longwall mining

Modelling of an Armoured Face Conveyor

David H. WaugeB.E. (Hons.) M.E.

Department of Mechanical Engineering

The University of Queensland

Masters of Engineering Science Thesis

August 19, 2002

Statement of originality

The work presented in this thesis is to the best of my knowledge original, with the exception of the

content acknowledged within the report. The material has not previously been submitted, either in

whole or in part, for a degree at The University of Queensland, or at any other university.

David H. Wauge

Abstract

An armoured face conveyor (AFC) is a chain conveyor, which is used in the longwall mining pro-

cess to transport material from the coal face. The integrity of the AFC chain is a critical factor in

determining the reliability of the AFC and maintaining the efficiency and profitability of a longwall

mine.

This thesis argues that the dynamic behaviour of an AFC drive has a significant influence

on the tension in the AFC chain, and is therefore critical in determining the reliability of the chain

and the entire AFC system. There are currently two drive types widely used to power the AFC; the

fluid coupling and the controlled slip transmission (CST) drives. This thesis explores the dynamic

behaviour of both drive types and their effect on chain tension using a computer model of the AFC.

This work was undertaken in two parts.

The first part involved the development of the equations of motion of common AFC com-

ponents, such as the asynchronous motor, fluid coupling, gearbox, CST, chain sprocket, and the

chain assembly. The equations governing the forces applied to the chain and the process of loading

the extracted material onto the AFC, were also developed.

In the second part of this thesis the dynamic model of the AFC was implemented on

a computer program. The computer simulation was used to study the performance of the fluid

coupling and CST drives under different loading scenarios. Inter alia, it was found that:

1. Critical performance parameters of the model can be found using a series of system identifi-

cation tests, which can be carried out on the target system in one shift.

2. After these system identification tests have been performed, the model is a good predictor of

the steady-state behaviour of the target system.

3. The dynamic behaviour of the drives has a significant effect on chain tension when the load

vi

applied to the chain rapidly increases.

4. When the chain is jammed, the CST drive produced lower chain tensions than the fluid cou-

pling drive.

5. To prevent adverse chain tensions during a chain jam, it is necessary to fit the fluid coupling

drive with a torque limiter.

6. The fluid coupling and CST were both effective in limiting the torque applied to the motors

when a large developing load (i.e a blockage) was applied to the chain.

It was found that the tension applied to the chain by both drive types, was a result of the

torque applied by the motors and the inertia of the drive components. For a fluid coupling drive that

is not fitted with a torque limiter, the inertia of the drive components contributed significantly to the

total tension in the chain.

Acknowledgments

I begin by giving thanks to my supervisor Professor Hal Gurgenci for his invaluable assistance

throughout the project and for his sincere and wise advice. I would also like to thank Dr. Ross

McAree for helping to provide the project with focus and for generously sharing his time.

I would like to thank the staff at Moranbah North Colliery for their kindness and hospi-

tality during my stay at the Moranbah North mine site.

A warm thank you to my friends and family who have given me their time and support. In

particular I would like to thank Shane Coles, Andrew Hall and Andrew Purchase for their selfless

contributions to the project.

I give my deepest thanks to Kathryn Staatz for her understanding, tolerance, love and

support.

Contents

Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

1 Introduction 11.1 Thesis aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Previous research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 AFC test site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Longwall Mining 52.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Longwall equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.1 Roof supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 Shearer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.3 Armoured face conveyor . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.4 Beam stage loader . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.5 Electrical system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3 Motor Modelling 213.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2 Three-phase model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2.1 Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3 Two-phase model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3.1 qd0 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.3.2 Flux linkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.3 Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.4 Electromagnetic torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.4 Mechanical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.5 Per unit equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.6 Motor torque-speed curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

ix

x Contents

4 Mechanical Modelling 394.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.2 Lagrange’s equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.3 Fluid coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.3.1 Transmitted torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.3.2 Performance variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.3.3 Equations of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.4 Gearbox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.4.1 Equations of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.4.2 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.5 Controlled slip transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.5.1 Equations of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.5.2 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.5.3 Clutch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.6 Torque limiting coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.7 Chain sprocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.7.1 Equations of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5 Chain and Load Model 675.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.2 Chain model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.2.1 AFC geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.2.2 AFC reference frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.2.3 Chain element mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.2.4 Equations of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.3 Material extraction and loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.3.1 Coal block density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.3.2 Shearer extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.3.3 AFC loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.3.4 Carry back . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.4 Externally applied forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.4.1 Sprocket force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.4.2 Inertial loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795.4.3 Gravitational loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805.4.4 Frictional loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815.4.5 Horizontal snaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.4.6 Chain jam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.4.7 Blockage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

6 AFC Simulation 936.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 936.2 MATLAB and SIMULINK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 936.3 Integration routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

Contents xi

6.4 AFC model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 946.4.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 946.4.2 Electrical subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 956.4.3 Drive subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 956.4.4 Chain subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 986.4.5 Loading subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1006.4.6 Load sharing subsystem (CST only) . . . . . . . . . . . . . . . . . . . . . 100

7 Comparison of Drive Configurations 1057.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1057.2 Analysis of drive system behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . 1067.3 Steady-state behaviour of the model . . . . . . . . . . . . . . . . . . . . . . . . . 1217.4 Dynamic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

7.4.1 Startup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1237.4.2 Ramp load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1247.4.3 Step load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

7.5 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1417.6 Time step independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1427.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

8 Summary and Conclusions 1498.1 Scope for future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Bibliography 153

A Glossary of terms 155

B Friction Coefficient 159B.1 Experimental procedure and results . . . . . . . . . . . . . . . . . . . . . . . . . . 160

B.1.1 No load test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160B.1.2 Recirculation load test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161B.1.3 Coal load test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

B.2 Friction factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162B.2.1 Chain assembly/pan friction . . . . . . . . . . . . . . . . . . . . . . . . . 162B.2.2 Carry back friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163B.2.3 Material friction (upper race) . . . . . . . . . . . . . . . . . . . . . . . . . 166

C Drive Specifications 168C.1 Motor specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168C.2 Fluid coupling specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170C.3 CST specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172C.4 Rated and base quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

C.4.1 Rated quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173C.4.2 Base quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

List of Figures

2.1 Plan view of the retreat longwall mining process . . . . . . . . . . . . . . . . . . . 62.2 Longwall equipment assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Roof collapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.4 Longwall roof support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.5 Shearer assembly overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.6 Shearer supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.7 Shearer cutting regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.8 A typical panline assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.9 Typical chain assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.10 A plan view of a typical fluid coupling drive . . . . . . . . . . . . . . . . . . . . . 192.11 A typical electrical network of an underground coal mine . . . . . . . . . . . . . . 20

3.1 A simplified representation of a 2-pole, 3-phase induction motor . . . . . . . . . . 373.2 Vector diagrams of a 2 and 3-phase motor . . . . . . . . . . . . . . . . . . . . . . 383.3 A typical motor torque-speed curve . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.1 Free body diagram of a fluid coupling . . . . . . . . . . . . . . . . . . . . . . . . 414.2 Fluid coupling torque-slip curve . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.3 Generic gearbox arrangement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.4 An overview of the CST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.5 Variation of CST output shaft speed with ring gear speed . . . . . . . . . . . . . . 634.6 The planetary gear arrangement of the CST . . . . . . . . . . . . . . . . . . . . . 644.7 A block diagram of the CST’s clutch . . . . . . . . . . . . . . . . . . . . . . . . . 664.8 A free body diagram of the chain sprocket body . . . . . . . . . . . . . . . . . . . 66

5.1 A simplified representation of the AFC chain . . . . . . . . . . . . . . . . . . . . 875.2 Shearer and coal face geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885.3 Engagement zones of sprocket teeth and chain elements . . . . . . . . . . . . . . . 895.4 Sprocket tooth/chain element interaction . . . . . . . . . . . . . . . . . . . . . . . 905.5 Gravitational and frictional force components applied to a chain element . . . . . . 915.6 Pan and flight bar interaction during snaking . . . . . . . . . . . . . . . . . . . . . 92

6.1 An overview of the AFC model fitted with CST drives . . . . . . . . . . . . . . . 96

xiii

xiv List of Figures

6.2 An overview of the fluid coupling and CST drive models . . . . . . . . . . . . . . 1026.3 The motor subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1036.4 An overview of the CST model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1036.5 The chain subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

7.1 Unloaded startup: decoupled fluid coupling drive . . . . . . . . . . . . . . . . . . 1127.2 Unloaded startup: decoupled CST drive . . . . . . . . . . . . . . . . . . . . . . . 1137.3 Loading scenarios: decoupled drives . . . . . . . . . . . . . . . . . . . . . . . . . 1147.4 Small step: decoupled fluid coupling drive . . . . . . . . . . . . . . . . . . . . . . 1157.5 Small step: decoupled CST drive . . . . . . . . . . . . . . . . . . . . . . . . . . . 1167.6 Large step: decoupled fluid coupling drive . . . . . . . . . . . . . . . . . . . . . . 1177.7 Large step: decoupled CST drive . . . . . . . . . . . . . . . . . . . . . . . . . . . 1187.8 Ramp: decoupled fluid coupling drive . . . . . . . . . . . . . . . . . . . . . . . . 1197.9 Ramp: decoupled CST drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1207.10 Startup: fluid coupling drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1297.11 PSD: Startup of fluid coupling drive . . . . . . . . . . . . . . . . . . . . . . . . . 1307.12 Startup: CST drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1317.13 PSD: Startup of CST drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1327.14 Ramp load: fluid coupling drive . . . . . . . . . . . . . . . . . . . . . . . . . . . 1337.15 PSD: Ramp load, fluid coupling drive . . . . . . . . . . . . . . . . . . . . . . . . 1347.16 Ramp load: CST drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1357.17 PSD: Ramp load, CST drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1367.18 Maximum chain tension: Ramp load . . . . . . . . . . . . . . . . . . . . . . . . . 1377.19 Step load: fluid coupling drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1387.20 Step load: CST drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1397.21 Maximum chain tension: Step load . . . . . . . . . . . . . . . . . . . . . . . . . . 1407.22 The maximum chain tension produced by the fluid coupling drive, with a change in

the critical performance parameters of the chain and sprocket. . . . . . . . . . . . 1447.23 The effect of a change in the fluid coupling and CST drives critical performance

parameters on maximum chain tension during a jam. . . . . . . . . . . . . . . . . 1457.24 Time step independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1467.25 Variation of maximum chain tension with a change in time step. . . . . . . . . . . 147

C.1 Motor torque-speed curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169C.2 Fluid coupling torque-slip curve . . . . . . . . . . . . . . . . . . . . . . . . . . . 170C.3 Fluid coupling fill level during startup . . . . . . . . . . . . . . . . . . . . . . . . 171C.4 CST reference speed during startup . . . . . . . . . . . . . . . . . . . . . . . . . . 172

List of Tables

3.1 Per unit base quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

6.1 The performance parameters of the electrical source . . . . . . . . . . . . . . . . . 976.2 Drive parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 996.3 Chain subsystem parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1016.4 Loading subsystem parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

7.1 A comparison between the motor voltage, current and power of the real and simu-lated AFCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

7.2 The first ten analytically determined natural frequencies of the chain and the poly-gon frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7.3 Model parameter variations during the sensitivity analysis . . . . . . . . . . . . . . 143

B.1 Performance parameters used for AFC testing . . . . . . . . . . . . . . . . . . . . 160B.2 Results of the no load test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161B.3 Results of the recirculation test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161B.4 Results of the coal load test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

C.1 Motor specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168C.2 Motor performance details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168C.3 Salient points on the motor torque-speed curve . . . . . . . . . . . . . . . . . . . 169C.4 Salient points on the fluid coupling torque-slip curve . . . . . . . . . . . . . . . . 170C.5 Rated quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173C.6 Base quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

xv

Nomenclature

Roman symbols

� chain damping coefficient

�� gearbox friction coefficient

�� CST friction coefficient

�� sprocket tooth damping

�� sprocket pitch circle diameter

�� sum of the external forces acting on a chain element �

� component of the external force acting on a chain element

�� fluid coupling fill level

�� fluid coupling design fill level

�� rated motor frequency

�� volume fraction of secondary material in a coal block ��

�� sprocket tooth/chain element engagement force

gravitational acceleration

� speed modification constant used in the motor load sharing algorithm

� phase current

� drive component inertia

� motor inertia

� chain stiffness

�� CST controller gain

�� sprocket tooth stiffness

Lagrangian � � � � � �

xviii Nomenclature

�� AFC length

�� chain length, ��

�� length of chain wrapped around a sprocket

�� stator leakage inductance

�� rotor leakage inductance

� referred magnetizing inductance

�� stator phase magnetizing inductance

� rotor phase self-inductance

�� mutual inductance between rotor phases

� stator phase self-inductance

�� mutual inductance between stator phases

�� maximum mutual inductance between a stator and rotor phase

�� material/component mass

� number of discrete chain elements in the model

�� total number of flight bars

�� gear ratio, ��

�� number of effective turns of a stator phase winding

�� normal force produced between flight bars and pan sigmas due to snaking

�� number of effective turns of a rotor phase winding

�� number of chain strands

�� synchronous speed

��

��, differential operator

�� stator winding resistance

�� rotor winding resistance

Nomenclature xix

� gear radius

�� rated apparent power of motor

��,�� safety triggers, as explained in Section 4.5.3

�� fluid coupling slip, ��

��

� kinetic energy of the system

� chain tension

� fluid coupling design torque

�� torque

� phase voltage

� potential energy of the system

�� rated voltage of motor

�� volume of secondary material in a coal block

�� stator line voltage

�� rotor line voltage

�� total volume of a coal block

�� energy

� reactance

�� shearer position

�� sprocket tooth position

Greek symbols

�� snaking angle

� electrical angular displacement between q and 1r coils

Æ� virtual displacement of generalized coordinate

xx Nomenclature

Æ� virtual work

�� change in element length due to pretensioning

�� efficiency

�� angular displacement

� flux linkage

�� friction coefficient

!� density

" AFC inclination

# flux linkage per second

$� base angular frequency

$� angular electrical rotor speed

$�� angular rotor speed

Abbreviations

AFC armoured face conveyor

BSL beam stage loader

CST controlled slip transmission

FLC full load current

FLS full load speed

FLT full load torque

MMF magnetomotive force

PCD pitch circle diameter

RMS root mean square

Chapter 1

Introduction

Longwall mining is a continuous mining process, which is used to extract coal from thin,

horizontal lying, underground deposits. An armoured face conveyor (AFC) is a type of chain con-

veyor used in a longwall mine to transport material from the coal face. It is the first in a series of

chain and belt conveyors that move the extracted material to the surface of the mine1.

The continuous, serial nature of the longwall mining process means that failure of one

component causes down-time in all other system components. In a series system such as this, the

total system reliability is a product of the reliability of the individual components in the series. It is

essential to maintain a tight control on the reliability of the individual components to maximise the

overall system reliability.

To reduce mine development costs, longwall panel widths and consequently the AFC

lengths have steadily increased. To accommodate the larger loads, the strength of the AFC compo-

nents and the capacity of the AFC drives have also increased. At present it is common to find three

�� asynchronous motors powering an AFC and there are currently plans to increase motor

capacity to �� .

The effects of the increasing motor capacity on peak chain tension is not well understood.�A detailed description of longwall machinery is presented in Chapter 2.

1

2 Chapter 1: Introduction

As drive capacity has increased, failures such as chain breakage, which were once a relatively

scarce occurrence, are now being seen in greater numbers. By previous design criteria that only

accounts for the static loads applied to the AFC, the increase in power should have had a limited, and

predictable effect on the reliability of the chain. The failure of the original equipment manufacturers

to maintain the chain reliability in larger systems, implies that there is a deficiency in the current

design methodology.

In this thesis we develop an argument that the dynamic interactions between different

components in an AFC drive system have a critical influence on the peak chain tension levels and

the resulting rates of failure.

1.1 Thesis aim

The aim is to study how the dynamic behaviour of the fluid coupling and controlled slip

transmission (CST) drives influences the tension in the AFC chain. The fluid coupling and the CST

drives were chosen because they are the drives most commonly used on current AFC’s. The per-

formance of the drives will be studied by using a computer simulation, which models the equations

describing the dynamics of the AFC components.

1.2 Previous research

There is no published work known to the author that explicitly studies the influence of the

dynamic behaviour of a drive type on the maximum tension in the chain. The majority of previous

research that has been performed by the equipment manufactures and by researchers, such as the

study by Morley et al. (1988) [11], is focused on obtaining estimates for the maximum chain tension

using a static force balance. They do not account for the influence that the dynamics of the drives

have on chain tension.

Chapter 1: Introduction 3

Broadfoot (1996) [2] studies the performance of several drive types using a computer

simulation. He develops the equations which describe the mechanical and electrical components of

several AFC drive configurations. He then implements these equations on a computer simulation,

which he uses to study the performance of the drives. Broadfoot defines performance in terms of the

ability of a drive to respond to different loading scenarios. Because his model does not incorporate

a dynamic model of the chain, the effect of the drive dynamics on chain tension is not considered.

Wolfe and Flote (2001) [19], investigate the causes of vibration related stress in an AFC

during a typical loading cycle. They compare the characteristics of chain tension data acquired

from a strain gauge, to the results of a computer model of the AFC. Their focus is on the analysis

of the frequency content of the chain tension signal. They do not use the real data or the model to

investigate the peak chain tension produced by the dynamics of the drives.

1.3 Thesis overview

Chapter 2 introduces the longwall mining process. It also overviews the major subsystems

of the longwall and provides a detailed description of the longwall components.

Chapter 3 develops the differential equations that describe the electrical and mechanical

dynamics of an idealized �-phase asynchronous motor. A generalized 3-phase model of the motor

is first developed. This is then transformed to a mathematically equivalent 2-phase representation.

The 2-phase representation improves the simulation speed of the model.

Chapter 4 develops the dynamic equations that describe the motion of standard AFC drive

components, such as the fluid coupling, gearbox, CST and chain sprockets.

Chapter 5 develops the differential equations that describe the motion of the AFC chain/flight

bar assembly. It also develops a model that describes the loading of material onto the AFC by the

shearer.

4 Chapter 1: Introduction

Chapter 6 provides an overview of the entire computer model. It also details the perfor-

mance parameters that are used to describe the components of the model.

Chapter 7 studies the performance of the fluid coupling and CST drive configurations

under different loading conditions. The simulation results are verified by using a sensitivity analysis

and by comparing the quasi-steady-state behaviour of the model to data acquired from a real AFC.

Finally, Chapter 8 summarizes the work performed in this thesis and makes further rec-

ommendations for work in this area.

There is a glossary of terms included at the end of this thesis, which details specific terms

related longwall mining (cf. Appendix A).

1.4 AFC test site

Throughout this thesis there is reference made to, “the real AFC at the test site”, which

refers to the AFC installed at Moranbah North Colliery (MNC). Various trends acquired from this

site are used in the study, as are the performance parameters of various drive components.

Chapter 2

Longwall Mining

2.1 Introduction

Longwall mining is a continuous mining process which is used to extract coal from thin,

horizontal lying, underground deposits. The longwall mining process originated in European coal

mines in the � �� century. However, it was not until the 1960s, after the realization of several sig-

nificant technical advances, that the longwall mining technique gained widespread acceptance [6].

Today, longwall production accounts for ��%�� of Australia’s raw black coal production, and �

of Australia’s total underground black coal production [1].

The two longwall mining methods commonly employed are retreat longwall mining and

advance longwall mining 1. Typically Australian longwall mines employ the retreat mining method.

European longwall mines, which are at greater depths and have poorer roof conditions, generally

use the advance mining method.

An overview of the retreat mining method is given in Figure 2.1. Two parallel gate road

headings, which are generally between 100 and 300m apart, are driven horizontally into the coal

seam from a trunk road. After reaching the required length, a roadway is driven between the gate

�Definitions of terms commonly used in this thesis are presented in a glossary in Appendix A

5

6 Chapter 2: Longwall Mining

Figure 2.1: Plan view of the retreat longwall mining process

Chapter 2: Longwall Mining 7

roads to form the longwall face. In Australia, typically two or three headings are developed to form a

gate, one of which forms the maingate and one the tailgate (cf. Figure 2.2). The maingate typically

houses the belt conveyor, beam stage loader (BSL) and the electric and hydraulic equipment2. The

maingate provides the primary access route to the longwall face and the tailgate acts as an auxiliary

access route. The armoured face conveyor (AFC) and roof supports are established on the longwall

face and are used to retreat the longwall towards to the trunk road.

Figure 2.2: Longwall equipment assembly (plan view)

Once a longwall panel has been extracted, longwall equipment such as the roof supports

are relocated to the next longwall face. Highly stressed and damaged components such as the AFC,

are sent for servicing. This cycle typically continues for the duration of the mine life.

�A detailed overview of the longwall equipment is given in Section 2.2


2.2 Longwall equipment

The longwall mining system can be subdivided into the following � major equipment

subsystems:

1. Roof supports

2. Shearer

3. Armoured face conveyor

4. Beam stage loader

5. Electrical equipment

The subsystems will be detailed in the following section.

2.2.1 Roof supports

During the mining process, the longwall equipment and personnel are protected by hy-

draulically actuated roof supports, which cover the length of the longwall face. The roof supports

control the collapse of the overlying strata and aid in stabilizing the coal face.

Each roof support is connected to an AFC pan via a hydraulic ram, which is utilized during

longwall advancement. As the face advances longitudinally along the panel, the roof collapses under

its own weight behind the roof supports, as shown in Figure 2.3. The collapsed area behind the roof

supports is commonly referred to as the goaf or gob. Controlling the collapse of the goaf is critical

to the efficiency and safety of a longwall mine.

There are two types of roof supports; shield and chock supports. The shield support has

either � or � hydraulic legs. A typical � legged shield support is depicted in Figure 2.4. The shield

has � forward leaning legs, which are attached to the canopy. The goaf shield is attached to the base


Figure 2.3: Roof collapse

with lemniscate linkages, which allow the front of the canopy to remain at a fixed distance from the

coal face independent of the height of the shield.

The chock supports have � vertical or inclined hydraulic legs, which are connected directly

to the canopy. This allows the angle of the canopy to be readily controlled.

Sprags are used to support the coal face. They are held against the face during various

stages in the cutting cycle to help prevent face collapse and to reduce spalling of the coal face

(slabbing).

2.2.2 Shearer

The cutting of the longwall coal face is performed by either a shearer or a coal plough,

however the shearer is the only cutting tool used in Australia. The plough is most often used in

Europe, but its use is slowly being phased out.

A pictorial overview of a typical shearer assembly is given in Figure 2.5. The shearer


Figure 2.4: Longwall roof support

uses cutting tools (picks) attached to two spinning metal drums, to dislodge material from the face.

Typically the drums have a diameter of �%�� and width of �%��, and are independently driven by

variable speed drives. Each drum is supported by a hydraulically actuated ranging arm, which can

provide the shearer with a cutting height of up to 5.0 meters. The cutting height is controlled by the

operator and is varied to suit face conditions and safety requirements.

The shearer traverses the face by sliding on the AFC pans and haulage track (cf. Fig-

ure 2.6). It is supported on the pans by shoes, which are situated under each corner of the shearer

body. Two sprockets driven independently by the shearer maingate and tailgate haulage motors,

engage a haulage track to provide the required motive force.

The primary function of the cowl is to clean the floor or bench as the shearer traverses the

face (see Figure 5.2 for an overview of the coal face). It is also argued that the cowl acts to reduce

dust emissions. The position of the cowl can be controlled by the operator and is varied during

different stages of the shearer cutting cycle.


Figure 2.5: Shearer assembly overview

Cutting method

The longwall face can be cut by using either the unidirectional or bidirectional cutting

regimes. For the unidirectional cutting method, the shearer takes two passes to cut the entire height

of the longwall face. This method is typically employed on high faces where spalling of the coal

face is a problem. For the bidirectional cutting method the entirety of the coal face is cut in one

pass. It is used when adequate ground and roof conditions are present.

For a typical unidirectional cutting regime the following sequence is followed (cf. Fig-

ure 2.7):

1. On the first pass (tailgate to maingate) the shearer cuts a distance of � � �� from the top of

the face. The panline is held against the longwall face.

2. After the shearer has passed a chock, the sprags are extended to support the exposed roof.


Figure 2.6: Shearer supports

3. On the return pass (maingate to tailgate) the remainder of the longwall face is extracted and

the floor is cleaned.

4. Behind the cutting line of the shearer the pans are pushed in sequence by hydraulic rams,

against the newly exposed face. This procedure is referred to as snaking.

5. The sprags are then retracted and the roof supports are advanced individually.

6. When the shearer reaches the tailgate the sequence is repeated.

The first pass is commonly referred to as shearing and the second pass as flitting. The

shearing and flitting speeds vary depending on mine conditions. The advancement process can be


performed either automatically or manually.

2.2.3 Armoured face conveyor

An AFC is a chain conveyor that is designed specifically for the longwall mining process.

The armoured face conveyor (AFC) conveys the coal from the longwall face to the beam stage

loader (BSL). It also acts to support the shearer and is used in the advancement of the longwall. It

is comprised of the maingate and tailgate drives and the panline assembly.

Panline assembly

The panline is comprised of interconnected pans, chains and equally spaced flight bars

(cf. Figure 2.8). The AFC pans support the chains and flight bars, which run in their upper and

lower races. They also support the transported material loaded onto the upper deck by the shearer.

Each pan is generally � � �� in length and is fixed via a hydraulic ram to a roof support. The

hydraulic ram allows the pan to be pushed forward when the longwall is advanced. The pans are

able to roll and pitch, which allows the AFC to advance and to accommodate an undulating floor.

The chain assembly is comprised of chain strands and cross members called flight bars.

Common chain and flight bar arrangements are shown in Figure 2.9. The twin in-board chain

configuration is often preferred over the single in-board chain configuration, because it allows larger

loads to be carried and also produces less wear on the sprocket teeth for a given load.

The spill plates prevent coal from being unloaded on the goaf side of the pans. They also

form part of the housing for the bretby, which supplies the shearer with power and lubrication.

The ramp plate is utilized during the advancement process to clean the floor and to load

excess material onto the pans.


Drives

Currently, either two or three drives are used to power an AFC. For a two drive AFC, one

drive is situated at the maingate and one drive is situated at the tailgate. For a three drive AFC, an

extra drive is added to the maingate. The two most widely used drives are the fluid coupling and

controlled slip transmission (CST) drives.

An overview of a typical fluid coupling drive is presented in Figure 2.10. The fluid cou-

pling drive consists of an asynchronous motor, fluid coupling, gearbox and chain sprocket. A cou-

pling that limits the torque applied to the chain sprocket, can also be fitted between the sprocket and

the gearbox. Limiting the torque applied to the chain sprocket prevents excess tension being applied

by the drives to the chain. The fluid coupling drive has traditionally been used to power AFC’s and

is currently the drive type most commonly employed.

The CST is a recent addition to the family of AFC drives, although similar technology has

long been used in other industries. The CST effectively replaces the fluid coupling, gearbox and the

torque limiting coupling. It was initially introduced to overcome the overheating problems of the

fluid coupling and to control the speed of chain sprocket during the starting of the AFC.

A detailed description of the components of the fluid coupling and CST drives is given in

Chapters 3 and 4.

Chain tensioner

The components of the tailgate drive are mounted on a sliding frame that can be extended

and retracted by hydraulic rams. Adjusting the extension of the rams alters the distance between the

AFC sprockets which effects chain tension. This practice allows a desired level of chain tension to

be maintained and is thought to improve chain life and to reduce sprocket wear. Chain tension is

typically monitored by observing the pressure in the hydraulic rams.

For the purposes of this research project the tension in the chain has been assumed to be


constant and to be equal to the level of pretension.

2.2.4 Beam stage loader

The beam stage loader (BSL) is a chain conveyor that transports the coal unloaded from

the AFC onto the outbye belt conveyor. Coal loaded onto the BSL is hauled through a crusher,

which breaks the coal to a size suitable for transport. Once passing through the crusher, the broken

material is loaded onto the belt conveyor. The belt conveyor transports the material to the processing

and handling facilities on the surface of the mine.

2.2.5 Electrical system

An overview of the electrical network of a typical underground coal mine, is shown in

Figure 2.11. The mine is supplied at the supply voltage, which is stepped down by the primary

surface transformer. This voltage powers the mine network, which includes the processing plant,

surface machinery and the underground mine.

Once underground the voltage is again stepped down by a secondary transformer. This

voltage is used to power pumps, underground machinery and the longwall. The voltage is fed to a

distribution control box (DCB), which supplies the power to electrical items at the longwall face.

The DCB connects the trailing cables of several mining machines to a single feeder cable. Each

cable outlet has its own contactor or circuit breaker, with its own controls and protection.

Typically, �-pole, �-phase asynchronous induction motors are used to drive the longwall.

They are generally started by direct-online switching and their starting sequence is controlled by a

PLC.

For the purposes of this project the dynamic effects of the electrical system will be ig-

nored. The voltage applied to the motors will be directly controlled.


Tailgate-maingate cutShearer drum position

Panline position

Maingate-tailgate cutShearer drum position

Panline position

Figure 2.7: Shearer cutting regime


Figure 2.8: A typical panline assembly


(a) Twin in-board chain assembly

(b) Single in-board chain assembly

Figure 2.9: Typical chain assemblies


Figure 2.10: A plan view of a typical fluid coupling drive


AC Supply

Cables

PrimaryTransformer

Cables

SecondaryTransformer

Prep. Plant Other

Cables

AFC Face DCB

MMMMMM

ShearerMaingate 2Maingate 1TailgateStage LoaderCrusherLights

Other

Figure 2.11: A typical electrical network of an underground coal mine

Chapter 3

Motor Modelling

3.1 Introduction

The following section details the differential equations that describe the electrical and

mechanical dynamics of an idealized three-phase induction motor. It provides an overview of the

dynamic equations and the assumptions made in their derivation.

A generalized 3-phase model of the motor will first be developed. The 3-phase model is

readily derivable from first principles and it therefore offers an intuitive introduction to the operation

of an induction motor. It also forms the basis of the models developed later in the chapter.

To improve the efficiency of the computer simulation of the motor, the 3-phase model will

be transformed to an equivalent 2-phase representation. The 2-phase model provides a mathemati-

cally concise representation of the 3-phase machine and removes several computationally intensive

steps when implementing the equations on a computer.

The equation of motion describing movement of the rotor, will be derived in terms of the

electromagnetic torque, the externally applied mechanical torque, the viscous damping losses and

the rotor inertia.

To preserve the generic nature of the discussion the electrical and mechanical equations

21

22 Chapter 3: Motor Modelling

of motion will be presented in per unit (non-dimensional) form. The per unit form is used in the

development of the motor simulation.

Finally an overview of the salient features of a typical motor torque-speed curve, will be

discussed.

3.2 Three-phase model

The 3-phase motor model describes an idealized, symmetrical, induction motor. It can be

used to model both wound and squirrel cage rotors.

In the following derivation the stator and rotor windings are assumed to be balanced and

to produce a rotating, sinusoidally distributed, magnetomotive force (MMF) wave, with the rotor

having the same number of poles as the stator. Core losses are assumed to be negligible and magnetic

saturation is ignored.

The motor parameters, as determined from the equivalent circuit, will be assumed to be

constant throughout the derivation. For a real motor, the motor parameters may vary from startup

to full-load speed for a given voltage and line frequency. However, for a motor running close to its

operating speed, it is reasonable to assume that the motor parameters remain constant because the

motor speed variation is small over a large torque range. For this reason the motor run parameters,

which represent the performance parameters of the motor at full load speed (cf. Section 3.6), have

been used in the simulation. The effects of thermal resistive changes are also neglected, because

under typical conditions their influence on the performance of the motor is negligible.

As the stator and rotor windings are assumed to produce a sinusoidal MMF wave, it

is possible to portray the individual phase windings as an equivalent single coil with the mutual

coupling between the phases being a function of the angle between their magnetic axes. Figure 3.1

depicts the equivalent coils of a 3-phase, 2-pole motor, with the rotor displaced at an electrical

Chapter 3: Motor Modelling 23

angular displacement, ��&�� from the stator.

3.2.1 Voltage

If the voltages for each stator and rotor phase are summed around a closed loop, then the

following expressions can be derived for the stator and rotor line-to-neutral voltages:

��

��

��

��

��

��

� ��

��

��

��

��

��

��

��

�� ' (3.1)

where

�� ' ��' ��

� ' �� ' ��' ��

� ' (3.2)

�� ' ��' ��

� ' �� ' ��' ��

� ' (3.3)

�� ' ��' ��

� ' �� ' ��' ��

� ' (3.4)

��

��

� ��

� � ��

�� ' �

��

��

� ��

� � ��

�� ' (3.5)

and� = phase voltage �� ,� = phase current �(�,� = flux linkage ��)%�*��,�� = stator winding resistance ��,�� = rotor winding resistance ��,� = differential operator,

=�

��.

Because no voltage is applied to the rotor of a squirrel cage motor, the rotor line-to-neutral volt-

ages, �� , �� and �� are zero.


To obtain the numerical solution of Equation 3.1, it is necessary to express flux-linkage

in terms of the current. If the machine is assumed to be balanced, it can be inferred that the sta-

tor windings have identical resistance and inductance; similarly for the rotor windings. Using this

assumption allows the following expression to be developed for flux-linkage in terms of the cur-

rent [13]:

��

��

��

��

��

��

��

��

��

��

��

��

�� % (3.6)

The terms of the inductance matrix submatrices in Equation 3.6 are expressed in the fol-

lowing form:

��

��

� ��

��

��

�� ' (3.7)

��

��

� ��

��

��

�� ' (3.8)

��

��

��

��

��

�� "� �� "�

�� "� �� "�

�� "� �� "� ��

�� ' (3.9)


where � = stator phase self-inductance �+�, � = rotor phase self-inductance �+�, �� = mutual inductance between stator phases �+�, �� = mutual inductance between rotor phases �+�, �� = maximum mutual inductance between a stator and rotor phase �+�,�� = rotor electrical angle ��&��," = phase angle ��&��,

= �� .

3.3 Two-phase model

A considerable problem with the 3-phase model is that the mutual inductance matrices

(�� , ��

�� ) in Equation 3.6 vary with ��. This can add significantly to the computation time,

as the inductance matrix needs to be inverted to determine the current from the flux linkage (cf.

Equation 3.6). It is possible to avoid the variation of mutual inductance by transforming the 3-

phase stator and rotor quantities such as voltage, current and flux-linkage to a common reference

frame. This procedure yields an equivalent 2-phase representation of the motor, which removes the

variation of mutual inductances with ��, and replaces them with constant inductances. This leads

to a simplification of the governing equations and an induction matrix with constant coefficients of

which the inverse is invariant.

3.3.1 qd0 transformation

The �� transformation is a means of eliminating the sinusoidal variation of inductances.

With reference to Figure 3.2, the �� transformation introduces the �� axes (direct and quadrature),

which travel at an arbitrary angular velocity $ � ��, with respect to the 3-phase stator axes.

Generally when analyzing an induction motor the �� axes are either fixed to the stator, or made

to travel at synchronous speed. In a similar manner to the 3-phase windings, the �� windings are

assumed to be sinusoidally distributed and to produce a sinusoidally distributed MMF wave. They

can therefore be represented as an equivalent coil that aligns with the associated magnetic axis.


For the following derivation the power of the 2-phase motor will be varied from that of

the 3-phase motor because of the convenient mathematical relationships that arise. It can be shown

that the most favorable power transformation occurs when the total 2-phase power is �� times the

total 3-phase power; ,�� ,��. This leads to following transformation from the &)� to the ��

reference frames [13]:

��

��

��

��

��

��

� ��

��

��

��

�� ' (3.10)

where

��

��

�

'

��

��

�

'

��

��

�

'

��

��

�

%

(3.11)

In the above equations the variable � can represent either voltage, current or flux linkage.

The individual stator and rotor transformation submatrices are given by:

��

�

�

��

��

�

��

��

�

��

��

�

��

�

��

��

��

�� ' (3.12)

��

�

�

��

��

�

��

��

�

��

��

�

��

�

��

��

��

�� ' (3.13)


where � = � � ��,� = displacement of the dq axes ��&��,�� = rotor displacement ��&��.

These transformation equations are valid for all voltage forms with the only restriction being that �

must be a continuous function of time [10].

The variables �� and �� represent the effect of zero sequence quantities and are zero

for a balanced machine with a disconnected neutral [10]. They are included in the analysis for

completeness.

The inverse of the transformation matrix is needed to produce a simplified expression for

the inductance matrix (cf. Equation 3.16). It is given by the following expression:

��

��

� ��

��

�

��

� ��

� ��

�� ' (3.14)

where

��

��

��

��

�

��

�

��

��

�

��

�

��

�� '

��

��

��

��

�

��

�

��

��

�

��

�

��

�� %

(3.15)

3.3.2 Flux linkage

Applying the transformation matrix to the 3-phase stator flux linkage equation (cf. Equa-

tion 3.6) leads to the following expression for the transformed flux linkage in terms of the trans-


formed current:

��

��

��

��

��

��

� ��

��

��

��

��

��

��

��

� ��

��

��

��

�� % (3.16)

The self inductance of a stator phase � can be expressed in terms of the stator leakage

inductance ��+� and the stator phase magnetizing inductance ��+�:

� � �� % (3.17)

For a balanced stator, �� = �� as the magnetic axes of the stator windings are dis-

placed at �� and �-�� = �� [7]. Similarly for the rotor phases. Using the above relationships

leads to the following expansion of Equation 3.16 [10]:

��

��

��

��

��

��

��

��

��

��

��

�

��

��

� ��

� � ��

��

��

� ��

��

� � � � � ��

��

��

��

��

��

��

��

��

��

��

� (3.18)

The primed quantities are the rotor parameters referred to the stator,

��

��' ��

��

��' ��

��

��' (3.19)

��

��' ��

��

��' ��

��

��' (3.20)


and

� ��

� ��

�

�

��

��

�

�

��

�� ' (3.21)

�

��

��

��

�

��% (3.22)

In the above expressions �� represents the number of effective turns of a stator phase

winding and �� represents the number of effective turns of a rotor phase winding. It should also

be noted that the stator leakage inductance ��, the referred rotor leakage inductance �� and the

referred magnetizing inductance �, are those that would be measured during a 3-phase parameter

test with all 3-phases excited [7]. They are therefore the parameters that appear in the equivalent

circuit of the 3-phase induction motor.

3.3.3 Voltage

Applying the transformation matrix to Equation 3.1 yields the following expression for

the transformed voltage matrix [13]:

��

��

��

��

��

��

� ��

��

��

��

� ��

��

��

��

��

�

��

��

� ��

��

��

� ��

��

��

� ��

��

��

��

�� '

(3.23)

which after much manipulation can be simplified to,

��

��

��

��

��

��

� ��

��

��

��

��

��

��

��

��

��

��

� ��

��

��

��

�� '(3.24)


where

��

��

�� ' (3.25)

��

��

��

�

�� ' (3.26)

�� $

��

� � �

��

� � �

�� ' (3.27)

�� $ � $��

��

� � �

��

� � �

�� ' (3.28)

$ ��

��' (3.29)

$� ��

% (3.30)

3.3.4 Electromagnetic torque

The rate of change of the mechanical energy output of the motor is expressed in terms of

the electromagnetic motor torque �� and the rotor mechanical speed .��&�� as [16],

��

�� .��' (3.31)

where

.�� .��,% (3.32)


In the above equations , represents the number of motor poles. As the principle of the

conservation of energy must apply, the mechanical energy output �� , can be expressed in

terms of the electrical energy input �� , the stator and rotor resistive losses �� and the

energy stored in the magnetic field �� ,

�� % (3.33)

Differentiating the above expression with respect to time yields an expression for mechan-

ical power:

��

��

��

��

��% (3.34)

The electrical power input for a doubly-fed polyphase motor can be expressed in the

following form:

� � ��

��

��

��% (3.35)

Applying the �� transformation to the above expression gives:

� ��

�

��

�

��

��

��

��

�% (3.36)

Substituting Equation 3.24 into Equation 3.36 yields an expression containing terms of

the form; ��, �� and $�� [13]. The sum of the �� terms represents the total resistive losses in

the windings �� and the �� terms represent the rate of change of magnetic field energy

�� . Therefore by Equation 3.34, the $�� terms must represent the rate that energy is

converted to a mechanical form, �� . If we substitute the $�� terms into Equation 3.31 then


the following expression can be developed for the electromagnetic torque output of a motor with ,

poles [13]:

� � ��

�

,

�� % (3.37)

3.4 Mechanical model

Using Newton’s second law of motion, leads to the following equation describing motion

of the rotor:

��$��

�� % (3.38)

In the above expression $�� is the mechanical speed of the rotor (cf. Equation 3.32), �

is the inertia of the rotor and � � is the expression developed for the electromagnetic motor torque

(cf. Equation 3.37). �� represents the torque applied to the rotor by an external load. ��

represents the viscous damping torque, which acts to retard the motion of the rotor. Its form is

dependent on the nature of the damping source.

3.5 Per unit equations

The per unit (non-dimensional) form of the equations of motion helps to preserve their

generality. Table 3.1 defines the base quantities that are used to place the motor equations in per

unit form. The base quantities are defined in terms of the rated RMS line-to-line motor voltage

�� , the rated apparent motor power �� , and the rated line frequency, �� .

Traditionally the base volt-ampere for a motor is taken as the rated output power of the

motor, which by definition is given in Watts. It should be noted that the choice for base quantities is


Base quantity Sym. Definition

Angular frequency $� �/�� ,Rotor speed $�� $��, ,

Voltage �� ,

Volt-ampere �� ,Torque �� $��.

Table 3.1: Per unit base quantities

purely arbitrary and differs depending on the preferred convention.

The following expressions for flux linkage per second �#� and reactance �� can be de-

veloped in terms of flux linkage ��, inductance � � and the base angular frequency:

# � $�� ' (3.39)

� � $� ��% (3.40)

Using the above relationships, the equations describing the mechanical and electrical be-

haviour of the motor can be rewritten in per unit form as follows [13]:

Stator and rotor voltage

��

$�#��

$

$�#�� '

��

$�#��

$

$�#�� '

��

$�#�� '

��

$�#�

��

$ � $�

$�

#�

��

��'

��

$�#�

��

$ � $�

$�

#�

��

��'

��

$�#�

��

��'

(3.41)


where��

��

��

��

��

��

��

��

��

��

��

�

��

��

� ��

� � ��

��

��

� ��

��

� � � � � ��

��

��

��

��

��

��

��

��

��

��

� (3.42)

Torque

� � ��

�

,

�$��#�� #�� % (3.43)

Equation of motion

� �$��$��

��

�

�+�� ' (3.44)

where

+ ��$�

��

��% (3.45)

3.6 Motor torque-speed curve

The motor torque-speed curve describes the mechanical torque output �� of a motor

when the motor runs at a constant speed. The salient points on a typical torque-speed curve, are

shown in Figure 3.3. In the figure, the torque output of the motor is given as a fraction of the full

load torque.

The locked rotor torque is the torque that the motor produces when the rotor is stalled

(locked). If the torque applied to the motor is less then the locked rotor torque, the motor will

accelerate. As the motor accelerates it will move into the region between the locked rotor torque


and the pull out torque. This region is associated with high motor currents, which if sustained, can

overheat the motor windings. It is therefore desirable to operate outside this region.

The pull out torque is the maximum torque that the motor can produce. Torques greater

than the pull out torque will stall the motor. Asynchronous motors are designed to operate on the

high speed side of the pull out torque, because the speed of the motor remains relatively constant

over a large torque range. The currents in the motor windings are also small compared those on the

low speed side of the pull out torque.

The full load torque represents the design torque of the motor. If a motor is well matched

to the load that it drives, it will operate at the full load torque.

For systems with high starting loads, such as the AFC, motors are often isolated from the

load when they are started (soft starting). This is one of the primary functions of the fluid coupling

and the CST. Isolating the load from the motor, allows the motor to rapidly run up to full speed.

This reduces the duration of the large currents at lower speeds, which helps to prevent overheating

of the motor windings. It also makes full use of the favourable properties of the torque-speed curve

on the high speed side of the pull out torque.

3.7 Conclusion

In this chapter the differential equations that model the electrical and mechanical be-

haviour of a 3-phase induction motor, were developed. The 3-phase representation of the motor was

reduced to an equivalent 2-phase representation, through the �� transformation. This transforma-

tion removes the variation of the mutual inductances in the inductance matrix (cf. Equation 3.9),

which improves the speed of the numerical solution of the equations.

The 2-phase representation of the motor was placed in per unit form, as described by

Equations 3.41 to 3.44. The per unit form of the equations was used in the development of the


computer simulation of the motor.


(a) Vector representation

(b) Circuit representation

Figure 3.1: A simplified representation of a 2-pole, 3-phase induction motor


Figure 3.2: Vector diagrams of a 2 and 3-phase motor

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

2.5

3

Speed (% Synchronous)

Tor

que

(p.u

.)

Pull out torque

Full load torqueLocked rotor torque

Figure 3.3: A typical motor torque-speed curve

Chapter 4

Mechanical Modelling

4.1 Introduction

The following chapter derives the equations of motion of standard AFC drive components

such as the fluid coupling, gearbox, CST and chain sprockets. Each model, with the exception of the

fluid coupling, is developed from first principles. This has been done with the intent of preserving

the generality of the final equations.

The equations of motion of the gearbox and the CST were derived using Lagrangian meth-

ods. Although the equations of motion of the gearbox are easily developed using Newtonian meth-

ods, they were derived using Lagrange’s equations to maintain a consistent methodology throughout

the thesis.

4.2 Lagrange’s equation

For a non-conservative, holonomic system, Lagrange’s equations can be expressed as,

39

40 Chapter 4: Mechanical Modelling

�

��

0

0 ��

�0

0��0�

0 �� 1' (4.1)

where � represents a chosen generalized coordinate [5]. There are � such equations for an �

dimensional system. The Lagrangian � �, as it is commonly referred to, is a function of the kinetic

energy �� and the potential energy of the system �� , and is given by � � �� . The dissipative

function �� represents the effects of dissipative forces acting on the system, the form of which is

dependent on the nature of the dissipative force [18]. Such forces include viscous and dry friction.

1 is a component of the generalized force in the direction of the generalized coordinate � . It is

defined as,

1 �Æ�

Æ��

��

2�0��0�

'

whereÆ� = total virtual work ��,Æ� = virtual displacement in the direction of the generalized coordinate ��,2� = externally applied force ��,�� = direction of applied force ��.

4.3 Fluid coupling

Fluid couplings have been extensively used for several decades to connect the motor to the

gearbox [4]. They are typically used to soft start the motor. Fluid couplings also equally distribute

the load between the drives (load share) without the use of an active control system.

The basic mechanical components of the fluid coupling are the impeller (driving half), the

turbine (driven half) and the enclosing shell in which the working fluid circulates (cf. Figure 4.1).

In modern AFC’s, the impeller is directly mounted onto the motor shaft and the turbine is directly

Chapter 4: Mechanical Modelling 41

mounted onto the input shaft of the gearbox [4]. The impeller adds momentum to the working fluid

via fast moving blades and the turbine absorbs the momentum from the fluid through blades which

slip (run slower) relative to those of the input shaft.

Figure 4.1: Free body diagram of a fluid coupling

4.3.1 Transmitted torque

Since a fluid coupling incorporates no reaction member, the torque produced by the im-

peller is equal to the torque applied to the turbine. The torque transmitted by the fluid coupling is

a function of the impeller speed, the speed difference between the impeller and the turbine, the fill

level of the working chamber and the temperature of the working fluid (viscosity) [9].

A typical fluid coupling torque-slip curve is shown in Figure 4.2. In the figure slip is

defined as:

��

�� ' (4.2)

where�� = impeller speed (rad/s),�� = turbine speed (rad/s).


The curve represents the torque that the fluid coupling can transmit when it is filled to its design

level and the impeller is operating at its design speed. The design speed is generally equal to the

full load speed of the motor.

01020304050607080901000

0.5

1

1.5

2

2.5

Slip(%)

Tor

que(

p.u.

)

Max torque

Full loadtorque (FLT)

Stall torque

Figure 4.2: Fluid coupling torque-slip curve

4.3.2 Performance variations

Fill level

To allow the motor to start unloaded (soft start), the fluid coupling is either empty or

partially filled while the motor is run up to speed. This disengages the motor from the load, which

helps to reduce high motor currents and minimizes drops in the source voltage. Once motor startup

has been completed, fluid is transferred at a predefined rate into the working chamber and torque

is transferred to the turbine. This process also provides better utilization of the motor torque-speed

curve [4].


For the following analysis it will be assumed that the torque transmitted by the fluid

coupling �� is linearly related to the fluid coupling fill level [9], and is given by,

��

��' (4.3)

where�� = fill level,�� = design fill level,� = design torque ��.

At the design fill level the torque transmitted by the fluid coupling is equal to the design torque,

which is given by the manufacturer’s torque-slip curve. The design fill level is typically �� of the

total volume of the working chamber. For the computer simulation the fill level is ramped at a spe-

cific time after motor startup and is held constant upon reaching the design fill level (see Appendix C

for details of the fill level curve).

Impeller speed

Due to centrifugal effects, the torque transmitted by the fluid coupling varies with the

square of the impeller (motor) speed for a given slip and fill level, see [9] and [14]. Equation 4.3

must therefore be augmented as follows:

��

��

��

��

' (4.4)

where�� = design speed of the fluid coupling.

As discussed in Section 3.6, the variation in �� is small under normal operating conditions. How-

ever, under large load changes the speed of the impeller may vary notably because of the transient

response of the motor.


Fluid temperature

For the current analysis it will be assumed that the temperature of the working fluid is

constant and therefore has no influence on the torque transmitted by the fluid coupling. This is

consistent with assuming that the energy lost to the fluid is either removed by convection to the

surrounding air or by the fluid couplings cooling circuit. This is a reasonable approximation under

normal operating conditions [4].

4.3.3 Equations of motion

If viscous friction losses are neglected, then the following equations can be written to

describe the motion of the impeller and turbine (cf. Figure 4.1):

Impeller

�� ' (4.5)

Turbine

�� ' (4.6)

where�� - impeller inertia ��,�� - turbine inertia ��,�� - angular acceleration of the impeller ��&��,�� - angular acceleration of the turbine ��&��,�� - input torque ��,�� - output torque ��.

As an approximation, the impeller inertia includes the inertia of the working fluid.

4.4 Gearbox

The gearbox acts to reduce the speed of rotation and to increase the transmitted torque to

a level which is appropriate for the motion of the sprocket and operation of the longwall.


The following derivation is made for a generic reduction gearbox with � shafts. Each

shaft is represented by an effective inertia �, which is the summation of the inertia of the shaft and

its mounted components such as gears, keys and hubs. Factors such as shaft deflection and backlash

have been assumed to have negligible influence over the dynamic behaviour of the gearbox. The

variation of the potential energy of the system due to gravity has been ignored.

Figure 4.3: Generic gearbox arrangement


As previously stated, Lagrangian methods will be used to derive the equations of motion

of the gearbox so as to provide a consistent methodology throughout the thesis.

The angular displacement of shaft � (��&��) has been chosen as the generalized coordi-

nate (cf. Figure 4.3). The following expression can be written to relate the angular displacement of

shaft � (��&�� to that of shaft � [8]:


��

��

� ' � � �' %%%%' �' (4.7)

where �� represents the gear ratio between shafts 3 and 3��. The kinetic energy of a gearbox

with � shafts, where shaft � is the output shaft, is given by,

� ��

�

��

� �� '

��

�

��

��

�� %%%%%%%% � � ��

��

�% (4.8)

Eliminating �� to �� using the the time differential of Equation 4.7, yields the total kinetic

energy of the system in terms of ��:

� ��

�

��

��

��

� %%%%%%��

��

��

��

��

��

��'

��

�

��

��

��

� %%%%%%%% ��

��

��%%%%�

��

��'

��

��

��' (4.9)

where

��

��

� %%%%%%%% ��

��

��%%%%�

��

% (4.10)


Physically, �� represents the inertia of the gearbox referred to the input shaft. It is often

provided by the gearbox manufacturer. As the variation in the potential energy of the system is

assumed to be negligible, the potential energy term will be omitted from the Lagrangian. The

Lagrangian is therefore given by the kinetic energy alone; � � .

For the gearbox, the damping function represents the losses produced by viscous friction.

It therefore has the following form:

� ��

�

��

�� ' (4.11)

��

�

��

�� %%%%%%%% ��

��

�' (4.12)

where �� is the friction coefficient of gear �. Using the time differential of Equation 4.7 to

eliminate �� to �� from the above expression, yields an equation in terms of ��,

� ��

�

��

��

��

� %%%%%%%% ��

��

��%%%%�

��

��' (4.13)

��

��

��' (4.14)

where

��

��

� %%%%%%%% ��

��

��%%%%�

��

% (4.15)

Like ��, �� represents the referral of all of the friction coefficients to the input shaft. A

method to calculate �� is given in Section 4.4.2.

As an external torque is applied to the input and output shaft of the gearbox only, the

following expression can be developed for the total virtual work:


Æ� � ��Æ�� Æ��' (4.16)

where�� = torque applied to the input shaft ��,�� = torque applied to the output shaft ��.

Substituting the equation of constraint relating �� to ��, into the above equation yields the following

expression:

Æ� �

��

��

��

��

��

�� Æ��% (4.17)

If it is assumed that the torque applied to the output shaft is in opposition to the angular

displacement of the output shaft (i.e. it retards motion), then the above equation can be re-expressed

as,

Æ� �

��

��

��

�� Æ��'

�

��

��

��

Æ��%

Rearranging gives an expression for the generalized force �1��,

1� �Æ�

Æ��

��

��' (4.18)


where

�� =��

��.

�� is the reduction ratio across the gearbox and is readily obtained from manufacturer’s speci-

fications. Substitution of Equations 4.9, 4.13 and 4.18, into Equation 4.1, yields the equation of

motion of the gearbox:

��

��

��% (4.19)

4.4.2 Efficiency

By definition, the power lost by the gearbox (,�� ) can be expressed in terms of the

input power (,�� ) and the gearbox efficiency ��,

,� � �� ,�% (4.20)

Under steady-state conditions, the inertial components are negligible and Equation 4.19

can be simplified to,

��

��

��% (4.21)

To yield an expression in terms of power, both sides of the above equation are multiplied

by ��:

��

��

��

��% (4.22)


The term on the left hand side of the above equation represents the power lost by the

gearbox due to viscous friction and the first term on the right hand side represents the input power.

Equation 4.20 can therefore be written as follows:

�� ' (4.23)

which can be re-expressed as,

��

��% (4.24)

If the efficiency of the gearbox is given at the full load conditions of the motor, and the

slip of the coupling is small, then �� can be approximated as the full load torque of the motor

�2 � �� and �� as the full load speed of the motor �2 ��&��, such that,

�� 2 �

2 �% (4.25)

4.5 Controlled slip transmission

The controlled slip transmission (CST)1 is an alternative to the fluid coupling and gearbox.

It is used primarily as a means for soft starting the motor and controlling the speed of the AFC.

However, it also limits the torque applied to the motor and actively shares the load between the

drives [15].

The CST is comprised of three coupled subsystems: the reduction stage, the planetary

gearset and the clutch (cf. Figure 4.4). The input shaft of the reduction stage is driven by the motor�The term controlled start transmission is also commonly used.


and the output shaft of the reduction stage is directly coupled to the sun gear shaft of the planetary

gearset. The planetary gearset is comprised of � sun gear, � planetary gears (which are fixed to the

output shaft but spin freely about their rotational axis) and a ring gear (cf. Figure 4.4(b)).

The angular velocity of the output shaft can be varied by adjusting the torque applied to

the ring gear by the clutch. Figure 4.5 depicts the behaviour of the output shaft when the sun gear

speed is held constant and the ring gear speed is varied. As shown in the figure, the speed of the

output shaft is inversely proportional to that of the ring gear. When no torque is applied by the

clutch to the ring gear, and the output shaft is locked, the ring gear will run at maximum velocity.

Conversely, if the ring gear is locked, the output shaft runs at maximum velocity. It is this principle

which allows the output speed of the CST and consequently the speed of the chain to be controlled.

Figure 4.4(a) details the arrangement of the clutch pack. Friction plates are fixed via

splines to both the rotating ring gear and the stationary housing of the CST. Pressure is applied to

the friction plates by an annular piston, which is driven by a hydraulic ram. The hydraulic ram is

controlled by a proportional hydraulic control valve, which is driven by a PLC system with closed

loop feedback [15].


In the following analysis the effects of shaft deflection, bearing inertia and backlash are

ignored. In a similar manner to the gearbox, the potential energy of the system is assumed to be

constant.

The input shaft angle (��) and ring gear angle (�), have been chosen as the generalized

coordinates for the analysis of the CST. To enhance the clarity of the derivation, the � planetary

gears will be represented by a single, physically equivalent planetary gear.

Referring to Equation 4.7, the angular velocity of shafts � and �, can be related through

the constraint equation,


��

% (4.26)

To facilitate the development of the equations of motion, the planetary gearset will be

analysed with the arbitrary instantaneous configuration shown in Figure 4.6.

With reference to Figure 4.6(b), the following expressions can be developed for the linear

velocity of the gears at the meshing points &, ) and �:

Point &

�� ' (4.27)

Point )

�� ' (4.28)

Point �

�� ' (4.29)

and

�� '

� �� ' (4.30)

where �� is the angular velocity of point � relative to point & and �� represents the

radius of gear � (cf. Figure 4.6(a)). Applying the appropriate manipulations to Equation 4.30 and

substituting Equations 4.26, 4.27 and 4.29 into the resulting expression, yields a constraint equation

relating the planetary gear speed �� to the speed of the generalized coordinates:


��

��

��

' (4.31)

where

�� ' ��

��%

With reference to Figure 4.6(b), it is evident that the following expression relates �� to ��,

and ��:

��

�% (4.32)

Substitution of Equations 4.26 to 4.29 into the above equation, yields the following con-

straint equation for the output shaft speed in terms of the generalized coordinates:

��

��

��

' (4.33)

where

�� ' � �

��%

In a similar manner to that of the gearbox, the kinetic energy of the CST is determined by

the sum of the kinetic energy of the individual shafts,


� ��

��

��

�

��

��

�

��

��

�

� ��

� �

�

� ��

�' (4.34)

where� = effective mass moment of inertia of shaft � ��.

It should be noted that the effective mass moment of inertia of the output shaft () includes the

inertia of the planet carrier arms, the output shaft and the inertia of the planetary gears about the

rotational axis of the sun gear.

Substitution of equations 4.26, 4.31 and 4.33, into Equation 4.34 yields an expression for

the total kinetic energy of the system in terms of the generalized coordinates,

� ��

��

��

�

�

��

��

��

��

��

��

��

��

��

� ��

� �

�

�

��

��

��

��

%

(4.35)

Because the potential energy of the CST does not vary, it will be omitted from the La-

grangian � � � �. The damping function represents the losses produced by viscous friction, it is

given by the following expression:

� ��

�

��

�� '

where �� is the friction coefficient corresponding to gear �. It is possible to express the above

equation in terms of �� and �� in a similar manner to Equation 4.35. However, if it is noted that ��

�� under normal operating conditions, and if the friction coefficients are of comparable magnitude,

then it is reasonable to assume that the gearbox loss is a function purely of terms involving the speed

of the input shaft. The damping function can then be expressed as,


� ��

��

��% (4.36)

Estimation of the friction coefficient �� will be discussed in Section 4.5.2.

If all external torques are assumed to be applied in the positive direction, then the follow-

ing expression can be developed for the total virtual work:

Æ� � ��Æ�� Æ� � �Æ�' (4.37)

where�� = input shaft torque ��,� = ring gear torque ��,� = output shaft torque ��.

Substitution of Equation 4.33 into Equation 4.37 yields an expression for the total virtual work

in terms of the virtual displacement of the generalized coordinates:

Æ� � ��Æ�� Æ� � �

Æ��

�Æ��

��

% (4.38)

Manipulating the above equation yields the following expressions for the generalized

forces:

1� � ��

��' (4.39)

and

1 � � ��

��% (4.40)


Substituting Equations 4.35, 4.36, 4.39 and 4.40 into Equation 4.1 gives the equations of

motion of the CST:

�� coordinate

��

��

' (4.41)

� coordinate

��

��' (4.42)

where

��

� �

��

��

��

��

��

�

��

��

' (4.43)

� � � �

��

��

��

' (4.44)

�

��

��

� �

��

% (4.45)

4.5.2 Efficiency

In a similar manner to the analysis of the gearbox, the friction coefficient (��) can be

expressed in terms of the full load efficiency of the CST ��, the full load torque of the motor and

the full load speed of the motor,

�� 2 �

2 �% (4.46)


4.5.3 Clutch

The block diagram of the clutch model, is shown in Figure 4.7(a). As shown in the figure,

the model of the clutch is comprised of the controller and the hydraulics subsystem, both of which

will be discussed in the following sections.

Controller

An overview of the controller of the maingate drive is shown in Figure 4.7(b). The con-

troller is comprised of a standard PI controller that is fitted with saturation bounds, and a safety

switch. It is the function of the controller to regulate the speed of the output shaft of the CST2 and

to ensure that the maingate and tailgate motors share load equally.

The input to the PI controller is the error �4� between the speed of the output shaft of the

CST � �� and a predefined reference speed �5�. The reference speed defines the desired speed of

the output shaft of the CST and is used to specify the startup ramp and normal running speed of the

sprocket.

The saturation bounds of the PI controller limit the input signal to the hydraulics. Physi-

cally, they limit the torque that can be applied to the ring gear by the clutch, which prevents excess

torque being transmitted to the motor. This protects the motor from stalling.

The safety isolates the hydraulic subsystem from the controller �� when the differ-

ence between the reference speed and the speed of the output shaft exceeds the critical speed error

�5 � �� 6 4��. A typical scenario where this may occur is when the sprocket rapidly decelerates

after the chain is jammed.

Isolating the hydraulics in this manner effectively releases the ring gear, which decouples

the load (chain) from the motor torque. This practice helps reduce the tension applied to the chain

�Because the output shaft of the CST and the sprocket are rigidly coupled, controlling the speed of the output shaft isequivalent to controlling the speed of the sprocket.


during an event such as a chain jam.

When more than one drive is used to power the conveyor, it is necessary to synchronize

the triggering of all the safety switches, so that all ring gears are released simultaneously. In Fig-

ure 4.7(b), ��, carries the trigger signals from the tailgate drive to the maingate drive, and ��

carries the trigger signal from the maingate drive to the tailgate drive. When either of these signals

are triggered, all of the ring gears are released.

Because the CST does not share load between the motors naturally, it was necessary to add

load sharing control. The load sharing control is implemented as follows: If the difference between

the root mean square (RMS) maingate and tailgate stator currents is greater than a predefined value

��, for a time exceeding ��, then the reference speed of the motor drawing the higher current

is reduced (5� � �� 5, where ��

� 7 �). This practice effectively forces the motor drawing the

smaller current to increase its load. The algorithm for load sharing control is shown in Algorithm 1.

Hydraulics

The hydraulics subsystem models the dynamics of the hydraulics and the torque applied

by the clutch plates to the ring gear. It will be represented as a first-order linear system of the form:

8��

� � � ��' (4.47)

where� = ring gear torque ��,�� = input voltage to hydraulics �� ,8 = hydraulic time constant ��,�� = system gain �� .

The hydraulic time constant is a measure of the time it takes for the hydraulics to either increase or

decrease the torque applied to the ring gear, in response to an input from the PI controller. If the

clutch is applying torque to the ring gear and the safety switch is tripped (i.e �� ), then the


hydraulic time constant represents the time it takes for the ring gear torque to reduce by ��.

If the ring gear is isolated from the controller input (i.e. the safety switch is tripped), then

the time constant represents the time that the ring gear torque takes to reduce by ��.

The system gain �� is a scaling factor that was used to determine the steady-

state torque applied by the clutch for a voltage input ��. It was arbitrarily set to yield PI controller

constants of a preferable magnitude.

As evident by the form of Equation 4.47, it has been assumed that the torque applied by

the clutch to the ring gear, is not dependent on the speed of the ring gear. If the clutch is a viscous

clutch, then a proportion of the torque applied by the clutch will be dependent on the speed of the

ring gear. However, this does not change the underlying principles by which the CST operates and

would not significantly vary the performance characteristics of the CST.

It has been assumed that the delay caused by the sampling time of the controller is small

relative to the response time of the hydraulics. It has therefore been ignored.

4.6 Torque limiting coupling

The torque limiting coupling, limits the torque that can be applied to the AFC sprocket by

the fluid coupling drive. Limiting the torque applied to the sprocket acts to limit the tension in the

AFC chain.

The torque limiting coupling is fitted between the gearbox and the sprocket. It consists of

a shaft and bush that are held together by oil pressure. Once a predefined torque is applied by the

gearbox the coupling slips, which absorbs energy and limits the tension in the chain.

As it is the goal of this thesis to compare the performance of a standard fluid coupling

drive to that of the CST drive, the safety coupling has been omitted from the analysis. It was

thought that the introduction of an unknown dynamic variable, such as the torque limiting coupling,


for which there is little published data, would not prove instructive on the evaluation of the drives.

Its supposed effect on the performance of the fluid coupling drive will be noted in the relevant

sections.

4.7 Chain sprocket

The chain sprocket is a means of converting the rotational motion of the drive components

to the linear motion of the chain. The chain sprocket can have a large influence on the efficiency of

an AFC and on the reliability of the chain.


The equations of motion of the body of the chain sprocket and that of the sprocket teeth

will be developed separately. The current section derives the equations of motion of the sprocket

body only. The equations of motion of the sprocket teeth are discussed in Section 5.4.1 in the

context of the AFC chain.

If the angular deflection and internal damping of the sprocket body is neglected, then the

following equation can be written to describe the motion of the sprocket (cf. Figure 4.8):

�� ' (4.48)

where�� = sprocket inertia ��,�� = sprocket acceleration ��&��,�� = input torque ��,�� = output torque ��.

The output torque of the sprocket body is equal to the sum of the torque applied by all the sprocket

teeth to the chain. If there are two drives powering the sprocket and it is assumed that each drive


has the same performance and state, then the torque applied to each drive is half the input torque

��.

As the sprocket has been assumed to have no internal damping, all sprocket losses will be

due to the interaction between the sprocket tooth and the chain. The sprocket losses will be detailed

in Section 5.4.1.

4.8 Conclusion

In this chapter the differential equations describing the motion of typical components of

the fluid coupling and CST drives, were developed.

A model of the fluid coupling detailing the change in the transmitted torque with impeller

speed and the fill level of the working chamber, was first developed. Lagrange’s equations were

then used to develop the equations of motion of a standard reduction gearbox and the CST. The

equations were put into a form that allows parameters supplied by the manufacturer to be used as

the model parameters.

Finally, an equation describing the motion of the sprocket body was developed. The

equations describing the interaction between the sprocket teeth and the AFC chain will be derived

in Section 5.4.1.


(a) CST plan view

(b) Planetary gearset

Figure 4.4: An overview of the CST


0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Out

put S

haft

Spe

ed (

% M

ax)

Ring Gear Speed (% Max)

(a) Variation of output shaft speed

(b) Ring gear fixed (c) Output shaft fixed

Figure 4.5: Variation of CST output shaft speed with ring gear speed


(a) Gear radii

(b) Linear velocities

Figure 4.6: The planetary gear arrangement of the CST


INPUT : RMS maingate and tailgate stator currents (�� , �� ), Time

(�), Maximum current difference (��), Maximum time

limit (��), Speed modification constant (� 7 �)

OUTPUT : Maingate and tailgate reference speed modifiers (�� ,��)

Initial conditions: �� (The time �� is first exceeded)

if �� 6 �� and �� 6 �� then

�� ;

�� ;

�� ;

else if �� 6 �� and �� 6 �� then

�� ;

�� ;

�� ;

else

�� ;

�� ;

�� ;

�� ;end

Algorithm 1: Reference speed modification algorithm


(a) Block diagram of the clutch

(b) Block diagram of the controller

Figure 4.7: A block diagram of the CST’s clutch

Figure 4.8: A free body diagram of the chain sprocket body

Chapter 5

Chain and Load Model

5.1 Introduction

The following chapter develops the differential equations describing the motion of the

chain/flight bar assembly and the loading of material onto the AFC.

The equations of motion of the chain assembly are derived for a chain under a constant

level of pretension. The constraints placed on the motion of the chain assembly are used to simplify

the 3-dimensional motion of the chain assembly to motion in 1-dimension only. This reduces the

number of equations, which improves the speed of the computer simulation.

The equations describing the external forces applied to the chain assembly and the loading

of material onto the AFC are derived in full to preserve the generality of the discussion. However,

under most operating conditions the equations can be simplified.

5.2 Chain model

In the following analysis a single chain will be used to model the chain/flightbar assembly.

The state and physical properties of the assembly are represented by that of the chain. Use of the

67

68 Chapter 5: Chain and Load Model

word chain will henceforth, directly refer to the representative single chain.

Due to the constraints placed on the chain/flightbar assembly by the pans, transverse

movement of the chain is small. Chain tension produced by transverse movement will therefore

be assumed to be negligible, when compared to the tension that results from the displacement of the

chain in the longitudinal direction.

5.2.1 AFC geometry

The length of the conveyor (��), will be defined as the linear distance between the

centre of the tailgate and maingate sprockets (cf. Figure 5.1(a)). The effect of AFC angularities,

such as snaking and floor roll on the length of the AFC and the chain, are not considered as they are

typically small.

If the angle of wrap (��&��) around each chain sprocket is assumed to be �� degrees,

then the length of chain wrapped around a sprocket (��), is given by,

�� '

� /��' (5.1)

where �� is equal to the pitch circle diameter (PCD) of the sprocket.

Because the transverse displacement of the chain is assumed to be negligible, the length

of the chain remains constant for a constant level of pretension. The total chain length can therefore

be expressed in terms of �� and �� as follows:

�� % (5.2)

Chapter 5: Chain and Load Model 69

5.2.2 AFC reference frames

As transverse movement of the chain has been ignored, the chain moves in the longitudinal

direction only. The chain can therefore be represented as being rolled out to a length of �� in 1-

dimension (cf. Figure 5.1(a)).

To solve the equations governing the motion of the chain, the chain is discretized into �

elements of equal length1 (cf. Figure 5.1(b)). The chain elements are assumed to be physically

identical and are coupled to adjacent elements via a spring and a damper.

To simplify the governing equations a global (9) and a local (�) reference frame have

been employed to track the chain elements. The global reference frame provides a means of map-

ping the position of an element directly onto the AFC. There exists only one global reference frame

and all points on the chain can be referenced to it. The origin of the global reference frame has been

arbitrarily fixed to the initial position of element �, which corresponds to point � on the continuous

chain (cf. Figure 5.1). As the length of the chain is assumed to be constant, a point on the chain can

only obtain a maximum global position of ��, which occurs immediately before it returns to the

origin. After passing through the origin, the global position of the point is reset to zero.

For convenience when simulating chain pretension, the local reference frame of an el-

ement is fixed to the initial position of the element on an unstretched chain. There are � such

reference frames for the � chain elements. Unlike the global coordinate, the local coordinate of an

element increases without bound during the motion of a chain element. The local coordinate can be

mapped to a point on the global reference frame, however there does not exist a one-to-one corre-

spondence between the two reference frames. A point with a local coordinate of �� at time, ��,

has the same global coordinate when at a local coordinate of �� at time ��.

�It can be shown that the discrete representation approaches the exact continuous representation as the number ofdiscrete elements becomes large [3].


5.2.3 Chain element mass

The mass of each chain element is given by following expression:

� �

��

��

!��

��

��

��

��' (5.3)

where� = chain element mass ��,�� = number of chain strands,!�� = mass per unit length of a chain strand ��,� = distance along chain ��,�� = flight bar mass��,�� = total number of flight bars,� = unstretched length of chain element��,

= ��.

If it is assumed that the unit mass of a chain strand is constant (!�� !��), then Equation 5.3

can be reduced to the following:

� � ��!��

�% (5.4)


For the following analysis it will be arbitrarily assumed that the position of element � is

held fixed during the pretensioning of the chain and that all elements are offset from it. As noted

in Section 5.2.2, the local reference frame of a chain element is fixed to its initial position on an

unstretched chain.

Assuming that the spacing between adjacent elements increases by a distance �� during

pretensioning, the following equations can be written to describe the motion of � chain elements in

terms of their local position:


Element �

� �� ' (5.5)

Elements � to ��

� �� ' (5.6)

Element �

� �� % (5.7)

where�� = local coordinate of chain element � ��,� = chain element mass ��,� = chain element stiffness ��,� = chain element damping ��.

Because a chain has no stiffness in compression, the chain element stiffness �� is given by

the following expression:

� �

�� if �� 6� ��'

� otherwise.

(5.8)

The �� terms in Equations 5.5 and 5.7 result from an increase in the length of the chain

during pretensioning and represent the pretensioning force. �� is the sum of the external forces

acting on element �. The details of the external force components will be discussed in Section 5.4.


5.3 Material extraction and loading

5.3.1 Coal block density

The average density of a coal block consisting primarily of coal and a secondary material

such as sandstone is expressed as,

!� � �� !� � ��!�' (5.9)

where !� is the density of the coal and !� is the density of the secondary material. �� is the volume

fraction of the secondary material. It is defined as,

��

��' (5.10)

where �� is the volume of the secondary material and �� is the total material volume.

5.3.2 Shearer extraction

The global reference frame developed in Section 5.2.2 will be used to determine the po-

sition of the shearer. The shearer’s velocity is therefore positive when it travels from the tailgate to

the maingate and negative when it travels from the maingate to the tailgate. As the shearer travels

on the upper race of the AFC only, it can obtain a maximum global displacement of ��.

To simplify the governing equations the entire cutting area of the shearer will be assumed

to be aligned with the centre of the maingate cutting drum (cf. Figure 5.2). This approximation can

be made to approach the ideal by an appropriate choice of initial conditions.


If the height of the cut made by the shearer �:�� is assumed to be constant for a given

cut direction and the depth of the cut �)�� is assumed to be a function of the shearer position,

then the mass of material extracted by the shearer can be expressed as,

�� !�:�

��

)�� ' (5.11)

where �� and �� are the initial and final positions of the shearer. If it is noted that the shearer

displacement is a function of time, ��, then Equation 5.11 can also be expressed as follows:

�� !�:�

��

)��

��' (5.12)

where �� and �� are the times corresponding to the shearer positions �� and �� respectively.

5.3.3 AFC loading

The mass of material loaded onto the AFC is dependent on the stage of the cutting cycle

and the position of the shearer. The material can either be loaded onto the AFC by the shearer, by

advancement of the AFC or by loose material falling from the face. This section details the equations

governing the mass of material that is loaded onto the AFC by the shearer and by advancement of

the AFC. The influence of large coal slabs falling on the AFC, ones capable of rapidly decelerating

the AFC sprockets, are treated as rare events and will be separately addressed in Sections 5.4.6

and 5.4.7. Minor loading caused by loose material falling from the face can be lumped with the

shearing term.

It will be assumed that the material cut during a total cutting cycle is loaded onto the AFC

at some time during that cycle.


Shearing

On an ordinary shearing run - one with little or no slabbing - the shearer loads the majority of the

material onto the AFC. The mass of material loaded onto the AFC by the shearer ��

between times �� and �� is expressed as:

��

��' (5.13)

where �� is the loading efficiency of the shearer and �� is the expression developed for

the mass of material extracted by the shearer (cf. Equation 5.12). The mass of material spilt by the

shearer in the gap between the AFC pans and the face (��), is given by the following equation:

��

��% (5.14)

The efficiency during the shear depends largely on the geometry of the face and the design

of the shearer [2].

Flitting

During flitting material is loaded onto the AFC by the shearer and by AFC advancement. It has been

assumed that all the material cut during a cycle is loaded onto the AFC during that cycle. Therefore

the material spilt at a point �� while shearing, will be loaded onto the AFC at �� during flitting.

If the snake occurs immediately in front of or behind the shearer it is reasonable to assume

that the material not loaded by the shearer at �� during flitting, is immediately loaded at �� by AFC

advancement. Noting the above assumption, and that the velocity of the shearer is negative during


flitting, the following expression can be developed for the mass of material loaded onto the AFC

between points �� and �� during flitting:

��

� ��

��' (5.15)

If during flitting, the shearer is at point �� at time �, and it is at point �� at time ��, then

Equation 5.15 can be re-expressed as follows:

��

��

��' (5.16)

where �� is given by Equation 5.12 and �� is given by Equation 5.14. For the

computer simulation it will be assumed that the chain element closest to the shearer is the only

element being loaded, and that the loaded material immediately assumes the state of the chain

element onto which it was loaded. The loaded material therefore assumes the same position, velocity

and acceleration as the chain element. The material can be thought of as loading a bin that is rigidly

attached to the chain element. The force required to bring the material to the speed of the chain

element is discussed in Section 5.4.2.

5.3.4 Carry back

Carry back is the name given to the material that does not load onto the BSL, but is carried

back on the bottom race of the AFC by the return chain. Carry back is an undesirable part of AFC

operation as it can cause unwanted frictional loading in the lower race. Significant carry back can

cause slack chain to develop under the maingate, which can result in the knuckling of chain links

and damage to the flight bars and sprockets.


The mass of material carried back by a chain element ��, is given by the following

expression:

�� ' (5.17)

where �� is the mass of material loaded onto a chain element before discharge at the main-

gate. The carry-back coefficient �� represents the fraction of material carried back. It is generally

less then � percent.

5.4 Externally applied forces

The external forces are the forces applied to the chain by its surrounding environment.

The following section describes the different components of the total external force applied to a

chain element ��, as was discussed in Section 5.2.4.

5.4.1 Sprocket force

The sprocket teeth transmit power from the drives to the chain assembly. The process of

tooth engagement and the degree to which load is shared between mated sprocket teeth, are both

complex and poorly understood. Several studies most notably that of Wang, K.W., 1992 [17], have

attempted to model the impact intensity of the chain and sprocket engagement. However, their

focus is largely directed toward the modelling of the steady state engagement of a roller chain with

its mating tooth and its effect on the transverse vibrations of the chain. For the purposes of the

current study, where the chain moves in the longitudinal direction only, their methods prove too

computationally expensive and add unnecessary complexity.


The current study will model the dynamics of the chain/sprocket interaction as a spring

and damper system. The zones of engagement shown in Figure 5.3, are a 1-dimensional represen-

tation of the regions in which the AFC sprocket teeth engage the chain elements. The length of

the engagement zones have been made equal to half the circumference of the sprocket (��) as the

angle of wrap has been assumed to be �� degrees. Each engagement zone is fixed in the global

coordinate system.

The sprocket teeth engage the links that reside in the horizontal plane (i.e. every second

link). For the computer simulation the chain element spacing has been made equal to the spacing of

the horizontal links.

The process of engagement between a single chain element and a sprocket tooth is shown

in Figure 5.4. In the simulation one representative maingate sprocket tooth and one representative

tailgate sprocket tooth is assigned to each chain element. There is therefore a total of � repre-

sentative maingate teeth and � representative tailgate teeth assigned to the � chain elements. This

representation of the sprocket teeth is used because it simplifies the algorithm for chain/sprocket

engagement. By default the sprocket teeth are initially aligned at the same local and global coordi-

nates as the teeth to which they mate. However, the initial position of each sprocket tooth can be

individually specified, which allows irregularities in the sprocket tooth spacing to be studied.

Once movement of the sprockets is initiated, the sprocket teeth proceed at a linear speed

equal to the speed at the PCD of their respective sprockets. For example, the linear velocity of the

maingate teeth are given as follows;

��

��

��

�' (5.18)

where�� = linear velocity of the maingate sprocket tooth ��,��

�� = PCD of the maingate sprocket ��,�� = angular speed of the maingate sprocket ��&��.


A similar equation describes the speed of the tailgate sprocket teeth. As implied by the above

equation all maingate teeth travel at the same speed and all tailgate teeth travel at the same speed.

When a chain element enters the zone of engagement corresponding to a sprocket tooth

(cf. Figure 5.4(b)), the tooth is able to apply a force (engage) with the chain element. When a chain

element exits the zone of engagement, the corresponding tooth and chain element disengage (cf.

Figure 5.4(c)).

The force applied by a sprocket tooth to a chain element, when a chain element resides

within its zone of engagement, is modelled by the following equation:

�� ' (5.19)

where�� = engagement force on element � ��,�� = tooth position ��,�� = local position of a chain element ��,�� = chain element velocity��,�� = sprocket tooth stiffness ��.�� = sprocket tooth damping ��.

The sprocket tooth stiffness �� has been made non-linear,

��

�� if �� 6� ��'

� otherwise%

(5.20)

Physically, this implies that a sprocket tooth can only apply a force to a chain element if it has a

greater displacement than the chain element (i.e. the tooth pushes the link). This is a reasonable

approximation of a real sprocket tooth, where the chain typically runs in one direction, and where

there is a large dead spot during torque reversals.


The torque applied to a sprocket �� by all of its engaged teeth (cf. Section 4.7), can

be expressed in terms of ��, �� and the sprocket efficiency �� as:

��

��

��

' (5.21)

where �� is the number of engaged sprocket teeth.

5.4.2 Inertial loading

By Newton’s second law of motion, the force (� ��) applied to a particle of mass��,

travelling at a speed ��, in a 1-dimensional inertial reference frame, can be stated as,

� � ��

�� '

��

��

��

��% (5.22)

The first term on the right hand side of Equation 5.22 represents the momentum flux. In the context

of the AFC, it is equal to the force applied to a chain element when material is loaded onto the chain

element. It can be expressed as follows:

��

��'

� ��' (5.23)

where �� is the rate that material is loaded onto the chain element. �� is given by the time derivative


of Equations 5.13 and 5.16. The velocity term � is equal to the change in velocity of the material

when it is loaded onto the AFC. It is given by:

� � �� ' (5.24)

where �� is equal to the velocity of the chain element onto which the material is loaded and ��

is equal to the velocity of the material prior to loading. If the material is loaded by the shearer,

�� , however if the material is loaded during advancement �� .

In terms of the AFC, the second term on the right-hand side of the Equation 5.22 repre-

sents the force required to accelerate or decelerate a mass, which has already been loaded onto a

chain element. It is expressed as follows:

��

��'

� ��&' (5.25)

where �� is the mass of material loaded onto an element, which is described by Equations 5.13, 5.16

and 5.17. As it has been assumed that the material takes on the state of the chain element onto which

it is loaded, the acceleration �&� is given by the acceleration of the loaded chain element, ��.

5.4.3 Gravitational loading

With reference to Figure 5.5, the component of the gravitational force, which acts on a

chain element, and is parallel to an inclined plane at an angle ", is given by the following expression:


�� *�9�� "' (5.26)

where �� is the acceleration of the particle due to gravity. In the context of the AFC, �

represents the sum of the mass of a chain element and the mass of material loaded onto the chain

element (� � � � ��) and " is the angle of inclination of the AFC. The angle of inclination

is defined as being positive when the tailgate sprocket is raised relative to the maingate sprocket.

*�9�� represents the change in the direction of the gravitational force when a chain element moves

from the upper race or the lower race. It is given by the following equation:

*�9��

��

� if � 7� 9� 7 ��'

�� if �� 7� 9� 7 ��'

(5.27)

where 9� is the global coordinate of chain element �.

5.4.4 Frictional loading

Under normal operating conditions, the frictional force is typically the largest resistive

load acting on the AFC. In general there exists � types of friction; viscous friction, which is propor-

tional to the velocity of a particle, and coulomb friction, which is proportional to the normal force

acting between a particle and its frictional surface. The coulomb frictional force acting on a particle

of mass �, on an inclined plane of angle ", is expressed as (cf. Figure 5.5),

�� "�� ' (5.28)


where �� is the velocity of a particle relative to its frictional surface and �� is the sign function. It

is equal to � when its argument is greater than zero and equal to �� otherwise. � is the coefficient

of friction, the magnitude of which depends on the displacement of an object from its point of

rest [12]. For small displacements (close to zero) � represents the static friction coefficient and

for larger displacements it represents the dynamic friction coefficient. In general the static friction

coefficient is greater than the dynamic friction coefficient by approximately ��.

As stated previously, the viscous friction force is proportional to the velocity of a particle.

Generally, viscous friction is negligible for a solid particle [12]. With regards to the AFC, effects

such as shearing between coal layers (tunneling) appears to be both a function of the loaded mass

and the rate at which an AFC chain travels. However, no published study known to the author

comprehensively explores this hypothesis or attempts to quantify these effects. The viscous losses

will therefore be approximated as being lumped with the coulomb friction loss.

On the AFC many sources of friction exist. For the purposes of estimation and simulation

they will be grouped into � broad categories; chain assembly/pan friction, coal friction and carry

back friction.

Chain assembly/pan friction, is a lumped representation of the losses incurred by friction

between the chain/flight bar assembly and the pans. Friction between the flight bars and the pan

sigmas will be discussed in the context of horizontal snaking in Section 5.4.5.

Coal friction refers to the losses caused by friction between coal loaded on the upper race

and the chain assembly, the pans, the spill plates and the static coal on the coal face. It also refers

to frictional losses produced between moving layers of the loaded coal.

The contribution of an individual source to the total friction depends largely on the quan-

tity of coal loaded per metre. When the quantity of coal loaded per metre is small, the coal/pan

friction component is dominant. There tends to be limited shearing between the coal layers and


there is insufficient coal to initiate frictional losses between the coal, the spill plates and the coal

face. The coal tends to move with relative uniformity to the discharge point at the maingate end.

When a large quantity of coal is loaded on the AFC further modes of friction become

present. Friction between the coal and the spill plates becomes influential, as does the friction

between the moving coal and the static coal on the coal face. A phenomena known as tunneling,

where the lower layers of loaded coal (close to the flight bars) move significantly faster than the top

layer of loaded coal, can also cause frictional losses.

Carry back friction refers to the frictional losses incurred by material that is not unloaded

onto the BSL at the maingate, but is carried back on the lower race of the AFC by the return chain

(cf. Section 5.3.4). It is therefore treated as being distinct from the coal friction losses, which only

account for the material loaded onto the upper race of the AFC. The losses incurred by carry back

are largely a function of the method used to discharge the coal.

As only one data set was able to be obtained for this analysis, the effect of varying the

loaded density of the conveyor �� and that of increasing the speed of the conveyor chain

were unable to be quantified. The chain assembly/pan friction coefficient � ��, the coal friction

coefficient � �� and the carry back friction coefficient � �� are assumed to be constant for all

loaded densities and chain speeds. They are estimated in Appendix B from real data obtained from

the conveyor at the test site.

5.4.5 Horizontal snaking

When a flight bar enters a region where snaking is present, a frictional force (��) is

developed between the flight bar and the pan sigmas (cf. Figure 5.6). This is analogous to a rope

being forced over a stationary pulley. The frictional force applied to a flight bar within the snake, is

given by the following equation:


�� ' (5.29)

where �� is the coefficient of friction between the flight bar and the sigma. �� is the normal

force acting between the two surfaces. As the chain has negligible rotational stiffness, it can be

considered as a series of chords that join the flight bars on the curve swept out by their centers.

The angle made by the flight bars, �� &��, will be approximated as being equal to the pan

articulation angle for all flight bar positions throughout the snake.

It is desired that an expression be developed for the snaking force in terms of the chain

tension on the tailgate side of the flight bar (� ). During forward running and under steady-state

conditions, this is generally the low tension side of the flight bar.

With reference to Figure 5.6(b), a summation of the forces in the radial direction results

in the following expression:

��

� � ��

'

� ��

��

' (5.30)

where � represents the change in chain tension due to the flight bar/sigma friction. As �� is

small, as is the case for a typical AFC, �� !� � � !�

� . If � is considered small relative to � ,

which is typically true when the snake is not at the tailgate when the conveyor is fully loaded, then

the product ��!� � can be neglected. Equation 5.30 can then be simplified to the following:

�� % (5.31)


Substituting Equation 5.31 into Equation 5.29 yields an expression for the force applied

to the flight bar during the snake,

�� % (5.32)

The coefficient of friction �� will be approximated as being equal to the chain assem-

bly/pan friction � ��, which was discussed in Section 5.4.4.

5.4.6 Chain jam

A chain jam is defined as a load which exerts a force that is able to rapidly decelerate a

chain element. It may have many sources and is in general a rare event. Mathematically, a chain

jam represents a step change in the force applied to a chain element ��, at a time ��:

�� *�� ' (5.33)

where � is the scaling coefficient and *�� is the unit step function given by:

*��

�� if � 7 ��'

� if � 6 ��%

(5.34)

5.4.7 Blockage

A blockage will be defined as a load which gradually builds a force sufficient to stall the

AFC sprockets. A blockage will be represented as a ramp increase in the load applied to a chain

element at time ��. The force applied by a blockage to the chain is given by,


�� *�� ' (5.35)

where �� is the scaling coefficient and *�� is the unit step function discussed previously.

5.5 Conclusions

In this chapter we have derived the discrete element representation of the differential

equations that describe the motion of the AFC chain/flight bar assembly. These equations model the

motion of a pretensioned chain that is subjected to external forces. The external forces include, the

force applied by the sprocket teeth, the inertial force, the gravitational force, the frictional force, the

snaking force and atypical forces such as that caused by jamming of the chain and by a blockage of

the AFC.

As part of the development of the external forces, the equations describing the mass of

material loaded onto the AFC, were also derived. These equations describe the mass of material

loaded onto the AFC by the shearer and by advancement of the AFC.


(a) A 1-dimensional representation of the AFC chain

(b) A discrete representation of the AFC chain

Figure 5.1: A simplified representation of the AFC chain


Figure 5.2: Shearer and coal face geometry


Figure 5.3: Engagement zones of sprocket teeth and chain elements


(a) Chain element and sprocket tooth initially aligned

(b) Chain and sprocket tooth mate as chain enters engagement zone

(c) Chain and sprocket tooth disengaged when chain exits engagement zone

Figure 5.4: Sprocket tooth/chain element interaction


Figure 5.5: Gravitational and frictional force components applied to a chain element


(a) Snake dimensions

(b) Forces applied to a flight bar during snake

Figure 5.6: Pan and flight bar interaction during snaking

Chapter 6

AFC Simulation

6.1 Introduction

The following chapter details the computer model that has been developed to simulate an

AFC. The model is discussed in the context of the equations of motion of the AFC drive components,

which were derived in Chapters 3, 4 and 5.

The performance parameters that define the model for the simulations discussed in Chap-

ter 7, are also detailed.

6.2 MATLAB and SIMULINK

The model of the AFC was developed using MATLAB version 6.1 and SIMULINK1

version 3. SIMULINK is a MATLAB toolbox that is used to model and simulate dynamic systems.

It has a graphical interface that allows the user to develop system models using block diagrams.

Once a model is defined it can be solved using one of a selection of integration routines. The

integration parameters and initial conditions of the simulation are selected by the user.

�MATLAB and SIMULINK are registered trademarks of The MathWorks, Inc.

93

94 Chapter 6: AFC Simulation

6.3 Integration routine

For the simulation, SIMULINK’s -�4�, fixed-step continuous solver was used. A fixed-

step solver calculates the continuous state of a model at equally spaced time steps by numerically

integrating the state derivatives specified by the model.

A step size of �� was used for all the simulations. It is shown in Section 7.6, that

the results of the simulation are invariant to further reductions in the step size.

6.4 AFC model

The SIMULINK model of an AFC fitted with CST drives, is shown in Figure 6.1. The

figure depicts the major subsystems of the model (shown in boxes) which describe the maingate

and tailgate electrical supplies, the maingate and tailgate drives, the CST’s load sharing control,

motion of the chain, and the loading of material onto the AFC. Each major subsystem is comprised

of further minor subsystems, the details of which will be discussed in the following sections. Note

that for an AFC fitted with fluid coupling drives there is no load sharing control.

The model parameters have either been obtained directly from the AFC at the test site, or

they have been estimated using good engineering judgement. The sensitivity of the results of the

simulation to inaccuracies in parameter values is addressed in Chapter 7.

6.4.1 Notation

Unless otherwise stated, the notation used to describe the variables of a subsystem is

consistent with that of previous chapters. Variables that do not appear in previous chapters are

defined in a table below the relevant figure.

Subsystems of the model are represented with boxes. When a variable is passed between

subsystems, it is shown by an arrow which connects the subsystems. A variable can also be passed

Chapter 6: AFC Simulation 95

between subsystems by using the “To” and “From” blocks (see the �� and �� signals in Figure 6.1).

The “To”-“From” pair is a SIMULINK convention and is equivalent to a line connecting the two

ports.

If a variable is enclosed in an oval, see Figure 6.2, it denotes that the variable is either an

input to, or an output from, a subsystem. When the superscripts � and � are appended to a vari-

able, it denotes that the variable originates from either the maingate or tailgate drives respectively.

Vectors are declared in bold font and they are connected by a thickened line.

If a figure number is placed within a subsystem box, it denotes the location of a detailed

overview of the subsystem within the current chapter. When an equation or section number is placed

within a subsystem box, it refers to the equation or section in the thesis that describes the subsystem.

To minimise repetition, not all symbols are defined in all figures. If a port or signal is not

defined in a figure, it is defined in a lower level figure or the section referenced. The symbols are

also defined in the nomenclature section.

6.4.2 Electrical subsystem

The electrical subsystem models a �-phase, sinusoidal voltage source, which feeds the

stator and rotor of an AC induction motor. The relationship between the phase voltage and phase

current is defined in Equation 3.1. The frequency and magnitude of the voltage applied to the stator

and rotor, can be independently specified.

The parameters of the maingate and tailgate electrical subsystems, which are equal by

default, are given in Table 6.1.

6.4.3 Drive subsystem

Figure 6.2 gives an overview of the subsystems that comprise the fluid coupling and CST

drive models. The drive subsystem shown models the equations of motion of the maingate drive


Sym. Vector Description

��

� '�� Voltage vector

�� ' �� Sprocket state vector�� Sprocket output torque�� ' �� Shearer state vector� RMS stator phase current

Figure 6.1: An overview of the AFC model fitted with CST drives

components, which were derived in Chapter 4. An analogous model exists for the tailgate drive.

The parameters, which define the drive subsystem, are given in Table 6.2. Note that

because the maingate and tailgate drives are typically identical, their parameters are equal. However,

they can be independently specified. If there are two drives powering a sprocket, then they are

described in the model by one representative drive, with half the total sprocket torque referred to

the drive.


Subsystem Description Sym. Units Default

Elec. source Stator line voltage �� 3300Rotor line voltage �� 0Line frequency �� +; 50

Table 6.1: The performance parameters of the electrical source

Motor

An overview of the motor subsystem is shown in Figure 6.3. The motor subsystem is an

implementation of Equations 3.41 and 3.44, which describe the electrical and mechanical dynamics

of a generic �-phase induction machine, in per unit form. Details of the motor, including the torque-

speed curve, are shown in Appendix C.

Fluid coupling

The fluid coupling subsystem in Figure 6.2(a) is an implementation of Equations 4.5

and 4.6, which describe the motion of the fluid coupling’s impeller and turbine. As the impeller

of the fluid coupling is rigidly fixed to the output shaft of the motor, its inertia has been lumped with

the inertia of the motor shaft in the simulation. The total inertia of the input shaft has been assumed

to be equal to the sum of the shaft inertia and the inertia of the working fluid at the design fill level.

The fluid coupling’s torque-slip curve, which defines the design torque transmitted by the

fluid coupling ��, at the design fill level �� and design speed � ��, is shown in Appendix C.

The curve defining the fill level of the fluid coupling ��, as a percentage of the design fill level

during the startup of the fluid coupling drive, is also shown in Appendix C. Note that for simulation

scenarios other than the startup of the fluid coupling drive, the fill level is held at the design fill level.


Gearbox

The gearbox subsystem in Figure 6.2(a) is an implementation of Equation 4.19, which

describes the motion of a reduction gearbox. As the input shaft of the gearbox and the output shaft

of the fluid coupling are rigidly fixed, the inertia of the gearbox was lumped with the inertia of the

output shaft of the fluid coupling for the simulation.

CST

An overview of the CST subsystem is shown in Figure 6.4. The CST subsystem models

the equations developed in Section 4.5, which describe the motion of the CST.

The curve which defines the reference speed of the output shaft �5� when the AFC is

started, is given in Appendix C. Note that the reference speed is held at the value shown in Table 6.2,

for all other loading scenarios.

Sprocket

The sprocket subsystem in Figure 6.2 is an implementation of Equation 4.48, which de-

scribes the motion of the sprocket body. In a similar manner to the gearbox, the inertia of the

sprocket is lumped with the inertia of either the output shaft of the fluid coupling or the output shaft

of the CST. If there are � drives powering a sprocket, then half the sprocket inertia is lumped with

each drive.

6.4.4 Chain subsystem

An overview of the chain subsystem is shown in Figure 6.5. The chain subsystem de-

scribes the equation of motion of the chain, which was detailed in Chapter 5. It consists of the

applied forces and loading, chain motion and sprocket force subsystems. The chain subsystem

parameters are defined in Table 6.3.



Motor No. of maingate motors 2No. of tailgate motors 1Rated power ,�� 800Rated voltage �� 3300Rated frequency �� +; 50Stator resistance �� 0.069Stator leakage reactance �� 0.869Referred rotor resistance �� 0.232Referred rotor leakage reactance �� 0.829Magnetizing reactance �� 41.28Motor inertia � �� 37.10Number of poles , 4Speed of the qd0 axes $ �&�� 0Synchronous speed �� 1500Full load torque 2 � �� 5122Full load speed 2 � �&�� 156

Coupling Input shaft inertia �� 7Output shaft inertia �� 5Impeller design speed �� &�� 155.6

Gearbox Referred gearbox inertia �� 1.33Total gear ratio �� 30.14Gearbox efficiency �� 0.95

CST Input shaft inertia � �� 1.95Sun gear inertia � �� 0.83Planetary gear inertia � �� 1.57Ring gear inertia �� 18Output shaft inertia �� 14Gear ratio shafts 1 & 2 �� 7.5Gear ratio shafts 2 & 3 �� 1Gear ratio shafts 2 & 5 �� 2Gear ratio shafts 3 & 4 �� 3Gear ratio shafts 4 & 5 � 2/3Proportional control constant <� 5Integral control constant �� 0.05Hydraulic time constant 8 � 0.05Torque constant �� 800PI saturation voltage �� 27.5

�� 0Critical speed error 4� �&�� 1Reference speed (steady-state) 5 �&�� 5.2Current limit �� ( 2Speed modification constant � 0.95Maximum time limit �� 2

Sprocket Sprocket inertia �� 182Sprocket efficiency �� 0.85Sprocket diameter �� 0.648

Table 6.2: Drive parameters

hal

smax

hal

Critical speed error


Applied forces and loading

The applied forces and loading subsystem, is based on the equations developed in Sec-

tion 5.4, which describe the external forces applied to a chain element. It also determines the mass

of material loaded on each element as described in Section 5.3.

Note that for the simulations detailed in Chapter 7, the effects of snaking on the tension

in the chain are not considered.

Chain motion

The chain motion subsystem represents the equation of motion of the chain elements, as

detailed in Equations 5.5 to 5.7.

Sprocket force

The sprocket force subsystem represents the force applied to the chain elements by the

sprocket teeth, which is described by Equation 5.4.1 .

6.4.5 Loading subsystem

The loading subsystem details the equations governing the motion of the shearer and the rate that

material is loaded onto the AFC (cf. Section 5.3). The relevant parameters of the loading subsystem are

shown in Table 6.4.

6.4.6 Load sharing subsystem (CST only)

The load sharing subsystem describes the CST’s load sharing algorithm, which was developed in

Section 4.5.3.



Sprocket tooth Tooth stiffness ��

Tooth damping �� 550

Chain Number of chain elements � 1730AFC length �� 263Wrap length �� 1.02Chain density !�� 183Element mass � � 55.6Chain element stiffness � �� %��

Chain element damping � �� 350Pretension force (total) 2� �-��4� 30Initial mass loaded per element �� 0

Snake Pan length �� 1.73Pans in snake �� 12Length of snake �� 20.76Pan articulation angle �� &� 0.16Radius of snake �� 107Elements between flight bars �� 4

Friction coeff. Chain assembly friction coeff. �� 0.25Carry back friction coeff. �� 0.3Coal friction coeff. �� 0.45

Load Carryback coefficient �� %��AFC angle " �4 4Gravitational acceleration g �� 9.8

Table 6.3: Chain subsystem parameters


Shearer Shearing speed �� 14Flitting speed �� 33Loading efficiency �� 0.95Shearing cut height :�� 3.5Flitting cut height :�� 1.5Web depth )� � 0.85Seam height :� � 5

Material Uncut material density !� �� 1450

Table 6.4: Loading subsystem parameters


(a) Fluid coupling drive

(b) CST drive


�

�� ' �� Motor state vector�� ' �� Fluid coupling turbine state vector�� ' �� Gearbox output shaft state vector ��' �� CST output state vector�� ' �� Sprocket state vector

Figure 6.2: An overview of the fluid coupling and CST drive models (The notation applies to themaingate drive. Replace “mg” with “tg” to obtain the diagram for the tailgate drive system.)



�� ' �� Transformed motor current vector#�� #��

� ' #�� Flux linkage per second vector

Figure 6.3: The motor subsystem


�

� � ��' �� CST input shaft state vector ��' �� CST ring gear state vector

Figure 6.4: An overview of the CST model



�� ' �� Chain element state vector � Loaded mass vector�� External force vector�� Sprocket force vector�� Total force vector

Figure 6.5: The chain subsystem

Chapter 7

Comparison of Drive Configurations

7.1 Introduction

In this chapter we will study the influence of the dynamic behaviour of the fluid coupling and CST

drives on the tension in the chain. This analysis will be undertaken in three parts.

In the first part of the chapter, different aspects of the AFC model will be verified. Section 7.2,

analyses the behaviour of the drives when they are isolated from the chain. It is the aim of this section to

ensure the behaviour of the drive types is physically realistic. Section 7.3 compares the quasi-steady-state

(slowly changing) behaviour predicted by the full model of the AFC (i.e. drives and chain) to that measured

from a real AFC under similar conditions. This section aims to ensure that the quantitative behaviour of the

model at steady-state describes that of a real AFC.

In the second part of the chapter the dynamic behaviour of the fluid coupling and CST drives, and

its effect on chain tension, will be analysed during different loading scenarios. It is the aim of this section to

assess the ability of each drive to mitigate chain tension.

In the third part of the chapter, a sensitivity analysis will be performed. Changes to the model

parameters, which are either of questionable accuracy or perceived to be critical in determining the level of

chain tension, will be analysed.

All results are presented in per unit (non-dimensional) form. The details of the base quantities that

105

106 Chapter 7: Comparison of Drive Configurations

are used to calculate the per unit values, are given in Appendix C.

7.2 Analysis of drive system behaviour

This section examines the behaviour of the fluid coupling and CST drives when they are isolated

from the chain. The load in this analysis is applied as a torque directly to the shaft of the chain sprocket. The

following scenarios are used to test the drives:

1. Unloaded startup

2. Small step load

3. Large step load

4. Ramping load

Each scenario is designed to exploit and explain different aspects of an AFC drives operation. The

details of the different loading scenarios are given in the following sections.

For the simulations detailed in this section, the inertia of the chain is lumped with the inertia of the

sprocket. The constant component of the load (chain/pan friction etc.) is ignored. Unless otherwise stated,

the AFC drive parameters are those given in Chapter 6.

Startup

The startup of the AFC drives describes the process from when voltage is first applied to the motor

terminals to when the chain sprocket has accelerated to its normal running speed. It is the starting point for

all other loading scenarios.

For the startup of the decoupled drives, no torque is applied to the sprocket. The torque that is

applied to the motor is due to the acceleration of the rotating drive components (including the chain inertia

which is lumped with the sprocket shaft) and the viscous friction of the gearbox or the CST only.

Figure 7.1 details the motor torque, motor current, motor speed, fluid coupling slip and chain

sprocket speed, during startup of the fluid coupling drive. Note that when using the per unit system, the speed

of the sprocket and the speed of the output shaft of both the CST and the fluid coupling, are equal.

Chapter 7: Comparison of Drive Configurations 107

At � � �� full voltage is applied to the motor terminals and the motor begins to produce torque.

To allow the motors to be started without load, the working chamber of the fluid coupling is left empty when

the motor accelerates. Details of the fill level of the fluid coupling during the startup of the fluid coupling

drive can be found in Appendix C.

The oscillations observed in the torque output and speed of the motor at � � ��, are due to the

motor overshooting the synchronous speed. This occurs because of the high gradient of the torque-speed

curve in this operating region and the electrical dynamics of the motor.

The figure shows a current �� being produced in the stator coils. This is less than the locked

rotor current of ��, which was quoted by the manufacturers (cf. Appendix C), because the motor run

parameters and not the start parameters were used for the simulation (cf. Section 3.2). With regards to the

startup of the motor, the run parameters have the effect of reducing the torque output of the motor at lower

speeds, which extends the time it takes to accelerate the rotor to full speed.

As shown by the fluid coupling fill curve in Appendix C, the fluid coupling begins filling at a time

of ��, and continues filling at a constant rate for a further ��. Note that only the first �� of the startup

procedure is shown in the Figure 7.1, because the displayed variables are approximately constant after this

time. As the fluid coupling fills, it starts to transmit torque. This is shown by the acceleration of the sprocket

and the increased motor torque and stator current. Continued filling of the fluid coupling causes the speed of

the sprocket to increase to its no load value. The speed of the motor remains constant because of the steep

gradient of the motor torque-speed curve in this operating region (cf. Section 3.6).

The startup procedure of the CST drive is shown in Figure 7.2. At � � ��, full voltage is applied

to the stator terminals and the motor begins to produce torque. To allow the motor to accelerate without load,

no torque is applied by the clutch to the ring gear. This is performed by setting the reference speed of the

output shaft of the CST to zero during this time period (cf. Section 4.5.3). Appendix C gives details of the

reference speed during the startup procedure.

As no torque is applied to the ring gear by the clutch, the rotor shaft and ring gear accelerate

unloaded. The oscillations observed in the motor torque and speed at � � ��, are again due to the motor

overshooting the synchronous speed.

The reference speed begins to increase at a time of ��. This results in torque being applied to


the ring gear by the clutch, which decelerates the ring gear and accelerates the chain sprocket. The speed of

the sprocket closely follows the reference speed.

When compared to the CST drive, the fluid coupling drive accelerates the sprocket more rapidly.

This results in a comparatively larger torque being applied to the motor for a shorter duration. As the torque

output of the fluid coupling is dependent on the fill level of the working chamber (cf. Section 4.3), a lower

fill rate would result in a smaller sprocket acceleration.

For a variable fill fluid coupling it should be possible to control the speed of the sprocket in a

similar manner to that of the CST. However, implementation of such a control system is beyond the scope of

this thesis.

Small step

Figure 7.3 details the torque that is applied to the sprocket shaft during the small step, large step

and ramping scenarios. All torques are applied �� after the end of the startup procedure. Note that the

startup procedure has been omitted from the presentation of the step and ramp loading scenarios, because it

is invariant.

The response of the CST drive to the small step load was used to tune the CST’s PI controller. The

controller constants were selected through a tradeoff between stability and response time.

Figure 7.4 shows the response of the fluid coupling drive to the small, step increase in the torque

applied to the sprocket shaft. As the torque is applied, the slip of the fluid coupling increases. This results

in greater torque being transmitted to the motor, which increases the current in the stator windings. The

transients in the motor torque and stator current, which are produced by the internal dynamics of the motor’s

electrical circuits, rapidly decay to a steady-state value that is determined by the size of the step. The change

in motor speed is small because of the large gradient of the torque-speed curve of the motor in this operating

region.

The response of the CST drive to the small step load is shown in Figure 7.5. When the step load is

initially applied to the sprocket shaft, the ring gear accelerates, which decelerates the sprocket. The decrease

in the speed of the sprocket increases the output of the proportional term in the PI controller. This actuates the

clutch to apply a greater torque, which opposes further acceleration of the ring gear. The delayed response of


the hydraulics also contributes to the increase in the speed of the ring gear.

As time progresses, the sustained error between the CST’s output shaft speed and the reference

speed increases the contribution of the integral term. This increases the torque applied by the clutch, which

decreases the speed of the ring gear and increases the speed of the CST’s output shaft to the reference speed.

Large step

As will be shown in Section 7.4.3, the response of the drive types to large step increases in torque

determines the tension in the chain during a jam situation.

Figure 7.6 depicts the response of the fluid coupling drive to a large step increase in the torque

applied to the sprocket shaft. Upon application of the load, the slip of the fluid coupling increases, which

increases the torque transmitted to the motor. The chain sprocket speed takes approximately second to

decelerate to its final value.

The transients in the motor torque and stator current, which are produced by the internal dynamics

of the motor electrical circuits, rapidly decay to a steady-state value that is determined by the size of the step.

The change in motor speed is small because of the large gradient of the torque-speed curve of the motor in

this operating region.

The level of fluid coupling slip and stator current could not be maintained at the levels shown,

because of the excessive heat that would be produced in the motor windings and in the working fluid. The

control system would intervene by either draining fluid from the fluid coupling or by cutting power to the

motor.

The response of the CST drive is depicted in Figure 7.7. The large step increase in sprocket torque

causes the ring gear to accelerate and the chain sprocket to decelerate. In a similar manner to the small step

load, the acceleration of the ring gear results from insufficient torque being applied by the clutch to oppose

the increase in sprocket torque.

For the large step, the error between the reference speed and the speed of the CST’s output shaft,

exceeds the critical speed error �� and the ring gear is released (refer to Section 4.5.3 for details of the

critical speed error). The ring gear is then accelerated and rotation of the output shaft ceases. It should be

noted that in this analysis that the critical speed error has been chosen arbitrarily to equal ��. This


corresponds to a �� drop in the speed of the sprocket relative to that of the reference speed at steady-state.

As shown in the figure, when there is a large, abrupt change in load, the CST isolates the load

from the motor torque by releasing the ring gear. The motor torque is then redirected into the acceleration

of the ring gear, and it reduces to its no load value once the ring gear has accelerated to full speed. For

the decoupled CST drive, the energy stored in the sprocket and the output shaft of the CST is absorbed by

the load. However, for a real AFC, the energy would be absorbed by the load and by extension of the AFC

chain. Conversely, when a large step load is applied to the fluid coupling drive, the increased slip of the fluid

coupling results in a larger torque being applied by the motor. For the decoupled drive the energy produced

by the motor, and that released by the deceleration of the sprocket, gearbox and driven half of fluid coupling,

must be absorbed by the load. For a real AFC the energy would either be absorbed by the load, through

extension of the chain, or by some other means such as a torque limiting coupling.

Note that the torque applied by deceleration of the fluid coupling and gearbox inertia is magnified

when referred to the sprocket because it is multiplied by the gearbox ratio �� .

Ramp

The ramping load was chosen to examine the behaviour of the drives under a progressively de-

veloping load, such as that which would be caused by a blockage. In particular, it is useful in exploiting

certain aspects of the behaviour of the CST drive that were masked by the safety switch in the large step load

simulation.

The behaviour of the fluid coupling drive during application of the ramping load is depicted in

Figure 7.8. Application of the ramping torque causes fluid coupling slip to increase, which increases the

torque applied to the motor. The increasing torque also causes the sprocket to decelerate. At a time of

�� the motor torque achieves a maximum. This point corresponds to the maximum torque that can be

transmitted by the fluid coupling (cf. Appendix C). After the maximum torque is reached, the motor torque

steadily decreases until the rotation of the sprocket ceases. At this point, the slip of the fluid coupling is equal

to one. If this state was maintained either the motor or fluid coupling would overheat. This would cause the

control system to either cut power from the motor, or drain the fluid coupling.

The response of the CST drive to the ramping torque is shown in Figure 7.9. The initial application


of the torque accelerates the ring gear, which decreases the speed of the sprocket. The sustained error between

the sprocket speed and the reference speed, causes the integration term in the PI controller to increase. In

response, the torque applied by the clutch increases, which results in the speed of the ring gear and the

sprocket being held constant.

At a time of ��, saturation of the PI controller causes the torque applied to the clutch to saturate,

which limits the torque that is transmitted to the motor. Because the torque applied to the clutch is held

constant, the ring gear accelerates under the increasing load. The acceleration of the ring gear results in the

deceleration of the sprocket. At a time of ��, the critical speed error is reached and the ring gear is

released. This causes the ring gear to accelerate to full speed and the rotation of the output shaft to cease.

It should be noted that the saturation level of the ring gear has been arbitrarily chosen to yield a

maximum motor current of twice the full load current. In a similar manner to the fluid coupling, it effectively

acts to prevent excessive torque being applied to the motor. It should be noted that it is possible to stall the

motors if the saturation level is chosen such that the maximum torque transmissible by the CST is greater

than the motor pull-out torque.

The ramp load highlights the ability of both drives to limit the torque applied to the motors. The

load limiting capabilities of the fluid coupling are inherent in its design, whereas the load limiting behaviour

of the CST is dependent on the the appropriate selection of the saturation limits of the PI controller.


Startup: decoupled fluid coupling drive NotesMotor torque

0 2 4 6 8 10 12 14 16 18 20−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

Time(s)

Torqu

e(p.u.

) At a time of ��the motor torque in-creases as the drivecomponents are ac-celerated.

Stator current (RMS)

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time(s)

Curre

nt(p.u

.)

Large startup cur-rents are producedby direct onlinevoltage application.At a time of ��there is an increasein current as thedrive components areaccelerated.

Motor speed

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

1.2

1.4

Time(s)

Spee

d(p.u.

)

Torque applied bythe motor acceleratesthe rotor. The speedchange is small as themotor accelerates thedrive components.

Fluid coupling slip and sprocket speed

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

Time(s)

Slip(

p.u.)

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

Spee

d(p.u

.) As the workingchamber is filledfluid coupling slipdecreases and thespeed of the sprocketincreases.

Figure 7.1: Unloaded startup: decoupled fluid coupling drive


Startup: decoupled CST drive NotesMotor torque

0 5 10 15 20 25 30 35−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

Time(s)

Torqu

e(p.u.

) Low acceleration ofthe load and drivecomponents appliesonly a small torque tothe motor.


0 5 10 15 20 25 30 350

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time(s)

Curre

nt(p.u

.)

Motor speed

0 5 10 15 20 25 30 35−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time(s)

Spee

d(p.u.

)

Ring-gear and sprocket speed

0 5 10 15 20 25 30 350

0.2

0.4

0.6

0.8

1

Time(s)

Ring

gear

spee

d(p.u

.)

0 5 10 15 20 25 30 350

0.2

0.4

0.6

0.8

1

Spro

cket

spee

d(p.u

.)

During motorstartup, the clutchdoes not applytorque, and the ringgear accelerates un-loaded. At � � ��torque is applied tothe ring gear. Thering gear then slowsand the sprocketaccelerates.

Figure 7.2: Unloaded startup: decoupled CST drive


0 2 4 6 8 10 12 14 16 180

0.5

1

1.5

2

2.5

3

Time(s)

Tor

que(

p.u.

)

Small stepLarge stepRamp

Load scenario Units Applied torque

Startup �%*% �

Small step �%*% �%�

Large step �%*% �

Ramp �%*% �%��

Figure 7.3: Loading scenarios: decoupled drives. Note that the base quantities used to determine the perunit values are shown in Appendix C.


Small step: decoupled fluid coupling drive NotesMotor torque

0 0.5 1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time(s)

Torqu

e(p.u.

)Motor torque in-creases rapidly as thestep load is applied.The transients resultfrom the electricaldynamics of themotor.


0 0.5 1 1.5 2 2.5 3 3.5 40.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

Time(s)

Curre

nt(p.u

.)

Motor speed

0 0.5 1 1.5 2 2.5 3 3.5 40.994

0.995

0.996

0.997

0.998

0.999

1

1.001

Time(s)

Spee

d(p.u.

)

The step load onlyproduces a smalldecrease in motorspeed, because of thesteep gradient of themotor torque-speedcurve.


0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

Time(s)

Slip(

p.u.)

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

Spee

d(p.u

.)

The slip of the fluidcoupling increases totransmit the appliedtorque.

Figure 7.4: Small step: decoupled fluid coupling drive


Small step: decoupled CST drive NotesMotor torque

0 0.5 1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time(s)

Torqu

e(p.u.

)Motor torque in-creases rapidly asthe step load is ap-plied. The transientbehaviour resultsfrom the coupling ofthe CST dynamicsand the dynamics ofthe motor electricalcircuit.


0 0.5 1 1.5 2 2.5 3 3.5 40.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Time(s)

Curre

nt(p.u

.)

Motor speed

0 0.5 1 1.5 2 2.5 3 3.5 40.99

0.995

1

Time(s)

Spee

d(p.u.

)

There is a onlya small decreasein motor speed,because of the steepgradient of the motortorque-speed curve.


0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

Time(s)

Ring

gear

spee

d(p.u

.)

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

Spro

cket

spee

d(p.u

.)

The step load in-creases ring gearspeed. An increasein the PI controllerintegral term in-creases the torqueapplied by the clutch.The ring gear thendecelerates and thesprocket acceleratesto its reference value.

Figure 7.5: Small step: decoupled CST drive


Large step: decoupled fluid coupling drive NotesMotor torque

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Time(s)

Torqu

e(p.u.

)

The motor torqueand stator currentincrease rapidlyas the step load isapplied. Transientoscillations rapidlydecay to the finalsteady-state value.


0 0.5 1 1.5 2 2.5 3 3.5 40.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

Time(s)

Curre

nt(p.u

.)

Motor speed

0 0.5 1 1.5 2 2.5 3 3.5 40.975

0.98

0.985

0.99

0.995

1

1.005

Time(s)

Spee

d(p.u.

)

Motor speed de-creases, in responseto the larger torque.


0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

Time(s)

Slip(

p.u.)

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

Spee

d(p.u

.)

As the torque is ap-plied the speed of thesprocket decreases,and fluid couplingslip increases. Thisresults in a greatertorque begin appliedto the motor.

Figure 7.6: Large step: decoupled fluid coupling drive


Large step: decoupled CST drive NotesMotor torque

0 0.5 1 1.5 2 2.5 3 3.5 4−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Time(s)

Torqu

e(p.u.

)

Application of theload causes an ini-tial increase in mo-tor torque. Releasingthe ring gear reducesmotor torque to its noload value.


0 0.5 1 1.5 2 2.5 3 3.5 40.27

0.28

0.29

0.3

0.31

0.32

0.33

0.34

Time(s)

Curre

nt(p.u

.)

Motor speed

0 0.5 1 1.5 2 2.5 3 3.5 40.996

0.997

0.998

0.999

1

1.001

1.002

1.003

1.004

1.005

Time(s)

Spee

d(p.u.

)

There is a rapid de-crease in motor speedas the load is applied.As the ring gear is re-leased the motor re-turns to its no loadspeed.

Ring gear and sprocket speed

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

Time(s)

Ring

gear

spee

d(p.u

.)

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

Spro

cket

spee

d(p.u

.)

As the sprocketdecelerates thecritical speed erroris violated and thering gear is released.The ring gear thenaccelerates and thesprocket rotationstops.

Figure 7.7: Large step: decoupled CST drive


Ramp: decoupled fluid coupling drive NotesMotor torque

0 2 4 6 8 10 12 14 16 180

0.5

1

1.5

2

2.5

Time(s)

Torqu

e(p.u.

)Motor torque in-creases with anincrease in load. At atime of �� motortorque reaches amaximum.


0 2 4 6 8 10 12 14 16 180

0.5

1

1.5

2

2.5

3

3.5

Time(s)

Curre

nt(p.u

.)

Motor speed

0 2 4 6 8 10 12 14 16 180.975

0.98

0.985

0.99

0.995

1

1.005

Time(s)

Spee

d(p.u.

)

The motor speedsteadily decreases asthe load is increased.


0 2 4 6 8 10 12 14 16 180

0.2

0.4

0.6

0.8

1

Time(s)

Slip(

p.u.)

0 2 4 6 8 10 12 14 16 180

0.2

0.4

0.6

0.8

1

Spee

d(p.u

.)

As the torque devel-ops fluid couplingslip increases, whichincreases the torqueapplied to the motor.At a time of ��maximum slip isreached and rotationof the sprocket isstopped.

Figure 7.8: Ramp: decoupled fluid coupling drive


Ramp: decoupled CST drive NotesMotor torque

0 5 10 15−0.5

0

0.5

1

1.5

2

Time(s)

Torqu

e(p.u.

)

At a time of ��the torque is cappedby saturation of thePI controller. At�� the ring gearis released and themotor torque returnsto its no load value.


0 5 10 150.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Time(s)

Curre

nt(p.u

.)

Motor speed

0 5 10 150.985

0.99

0.995

1

1.005

1.01

1.015

1.02

1.025

Time(s)

Spee

d(p.u.

)

The speed of themotor gradually de-creases as the load isapplied. It returns toits no load speed af-ter the ring gear isdisengaged.


0 5 10 150

0.2

0.4

0.6

0.8

1

Time(s)

Ring

gear

spee

d(p.u

.)

0 5 10 150

0.2

0.4

0.6

0.8

1

Spro

cket

spee

d(p.u

.)

The integration termof the PI controllerholds the speed ofthe ring gear andsprocket constant. At�� the controllersaturates. At ��the critical speed er-ror is exceeded andthe ring gear is re-leased.

Figure 7.9: Ramp: decoupled CST drive


7.3 Steady-state behaviour of the model

In the following section a discrete-element representation of the chain that includes real AFC

effects such as shearer loading, will be coupled to the fluid coupling drive model. The predicted steady state

behaviour of the model will be tested against data collected from the real AFC at the test site.

The dynamic predictions of the model cannot be tested, because the data obtained from the real

AFC was not at a sufficiently high sampling rate. However, the quasi-steady-state, or slowly changing be-

haviour predicted by the model, can be compared to the behaviour of the actual AFC. Because the AFC at

the test site was used as the real AFC, the model has been setup with the parameters detailed in Chapter 6.

Motor current and motor voltage were collected from the real AFC at the test site. They were used

with the parameters of the motor (cf. Appendix C), to determine the real power consumed by the motor. The

motor current, voltage and power of the real AFC, were then compared to the predictions of the model. The

trends were measured when the AFC was running unloaded, and when the AFC was loaded by the shearer

cutting towards the maingate. The results from the real AFC and the model are given in Table 7.1.

The variables stated in the table represent an average of the measured trends during a �� inter-

val, over the region of interest. The error represents the percentage difference between the model predictions

and the average measurements.

For both the unloaded and loaded tests, it is evident that the total motor power determined for both

the real and simulated AFC are in good agreement. This implies that the estimates used in the model for the

chain assembly/pan friction and coal friction, adequately model those of the real AFC. Because the losses

caused by coal friction dominate the carry back losses under normal circumstances, it is difficult to quantify

the accuracy of the carry back friction coefficient using these tests.

It is of interest to note that the average total power consumed by both the real and simulated AFC,

under quasi-steady-state conditions, can be determined from simple static calculations.

7.4 Dynamic analysis

In the following section the drives are coupled to the discrete-element representation of the chain.

This model is used to study the influence that the dynamic behaviour of each drive type has on chain tension.


Trend Drive Units Test AFC Model Error %

Unloaded AFCLine voltage MG1 V 3350 3340 -0.3

MG2 V 3330 3340 0.3TG V 3390 3390 0

Stator current MG1 A 55 58 5.5MG2 A 56 58 3.6TG A 56 57 1.7

Power MG1 kW 175 190 8.5MG2 kW 180 190 5.5TG kW 185 190 2.5

Total drive power kW 540 570 5.5

Loaded AFCShearer Position m 100 100 0

Speed m/s 0.27 0.27 0Web depth m 0.85 0.85 0Cut height m 3.5 3.5 0

Line Voltage MG1 V 3270 3260 -0.3MG2 V 3250 3360 0.3TG V 3300 3300 0.0

Current MG1 A 110 115 4.5MG2 A 120 115 -4.2TG A 125 114 -8.8

Power MG1 kW 515 550 6.8MG2 kW 570 550 -3.5TG kW 605 550 -9.0

Total motor power kW 1690 1650 -2.4

Table 7.1: A comparison of motor voltage, current and power of the real and simulated AFCs


The behaviour of the drives will be examined when they are started unloaded, and when step and ramp

loads are applied to the chain. The details of the loading conditions are given in the relevant sections. The

specifications for the AFC used in the following section, are given in Chapter 6.

7.4.1 Startup

The startup procedure is included separately in the following analysis because it is common to

both the ramp and step load cases. In a similar manner to the decoupled drive scenarios, the step and ramp

loads are initiated after the completion of the startup procedure.

When compared to the ramp and step loads, the startup load case has a relatively benign influence

on chain tension. The maximum tension applied to the chain is only dependent on the maximum torque

transmitted by either the fluid coupling or the CST (when adjusted by the gearbox ratio). The main interest

in this section is the procedure by which the drives are started.

Figure 7.10 depicts the startup of the fluid coupling drive 1. All motors are started with the working

chamber of their fluid coupling drained, so that they start unloaded. The motor therefore rapidly approaches

its no load speed.

At a time of �� the fluid couplings begin to fill. The maingate sprocket initially runs faster than

the tailgate sprocket. This occurs because when the drives are started, the maingate drives apply a force to

the chain on the upper race and the tailgate drive applies a force to the chain on the lower race. Therefore,

the maingate drives effectively pull the same mass of chain as the tailgate drive, with twice the amount of

torque. After the initial take up period, the maingate and tailgate drives share load equally throughout the

startup procedure.

The power spectral density (PSD) plot of the motor speed is depicted in Figure 7.11. For reference,

the first ten analytically determined natural frequencies of the chain and the polygon frequency, which is the

frequency that the sprocket teeth impact the chain at the normal running speed, are shown in Table 7.2. As

shown in the figure, the most dominant frequency is the polygon frequency. The other dominant frequencies

correspond to the natural frequencies of the chain.

The startup of the CST drive is shown in Figure 7.12. At a time of ��, the reference speed

�Note that the key to the figures is displayed at the bottom of the page within the figure title.


increases, which increases the torque applied by the clutch. This decelerates the ring gear and accelerates the

chain sprocket.

Initially the torque applied by the tailgate motor is larger than that applied by the maingate drive.

This is a consequence of the tailgate drive needing to apply a greater torque than the two maingate drives,

to accelerate the chain to the required speed. The load sharing algorithm then forces the maingate drives to

take up load from the tailgate drive, which is shown by the good correlation in the motor torques and currents

after the take up period.

The PSD plot of motor speed is shown in Figure 7.13. As evident from the figure the polygon

frequency is dominant.

Natural frequencies Freq(Hz)

$� 2.8$� 5.6$� 8.4$ 11.3$ 14.0$ 16.8$� 19.6$� 22.3$� 25.1$�� 27.9

Polygon frequency Freq(Hz)

$� 5.4

Table 7.2: The first ten analytically determined natural frequencies of the chain and the polygonfrequency

7.4.2 Ramp load

The ramp load models a progressively developing blockage at the maingate. It was implemented

by loading a group of �� moving chain elements, which were on the top race, near the maingate end, at the

rate of �� per element. The load is implemented directly after the startup of the AFC is completed.

Figure 7.14 shows the response of the fluid coupling drive to the ramping load. The increasing

load causes the slip of the fluid coupling to increase, which increases the torque transmitted to the motor. It


also decelerates the chain sprockets.

As shown in the figure torque applied by the maingate motors increases faster than the torque

applied by the tailgate motor. This occurs because the loaded chain elements are closer to the maingate end,

which causes the maingate motors to respond at an earlier time to the increasing load.

At a time of ��, the maingate and tailgate motor torques converge and remain approximately

equal for the remainder of the ramp duration. This is a result of the fluid coupling torque-slip curve becoming

flatter at large slips (cf. Figure 4.2), which makes the motor torque less sensitive to changes in the speed of

the sprocket.

At a time of �� the torque applied by the maingate and tailgate motors achieves a maximum.

This point corresponds to the maximum torque that can be transmitted by the fluid coupling. After the

maximum torque is reached, the motor torque steadily decreases and the increasing load causes rotation of

the sprocket to cease. At this point the slip of the fluid coupling is equal to one and the simulation is stopped.

For a real AFC, if the large load was to be sustained, either the motor or fluid coupling would overheat. This

would cause the control system to either cut power to the motor, or drain the fluid coupling.

The PSD plot of the motor speed during the ramp is shown in Figure 7.15. As for the startup

of the fluid coupling the polygon frequency is dominant. The second most dominant frequency at ��

corresponds to the second natural frequency of the chain.

Figure 7.16 shows the response of the CST drive to the ramping load. As the load increases, the

clutch applies a greater torque to the ring gear to maintain the velocity of the sprocket at the reference speed.

The increase in ring gear torque increases the torque applied to the motor.

In a similar manner to the fluid coupling drive, the torque applied by the maingate motors increases

faster than the tailgate motor torque. This is again a consequence of the loaded elements being closer to the

maingate end, which causes the maingate drives to respond to the increase in load before the tailgate drive.

For the duration of the ramp the load sharing control prevents the maingate and tailgate motor currents from

diverging.

At a simulation time of �� the PI controller saturates, which prevents the clutch from further

increasing the torque applied to the ring gear. The controller saturation limits the torque applied to the motor,

which is shown by the flat gradient of the maingate motor torque after saturation has occurred.


At a time of �� the increasing load, which is no longer opposed by an increase in ring gear

torque, causes the sprocket to decelerate and the critical speed error to be violated. The ring gears of all the

drives are then released and the motor torque reduces to its no load value.

As shown in the figure, the speed of the sprocket becomes negative after the ring gear is released.

This occurs because the chain now applies a greater torque to the sprocket than the drives. The negative speed

of the sprocket would eventually cause the sprocket teeth to disengage from the chain links (cf. Section 5.4.1).

Simulation of the AFC after the teeth disengage in this manner, is beyond the scope of the model.

The PSD plot of motor speed is shown in Figure 7.17. As for the fluid coupling drive, the largest

power is at the polygon frequency. However, for the CST there are also several frequencies adjacent to the

polygon frequency, which result from the dynamics of the CST.

The maximum tension developed in the chain by the CST and fluid coupling drive, is shown in

Figure 7.18. As assumed in the development of the discrete-element chain model (cf. Section 5.2.2), the chain

is represented as being rolled out from the tailgate, with the tailgate-maingate section (TG-MG) representing

the chain on the top race and the MG-TG section representing the chain on the bottom race.

For the ramp load, the maximum tension developed by the fluid coupling drive is higher than that

of the CST. This is because the maximum torque that can be transmitted by the CST, which is dependent on

the saturation limits of the PI controller, is less than the maximum torque that can be transmitted by the fluid

coupling. As previously mentioned, the saturation limits are arbitrary and could have been set to yield higher

or lower motor torques. The torque applied by the fluid coupling would have been limited by the use of a

torque limiting coupling (not included in this analysis).

With or without the torque limiting coupling, the fluid coupling drive would continue to apply

torque to the load once the sprocket had been stalled. If the stall was to continue the fluid coupling drive would

rely on the intervention of the control system to prevent overheating of the drive components. Conversely,

releasing the ring gear prevents the need to cut power to the motors.

7.4.3 Step load

The step load was chosen to simulate the worst foreseeable load that could be applied to the AFC.

For an AFC with two motors at the maingate, as is the case for the current model, jamming the chain on the


upper race, close to the maingate sprocket, is potentially the most damaging.

The step load was implemented by applying a large mass to �� chain elements, which at their

closest point are one metre from the maingate end. This rapidly stops the chain elements, which simulates a

chain jam. The step has been applied �� after the beginning of the simulations.

The response of the fluid coupling drive to the application of the step load is shown in Figure 7.19.

The increase in sprocket torque causes the slip of the fluid coupling to increase, which results in a greater

torque being transmitted to the motor. At ��, the maximum torque capacity of the fluid coupling is

reached. Any further increase in slip leads to a reduction in the torque applied to the motor, which causes the

motor to accelerate.

At a time of �� the slip of the maingate fluid coupling becomes greater than , and the

simulation is stopped. Treatment of fluid coupling slips greater than are beyond the capabilities of the

model.

Figure 7.20 details the response of the CST to the step load. Application of the load results in

the rapid deceleration of the maingate sprocket. At a time of ��, the speed of the maingate sprocket

reduces below �� and the critical speed error is exceeded (cf. Section 4.5.3). The ring gears of all the

drives are subsequently released. Releasing the ring gears causes the maingate ring gear to accelerate and

the maingate sprocket to decelerate. The motor torque is now redirected into the acceleration of the ring

gear, which effectively decouples the sprocket from the motor. The behaviour of the tailgate drive is not yet

affected, because the applied load has not been transmitted to it.

Because the change in motor speed is small, the sprocket speed decrease mirrors the speed increase

of the ring gear (cf. Equation 4.33). At a time of �� the speed of the sprocket becomes negative and

the ring gear speed becomes greater than . The minimum speed of�� obtained by the sprocket occurs

when the ring gear has a maximum speed of ��. As the torque applied by the clutch has not yet fallen to

zero, because of the delay in the hydraulics, the ring gear decelerates to its no load speed �� and rotation

of the sprocket ceases.

The maximum chain tension developed by both the fluid coupling and CST drives is shown in

Figure 7.21. It is evident from the figure, that the fluid coupling drive produces a maximum chain tension

three times that of the CST and nearly exceeds the proof load, which is used non-dimensionalise chain


tension. The tension applied by the fluid coupling is a result of the torque applied by the drives, which

accounts for approximately half of the tension, and the torque applied by the decelerating drive components,

which accounts for the remainder of the chain tension. As noted in Section 7.2, the contribution of the fluid

coupling and gearbox inertia to the sprocket torque is magnified because it is multiplied by the gearbox ratio.

It is important to note that if the fluid coupling drives were fitted with a torque limiting coupling,

the tension in the chain would have been limited to a predefined value. However, the fluid coupling drive

would still continue to apply torque to the load once the sprocket had been stalled. If the stall continued, the

fluid coupling drive would rely on the intervention of the control system to prevent overheating of the drive

components.

The maximum chain tension produced by the CST drive results from the motor torque and from

the deceleration of the sprocket and output shaft of the CST. The maximum chain tension produced by the

CST drive is comparatively low, because the motor torque is redirected into acceleration of the ring gear. The

motor torque also decreases as ring gear torque is decreased.


Startup: fluid coupling driveFl

uid

coup

ling

slip

05

10

15

20

25

0

0.2

0.4

0.6

0.81

Tim

e(s

)

Slip(p.u.)

Spro

cket

spee

d

05

10

15

20

25

−0

.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Tim

e(s

)

Speed(p.u.)

Not

es:

Lar

ger

torq

ueap

plie

dby

the

mai

ngat

edr

ives

resu

ltsin

am

ore

rapi

din

itial

acce

lera

tion

ofth

em

aing

ate

spro

cket

rela

tive

toth

eta

ilgat

esp

rock

et.

9.5

10

10

.51

11

1.5

12

0

0.0

2

0.0

4

0.0

6

0.0

8

0.1

0.1

2

Tim

e(s

)

Speed(p.u.)

Mot

orto

rque

05

10

15

20

25

−2

.5−2

−1

.5−1

−0

.50

0.51

1.52

2.5

Tim

e(s

)

Torque(p.u.)

Stat

orcu

rren

t(R

MS)

05

10

15

20

25

0

0.51

1.52

2.53

3.54

4.55

Tim

e(s

)

Current(p.u.)

Mot

orsp

eed

05

10

15

20

25

0

0.2

0.4

0.6

0.81

Tim

e(s

)

Speed(p.u.)

Figure 7.10: Startup: fluid coupling drive, (— �&��&�4, — �&��&�4)


0 5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x 10

−3 PSD of Xcp1

Frequency (Hz)

Mag

nitu

de

Figure 7.11: PSD: Startup of fluid coupling drive


Startup: CST driveR

ing

gear

spee

d

05

10

15

20

25

30

35

0

0.2

0.4

0.6

0.81

1.2

1.4

Tim

e(s

)

Speed(p.u.)

Spro

cket

spee

d

05

10

15

20

25

30

35

−0

.20

0.2

0.4

0.6

0.81

Tim

e(s

)

Speed(p.u.)

Not

es:

Lar

ger

torq

ueap

plie

dby

the

mai

ngat

edr

ives

resu

ltsin

am

ore

rapi

din

itial

acce

lera

tion

ofth

em

aing

ate

spro

cket

rela

tive

toth

eta

ilgat

esp

rock

et.

9.5

10

10

.51

11

1.5

12

0

0.0

2

0.0

4

0.0

6

0.0

8

0.1

Tim

e(s

)

Speed(p.u.)

Mot

orto

rque

05

10

15

20

25

30

35

−2

.5−2

−1

.5−1

−0

.50

0.51

1.52

2.5

Tim

e(s

)

Torque(p.u.)

Stat

orcu

rren

t(R

MS)

05

10

15

20

25

30

35

0

0.51

1.52

2.53

3.54

4.55

Tim

e(s

)

Current(p.u.)

Mot

orsp

eed

05

10

15

20

25

30

35

−0

.20

0.2

0.4

0.6

0.81

1.2

Tim

e(s

)

Speed(p.u.)

Figure 7.12: Startup: CST drive, (— �&��&�4, — �&��&�4)


0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

3.5

4x 10

−3

Frequency (Hz)

Mag

nitu

de

Figure 7.13: PSD: startup of CST drive


Ramp load: fluid coupling driveFl

uid

coup

ling

slip

05

10

15

20

25

30

0

0.2

0.4

0.6

0.81

Tim

e(s

)

Slip(p.u.)

Spro

cket

spee

d

05

10

15

20

25

30

0

0.2

0.4

0.6

0.81

Tim

e(s

)

Speed(p.u.)

Not

es

Mot

orto

rque

05

10

15

20

25

30

0

0.51

1.52

2.5

Tim

e(s

)

Torque(p.u.)

Stat

orcu

rren

t(R

MS)

05

10

15

20

25

30

0

0.51

1.52

2.53

3.5

Tim

e(s

)

Current(p.u.)

Mot

orsp

eed

05

10

15

20

25

30

0.9

75

0.9

8

0.9

85

0.9

9

0.9

951

Tim

e(s

)

Speed(p.u.)

Figure 7.14: Ramp load: fluid coupling drive, (— �&��&�4, — �&��&�4)


0 5 10 15 20 25 300

0.005

0.01

0.015

0.02

0.025

0.03

Frequency (Hz)

Mag

nitu

de

Figure 7.15: PSD: Ramp load, fluid coupling drive


Ramp load: CST driveR

ing

gear

spee

d

05

10

15

20

25

0

0.51

1.52

2.5

Tim

e(s

)

Speed(p.u.)

Spro

cket

spee

d

05

10

15

20

25

−1

.5−1

−0

.50

0.51

1.5

Tim

e(s

)

Speed(p.u.)

Not

es

At�

��

the

PIco

ntro

ller

satu

rate

s,w

hich

limits

the

torq

ueap

plie

dto

the

mot

or.A

t��

the

ring

gear

isre

leas

ed.

Mot

orto

rque

05

10

15

20

25

−0

.50

0.51

1.52

Tim

e(s

)

Torque(p.u.)

Stat

orcu

rren

t(R

MS)

05

10

15

20

25

0.2

0.4

0.6

0.81

1.2

1.4

1.6

1.82

2.2

Tim

e(s

)

Current(p.u.)

Mot

orsp

eed

05

10

15

20

25

0.9

85

0.9

9

0.9

951

1.0

05

1.0

1

1.0

15

1.0

2

1.0

25

Tim

e(s

)

Speed(p.u.)

Figure 7.16: Ramp load: CST drive, (— �&��&�4, — �&��&�4)


0 5 10 15 20 25 300

0.02

0.04

0.06

0.08

0.1

0.12

Frequency (Hz)

Mag

nitu

de

Figure 7.17: PSD: Ramp load, CST drive


Maximum chain tensionFluid coupling

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Position (p.u.)

Ten

sion

(p.

u.)

TG MG TG

CST

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Position (p.u.)

Ten

sion

(p.

u.)

TG MG TG

Figure 7.18: Maximum chain tension: Ramp load


Step load: fluid coupling drive

Flui

dco

uplin

gsl

ip

00

.02

0.0

40

.06

0.0

80

.10

.12

0.1

40

.16

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

Tim

e(s

)

Slip(p.u.)

Spro

cket

spee

d

00

.02

0.0

40

.06

0.0

80

.10

.12

0.1

40

.16

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

Tim

e(s

)

Speed(p.u.)

Not

es

The

reis

ara

pid

incr

ease

inth

em

aing

ate

mot

orto

rque

and

cur-

rent

asth

est

epis

appl

ied.

At

��

��

the

spee

dof

the

mai

ngat

esp

rock

et,b

ecom

esne

gativ

ean

dflu

idco

uplin

gsl

ipbe

-co

mes

grea

ter

than

1.

Mot

orto

rque

00

.02

0.0

40

.06

0.0

80

.10

.12

0.1

40

.16

0

0.51

1.52

2.53

3.5

Tim

e(s

)

Torque(p.u.)

Stat

orcu

rren

t(R

MS)

00

.02

0.0

40

.06

0.0

80

.10

.12

0.1

40

.16

0

0.51

1.52

2.53

Tim

e(s

)

Current(p.u.)

Mot

orsp

eed

00

.02

0.0

40

.06

0.0

80

.10

.12

0.1

40

.16

0.9

55

0.9

6

0.9

65

0.9

7

0.9

75

0.9

8

0.9

85

0.9

9

0.9

951

Tim

e(s

)

Speed(p.u.)

Figure 7.19: Step load: fluid coupling drive, (— �&��&�4, —�&��&�4)


Step load: CST driveR

ing

gear

spee

d

00

.02

0.0

40

.06

0.0

80

.10

.12

0.1

40

.16

0.1

80

.20

0.2

0.4

0.6

0.81

1.2

1.4

Tim

e(s

)

Speed(p.u.)

Spro

cket

spee

d

00

.02

0.0

40

.06

0.0

80

.10

.12

0.1

40

.16

0.1

80

.2−

0.4

−0

.20

0.2

0.4

0.6

0.81

Tim

e(s

)

Speed(p.u.)

Not

es

Ata

time

of

��

the

criti

cals

peed

erro

ris

viol

ated

and

allt

heri

ngge

ars

are

rele

ased

.A

t ��

the

spee

dof

the

mai

n-ga

tesp

rock

etbe

com

esne

gativ

ean

dth

eri

ngge

arsp

eed

rise

sab

ove

1p.u

.

Mot

orto

rque

00

.02

0.0

40

.06

0.0

80

.10

.12

0.1

40

.16

0.1

80

.2−

0.0

50

0.0

5

0.1

0.1

5

0.2

0.2

5

0.3

Tim

e(s

)

Torque(p.u.)

Stat

orcu

rren

t(R

MS)

00

.02

0.0

40

.06

0.0

80

.10

.12

0.1

40

.16

0.1

80

.20

.28

0.2

9

0.3

0.3

1

0.3

2

0.3

3

0.3

4

Tim

e(s

)

Current(p.u.)

Mot

orsp

eed

00

.02

0.0

40

.06

0.0

80

.10

.12

0.1

40

.16

0.1

80

.20

.99

85

0.9

99

0.9

99

51

1.0

00

5

1.0

01

1.0

01

5

1.0

02

1.0

02

5

Tim

e(s

)

Speed(p.u.)

Figure 7.20: Step load: CST drive, (— �&��&�4, —�&��&�4)


Maximum chain tensionFluid coupling

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Position (p.u.)

Ten

sion

(p.

u.)

TG MG TG

CST

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Position (p.u.)

Ten

sion

(p.

u.)

TG MG TG

Figure 7.21: Maximum chain tension: Step load


7.5 Sensitivity analysis

It is the aim of the sensitivity analysis to gauge the response of the drives to changes in model

parameters, which are either of questionable accuracy, or may have a significant influence on the findings of

this thesis. As the step load is the most critical loading scenario, it was used to test the response of the drives

to changes in the parameters.

Table 7.3 details the model parameters used in the sensitivity analysis. With the exclusion of the

CST’s hydraulic time constant, the middle value for the model parameters represents that which is typically

used. Because the fluid coupling drive produces the largest chain tension during the step load all changes in

the model parameters, with the exception of the hydraulic time constant, will be tested on the fluid coupling

drive only.

Figure 7.22 depicts the maximum chain tension produced by the fluid coupling drive when a

variation is made in the chain and sprocket performance parameters. As shown in the figure, chain and

sprocket damping have negligible effect the maximum tension in the chain. This can be attributed to the

small damping ratio �� that was used for both the sprocket and the chain. The sprocket stiffness

also appears to have little effect on the magnitude of the maximum chain tension. However, it increases the

level of oscillation in the chain tension.

The stiffness of the chain has a definite effect on the maximum chain tension. The greater the chain

stiffness, the larger the maximum chain tension. The larger tension results from the stiffer chain applying a

greater force for a given extension of the chain. This results in a more rapid deceleration of the sprocket,

which produces a greater tension in the chain.

As shown in Figure 7.23, the maximum chain tension increases with an increase in the inertia of

the driven half of the fluid coupling (turbine). This results from the larger kinetic energy stored in the rotating

drive components, which increases the extension of the chain during the jam and increases chain tension.

The effect of a change in the CST’s hydraulic time constant is also depicted in Figure 7.23. As

discussed in Section 4.5.3, the hydraulic time constant is a gauge of the rate at which the torque applied by

the ring gear is either increased, or decreased, in response to a change in input from the PI controller. In the

current context, the time constant represents the time that the ring gear torque will take to reduce by � �

once the ring gear is released.


The first value for the time constant shown in Table 7.3, is the value typically used for the simula-

tion of the CST. As the CST was superior in its performance during a jam situation, it is of interest to see by

how much its performance degrades when its model parameters degrade.

As shown in the figure, the maximum tension applied by the CST drive shows only a slight in-

creases with an increase in the CST’s hydraulic time constant. This can be explained as follows. When a

step load is applied, the ring gear accelerates because the clutch has not yet developed sufficient torque to

overcome the increase in load. This increase in ring gear speed results in the deceleration of the sprocket. For

large loads, the sprocket deceleration is rapid and the time between when the load is applied and when the

ring gear is released, is small. Therefore, for a large time constant, the clutch torque increase would be limited

before the ring gear is released. Because the torque transmitted to the motor depends on the torque applied

to the ring gear by the clutch, the increase in motor torque is only small before the ring gear is released (see

for example Figure 7.20). The contribution of the motor torque to chain tension is therefore not significantly

affected by an increase in the hydraulic time constant.

7.6 Time step independence

The independence of the results of the computer simulation to a change in the integration time

step ensures that the chosen time step is of high enough resolution. Because the step load, which represents

a chain jam, is the most rapidly varying load, it was chosen as the bench mark for selection of the time step.

The time step which was chosen is � ��. It was compared to a time step of ��

Figures 7.24 and 7.25 show the comparison of the variation in the drive trends and the maximum

chain tension with a refinement of the time step. As shown in the figure there is good agreement between the

coarse and the fine time steps.


Variable Sym. Unit Value

Sprocket parameters�%� � ��

Tooth stiffness �� %� � ��

�%��

��Tooth damping ��

� �

Chain parameters�%� � ��

Stiffness � �� %� � ��

�%� � ��

� �Damping � ��

��

Fluid coupling drive�

Coupling inertia ��

CST drive��

Time constant 8 ��

Table 7.3: Model parameter variations during the sensitivity analysis


Maximum chain tension NotesSprocket tooth stiffness ��

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Position (p.u.)

Tens

ion (p

.u.)

TG MG TG

kt=4e8kt=4e9kt=4e10

There is only a slightchange in chain ten-sion with increasingtooth stiffness.

Sprocket tooth damping ��

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Position (p.u.)

Tens

ion (p

.u.)

TG MG TG

ct=425ct=550ct=675

Sprocket toothdamping does nothave a significanteffect on chaintension

Chain stiffness ��

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Position (p.u.)

Tens

ion (p

.u.)

TG MG TG

k=1.3e9k=2.6e9k=3.9e9

Maximum chain ten-sion increases withan increase in chainstiffness.

Chain damping ��

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Position (p.u.)

Tens

ion (p

.u.)

TG MG TG

c=270c=350c=430

Chain damping doesnot have a significanteffect on chain ten-sion

Figure 7.22: The maximum chain tension produced by the fluid coupling drive, with a change in thecritical performance parameters of the chain and sprocket.


Maximum chain tension NotesFluid coupling inertia ��

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Position (p.u.)

Ten

sion

(p.

u.)

TG MG TG

I1I2I3

An increase in fluidcoupling inertiaincreases chaintension. For a higherinertia there is morekinetic energy storedin the drives, whichis absorbed by thechain during the jam.

Hydraulic time constant ��

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Position (p.u.)

Ten

sion

(p.

u.)

TG MG TG

T=50msT=100msT=250ms

A change in the hy-draulic time constanthas little effect on themaximum chain ten-sion.

Figure 7.23: The effect of a change in the fluid coupling and CST drives critical performanceparameters on maximum chain tension during a jam.


Time step independence

Flui

dco

uplin

gsl

ip

00

.02

0.0

40

.06

0.0

80

.10

.12

0.1

40

.16

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

Tim

e(s

)

Slip(p.u.)

Spro

cket

spee

d

00

.02

0.0

40

.06

0.0

80

.10

.12

0.1

40

.16

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

Tim

e(s

)

Speed(p.u.)

Not

es

Mot

orto

rque

00

.02

0.0

40

.06

0.0

80

.10

.12

0.1

40

.16

0

0.51

1.52

2.53

3.5

Tim

e(s

)

Torque(p.u.)

Mot

orcu

rren

t(R

MS)

00

.02

0.0

40

.06

0.0

80

.10

.12

0.1

40

.16

0

0.51

1.52

2.53

Tim

e(s

)

Current(p.u.)

Mot

orsp

eed

00

.02

0.0

40

.06

0.0

80

.10

.12

0.1

40

.16

0.9

55

0.9

6

0.9

65

0.9

7

0.9

75

0.9

8

0.9

85

0.9

9

0.9

951

Tim

e(s

)

Speed(p.u.)

Figure 7.24: Time step independence: (— � � ��, — � � �� )


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Position (p.u.)

Ten

sion

(p.

u.)

TG MG TG

tstep=1e−5tstep=5e−6

Figure 7.25: Variation of maximum chain tension with a change in time step

7.7 Conclusion

In this chapter we have studied the influence that the dynamic behaviour of the fluid coupling and

CST drives, has on the tension in the chain. This analysis was undertaken in three parts.

In the first part of the chapter the behaviour of certain aspects of the model was verified. It was

shown that the behaviour of both the drive types, when they were decoupled from the chain, was physically

realistic and qualitatively correct.

The drives were then coupled to the discrete-element representation of the chain, to test the quasi-

steady-state behaviour of the full AFC simulation. The results of the simulation were compared to trends

acquired from a real AFC operating under the same conditions. It was shown that the quasi-steady-state

behaviour of the simulated AFC, compared favorably to that of the real AFC.

The second part of the chapter studied the influence that the dynamic behaviour of the drives has

on the tension in the chain. Inter alia, the analysis of the drives revealed that;

1. The dynamic behaviour of the drives has a significant effect on chain tension, when the load applied


to the chain rapidly increases.

2. When the chain is jammed, the CST drive produces lower chain tensions than the fluid coupling drive.

3. To prevent adverse chain tensions during a chain jam, the fluid coupling drive should be fitted with a

torque limiting coupling.

4. The fluid coupling and CST were both effective in limiting the torque applied to the motors during a

blockage.

The maximum chain tension produced by the fluid coupling drive during the chain jam was three

times that of the CST drive and almost 0.9 times the proof load. The comparatively large tension produced

by the fluid coupling drive was found to be a result of the decelerating drive inertia and the torque applied by

the motors. Considering this result, it is imperative that a fluid coupling drive be fitted with a torque limiting

coupling, to limit chain tension. The CST was found to prevent large chain tensions because it isolated the

motor from the load, by releasing the ring gear.

In the third part of the chapter, a sensitivity analysis was performed to test the change in maximum

chain tension with a variation in the critical model parameters of the chain and drives. It was found that for

the fluid coupling drive, the tension produced during a chain jam increases with an increase in the inertia of

the driven fluid coupling half, and with an increase in the stiffness of the chain. A change in the sprocket

tooth stiffness and the chain and sprocket damping was found to have negligible effect on chain tension. For

the CST drive it was shown that a change in the hydraulic time constant, had little effect on chain tension. It

was shown that the result of the simulation did not vary with a further reduction in time step.

Chapter 8

Summary and Conclusions

It was the aim of this research to study the influence that the dynamic behaviour of the fluid

coupling and controlled slip transmission (CST) drives has on the tension in the AFC chain. The fluid

coupling and the CST drives were chosen because they are currently the drives most commonly used on AFCs.

The performance of the drives was studied by using a computer simulation, which models the equations

describing the dynamics of the AFC components. The work was undertaken in two parts.

The first part of the study developed the equations that govern the motion of the following AFC

components: the asynchronous motor, fluid coupling, CST, gearbox, chain sprocket and chain/flight bar

assembly.

A 3-phase representation of an idealized asynchronous motor was developed. This can be used to

model both squirrel-cage and wound-rotor motors. The motors on the test system are squirrel-cage motors.

This 3-phase representation was then reduced to an equivalent 2-phase representation, through the �� trans-

formation. The 2-phase representation is mathematically equivalent to the 3-phase representation, however

it is more concise and it also improves the speed that the equations are solved numerically. The 2-phase

representation was then placed in per unit form.

The model of the fluid coupling describes the motion of the impeller and the turbine. It uses the

manufacturer’s torque-slip curve to calculate the torque transmitted by the fluid coupling as a function of the

impeller speed and the fill level of the working chamber.

149

150 Chapter 8: Summary and Conclusions

The equations of motion of the reduction gearbox and the CST were developed using a Lagrangian

approach. All the gearbox parameters were referred to the motor side so that standard performance parameters

supplied by the manufacturer can be used in the model.

The model of the CST describes the motion of its three coupled subsystems; the reduction stage,

the planetary gearset and the clutch. Constraint equations were used to place the equations of motion in terms

of the speed of the input shaft of the reduction stage, and the speed of the ring gear of the planetary gearset.

The model of the clutch describes the clutch components, such as the friction plates, the hydraulics

and the controller. The friction plates and the hydraulics are modelled by a first-order linear system. The

clutch is controlled by a PI controller with saturation bounds that limit the torque applied to the motor and a

safety switch, which decouples the motor from the chain when the deceleration of the sprocket is excessive.

In addition to controlling chain tension the controller also controls the sharing of load between the drives.

The chain/flight bar assembly is modelled by a discrete element representation of the equations

of motion of a continuous chain. These equations describe the motion of a pretensioned chain subjected to

external forces. The external forces are the force applied by the sprocket teeth, the inertial force of the loaded

material, the gravitational force, the frictional force, the snaking force and atypical forces, such as that caused

by the jamming of the chain and by a blockage of the AFC.

As part of the description of the external forces, equations describing the rate that material is

loaded onto the AFC by the shearer and by advancement of the panline were developed. They incorporate a

wide range of parameters, such as the geometry of the coal face and the speed and geometry of the shearer.

All equations have been reduced to a readily usable form.

In the second part of this thesis the dynamic model of the AFC was implemented on a computer

program. The computer simulation was used to study the performance of the fluid coupling and CST drives

under different loading scenarios.

An overview of the computer simulation, which was developed on SIMULINK, was firstly pre-

sented. SIMULINK subsystem blocks were created using the equations developed in earlier chapters. The

performance parameters of the AFC components were also detailed.

The simulation of the fluid coupling and CST drives was then verified. The drives were first tested

in isolation of the chain, where it was demonstrated that their behaviour was physically realistic. The drives

Chapter 8: Summary and Conclusions 151

were then coupled to the discrete-element representation of the chain, to test the quasi-steady-state behaviour

of the full AFC simulation. The results of the simulation were compared to trends acquired from a real AFC

operating under the same conditions. It was shown that the quasi-steady-state behaviour of the simulated

AFC compared favorably to that of the real AFC. The dynamic prediction of the model could not be tested

because the data was not sampled at a high enough rate and the chain tension could not be acquired.

The influence of the dynamic behaviour of the drives on AFC chain tension was then studied. The

drives were subjected to step and ramp loads, which simulate the jamming of the chain and blockage of the

conveyor. Inter alia, the analysis of drive performance revealed that;

1. When the chain load varies rapidly, the drive dynamics determine the peak chain tension.

2. When the chain is jammed, the CST drive produces lower chain tensions than the fluid coupling drive.

3. To prevent adverse chain tensions during a chain jam, it is necessary to fit the fluid coupling drive with

a coupling that limits the torque applied to the chain sprocket.

4. The fluid coupling and CST were both effective in limiting the torque applied to the motors when a

large developing load (i.e a blockage) was applied to the chain.

The main conclusion from this analysis is that the tension applied to the chain by both drive types

depends on the motor torque and the deceleration rate of the drive components. For a fluid coupling drive not

fitted with a torque limiting coupling, large chain tensions are predicted during a chain jam. This is a result

of the energy stored in the decelerating drive inertia and the energy produced by the motor being directly

absorbed by the chain. Conversely, the ability of the CST drive to isolate the motor torque and the inertia of

the reduction gearbox from the chain, substantially reduced chain tension.

8.1 Scope for future research

The most obvious avenue for future research, is the experimental validation of the dynamic be-

haviour of the model. This would involve the comparison of trends acquired from a real AFC, such as chain

tension, motor voltage, motor current etc., to that of the model during periods where the load varies rapidly.

152 Chapter 8: Summary and Conclusions

The assumptions made in the development of the model could then be tested and the models performance

updated.

Another avenue for application of the model is to investigate the different drive control options.

These may include the updating of the drive’s control parameters or implementation of other control algo-

rithms. The model may also be used as part of a model based fault detection scheme, which promises to

feature heavily in the process of automating the AFC. It could also be used for on-line parameter estimation

to identify changing trends and different operating regimes.

This research has highlighted the opportunity for further investigation into the local interaction

between the chain links and the sprocket teeth. This may involve a study of the impact dynamics of the chain

and sprocket and the resulting local and global stresses in both the sprocket tooth and the engaged chain links.

Bibliography

[1] Longwall mining [online]. Available:http://www.uow.edu.au/eng/current/longwall[2002,Jan,8].

[2] A. R. Broadfoot. Analysis and design of an enhanced longwall armoured face conveyor system.PhD thesis, The University of Newcastle, 1996.

[3] J. L. Davis. Wave propagation in solids and fluids. Springer-Verlag, New York, 1988.

[4] R. Finzel, W. Wolfgang, and H. Holler. Water flow-controlled turbo couplings of the newgeneration to drive afc’s. Technical report, Voith Turbo GmbH and Co. KG, June 2000.

[5] H. Goldstein. Classical mechanics. Addison-Wesley, Reading, Mass, 1950.

[6] H. L. Hartman. Introductory mining engineering. Wiley, New York, 1987.

[7] J. Hindmarsh. Electrical Machines and their Applications. Permagon, Oxford, fourth edition,1984.

[8] R. C. Juvinall and K. M. Marshek. Fundamentals of Machine Components Design. Wiley,U.S.A, 1991.

[9] R. Keller. The startup of hydrodynamic couplings. Technical Report 73, Voith, 1963.

[10] P. C. Krause. Simulation of symmetrical induction machinery. IEEE Transactions on PowerApparatus and Systems, 84(11):1038–1053, 1965.

[11] L. Morley, J. Kohler, and H. Smolnikar. A model for predicting motor load for an armoredface-conveyor drive. IEEE Transactions on Industry Applications, 24(4):649–659, 1988.

[12] N. K. Myshkin, C. K. Kim, and M. I. Petrokovets. Introduction to tribology. Cheong MoonGak, Seoul, Korea, 1997.

[13] C.M. Ong. Dynamic Simulation of Electric Machinery. Prentice Hall, New Jersey, 1997.

[14] G. Schulz. Futher results in the analysis of dynamic characteristics of belt conveyors. Bulksolids handling, 13(4):705–710, 1993.

[15] S. Shadow, P. E. Sollars, and J. J. Maloney. The application of hydroviscous and ac inductionbrakes on a long regenerative panel conveyor. SME Bulk Material Handling, 1998.

[16] P. Vas. Vector Control of AC Machies. Oxford University Press, New York, 1990.

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[17] K. W. Wang, S. P. Liu, S. I. Hayek, and F. H. K. Chen. On the impact intensity of vibratingaxially moving roller chains. Vibration and Acoustics, 144:397–403, 1992.

[18] D. A. Wells. Lagrangian Dynamics. McGraw-Hill, Sydney, 1967.

[19] M. Wolfe and K. Flote. Causes of vibration and stress loadings of chain-operated face-workmachinery attributable to vibration. In High-performance longwall operations, Aachen, Ger-many, 2000.

Appendix A

Glossary of terms

armoured face conveyor A chain conveyor that is used in the longwall mining process to trans-

port material from the longwall face.

belt conveyor A conveyor which transports material on a endless belt. Belt conveyors

are used to transport material from the longwall to the processing plant

on the surface of the mine.

bi-directional cutting The shearer cuts the full height of the coal face each time it traverses

the coal face.

black coal Coal which is of either anthracite, bituminous or sub-bituminous rank.

beam stage loader (BSL) A chain conveyor that transports coal unloaded from the AFC to the belt

conveyor.

155

156 Appendix A: Glossary of terms

chain conveyor A conveyor that transports material by dragging it across flat steel pans

using horizontal lying steel bars (flight bars), which are connected by

chains. The armoured face conveyor and the beam stage loader are

specific types of chain conveyors.

crusher A machine that crushes large lumps of coal before they are loaded onto

the belt conveyor by the beam stage loader.

flight bars Horizontal lying steel bars which drag material along the chain con-

veyor pans.

flitting The second pass made by the shearer on a coal face when using the

uni-directional cutting method.

goaf (gob) The material that collapses behind the roof supports after the coal has

been extracted.

headings Parallel roadways which are driven into a coal block from a trunk road.

Two headings are joined to create the longwall face.

inbye Towards the longwall face.

longwall mining A continuous mining process used for extracting coal from underground

deposits.

maingate The primary access route to the longwall face.

load sharing The degree to which the AFC drives equally share the load applied by

the chain.

Appendix A: Glossary of terms 157

outbye Away from the longwall face.

panel A rectangular block of coal that is formed for the purpose of longwall

mining.

pass The process where the shearer cuts along the full length of the coal face.

pillar A block of coal that is left to stabilize the surrounding roof.

plough The coal plough consists of a series of steel picks which are scraped

along the coal face to dislodge coal. It is most suitable for coal seams

that are relatively soft.

ribs The walls of an underground roadway.

roof support A support which helps to stabilize the overlying strata. In a longwall

mine they are typically hydraulically powered.

shearer The shearer uses steel picks that are attached to two spinning drums, to

dislodge material from the coal face.

shearing The first pass made by the shearer on a coal face when using the uni-

directional cutting method.

slabbing Defines the process where large blocks of coal (slabs) fall from the long-

wall face onto the AFC.

soft starting The process whereby the motors are decoupled from the chain when

they are started.

158 Appendix A: Glossary of terms

spalling The term broadly used to describe the process by which material freely

dislodges from the longwall face.

tailgate An auxilliary access route to the longwall face.

tunneling When the top layer of material loaded onto the AFC pans moves slower

then material on the bottom layer (close to the flight bars).

uni-directional cutting The shearer cuts a fraction of the face height on the first pass and then

cuts the remainder of the face on the second pass.

Appendix B

Friction Coefficient

The following appendix outlines a procedure for calculating the friction coefficient of the chain

assembly ��, the material loaded on the upper race �� and the material carried back on the lower race

�� (cf. Section 5.4.4).

The friction coefficients will be determined from data obtained from the test site’s AFC. The

data was supplied by the AFC manufacturer. The tests were used by the manufacturer to determine the

power consumed by the chain assembly, by material loaded on the upper race and by material carried back

(recirculated) along the lower race.

The tests were performed when the AFC utilized a chain of �� diameter. At the time of writing

this thesis a �� chain is used. This is not expected to affect the friction calculations because the flight bar

spacing has remained constant 1.

The data was gathered using the data acquisition system fitted to the AFC. The accuracy and

sampling rate of the data were not made available by the manufacturer. A summary of the AFC’s performance

parameters and the test conditions is given in Table B.1.

�Empirical manufacturer data suggests that the flight bar spacing affects the friction coefficient of the chain assembly.

159

160 Appendix B: Friction Coefficient

Variable Sym. Units Qty.

DrivesMaingate power (full load) �� 800Tailgate power (full load) �� 800Gearbox ratio �� 30.14Gearbox efficiency �� 0.95Fluid coupling efficiency �� 0.95Sprocket PCD �� 648Sprocket efficiency �� 0.85

Pan lineFace length �� 263Chain size �� 42Chain density !�� 159Chain length �� 528Chain speed(full load) �� 1.67AFC gradient(favourable) " �4% 4Carry back coefficient �� 0.02

GeologicalUncut material density !� �� 1450

ShearerLoading efficiency �� 0.95

Table B.1: Performance parameters used for AFC testing

B.1 Experimental procedure and results

B.1.1 No load test

The no load test determines the power consumed by the AFC motors when moving the unloaded

chain/flight bar assembly at a constant speed. It will be used to determine the coefficient of friction of the

chain/flight bar assembly ��.

During the no load test an unloaded AFC is run up to a constant speed and the real power consumed

by each motor is recorded. The results of the no load test are given in Table B.2.

Appendix B: Friction Coefficient 161

Variable Sym. Units Qty.

Maingate power ,�� 228Tailgate power ,�� 189No load power ,�� ,�� ,�� 417

Table B.2: Results of the no load test

B.1.2 Recirculation load test

The recirculation load test determines the power that is drawn by the motors when pulling coal

that is carried back on the lower race. It is used to determine the carry-back friction coefficient �� .

For the test, the AFC is loaded at a constant rate by the shearer. When coal has recirculated along

the entire length of the lower race, cutting is stopped and the coal on the upper race is allowed to empty onto

the BSL. When the last piece of coal discharges from the upper race of the AFC, the power consumed by the

motors is recorded. When the chain has completed one further cycle, so that there is no coal loaded on either

race, the power is again recorded. The difference between the two recorded powers determines the power

consumed by recirculating material.

Variable Sym. Units Last lump + 1 cycle

Web depth )� � 0.85Extracted height :� � 3.5Shearer speed �� 17Maingate power ,�� 200 192Tailgate power ,�� 208 184Total power ,��, ,�� 408 376Recir. load power ,� � ,�� ,�� 32

Table B.3: Results of the recirculation test

B.1.3 Coal load test

The coal load test is used to determine the power drawn by the AFC motors when pulling coal

loaded on the upper race of the AFC. It will be used to determine the friction coefficient of the coal loaded

on the upper race ��.

During the test a running conveyor is loaded at a constant rate by the shearer. When a predefined


length of the AFC has been loaded with material, the power consumed by the drives is recorded. The results

of the coal load test are given in Table B.4.

Description Sym. Units Qty.

Web depth )� � 0.85Extracted height :� � 3.5Loaded distance �� 170Shearer speed �� 17Maingate power ,�� 788Tailgate power ,�� 871Coal load power ,�� ,�� ,�� kW 1659

Table B.4: Results of the coal load test

B.2 Friction factors

In the following section the friction factors will be determined. It will be assumed that frictional

and gravitational forces are the dominating forces on the AFC. All other forces will be ignored. Unless stated

otherwise, the variables used in the analysis are those given in Tables B.1 to B.4.

B.2.1 Chain assembly/pan friction

The total efficiency of the drive �� is equal to the product of the efficiency of the individual drive

components,

�� (B.1)

The power needed to move the unloaded chain assembly �� is given by the product of

the total drive efficiency �� and the no load motor power �� ,

�� (B.2)


The total force required to pull the chain assembly �� is expressed in terms of the power

required to pull the chain assembly and the speed of the chain assembly �� , as follows:

�� (B.3)

Because there is an equal mass of chain on the upper and lower race, the total gravitational force

acting on the chain assembly is equal to zero. The force required to pull the chain assembly is therefore equal

to the frictional force ��,

�� (B.4)

where �� is the chain assembly/pan friction coefficient, �� is the total mass of the chain assembly,

�� is the acceleration due to gravity and � is the articulation angle of the AFC.

�� is given by the product of the density of the chain/flight bar assembly � �� and the

total chain length ��,

�� (B.5)

Substituting Equation B.5 into Equation B.4 and rearranging the resulting expression, yields the

following expression for the chain assembly/pan friction coefficient;

��

��

� � ��

�� (B.6)

B.2.2 Carry back friction

The power consumed by material carried back (recirculated) on the lower race �� is

expressed in terms of the power consumed by the motors �� and the total drive efficiency as,

�� (B.7)


The total force required to move the recirculated material �� is expressed in terms of ��

and �� as,

�� (B.8)

�� is equal to the sum of the gravitational �� and frictional forces �� acting on

the recirculated material,

�� (B.9)

The gravitational force is expressed as (cf. Equation 5.26),

�� (B.10)

where �� is the total mass of material carried back on the lower race. �� is given by the product of

the mass of material carried back per metre �� and the length of the AFC ��,

�� (B.11)

�� can be expressed in terms of the mass of material loaded on the upper race per metre �� and

the carry back coefficient ��,

�� (B.12)

If it is assumed that material is loaded onto the AFC by the shearer only, then the rate that material

is loaded onto the AFC � �� is given in terms of the shearer loading efficiency �� and the shearer

extraction rate � �� (cf. Equation 5.12),


��

� �� !��

� ��

� �� (B.13)

The mass of material loaded onto the AFC per metre is expressed in terms of the loading rate and

the velocity of the shearer relative to that of the chain as follows:

��

��

��

��

� �� (B.14)

Using the above result �� is given by,

�� (B.15)

which yields the following value for ��,

�� (B.16)

Substituting the value for �� into Equation B.10, gives the gravitational force acting on the

recirculated material:

�� (B.17)

Substituting Equations B.8 and B.17 into Equation B.9 and rearranging the resulting expression,

gives the total frictional force applied to the recirculating material,


�� (B.18)

The coefficient of friction is therefore equal to the following:

��

��

��

�� (B.19)

B.2.3 Material friction (upper race)

The power consumed by the motors to move the material that is loaded on the upper race ��

is given by,

�� (B.20)

Accounting for the drive efficiency, the power that is supplied to the chain to move the material on

the upper race is expressed as,

�� (B.21)

The total force needed to move the material loaded on the upper race �� , is given by,

�� (B.22)

The mass of material on the upper race � �� can be expressed in terms of the mass of material

loaded on the upper race per metre � �� and the loaded length of the AFC ��,

� � �� (B.23)

where the mass of material loaded per meter � � is the same as that given by Equation B.14.


�� is equal to the sum of the frictional force �� and gravitational force ��

acting on the loaded material,

��

The gravitational force is negative because it assists movement towards the maingate end. Re-

arranging the above equation yields the following value for � ��,

�� (B.24)

� �� (B.25)

� �� (B.26)

With reference to Equation 5.28, the coefficient of friction of the material loaded on the upper race

�� is equal to the following:

��

�� "��

��

�� (B.27)

Appendix C

Drive Specifications

C.1 Motor specifications

Variable Units Value

Type Squirrel-cagePower output kW 800Line voltage V 3300Phases 3Line frequency Hz 50Poles 4Stator connection Star

Table C.1: Motor specifications

Load Efficiency Power factor Current(A) Speed(rpm) Torque (Nm)

100% 97.2 0.887 162.3 1491 5122.175% 97.3 0.869 124.2 1493 3835.750% 96.9 0.810 89.2 1495 2553.525% 95.1 0.617 59.7 1497 1275.0

No load 0.35 46.2 1500

Table C.2: Motor performance details

168

Appendix C: Drive Specifications 169

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

2.5

3

Speed (% Synchronous)

Tor

que

(p.u

.)

Pull out torque

Full load torqueLocked rotor torque

Figure C.1: Motor torque-speed curve

Description Torque(Nm) Speed(rpm) Current(A) Power factor

Locked rotor 5203 0 1111 0.169Full load 5122.1 1491 162.3 0.887Pull out 14187 1455 - -

Table C.3: Salient points on the motor torque-speed curve

170 Appendix C: Drive Specifications

C.2 Fluid coupling specifications

01020304050607080901000

0.5

1

1.5

2

2.5

Slip(%)

Tor

que(

p.u.

)Stalltorque

Maximumtorque

Full loadtorque

Figure C.2: Fluid coupling torque-slip curve

Description Torque(Nm) Slip(%)

Full load torque 5122 7.8Maximum torque 12930 75Stall torque 11400 100

Table C.4: Salient points on the fluid coupling torque-slip curve


0 5 10 15 20 25 30 350

10

20

30

40

50

60

70

80

90

100

Time (s)

Fill

leve

l (%

des

ign)

Figure C.3: Fluid coupling fill level during startup


C.3 CST specifications

0 5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time(s)

Ref

eren

ce s

peed

(p.u

.)

Figure C.4: CST reference speed


C.4 Rated and base quantities

C.4.1 Rated quantities

The rated quantities were used to define the per unit form of the motor equations, which were

derived in Section 3.5.

Rated quantities Sym. Units Qty.

Line-to-line voltage �� V 3300Apparent power �� VA 800Line frequency �� Hz 50

Table C.5: Rated quantities


C.4.2 Base quantities

The base quantities were used to non-dimensionalize the plots throughout the thesis.

Variable Base quantity Sym. Units Qty.

MotorMotor torque Full-load torque 2 � Nm 5122Stator current Full-load current 2 � A 162Motor speed Synchronous speed �� &�� 157

Fluid couplingTorque Full-load torque 2 � Nm 5122Impeller speed Synchronous speed �� &�� 157Turbine speed Synchronous speed �� &�� 157

CSTInput shaft speed Synchronous speed �� &�� 157Output shaft speed �� - �&�� 5.2

SprocketSpeed �� - �&�� 5.2

ChainTension Proof load (per strand) 2�� -��4� 258

Table C.6: Base quantities

longwall mining

Documents

moranbah north

primary access

beam stage

chainight

board chain

loose material

free body

typical chain