Discrete Element Method in the Design of Transport Systems: Verification and Validation of 3D Models [1st ed.] 978-3-030-05712-1, 978-3-030-05713-8

Table of contents :
Front Matter ....Pages i-xxi
Introduction (Daniel Gelnar, Jiri Zegzulka)....Pages 1-3
Basic Description of DEM (Daniel Gelnar, Jiri Zegzulka)....Pages 5-15
Basic Description of Bucket Elevators (Daniel Gelnar, Jiri Zegzulka)....Pages 17-25
Bucket Elevator Filling and Discharge (Daniel Gelnar, Jiri Zegzulka)....Pages 27-47
The New Method of Design and Optimization (Daniel Gelnar, Jiri Zegzulka)....Pages 49-50
Input Parameters for DEM – Bulk Material (Daniel Gelnar, Jiri Zegzulka)....Pages 51-74
Input Parameters for DEM – Geometry of the 3D Model and Validation Machine (Daniel Gelnar, Jiri Zegzulka)....Pages 75-88
Input Parameters – Kinematic Properties (Daniel Gelnar, Jiri Zegzulka)....Pages 89-93
Process Validation and Calibration (Daniel Gelnar, Jiri Zegzulka)....Pages 95-129
The Results for the Optimization of Bucket Filling and Discharge (Daniel Gelnar, Jiri Zegzulka)....Pages 131-164
The Results for Optimization of Filling Bulk Material in the Bucket to Minimize Travel Resistance and Impacts (Daniel Gelnar, Jiri Zegzulka)....Pages 165-170
The Results for Process Optimization of Bulk Material Filling into the Bucket to Minimize Abrasive and Destructive Impacts of the Bucket Edge on the Transported Mass (Daniel Gelnar, Jiri Zegzulka)....Pages 171-184
The Optimization of Bucket Discharge to Maximize the Transported Volume and to Minimize Material Fall Down the Shaft (Daniel Gelnar, Jiri Zegzulka)....Pages 185-192
Conclusion (Daniel Gelnar, Jiri Zegzulka)....Pages 193-195
Back Matter ....Pages 197-208

Citation preview

Daniel Gelnar · Jiri Zegzulka

Discrete Element Method in the Design of Transport Systems Verification and Validation of 3D Models

Discrete Element Method in the Design of Transport Systems

Daniel Gelnar • Jiri Zegzulka

Discrete Element Method in the Design of Transport Systems Verification and Validation of 3D Models

Daniel Gelnar Technical University of Ostrava Ostrava, Czech Republic

Jiri Zegzulka Technical University of Ostrava Ostrava, Czech Republic

ISBN 978-3-030-05712-1    ISBN 978-3-030-05713-8 (eBook) https://doi.org/10.1007/978-3-030-05713-8 Library of Congress Control Number: 2018964900 © 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, express 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 book presents an innovative proposal to optimize bucket elevators and related transport processes using discrete element method (DEM). The book contents are based on real and simulated measurements, procedures, and patents acquired when working on the dissertation by Gelnar [1]. Before the book introduces and describes the newly improved design and optimization method based on DEM, it opens with the description of the conventional method applied in the design of machinery using computer-aided design. Because the newly proposed design and optimization method was studied and applied on bucket elevators, bucket elevators are briefly described, including related calculations. The body of the book deals with the optimization of filling and discharge of the bucket elevators using DEM. The reported measurements of physical properties of selected materials serve as input values for the simulation method and basic calibration of the model bulk material in the DEM simulation. Next, a 3D simulation model is proposed, which is a digital twin of the validation bucket elevator. The model works with programmed movements, speeds, and geometry to simulate the filling and discharge of the transported material. As the use and accuracy of the simulation results must be validated against real results, the book continues with a validation of the dynamic flow of bulk materials on a newly designed, patented validation bucket elevator, i.e., a laboratory-scale validation bucket elevator. When the simulation outputs are validated for the head section, simulations are made for the boot of the bucket elevator. All the results are used to continuously optimize the laboratory-scale validation bucket elevator and calibration of the bulk material. The simulation method was also verified in real conditions. It was used for the simulation and optimization of material filling and discharge of a real bucket elevator used in the transport of abrasive materials. Based on the results, basic structural modifications are proposed to increase the bucket elevator performance. We believe that in the future this innovative design method shall become more accurate and the

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Preface

calculations will be obtained in a faster and more efficient manner. The book also contains short videos – see the link http://bsc.vsb.cz, which shall hopefully enrich the learning experience for students or help in the practice when designing bucket elevators and similar equipment. Ostrava, Czech Republic

Daniel Gelnar Jiri Zegzulka



Reference 1. Gelnar, D.: Verification and validation of DEM models of bulk materials used with bucket elevators, and of possible real situation solutions in practice, when filling and discharging the buckets. Ostrava: VŠB - Technical University of Ostrava, supervisor of dissertation: Prof. Ing. Jiří Zegzulka, CSc. Report ISBN 978–80–248-3795-6 (2015)

Acknowledgment

Thanks to Bulk Solids Center Czech Republic (ENET, HGF VŠB-TUO) for creating conditions for interdisciplinary research. This paper was conducted within the framework of the project LO1404: Sustainable development of ENET Centre, the project SP2018/47: Calibration and experimental devices for the research and validation of simulation models and the project Innovative and additive manufacturing technology - new technological solutions for 3D printing of metals and composite materials, reg. no. CZ.02.1.01/0.0/0. 0/17_049/0008407 financed by Structural Founds of Europe Union.

vii

Contents

1 Introduction  ��������������������������������������������������������������������������������������������    1 2 Basic Description of DEM ����������������������������������������������������������������������    5 References ������������������������������������������������������������������������������������������������   14 3 Basic Description of Bucket Elevators ��������������������������������������������������   17 References ������������������������������������������������������������������������������������������������   25 4 Bucket Elevator Filling and Discharge  ������������������������������������������������   27 4.1 Discharge of Buckets  ����������������������������������������������������������������������   31 4.1.1 Gravity Discharge  ����������������������������������������������������������������   33 4.1.2 Mixed Discharge  ������������������������������������������������������������������   34 4.1.3 Centrifugal Discharge  ����������������������������������������������������������   35 4.2 Bucket Filling  ����������������������������������������������������������������������������������   38 4.2.1 Direct Flow of Material Filling ��������������������������������������������   38 4.2.2 Theoretical Calculation of Direct Flow Filling ��������������������   39 4.2.3 Scooping of Material  �����������������������������������������������������������   41 4.2.4 Combined Method of Bucket Filling  ����������������������������������   42 4.2.5 Theoretical Calculation of Scooping  ����������������������������������   42 References ������������������������������������������������������������������������������������������������   46 5 The New Method of Design and Optimization  ������������������������������������   49 6 Input Parameters for DEM – Bulk Material ����������������������������������������   51 6.1 Selection of Particle Shape for Simulation and Real Measurements  ������������������������������������������������������������������   51 6.2 Measurements of Apparent Density and Volumetric Weight  ����������   55 6.3 Measurements of Internal Friction ��������������������������������������������������   56 6.4 Measurements of External Friction ��������������������������������������������������   57 6.5 Measurements of Repose Angle  ������������������������������������������������������   59 6.6 Measurements of Particle Size Distribution ������������������������������������   61 6.7 Measurements of Coefficient of Restitution ������������������������������������   64

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Contents

  6.8 Measurements of Sliding Friction ��������������������������������������������������   65   6.9 Measurements of Rolling Friction  ������������������������������������������������   68 6.10 Summary of Results for DEM Input Parameters  ��������������������������   72 References ������������������������������������������������������������������������������������������������   74 7 Input Parameters for DEM – Geometry of the 3D Model and Validation Machine ��������������������������������������������������������������   75 7.1 Creation of Simulation Environment  ����������������������������������������������   75 7.2 Design and Creation of the Validation Bucket ��������������������������������   78 Reference ��������������������������������������������������������������������������������������������������   88 8 Input Parameters – Kinematic Properties ��������������������������������������������   89 9 Process Validation and Calibration  ������������������������������������������������������   95 9.1 Direct Measurements and the Validation Bucket Elevator ��������������   95 9.2 Evaluation of the Direct Method Using DS-NET Strain Gauge System ������������������������������������������������������������������������   95 9.3 Indirect Measurements and the Validation Bucket Elevator ������������   96 9.4 Evaluation of the Indirect Method Using PIV Software (Particle Image Velocimetry)  ����������������������������������������������������������   96 9.5 Validation – Preparation of Measurements ��������������������������������������  100 9.6 Validation – Measurement Results ��������������������������������������������������  104 10 The Results for the Optimization of Bucket Filling and Discharge ������������������������������������������������������������������������������������������  131 10.1 The Results for Optimization of Bucket Discharge  ����������������������  131 10.2 The Results for Optimization of Bucket Filling ����������������������������  137 11 The Results for Optimization of Filling Bulk Material in the Bucket to Minimize Travel Resistance and Impacts  ����������������  165 12 The Results for Process Optimization of Bulk Material Filling into the Bucket to Minimize Abrasive and Destructive Impacts of the Bucket Edge on the Transported Mass ������������������������  171 13 The Optimization of Bucket Discharge to Maximize the Transported Volume and to Minimize Material Fall Down the Shaft ����������������������������������������������������������������������������������������  185 14 Conclusion  ����������������������������������������������������������������������������������������������  193 Interesting Links  ��������������������������������������������������������������������������������������������  197 Awards ��������������������������������������������������������������������������������������������������������������  199 References ��������������������������������������������������������������������������������������������������������  201 Index ����������������������������������������������������������������������������������������������������������������  205

Abbreviations

CAD Computer-aided design CCD camera Charge-coupled device – a camera with a light-sensitive chip able to bind electric charge CFD Computational fluid dynamics DEM Discrete element method EDEM Software using the discrete element method to simulate bulk materials FEM Finite element method MBD Multibody dynamics PIV Particle image velocimetry  – a method using the pixel difference between two images to determine the speed and travel of particles in time

xi

List of Quantities and Symbols

A Ah B E E* FA Fc FCE FHRA Fn Fnd Fh Fhs Fh max FNA Fs Ft Ftd F1 F2 G GM H Hp I L M MCE Mt Mr

Work for scooping Specific work for scooping Width of belt Young’s modulus of elasticity Equivalent Young’s modulus of elasticity Counterweight force Centrifugal force effecting on the content of bucket Total force effecting on the particle Digging force Normal force Normal damping force Scooping drag force Mean scooping drag force Maximum scooping drag force Direct flow force Drag caused by filling the buckets Tangential force Tangential damping force Shear force Shear force Gravity force of bucket content Shear modulus Height Particle fall height Moment of inertia Length Image magnification factor Total moment of particle Tangential torque Rolling friction torque

[J] [J·kg−1] [m] [MPa] [MPa] [N] [N] [N] [N] [N] [N] [N] [N] [N] [N] [N] [N] [N] [N] [N] [N] [Pa] [m] [m] [kg·m2] [m] [−] [N·m] [N·m] [N·m] xiii

xiv

N P Ph R R* T U VT Vp Vk Vw Qh Qv Sn St Sw W Ww X a b c ck d dmax e f ffc g hh hk hp h1 i ik k kk kφ kφ lp m m* mb mh

List of Quantities and Symbols

Normal force on the RST-01 Power consumption of electric motor Power consumption for scooping Radius of sphere Equivalent radius Temperature Electric motor supply voltage Total volume (particle with water) Volume of particles Water volume of bucket Volume of water Gravimetric transport output Volumetric transport output Normal stiffness Tangential stiffness Shear force of external friction Width Humidity Displacement vector (on CCD) Acceleration Width of buckets Dimension of discharge bucket Bucket spacing factor Diameter of particle Maximum size of particle Restitution coefficient Frequency Flow factor Gravitational acceleration Level height of bucket filling Height of bucket Particle bounce height Material fall height Gear ratio Number of buckets Flowability coefficient Rigidity coefficient Filling factor Mean filling factor Pole distance Mass Equivalent of mass Weight of material in bucket Weight of particles at discharge hopper

[N] [kW] [W] [m] [m] [ºC] [V] [m3] [m3] [m3] [m3] [t·h−1] [m3·h−1] [N] [N] [N] [m] [%] [m] [m·s−2] [m] [m] [−] [m] [m] [−] [Hz] [−] [m·s−2] [m] [m] [m] [m] [−] [pcs] [−] [−] [−] [−] [m] [kg] [kg] [kg] [kg]

List of Quantities and Symbols

n n1 q r r1 r2 rs s t tk tr v vp v nrel vtrel v1 x y z zk

Electric motor speed Drive drum speed Specific weight of transported material Rotation radius Radius circumscribed by bucket outer edge Radius circumscribed by bucket inner edge Distance of bucket mass point center of gravity projection Bucket trajectory Time Bucket spacing (pitch) Relative bucket cycle Transport speed (belt) Particle speed (velocity) Normal relative velocity Tangential relative velocity Material impact speed Horizontal coordinate of material particle Vertical coordinate of material particle Z coordinate of material particle Number of concurrently scooping buckets

xv

[min−1] [min−1] [kg·m−1] [m] [m] [m] [m] [m] [s] [m] [−] [m·s−1] [m·s−1] [m·s−1] [m·s−1] [m·s−1] [m] [m] [m] [−]

List of Greek Letters

α αk α kor α smyk α val β γ Δt δ δn δt μs μr ν ζ ρp ρv ρs σ1 σ2 σc τc φe φlin φw ψs ω ωsm

Rotation angle of bucket Rotation angle of bucket elevator Tilt of bucket elevator Angle of sliding friction Angle of rolling friction Damping coefficient Angle determining the start of bucket discharge Time interval for step Start angle of bucket discharge Normal overlap Tangential overlap Static friction coefficient Rolling friction coefficient Poisson’s ratio End angle of bucket discharge Volumetric weight of particles Volumetric weight of transported material Apparent density of transported material Main vertical stress Main horizontal stress Shear strength Initial cohesive stress Effective angle of internal friction Linearized angle of internal friction Angle of external friction Angle of repose Angular speed Angular speed of mixed discharge

[°] [°] [°] [°] [°] [−] [°] [s] [°] [m] [m] [−] [−] [−] [°] [kg·m−3] [kg·m−3] [kg·m−3] [Pa] [Pa] [Pa] [Pa] [°] [°] [°] [°] [s−1] [s−1]

xvii

List of Subscripts

* i j n p r s t x,y,z

equivalent particle i particle j normal particles rolling static tangential Cartesian vector components

xix

Contribution to the Discipline and Practice

Based on the observations and evaluations of dynamic processes of bulk materials, it is possible to improve and accelerate the equipment design processes, and unplanned outages due to machine malfunction or failure may be minimized. After validation and calibration, these results complement fully the experience and empiric relations necessary for design of such equipment. Using charts, videos, animations, image libraries, and exact definitions of various dependences, e.g., forces, temperatures, moments, required machines may be designed with utmost effectivity. This way, we can design a transport system that will adapt itself to the mechanical and physical properties of the material and will cumulate several functions. For example, in addition to the transport of bulk material, the machine will perform drying and mixing. This book shows how to validate, calibrate, and optimize the dynamic processes for bucket elevators. Along with the continual improvements in accuracy of the methods, and improvements in computer productivity, DEM simulations will become an indispensable standard in the design and verification of innovative transport and storage equipment.

xxi

Chapter 1

Introduction

In practice, the design of transport equipment is implemented based on the ­knowledge of input parameters. New equipment should be designed with respect to the properties of transported materials. The key input parameter of such systems is the knowledge of mechanical and physical properties of transported bulk materials. Based on measurements and determination of such properties, we can calibrate and verify the behavior of such materials using computers. Specific types of elevators or hoppers require specific approaches. These lead to new design methods for transport systems and their optimization and development. Fig. 1.1 shows the existing method of 3D design of transport and storage equipment. Clearly, the whole process of design starts with an assignment and research into the given issue. The process continues with the identification of mechanical and physical properties of the transported material/particle properties. If not available, these must be measured in the laboratory. The properties are inserted into the calculation, which renders dimensional and conceptual ideas about the equipment. Furthermore, the equipment is designed in CAD software, thus providing a specific visualization in 3D. Manufacturing documentation is prepared to be used to produce a prototype. However, the manufacturing of a prototype is often skipped and the equipment is manufactured directly. The existing 3D design approach has many advantages when compared to old 2D design, for example: • Fast production of drawing manufacturing documentation projected from 3D model. • Performance of strength analysis using a 3D model (deformations, strain states). • Fast determination of the properties of the different components (weight, centers of gravity, dimensions, volumes, surface areas, moments of inertia, etc.) • Fast and clear check of conflicts between the components, which decreases the amount of errors in manufacturing documentation. • Modifications of the design (appearance, color, material texture).

© Springer Nature Switzerland AG 2019 D. Gelnar, J. Zegzulka, Discrete Element Method in the Design of Transport Systems, https://doi.org/10.1007/978-3-030-05713-8_1

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2

1 Introduction

Fig. 1.1  3D design of transport and storage equipment

Fig. 1.2  Improved design of transport and storage equipment

• Promotion of the design at various presentations (animations and visualizations in 3D and basic movements may be shown to customers). The disadvantage of 3D approach is the absence of potential simulation tests using the equipment before it is produced. This disadvantage is solved by incorporating DEM into the 3D design approach of transport and storage equipment. One extra dimension means that there is an option to test the dynamic flow of bulk materials in a 3D model and to verify its functionality. It can be seen that the design flow chart (Fig. 1.2) is similar to the existing 3D design approach.

1 Introduction

3

The changes are in the first section, where the DEM simulation library is used to consider functions and calculations of the equipment before the constructional design. This way, it is possible to determine the impact point upon discharge more precisely in bucket elevators, and thus, the position and inclination of the discharge hopper may also be more accurate. The second section of the flow chart shows how the DEM calculation relates to the design proposal, where the completed simulation model is already tested. Using this method, we are able to simulate the dynamic flow of particulate matter using a 3D model of the equipment and to determine whether it functions under the given conditions with the given material – before the equipment is manufactured. This is the main advantage of this new approach to design. Other advantages of the new design approach: • Simulation tests of already manufactured functional or nonfunctional equipment leading to time and money savings. • Fast checks of particulate matter throughput through the transport and storage equipment or entire transport lines. • Equipment testing under critical or destructive conditions. • Testing of new materials and various mixtures, for which the equipment was not designed. Determination of functionality in various positions and conditions, for example, with increased or decreased gravity. • Fast identification of problematic locations and follow-up modification and check of the correct function. • Improved and more accurate conventional calculation methods, creation of libraries of material dynamic flows and charts to speed up the automated design. • Search for new transport principles and innovations. • Concurrent tests using the same machine in several workplaces. • Fast transfer and copying of the equipment 3D model to cooperate online.

Chapter 2

Basic Description of DEM

Discrete Element Method (DEM) is a numerical method that considers the mutual interactions of discrete particles in contact and enables evaluations of mutual force interactions. This method requires equations of translation movement and equations of rotation movement for each particle. The basic model is solved using the linear visco-elasticity  (Fig. 2.1). This calculation uses the parallel connection of the damper with spring (Voight model) as a substitution scheme for each contact, which incorporates rolling and shear friction. More complex calculations also use other inputs, e.g., plastic deformation. In these models, the components of normal forces are calculated according to the theory of Herz’s contacts [1]. In the kinetic Eq. (2.1), there are also the tangential forces that were defined by Mindlin [2] and Mindlin Deresiewicz [3]. The basis of these frictional tangential forces is the Coulomb law of the friction model, which is explained in Cundall and Strack [4]. The equations also include the damper components of normal and tangential force for which the coefficient of damping relates to the coefficient of restitution. These parameters were explained in Tsuji, Tanaka, and Ishida [5]. The input values that need to be included in DEM before the calculation are related to the used substitution scheme of contact. For contact (particle-particle) and (particle-geometry) static friction, coefficient of rolling friction and the coefficient of restitution must be defined. Other parameters, such as grain size (granulometry), angle of internal and external friction, cohesive bond angle of repose (moisture), density, and others, serve us to describe the bulk material and bulk particle formation in DEM (Fig. 2.2). There are ten possible mechanisms of the flow of particles in the bulk material according to the theory by Jiří Zegulka [6]. If the models of contacts are arranged in individual mechanisms, we can examine the input parameters in DEM from a higher perspective. The percentage representation of individual basic flow mechanisms in bulk materials determines the parameter of the internal and external friction, and it is useful to use them as additional mechanical-physical parameters in the DEM for faster calculations (Fig. 2.3). Translation movement equations: © Springer Nature Switzerland AG 2019 D. Gelnar, J. Zegzulka, Discrete Element Method in the Design of Transport Systems, https://doi.org/10.1007/978-3-030-05713-8_2

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2  Basic Description of DEM

Fig. 2.1  Substituting visco-elastic scheme of contacts between particles

mi

    dvi  = ∑FCEij = ∑ Fijn + Fijt + mi ·g dt j j

(

)

(2.1)

Equation of particle rotation: Ii

    dωi = ∑MCEij = ∑ Mijt + Mijr dt j j

(

)

(2.2)

Hertz-Mindlin contacts and other contacts are defined and used in EDEM software in Fig. 2.4, which was used to simulate calculations in this book. This way, the user does not need to know and program these equations but just chooses the most suitable contact required by the equipment according to the mechanical and physical principles. The software is under continuous development, and new functions are added into the programs to improve the accuracy of the simulated results. The equations of individual contacts are also listed in the manual of Edem software. For basic Herz-Midling contact (no slip), this manual lists the following equations. In particular, the normal force, Fn, is a function of normal overlap δnand is given by



Fn =

3 4 ∗ ⋅ E ⋅ R∗ ⋅ δ n2 3

(2.3)

2  Basic Description of DEM

7

Fig. 2.2  Schematic of simplified Hertz-Mindlin contact model between two particles

where the equivalent Young’s Modulus E∗ and the equivalent radius R∗are defined as

(

) (



1 −ν i2 1 −ν 2j 1 = + Ei Ej E∗



1 1 1 = + ∗ Ri R j R

)

(2.4) (2.5)



2  Basic Description of DEM

8

Fig. 2.3  Mechanism of the flow – a new perspective on the calculation of internal friction

Fig. 2.4  Contact models in EDEM

with Ei, νi, Ri, and Ej, νj, Rj being the Young’s Modulus, Poisson ratio, and Radius of each sphere in contact. Additionally there is a damping force, Fnd , given by



Fnd = −2 ⋅

5  ⋅ β ⋅ vnrel ⋅ Sn ·m∗ 6

(2.6)

−1



 1 1  m∗ =  +  m m  j   i

(2.7)

2  Basic Description of DEM

9

 where m∗ is the equivalent mass, vnrel is the normal component of the relative velocity and β and Sn (the normal stiffness) are given by

β=

lne



ln e + π 2



Sn = 2 ⋅ E ∗ ⋅ R ∗ ⋅ δ n

(2.8)

2

(2.9)



where e is the coefficient of restitution. The tangential force, Ft, depends on tangential overlap δt and the tangential stiffness St.

with Ft = −St ⋅ δ t



St = 8 ⋅ GM∗ ⋅ R∗ ⋅ δ n

(2.10) (2.11)



here GM∗ is the equivalent shear modulus. Additionally, tangential damping is given by:



Ft d = −2 ⋅

5  ⋅β ⋅ vtrel ⋅ St ⋅ m∗ 6

(2.12)

 where vtrel is the relative tangential velocity. The tangential force is limited by Coulomb friction μs · Fn where μs is the coefficient of static friction. For simulations in witch rolling friction is important, this is accounted for by applying a torque to the contacting surfaces.

τ i = − µr ⋅ Fn ⋅ Ri ⋅ ωi

(2.13)

where μr is the coefficient of rolling friction, Ri is the distance of the contact point from the center of mass and ωi, the unit angular velocity vector of the object at the contact point. The tangential torque is defined by:

MijT = Ri ⋅ nij ⋅ FijT

(2.14)



and rolling friction torque is defined by: Mijr = − µr ⋅ Ri ⋅ FijN ⋅

ωi − ω j ωi − ω j

(2.15)

All these basic equations are processed and used by the program to calculate the forces and moments in the individual cycles, always shifted by the time step (Fig. 2.5).

2  Basic Description of DEM

10

Fig. 2.5  Calculation procedure involved in DEM simulation

This time step is an important parameter and it is necessary to select it correctly. If this parameter is selected incorrectly, the calculation is unstable and the simulation does not work or is distorted. Increasing the number and complexity of contacts, the time intensity of the calculation increases too. The critical step is calculated according to the formula:



ρ  π · R·  p   GM  TR = ( 0.1631·v + 0.8766 )

(2.14)

where R is the particle’s radius, ρp its density, GM the shear modulus, and v the Poisson’s ratio. To optimize the transport equipment via simulations, we need to verify whether the dynamic flow calculation corresponds to the real situation. First of all, we perform a basic calibration of the material in which we form and calibrate the model of bulk material according to the mechanical and physical properties. Therefore, simulations must be validated and calibrated in simple processes as they need to be the same also in simulating more complex transport and storage processes, or with the smallest possible deviation from the real situation (see Fig. 2.6). Each transport and storage equipment is somehow specific as well as the dynamic processes of material behavior in such machines. It is therefore necessary to perform the validation and calibration directly on the given machine. Figure 2.8 describes the use of validation with the real model and theoretical calculation of the equipment. The validation according to this theory is distorted, though, since the calculations related to filling and discharge from the equipment are calculated by means of the mass point. As a result, validation using a physical model is used. The basic calibration data required as inputs for DEM are measured in the laboratory using various world-renowned measuring devices or using new experimental devices. For example, see the calibration measurement of a bulk angle of repose according to the patent [7, 8] (Fig. 2.7).

2  Basic Description of DEM

Fig. 2.6  Calibration and validation process

11

12

2  Basic Description of DEM

Fig. 2.7  Basic material calibration

The subsequent validation of the flow of bulk material and the detailed calibration of the properties of this bulk material is measured on the validation machines [9–23], which are real twins of the digital simulation models (Fig. 2.8).

2  Basic Description of DEM

Fig. 2.8  Detail calibration and validation of the validation equipment

13

14

2  Basic Description of DEM

Fig. 2.9  Software for DEM computing

The noncommercial and commercial DEM software is used as a tool for these simulation calculations of force effects and moments (see Fig. 2.9.). These days the majority of these programs can be used with FEM [24], CFD [25], or MBD [26] methods.

References 1. Hertz, H.: On the contact of elastic solids. J. reine und angewandte Mathematik. 92, 156–171 (1882) 2. Mindlin, R.D.: Compliance of elastic bodies in contact. J. Appl. Mech. 16, 259–268 (1949) 3. Mindlin, R.D., Deresiewicz, H.: Elastic spheres in contact under varying oblique forces. Trans. ASME, J. Appl. Mech. 20, 327–344 (1953) 4. Cundall, P.A., Strack, O.D.: A discrete numberical model for granular assemblies. Geotechnique. 29, 47–65 (1979) 5. Tsuji, Y., Tanaka, T., Ishida, T.: Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technol. 71, 239–250 (1992) 6. Zegzulka, J.: Mechanics of Bulk Materials, 1st edn, p.  186. VŠB  - Technical University of Ostrava, Ostrava (2004). ISBN 80-248-0699-1

References

15

7. Gelnar, D., Zegzulka, J., Šooš, Ĺ., Nečas, J., Juchelková, D.: Validation device and method of measuring static and dynamic angle of discharge. VŠB - Technical University of Ostrava, ­patent number 306123 (2015) 8. Gelnar, D., Rozbroj, J., Zegzulka, J., Nečas, J.: Measuring equipment of angle repose. VŠB Technical University of Ostrava, industrial design number 36213 (2013) 9. Gelnar, D., Zegzuka, J., Nečas, J., Juchelková, D.: Validation bucket elevator for modelling of mechanical processes and method of modelling of mechanical processes. VŠB - Technical University of Ostrava, patent number 304329 (2013) 10. Gelnar, D., Zegzulka, J., Nečas, J., Juchelková, D.: Validation bucket elevator for modelling of mechanical processes. VŠB - Technical University of Ostrava, utility model number 26154 (2013) 11. Gelnar, D., Zegzulka, J., Nečas, J., Juchelková, D.: Validation bucket elevator. VŠB - Technical University of Ostrava, industrial design number 35542 (2012) 12. Zegzulka, J., Bortlík, P., Dokoupil, O., Brázda, R., Nečas, J.: Method of simulating kinetics of movement of bulk material particles and device for making the same. VŠB  - Technical University of Ostrava, patent number 303348 (2008) 13. Rozbroj, J., Zegzulka, J., Nečas, J., Gelnar, D.: Validation vertical screw conveyor and method of modeling mechanical processes by making use thereof. VŠB  - Technical University of Ostrava, patent number 305150 (2013) 14. Gelnar, D., Zegzulka, J., Nečas, J., Juchelková, D.: Method of modeling mechanical processes of bulk materials and device for making the same. VŠB - Technical University of Ostrava, patent number 305194 (2013) 15. Gelnar, D., Zegzulka, J., Nečas, J., Juchelková, D.: Device for modeling mechanical processes of bulk materials VŠB - Technical University of Ostrava, utility model number 27421 (2014) 16. Gelnar, D., Zegzulka, J., Nečas, J., Juchelková, D.: Validation vibration conveyor. VŠB  Technical University of Ostrava, industrial design number 35809 (2012) 17. Žídek, M., Zegzulka, J., Nečas, J., Juchelková, D.: Validation chain conveyor with drivers and method of modeling mechanical processes by making use thereof. VŠB - Technical University of Ostrava, patent number 305136 (2013) 18. Žurovec, D., Gelnar, D., Zegzulka, J., Nečas, J.: Validation storage device for measuring flow processes of bulk material using electrical capacitance tomography method. VŠB - Technical University of Ostrava, patent number 306017 (2014) 19. Žurovec, D., Gelnar, D., Zegzulka, J., Nečas, J.: Validation storage device for measuring flow processes by tomographic method. VŠB - Technical University of Ostrava, utility model number 28424 (2015) 20. Žídek, M., Rozbroj, J., Zegzulka, J., Nečas, J., Marschalko, M.: A validation system of traction and pressing tools. VŠB - Technical University of Ostrava, patent number 306578 (2015) 21. Žídek, M., Rozbroj, J., Zegzulka, J., Nečas, J., Marschalko, M.: Validation bucket elevator for modelling of mechanical processes. VŠB - Technical University of Ostrava, utility model number 28181 (2015) 22. Rozbroj, J., Zegzulka, J., Nečas, J., Gelnar, D.: Validation vertical screw conveyor. VŠB  Technical University of Ostrava, utility model number 28349 (2015) 23. Hlosta, J., Žurovec, D., Zádrapa, F., Zegzulka, J.: Device for measuring the aeration properties of powders and loose materials with a cylindrical chamber. VŠB - Technical University of Ostrava, industrial design number 40388 (2015) 24. Forsström, D., Pär, J.: Calibration and validation of a large scale abrasive wear model by coupling DEM-FEM: local failure prediction from abrasive wear of tipper bodies during unloading of granular material. Eng. Fail. Anal. 66, 274–283 (2016) 25. Hendrik, O., Kerst, K., Roloff, C., Janiga, G., Katterfeld, A.: CFD-DEM simulation and experimental investigation of the flow behavior of lunar regolith JSC-1A. Particuology. (2018). in press 26. Barrios, G.K., Tavares, L.M.: A preliminary model of high pressure roll grinding using the discrete element method and multi-body dynamics coupling. Int. J. Miner. Process. 156, 32–42 (2016)

Chapter 3

Basic Description of Bucket Elevators

Bucket elevators have long been inseparable parts of transport systems. In practice, the most common designs are direct vertical, inclined, or discharge conveyors (Fig. 3.1) according to ČSN 262001 [1]. Figure 3.2 below gives a more detailed division and the bucket elevators are structurally divided according to ČSN 262001 [1]. The figure shows: (a) The vertical high speed bucket elevator – (v ≥ 1 m·s−1) with centrifugal discharge and with direct flow external filling with a chain or belt conveyor with a single or double shaft. (b) The vertical slow bucket elevator – (v ≤ 0.8 m·s−1) with internal gravity discharge and internal filling with a chain conveyor with buckets in close connection and with a single or double shaft. (c) The vertical slow bucket elevator – (v ≤ 0.8 m·s−1) with external gravity discharge and direct flow filling with a chain conveyor with buckets in close connection and a single or double shaft. (d) The vertical slow bucket elevator – (v ≤ 0.8 m·s−1) with internal gravity discharge and with direct flow or scooping filling with a chain conveyor with a single or double shaft. (e) The vertical slow bucket elevator – (v ≤ 0.8 m·s−1) with external gravity discharge and direct flow or scooping filling with a chain conveyor with a single shaft. The discharge is easy due to the deflected chain wheels. (f) The inclined bucket elevator – (v ≤ 1 m·s−1) with external gravity discharge and direct flow or scooping filling with chain or belt conveyor with or without a shaft. (g) The desk (shelf elevator) (v ≤ 0.8 m·s−1) with side filling and discharge with one or two chains conveyors on which shelves are attached with or without a shaft. (h) The pocket elevator (v ≤ 0.8 m·s−1) with external discharge and with direct flow or external filling with a belt that forms pockets as a conveyor with or without a shaft.

© Springer Nature Switzerland AG 2019 D. Gelnar, J. Zegzulka, Discrete Element Method in the Design of Transport Systems, https://doi.org/10.1007/978-3-030-05713-8_3

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18

Fig. 3.1  Basic types of bucket elevators

Fig. 3.2  Types of bucket elevators

3  Basic Description of Bucket Elevators

3  Basic Description of Bucket Elevators

19

(i) The gravity bucket elevator (v about 0.5 m·s−1) with external or internal gravity discharge of dump buckets and with direct or external filling with a chain conveyor with or without a shaft. They are popular due to their high performance in vertical direction, their simple design, small built-up area, and broad usage options in various branches of the industry. In the past, these machines were used predominantly to transport water (Fig. 3.3); however, with the development of pumps, the use of bucket elevators has changed. As for the transported materials, they switched to fine-grained or fine-­ shredded bulk materials. Bulk materials are transported in the vertical or inclined direction upwards, in the containers called buckets. According to the type of industry or transported material, the buckets may be made of steel sheet, aluminum cast, or plastic, and attached with bolts or pins to the pulling device. Such a pulling device may consist of a simple belt (rubber, PVC, mesh), buckle or link chains, or even a rope (Fig. 3.4).

Fig. 3.3  Bucket elevators as lift pumps

Fig. 3.4  Variants of bucket attachment

20

3  Basic Description of Bucket Elevators

Except for the buckets (Fig. 3.5) and pulling device, which are adjusted so as to create an endless system, the conveyor in its upper section also includes a power train, with a drive drum and the drive itself. This part is called the elevator head. The bottom section, called the elevator boot, includes a tensioner with a tensioning drum. The entire conveyor mechanism is encapsulated in the dustproof shaft which protects the surroundings against the unfavorable influences of the material (dust) and covers the moving parts of the machine. Bucket elevators are made of materials resistant to damage, and they can be used both indoors and outdoors. Figure 3.6 shows the main components of the bucket elevator. Although mechanical elevators have had a long history, there is still a lot to improve in order to increase their efficiency, decrease power consumption, and avoid the wear of the machine parts. Companies that focus on the development and manufacture of bucket elevators usually employ 3D design methods. The outputs of such methods are 3D models used to determine many unknown quantities, for example, weight, volume, design, strength parameters, and center of gravity. 3D models also help to create the drawing documentation and check for correctness, which naturally makes the design of the equipment cheaper and faster. This way, expensive prototypes may be avoided. Until recently, the most important factor, i.e., whether the equipment will function with the specific particulate matter, could not be verified without manufacturing a prototype and subsequent tests, or without designers and developers’ long-term experience  (Fig.  3.7). The requirements imposed on any developed equipment are much higher today. Therefore, it is necessary to look at the issue also from the scientific point of view and apply new design methods for the development and validation. In order to be able to design a bucket elevator that will function at maximum efficiency and free of failure, it is first necessary to understand the mechanical and physical properties of the bulk materials transported by a bucket elevator. There are many parameters that influence the movement of a particle in the bucket conveyor, for example, internal friction, external friction, rolling friction, repose angle, granulometry, shape of particles, apparent density, humidity (cohesive bonds), temperature, or bounce of particles. In order to select the proper type of bucket elevator and do the basic design calculations, these parameters must first be measured in the laboratory. Of course, determining the mechanical and physical properties is only a part of the information we need to develop the bucket elevator. It is the dynamic behavior of the material in the given process that may render the overall picture for the design of such machines. In general, the design and testing are being gradually simplified thanks to advanced hardware and software means. Many applications have been made to calculate the dynamics of particles. At present, science employs more visual means of communication, and the results may be presented in the form of photographs and video clips, which makes science more accessible to broader audiences of developers and designers. They do not need to solve complex differential motion equations,

3  Basic Description of Bucket Elevators

Fig. 3.5  Division of buckets according to ČSN 26 2008 and DIN standard [2–7]

21

22

3  Basic Description of Bucket Elevators

Fig. 3.6  Structure of a bucket elevator

integrals, and derivations, since these are already hidden deep inside the calculation applications. They only need to feed the measured values and observe what is happening on the designed conveyor in the given moment. Due to the high speed of the action, the material dynamic flow is difficult to observe in such equipment. Therefore, the motion is slowed down using a high-speed camera. Using DEM, the dynamic flow of the bulk material can be stopped or played slowly directly after the calculation of simulation, using various frame rates. Figure 3.8 shows some issues that can occur on the bucket elevators. These issues reduce the production rate of the machine and increase the energy intensity, which is caused by poor filing of the bucket, poor material guidance into the hopper or drop of the material through the shaft to the boot of the elevator, etc. These defects cannot be seen in the design of this conveyor by computing the basic equations, but if we create a DEM simulation we can observe these defects and set the conveyor to work better.

3  Basic Description of Bucket Elevators

Fig. 3.7  Main dimensions of bucket elevator modified according to [8]

23

24

Fig. 3.8  Problems on the bucket elevators

3  Basic Description of Bucket Elevators

References

25

References 1. ČSN 26 2001: Device for Continuous Transport of Loads: Bucket and Swing-Tray Elevators, Classification, p. 12. Czech Institute for Standardization, Prague (1994) 2. ČSN 26 2008: Vertical Bucket Elevators: Basic Parameters and Dimensions, p.  8. Czech Institute for Standardization, Prague (1993) 3. DIN 15231: Continuous mechanical handling equipment; bucket elevators, shallow buckets: standard by Deutsches Institut Fur Normung E.V. (German National Standard) (1980–04) 4. DIN 15232: Continuous mechanical handling equipment; bucket elevators, shallow, rounded buckets: standard by Deutsches Institut Fur Normung E.V. (German National Standard) (1980–04) 5. DIN 15233: Continuous mechanical handling equipment; bucket elevators, medium deep buckets: standard by Deutsches Institut Fur Normung E.V. (German National Standard) (1980–04) 6. DIN 15234: Continuous mechanical handling equipment; bucket elevators, deep buckets with flat rear wall: standard by Deutsches Institut Fur Normung E.V. (German National Standard) (1980–04) 7. DIN 15235: Continuous mechanical handling equipment; bucket elevators, deep buckets with curved rear wall: standard by Deutsches Institut Fur Normung E.V. (German National Standard) (1980–04) 8. Polák, J., Bailotty, K., Pavliska, J., Hrabovský, L.: Transport and Handling Devices II, 1st edn, p. 104. VŠB - Technical University of Ostrava, Ostrava (2003). ISBN 80-248-0493-X

Chapter 4

Bucket Elevator Filling and Discharge

The industry requires high working heights of bucket elevators, high performance in transport and speeds under simultaneous reductions in production costs, power consumption, wear, and noise. This calls for the design of transport equipment using innovative approaches in the field to limit all possible losses during the conveyor operation. The loss may be significantly reduced through the choice of right parameters from the very start of the development of the transport equipment, for example: • • • • • • • •

Selection of the design variant Modification of mechanical and physical properties of the material Modification of mechanical and physical properties of the surroundings Adjusting the shape of the filling and discharge area The shape, material, and size of the buckets Adjusting the buckets spacing Distributing the buckets on the belt Machine transport speed

All these aspects are interdependent, as implied in the formula to calculate transport volume of a bucket elevator. According to this formula (4.1) [1–5], we may calculate the hourly amount of material important for the initial specification of the machine. However, this formula contains one value we cannot predict accurately without measurements on the specific manufactured machine. This is the so-called filling factor kφ (Fig. 4.1). This value fluctuates in dependence on other parameters in the formula, as well as on the geometry of the machine and its buckets.

Qh = Vk ⋅ kϕ ⋅

v ⋅ 3.6 ⋅ ρ s t ⋅ h −1  (4.1) tk

© Springer Nature Switzerland AG 2019 D. Gelnar, J. Zegzulka, Discrete Element Method in the Design of Transport Systems, https://doi.org/10.1007/978-3-030-05713-8_4

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4  Bucket Elevator Filling and Discharge

Fig. 4.1  Filling factor

where Vk – Water volume of buckets [m3], kφ – Filling factor [−], v – Transport speed [m·s−1], tk – Bucket spacing [m], ρs – Apparent density of material [kg·m3].

4  Bucket Elevator Filling and Discharge

29

The choice of the incorrect filling factor in the initial phase can lead to overdesigning or inadequate sizing of the machine. This is presently considered the major problem as it incurs costs both to the manufacturer during production and to the customer during operation and maintenance. Exploring the bucket elevator transport process in detail, it is possible to identify areas to influence the efficiency of the machine and to lower the losses to minimum. These areas are where the dynamic flow of material changes and they are two in regular bucket conveyors. One serves to fill the material into the bucket, at the boot, the other for its discharge at the elevator head (Fig. 4.2). Many design errors occur during the design phase due to insufficient knowledge of flow dynamics during filling or discharge of the machine. The dimensions and distribution of such spaces/components are estimated by designers based on their instinct or experience from previously manufactured equipment. At present, when time and money play the major role in design, it is no longer possible to oversize equipment or to ignore their excessive power consumption. Quite contrary, these parameters deserve due attention. Thanks to limiting losses in the areas mentioned above, the machine may be reclassified into a better power consumption class, ahead of the competitors. This, however, must build on new scientific findings, and more accurate design methods for such machines need to be selected. In the past, many outstanding scientists were interested in increasing the efficiency, particularly

Fig. 4.2  Bucket elevator filling and discharge methods

30

4  Bucket Elevator Filling and Discharge

Fig. 4.3  Bucket elevator discharge – mass point

looking at what was happening to the material during transport in the bucket elevator. This led to various theories that helped to improve many types of equipment. The first document was published in 1913 by Hauffstengel [6]. Later on, this issue was investigated by Beumer, Weihner, [7] Koster [8], and many others. They tried to improve the basic calculation of the discharge process, namely, the method known as the “pole method.” This method, however, has had one drawback. It does not consider the bulk material as an assembly of particles, but it uses the so-called mass point. The mass point is located in the bucket center of gravity during the discharge until the instant, when it gets separated. Consequently, this mass point moves over the throw parabolic trajectory. Figure  4.3 shows the mass point at the instant of separation. Scientists also investigated the behavior of bulk material level in the bucket during discharge. For example, Müller [9] considered the surface area of fluid to be always perpendicular to the resultant of effecting forces. This was disproved by Beumer and Weiner [7], who stated that the material level in the bucket could not be determined precisely since it was also necessary to consider the internal and external friction of the particulate matter against the bucket surfaces. Furthermore, it was presumed that the material level was shaped to a logarithmic spiral starting at the pole of the bucket elevator, the normal of which formed an internal friction angle with the level surface [10–12]. In any case, these theories and calculations were still related to the mass point only. In 1990, Dokoupil [13] and in 1993 Helmut [14] published documents of a completely new insight into the issue. They proposed and created an approximation software to calculate throw trajectory able to determine the level and shaped distribution of the thrown material depending on the shape of the bucket. However, these theories and calculations focus only on the bucket elevator head and cannot be used for a global evaluation of the material dynamic flow throughout the entire transport equipment. Moreover, these mass point calculations are distorted and inaccurate. Nowadays, the limitations to such calculations have been overcome since we have software able to predict the behavior of discrete particles in dependence on mechanical and physical properties, as well as their mutual interactions. This offers a new perspective on the design of such equipment and

4.1  Discharge of Buckets

31

Fig. 4.4  Bucket elevator discharge – DEM

related solutions. Such tools can be used to concentrate on any location of a bucket elevator loaded with a dynamic flow of bulk material (Fig. 4.4). The bulk material flow can be viewed in 3D, enabling evaluation of the different speed and travel vectors. Next, impacts, bounces, and many of other phenomena can be observed, which helps us optimize the capacities of the designed machine with maximum accuracy, while considering various methods of filling and discharge. Katerfeld [15, 16] was among the first to use this method to observe the material dynamic flow during discharge of bucket elevators. In 2014, two documents were published by the Bulk Solids Centre, which deal with the idea to use validated simulation in the design of transport and storage equipment. The first paper was published by Rozbroj and deals with the design of screw conveyors [12, 17]. The second paper by Vyletělek deals with the optimization of hoppers discharge [18, 19]. For the first time, researchers investigated in detail various methods of validation and measurements, which is now expanded in this work to validate and optimize bucket elevators.

4.1  Discharge of Buckets There are three methods of bucket elevator discharge – gravity, mixed, and centrifugal. The abovementioned pole method is good enough to make a quick basic judgment how the proposed bucket elevator will discharge (Fig. 4.5). Using similarity of triangles determined by 0, P, S apexes and parallelogram of forces G, Fc, and v, the following is valid: lp

rs

=

G m⋅g = Fc m ⋅ rs ⋅ ω 2

(4.2)

32

4  Bucket Elevator Filling and Discharge

Fig. 4.5  Bucket elevator discharge – pole method

lp – Distance of poles [m], G – Gravity force of bucket content [N], Fc – Centrifugal force affecting the content of bucket [N], m – Weight of material in bucket [kg], g – Gravitational acceleration [m·s−2], r1 – Radius circumscribed by bucket outer edge [m], r2 – Radius circumscribed by bucket inner edge [m], rs – Distance of mass point center of gravity projection [m]. Modifying the previous equation, the resulting distance of poles is:



lp =

g ω2

[m ]



(4.3)

Method of bucket discharge will be: lp ≥ r2 for gravity discharge lp ≤ r1 for centrifugal discharge if r1 ≤ lp ≤ r2, the discharge method is mixed. Since the abovementioned condition is valid for rs = > r1 ≤ rs ≤ r2, we may identify the angular speed of mixed discharge per given distance of mass point center of gravity projection rs, which is located in the bucket’s center of gravity. The angular speed in the mixed discharge is as follows:

33

4.1  Discharge of Buckets

Fig. 4.6  Bucket elevator discharge methods

ωsm =

g rs

s−1 

(4.4)

If we substitute various radii of projection into Eq. (4.4) depending on rotations, we obtain a chart (Fig. 4.6) that can be divided into two areas based on the pole method. The first is the area of centrifugal discharge; the second is the area of gravity discharge. The red line of mixed discharge is the border between those two.

4.1.1  Gravity Discharge This discharge method is characteristic of slow bucket elevators. It is suitable for abrasive and heavy materials, the particles of which accelerate during discharge until the point of impact due to their own mass energy only. In the first phase, the particles depicted in the three colored layers (Fig. 4.7) remain in the bucket, each in its original position. When the bucket gets rotated over the upper part of drive drum, the material starts to relocate. The particles shift from upper positions over the gradient created by the pile inside the bucket, depending on the dynamic repose angle, and internal and external friction of particles against the bucket walls. In the final phase of rotation, the bucket leaves the top dead center and is already rotated with open side down. The material has a free course now and falls into the discharge hopper along the throw trajectory. When the rotational speed of buckets is increased, the

34

4  Bucket Elevator Filling and Discharge

Fig. 4.7  Description of the material layer transfer in gravity discharge

centrifugal forces start to affect the material. This force influences the formation of a pile as well as the relocation of particles, since the friction and repose angle changed as well. This dynamic repose angle usually increases with the speed as the gravitational effect of the transported particles is decreased by the centrifugal force. Therefore, these particles have less energy for intra-bonding permeance (see also other work by Zegzulka [20] focused on flow mechanisms, particle permeance, and calculations of dissipation work).

4.1.2  Mixed Discharge If the speed is continuously increased at gravity discharge, or the diameter of drive drum is decreased (technically the latter is less real), the equilibrium between the centrifugal and gravitational forces is reached in the top dead center. This way, mixed discharge occurs (Fig.  4.8). Particles may be said to be momentarily in weightlessness. In the top dead center, the particles float in the space of bucket and only minimally change their position until they leave the bucket. When the drive drum top dead center is passed, the trajectory opens due to fact the bucket is rotated with open side downwards and the material starts to get loose due to gravity and leaves the bucket over the throw trajectories as a single cluster. The shape of the

4.1  Discharge of Buckets

35

Fig. 4.8  Description of the material layer transfer in mixed discharge

bulk body depends on the bucket geometry. This mixed discharge is suitable for fine and dusty materials due to their smaller dispersion in the elevator head. This prevents dust formation and progressive fall of material via return branch back to the elevator boot, or outside the transport system.

4.1.3  Centrifugal Discharge The centrifugal force has the major influence in the discharge due to high rotation speed of the bucket. The force pushes the particles to the inner surface of the outer bucket wall. There is an internal friction between the particles, but this time it is not caused by the gravity, but the centrifugal force. Also, there is movement over the pile with repose angle, as in gravity discharge, but this time it occurs in the negative and variable coordinate system, which is rotated from the rotation center in relation to the bucket position (Fig. 4.9). When particles leave the bucket, they decelerate and progressively lose their centrifugal force. When this force is zero, the particles already move due to gravity over the throw trajectories. In order to use such

36

4  Bucket Elevator Filling and Discharge

Fig. 4.9  Description of the material layer transfer in centrifugal discharge

centrifugal force, imposed on the particles by the supporting element, we block them with outer guiding panels mounted on the elevator head. Due to the bounce, we use this energy and accelerate the material movement into the discharge hopper. The discharge of a bucket elevator can be calculated according to basic theoretical formulas using the equation of gravity force and centrifugal force, as well as using the parametric equations of throw trajectories in uniplanar Cartesian coordinates (Figs. 4.9 and 4.10). Gravity force: G = m ⋅ g = VK ⋅ kϕ ⋅ ρ v ⋅ g [ N ]



(4.5)

Centrifugal force:

Fc = m ⋅ rs ⋅ ω 2 [ N ] (4.6) If the gravity and centrifugal forces are identical, the equilibrium is as follows:



m ⋅ rs ⋅ ω 2 ⋅ sin γ = m ⋅ g

(4.7)

37

4.1  Discharge of Buckets

Fig. 4.10  Forces in centrifugal discharge

This equilibrium condition can be used to derive the start angle of bucket discharge:

γ = arcsin⋅

g  °  (4.8) rs ⋅ ω 2  

Material particles that already left the bucket move along the throw trajectories, the parametric equations are as below:

x = v ⋅ sin γ ⋅ t

(4.9)



1 y = v ⋅ cosγ ⋅ t − ⋅ g ⋅ t 2 2

(4.10)

where x – Horizontal coordinate of material particle [m], y – Vertical coordinate of material particle [m], v – Transport speed [m·s−1], γ – Angle determining the start of bucket discharge [°], t – Time [s]. To visualize and verify the dependence of the equations, Excel was used to create an interactive chart to test the setup of different bucket discharge hopper parameters. This way, throw trajectories may be verified according to the theoretic calculations and real results (Fig. 4.11).

38

4  Bucket Elevator Filling and Discharge

Fig. 4.11  Interactive chart to compare throw trajectories and real results

4.2  Bucket Filling Material feeding into the buckets and even distribution of the fed material is important to maintain the correct function of the elevator. The buckets cannot be overfilled or underfilled. Buckets can be filled by direct flow, scooping or combining the direct flow and scooping.

4.2.1  Direct Flow of Material Filling This method is preferred due to a lower drag force during filling and lower wear of the buckets. If a uniform supply of material is not ensured, a suitable feeder or batching component needs to be added upstream the hopper. The process of bucket filling starts when the material flow is released from the hopper at the instant the previous bucket leaves the filling area. The material falls due to gravity along the throw trajectories into the bucket. This way, particles increase their speed until the impact into the bucket. A dynamic force is created in relation to this speed, which functions as a drag against the bucket move-

39

4.2  Bucket Filling

Fig. 4.12  Filling of a bucket elevator with thrown material

ment (Fig. 4.12). If the pulling component (belt) is not tensioned properly, it gets deflected by the material from its usual trajectory. When the edge of the bucket approaches the height of hopper, this edge starts to “cut” the bulk material shaped according to geometry of the hopper. The speed of the bucket, filling trajectory depending on bucket spacing, and the gradient of filling all influence the material volume that can be gathered by the bucket in the filling area. In dependence on the shaft dimensions, the dimension of the bucket influences the possible fall of material into the elevator boot. When the bucket passes the filling area, the material flow gets stabilized. The entire cycle repeats with the next bucket (Fig. 4.13).

4.2.2  Theoretical Calculation of Direct Flow Filling In filling the buckets, it is more important to investigate the drags that must be taken into account when designing power consumption of the drive unit. The drag created during direct flow filling of buckets is as follows (Fig. 4.14): Fs = Vk ⋅ kϕ ⋅ ρ v ⋅ ( v1 + v ) ⋅

v tk

[N]

(4.11)

Material impact speed:

v1 = 2 ⋅ g ⋅ h1

m ⋅ s−1  (4.12)

40

4  Bucket Elevator Filling and Discharge

Fig. 4.13  Filling of a bucket elevator – cutting the bulk material

Fig. 4.14  Diagram of direct flow filling method

where v – Transport speed [m·s−1], v1 – Material impact speed [m·s−1], h1 – Material fall height [m], ρv – Volumetric weight of transported material [kg·m−3], Vk – Volume of bucket [m−3], kφ – Filling factor [−],

4.2  Bucket Filling

41

Fig. 4.15  Bucket edge digging into the bulk material

Fig. 4.16  Filling the bucket with material

tk – Bucket spacing [m], g – Gravitational acceleration [m·s−2].

4.2.3  Scooping of Material This method of filling takes place at the bucket elevator boot under the return drum. The elevator boot is filled with particulate material from the hopper and the bucket executes four phases of scooping. In the first phase, the edge of the bucket gets dug in the bulk material and disturbs the surface of the bulk, which creates the impact and bending moment into the support component, fixation, and pulling component. In this first phase, the correct shape and inclination of the penetrating edge are important since this part is most strained and worn (Fig. 4.15). The next phase is the filling of material into the space of the bucket, when the cut layer of the bulk material is shifted upwards over the internal curved wall of the bucket (Fig. 4.16). The third phase includes the scooping of material along the trajectory in front of the bucket to fill its internal volume. The bucket creates a furrow, into which the material is filled for the next bucket (Fig. 4.17).

42

4  Bucket Elevator Filling and Discharge

Fig. 4.17  Scooping of material in front of the bucket

Fig. 4.18  Completing a scoop with material level stabilization

The last phase includes the movement of bucket out of the engagement and stabilization of material level (Figs. 4.17 and 4.18).

4.2.4  Combined Method of Bucket Filling This method combines the direct flow and scooping methods of material filling. The “chip,” or part of the bulk material annulus, is not taken from the lower part of the boot under the return drum, but the filling is shifted to the location in front of the connection of elevator boot to the working shaft.

4.2.5  Theoretical Calculation of Scooping The scooping method of filling is suitable only for nonabrasive and light materials. It consumes more power and the buckets get more worn. The power consumption for scooping is to be determined as follows: Ph = ck ⋅ Ah ⋅

Vk ⋅ ρ v ⋅ kϕ ⋅ v tk

[W ]

(4.13)

4.2  Bucket Filling

43

Fig. 4.19  Chart of relative cycle tr depending on bucket spacing factor ck [1]

where ck is the bucket spacing factor (see Fig. 4.19), which is the function of a relative bucket cycle tr = 0.224 ⋅

tk rs ⋅ v

(4.14)

rs – Distance of bucket mass point center of gravity projection [m], Ah – Specific work, scooping [J·kg−1]. The specific work of scooping is work A [J] of scooping buckets when filling the material and related to the mass unit:

Ah =

A  J ⋅ kg −1  (4.15) Vk ⋅ kϕ ⋅ ρ v ⋅ zk 

where zk – Number of concurrently scooping buckets [−], kϕ  – Mean filling factor of the buckets taking into account that not all concurrently scooping buckets are filled to the same volume [−].

44

4  Bucket Elevator Filling and Discharge

Fig. 4.20  Diagram of bucket filling by scooping [1]

Taking into account the specific work of scooping enables us to use the results gained by measurements. The work of scooping is given by the surface area under the curve determining the scooping drag Fh [N] in dependence on the bucket trajectory s[m]. If the ideal course is considered as per Fig. 4.20, the scooping work is determined by the mean scooping drag factor Fhs [N] and trajectory of bucket edge s. A = ∫ Fh ⋅ ds = Fhs ⋅ s



[J ]

(4.16)

Mean scooping drag factor: Fhs =



V ⋅ kϕ ⋅ ρ v ⋅ zk A = Ah ⋅ k [ N ] (4.17) s s

Considering that: Vk ⋅ kϕ ⋅ ρ v = q ⋅ t k



(4.18)

will be:



Fhs = Ah ⋅ q ⋅

kϕ ⋅ zk ⋅ t k = Ah ⋅ q ⋅ ck s ⋅ kϕ

q=

Qv ⋅ ρ v Vk = ⋅ ρ v ⋅ kϕ 3600 ⋅ v t k

[N]

(4.19)

where



(4.20)

is the specific weight of the transported material [kg·m−1].

45

4.2  Bucket Filling

Fig. 4.21  Specific digging work in dependence on transport speed [1]

Table 4.1  Properties of bulk material (related to Fig. 4.21) [1] 1. Portland cement 2. Grain 3. Sand, gravel 4. Lumpy cement 5. Black coal, nut

ρv = 1200 kg⋅m–3 ρv = 740 kg⋅m–3 ρv = 1500 kg⋅m–3 ρv = 1250 kg⋅m–3 ρv = 750 kg⋅m–3

Granularity 0.05 mm Granularity 3–5 mm Granularity 2–10 mm Granularity 5–20 mm Granularity 18–30 mm

The values of the specific scooping work are given in Fig. 4.21 for various materials  (Table  4.1) in dependence on the transport speed. The scoop friction drag decreases sharply with a decrease in bucket spacing (Fig. 4.22). However, the bucket spacing cannot be set too small since it would impact the correct filling of buckets. The combined (mixed) method of filling occurs when the direct flow is imperfect and part of the material falls around the buckets to the shaft bottom, from where it is lifted again. To calculate the discharge and filling, the available formulas and charts are suitable only for the very first approach to determine the volume of transported bulk material and power of the drive unit. These formulas and charts [1] are available only for five types of material. Furthermore, it is not clear which bucket shape and elevator boot geometry they were determined for. If we need to make calculations for different materials than those in charts, the scooping force must be measured and scooping work calculated using calculation formulas for power consumption. However, we may use the discrete element method and determine these values via simulation.

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4  Bucket Elevator Filling and Discharge

Fig. 4.22  Digging force in dependence on bucket spacing [1]

References 1. Dražan, F.: Theory and Design of Conveyors, 1st edn, p.  290. Czech Technical University Prague, Prague (1983) 2. Dražan, F., Jeřábek, K.: Handling the Material, 1st edn, p. 456. SNTL – Nakladatelství technické literatury, Prague (1979) 3. Feda, J.: Mechanics of Particulate Materials—The Principles, 2nd edn. Academia Prague, Prague (1982). ISBN 0-444-99712-X 4. Malášek, J.: State of stress identification of transformed  – deformed particular materials. In: Engineering Mechanics 2007, pp.  173–174. Institute of Thermomechanics Academy of Sciences of the Czech Republic, v.v.i, Prague ISBN 978-80-87012-06-2 5. Jasaň, V.: Theory and Design of Conveyors, p. 336. TU Košice, Alfa Bratislava (1984) 6. Hauffstengel, G.J.: Kraftverbrauch von Fördermitteln. Mitteilung über Forschungsarbeiten auf dem Gebiet des Ingenieurwesens, Berlin (1913) 7. Beumer, B., Wehmeier.: Zur Frage des Schopfwiederstandes und Auswurfverhaltnisse bei Becherwerken, Fordern und heben. 1960, 1061 8. Koster, H.K.: Hochleistungsbecherwerke für den Bergbau, Glückauf-forschungshefte. 41/1980, 181–186 9. Müller, C.A.E.: Beitrag zur Klärung des Entleerungsvorganges bei schnellaufenden Becherwerken. Mühlen und Speicherbau 9, 1918 10. Krause, H.: Entleerungsvorgang bei zellenlosen Schaufelradern. 5/1972, 69–76 11. Khosravi, A.M.: Zur Theorie des Schaufelrade. Fordern und Heben, 23/1973, 787–793

References

47

12. Fort, C.J.: Berechnung und Auslegung von Becherwerken. Forder und Heben, 23/1973, 432–436 13. Dokoupil, O.  Emptying of high power bucket elevators. Tutor of dissertation: Prof. Ing. Jaromír Polák, CSc, VŠB - Technical University of Ostrava, Ostrava (1990) 14. Helmut, T.: Einfluß des Entleerungsverhaltens auf Becherform und Becherteilung zur Erhöhung der Leistungsfähigkeit von Becherförderern. Dissertation, Otto-von-Guericke-­ Universität, Magdeburg (1993) 15. Krause, F., Katterfeld, A.: Usage of the Discrete Element Method in Conveyor Technologies. Institute for Conveyor Technologies (IFSL), The Otto-von-Guericke-University of Magdeburg, P.O.Box 4120, D-39016 Magdeburg 16. Katterfeld, A., Donohue, T.J.D.: Application of the discrete element method in mechanical conveying of bulk materials, In: 7th International Conference for Conveying and Handling of Particulate Solids (ChoPS), 7 (Friedrichshafen) 2012.09.10–13 17. Rozbroj, J.: Simulation (DEM) of particular mass movement in screw conveyor applied on structure of vertical screw. Tutor of dissertation: Prof. Ing. Jiří Zegzulka, CSc, VŠB - Technical University of Ostrava, Ostrava (2013) 18. Rozbroj, J.: Use of DEM in the determination of friction parameters on a physical comparative model of a vertical screw conveyor. Chem. Biochem. Eng. Q J ISSN 03529568. (2015-4-6) 19. Vyletělek, J.: Simulation of particular mass movement in hopper applied on structure of hopper model. Tutor of dissertation: Prof. Ing. Jiří Zegzulka, CSc, VŠB - Technical University of Ostrava, Ostrava (2013) 20. Zegzulka, J.: Mechanics of Bulk Materials, 1st edn, p.  186. VŠB  - Technical University of Ostrava, Ostrava (2004). ISBN 80-248-0699-1

Chapter 5

The New Method of Design and Optimization

To optimize the transport equipment via simulations, we need to verify whether the dynamic flow calculation corresponds to the real situation. Therefore, simulations must be validated and calibrated in simple processes as they need to be the same also in simulating more complex transport and storage processes, or with the smallest possible deviation from the real situation (Fig. 5.1). Each transport and storage equipment is somehow specific as well as the dynamic processes of material behavior in such machines. It is therefore necessary to perform the validation and calibration directly on the given machine. Figure 5.2 describes the use of validation with the real model and theoretical calculation of bucket elevators. The validation according to this theory is distorted, though, since the calculations related to filling and discharge from the bucket elevator are calculated by means of the mass point. As a result, validation using a physical model is used.

© Springer Nature Switzerland AG 2019 D. Gelnar, J. Zegzulka, Discrete Element Method in the Design of Transport Systems, https://doi.org/10.1007/978-3-030-05713-8_5

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5  The New Method of Design and Optimization

Fig. 5.1  Validation and detail calibration of the bucket elevator

Fig. 5.2  Validation and calibration schema of the bucket elevator

Chapter 6

Input Parameters for DEM – Bulk Material

The accuracy of each simulation calculation strongly depends on the accuracy of measured input data. It is necessary to ensure that these input values are the same in simulation as in reality. The data input in DEM fall into three groups: Mechanical and Physical Properties of Transported Material and Its Behavior: –– Apparent density, volumetric weight –– Frictional parameters – static, rolling –– Repose angle –– Granulometry (shape of particles) –– Restitution coefficient

6.1  S  election of Particle Shape for Simulation and Real Measurements In order to simulate the dynamic process, it is necessary to define and model the transported material according to the real bulk material. Shape, dimensions, and mechanical and physical properties are to be set for these particles. These parameters are programmed in DEM software in processes according to the measured granulometry and other measured input values. This way, we produce a mixture for dynamic simulations. The basic particle for DEM is a sphere (Fig. 6.1). Other more complex shapes are created by combining the particles. The accuracy of the element depends on the assignment. The shape accuracy is described in Fig. 6.2. The more accurate the definition of the element, the more demanding the calculation. For example, to simulate filling a bucket with 10,000 cubes, the calculation is not executed with this amount, but it is multiplied by the number of particles from which the cube is composed. This means that if we use a cube with the small-

© Springer Nature Switzerland AG 2019 D. Gelnar, J. Zegzulka, Discrete Element Method in the Design of Transport Systems, https://doi.org/10.1007/978-3-030-05713-8_6

51

Fig. 6.1  Basic calibration particles of the smallest shape accuracy for simulation measurements

52 6  Input Parameters for DEM – Bulk Material

6.1  Selection of Particle Shape for Simulation and Real Measurements

53

Fig. 6.2  Various shape accuracy of a cube composed of spherical particles

Fig. 6.3  Real and 3D models of calibration particles for DEM

est shape accuracy composed of eight spheres, the simulation calculates with 80,000 particles. This difference leads to excessive prolongation of the calculation time. For the initial examination of dynamic flow, it is good to select the generated number of particles up to 500,000 pieces, when a standard desktop computer is used. Exceeding this amount, it is necessary to use a more powerful workstation to avoid long computational times. Further to the above mentioned, the simplest shape of calibration particle is selected, i.e., a sphere. It is the basic structural element in EDEM software to simulate the geometry of bulk material and it is the most shape accurate within DEM. For this reason, we selected spherical particles for the real bulk material. Airsoft pellets were the best fit. Airsoft pellets have a stable shape and their properties do not change along with the surrounding conditions during later validation. Furthermore, airsoft pellets are accurate in dimensions as the plastic spherical particle has a diameter of 6 mm. They are usually sold from 2000 to 5000 pcs in various colors, as ammunition for airsoft guns (Fig. 6.3). For the initial research in the methods of measurement, imaging, and settings of the equipment, discrete particles were discharged from the bucket. Glass spheres in three dimensions were used. Since spherical particles are not the usual bulk material transported in bucket elevators, we tested other materials of various shapes and sizes. These were mutually compared during the dynamic flow to determine the

54

6  Input Parameters for DEM – Bulk Material

Fig. 6.4  Measurement materials

extent of their dissimilarity from spherical calibration particles that are always for the initial DEM design assessment. We used 2 types of pellet materials, 12 agricultural materials, and 4 blasting materials. The last were tested under the project by the Technology Agency of the Czech Republic TA0301158 “Innovative solution of devices burdened with abrasiveness.” The materials are depicted in Figs. 6.4 and 6.5. When the examined materials are selected, we can continue to measure and determine their mechanical and physical properties. In this case, the experiments were carried out in the Bulk Solids Centre, which is fully equipped to determine all the key parameters (Fig. 6.6).

6.2  Measurements of Apparent Density and Volumetric Weight

55

Fig. 6.5  Measurement materials

Fig. 6.6  Premises of the Bulk Solids Centre

6.2  M  easurements of Apparent Density and Volumetric Weight Volumetric weight of the samples was measured using a measuring cylinder and precise scale. The measuring cylinder was filled with water of exact volume. Next, calibration particles were weighed and poured into the water in the measuring cylinder. The difference in volume defined the volume of inserted particles (Eq. 6.1).

56

6  Input Parameters for DEM – Bulk Material

Fig. 6.7  Measurement of volumetric weight – black particles

This value was subsequently used to calculate the volumetric weight – see calculation (6.2). Volume of particles [m3]:

Vp = VT − Vw ,



Vp = 0.234 − 0.15 = 0.084 l = 0.000084 m 3

(6.1)



Particle weight was determined before they were inserted into the measuring cylinder: mp = 0.15 kg. Volumetric weight of particles: ρp = [kg·m−3]

ρp =



ρp =

mp Vp 0.15 = 1785.71kg.m −3 0.000084

(6.2)

This measurement method of apparent density was used only for calibration spherical particles since this parameter is generated automatically when measuring the internal friction at Schulze shear machine (Fig. 6.7).

6.3  Measurements of Internal Friction Internal friction is another material parameter to be determined. It is important particularly for the scooping method of bucket filling, being one of the drags preventing the buckets to be filled. The measurements were executed using a ring shear tester which measures the internal and external friction by simply changing the measuring accessories. It also compares the results. The instrument is connected to a computer

6.4  Measurements of External Friction

57

Fig. 6.8  Schulze shear machine, RST-01, in the Bulk Solids Centre

unit delivered with RST-95 standard software. The principle of internal friction angle measurement in shear testers is based on the measurement of time-shear forces dependence, necessary to transform the bulk body in the shear chamber by means of a shear zone under the action of normal load for the given density of bulk material. The density for the given measurement is ensured via consolidation (compaction) under known loading force. This system enables us to record changes in the mechanical and physical properties of bulk materials in dependence on the changes of tension of stress. The shear force is caused by the rotation of the entire instrument, and the torque is transferred by two pull rods attached to the shear cover during the test (Figs. 6.8 and 6.9).

6.4  Measurements of External Friction The external friction angle was measured using a Jenike reciprocating shear machine. The principle is based on measuring time-shear forces dependence necessary to transform the bulk body in the shear chamber by means of a shear zone under the action of normal load for the given density of bulk material. The density for the given measurement is ensured via consolidation (compaction) under preset,

58

6  Input Parameters for DEM – Bulk Material

Fig. 6.9  Internal friction angle measurement results in black spheres (see Appendix 1)

6.5  Measurements of Repose Angle

59

Fig. 6.10  Jenike reciprocating shear machine in the Bulk Solids Centre

known loading force, i.e., the tension in the bulk material volume in the shear chamber. This system enables us to record changes in the mechanical and physical properties of bulk materials in dependence on tension, i.e., on bulk material layer height in the hopper, which influences the density. The shear forces are induced by the moving arbor with a strain gauge located on its end. The strain gauge deformations are sensed, converted into electric signal, and recorded (Figs. 6.10 and 6.11).

6.5  Measurements of Repose Angle The repose angle was measured using a Zenegero machine that measures static and dynamic repose angles, etc., patent [1]. The instrument contains a vibrating feeder which transfers the measured material above the directing funnel. After passing the funnel, the material falls on a steel tray, where a pile is created. The tray starts to rotate when the pile is created to record the particles with a camera from all sides. Next, to measure repose angle, the data stored in the form of photographs and video clips are analyzed using software (Figs. 6.12, 6.13, and 6.14).

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6  Input Parameters for DEM – Bulk Material

Fig. 6.11  External friction angle measurement results in black spheres

6.6  Measurements of Particle Size Distribution

61

Fig. 6.12  Repose angle measurement in the Bulk Solids Centre

Fig. 6.13  Zenegero machine without covering panels

6.6  Measurements of Particle Size Distribution This measurement was executed using a CILAS particle size laser analyzer. The instrument measures the distribution of particle sizes in a sample of a continuous dimension from 0.04 to 2500 μm, without optical configuration or calibration of the instrument. The instrument is also equipped with a microscope and CCD camera to display the shapes of the particles (Fig. 6.15). The measurements are carried out with material samples using the dry or wet method. The coherent light from a low-power laser diode, emitted at 830 nm wave length, passes the cuvette with the analyzed sample dispersed in the fluid or air. The light beam gets scattered.

62

6  Input Parameters for DEM – Bulk Material

Fig. 6.14  Results of repose angle measurement results in black spheres

6.6  Measurements of Particle Size Distribution

63

Fig. 6.15  CILAS 1190 measuring instrument in the Bulk Solids Centre

The distribution of the light energy in the distribution pattern depends on the particle size, on which the scattering takes place. If all the particles have a spherical shape and identical size, the scattered energy creates the so-called AIRY pattern, which means we obtain an infinite set of the mean path and a series of concentric circles, the diameters of which are inversely proportional to the particle diameter. The smaller the particles, the larger the scattering angle. On the contrary, if particles vary in dimensions, the scattering pattern in monotonous. The particle size distribution can only be determined by the analysis of energy distribution between the various coronas displayed at the plane of lens image. Since this instrument can measure particle size only up to 2 mm, it was necessary to use another measuring instrument, CAMSIZER, for larger particle sizes. This granulometer is an optoelectronic instrument to measure size and shape of particles of freely flowing bulk materials from 30 μm to 30 mm. The instrument contains a planar source of light, measured material feeder, two CCD cameras to make images of the bulk materials, cleaning pneumatic unit, and a computer with analyzing software. The measured sample is inserted into the funnel, from where the bulk material is taken by means of a small vibrating feeder. The feeder supplies the material above the measuring zone, where the discrete particles fall over the edge of the gutter and pass through the instrument. During the passage, images are made using one or both CCD cameras, which are later analyzed (Fig. 6.16).

6  Input Parameters for DEM – Bulk Material

64

Fig. 6.16  CAMSIZER measuring instrument in the Bulk Solids Centre

6.7  Measurements of Coefficient of Restitution The coefficient of restitution is measured on a height-adjustable stand, from which a particle falls down (see Fig. 6.25). The particle falls on a pad made of the same material as in the bucket elevator to simulate the interactions. Mathematically, the restitution coefficient is given by the following formula (6.3): e=

hp Hp

[ −]

(6.3)

It was necessary to map the trajectory of the particle to determine the heights hp and Hp according to Fig. 6.17. Since this phenomenon is quite fast, the bounce of the particle is recorded on an I-SPEED 2 high-speed camera. The camera is equipped with software able to trace the particle trajectory and put it in the uniplanar Cartesian coordinate system. Thanks to calibration, the shift in pixels can be converted to millimeters and the coordinates exported to Microsoft Excel, which subtracts the heights necessary to calculate the coefficient (Figs. 6.18, 6.19, and 6.20).

6.8  Measurements of Sliding Friction

65

Fig. 6.17  Recorded heights to calculate the coefficient of restitution

Fig. 6.18  Olympus high-speed camera with traced trajectory of particle bounce

6.8  Measurements of Sliding Friction Sliding friction is another parameter vital for DEM. This value is measured using an inclined plane, along which a plate created from the transported material (spherical particles) moves (Figs. 6.21, 6.22 and 6.23). When the plane is inclined, the plate made of particles starts moving. The entire cycle of one measurement closes, when this plate stops. Next, the inclination of plane reverses and the measurements continue. Video clips from the measurements are recorded, which can be used to evaluate the instant the plate starts to shift in dependence on the angle of inclination. The angle is recorded by a Bosch digital protractor. The angle tangent represents the sliding friction of measured particles in the interaction with plates made of the given

66

6  Input Parameters for DEM – Bulk Material

Fig. 6.19  Measurements of the coefficient of restitution in black spheres

6.8  Measurements of Sliding Friction

Fig. 6.20  Restitution coefficient measurement results in black spheres – jump

67

68

6  Input Parameters for DEM – Bulk Material

Fig. 6.21  Diagram of sliding friction measurements

Fig. 6.22  Measuring instrument in the Bulk Solids Centre – patent [2]

material in contact with particles during the dynamic flow inside the instrument. Such friction can be measured also on Jenike or Schulze shear machines.

6.9  Measurements of Rolling Friction The measurements of rolling friction were executed in the similar manner as above (sliding friction). It is also measured using an inclined plane, along which a plate interacting with spherical particles moves (Figs.  6.24, 6.25 and 6.26). When the plate is inclined, the upper plate loaded with 1.1 kg weight starts to move. The entire

6.9  Measurements of Rolling Friction

Fig. 6.23  Sliding friction measurement results in black spheres

69

70

6  Input Parameters for DEM – Bulk Material

Fig. 6.24  Diagram of rolling friction measurements

Fig. 6.25  Measuring instrument in the Bulk Solids Centre – patent [2]

cycle of one measurement closes, when this plate stops at the end stop. The inclination of the plate reverses and the measurements continue in the reverse direction. Video clips from the measurements are recorded to evaluate the instant the plate starts to move in dependence on the angle of inclination. The plate inclination angle is recorded by a Bosch digital protractor. The angle tangent represents the rolling friction of the measured particles interacting with plates made of the given material in contact with particles during the dynamic flow inside the instrument.

6.9  Measurements of Rolling Friction

Fig. 6.26  Rolling friction measurement results in black spheres

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6  Input Parameters for DEM – Bulk Material

72

6.10  Summary of Results for DEM Input Parameters Tables 6.1 and 6.2 summarize the measured and tabular parameters to be used for DEM. The tabular values of Poisson’s ratio and shear modulus were taken over from the globally recognized Autodesk Inventor material database. Further summary of the measured results is given in the material sheet in Fig. 6.27. Some of the measured results mentioned in the material sheet were not used for DEM validation, and thus, their measurement may seem pointless. This is not true, though, since each measured parameter adds to the understanding how a given property relates to the optimization of the transport equipment. The current DEM simulation methods are in their outset, and they use simple equations, into which only several parameters need to be fed. Along with the expected developments in the area of DEM simulations in the future, the equations will get more complex. Therefore, we are already trying to determine the parameters that influence the transport flow, which will be added into the equations during the further development of DEM.

Table 6.1  Mechanical and physical properties of contact materials Contact material Poisson’s ratio v [−] Shear modulus GM [Pa] Volumetric weight ρp [kg⋅m−3]

ABS plastic, Steel Glass printed 0.3 0.19 0.35 8.08⋅1010 2.86⋅1010 8.89⋅108

ABS plastic particles Plexiglas Rubber 0.35 0.38 0.38 8.89⋅108 8.26⋅108 3.6⋅107

7850

1780

2180

1780

1180

1130

Table 6.2  Mechanical and physical properties of contact material interactions Interactions with plastic particles Restitution coefficient e [−] Static friction coefficient μs [−] Rolling friction coefficient μr [−]

Steel 0.76 0.44

Glass 0.88 0.5

ABS plastic printed 0.34 0.54

ABS plastic particles 0.49 0.4

Plexiglas 0.79 0.54

Rubber 0.49 0.73

0.013

0.005

0.024

0.021

0.004

0.05

6.10  Summary of Results for DEM Input Parameters

Fig. 6.27  Material sheets – black sphere

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6  Input Parameters for DEM – Bulk Material

References 1. Gelnar, D., Zegzulka, J., Šooš, Ĺ., Nečas, J., Juchelková, D.: Validation device and method of measuring static and dynamic angle of discharge. VŠB - Technical University of Ostrava, patent number 306123 (2015) 2. Zegzulka, J., Bortlík, P., Dokoupil, O., Brázda, R., Nečas, J.: Method of simulating kinetics of movement of bulk material particles and device for making the same. VŠB  - Technical University of Ostrava, patent number 303348 (2008)

Chapter 7

Input Parameters for DEM – Geometry of the 3D Model and Validation Machine

Another condition to carry out simulations was the creation of the working environment. In this case, we created a validation and optimization bucket elevator to verify the mathematical calculation simulations with 3D visualization output and calibration bucket. Geometric Parameters of the Equipment • Shape, material, and dimensions of the bucket and material of the whole equipment • Other dimensions and shapes (case, hopper, discharge hopper, bucket spacing) Kinematic Parameters of the Equipment • Translations, rotations, speeds, accelerations, frequencies

7.1  Creation of Simulation Environment In order to be able to use the equipment for various purposes, conditions as in Fig. 7.1 were defined for the design and construction of the machine. Using Autodesk Inventor software and complying with all the abovementioned conditions, we designed, calculated, and modeled a validation bucket elevator, i.e., a 3D simulation model. To compare the real and simulated flows, the 3D model was used to produce manufacturing documentation and to build a real model (Fig. 7.2). Due to the innovative character of the equipment, patent, utility model, and industrial design applications were submitted. These documents protect the equipment, method, and the validation process. The references to the documents are mentioned at the end of the book. The main components of the machine are described in Fig. 7.3 (Table 7.1).

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· · · · · · · · · · · · ·

Mobility Laboratory-size dimensions Options to disassemble and modify the machine Transport of various types of materials Tests under various speeds Sufficient height (trajectory) Changes in carriers Changes in the input and output geometry Transparent cover panels of the machine Continuous or circulation operation Tilting options Attachment of sensors Regular 230°VAC power supply

Fig. 7.1  Conditions for the construction of the validation machine

Fig. 7.2  3D model of the validation bucket elevator and built real model

7.1  Creation of Simulation Environment

Fig. 7.3  Description of validation bucket elevator

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Table 7.1  Specifications of the validation bucket elevator Designation Main dimensions Electric motor power Electric motor speed Electric motor supply voltage Gear ratio Drive drum speed Number of buckets Tilt of bucket elevator Speed control

Values H × W × L – 2002 × 926 × 1220 [mm] P = 0.18 [kW] n = 1350 [min−1] U = 220/400 [V] at 50 [Hz] i = 20 [−] nl = 67.5 [min−1] ik = 18 [pcs] αkor = ± 360 [°] Frequency converter - Siemens

The 3D model must be converted into a suitable format, which may be imported into EDEM simulation software. The machine is quite variable and can be adjusted to different situations incurred in practice – see Figs. 7.4, 7.5, and 7.6. The machine can be easily disassembled, converted, or upgraded as it consists of ITEM grooved aluminum sections.

7.2  Design and Creation of the Validation Bucket To validate DEM, we designed a new universal bucket. First, we made a 3D model of the bucket in Autodesk Inventor software. Next, the bucket 3D model was converted into the suitable format and printed on a 3D printer (Fig.  7.5). This way, technical drawings need not be made and the bucket is produced quickly and accurately. Figure 7.7 gives a simplified dimensional drawing of the bucket. To determine the transport capacity of the bucket, Autodesk Inventor was used to calculate several filled volumes for various levels (see the chart in Fig. 7.8). Real verification measurements with water and plastic spheres followed (Fig. 7.9). Note that the filling height of the bucket is not the same as the volumetric filling. Also, when the bucket is test-filled, it has to be in the working position, since the

7.2  Design and Creation of the Validation Bucket

Fig. 7.4  Different settings of the validation bucket according to the patent [1]

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Fig. 7.5  Another possible variant configuration of the machine according to the patent [1]

7.2  Design and Creation of the Validation Bucket

Fig. 7.6  Rebuilding the machine to another type of machine

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Fig. 7.7  3D model of the calibration (validation) bucket and the printed real model

Fig. 7.8  Main dimensions of the calibration (validation) bucket

7.2  Design and Creation of the Validation Bucket

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Fig. 7.9  Volumes measured in Autodesk Inventor, levels 0–49 mm

volume is also influenced by the elevator inclination (Figs. 7.10, 7.11, 7.12, 7.13, 7.14, 7.15 and 7.16). Because buckets are made of different materials and have different shapes, we tested several commercially available buckets by different manufacturers. Their 3D models were first prepared in order to import them into the simulation. 3D scanning of the surfaces was used as it allows the generation of accurate models for DEM simulations.

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Fig. 7.10  Calibration of validation bucket filling

7.2  Design and Creation of the Validation Bucket

Fig. 7.11  Verification of the material quantities inside the bucket

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Fig. 7.12  Scanning of the buckets using Handyscan 3D instrument

Fig. 7.13  Replacing the bucket with a validator bucket elevator

7.2  Design and Creation of the Validation Bucket

Fig. 7.14  Commercially available plastic buckets

Fig. 7.15  Commercially available steel buckets

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Fig. 7.16  Commercially available steel bucket and prototype of the validation bucket for calibration

Reference 1. Gelnar, D., Zegzuka, J., Nečas, J., Juchelková, D.: Validation bucket elevator for modelling of mechanical processes and method of modelling of mechanical processes. VŠB - Technical University of Ostrava, patent number 304329 (2013)

Chapter 8

Input Parameters – Kinematic Properties

To observe the dynamic flow in dependence on the function of the bucket elevator, it is necessary to set the 3D model of the bucket elevator in motion (Fig. 8.1). In the bucket elevator, it is the bucket that we need to put in the linear or rotation motion. To respect the accurate bucket spacing, it is necessary to program the movement of all the buckets from a single point. In this case, it was the bottom zero position at the elevator boot. Four positions in a single cycle are set for each bucket, namely, the movement upwards, rotation in the elevator head, movement downwards, and rotation in the elevator boot. These movements must be accurately tied together, and it is necessary to know the beginning and end times calculated from the speed and length of the bucket trajectory. Since the buckets start moving from one place, it is necessary to calculate the time dependence between the individual buckets based on their spacing. Since the manual calculation for the buckets is demanding, we prepared an application in Excel to calculate all the data (Fig. 8.2). Next, we feed in the input parameters, such as speed, drum radius, spacing, and the movement beginning and end point coordinates. Other parameters, for example, the timing of the movement beginning and end point, are automatically calculated by the program. These values are fed into DEM simulation. To program one cycle of the bucket, it is necessary to feed 20 values. There are 18 buckets and for each, we need to program 2 rotation cycles. Therefore, 720 values must be fed into the program to investigate only one speed. This is also the reason why only one bucket is programmed for the different speeds during the validation. To observe all the conditions of bucket filling and discharge on the real validation machine, it was equipped with a frequency converter. The basic speed at 50  Hz frequency (without a frequency converter) was calculated using the pole method and firmly set on the transmission in order to reach the mixed method of discharge. The calculation shows the speed of 71.4  min−1. Decreasing the frequency at the converter, we lower the speed and the machine shifts into gravitational discharge, and vice versa. The frequency was increased at 5 Hz increments, in the range from 20 to 100 Hz, in order to investigate all the areas in detail. This rendered 17 ­measured © Springer Nature Switzerland AG 2019 D. Gelnar, J. Zegzulka, Discrete Element Method in the Design of Transport Systems, https://doi.org/10.1007/978-3-030-05713-8_8

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Fig. 8.1  Imported 3D model of the elevator in DEM simulation environment

validation speeds of the validation machine (Table 8.1). To have an idea what speeds are running at specific set frequency, the frequencies were converted into speeds and verified during the measurements using a Voltcraft laser tachometer (Figs. 8.3, 8.4 and 8.5). If the movements of the bucket elevator are programed in the simulation, the material follows. For this purpose, there are generating surfaces in the program (Fig. 8.6), with which we can set the required material shape and locate it for example inside the bucket elevator hopper. Next, we set the amount of particles to be generated by the program in a specific time and the speed of the particle dynamic flow from the generating surface. When these parameters are set, we are ready to run the calculation.

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Fig. 8.2  Time and speed calculation program for the buckets, and a view of input fields in EDEM software

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Table 8.1  Frequencies used during the validation measurements, with conversion to drum speed and belt speed

Frequency f 20 Hz 25 Hz 30 Hz 35 Hz 40 Hz 45 Hz 50 Hz 55 Hz 60 Hz 65 Hz 70 Hz 75 Hz 80 Hz 85 Hz 90 Hz 95 Hz 100 Hz

Fig. 8.3  Setting spacing between buckets

Drive drum speed n1 29.9 min−1 37.6 min−1 45.3 min−1 53 min−1 60.7 min−1 68.4 min−1 76 min−1 83.7 min−1 91.3 min−1 98.7 min−1 106.1 min−1 113.6 min−1 121.1 min−1 128.5 min−1 136.1 min−1 143.5 min−1 150.6 min−1

Transport speed v 0.39 m⋅s−1 0.49 m⋅s−1 0.59 m⋅s−1 0.69 m⋅s−1 0.79 m⋅s−1 0.89 m⋅s−1 0.99 m⋅s−1 1.09 m⋅s−1 1.19 m⋅s−1 1.29 m⋅s−1 1.38 m⋅s−1 1.48 m⋅s−1 1.58 m⋅s−1 1.68 m⋅s−1 1.78 m⋅s−1 1.87 m⋅s−1 1.97 m⋅s−1

8  Input Parameters – Kinematic Properties

Fig. 8.4  Setting the frequency by means of a computer or manual control panel Fig. 8.5  Verification of the speed using a Voltcraft laser tachometer

Fig. 8.6  Generation of particles to fill 150 g in the bucket during validation

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Chapter 9

Process Validation and Calibration

For the calibration, we selected locations on the validation machine (Fig.  9.1), where the material dynamic flow parameters varied significantly. Mechanical and physical properties were measured at these locations using the direct and indirect methods. The measured data were used to validate and rectify the 3D DEM model.

9.1  Direct Measurements and the Validation Bucket Elevator Various measuring sensors, e.g., strain gauges, temperature sensors, inductive sensors, humidity sensors, are placed along the trajectory of the dynamic processes to ensure the direct measurements. These are able to directly detect the particulate matter and its behavior in the bucket elevator (Fig. 9.2).

9.2  E  valuation of the Direct Method Using DS-NET Strain Gauge System To acquire the output signals from various sensors used along the validation machine via a single system, we use a DS-NET measuring and validation system in the laboratory. This system is designed for demanding applications, particularly in the area of component, engine, and process testing, and for structural observations (Fig. 9.3). The system has measurement modules (measurement cards) ready to be connected to various sensors, analogue, or digital inputs. A wide range of DS-NET modules are available to support almost any input and output signal types. These functional modules can be combined and provide data records and process control options. They are used to measure pressure, vibrations, torque, strength, t­ emperature, noise, speed, weight, various optical parameters, time measurements, and combinations of these parameters (Fig. 9.4). © Springer Nature Switzerland AG 2019 D. Gelnar, J. Zegzulka, Discrete Element Method in the Design of Transport Systems, https://doi.org/10.1007/978-3-030-05713-8_9

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Fig. 9.1  Validation bucket elevator

9.3  I ndirect Measurements and the Validation Bucket Elevator In indirect measurements, the dynamic processes are observed and recorded using a high-speed camera. The recordings are evaluated using the PIV (particle image velocimetry) method and compared using DEM. Another method to be used is the industrial tomography. Figure 9.5 shows the examples of camera locations.

9.4  E  valuation of the Indirect Method Using PIV Software (Particle Image Velocimetry) PIV method uses high-speed cameras to record the particle movement in very short, consecutive time periods. Powerful lasers or lights are used to highlight the particles in 2D. The particle speed field is displayed and assessed by software (Fig. 9.6).

9.4  Evaluation of the Indirect Method Using PIV Software (Particle Image Velocimetry)

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Fig. 9.2  Suggested location of sensors for bucket elevator measurements

The plane of the measured space is lit with a laser or light. The measured area is bordered by the camera’s field of vision located perpendicularly to the measured plane. The images are taken under a known frequency. PIV software determines the

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Fig. 9.3  Strain gauge equipment in the Laboratory of Bulk Materials

Fig. 9.4  Image of measurement of the speed on the validation bucket elevator

position of particles in each image and evaluates their shift. To determine the movement, the program divides the images into elements, in which the shift of the different particles is determined. The camera uses a special program which processes the data and creates a vector map of the speed field.

9.4  Evaluation of the Indirect Method Using PIV Software (Particle Image Velocimetry)

Fig. 9.5  Suggested locations of cameras in bucket elevator measurements

Fig. 9.6  LAVISION high-speed camera in the Laboratory of Bulk Materials

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Measurement Outputs (Fig. 9.7)

· · · · · · ·

Vector field of speed Spectral field of speed Video sequence Image sets Raster image analysis Visualization of particle movement Charts

Fig. 9.7  Output data from a LAVISION high-speed camera

9.5  Validation – Preparation of Measurements At first, we prepared the validation bucket elevator and the laboratory for the execution of all the experiments. The same raster image was placed on the validation machine as was used in the simulation. The raster dimensions were selected according to the elevator head dimensions to read and compare the particle travels and to capture the bucket rotation angle. The dimensions are given in Fig. 9.8. It was difficult to find the right place for measurements. It showed that the light conditions in the laboratory were unsatisfactory. The surrounding light and room illumination caused shadows on the raster located at the rear wall of the elevator head. Therefore, these influences had to be eliminated first, and the measuring space was illuminated using a powerful laboratory halogen light. Next, we had to experiment with the distance of the high-speed camera from the elevator head (Fig. 9.9) to identify the suitable distance. At insufficient distances, the image displaying the entire measured area may be distorted. This emphasizes the convenience of simulation which is not limited by any space or light limitations. When the camera was located and adjusted so as to cover the entire elevator head, it was necessary to perform the length calibration, which served as a scale to evaluate the vector field of speeds and travels. It is set up according to the know distance at the machine (Fig. 9.10). The frame rate was set to 500 frames per second, which was tested and found sufficient to detect the bucket speed. Using two bolts and nuts, the printed plastic calibration bucket was attached to the PVC belt of validation bucket elevator. One bucket was selected in order to save the recording time and to decrease the file size on the computer disc. This bucket was positioned in the lower section of the working branch (Fig. 9.11).

9.5  Validation – Preparation of Measurements

Fig. 9.8  Dimensions of the measuring space raster in the elevator head

Fig. 9.9  Setup of the measuring space

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Fig. 9.10  Length calibration settings to create the scale for vector and speed fields

Fig. 9.11  Diagram of the validation experiment

9.5  Validation – Preparation of Measurements

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Fig. 9.12  Output from a high-speed camera and evaluated speed vector fields

Putting the machine in operation, this position ensures a sufficient travel to accelerate the bucket to necessary speed before the material is discharged. The filling opening is also located in this area. This opening was used to fill the bucket with exactly weighed quantities of test material of 150 g. This quantity was selected to enable comparison of various buckets, considering the size of the smallest bucket. Being prepared for measurements, the different speeds were set, and the movement was captured by a high-speed camera. The recording always took several seconds only, but saving the data from the camera to the computer, export, and evaluation always required 2–4 h per one speed. The camera output file was exported into photographs, which were suitable for the evaluation and comparison of throw trajectory shapes on the raster (Fig. 9.12). The slowed recording also enables us to determine the speed and shift color spectrum (Fig. 9.12) for the following validation of the material flow using DEM. The analyzed output of vector field of speeds was plotted in a chart. When plotting the chart, it is necessary to set the evaluation window of the flow area, from which data for chart generation will be taken. Occasional errors occur when evaluating the vector map, caused by reflexes, shadows, and overlay of particles. Therefore, it is necessary to select the smallest dimensions of the measuring space as possible to reduce the errors that influence the averaged results. Three locations were always determined at the beginning of discharge, during discharge, and at the end of discharge (Fig. 9.13) for validation. Three particle speeds in time were generated from one belt speed. These were compared with simulation, where these measurement areas were set to the same location according to the raster. It is also necessary to perform identical experiments in the simulation as in the real physical experiments. The 3D model of the validation machine was imported into DEM, including the mechanical and physical parameters of the machine and of the transported black calibration spheres. Using DEM simulation, 150 grams of the material was generated in the bucket. Calculations were performed under 17 speeds (Table 8.1). The set simulation calculation for one speed takes approximately 1–2 h, including the

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Fig. 9.13  Measured areas to determine the particle speeds during the bucket discharge

evaluation. However, the import of the machine into DEM, calculations, and programming of all the parameters and speeds takes 1 week. The same output format and scale were set for the data calculated in the simulation, as were used for real measurements. This described setup is ideal as images can be mutually compared even if overlaid.

9.6  Validation – Measurement Results During the real measurements and simulations, approximately 3000 frames were recorded and calculated. In the Appendix, there are 20 images for each speed at 30–220° rotation of the bucket, at 10° step. Only two results are given for the real measurements. The first is the paused image of the dynamic flow at a specific angle and the other is the calculated vector field of such flow. This is due to the different method used to plot the calculation. In the real measurements, there is no coloration of the particles during the display of color spectra of speeds as in DEM. Only the environment is colored, where the particles are located. The color field overlays the particles and these are not distinct enough to evaluate the accurate position of the throw trajectory. The resulting calculated and recorded movements for each speed are displayed in Figs. 9.14, 9.15 and 9.16. All the validation results are in the second Appendix of the dissertation, and high-resolution images of the different bucket rotations are available on a DVD.

9.6  Validation – Measurement Results

Fig. 9.14  Results of real dynamic flow at belt speed of 0.39 m·s−1

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Fig. 9.15  Results of calculated field of speeds at belt speed of 0.39 m·s−1

9.6  Validation – Measurement Results

Fig. 9.16  Results of calculated simulation at belt speed of 0.39 m·s−1

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The geometry and speed of these results were mutually compared (Figs. 9.17 and 9.18). The figures clearly imply whether the simulation is plausible and corresponding to the reality. Figures 9.19, 9.20, 9.21, 9.22, 9.23, 9.24, 9.25, 9.26, 9.27, 9.28, 9.29, 9.30, 9.31, 9.32, 9.33, 9.34, 9.35, 9.36, 9.37, 9.38, 9.39, 9.40, 9.41, 9.42, 9.43, 9.44, 9.45, 9.46, 9.47, 9.48, 9.49, 9.50, 9.51, 9.52, 9.53 and 9.54 show selected validation results and the usage of these results.

Fig. 9.17  Validation of the real measurements and simulation based on the geometric parameters of throw trajectories

Fig. 9.18  Validation of the real measurements and simulation based on the color spectrum of particle speed field

9.6  Validation – Measurement Results

Fig. 9.19  PIV and DEM validation – belt speed of 0.39 m·s−1, bucket rotation of 130°

Fig. 9.20  PIV and DEM validation – belt speed of 0.39 m·s−1, bucket rotation of 140°

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Fig. 9.21  PIV and DEM validation – belt speed of 0.39 m·s−1, bucket rotation of 150°

Fig. 9.22  Chart of particle speed at the beginning of discharge – belt speed of 0.39 m·s−1

9.6  Validation – Measurement Results

Fig. 9.23  Chart of particle speed during discharge – belt speed of 0.39 m·s−1

Fig. 9.24  Chart of particle speed at the end of discharge – belt speed of 0.39 m·s−1

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Fig. 9.25  PIV and DEM validation – belt speed of 0.59 m·s−1, bucket rotation of 150°

Fig. 9.26  PIV and DEM validation – belt speed of 0.59 m·s−1, bucket rotation of 160°

9.6  Validation – Measurement Results

Fig. 9.27  PIV and DEM validation – belt speed of 0.59 m·s−1, bucket rotation of 170°

Fig. 9.28  Chart of particle speed at the beginning of discharge – belt speed of 0.59 m·s−1

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Fig. 9.29  Chart of particle speed during discharge – belt speed of 0.59 m·s−1

Fig. 9.30  Chart of particle speed at the end of discharge – belt speed of 0.59 m·s−1

9.6  Validation – Measurement Results

Fig. 9.31  PIV and DEM validation – belt speed of 0.79 m·s−1, bucket rotation of 170°

Fig. 9.32  PIV and DEM validation – belt speed of 0.79 m·s−1, bucket rotation of 180°

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Fig. 9.33  PIV and DEM validation – belt speed of 0.79 m·s−1, bucket rotation of 190°

Fig. 9.34  Chart of particle speed at the beginning of discharge – belt speed of 0.79 m·s−1

9.6  Validation – Measurement Results

Fig. 9.35  Chart of particle speed during discharge – belt speed of 0.79 m·s−1

Fig. 9.36  Chart of particle speed at the end of discharge – belt speed of 0.79 m·s−1

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Fig. 9.37  PIV and DEM validation – belt speed of 1.19 m·s−1, bucket rotation of 180°

Fig. 9.38  PIV and DEM validation – belt speed of 1.19 m·s−1, bucket rotation of 190°

9.6  Validation – Measurement Results

Fig. 9.39  PIV and DEM validation – belt speed of 1.19 m·s−1, bucket rotation of 200°

Fig. 9.40  Chart of particle speed at the beginning of discharge – belt speed of 1.19 m·s−1

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Fig. 9.41  Chart of particle speed during discharge – belt speed of 1.19 m·s−1

Fig. 9.42  Chart of particle speed at the end of discharge – belt speed of 1.19 m·s−1

9.6  Validation – Measurement Results

Fig. 9.43  PIV and DEM validation – belt speed of 1.58 m·s−1, bucket rotation of 180°

Fig. 9.44  PIV and DEM validation – belt speed of 1.58 m·s−1, bucket rotation of 190°

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Fig. 9.45  PIV and DEM validation – belt speed of 1.58 m·s−1, bucket rotation of 200°

Fig. 9.46  Chart of particle speed at the beginning of discharge – belt speed of 1.58 m·s−1

9.6  Validation – Measurement Results

Fig. 9.47  Chart of particle speed during discharge – belt speed of 1.58 m·s−1

Fig. 9.48  Chart of particle speed at the end of discharge – belt speed of 1.58 m·s−1

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Fig. 9.49  Validation of the real measurements and simulation based on the geometric parameters of throw trajectories

9.6  Validation – Measurement Results

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Fig. 9.50  Validation of the real measurements and simulation based on the color spectrum of particle speed field

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Fig. 9.51  Validation of the real measurements and simulation based on the color spectrum of particle speed field

9.6  Validation – Measurement Results

Fig. 9.52  Using results for basic optimization – part 1

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Fig. 9.53  Using results for basic optimization – part 2

9  Process Validation and Calibration

9.6  Validation – Measurement Results

Fig. 9.54  Simulation of bucket discharge on Earth, Mars, and Moon

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Chapter 10

The Results for the Optimization of Bucket Filling and Discharge

As mentioned at the beginning of this book, there are several options to optimize the filling and discharge of the bucket elevator. The change in transport speed is the best way to improve the operation of the bucket elevator. For this reason, most conveyors nowadays are equipped with a frequency converter. However, characteristics of optimum settings of elevator speed are still missing. Although the characteristics differ in various designs of bucket elevators, we have the opportunity to test various machines and determine the influence of speed on the bulk material filling and discharge methods. The acquired data are naturally influenced by the geometric setup and design of the machines.

10.1  The Results for Optimization of Bucket Discharge Results from previous measurements may be used for optimizations and validations in DEM. In this case, the calibration bucket was filled with 150 grams of material in the lower part of the machine, and it was discharged at 17 different speeds ranging from 0.39 to 1.97 m·s−1 (see Table 8.1). This way, it was possible to investigate all methods of discharge: gravity, mixed, and centrifugal. All the measured materials mentioned above were tested and recorded during the optimization to compare the input flow characteristics of the materials with those of the spherical calibration particles (Fig. 10.1). The use of spheres in the initial investigation of flow and DEM validation appears unreliable to people in the industry, and thus, the book also provides comparative results. Figures 10.2, 10.3, 10.4, 10.5, 10.6 and 10.7 compare the gravity discharge at speed of 0.39  m·s−1. The mixed discharge is displayed in Figs. 10.8, 10.9, 10.10, 10.11, 10.12 and 10.13. The centrifugal discharge is detailed in Figs. 10.14, 10.15, 10.16, 10.17, 10.18 and 10.19. The comparisons imply that it is possible to use spheres for the preliminary determination of the material flow within the bucket elevator. It shows that the spherical particles of 6 mm in diameter have a similar course of discharge as the particles of different shapes under the © Springer Nature Switzerland AG 2019 D. Gelnar, J. Zegzulka, Discrete Element Method in the Design of Transport Systems, https://doi.org/10.1007/978-3-030-05713-8_10

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Fig. 10.1  Scheme of measurement on the validation bucket elevator

10.1  The Results for Optimization of Bucket Discharge

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Fig. 10.2  Gravity discharge – belt speed 0.39 m·s−1; material weight 150 g

Fig. 10.3  Gravity discharge – belt speed 0.39 m·s−1; material weight 150 g

identical environment and similar sizes (approximately 6 mm ± 4 mm) (Fig. 10.20). If the size of particles is smaller by several orders, for example, sugar, the flow is clearly different in material distribution and throw angle. All these results are detailed in Appendix 2 to the dissertation, which provides the discharge for 20 rotation angles from 30° to 220°. The recorded images enable us to determine a lot of data and results; however, within optimization, the bucket elevator discharge speed was observed (Figs. 10.22, 10.23, 10.24, 10.25, 10.26, 10.27, 10.28, 10.29 and 10.30). The figures show that the material movement is accelerated at the elevator head as the translation movement changes to rotational movement. There are different speeds in the area of the bucket, which differ in dependence on particle movement trajectory radius (Fig. 10.21). According to this dependence, the particles have a higher speed at the

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Fig. 10.4  Gravity discharge – belt speed 0.39 m·s−1; material weight 150 g

Fig. 10.5  Gravity discharge – belt speed 0.39 m·s−1; material weight 150 g

bucket discharge than that of the belt. Not only the speed value is interesting, but also the information how these speeds change their speed field during rotation. Calculation of the speeds at belt speed of 0.79 m·s−1:



ω= ω=

v r

s−1 



0.79 = 6.32 s−1 0.125

Material speed at rotation radius of 0.14 m for mixed discharge:

(10.1) (10.2)

10.1  The Results for Optimization of Bucket Discharge

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Fig. 10.6  Gravity discharge – belt speed 0.39 m·s−1, material weight 150 g

Fig. 10.7  Gravity discharge – belt speed 0.39 m·s−1; material weight 150 g



vp = ω ⋅ r

m ⋅ s−1 

vp = 6.32 ⋅ 0.14 = 0.88 m ⋅ s−1

(10.3)

(10.4)

Studying the different 17 speeds and shapes of flow profiles, we determined the border between the different types of discharge. Discharge border: Gravity discharge takes place in the range from 0.39 to 0.69 m·s−1 Mixed discharge takes place at 0.79 m·s−1 Centrifugal discharge takes place in the range from 0.89 to 1.97 m·s−1

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Fig. 10.8  Mixed discharge – belt speed 0.79 m·s−1; material weight 150 g

Fig. 10.9  Mixed discharge – belt speed 0.79 m·s−1; material weight 150 g

Another interesting parameter determined from the images is the start and end angles of bucket discharge when the bucket filled with 150 g of material. The chart in Fig. 10.31 shows that the start angle of the bucket discharge increases up to speed of 0.87 m·s−1. Then the discharge angle decreases again. The chart also shows that the shortest discharge time is at speeds from 0.8 to 0.9 m·s−1. To decrease possible losses and prevent the material from falling back into the working branch, it is important for the start of discharge to be as late as possible. On the contrary, the end of discharge must not be too late to prevent material from falling into the return branch of the elevator (Fig. 10.32). The findings may be used to propose the speed and geometry of elevator discharge properly (Figs.  10.33, 10.34, 10.35, 10.36, 10.37, 10.38, 10.39, 10.40 and 10.41).

10.2  The Results for Optimization of Bucket Filling

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Fig. 10.10  Mixed discharge – belt speed 0.79 m·s−1; material weight 150 g

Fig. 10.11  Mixed discharge – belt speed 0.79 m·s−1; material weight 150 g

10.2  The Results for Optimization of Bucket Filling In dealing with the filling optimization tasks, it was necessary to fill the elevator boot with material, i.e., spheres of 6  mm. We selected two quantities for filling: 5000 particles (1 kg of material) and 10,000 particles (2 kg of material). The validation machine was tested at 17 different speeds ranging from 0.39 to 1.97  m·s−1. During the experiments, the actual transported material volume in the discharge hopper was measured – see Fig. 10.42. Next, we simulated scooping filling at three speeds to determine the field of speed and travel (see Figs. 10.43, 10.44, 10.45, 10.46, 10.47, 10.48, 10.49, 10.50 and 10.51). The three bucket elevator speeds are characteristic for gravity, mixed, and centrifugal methods of discharge. When comparing the speed fields, in the ini-

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Fig. 10.12  Mixed discharge – belt speed 0.79 m·s−1; material weight 150 g

Fig. 10.13  Mixed discharge – belt speed 0.79 m·s−1; material weight 150 g

tial phase the travel dynamics and field creation are the same in scooping, only the speeds of the speed field increase along with a rise in the belt speed. An interesting moment is when the bucket runs out of the scooping area of the elevator boot. In this phase of the process, the material flow changes in a way it influences the filled volume (Figs. 10.52, 10.53 and 10.54). While at the speed 0.39 m·s−1 the material is relatively stabilized in the bucket, at the speed of 1.58 m·s−1 the material tries to escape from the bucket in the direction of centrifugal force, which leads to losses as the material falls back into the shaft and the elevator head. The simulation results can be used to design the surface of the bucket filling area to reduce the loss (Figs. 10.55, 10.56, 10.57, 10.58, 10.59, 10.60, 10.61, 10.62, 10.63, 10.64, 10.65, 10.66, 10.67, 10.68, 10.69, 10.70 and 10.71).

10.2  The Results for Optimization of Bucket Filling

Fig. 10.14  Centrifugal discharge – belt speed 1.58 m·s−1; material weight 150 g

Fig. 10.15  Centrifugal discharge – belt speed 1.58 m·s−1; material weight 150 g

Fig. 10.16  Centrifugal discharge – belt speed 1.58 m·s−1; material weight 150 g

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Fig. 10.17  Centrifugal discharge – belt speed 1.58 m·s−1; material weight 150 g

Fig. 10.18  Centrifugal discharge – belt speed 1.58 m·s−1; material weight 150 g

Fig. 10.19  Centrifugal discharge – belt speed 1.58 m·s−1; material weight 150 g

10.2  The Results for Optimization of Bucket Filling

Fig. 10.20  Airsoft balls as replacements of other materials in DEM simulations

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Fig. 10.21  Color spectrum of various material speeds in dependence on the rotation radius; speed 0.79 m·s−1, rotation angle 90°

Fig. 10.22  Material speed in the bucket at belt speed of 0.39 m·s−1

Fig. 10.23  Material speed in the bucket at belt speed of 0.39 m·s−1

10.2  The Results for Optimization of Bucket Filling

Fig. 10.24  Material speed in the bucket at belt speed of 0.39 m·s−1

Fig. 10.25  Material speed in the bucket at belt speed of 0.79 m·s−1

Fig. 10.26  Material speed in the bucket at belt speed of 0.79 m·s−1

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Fig. 10.27  Material speed in the bucket at belt speed of 0.79 m·s−1

Fig. 10.28  Material speed in the bucket at belt speed of 1.58 m·s−1

Fig. 10.29  Material speed in the bucket at belt speed of 1.58 m·s−1

10.2  The Results for Optimization of Bucket Filling

Fig. 10.30  Material speed in the bucket at belt speed of 1.58 m·s−1

Fig. 10.31  Chart of start and end angles of bucket discharge in dependence on speed

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Fig. 10.32  Chart of transported mass of material in dependence on bucket speed in scooping

10.2  The Results for Optimization of Bucket Filling

Fig. 10.33  Front view of discharging bucket elevator; speed 0.39 m·s−1

Fig. 10.34  Front view of discharging bucket elevator; speed 0.79 m·s−1

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Fig. 10.35  Front view of discharging bucket elevator; speed 1.58 m·s−1

Fig. 10.36  Gravity discharge of the bucket filled at 50%, 75%, and 100%; belt speed 0.39 m·s−1

10.2  The Results for Optimization of Bucket Filling

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Fig. 10.37  Mixed discharge of the bucket filled at 50%, 75%, and 100%; belt speed 0.79 m·s−1

Fig. 10.38  Centrifugal discharge of the bucket filled at 50%, 75%, and 100%; belt speed 1.58 m·s−1

Fig. 10.39  Gravity discharge of three types of bucket, filled with 150 g; belt speed 0.39 m·s−1

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Fig. 10.40  Mixed discharge of three types of bucket, filled with 150 g; belt speed 0.79 m·s−1

Fig. 10.41  Centrifugal discharge of three types of bucket, filled with 150 g; belt speed 1.58 m·s−1

Fig. 10.42  Elevator boot filled with spherical particles (10,000 particle/2 kg)

10.2  The Results for Optimization of Bucket Filling

Fig. 10.43  Speed field in scooping – speed 0.39 m·s−1, rotation 240°

Fig. 10.44  Speed field in scooping – speed 0.39 m·s−1, rotation 270°

Fig. 10.45  Speed field in scooping – speed 0.39 m·s−1, rotation 300°

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Fig. 10.46  Speed field in scooping – speed 0.79 m·s−1, rotation 240°

Fig. 10.47  Speed field in scooping – speed 0.79 m·s−1, rotation 270°

Fig. 10.48  Speed field in scooping – speed 0.79 m·s−1, rotation 300°

10.2  The Results for Optimization of Bucket Filling

Fig. 10.49  Speed field in scooping – speed 1.58 m·s−1, rotation 240°

Fig. 10.50  Speed field in scooping – speed 1.58 m·s−1, rotation 270°

Fig. 10.51  Speed field in scooping – speed 1.58 m·s−1, rotation 300°

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Fig. 10.52  Assessment of particles speed field in scooping speed of 0.39 m·s−1

Fig. 10.53  Assessment of particles speed field in scooping speed of 0.79 m·s−1

Fig. 10.54  Assessment of particles speed field in scooping speed of 1.58 m·s−1

10.2  The Results for Optimization of Bucket Filling

Fig. 10.55  Chart of digging force affecting the bucket – belt speed 0.39 m·s−1

Fig. 10.56  Chart of digging force affecting the bucket – belt speed 0.79 m·s−1

Fig. 10.57  Chart of digging force affecting the bucket – belt speed 1.58 m·s−1

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Fig. 10.58  Using results for basic optimization

10.2  The Results for Optimization of Bucket Filling

Fig. 10.59  Detail of speed field in direct flow filling – belt speed 0.39 m·s−1

Fig. 10.60  Detail of speed field in direct flow filling – belt speed 0.39 m·s−1

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Fig. 10.61  Chart of direct flow force affecting the bucket – belt speed 0.39 m·s−1

Fig. 10.62  Detail of speed field in direct flow filling – belt speed 0.79 m·s−1

10.2  The Results for Optimization of Bucket Filling

Fig. 10.63  Detail of speed field in direct flow filling – belt speed 0.79 m·s−1

Fig. 10.64  Chart of direct flow force affecting the bucket – belt speed 0.79 m·s−1

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Fig. 10.65  Detail of speed field in direct flow filling – belt speed 1.58 m·s−1

Fig. 10.66  Detail of speed field in direct flow filling – belt speed 1.58 m·s−1

10.2  The Results for Optimization of Bucket Filling

Fig. 10.67  Chart of direct flow force affecting the bucket – belt speed 1.58 m·s−1

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Fig. 10.68  Using results for basic optimization

10.2  The Results for Optimization of Bucket Filling

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Fig. 10.69  Direct flow filling, speed of 0.39 m·s−1, circulation back to hopper, filling of 25,000 particles

Fig. 10.70  Direct flow filling, speed of 0.79 m·s−1, circulation back to hopper, filling of 25,000 particle

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Fig. 10.71  Direct flow filling, speed of 1.58 m·s−1, circulation back to hopper, filling of 25,000 particles

Chapter 11

The Results for Optimization of Filling Bulk Material in the Bucket to Minimize Travel Resistance and Impacts

DEM can also be used to evaluate the contact forces with which the transported material affects the bucket surfaces, or other parts of the bucket elevator. Therefore, we conducted an experiment, when the elevator boot was filled with 10,000 calibration particles for simulation. Next, several scooping cycles were carried out at different elevator speeds, according to Table 8.1. These forces were evaluated in a chart in dependence on time. For clarity, the charts give only three speeds of material filling into the bucket. The scooping is plotted in Fig. 11.1, whereas the direct flow filling is given in Fig. 11.2. In the scooping method, we can see that the digging force at speed of 0.39 m·s−1 is 6 times smaller than at belt speed of 1.58 m·s−1. When recalculating these values to necessary electric input, it is determined that at speed of 0.39 m·s−1 the total resistance at the conveyor shall be increased only by 6 W. At speed of 1.58 m·s−1, the increase shall be 143 W, which is 23.8 times more. Due to this fact, the scooping method is not suitable for high speeds since it has high power consumption and abrasion at high speeds (Figs. 11.3, 11.4, 11.5 and 11.6).

© Springer Nature Switzerland AG 2019 D. Gelnar, J. Zegzulka, Discrete Element Method in the Design of Transport Systems, https://doi.org/10.1007/978-3-030-05713-8_11

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Fig. 11.1  Curves of forces in dependence on time at three elevator speeds for one bucket

Fig. 11.2  Curves of direct flow forces in dependence on time at three elevator speeds for one bucket

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Fig. 11.3  Comparison of digging and direct flow forces in dependence on time at three speeds for one bucket

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Fig. 11.4  Using results for basic optimization

11  The Results for Optimization of Filling Bulk Material in the Bucket to Minimize…

Fig. 11.5  Using results for basic optimization

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Fig. 11.6  Using results for basic optimization

Chapter 12

The Results for Process Optimization of Bulk Material Filling into the Bucket to Minimize Abrasive and Destructive Impacts of the Bucket Edge on the Transported Mass

When a bucket elevator needs to be operated at the lowest possible costs, we need to take the service life of the different components into account as no part is everlasting. We need to employ scientific findings and measurements to set the service life according to relevant maintenance schedules. When a component has an insufficient service life, machine manufacturers may blame the type and strength of materials. However, this need not be the only option how to improve the service life. For example, the shape and inclination of the bucket also influences the service life of the bucket during the operation. The operation of any machine will show, in due time, which components must be replaced and why. However, in the design, the wear may be accelerated in order to avoid faulty designs via the identification of the sites of extreme wear. In this book, abrasion is investigated using sprayed multilayer coatings of the buckets (Fig. 12.1). This leads to a faster wear of the thin coating layers instead of the wear of the bucket itself. In short time, the wear can be seen in various color depths, similarly to FEM deformation analysis (Fig. 12.2). This way, the ground color areas and simulation outputs of speed fields can be used to improve the design of specific parts and, for example, via reinforcement or strengthening of strained locations. To determine abrasion, the experiment was carried out on the validation machine in the circulation mode. The discharge hopper was connected to the scooping hopper using the return branch. The elevator boot was filled with strongly abrasive material, in this case Steel Grit GH50 (steel shots). The maximum speed of 1.97 m·s−1 was set on the machine, as mentioned in Table 8.1. The bucket sprayed with three color layers was employed and loaded in the scooping process. Based on previous experience, the loading time was set to 10 min (Fig. 12.3). The physical measurements were carried out using three types of buckets, namely, a Grabelt plastic bucket, deep steel bucket, and shallow pressed steel bucket. The results of the abrasion experiments are depicted in Figs. 12.4, 12.5 and 12.6. The figurers imply that the front edge and front inner surface of the bucket are the most strained sections. The figures also show that the other surfaces are almost intact. The color spectra show the area, and the individual colors also the magnitude © Springer Nature Switzerland AG 2019 D. Gelnar, J. Zegzulka, Discrete Element Method in the Design of Transport Systems, https://doi.org/10.1007/978-3-030-05713-8_12

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Fig. 12.1  Sprayed coating in layers

Fig. 12.2  Color mapping of bucket deformation in ANSYS software

of wear. It is widely established that the higher the speed, the higher the wear. But only DEM simulation enables us to quickly determine, where the originating point of wear is. This is an advantageous finding for optimization of the element or of the whole machine.

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Fig. 12.3  Bucket in the validation machine after 10-min operation

Fig. 12.4  Color field determining the wear of a deep plastic bucket

Fig. 12.5  Color field determining the wear of a deep steel bucket

Real experiments can be used to further determine the wear of such components. For example, the measurements can be improved through experimenting with the thickness of coating or the number of layers. In this case, further improvements were proposed using a computer and DEM simulations. In the DEM simulation, we can observe regroupings of the speed fields during scooping. Where the system

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Fig. 12.6  Color field determining the wear of a steel bucket Fig. 12.7  Color field determining the wear of a medium-deep steel bucket

shows the friction contact between the particles and bucket surface at the highest speed, such place is defined as the wear-risk area. Current software is able to draw the wear simulation for components strained by dynamic material flows. However, we did not have the software during experiments; therefore, the objective was solved by evaluation of speed field with physical verification (Fig. 12.7). Below, to give a real example from the practice, we describe a real and fully functional bucket elevator which we tested via simulations. In order to provide a mobile solution of a blasting station (Fig.  12.8), the manufacturer modified the geometry and height of the machine to fit it in an ISO container. Since major design changes were made due to height limitations, they requested a check of the dynamic flow and functions of the modified machine. The 3D model provided by the manufacturer was converted into the suitable format. Next, we programed the movement of buckets according to the table of speeds (Table 8.1), followed by the calculations of simulated abrasive dynamic flow during filling and discharge of the machine. The vector speed fields for scooping were applied to determine the risk locations with the highest wear (see Fig. 12.9). For such evaluations, images of vector fields are not sufficient, and thus animations had to be made. This way, it is easily possible to define areas, where the particles (Fig. 12.10) perform the abrasive friction travel at the maximum speed.

12  The Results for Process Optimization of Bulk Material Filling into the Bucket…

Fig. 12.8  Wista bucket elevator for the transport of abrasives

Fig. 12.9  Color field of speeds with determined bucket wear areas during scooping

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Fig. 12.10  Modeled grain shapes, Steel Grit GH 50 material, two sizes

This bucket elevator is interesting in that it has two coupled transport branches. The first branch serves to transport unsized abrasives, while the second to transport sized abrasive (Fig. 12.11). To perform a more detailed analysis, the particle shape was modeled in the simulation according to the most frequently occurring shape of randomly selected abrasive grain. Mean particle size in overall granulometry is 684.39  μm (Table  12.1). Unfortunately, for such size, a standard desktop computer is unable to execute the calculation in reasonable time. Therefore, the grain shape was selected according to type of abrasive, but the particle size was increased to enable the calculation with standard desktop computer. Grain size for the first mixture was selected as W 5 mm × H 5 mm × L 8 mm, and for the second mixture it was W 10 mm × H 10 mm × L 14 mm. Such grain size is fully sufficient to initial determination of the mixture flow behavior. For the detailed analysis, it is necessary to find the problematic locations and then to execute the simulation calculation with true particle size. The results are given in Figs.  12.12, 12.13, 12.14, 12.15, 12.16, 12.17, 12.18, 12.19, 12.20, 12.21, 12.22, 12.23, 12.24, 12.25, 12.26, 12.27, 12.28 and 12.29. The abovementioned results determine the vector speed fields for filling the bucket with abrasives. To analyze the location of the maximum wear, the calculated animation of filling movement was observed. This animation shows what happens in the elevator boot as well as the locations with abrasion load. The simulation calculation shows that when larger grain sizes are transported, the abrasion area of the material grows due to a chain reaction caused by the mutual impacts between the grains. Figure 12.30 on the left shows that material with smaller grain size abrades only the bucket, while the boot covering is protected against the wear due to the

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Fig. 12.11  Simulation calculation for scooping filling of buckets in two transport branches Table 12.1  Output values for Steel grit GH 50, measured with CILAS Granulometer

layer of abrasive material. If the grain size increased, as shown in Fig. 12.30 on the right, the abrasion travel reach also increases, which also impacts the machine cover. This is an undesirable influence, though, since the replacement of the machine cover, including the geometric optimization of the elevator boot, is financially more demanding than the replacement of the buckets. During the inspection of the bucket elevator, we found that the elevator boot was designed properly. Steel grit material creates a protective layer for the machine covers, thanks to the grain size, and only the bucket is worn during the belt movement up to the speed of 0.39 m·s−1. To decrease the scooping drags, it is suitable to use direct flow filling at the boot, which is difficult with regard to the machine height limitations. If the manufacturer manages to change the filling from scooping to direct flow, it will have a positive influence on the bucket service life.

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Fig. 12.12  Scooping filling, grain sized to 10 × 10 × 14 mm, speed 0.39 m·s−1, rotation angle 250°

Fig. 12.13  Scooping filling, grain sized to 10 × 10 × 14 mm, speed 0.39 m·s−1, rotation angle 270°

Fig. 12.14  Scooping filling, grain sized to 10 × 10 × 14 mm, speed 0.39 m·s−1, rotation angle 290°

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Fig. 12.15  Scooping filling, grain sized to 5 × 5 × 8 mm, speed 0.39 m·s−1 rotation angle 250°

Fig. 12.16  Scooping filling, grain sized to 5 × 5 × 8 mm, speed 0.39 m·s−1 rotation angle 270°

Fig. 12.17  Scooping filling, grain sized to 5 × 5 × 8 mm, speed 0.39 m·s−1 rotation angle 290°

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Fig. 12.18  Scooping filling, grain sized to 10 × 10 × 14 mm, speed 0.79 m·s−1, rotation angle 250°

Fig. 12.19  Scooping filling, grain sized to 10 × 10 × 14 mm, speed 0.79 m·s−1, rotation angle 270°

Fig. 12.20  Scooping filling, grain sized to 10 × 10 × 14 mm, speed 0.79 m·s−1, rotation angle 290°

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Fig. 12.21  Scooping filling, grain sized to 5 × 5 × 8 mm, speed 0.79 m·s−1 rotation angle 250°

Fig. 12.22  Scooping filling, grain sized to 5 × 5 × 8 mm, speed 0.79 m·s−1 rotation angle 270°

Fig. 12.23  Scooping filling, grain sized to 5 × 5 × 8 mm, speed 0.79 m·s−1 rotation angle 290°

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Fig. 12.24  Scooping filling, grain sized to 10 × 10 × 14 mm, speed 1.58 m·s−1, rotation angle 250°

Fig. 12.25  Scooping filling, grain sized to 10 × 10 × 14 mm, speed 1.58 m·s−1, rotation angle 270°

Fig. 12.26  Scooping filling, grain sized to 10 × 10 × 14 mm, speed 1.58 m·s−1, rotation angle 290°

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Fig. 12.27  Scooping filling, grain sized to 5 × 5 × 8 mm, speed 1.58 m·s−1 rotation angle 250°

Fig. 12.28  Scooping filling, grain sized to 5 × 5 × 8 mm, speed 1.58 m·s−1 rotation angle 270°

Fig. 12.29  Scooping filling, grain sized to 5 × 5 × 8 mm, speed 1.58 m·s−1 rotation angle 290°

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Fig. 12.30  Steel Grit – speed 1.58 m·s−1, rotation angle 270°

Chapter 13

The Optimization of Bucket Discharge to Maximize the Transported Volume and to Minimize Material Fall Down the Shaft

In order to propose possible optimizations, the Wista bucket elevator was also used to observe the discharge of buckets and whether it causes any loss due to material falling back into the return or working shafts. The material flow was simulated and computed in both shafts of the bucket elevator. The simulation results were evaluated via the vertical cut of the buckets to investigate the behavior of speed fields inside the bucket. Figure 13.1 shows the cut of the first shaft in 3D. The shaft transports Steel grit, grain size W 5 mm × H 5 mm × L 8 mm. Another cut used for the evaluation shows the second shaft. This shaft transports Steel grit, grain size W 10 mm × H 10 mm × L 14 mm. The simulations were calculated for 17 speeds, from 0.39 m·s−1 to 1.97 m·s−1. Figures 13.2, 13.3, 13.4, 13.5, 13.6, 13.7, 13.8, 13.9, 13.10, 13.11, 13.12, 13.13 and 13.14 show selected results for the gravity, mixed, and centrifugal discharge. Thanks to the 3D simulation, a major design error was identified on the 3D model of Wista bucket elevator. This was caused by decreasing the height of the discharge hopper in order to fit the bucket elevator in an ISO container. Should the bucket elevator be manufactured in this design, it would not be able to transport abrasive material. If the speed is optimized, the machine can transport the material but under a huge loss amounting to 50%. Since the increase in speed is not suitable and relatively ineffective due to the properties of abrasive materials, it is necessary to opt for other optimization methods. According to the calculated simulations of the dynamic flow at belt speed of 0.39 m·s−1, we need to modify the geometry of the discharge hopper, bucket spacing, and other parameters according to Fig. 13.8.

© Springer Nature Switzerland AG 2019 D. Gelnar, J. Zegzulka, Discrete Element Method in the Design of Transport Systems, https://doi.org/10.1007/978-3-030-05713-8_13

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Fig. 13.1  3D view of the bucket elevator head in the second shaft

Fig. 13.2  Gravity discharge of the bucket, speed 0.39 m·s−1

13  The Optimization of Bucket Discharge to Maximize the Transported Volume…

Fig. 13.3  Mixed discharge of the bucket, speed 0.79 m·s−1

Fig. 13.4  Centrifugal discharge of the bucket, speed 1.58 m·s−1

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Fig. 13.5  Incorrect spacing, speed 0.39 m·s−1

Fig. 13.6  Steel grit – speed 0.79 m·s−1, rotation angle 180°

13  The Optimization of Bucket Discharge to Maximize the Transported Volume…

Fig. 13.7  Steel grit – speed 1.58 m·s−1, rotation angle 220°

Fig. 13.8  Geometric optimizations of the proposed elevator prototype

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Fig. 13.9  Control simulation design of the new hopper design

Fig. 13.10  Gravity discharge of the bucket, speed 0.39 m·s−1

13  The Optimization of Bucket Discharge to Maximize the Transported Volume…

Fig. 13.11  Gravity discharge of the bucket, speed 0.39 m·s−1

Fig. 13.12  Gravity discharge of the bucket, speed 0.39 m·s−1

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Fig. 13.13  Gravity discharge of the bucket, speed 0.39 m·s−1

Fig. 13.14  Gravity discharge of the bucket, speed 0.39 m·s−1

Chapter 14

Conclusion

The book describes the innovative method of simulation design and optimization of bucket elevators, as well as of other equipment working on similar principles. The introduction describes bucket elevators and related transport processes, along with the methods of filling and discharge of bulk material. The book also describes the differences between the current procedures of bucket elevator design using CAD applications and the innovative simulation method of bucket elevator design and optimizations using DEM. The main objective is to describe the use of DEM to optimize the operation of bucket elevators. The optimization concerns both the filling and discharge sections of bucket elevators. Before optimizations, measurements of mechanical and physical properties of selected materials are discussed, which serve as input values for the simulation. Next, the reader learns about the environment design process, in which the simulation is executed. In this case, the book gives a detailed description of the development of a 3D model of validation bucket elevator using Autodesk Inventor software. The model was later on converted into a suitable format and imported into DEM. The book continues with the results of material dynamic flow validation of speed, time, and geometry during the bucket elevator discharge at 17 belt speeds, ranging from 0.39 to 1.97  m·s−1. The research results imply that the simulation results comply with the results of physical experiments and that the simulation is applicable for further optimization of bucket elevators. The results also show that it is necessary to better screen and filter out the speed results of PIV method to execute speed validation of the machine. The chapter dedicated to the optimization of bucket elevators provides real and simulated results, as well as options for bucket elevator modifications, which shall help to improve the transport efficiency. The speed field is investigated both for discharge and filling of bulk material into the bucket. These speed fields and travels of bulk material can be used to further optimize the geometry of validation machines at filling and discharge areas. The provided photographs show that the validation machine is able to transport bulk material at all speeds. Later on, it depends on the assignment, i.e., the transported material and working conditions of the machine. Appropriate are selected from the © Springer Nature Switzerland AG 2019 D. Gelnar, J. Zegzulka, Discrete Element Method in the Design of Transport Systems, https://doi.org/10.1007/978-3-030-05713-8_14

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14 Conclusion

libraries necessary for the required optimization (based on input conditions) and aim for maximum transport efficiency. The result is not one specific value but quite an extensive data library, which can be used to generate the machine optimization data for various input conditions. This shall serve to fulfill all requirements imposed on the machine to transport bulk material. Simulations are used to calculate the forces affecting the bucket geometry. These are subsequently plotted in a chart and compared under various belt speeds ranging from 0.39 to 1.97 m·s−1, both for direct flow and scooping methods of filling. At speeds from 0.39 to 0.49 m·s−1, the drag forces are almost similar for both filling methods. If the machine is operated at belt speeds from 0.49 to 1.97 m·s−1, comparing the drag forces it is obvious that the results differ. The direct flow method of filling is several times more efficient at those speeds. The results are simulated calculations for the elevator boot, which can be used to conclude that the speed optimization minimizes drag forces. Again, based on the assignment and transport requirements, necessary data can be selected from the results database and used to optimize the shape and size of the bucket, as well as the geometry of the elevator boot at various belt speeds and methods of material filling. This way, the efficiency of bulk material transport may be increased. Optimizations are highly desirable in abrasive materials. Thus, we focused on the changes in speed to optimize the influence of abrasive material on the bucket and elevator boot. Since the available version of EDEM software at the time of the experiments did not contain the module to determine parts’ wear, we used animations of material filling to observe the shape and movement of bulk material speed fields. Using the movement of these fields, it is possible to find the areas of bucket and elevator boot wear. We carried out real tests with multilayer paint coatings on the bucket surface and load at the highest belt speed of 1.97 m·s−1 to identify the areas worn by abrasion. The wear can be observed according to how the multiple color depths of paint coatings disappear at different strained locations. The results are thus calculated speed fields, along with the verification of several types of buckets. We observed that the most strained part was the front internal edge of the bucket. Such calculated and measured data, in dependence on input conditions, may be used to conveniently optimize the bucket and elevator boot. Finally, we tested a specific bucket elevator used in the industry to transport abrasive materials. The results are simulations of the bulk material dynamic flow calculated using the 3D model of the bucket elevator that was geometrically modified for the transport of abrasive materials on a blasting line built in an ISO container. We tested the bucket elevator head and boot. The results show that the elevator boot was designed correctly, but the elevator head shows a design flaw because the material falls back into the return branch of the bucket elevator at the belt speed of 0.39  m·s−1. Although the progressive increase in speed leads to the transport of material, it shows 50% loss caused by the material falling back into the return shaft. Therefore, we also attempted to optimize the bucket elevator geometry to eliminate

14 Conclusion

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the problem of material falling back into the return branch of the bucket elevator. Using the procedures described in this book, it is possible to identify errors as early as in the development stage and to modify and verify the design before the proposed design is finalized or the prototype is built. To get more information about the validation machine and the method dealing with the weaknesses during design of such machines, we refer you to the patent called “Validation bucket elevator for modelling of mechanical processes and method of modelling of mechanical processes,” No. 304329, at www.upv.cz.

Interesting Links

http://www.dem-solutions.com http://www.lavision.de/en/techniques/piv.php http://www.dewesoft.com http://www.lavision.de/en/

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Awards

ZEGZULKA, J., GELNAR, D., NEČAS, J., JUCHELKOVÁ, D. Validation bucket elevator. Exhibition of inventions, INVENTO Prague, 2013, awards at international contest for the most interesting invention or innovation  - INVENTO Prague AWARD.

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References

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35. Polák, J., Bailotty, K., Pavliska, J., Hrabovský, L.: Transport and Handling Devices II, 1st edn, p. 104. VŠB - Technical University of Ostrava, Ostrava (2003). ISBN 80-248-0493-X 36. Dražan, F.: Theory and Design of Conveyors, 1st edn, p.  290. Czech Technical University Prague, Prague (1983) 37. Dražan, F., Jeřábek, K.: Handling the Material, 1st edn, p. 456. SNTL – Nakladatelství technické literatury, Prague (1979) 38. Feda, J.: Mechanics of Particulate Materials—The Principles, 2nd edn. Academia Prague, Prague (1982). ISBN 0-444-99712-X 39. Malášek, J.: State of stress identification of transformed  – deformed particular materials. In: Engineering Mechanics 2007, pp.  173–174. Institute of Thermomechanics Academy of Sciences of the Czech Republic, v.v.i, Prague ISBN 978-80-87012-06-2 40. Jasaň, V.: Theory and Design of Conveyors, p. 336. TU Košice, Alfa Bratislava (1984) 41. Hauffstengel, G.J.: Kraftverbrauch von Fördermitteln. Mitteilung über Forschungsarbeiten auf dem Gebiet des Ingenieurwesens, Berlin (1913) 42. Beumer, B., Wehmeier.: Zur Frage des Schopfwiederstandes und Auswurfverhaltnisse bei Becherwerken, Fordern und heben. 1960, 1061 43. Koster, H.K.: Hochleistungsbecherwerke für den Bergbau, Glückauf-forschungshefte. 41/1980, 181–186 44. Müller, C.A.E.: Beitrag zur Klärung des Entleerungsvorganges bei schnellaufenden Becherwerken. Mühlen und Speicherbau 9, 1918 45. Krause, H.: Entleerungsvorgang bei zellenlosen Schaufelradern. 5/1972, 69–76 46. Khosravi, A.M.: Zur Theorie des Schaufelrade. Fordern und Heben, 23/1973, 787–793 47. Fort, C.J.: Berechnung und Auslegung von Becherwerken. Forder und Heben, 23/1973, 432–436 48. Dokoupil, O. Emptying of high power bucket elevators. Tutor of dissertation: Prof. Ing. Jaromír Polák, CSc, VŠB - Technical University of Ostrava, Ostrava (1990) 49. Helmut, T.: Einfluß des Entleerungsverhaltens auf Becherform und Becherteilung zur Erhöhung der Leistungsfähigkeit von Becherförderern. Dissertation, Otto-von-Guericke-Universität, Magdeburg (1993) 50. Krause, F., Katterfeld, A.: Usage of the Discrete Element Method in Conveyor Technologies. Institute for Conveyor Technologies (IFSL), The Otto-von-Guericke-University of Magdeburg, P.O.Box 4120, D-39016 Magdeburg 51. Katterfeld, A., Donohue, T.J.D.: Application of the discrete element method in mechanical conveying of bulk materials, In: 7th International Conference for Conveying and Handling of Particulate Solids (ChoPS), 7 (Friedrichshafen) 2012.09.10–13 52. Rozbroj, J.: Simulation (DEM) of particular mass movement in screw conveyor applied on structure of vertical screw. Tutor of dissertation: Prof. Ing. Jiří Zegzulka, CSc, VŠB - Technical University of Ostrava, Ostrava (2013) 53. Rozbroj, J.: Use of DEM in the determination of friction parameters on a physical comparative model of a vertical screw conveyor. Chem. Biochem. Eng. Q J ISSN 03529568. (2015-4-6) 54. Vyletělek, J.: Simulation of particular mass movement in hopper applied on structure of hopper model. Tutor of dissertation: Prof. Ing. Jiří Zegzulka, CSc, VŠB - Technical University of Ostrava, Ostrava (2013)

Index

A Abrasive materials, 194 Airsoft balls, 141 Airsoft guns, 53 AIRY pattern, 63 ANSYS software, 172 Autodesk Inventor software, 78, 83, 193 B Bosch digital protractor, 65, 70 Bucket discharge, 129 bucket elevator, 147, 148 calibration, 131 centrifugal, 35–37, 131, 135, 139, 140, 149, 150, 187 color spectrum, 142 geometric optimizations, 189 gravity, 33, 34, 131, 133–135, 148, 149, 186, 190–192 hopper design, 190 material distribution and throw angle, 133 material movement, 133 material speed of 0.39 m·s-1, 142, 143 material speed of 0.79 m·s-1, 143, 144 material speed of 1.58 m·s-1, 144, 145 method, 32 mixed, 32, 34, 35, 134–138, 149, 150, 187 optimization methods, 185 parametric equations, 37 shaft transports, 185 speed calculation, 134 start and end angles, 136, 145 steel grit, 185, 188 3D model, 185

throw trajectories vs. real results, 38 transported mass, 146 working shafts, 185 Bucket elevator blasting station, 174 bulk material, 31 color field, 175 components, 20 DEM simulation, 31, 172, 173 design and testing, 20 dynamic material flows, 174 energy intensity, 22 FEM deformation analysis, 171 filling and discharge methods, 29 grain size, 176 high-speed camera, 22 layer of abrasive material, 177 lift pumps, 19 mechanical and physical properties, 20 medium-deep steel, 174 parameters, 20 physical measurements, 171 power consumption, 29 problems, 24 pulling device, 19, 20 scooping filling, 177–183 screw conveyors, 31 service life, 171 spraying of color layers, 172 structure, 22 3D design methods, 20 transport branches, 176, 177 transport process, 29 transport sized abrasives, 176 transport systems, 17

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206 Bucket elevator (cont.) transport unsized abrasives, 176 types, 17, 18 types of bucket deep plastic, 173 deep steel, 173 steel, 174 validation (see Validation machine) validation and calibration, 50 variants attachment, 19 vertical, inclined conveyors, 17 Bucket filling digging force, speed 0.39 m·s-1, 155 digging force, speed 0.79 m·s-1, 155 digging force, speed 1.58 m·s-1, 155 direct flow filling, speed 0.39 m·s-1, 157, 158, 163 direct flow filling, speed 0.79 m·s-1, 158, 159, 163 direct flow filling, speed 1.58 m·s-1, 160, 161, 164 direct flow material, 38–40 elevator boot, 138, 150 optimization tasks, 137 quantities, 137 scooping material, 41–45 scooping speed 0.39 m·s-1, 151, 154 scooping speed 0.79 m·s-1, 152, 154 scooping speed 1.58 m·s-1, 153, 154 Bulk Solids Centre, 31, 54, 55 C CAD applications, 193 CAD software, 1 Calibration, 10, 12, 52, 53, 75, 100, 102, 103, 131 CAMSIZER, 63, 64 CILAS 1190 measuring instrument, 63 Coefficient of restitution, 64–67 Computer/manual control panel, 93 Coulomb law of the friction model, 5 D Deep steel bucket, 171 DEM simulation, 3, 83, 172, 173 Digging vs. direct flow forces, 167 Direct flow method, 194 Direct flow vs. scooping filling, 165 Discrete element method (DEM) apparent density, 56 calculation procedure, 3, 10 calibration and validation process, 11–13 computing, 14

flow mechanism, 5, 8 force effects and moments, 14 material sheets, 73 measurement materials, 54, 55 mechanical and physical properties, 10, 51, 72 parameters, 5 plastic deformation, 5 rolling friction torque, 9 shape accuracy, 53 simulation and real measurements, 51–54 tangential torque, 9 translation and rotation movement, 5 transport and storage processes, 10 visco-elastic scheme, 6 volumetric weight, 55, 56 DS-NET strain gauge system, 95 E EDEM software, 6, 8, 78, 91, 194 Elevator boot, 177 Elevator head, 20 Elevator speeds, 165, 166 Equipment prototype, 1 External friction, 57, 59, 60 F FEM deformation analysis, 171 Filling factor, 27–29 G Grabelt plastic bucket, 171 Granulometer, 63 Granulometry, 176 H Handyscan 3D instrument, 86 Hertz-Mindlin contact model, 7 Herz-Midling contact, 6 Herz’s theory, 5 Hoppers, 1 I Industrial tomography, 96 Internal friction, 8, 30, 56–58 J Jenike reciprocating shear machine, 57, 59

Index K Kinematic properties bucket trajectory, 89 DEM simulation, 89, 90 gravitational discharge, 89 linear or rotation motion, 89 mixed method of discharge, 89 setting spacing, 92 3D model of the bucket elevator, 89 validation machine, 89 L LAVISION high-speed camera, 99, 100 M Mass point, 30 N New design approach, 3 O Olympus high-speed camera, 65 P Particle image velocimetry (PIV), 96, 97, 193 Particle size distribution, 61, 63 Poisson’s ratio, 8, 72 Pole method, 30, 32, 33 R Real model, 49 Repose angle, 59, 61, 62 Results for optimization, 127, 128, 156, 168–170 Rolling friction, 68, 70, 71 RST-95 standard software, 57 S Schulze shear machine, 57 Scooping filling, 177–183 Scooping method, 165 bucket edge digging, 41 bucket filling, 42 bucket material, 41 bucket spacing, 45 bulk material, 45 color layers, 171 digging force, 46

207 direct flow, 194 drag factor, 44 elevator boot, 41 engagement and stabilization, 42 mass unit, 43 power consumption, 42 transport speed, 45 Sensors, 95, 97 Shallow pressed steel bucket, 171 Shear modulus, 72 Simulation environment, 90 Sliding friction, 65, 68, 69 Steel buckets, 87, 88 Steel grit, 177, 184, 185 Steel Grit GH50 (steel shots), 171, 176, 177 Storage equipment, 1, 2 Strain gauge equipment, 98 T Table of test speeds, 92 Tangential damping, 9 Theoretical model, 49 3D DEM model, 95 3D design approach, 1, 2 3D model of the calibration, 82 3D simulation model, 75 Transport equipment, 1, 2, 27 U Uniplanar Cartesian coordinate system, 64 V Validation and calibration schema, 50 Validation bucket elevator, 75–78, 195 Validation machine belt speed of 0.39 m·s-1, 109–111 belt speed of 0.59 m·s-1, 112–114 belt speed of 0.79 m·s-1, 115–117 belt speed of 1.19 m·s-1, 118–120 belt speed of 1.58 m·s-1, 121–123 bucket elevator, 96 bucket filling, 84 calculated field of speeds, 106 calculated simulation, 107 calibration bucket, 75 camera locations, 96, 99 color spectrum of particle speed field, 108, 125, 126 construction, 76 DEM simulation, 103 description, 77 direct measurements, 95

Index

208 Validation machine (cont.) frame rate, 100 geometric parameters, 75 geometric parameters of throw trajectories, 108, 124 high-speed camera and evaluated speed vector, 103 indirect measurements, 96 kinematic parameters, 75 length calibration, 100, 102 measured areas, 103, 104 PIV, 96, 97 raster dimensions, 100, 101 real dynamic flow speed, 105 real measurements and simulations, 104 rebuilding, 81 settings, 79 setup of measuring space, 100, 101 simulation environment, 75 specification, 78

speed measurement, 98 3D model, 76 universal bucket, 78 volumetric filling, 78 Verification of speed-laser tachometer, 93 Voight model, 5 Voltcraft laser tachometer, 90, 93 W Wista bucket elevator, 175, 185 Y Young’s Modulus, 7, 8 Z Zenegero machine, 59, 61