Designing metalworking tools and tooling in T-FLEX CAD, Moscow (2007). (in Russian) 9. Shelofast, V.V., Chugunova, T.B.: Basics of designing machines. Examples of problem solving, Moscow (2004). (in Russian) 10. Zamriy, A.A.: Practical training course CAD/CAE APM WinMachine. Teaching manual, Moscow (2007). (in Russian) 11. Rozinsky, S., Shanin, D., Grigoriev, S.: Parametric capabilities of the graphic module APM Graph of the APM WinMachine system. CAD and graphics, vol. 11, pp. 37–40 (2001). (in Russian) 12. Romanov, V.F.: Calculation of gear tools, Moscow (1969). (in Russian) 13. Shevchenko, S., Mukhovaty, A., Krol, O.: Gear clutch with modified tooth profiles. Procedia Eng. 206, 979–984 (2017). https://doi.org/10.1016/j.proeng.2017.10.581 14. Sakharov, G.N.: Contour machining tools, Moscow (1989). (in Russian) 15. Inozemtsev, G.G.: Design of metal-cutting tools, Moscow (1984). (in Russian) 16. Shchegolkov, N.N., Sakharov, G.N., Arbuzov, O.B.: Cutting tool. Laboratory Workshop, Moscow (1984). (in Russian) 17. Ordinartsev, I.A., Filippov, G.V., Shevchenko, A.N.: Toolmaker Handbook, Leningrad (1987). (in Russian) 18. Freifeld, I.A.: Calculations and designs of special metal-cutting tools, Moscow (1959). (in Russian) 19. Yulikov, M.I., Gorbunov, B.I.: Design and manufacture of cutting tools, Moscow (1987). (in Russian) 20. Shagun, V.I.: Cutting tool. Fundamentals of the theory for design, Minsk (1998). (in Russian) 21. Kozhevnikov, D.V., Grechishnikov, V.L., Kirsanov, S.V.: Cutting tool, Moscow (2005). (in Russian) 22. Karpus, V.E., Ivanov, V.A.: Choice of optimal configuration of modular reusable fixtures. Russ. Eng. Res. 32(3), 213–219 (2012). https://doi.org/10.3103/S1068798X12030124 23. Sokolov, V., Krol, O.: Determination of transfer functions for electrohydraulic servo drive of technological equipment. In: Advanced in Design, Simulation and Manufacturing DSMIE 2018, pp. 364–373 (2019). https://doi.org/10.1007/978-3-319-93587-4_38 24. Krol, O., Sokolov, V.: Modeling of spindle nodes for machining centers. J. Phys.: Conf. Ser. 1084, 012007 (2018). VSPID-2017, 52–60. https://doi.org/10.1088/1742-6596/1084/1/ 012007 25. Ivanov, V., Mital, D., Karpus, V., et al.: Numerical simulation of the system “fixture – workpiece” for levers machining. Int. J. Adv. Manuf. Technol. 91(1–4), 79–90 (2017). https://doi.org/10.1007/s00170-016-9701-2 26. Krol, O., Sokolov, V.: Development of models and research into tooling for machining centers. Eastern-Eur. J. Enterprise Technol. 3(1), 12–22 (2018). https://doi.org/10.15587/ 1729-4061.2018.131778 27. Krol, O.S.: Parametric modeling of metal-cutting tools and instruments. Monograph, Lugansk (2012). (in Russian)

Verification of Machine Tool Set-Up Stability Using a Simplified Wolfram Language-Based Model Andrzej Gessner(&), Paweł Łuszczewski, and Krzysztof Starosta Poznan University of Technology, Poznań, Poland [email protected]

Abstract. Modern CNC machine tools are characterized by substantive dynamics of their main and forward movements which contributes to load fluctuation in course of their work. Generation of alternating forces is additionally exacerbated by imbalance of the rotating elements of the machine as well as external interactions influencing its foundation or supporting structure. Appropriate selection and distribution of elements coupling the foundation and the base of the machine tool affords minimization of assorted vibrations and ensures the required operational stability specific to each device. Here, we describe a method enabling quick verification of set-up stability of a machine tool at its construction stage. Results of theoretical analyses were corroborated by the outputs of empirical investigations conducted on a Wolfram Languagebased model. Keywords: Machine tool foundation Wolfram Language


Stability
Kinetostatics


1 Introduction Structural systems of machine tool foundations have been investigated extensively [1– 7]. However a few available reports deal with the methodology of foundation type selection dependent on the machine tool application characteristics [8, 9]. Structural deformation of machine tool bed significantly depends on the pretightening sequence of anchor bolts [10]. Variance constraint of reaction forces could reduce the maximum value and improve the uniformity of the reaction forces [11]. Long-period deformation of foundations causes time-dependent structural deformations of the machine body [12]. Among the crucial goals of appropriate implementation of foundational structures, the following deserve special consideration: transfer of load to the ground, isolation from vibrations – be it environmental or generated within the cutting area (active and passive vibro-isolation), reinforcement of the machine tool stiffness, and ascertaining its stable operation through enhancement of the system mass [4]. There are two main variants of machine tool set-up. First, directly upon foundation plates placed on the ground or on the load-bearing structure of the building. Second, upon special foundational blocks embedded on spring-damping elements selected according to the

© Springer Nature Switzerland AG 2019 B. Gapiński et al. (Eds.): Advances in Manufacturing II - Volume 4, LNME, pp. 12–24, 2019. https://doi.org/10.1007/978-3-030-16943-5_2

Verification of Machine Tool Set-Up Stability

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structural specifications of the foundation [5]. Taking into account the enumerated structural solutions, cutting machine tool-dedicated foundations can be classified as: block foundations, frame foundations, or supporting structures (struts). Selection of the optimal foundation structure is dependent on the type of application of the machine tool, its weight, assessment of its structural stiffness, and the desired level of its machining accuracy [4]. Machine tools set up on the supporting structures, in most cases, do not require fixation by means of foundation screws, whereas those established on separate foundations – block as well as frame – are usually stabilized by virtue of anchor screws. Further, bearing in mind the case scenario analyzed below, it is worth noting that the set-up of a machine tool upon the supporting structure is accomplished via utilization of damping (vibro-isolating) pads – these ascertain minimization of vibrations within the machine tool-foundation plate system – or stiff, steel/cast iron pads, which are inferior in terms of vibro-isolation but sufficient to install devices applied in machining of medium-sized elements [13].

2 Impact of Structural Set-Up on the Possibility of Machine Tool Damage In agreement with the guidelines characterizing supporting structures [6], this type of foundation should take over and compensate the machine tool operational loads while the substitute center of gravity of the device should be as close as possible to that of the foundation plate on which it was set up. According to the technical documentation of one of the investigated milling machines set up on stiff pads (regulated cast iron feet), it is required that the foundation plate, in its elevation plan, encompass the entire machine tool outline and constitute one continuous cement block. When a machine tool is set up on stiff pads without anchoring, the dynamics inherent to its operation carry a risk of several undesired phenomena. One is the sliding of the pads along the plane of the foundation plate as a result of crossing the limits of friction. Another, most likely to occur, is the detachment of the regulated pads from the foundation leading to the change in direction of reaction forces within the machine tool struts arising from the fluctuating acceleration forces of its individual moving systems. The third, seemingly obvious aberration is the occurrence of self-vibrations. These are generated as a result of deviation of an elastic system from its state of equilibrium due to momentary forces or torques (e.g., sudden deceleration or acceleration of the machine tool systems, etc.). Importantly, self-vibrations have no adverse effects on the machine tool working processes as they are characterized by diminishing amplitudes [13]. Structural establishment of machine tool foundations usually involves dynamic analysis affording determination of the response to induction of vibrations characteristic of a given system and its capacity to dampen the resulting resonances. However, in the case of mediumsized machine tools such in-depth investigation is not necessary and, in the main, static analysis proves a sufficient method of assessment of accuracy of the designed foundation type [6].

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In the current study, our goal was to corroborate correct operation of a structurally modified three-axis milling center. The alterations introduced by the manufacturer resulted in a significant shift of the gravitational center of the machine tool spurring concerns regarding its operational stability, which could be perturbed due to forces generated by fast movements of the headstock system and the slide of the Y axis. In-depth literature review failed to reveal any reports on the loss of stability of machine tools following the change in direction of reaction forces arising from the transfer of loads from the regulated feet of the device to the ground. Undoubtedly, such phenomena adversely affect machine tool life span. With time, the machining accuracy will deteriorate, the device will become more and more susceptible to mechanical damage, and its technical parameters will worsen, e.g., through increase of the positioning error. To effectively prolong the life span of any machining center, it is paramount to boost its reliability. Machine tool reliability enhancement can be achieved through implementation of pre-operational and operational methods [9]; their classification is depicted in Fig. 1.

Fig. 1. Classification of machine tool reliability enhancement methods [14].

Pre-exploitation, the boost in machine tool reliability is primarily achieved through application of structural enhancement methods [14]. The machine tool structure design procedure involves pre-determination of boundaries of the device’s operational parameters, such as maximum acceleration and velocity of its linear and rotational axes, positioning reproducibility, machining accuracy, etc. Lack of any undue influence of

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the designed parameters (leading to the aforementioned, unexpected phenomena) has to be corroborated prior to the machine tool manufacture. The relevant analysis can be conducted via the finite element method (FEM). Due to structural complexity of machine tools, however, application of FEM is difficult and time consuming, and thereby, expensive. Moreover, structural modifications introduced in later production series often necessitate additional FEM verification; unfortunately, time constraints of the production process and financial considerations preclude its implementation. Here, we propose a time-efficient and straightforward verification method. The postulated approach affords determination of machine tool operational parameter limits that ascertain its stability, i.e., uninterrupted adherence of the stiff pads supporting the device to its foundation plate.

3 Theoretical Model Figure 2 shows the block model of the investigated machine tool. It further includes schematic representation of the forces acting on the device during its operation. In accord with the aforementioned methodology of machine tool set-up on supporting structures, our investigation was aimed at corroboration of the machine tool stability when subjected to the forces inherent to its exploitation dynamics.

Fig. 2. Model of the investigated machine tool and the forces acting on the device during its operation: ay – acceleration towards the OY axis, az – acceleration towards the OZ axis, GCS – global coordinate system, LCS – local coordinate system, ms – mass of the slide system Y; mh – mass of the headstock system, Qn – weight of elements not moving along the axes OZ and OY (body, table, covers, etc.), Qsh – weight of the slide (Y) and headstock systems, R1,2,3,4,5,6 – reaction forces.

As dictated by the fundamental laws of mechanics, the system maintains equilibrium as long as the vector sum of all forces and torques acting upon it equals zero [15]. The system investigated in this study is three-times statically indeterminate due to the

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six leveling screws upon which the device is set up. There is no need to determine all the reaction forces, however. The research question can be answered through implementation of appropriate, selected equations of kinetostatics (sum of force plans on the OZ axis and sum of torques relative to the OX and OY axes). The analysis was conducted in accord with the axiom of statics stating that the rules governing the state of force equilibrium of a deformable solid remain valid in case of its rigid counterpart [4, 14]. Thus, the potentially dangerous change in direction of reaction forces will take place in both struts 1 and 2 and the rotation axis (OX) will align along the outer edges of the regulated feet 3, 4, 5, and 6. The key equation in our analysis was that describing the sum of all torques relative to the OX axis (1). The relevant forces were: weights of all machine tool elements, reaction forces, and inertial forces stemming from acceleration of the OY axis slide system and the headstock system. X

MR þ

X

MQ þ

X

MB ¼ 0;

ð1Þ

where: MR is the torque of reaction forces relative to the OX axis; MQ is the torque of weights of the individual machine tool elements relative to the OX axis; MB is the torque of inertial forces of the Y axis slide system and the headstock system. In order to perform detailed analyses, several local coordinate systems (LCSs) were established as depicted in Fig. 3. These included: LCS 1 – located within the center of gravity of the immobile machine tool elements (n), LCS 2 – situated in the center of gravity characteristic of the headstock (h), and LCS 3 – embedded within the gravitational center of the slide (s). According to the established designations, torque of the reaction forces is positive when the machine tool is stable. The sum of all other torque values needs to be less than zero; otherwise, the direction of reaction forces acting upon the struts 1 and 2 will point downward. Thus, the torques of all remaining relevant forces have to fulfill the equation: X

MQ þ

X

MB \0;

ð2Þ

where: the sum of torques of weights, X

MQ ¼ Qn
yn þ Qs
ys þ Qh
yh ;

ð3Þ

Verification of Machine Tool Set-Up Stability

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Fig. 3. Local coordinate systems established to afford the proposed analysis

the sum of torques of inertial forces, X

MB ¼ ay ðms
zs þ mh
zh Þ þ az ðmh
yh Þ;

ð4Þ

the coordinates yh and ys are bound according to, yh ¼ ys  n;

ð5Þ

with: yn – distance between LCS 1 and the LCS along the OY axis, ys – distance between LCS 3 and the LCS along the OY axis, yh – distance between LCS 2 and the LCS along the OY axis, zs – distance between LCS 3 and the LCS along the OZ axis, zh – distance between LCS 2 and the LCS along the OZ axis, n – distance between LCS 2 and LCS 3 along the OY axis. The Eq. (4) is characterized by four variables. Two stemming from the position of the machine tool moving elements (ys, zh) and two related to their acceleration (ay, az). In order to determine the value of one of the variables, those of the remaining three

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have to be assumed as known. For example, the maximum value of acceleration in the direction y (ay) for the given position of the headstock (zh) and the acceleration az can be calculated according to: P MB þ az ðmh
yh Þ ay ¼ : ð6Þ ðms
zs þ mh
zh Þ Figure 4 depicts the Wolfram Language interface of the proposed analytical procedure programmed to calculate the values of ay for freely selected coordinates of the center of mass of the headstock (y, z) and the vertical element of its acceleration (az), with all remaining variables known. The values of y and z are given as appropriate settings in the machine tool coordinate system, where: y 2 [m], z 2 < −0.51, 0> [m].

Fig. 4. Interface of the program calculating possible values of the machine tool headstock acceleration in the direction y(ay).

Graphical representation of the obtained results is depicted in Figs. 5 and 6. The continuous line in Fig. 5 describes the maximum acceleration of the headstock (ay) as a function of its y coordinate with the given values of a and z, assuming that the headstock is located in its uppermost (maximum) position and that its acceleration equals zero. The shaded area represents the safe operational range bearing no risk of detachment of the machine tool struts from its foundation plate.

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Fig. 5. Acceptable acceleration (ay) of the headstock and the Y axis slide system as a function of y (az = 0, z = 0).

Similarly, Fig. 6 illustrates the presupposed maximum position of the headstock, which affords expanded, in-depth analysis. The left-most value in Fig. 5 corresponds to the value in the center of the graph in Fig. 6.

Fig. 6. Acceptable acceleration of the headstock and the Y axis slide system as a function of az (y = −0.56, z = 0).

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4 Experimental Studies Our experimental investigation, aimed at the review of machine tool stability under operational conditions and corroboration of the calculation results obtained in course of the proposed verification analysis, was conducted using weight sensors. These were placed under all of the machine tool feet in order to determine the acting force of each foot on the foundation plate of the device. The empirical data were collected for 18 alternative configurations of position and movement of the following machine tool systems: the headstock, the table, and the Y axis slide. The obtained results describe changes in the reaction forces acting along the axes of the machine tool feet as a function of time in course of the travel of its moving elements (Fig. 7). The graph shows the case scenario in which the headstock was in its uppermost (maximal) position (z = 0) and did not accelerate vertically (az = 0), while the slide system was located in its closest possible position to the rotation axis OX. The illustrated movement was initiated up front, proceeded backwards, and was put to a stop along the OY axis. The table was situated on the left side of the machine tool, its position having no influence on the theoretical calculations but explaining the large disproportion of forces transferred along the individual struts. The numbering of weight sensors (W1–W6) corresponds to that of the machine tool feet depicted in Fig. 2.

Fig. 7. Strut forces measured in course of operation of the investigated machine tool. W1–W6: weight sensors 1–6.

At the time point t1 = 0.35 s, the acceleration of the slide and headstock system along the OY axis was ay = 4.3 m/s2, thus showing the expected decrease in reaction forces characteristic of struts 1 and 2. It is worth noting that the minimum values of the

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load of 1 and 2 are almost equivalent, which points to their simultaneous detachment following an extreme case scenario and further corroborates the aforementioned stiffness assumption. Fortunately all values of the reaction forces at struts 1–6 are positive in total simulation period, so there is no hazard of detachment of any support from the ground. The experimental outcomes provide the basis for validation of the theoretical calculations as both analyses are characterized by the same given parameters. Determining the value of torque relative to the OX axis enables calculation of the sum force transferred through the struts 1 and 2 into the ground according to the equation: P P MB MQ þ ¼ F; ð7Þ l where: l – distance between the struts 1, 2 and the OX axis. Figure 8 depicts the interface of the programmed procedure affording determination of the sum force of the feet 1 and 2 with the given parameters.

Fig. 8. Interface of the program calculating the load of the machine tool struts 1 and 2 transferred to the ground.

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Selected results of other, representative parameter configurations (position and movement of the headstock and the Y axis slide system) are shown in Table 1. Table 1. Load of the machine tool feet 1 and 2 Load on W1 and Measurement Measurement Measurement W2 [N] 1 2 3 Calculated 9619 8753 15500 Measured 9976 9142 16697 Error* 3.58% 4.26% 7.17% *Calculated for experimental results as the quotient of difference between the measured value and the measured value.

Measurement 4 21994 22769 3.41% calculated and

The measured value of Measurement 2, as presented in Table 1, corresponds to the load force of the struts 1 and 2 at t1 = 0.35 s (see Fig. 7). Measurements were done for respectively: 1 for front-to-back movement of the headstock and the Y axis slide; maximum (top) headstock position, 2 for front-to-back movement of the headstock and the Y axis slide; maximum (top) headstock position, 3 for bottom-to-top movement of the headstock; maximum (front) position of the Y axis slide system and 4 for bottomto-top movement of the headstock; minimum (back) position of the Y axis slide system. The discrepancies between the experimental and theoretical results may stem from several sources. Whereas our calculations assumed non-deformability of the machine tool, some elastic deformations are bound to occur during its real-time operation. Further, dynamic measurements are burdened with certain inertia characteristic of the measurement devices and influencing the accuracy of experimental outcomes. Another

Fig. 9. Course of changes in load of machine tool struts 1 and 2 transferred to the ground as a function of accelerations ay and az (y = −0.56, z = 0)

Verification of Machine Tool Set-Up Stability

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possible error source is inadequate determination of the center of gravity of the machine tool and its moving subsystems which may significantly affect the calculated force values. Figure 9 further illustrates the results of our numerical simulation in 3D. The graph (Fig. 9) shows the safe acceleration range (plane depicted in yellow, above that in blue) corresponding to the position applied in our experiment.

5 Conclusions All machining centers are characterized by a potential reliability achieved only when the conditions of their manufacture and exploitation do not deviate from those expected. In practice, such compliance is extremely rare; thus, the actual reliability of a given center is substantially lower than its presupposed ideal. Bearing that in mind, in course of the design process of any machining center, its reliability should be determined as higher than required [14]. In the present study, we propose practical application of kinetostatics as a solution to the seemingly problematic issues of stability commonly encountered in the machining industry. The error values determined in course of our theoretical analyses were sufficiently low, as compared to the experimental results, to estimate the stability of the investigated machine tool in a timely and effective fashion using the presented Wolfram Language-based program; the obtained safety coefficient was significantly higher than the errors. The proposed calculation approach, reinforced by the experimental corroboration of its validity, is therefore a viable alternative to the finite element method routinely applied for evaluation of stability of machine tools set up on more than three struts.

References 1. Yunusa-Kaltungo, A., Sinha, J.K., Nembhard, A.D.: Use of composite higher order spectra for faults diagnosis of rotating machines with different foundation flexibilities. Measurement 70, 47–61 (2015) 2. Gazetas, G.: Analysis of machine foundation vibrations: state of the art. Soil Dyn. Earthq. Eng. 2(1), 2–42 (1983) 3. Pennacchi, P., Bachschmid, N., Vania, A., Zanetta, G.A., Gregori, L.: Use of modal representation for the supporting structure in model-based fault identification of large rotating machinery: part 1 – theoretical remarks. Mech. Syst. Signal Process. 20, 662–681 (2006) 4. Lipiński, J.: Foundations for Machines. Arkady, Warsaw (1985) 5. Marchelek, K.: Dynamics of Machine Tools. WNT, Warsaw (1991) 6. Srinivasulu, P., Vaidyanathan, C.V.: Handbook of Machine Foundations. McGraw-Hill, New York (1977) 7. Samui, P.: Support vector machine applied to settlement of shallow foundations on cohesionless soils. Comput. Geotech. 35, 419–427 (2008)

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8. Mao, K., Li, B., Wu, J., Shao, X.: Stiffness influential factors-based dynamic modeling and its parameter identification method of fixed joints in machine tools. Int. J. Mach. Tools Manuf. 50, 156–164 (2010) 9. Hijink, J.A.W., Van Der Wolf, A.C.H.: Analysis of a milling machine: computed results versus experimental data. In: Proceedings of 14th International MTDR Conference, Manchester, UK, Ed. J. M. Alexander, pp. 553–558 (1973) 10. Liu, H., Wu, J., Liu, K., Kuang, K., Wang, Y.: Pretightening sequence planning of anchor bolts based on structure uniform deformation for large CNC machine tools. Int. J. Mach. Tools Manuf. 136, 1–18 (2019) 11. Gao, T., Qiu, L., Zhang, W.: Struct. Multidisc. Optim. 56, 755 (2017). https://doi.org/10. 1007/s00158-017-1742-0 12. Bosetti, P., Bruschi, S.: Enhancing positioning accuracy of CNC machine tools by means of direct measurement of deformation. Int. J. Adv. Manuf. Technol. 58, 651–662 (2012) 13. Wrotny, L.T.: Foundations of Machine Tool Design. WNT, Warsaw (1973) 14. Legutko, S.: Foundations of Machine and Equipment Operation. School and Pedagogic Publishing, Warsaw (2007) 15. Bedford, A., Fowler, W.: Engineering Mechanics – Statics. Prentice Hall, Pearson (2008)

Balancing of a Wire Rope Hoist Using a Cam Mechanism Jacek Buśkiewicz(&) Poznan University of Technology, Poznań, Poland [email protected]

Abstract. To design machines that perform their mechanical functions with minimal power consumption is an important and challenging issue. It may be obtained by applying a gravity balanced mechanical systems. The objective of the paper is to design a cam-roller follower mechanism to gravity balance a wire rope hoist for lifting loads. It is analysed how various geometric features affect the applicability of the cam mechanism (jerks, pressure angle, roller radius). The paper provides the method to synthesize cams with different geometries realizing the same performance, among which a designer can choose the one that is optimal with respect to strength properties. Keywords: Cam


Wire rope hoist
Gravity balancing

1 Introduction Lifts, hoists, elevators and all the machines that raise or lower a load have an enormous number of applications in industry. In numerous cases they require high power engines to operate. The minimization of power consumption then is an important issue. It may be obtained, for example, by applying an additional, i.e. gravity balanced, mechanical system. The literature on gravity balancing is very extensive. The attention is focused on spring-linkage systems. Either zero-free-length springs or non-zero-free-length springs are utilised to statically balance various spatial and planar mechanical systems [1–12]. Compared to counterweights, springs do not increase significantly the mass of the mechanism. Cams are also used to counterbalance mechanisms. An interior cam mechanism is applied as gravity-balancing mechanism for robot arms [13]. Cam is a convenient device for transforming one type of motion into another. The large number of cam-follower combinations has been designed and applied in various applications [14–19]. Their major advantage over the mechanisms with lower kinematic pairs is simpler synthesis [14]. Nonetheless, a lower number of scientific papers deals with the applications of cams in balancing of various systems. It is not a trivial problem to effectively optimise the cam geometry for the prescribed performance. The influence of various parameters on under-cutting and pressure angle problems is underlined in [14]. The objective of the paper is to design a cam mechanism to gravity balance a wire winch hoist for raising a load. A cam-roller follower along with spring is proposed to either minimise the power of the engine or shorten the time of lifting. The cams are synthesized for a prescribed set of initial parameters: the load mass, the height to which © Springer Nature Switzerland AG 2019 B. Gapiński et al. (Eds.): Advances in Manufacturing II - Volume 4, LNME, pp. 25–35, 2019. https://doi.org/10.1007/978-3-030-16943-5_3

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a load is elevated and the spring stiffness. It is analysed how the geometric features affect the properties of cams which are responsible for a proper machine functioning (jerks, pressure angle, roller radius). Such an analysis of cams applied in the gravity balanced cable drum hoists is not widely dealt with in the literature.

2 The Concept of the Mechanical System Figure 1 presents the system which consists of the rope drum (winch), spur gears, camroller follower and spring. The sizes of all the elements may not correspond to the their sizes in an actual hoist as the scheme is to distinctly illustrate all the components. The drum wraps around a rope with the platform attached at the free end. The weight of the load determines the power of the hoist engine. To increase the area of the possible applications, spur gears are applied. Without gears the hoist elevates the loads to relatively low heights (i.e. devices for elevating patients with disabled neuro-muscular systems) – the working cycle lasts one full rotation of the cam and drum. One spur gear and rope drum are assembled along with an engine on the first shaft, whereas the other gear and cam are mounted on the other shaft. When a load is being elevated, the cam through the roller follower compresses the spring in such a way that the potential energy of the system is conserved. Let the following data be given: m - the mass of the hoist platform and load, k - the spring stiffness, a - the radius of the rope drum, ymax - the maximum height of the platform, i - gear transmission ratio. It is also denoted: u - the displacement of the follower and spring compression, umax, umin - the maximum and minimum spring compression, y - the height of the platform measured from the lowest position, / - the angular position of the cam (/ varies from 0, corresponding to the lowest platform position, and /max at which the platform is in the highest position), r0 - the radius of the cam base circle, e - the eccentricity of the follower, rk - radius of the roller. The displacement of the follower is derived from the principle of the potential energy conservation. If the potential energy is conserved for any platform position, the mechanism is in equilibrium at each position. Assuming that friction forces can be disregarded, the total energy is the sum of the gravitational potential energy of the load and elastic spring potential energy. 1 V ¼ ku2 þ mgy ¼ C: 2

ð1Þ

Balancing of a Wire Rope Hoist Using a Cam Mechanism

27

Fig. 1. The concept of a hoist.

When the cam rotates about u, the drum rotates by iu and, as a consequence, the length of the rope wrapped around the drum equals aiu. Then by equalling the potential energies at the highest and arbitrary positions. 1 1 V ¼ ku2max ¼ ku2 þ mgaiu; 2 2

ð2Þ

one obtains the follower displacement: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2mgaiu uðuÞ ¼ u2max  ; k

ð3Þ

where: 0  u  umax . The parameters: umax, m, a, k have to be prescribed. The hoist then is designed for a preset mass of the load. In order not to change the mechanism when mass m of the load is changed, one has to select new stiffness k of the spring. The compression function u fails to change, when m=k is constant. The radius a cannot be changed since then ymax will change.

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Properties of the cam-roller follower The displacement of the follower is frequently defined in the intervals to regard various phases of the mechanism operation. The displacement is measured from the base circle to the tracer point i.e. the centre of the roller which generates the pitch circle. 8 s1 ; 0  u\u1 > > < s2 ; u1  u\u2 f ¼ > > : sn ; un1  u\un

ð4Þ

The pressure angle is an important parameter for a proper functioning of the cam. It is the angle between the axis of the follower and the normal to the cam profile. The angle is kept as small as possible. If this angle becomes too large, the cam shaft will be excessively bent. In the case of the cam-roller follower, the tangent of this angle is expressed as:   tga ¼ f;u  e =f :

ð5Þ

Sometimes, it is convenient to assemble the follower eccentrically with respect to the cam shaft. When eccentricity e is non-zero, the trajectory coordinates of roller centre A (pitch circle) for cam angular position u are as follows. yA ¼ e sin u þ f cos u;

ð6:1Þ

xA ¼ e cos u þ f sin u.

ð6:2Þ

To prevent from under-cutting effect and enable the proper motion of the roller on the cam, the roller radius must be less than the curvature radius of the pitch circle. The curvature formula is expressed as follows: 2 f 2 þ 2f;u  ff;uu 1=q ¼ j ¼  3=2 : 2 2 f þ f;u

ð7:1Þ

When the follower is shifted eccentrically, it is convenient to compute the curvature using formula: 1=q ¼ j ¼

yA;uu xA;u  yA;u xA;uu  3=2 : x2A;u þ y2A;u

ð7:2Þ

The cam profile is the envelope of circles with radii equal to the roller radius and centred at point A.

Balancing of a Wire Rope Hoist Using a Cam Mechanism

FðxOK ; yOK ; uÞ ¼ ðxOK  xA ðuÞÞ2 þ ðyOK  yA ðuÞÞ2  rk2 ¼ 0;

29

ð8:1Þ

@FðxOK ; yOK ; uÞ dxA ðuÞ dyA ðuÞ ¼ 2ðxOK  xA ðuÞÞ  ðyOK  yA ðuÞÞ ¼ 0: ð8:2Þ @u du du The cam profile is then computed as the equidistance of the pitch circle using the following equations: xOK ¼ xA þ rk yA;u =

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2A;u þ y2A;u ;

ð9:1Þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y2A;u þ x2A;u ;

ð9:2Þ

yOK ¼ yA  rk xA;/ =

which satisfy Eqs. (8.1 and 8.2). The greater roller radius, the smaller stresses in the contact surface of the cam and roller.

3 Numerical Analysis and Discussion It is assumed that the following parameters are given: – – – – – –

spring stiffness k = 40000 N/m, load and platform mass m = 50 kg, maximum load rise ymax = 2 m, eccentricity e = 0, 0.1, 0.15 m, gear transmission ratio i = 1, 2; minimum spring compression umin = 0.1, 0.2 m.

The solutions for various: minimum spring compression, eccentricity e, and transmission ratios are presented. The displacement of the follower is determined from the formula resulting from the principle of the potential energy conservation. This formula is not harmonic, therefore the cam profile obtained for the full rotation would be open. It is assumed that the cam turns by umax ¼ 3=2p when raising a load to the highest level. The cam profile for the angle from /max to 2p is determined for the following, prescribed motion conditions: – s2 ¼

5 P

ai t i ,

i¼0

– the contour must be continuous, – the velocity and acceleration of the follower at the boundary points umax ; 2p are continuous. Velocities and accelerations are not essential in this analysis, but the demand for the continuity up to the second derivatives ensures the continuous curvature along the whole profile. Then the follower displacement measured from the base circle is as follows:

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qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8 2mgaiu > < s1 ¼ u2max  k ; 0  u\umax ; f ¼ 5 P > : s2 ¼ ai ti ; umax  u\2p

ð10Þ

i¼0

As the minimum string compression is non-zero, the displacement function f is also non-zero, and, as a consequence, the base circle radius can be 0. Table 1 presents the parameters corresponding to the cases that are analysed. Parameters: umin, i and e are the input data, whereas the remaining umax, rk, a and a are computed as the functions of the input parameters. The spring is maximally compressed in the initial (lowest) position, whereas the spring compression is minimal when the load is in its upper position. Table 1. The set of geometric parameters of the system Case umin [m] I 0.1 II 0.1 III 0.1 IV 0.1 V 0.1 VI 0.2 VII 0.2

i e [m] 1 0 1 0.1 1 0.15 2 0 2 0.1 1 0 1 0.1

umax [m] 0.243 0.243 0.243 0.243 0.243 0.298412 0.298412

rk [m]