Gary_Styger_M_Phil_Dissertation

AN INVESTIGATION OF THE EFFECT OF THE
MANUFACTURING PROCESS ON THE
PERFORMANCE OF CONVEYOR PULLEYS
by
GARY STYGER
a dissertation submitted in partial fulfilment of the requirements for the
degree of
MAGISTER PHILOSOPHIAE
In
MECHANICAL ENGINEERING
in the
FACULTY OF ENGINEERING AND THE BUILT
ENVIRONMENT
at the
UNIVERSITY OF JOHANNESBURG
Supervisor: Professor R F Laubscher

An investigation of the effect of the manufacturing process on the performance of conveyor pulleys - G Styger
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ABSTRACT
Pulleys are critical items in belt conveyors. Their primary role is to drive large mining conveyor
systems, facilitating the transportation of ore over extensive distances, both in South Africa
and abroad.
The effect of the manufacturing process (with specific emphasis on the induced residual
stresses) on the fatigue performance of conveyor pulleys is herein investigated and reported.
A pre-selected pulley was chosen based on size, suitable for experimental work as well as
practical specifications. The static and fatigue performance of the pulley were investigated
both with the current design criteria as well as Finite Element Analysis, with comparisons
drawn.
The material data for the Finite Element Models was obtained experimentally with tensile
tests of the SANS 1431 350 WA plate. The magnitude of the residual stresses were obtained
experimentally by using the incremental hole-drilling technique for non-uniform residual
stresses. The method was verified by comparison with the Finite Element Analysis results for
the non-linear material analysis of the roll-bending of the shell.
The fatigue analysis revealed that the stress ranges of interest for the pulley were below the
non-propagating stress range, and hence theoretically infinite fatigue life would be possible
under constant amplitude conditions. The operational fatigue life required for the pulley would
be possible, when considering the latest S-N curve for "very high cycle fatigue". The stress
intensity factors for the weld details were also below the threshold value and hence crack
growth should not occur, upon crack initiation.
A new design criteria was proposed for the fatigue analysis considering either fatigue
assessment standards or fracture mechanics for the assessment of the butt-welds.
This investigation showed that the manufacturing-induced residual stresses may play a
significant role in the fatigue life of a pulley. The fatigue strength of a machined stress -
relieved joint is higher if the stress range is partly compressive. The fatigue strength of a
machined as-welded joint is higher than estimated by the fatigue classifications. This is due to
residual stress relaxation that occurs at the weld toe because of yielding and hence a
subsequent reduction and redistribution of the residual stresses. This reduction in the mean
stress level, with a stress range that is partly compressive, would mean an increase in the
fatigue strength of the joint.

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This would in conclusion result in similar fatigue strengths for a stress-relieved and an as-
welded joint. This would additionally depend on the extent of the reduction of the residual
stress in the as-welded joint.
Recommendations were suggested for further experimental and numerical work for both the
T-bottom and Turbine-type pulleys.

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ACKNOWLEDGEMENTS
I would like to thank the following people for their contribution to this dissertation:
Professor R.F. Laubscher for his valued inputs and comments as well as continued support
during this process.
Mr. R. Shuma for the assistance with purchasing raw materials that were required for the
experimental work. Mr. W. Dott for preparing the tensile samples. Mr. M. Mukhawana for the
assistance with the tensile testing and residual stress measurement at the University of
Johannesburg.
Doug and Steve of CPM Engineering for the fabricated samples and information for the pre-
selected pulley.
Mr. W. Rall and Professor D.A. Hattingh from the Nelson Mandela Metropolitan University,
whose support and assistance during the incremental hole-drilling was invaluable. I very
much appreciated their insight.
The support from Mr. P.E. Marsden and Dr. A. Kolahi of LUSAS was highly appreciated
during the preparations of the FE models.
My wife Dalene, whom has been a continuing support and understanding partner during this
dissertation.
My mother and father whose support and understanding was greatly appreciated.

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TABLE OF CONTENTS
ABSTRACT _________________________________________________ 2
ACKNOWLEDGEMENTS_______________________________________ 4
1. INTRODUCTION__________________________________________ 25
1.1 Introduction ................................................................................................... 25
1.2 Aims of Investigation ..................................................................................... 27
1.3 Scope of Investigation ................................................................................... 28
1.4 Document layout ............................................................................................ 29
2. LITERATURE REVIEW ____________________________________ 30
2.1 Introduction ................................................................................................... 30
2.2 Conveyor pulley design ................................................................................. 30
2.2.1 Historic perspective ________________________________________________30
2.2.2 Conveyor pulley configurations _____________________________________31
2.2.3 Design procedure according to King _________________________________42
2.2.4 Design procedure according to Perry ________________________________48
2.3 Experimental investigation of conveyor pulleys ............................................ 59
2.3.1 Stress condition in belt conveyor drums______________________________59
2.3.2 Comparison of Experimental results and FEM for test pulley ____________62
2.4 Conveyor pulley standards ............................................................................ 64
2.4.1 Sizing of the pulley from SANS 1669-1:2005___________________________64
2.4.2 Design and manufacture of the pulleys according to Anglo American ____66
2.4.3 Anglo American Standard Pulleys ___________________________________68
2.5 Conveyor pulley failures................................................................................ 70
2.5.1 Conveyor pulley failures in South Africa ______________________________70
2.5.2 Failure analysis of conveyor pulleys _________________________________72
2.5.3 Case Study 1 : Fatigue failures of welded conveyor drums______________73
2.5.4 Case Study 2 : Fatigue in the shell of a conveyor drum _________________74
2.5.5 Case Study 3: Fracture analysis of a collapsed heavy-duty pulley in a long-
distance continuous conveyor application __________________________________75
2.6 Conveyor pulley manufacture ........................................................................ 76

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2.6.1 The pulley shaft ___________________________________________________76
2.6.2 The locking element________________________________________________76
2.6.3 The end-disk ______________________________________________________77
2.6.4 The pulley shell____________________________________________________78
2.6.5 The pulley_________________________________________________________80
2.6.6 Assemble of the pulley _____________________________________________83
2.7 Residual stresses........................................................................................... 84
2.8 Residual stress due to butt-welds.................................................................. 86
2.8.1 Typical transverse and longitudinal residual stress in a butt-weld _______86
2.8.2 Estimated residual stress levels according to BS 7910 _________________86
2.8.3 Residual stresses in butt-welds of conveyor pulleys ___________________88
2.9 Reduction of residual stress due to thermal stress-relieving......................... 88
2.9.1 Stress relief procedures for welded low-carbon mild steel ______________88
2.10 Residual stress measurement methods......................................................... 89
2.10.1 Mechanical stress measurement methods ____________________________89
2.10.2 Residual stress measurements by diffraction _________________________91
2.11 Incremental Hole-Drilling for Non-Uniform Residual Stresses....................... 93
2.11.1 Incremental Strain Method __________________________________________93
2.11.2 Average Stress Method _____________________________________________94
2.11.3 Power Series Method _______________________________________________94
2.11.4 Integral Method ____________________________________________________95
2.11.5 Comparison of the methods_________________________________________95
2.11.6 Discussion of the non-uniform residual stress methods available _______96
2.12 Fatigue assessment in welds......................................................................... 96
2.12.1 Constant amplitude stress-life method _______________________________98
2.12.2 Constant amplitude strain-life method_______________________________107
2.12.3 Constant Amplitude Crack Growth __________________________________115
2.12.4 Nominal fatigue assessment according to BS 7608 ___________________120
2.13 Fatigue assessment according to classification standards ..........................122
2.13.1 Consideration of the mean stress influence in classification standards _122
2.13.2 Residual stress relaxation consideration in classification standards ____124

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2.13.3 Residual stress relaxation considerations according to IIW-1823-07 ____126
2.13.4 "Very high cycle fatigue" for constant amplitude loading ______________128
2.13.5 Modern conveyor pulley assessment________________________________128
2.14 Stress-relieving of conveyor pulleys.............................................................130
2.15 Finite Element Method ..................................................................................130
2.15.1 Introducing the Finite Element Method ______________________________130
2.15.2 Brief history of the Finite Element Method ___________________________131
2.15.3 Finite Element Method Formulation _________________________________132
2.15.4 Finite Element Method Process _____________________________________133
2.15.5 Description of the LUSAS Finite Elements ___________________________133
2.15.6 Use of the Finite Element Method in the assessment of pulleys ________139
2.15.7 Checking procedure for the Finite Element Method ___________________150
3. EXPERIMENTAL WORK __________________________________ 152
3.1 Introduction ..................................................................................................152
3.2 Tensile testing of SANS 1431 GR 350 WA plate ............................................152
3.2.1 Experimental procedure (Tensile Tests) _____________________________152
3.2.2 Discussion of the tensile test results ________________________________157
3.3 Residual stress measurement.......................................................................157
3.3.1 Residual stress measurement method_______________________________157
3.3.2 Preparation of the cylindrical sample (residual stress measurement) ___162
3.3.3 Heat input of the welds ____________________________________________166
3.3.4 Thermal stress-relieving of sample__________________________________168
3.3.5 Experimental procedure (residual stress measurement) _______________169
3.3.6 Uncertainty analysis (residual stress measurement) __________________175
3.3.7 Results of the residual stress measurement _________________________179
3.4 Material study of the cylindrical samples......................................................181
3.4.1 Experimental procedure (Material Study) ____________________________181
3.4.2 Results of the material study _______________________________________182
4. NUMERICAL AND ANALYTICAL WORK _____________________ 188
4.1 Introduction ..................................................................................................188
4.2 The Finite Element Models............................................................................188

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4.2.1 Description of the geometry________________________________________189
4.2.2 Material Properties________________________________________________192
4.2.3 Analyses_________________________________________________________193
4.2.4 Load and boundary conditions _____________________________________194
4.2.5 Finite Element Mesh_______________________________________________200
4.2.6 Number of Fourier harmonic components required ___________________205
4.3 Final Analyses...............................................................................................206
4.3.1 Results for the pulley______________________________________________206
4.3.2 Results for the shell_______________________________________________209
4.4 Comparison of current design techniques to the numerical study ...............211
4.4.1 Discussion of the conveyor design comparison ______________________213
4.5 Comparison of the bending residual stresses in the shell ............................213
4.5.1 Discussion of the results of the bending residual stress comparison study
214
4.6 Comparison of the Welding Residual Stresses in the Shell ..........................215
4.6.1 Discussion of the results of the welding residual stress comparison study
215
4.7 Fatigue Performance of the Pulley................................................................216
4.7.1 Fatigue assessment results according to the classification standards __218
4.7.2 Discussion of the fatigue performance assessment of the pulley _______221
4.8 Fatigue Assessment according to fundamental theory.................................222
4.8.1 Discussion of the results __________________________________________226
5. INFLUENCE OF RESIDUAL STRESS IN PULLEY DESIGN _______ 228
6. CONCLUSIONS AND RECOMMENDATIONS__________________ 232
6.1 Overview .......................................................................................................232
6.2 Literature Review ..........................................................................................232
6.3 Experimental Work........................................................................................234
6.4 Numerical Work ............................................................................................235
6.5 New criteria for conveyor pulley design........................................................236
6.6 Overall Conclusion .......................................................................................236
6.7 Recommendations ........................................................................................237

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APPENDIX 1 : TENSILE RESULTS_____________________________ 245
APPENDIX 2 : RESIDUAL STRESS RESULTS____________________ 247
APPENDIX 3 : CERTIFICATES ________________________________ 259
APPENDIX 4 : MATERIAL CERTIFICATES ______________________ 261
APPENDIX 5 : HEAT TREATMENT CERTIFICATES _______________ 263
APPENDIX 6 : NON-DESTRUCTIVE INSPECTION SHEET __________ 265
APPENDIX 7 : RESIDUAL STRESS MEASUREING EQUIPMENT
COMPLIANCE CERTIFICATE _________________________________ 266
APPENDIX 8 : CONTOUR PLOTS OF THE RESULTS OF THE ROLL-
BENDING SIMULATION _____________________________________ 267
APPENDIX 9 : INPUT DATA FILE OF THE 3D FINITE ELEMENT MODEL
OF THE PULLEY ___________________________________________ 277
APPENDIX 10 : INPUT DATA FILE OF THE 2D FOURIER FINITE
ELEMENT MODEL OF THE PULLEY ___________________________ 280
APPENDIX 11 : INPUT DATA FILE OF THE 2D FINITE ELEMENT MODEL
OF THE SHELL ____________________________________________ 291

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LIST OF FIGURES
Figure 1.1 : Typical layout of a Conveyor System [1].................................................... 25
Figure 1.2 : The components of a Conveyor Pulley [1] ................................................. 26
Figure 2.1 : Typical pulley configurations used in South Africa [5] .............................. 32
Figure 2.2 : Boss-type pulley [10] ................................................................................. 32
Figure 2.3 : Turbine-type pulley [10] ............................................................................. 33
Figure 2.4 : L-Bottom type pulley [10] ........................................................................... 34
Figure 2.5 : T-Bottom type pulley [10] ........................................................................... 35
Figure 2.6 : Weld along the face of the shell for the T-Bottom type pulley [11] ............. 37
Figure 2.7 : Large heavy shell rim bending decay [6].................................................... 38
Figure 2.8 : Small thin shell rim bending decay [6] ....................................................... 38
Figure 2.9 : Inside fillet and full penetration weld of Turbine-type pulley [11]............... 39
Figure 2.10 : Locking element Type "A" [11]................................................................. 40
Figure 2.11 : Locking element Type "B" [11]................................................................. 41
Figure 2.12 : Locking element Type "C" [11]................................................................. 42
Figure 2.13 : Static and fatigue stress model [6] ........................................................... 43
Figure 2.14 : Belt loading on the pulley diameter [6]..................................................... 43
Figure 2.15 : Rim bending of the shell [6] ..................................................................... 45
Figure 2.16 : S-N Curve for steel [15] ............................................................................ 48
Figure 2.17 : Stress concentration factors for filleted shafts in bending [16] ............... 49
Figure 2.18 : Surface finish modification factors for steel [7] ....................................... 49
Figure 2.19 : Modified Goodman diagram [7] ................................................................ 50
Figure 2.20 : Support and load distribution assumption for the shell [3] ...................... 50
Figure 2.21 : Circumferential load distribution assumption shell [3] ............................ 51
Figure 2.22 : Calculated and measured axial stresses in the pulley shell [3] ................ 51
Figure 2.23 : Mean - 2 standard deviation S-N curve [17].............................................. 52
Figure 2.24 : Determination of radial and hoop stress through the end-disk [4]........... 56
Figure 2.25 : Effect of disk shape [3]............................................................................. 58
Figure 2.26 : Effect of hub diameter/pulley diameter [3] ............................................... 59
Figure 2.27 : Diagram of drum with attached pick-ups [18]........................................... 60
Figure 2.28 : Analytical and experimental results in the middle of the shell (A-A) [18] . 61
Figure 2.29 : Analytical and experimental results in the extreme section of the shell (B-
B) [18] ........................................................................................................................... 61
Figure 2.30 : Analytical and experimental results in the external contour section of the
end-disk (C-C) [18] ....................................................................................................... 61
Figure 2.31 : Analytical and experimental results in the internal contour section of the
end-disk (C-C) [18]........................................................................................................ 62
Figure 2.32 : Stresses measured on the test pulley [9] ................................................. 62
Figure 2.33 : Finite element analysis - shaft axial range stress [9] ............................... 63

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Figure 2.34 : Finite element analysis - Disk radial stress range [9]............................... 63
Figure 2.35 : Stresses measured on the test pulley during start-up [9] ........................ 64
Figure 2.36 : Dimensions of the conveyor pulley [20]................................................... 64
Figure 2.37 : Dimensions and tolerances of the turbine-type pulley [25] ...................... 69
Figure 2.38 : Full penetration fillet welds of the end-disk-to-shell interface of the
turbine-type pulley [25] ................................................................................................. 69
Figure 2.39 : Dimensions and tolerances of the T-bottom type pulley [25] ................... 70
Figure 2.40 : Ground full penetration double butt-welds of the end-disk-to-shell
interface of the T-bottom type pulley [25] ..................................................................... 70
Figure 2.41 : Position of position of failure at the weld root of a single -sided welded
turbine-type pulley [6]................................................................................................... 71
Figure 2.42 : Shaft fatigue failure at locking element device shoulder [9]..................... 72
Figure 2.43 : Finish criteria of a shell circumferential weld in a T-bottom type pulley [9]
...................................................................................................................................... 72
Figure 2.44 : Shell fatigue failure at disk/shell circumferential weld [9]........................ 73
Figure 2.45 : Possible design of the shoulder in the end-disk [27] ............................... 74
Figure 2.46 : A fatigue region indicating beach marks and stress raisers [28] ............. 75
Figure 2.47 : Manufacture of a locking element ............................................................ 77
Figure 2.48 : T-bottom and turbine type end-disks ....................................................... 77
Figure 2.49 : Final machined end-disks ........................................................................ 78
Figure 2.50 : Roll-bending of the plate to produce the pulley shell............................... 78
Figure 2.51 : Sub-merged arc welding of the seam of the shell .................................... 79
Figure 2.52 : Ends of the shell being joined with sub -merged arc welding................... 79
Figure 2.53 : Inner weld of a T-bottom type pulley........................................................ 80
Figure 2.54 : Machining of the outer weld to return to sound weld............................... 80
Figure 2.55 : Dye penetrate testing of the machined weld before the final outer diameter
circumferential weld runs are performed...................................................................... 81
Figure 2.56 : Completed outer diameter circumferential weld....................................... 81
Figure 2.57 : Machining of the outer diameter of the shell ............................................ 82
Figure 2.58 : Stress-relieved pulley............................................................................... 82
Figure 2.59 : Lagging on the pulley............................................................................... 83
Figure 2.60 : Balance weights welded to the outer radius of the end-disk.................... 83
Figure 2.61 : Complete pulley with Plummer block bearings mounted in position ....... 84
Figure 2.62 : Different cases of macro and micro residual stresses [31] ...................... 85
Figure 2.63 : Graph of the length scale indicating the different types of residual
stresses verses grain size [31] ..................................................................................... 85
Figure 2.64 : Longitudinal and transverse residual stresses in a single-butt weld [33] 86
Figure 2.65 : Typical residual stress distribution in welded joints [32] ......................... 87
Figure 2.66 : Residual stress distribution measured from a shot-peened Ni alloy using
hole-drilling method [31]............................................................................................... 90

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Figure 2.67 : Hoop, axial and shear stress through thickness [36] ............................... 90
Figure 2.68 : Contour method and neutron diffraction residual stress measurement
comparison of the normal residual stress distribution in a welded plate [38] .............. 91
Figure 2.69 : Comparison of the calculation methods [39]............................................ 96
Figure 2.70 : Nominal stress approach for fatigue assessment of welds [41] ............... 97
Figure 2.71 : Structural stress approach for a weld [41] ............................................... 97
Figure 2.72 : Local strain approach for welds [41] ........................................................ 98
Figure 2.73 : Crack growth approach for welds [41] ..................................................... 98
Figure 2.74 : Log S-N curve fitted to data [41]............................................................... 99
Figure 2.75 : Correlation of fatigue strength and tensile strength of a material [42] ....100
Figure 2.76 : Determination of the S-N curve of a material [41]....................................101
Figure 2.77 : Effects of surface finish on the fatigue limit of steel [43] ........................101
Figure 2.78 : Surface finishes compared to fatigue limit and ultimate tensile strength
[44]...............................................................................................................................102
Figure 2.79 : Stress concentration factors for aluminium alloys [45]...........................104
Figure 2.80 : Notch sensitivity for different material hardness [46] .............................104
Figure 2.81 : The affect of the fatigue notch factor on the fatigue life of a component
[41]...............................................................................................................................105
Figure 2.82 : Goodman diagram [41]............................................................................106
Figure 2.83 : Axial strain range in a notch subjected to alternating stress [41] ...........107
Figure 2.84 : Cyclic stress-strain hysteresis loop [41] .................................................108
Figure 2.85 : Strain-life curve [41]................................................................................108
Figure 2.86 : Determination of the strain-life curve [41] ...............................................109
Figure 2.87 : Cyclic stress-strain curve [41].................................................................109
Figure 2.88 : Affect of surface finish on the strain-life curve [41] ................................110
Figure 2.89 : Fatigue notch factor as compared to weld toe radius [41] ......................111
Figure 2.90 : Local elastic-plastic stresses determined from nominal stresses [41]....112
Figure 2.91 : Stable cyclic stress-strain hysteresis loop [41].......................................113
Figure 2.92 : The affect of mean stress on the cyclic stress-strain hysteresis loop [41]
.....................................................................................................................................114
Figure 2.93 : The influence of residual stress on the cyclic stress-strain hysteresis loop
[41]...............................................................................................................................115
Figure 2.94 : Stress field around a crack [41]...............................................................116
Figure 2.95 : Geometry of cracks depending on position and loading [41] ..................116
Figure 2.96 : Sigmoidal da/dN - ΔK curve [41] .............................................................118
Figure 2.97 : Typical semi-elliptical shape for a surface crack [41]..............................119
Figure 2.98 : Edge and center cracks [41] ....................................................................119
Figure 2.99 : Weld classifications of two fillet welds [23].............................................120
Figure 2.100 : Mean-Line Weld classifications [23] ......................................................121

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Figure 2.101 : Scatter in the experimental results of fatigue tests of welded members
[23]...............................................................................................................................122
Figure 2.102 : Influence of the residual stress on a stress cycle of an as-welded joint
[33]...............................................................................................................................123
Figure 2.103 : Tensile mean stress due to the applied loading in a stress-relieved joint
[33]...............................................................................................................................123
Figure 2.104 : Reduction of the stress range due to stress-relieving [49]....................124
Figure 2.105 : Reduction factor of the stress cycle for stress-relieving [50]................124
Figure 2.106 : Enhancement factor f(R) for residual stress level versus stress ratio [53]
.....................................................................................................................................127
Figure 2.107 : Constant amplitude S-N curves for Steel for "very high cycle fatigue" [53]
.....................................................................................................................................128
Figure 2.108 : Stress ranges assessed at the weld toes for the T-bottom type pulley as
per BS 7608 [24]...........................................................................................................128
Figure 2.109 : Stress ranges assessed at the weld toes for the Turbine-type pulley as
per BS 7608 [24]...........................................................................................................129
Figure 2.110 : Stress cycle below the endurance limit of a joint [50] ...........................129
Figure 2.111 : Finite Element Model of a structure [55] ................................................131
Figure 2.112 : Nodal configuration for Standard 2D Isoparametric element [55]..........132
Figure 2.113 : 3D beam element degrees of freedom [55] ............................................133
Figure 2.114 : 2D plane strain problem and finite element mesh [55] ..........................134
Figure 2.115 : Axisymmetric problem and finite element mesh [55] ............................134
Figure 2.116 : Stress output of the Axisymmetric element [55]....................................135
Figure 2.117 : Fourier element definition [55] ..............................................................135
Figure 2.118 : 3D element library [55] ..........................................................................138
Figure 2.119 : 3D mesh of component [55] ..................................................................139
Figure 2.120 : Stress outputs for the 3D element [55] ..................................................139
Figure 2.121 : King's analytical procedure compared with finite element analysis for
Turbine and T-bottom type pulleys [6] .........................................................................140
Figure 2.122 : Cross-section of a pulley assembly [9] .................................................141
Figure 2.123 : Quadrant section of the finite element mesh [9]....................................142
Figure 2.124 : Effect of number of Fourier terms on belt (radial) loading approximation
[9].................................................................................................................................143
Figure 2.125 : Effect of number of Fourier terms on torque (shear) loading
approximation [9].........................................................................................................143
Figure 2.126 : Maximum von mises stress plot [9].......................................................144
Figure 2.127 : Quadrant section deformed shapes at different angles of wrap [9] .......144
Figure 2.128 : Comparison of the Finite Element Analysis and PSTRESS results [9] ..145
Figure 2.129 : Geometry and mesh of Option 1 and 2 respectively [27] .......................146

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Figure 2.130 : Quarter symmetry 3D mesh depicting loads and boundary conditions
[27]...............................................................................................................................147
Figure 2.131 : Von mises contour plot of the quarter symmetry model [27] ................147
Figure 2.132 : Stresses vs angular position for the hot spot in option 1 (continuous
duty : 250 kN) [27]........................................................................................................148
Figure 2.133 : Stresses vs angular position for the hot spot in option 2 (continuous
duty : 250 kN) [27]........................................................................................................148
Figure 2.134 : Geometry of the half model for the finite element analysis [24] ............149
Figure 2.135 : Typical stress distribution in a T-bottom type pulley [24] .....................149
Figure 3.1 : Dimensions of the tensile specimen .........................................................154
Figure 3.2 : Machined tensile specimens.....................................................................154
Figure 3.3 : Instron 1195 universal testing machine ....................................................155
Figure 3.4 : Extensometer............................................................................................155
Figure 3.5 : Drilling through the centre of the strain gauge rosette [66] ......................158
Figure 3.6 : MTS-3000 RESTAN hole-drilling system [67] ............................................159
Figure 3.7 : Relieved stress at P along with the variation of the principal strains a
distance away from the centre of the hole [68] ............................................................159
Figure 3.8 : Typical strain gauge rosette arrangement used for determining residual
stress [64]....................................................................................................................160
Figure 3.9 : Biaxial uniform residual stress in a component [64] .................................160
Figure 3.10 : Biaxial non-uniform residual stress in a component [64] ........................160
Figure 3.11 : Dimensions of the weld preparation detail for the plate (all dimensions are
in mm)..........................................................................................................................162
Figure 3.12 : Weld run-off plates at each end of roll-bent plate for longitudinal seam
welds...........................................................................................................................163
Figure 3.13 : Sub-merged arc welding of the longitudinal seam ..................................163
Figure 3.14 : Back-gouging of the outer diameter weld ...............................................164
Figure 3.15 : Inner and outer diameter longitudinal seam welds ground -flush ............164
Figure 3.16 : Re-rolling of the cylindrical samples.......................................................165
Figure 3.17 : Circumferential weld runs .......................................................................165
Figure 3.18 : Back-gouging of the outer diameter weld ...............................................166
Figure 3.19 : Completed fabrication of the cylindrical shell sample ............................166
Figure 3.20 : Diagram of the RESTAN equipment experimental set-up [69].................169
Figure 3.21 : Measurement positions on the inside and outside diameter...................170
Figure 3.22 : Polished surface for application of the strain gauge...............................171
Figure 3.23 : EA-062RE-120 residual stress strain gauge rosette (Type A rosette) ......171
Figure 3.24 : Positioning of the strain gauge ...............................................................171
Figure 3.25 : RESTAN system secured in position over the strain gauge ....................172
Figure 3.26 : Method of optimising the degree of the polynomial [69] .........................173
Figure 3.27 : A typical polynomial fitted strain vs depth graph ....................................173

15
Figure 3.28 : A typical stress vs depth graph...............................................................174
Figure 3.29 : Stress-relieved and as-welded cylindrical samples.................................181
Figure 3.30 : Samples prior to sectioning ....................................................................181
Figure 3.31 : Macro showing the cross-section through the weld for the stress-relieved
condition......................................................................................................................182
Figure 3.32 : Macro showing the cross-section through the weld for the as-welded
condition......................................................................................................................182
Figure 3.33 : Hardness profile across the weld bead for both conditions ....................183
Figure 3.34 : Micrograph showing the structure of the parent material for the stress-
relieved condition ........................................................................................................184
Figure 3.35 : Micrograph showing the structure of the parent material for the non
stress-relieved condition .............................................................................................184
Figure 3.36 : Micrograph showing the structure of the heat-affected zone for the stress-
Figure 3.37 : Micrograph showing the structure of the heat-affected zone for the non
stress-relieved condition .............................................................................................185
Figure 3.38 : Micrograph showing the structure of the weldment for the stress-relieved
condition......................................................................................................................186
Figure 3.39 : Micrograph showing the structure of the weldment for the non stress-
Figure 4.1 : Pulley assembly ........................................................................................190
Figure 4.2 : Exploded view of the pulley assembly ......................................................190
Figure 4.3 : Cross-section of the FE prepared pulley geometry (half symmetry model)
(all dimensions are in mm)...........................................................................................191
Figure 4.4 : Dimensions of the end disk (all dimensions are in mm)............................191
Figure 4.5 : Half model of the pulley geometry in the FE system.................................191
Figure 4.6 : Quarter model of the 3D pulley .................................................................192
Figure 4.7 : Half model of the FE shell geometry .........................................................192
Figure 4.8 : Uniaxial yield stress vs total strain defined in LUSAS
@
[55] .....................194
Figure 4.9 : Self-weight applied to the FE model..........................................................195
Figure 4.10 : Belt pressure distribution over the circumference of a driven pulley [79]
.....................................................................................................................................195
Figure 4.11 : Graph of the Belt pressure vs circumferential position for the mesh
sensitivity analysis ......................................................................................................196
Figure 4.12 : Graph of the Belt pressure vs circumferential position for the final Fourier
analysis .......................................................................................................................197
Figure 4.13 : Various functions used to apply the belt pressure over the belt width [3]
.....................................................................................................................................197
Figure 4.14 : Belt pressure applied to the half model of the pulley..............................197

16
Figure 4.15 : Locking element interface pressure applied to the model for the end disk
and shaft......................................................................................................................198
Figure 4.16 : Built-in boundary conditions for the mesh sensitivity and harmonic
component assessment...............................................................................................198
Figure 4.17 : Simply-supported boundary condition of the final analysis of the pulley
.....................................................................................................................................199
Figure 4.18 : Quarter symmetry model for the 3D analysis ..........................................199
Figure 4.19 : Graph of loading for the non-linear analysis...........................................199
Figure 4.20 : Loading of the shell.................................................................................200
Figure 4.21 : Symmetry and simply-supported boundary conditions of the shell........200
Figure 4.22 : Typical mesh of 2D analysis of the pulley...............................................201
Figure 4.23 : Typical mesh of the 2D plane strain analysis of the shell .......................201
Figure 4.24 : Contour plot of the maximum vertical displacement for the 3D analysis 202
Figure 4.25 : Contour plot of the maximum radial displacement of the pulley shell ....207
Figure 4.26 : Contour plot of the Von Mises stress in the pulley shell .........................207
Figure 4.27 : Contour plot of the axial stress in the pulley shell ..................................208
Figure 4.28 : Radial stress due to the assemble of the pulley......................................209
Figure 4.29 : Hoop stress due to the assembly of the pulley .......................................209
Figure 4.30 : Maximum bending stress through the thickness ....................................210
Figure 4.31 : Residual bending stress through the thickness......................................211
Figure 4.32 : Constant amplitude bending stress range ..............................................217
Figure 4.33 : Weld measurement position of the pulley...............................................217
Figure 4.34 : Weld measurement position of the pulley...............................................217
Figure 4.35 : True Stress-Strain Curve for NSR2..........................................................225
Figure 5.1 : Suggested modified design procedure for conveyor pulleys....................231

17
LIST OF TABLES
Table 2.1 : Basic outer diameter of the pulley [20]........................................................ 65
Table 2.2 : Preferred shaft and bearing journal diameters pulley [20].......................... 65
Table 2.3 : Surface finish of the shaft [29]..................................................................... 76
Table 2.4 : Surface finish of the locking element [29] ................................................... 77
Table 2.5 : Surface finish of the end-disk [29]............................................................... 77
Table 2.6 : Surface finish of the shell [29] ..................................................................... 79
Table 2.7 : Parametric ranges for recommended residual stress distributions [32] ...... 86
Table 2.8 : Summary of the measurement technique and their attributes [31] .............. 92
Table 2.9 : Determination of surface factor based on tensile strength of the material
[41]...............................................................................................................................102
Table 2.10 : Load factor for type of loading condition [41]...........................................103
Table 2.11 : Evolution cases for typical welded components for reduction in residual
stress [52]....................................................................................................................126
Table 2.12 : Weld classification according to BS 7608 [23] ..........................................129
Table 2.13 : Manufacturing specifications of both options [27] ...................................146
Table 3.1 : SANS 1431 GR 350 WA Tensile specimen information ...............................154
Table 3.2 : SANS 1431 GR 350 WA Mechanical properties for the specimens .............156
Table 3.3 : SANS 1431 GR 350 WA Average Mechanical Properties for the Specimens
.....................................................................................................................................157
Table 3.4 : Placement of the principal angle β [64] ......................................................162
Table 3.5 : Longitudinal seam weld of shell 1 (Inner Diameter)....................................167
Table 3.6 : Longitudinal seam weld of shell 1 (Outer Diameter)...................................167
Table 3.7 : Longitudinal seam weld of shell 2 (Inner Diameter)....................................167
Table 3.8 : Longitudinal seam weld of shell 2 (Outer Diameter)...................................167
Table 3.9 : Circumferential weld of the shell (Inner Diameter)......................................168
Table 3.10 : Circumferential weld of the shell (Outer Diameter)...................................168
Table 3.11 : Holding temperature for stress-relieving..................................................168
Table 3.12 : Contributions of uncertainty in residual stress measurement [70]: ..........176
Table 3.13 : ASTM E837-08 Non-Uniform maximum stress results nearest to the surface
for the as-welded and stress-relieved conditions........................................................179
Table 4.1 : Overall dimensions of the pulley................................................................190
Table 4.2 : SANS 1431 GR 350 WA Average mechanical properties for the specimens
.....................................................................................................................................193
Table 4.3 : Uniaxial stress vs total strain for the 350 WA plate ....................................194
Table 4.4 : Circumferential belt pressure for the mesh sensitivity analysis.................196
Table 4.5 : Circumferential belt pressure for the final Fourier analysis .......................196
Table 4.6 : Types of elements used for the analyses [55] ............................................200
Table 4.7 : Results of mesh sensitivity assessment of the 3D Linear Analysis............202

18
Table 4.8 : Results of mesh sensitivity assessment of the axisymmetric analysis ......203
Table 4.9 : Results of the mesh sensitivity assessment of the Fourier analysis..........204
Table 4.10 : Results of the mesh sensitivity assessment of the Non-Linear Analysis .204
Table 4.11 : The results of the harmonic component assessment ...............................205
Table 4.12 : Results of the final analysis......................................................................206
Table 4.13 : Results of the assembly analysis .............................................................208
Table 4.14 : Results after loading for the bending analysis .........................................210
Table 4.15 : Results after unloading for the bending analysis .....................................210
Table 4.16 : Comparison of King's design calculation to the FEA for the static results
.....................................................................................................................................212
Table 4.17 : Comparison of the King's design calculation to the FEA for the fatigue
results..........................................................................................................................212
Table 4.18 : Comparison of Perry's design calculation to the FEA for the displacement
results..........................................................................................................................212
Table 4.19 : Comparison of Perry's design calculation to the FEA for the static results
.....................................................................................................................................212
Table 4.20 : Comparison of the Perry's design calculation to the FEA for the fatigue
results..........................................................................................................................213
Table 4.21 : Comparison of estimated residual stress .................................................214
Table 4.22 : Comparison of measured and estimated residual stress for the as-welded
condition......................................................................................................................215
Table 4.23 : Comparison of measured and estimated residual stress for the stress-
Table 4.24 : (BS EN 1993-1-9) - Fatigue ratio in the hoop direction for the as-welded
condition......................................................................................................................218
Table 4.25 : (BS EN 1993-1-9) - Fatigue ratio in the axial direction for the as-welded
condition......................................................................................................................218
Table 4.26 : (BS 7608) - Fatigue ratio in the hoop direction for the as-welded condition
.....................................................................................................................................218
Table 4.27 : (BS 7608) - Fatigue ratio in the axial direction for the as-welded condition
.....................................................................................................................................218
Table 4.28 : (RP-C203) - Fatigue ratio in the hoop direction for the as-welded condition
.....................................................................................................................................218
Table 4.29 : (RP-C203) - Fatigue ratio in the axial direction for the as-welded condition
.....................................................................................................................................219
Table 4.30 : (IIW-1823-07) - Fatigue ratio in the hoop direction for the as-welded
condition......................................................................................................................219
Table 4.31 : (IIW-1823-07) - Fatigue ratio in the axial direction for the as-welded
condition......................................................................................................................219

19
Table 4.32 : (BS EN 1993-1-9) - Fatigue ratio in the hoop direction for the stress-relieved
condition......................................................................................................................219
Table 4.33 : (BS EN 1993-1-9) - Fatigue ratio in the axial direction for the stress-relieved
condition......................................................................................................................220
Table 4.34 : (BS 7608) - Fatigue ratio in the hoop direction for the stress-relieved
condition......................................................................................................................220
Table 4.35 : (BS 7608) - Fatigue ratio in the axial direction for the stress-relieved
condition......................................................................................................................220
Table 4.36 : (RP-C203) - Fatigue ratio in the hoop direction for the stress-relieved
condition......................................................................................................................220
Table 4.37 : (RP-C203) - Fatigue ratio in the axial direction for the stress-relieved
condition......................................................................................................................221
Table 4.38 : (IIW-1823-07) - Fatigue ratio in the hoop direction for the stress-relieved
condition......................................................................................................................221
Table 4.39 : (IIW-1823-07) - Fatigue ratio in the axial direction for the stress-relieved
condition......................................................................................................................221
Table 4.40 : Fatigue properties for the assessment .....................................................224
Table 4.41 : Fatigue outputs for the as-welded condition of the pulley........................224
Table 4.42 : Fatigue outputs for the stress-relieved condition of the pulley ................225
Table 4.43 : Fatigue outputs for the as-welded condition of the pulley (Residual Stress
= Yield Strength) ..........................................................................................................226
Table 4.44 : Allowable stress range for "very high cycle" constant amplitude fatigue of
the pulley, according to IIW-1823-07............................................................................226

20
LIST OF SYMBOLS
a Asymmetric term
am Fourier coefficient for the cosine function
α Angle of wrap (radians)
b Inner diameter of the end-disk (mm)
bm Fourier coefficient for the sin function
B Bearing center (mm)
a, b and u Constants depending on the shape of the end-disc
C.V. Coefficient of Variance
d Shaft diameter under the end-disk (mm)
D Pulley diameter (mm)
Di Inside diameter of the shell (mm)
ds Bearing shaft diameter (mm)
Ds Stepped-up shaft diameter (mm)
E Young's modulus (MPa)
F Functions of the poisson's ratio
F Vector of known forces (N)
H Non-dimensional depth from surface
h Contact length/width of the locking element (mm)
h1 Width of the hub (mm)

21
hr Width of the hub at the radius of interest (mm)
Hb Rim section force (N)
Is Second Moment of Area of shaft (mm
4
)
I Current (Amp)
k Constant for the geometry of the shell
k distance from fillet to disc centre (mm)
K Global stiffness matrix
K5 End-disk stiffness constant
K6 Shaft stiffness constant
K7 End-disk stiffness constant
l Belt width (mm)
L Spacing between end-disks (mm)
m Fourier component number
m The total number of harmonics in the series from n = 0, or n = 1 to n
= m
Mb Rim bending section moment (N.mm)
M Shaft bending moment (N.mm)
Md End-disk bending moment (N.mm)
n Harmonic component number
Pb Belt pressure (MPa)
Ph Locking element hub pressure (MPa)

22
Pu Locking element pressure on the shaft (MPa)
PL Pressure loss in contact due to the belt forces (MPa)
P1 Locking element pressure on the inner radius of the end-disk (MPa)
Pm Mean pressure (MPa)
Q Heat input per unit length (kJ/mm)
ra Radius of the drilled hole (mm)
rb Rim bending radial deflection due to belt pressure (mm)
r1 Radial expansion due to the locking element pressure (mm)
R Ratio of end-disk diameters
rt Radius of the shell (mm)
Red Ratio of the hub diameter/pulley diameter
r1 Inner radius of the end-disk (mm)
rr Radius of interest at the hub portion of the end-disk (mm)
rm Mean radius of the strain gauge circle (mm)
s Symmetric term
s Standard Deviation
s Velocity (mm/s)
σb Hoop stress due to belt pressure (MPa)
σ1 Hoop stress at the inside diameter of the shell (MPa)
σab Axial rim stress (MPa)

23
σhb Hoop rim stress (MPa)
σd Radial direct stress (MPa)
σa Axial bending stress (MPa)
σa max. Maximum axial stress (MPa)
σh max. Maximum hoop stress (MPa)
σXG Axial stress (MPa)
σYG Hoop stress (MPa)
σR Radial stress (MPa)
σH Hoop stress (MPa)
σf Flow stress for a plane strain elastic-perfectly plastic isotropic
material (MPa)
σY Yield or 0.2% Off-Set Strength of the material (MPa)
σX Bending stress on the top and bottom surface (MPa)
σ‟X Bending residual stress on the top and bottom surface (MPa)
T1 Tight belt tension (N)
T2 Slack belt tension (N)
T Instantaneous belt tension (N)
Te Equivalent belt tension (N)
t Shell thickness (mm)
ted Thickness of the end-disk (mm)

24
Tx Tension distribution along the belt width (N)
τXυ Shear stress (MPa)
tLE Contact length/width of the locking element (mm)
θ Active drive arc (radians)
θ Angular position (degrees)
θs Deflection angle (minutes)
ν Poisson's ratio
V Volt (V)
W Belt width (mm)
̅ Mean
X Functions of the poisson's ratio
XF Functions of the poisson's ratio
X Vector of unknown field quantities such as displacement (mm)
z Hole depth (mm)
Z Shell constant (mm), Depth from surface (mm)
λ Constant for the shape of the shell

25
1. INTRODUCTION
1.1 Introduction
The mining and industrial sectors process raw material into final products to be used by
various industries. The distances between the raw material delivery and the subsequent
process undertaken are often large, and require an automated means of transportation of the
material.
Conveyor systems facilitate the automation of the moving of goods, removing the requirement
for expensive labour and allowing it to be done safely. Materials handling and packaging
industries are the main users of this effective transportation system. Different configurations
of conveyor systems exist, such as:
 Chain conveyor
 Screw conveyor
 Belt conveyor
The typical layout of a belt conveyor system configuration, as used by the mining industry is
shown in Figure 1.1 (below). The main components, the head and tail pulleys, are an integral
part of the system, and are the focus of this dissertation.
Figure 1.1 : Typical layout of a Conveyor System [1]
The head pulley is often referred to as the drive-end pulley, as the motor and gearbox are
mounted on this end, to drive the system. The tail end pulley is positioned on the non-drive
end of the system. The snub pulley is appropriately positioned to achieve the required angle
of wrap for the head pulley. The bend pulleys guide the belt towards the take-up pulley. The

26
take-up pulley supports a weight, which provides the initial tension for the system. Idlers are
positioned on each side of the belt between the head and tail pulleys.
A typical conveyor pulley assembly is presented in Figure 1.2 (below):
Figure 1.2 : The components of a Conveyor Pulley [1]
The pulley consists of the following components:
 The shell is constructed from rolled plate, with the ends of the plate welded together.
 The lagging is a rubber layer with cut grooves, to assist with traction and grip
between the pulley and conveyor belt.
 The end plate or end-disk is machined from forged or rolled plate.
 The shaft is machined from low-carbon steel round bar.
 The locking element is machined from high-strength steel and is used to induce a
“press-fit” between the shaft and the pulley, once assembled.
The manufacturing process of the pulley is typically as follows:

27
 An end-disk is circumferentially welded into each end of the shell. Two different end
plate configurations currently exist, and these will be discussed later.
 The end-user may specify that the pulley is stress-relieved before the final assembly.
 The rubber lagging is applied to the shell of the pulley.
 The locking elements are placed in each end plate, with the shaft in position. The
locking elements are then bolted up to the required torque, thereby inducing the
appropriate contact pressure, between the shaft and pulley. The contact pressure is
induced due to the cone angle of the locking element faces, which ensures that the
inner and outer rings, contract and expand respectively.
 The completed pulley assembly is then placed into the bearing assemblies, which are
in turn bolted to the conveyor system structure.
The design of the pulleys is based on an empirical approach that considers calculations
separately for each component, and in turn their effect on each other. Static and fatigue
loading are considered in the evaluation of the design, by the choice of appropriate design
applied service loads. The current design philosophy for conveyor pulleys does not, however,
consider the effect of the manufacturing process as part of the design philosophy. The design
process allows for the inclusion of the assembly and in-service induced loads only. Because
of the nature of the manufacturing techniques employed, residual stresses may also be
additionally introduced and could therefore affect the in-service performance. Currently these
are ignored for smaller-sized pulleys. Larger pulleys are sent for stress relieving.
The current design philosophy therefore does not specifically cater for residual stresses
introduced by the manufacturing. It's perceived effect is however widely recognised and
addressed by appropriate stress relieving. The nature and effectiveness of the stress relieving
is however not well documented.
1.2 Aims of Investigation
The main aim of this investigation is, therefore to assess the effect of the manufacturing
process (with specific emphasis on the introduced residual stresses) on the structural integrity
of a conveyor pulley, in-service. This implies the following:
1. Investigating the current conveyor pulley design philosophy and manufacturing
technique, with specific emphasis on the introduction of residual stresses.

28
2. Identifying possible sources of manufacturing-induced residual stresses, and
quantifying and assessing their severity.
3. Investigating the effect of these residual stresses on pulley performance, in order to
develop a guideline of how it may be included in a conveyor pulley design.
1.3 Scope of Investigation
To achieve the stated aims above the scope of the investigation are then summarised in the
following steps:
1. Complete a detailed literature review of pulley manufacture and design to ascertain
the current state of the technology.
1
2. Review the manufacturing techniques employed to determine their effect on the
introduction of residual stresses.
3. Experimentally determine the residual stress state of the critical components of a pre-
selected T-Bottom type pulley.
4. Evaluate the effectiveness of the stress-relieving process by duplicating the
experimental investigation mentioned above, for a stress-relieved T-Bottom type
pulley.
5. Evaluate the effect of the experimentally determined residual stresses by appropriate
finite element analysis of a pulley subjected to in-service loads.
6. Reach a conclusion regarding the relevance of the manufacturing-induced residual
stresses and the use of stress-relieving to reduce their effect. Recommend possible
inclusion into the design process.
1
The literature review is extensive and may seem excessively long. It is how ever seen as one of significant
contribution of this dissertation as it summarises a complex design issue of an important mechanical engineering
product in a compact and easily accessible (UJ Open Library) document.

29
1.4 Document layout
Chapter 2 presents a literature review, to ascertain the current state of the technology relating
to conveyor pulley design. It also introduces the reader to the manufacturing techniques
employed and the effect thereof. A brief introduction of the Finite Element Method, is also
presented.
Chapter 3 describes the experimental work conducted for a pre-selected T-Bottom type pulley
to determine the levels of the residual stresses induced due to the manufacturing processes
employed. The findings of the tensile tests for determining the material properties and
residual stress measurements, are reported, for both the stress-relieved and non stress-
relived states.
Chapter 4 describes a numerical and analytical evaluation of the effect of residual stress on a
pre-selected T-Bottom type pulley. A comparison is made between the current design process
and the results of the finite element analysis. The performance of the pulley is estimated
based on high cycle, low stress fatigue life, and is compared with relevant fatigue standards.
Chapter 5 discusses the influence of the residual stresses and their possible implementation
in the current empirical and numerical design processes as described in a flow chart.
Chapter 6 presents the conclusions drawn on the relevance of the residual stresses and the
use of stress-relieving to reduce them. Recommendations are also made regarding the
possible inclusion of this effect within the current empirical and numerical design processes.

30
2. LITERATURE REVIEW
2.1 Introduction
This chapter is a literature review of the current state of the technology regarding conveyor
pulley design. The manufacturing techniques employed and the effect thereof are also
introduced. The chapter concludes with a brief introduction to the Finite Element Method.
2.2 Conveyor pulley design
The history of the design of conveyor pulleys over the past 80 years, both in Europe and in
South Africa is discussed. Different pulley configurations are then outlined, along with their
advantages from a functional and manufacturing point of view. The keyless connections used
in pulley design are detailed as well as the implications of the various configurations. The
design procedures by King and Perry as used in South Africa are discussed in detail. Current
conveyor pulleys standards that are used in industry, are reviewed. Prominent conveyor
pulley failures experienced in industry, and the affect on the design of pulleys, are also
discussed.
2.2.1 Historic perspective
The origins of systematic conveyor pulley design can be traced back to the 1930s and 1940s
when classical theory of plates and shells, as developed by Timoshenko et al. [2], was
utilised. The research that followed in the 1960s and 1970s in Germany, then set the
benchmark for the fundamental understanding of pulley behaviour, which is still used today.
Lange [3] was the first to formalise the representation of the triaxial stress state in the pulley
shells and end-disks as a Fourier series expansion.
Schmoltzi [4] investigated the contact stress field of the keyless locking element connections
(which became popular at the time) used between the shaft and pulley. These workers also
conducted extensive strain gauging to verify their work. Their work will be described in further
detail in a subsequent section.
The application of the work of Lange and Schmoltzi in South African industry was discussed
by King [5] in 1983. He concluded that the reasons for the slow uptake of these practices into
local design offices related to their highly technical and mathematical nature. He also
subsequently compared local manufacturing practices with those employed in Europe. He
identified the following differences:

31
 The European shaft and end-disk materials were of significantly higher tensile
strength than used in local construction.
 European pulley diameters were larger (1 000 to 1 750 mm), while the pulley widths
were similar to local practices of the time.
 The European manufacturing methods aimed at low mass. The local methods of
focused less on mass due to lack of standardisation and the undemanding conditions
under which local pulleys operated.
King [6] developed a design procedure for the pulleys that could be used in a drawing office.
His work considered both steady-state static and fatigue conditions of the pulley, and is still
extensively used by the local industry. Perry [7] used fundamental fatigue theory and the
works of Lange and Schmoltzi to develop a design procedure for conveyor pulleys. These
design procedures will be detailed in a subsequent section.
Qiu et al. [8] developed a new pulley stress analysis system based on the modified matrix
method. The system allowed for simpler analyses than was possible with Finite Element
Analysis (FEA) at the time. The system could also correctly determine the complex stress
state at the shell-to-end-disk interface which had not previously been possible. The integrated
analysis of the pulley and shaft as in FEA, was also possible. Sethi et al. [9] described the
Conveyor Dynamics, Inc. (CDI) design criteria of pulleys, with a test case investigated
empirically, as well as with FEA and experimental work.
Recently, FEA has been used more frequently in conveyor pulley design due to its
widespread use and ability to model the complex interaction of the shell and shaft under the
bending conditions resulting from belt tensions.
2.2.2 Conveyor pulley configurations
The pulley construction configurations have developed based on the critical areas of
connection between the components, namely the end-disk to shell and the end-disk to the
shaft. The end-disks are typically welded inside the shell or along the face of the shell. The
end-disk is connected to the shaft via a keyed connection or shrink-fit, or by the currently
used keyless connection utilising locking elements to induce an interference-type fit between
the shell and the shaft.
King [5] reviewed typical pulley construction configurations used in South Africa (Figure 2.1,
below). Shaded areas indicate the stress levels, within the pulley. A darker shading indicates
a higher stress level.

32
Figure 2.1 : Typical pulley configurations used in South Africa [5]
The most commonly used pulley configurations along with their advantages and
disadvantages, are now discussed.
2.2.2.1 Boss-type pulley
This pulley (see Figure 2.2) is specifically suited for light to medium duty applications. The
pulleys incorporated plates fillet welded to mild steel bosses fitted to the shaft with an
interference-fit. Drive pulleys used parallel keys if the torque requirements were high.
Figure 2.2 : Boss-type pulley [10]
The typical dimensions for this type of pulley are:
 Diameters of 200 to 1 000 mm.
 Belt widths of 500 to 1 200 mm.
 Shaft diameters of 40 to 150 mm.

33
The advantages of this type of pulley construction are:
 Low cost.
 Maintenance-free.
 Shaft fixed for life of the pulley.
 Tolerates higher deflection.
The main disadvantage of this type of pulley construction is:
 Shaft is not removable.
2.2.2.2 Turbine-type pulley
This pulley (Figure 2.3) is suited to medium duty applications, with the option of a removable
shaft. The end-disk is designed to allow flexure near the shell, by virtue of a reduced
thickness. This reduces stress levels in the weld at the end-disk-to-shell interface and the
locking element. The end-disk is then thicker at the hub, in order to distribute the induced
pressure of the locking element into the end-disk and then into the shell. The locking
elements must be sized correctly to ensure that the transmittable torque is not exceeded
during operation.
Figure 2.3 : Turbine-type pulley [10]

34
 Cost effective.
 Removable shaft.
 Solid end-disk - no welds in the shaft area.
The disadvantages of this type of pulley construction are:
 Locking element failure if overloaded.
 Tolerates less deflection than the boss-type pulley.
 Locking element bolts protrude past end-disk face.
2.2.2.3 L-Bottom type pulley
The stresses in the weld of the end-disk-to-shell interface is reduced in this type of pulley, by
being moved along the face of the shell. This type of pulley is normally used when shaft
diameters are greater than or equal to 200 mm, and the pulleys are non-drive. The pulleys
can be utilised for the drive-end, as long as the turbine-type narrow locking elements torque
capacity is not exceeded. Wide bearing centers can only be used for this type of pulley.
Stress-relieving of the pulley shell is recommended.
Figure 2.4 : L-Bottom type pulley [10]

35
 Solid end-disk - no welds in the shaft area.
 Shell weld is in a low bending stress area.
 Locking element failure if overloaded.
 Tolerates less deflection than boss type.
 Difficult to handle, as it has no lip on the shell.
2.2.2.4 T-Bottom type pulley
The T-bottom pulley (Figure 2.5) also uses the principle of an off-set face welded end-disk to
the shell as in the L-bottom type pulley. The pulley is typically used when the shaft diameters
are greater than or equal to 200 mm. The wider end-disk is suitable in drive-end applications
when the turbine-type locking element torque transmission capacity has been exceeded, and
the wider locking element must be used. This pulley is also suitable for heavy-duty
applications for non-drive pulleys. This type of pulley can only be used on wide bearing
centers, and stress-relieving of the pulley shell is recommended.
Figure 2.5 : T-Bottom type pulley [10]

36
 Heavy duty.
 Solid end-disk - no welds in shaft area.
 Shell weld is in low-bending stress area.
 Expensive.
 Tolerate less deflection than boss type.
2.2.2.5 Summary of the behaviour of the commonly used end-disk types
Summary of the behaviour of T-bottom end-disk type:
 As previously mentioned, the critical concern in the design of a pulley shell is the
configuration of the end-disk. This is particularly with regard to the degree of flexibility
at the end-disk-to-shell interface, and the correct sizing of the diameters of the hub
portion of the end-disk required, due to the locking element pressure induced.
 The T-bottom pulley type is best suited to medium and heavy duty applications, as
the main circumferential weld is located away from the high stress zone, caused by
bending and the end-disk locking expansion (see Figure 2.6). The weld‟s location
away from the end-disk also make it easier for a high quality butt-weld to be
achieved.

37
Figure 2.6 : Weld along the face of the shell for the T-Bottom type pulley [11]
 The large radii used in the T-bottom type end-disk reduces the stress concentrations
and allows the stresses to redistribute more uniformly (see Figure 2.5).
 The end-disk is profiled to ensure the stresses throughout are constant, the stress
concentrations are minimised, and the thicknesses are not excessive This allows
appropriate flexibility for the critical interfaces.
 The T-bottom type of end-disk is expensive to manufacture. This is due to the amount
of machining required to achieve the T-bottom profiled shape of the section. It is
therefore only recommended for heavy-duty applications, where possible.
 This configuration positions the weld away from the highest radial and axial stresses.
However, there is still a reasonable level of stress that should not be ignored. Figures
Figure 2.7 and Figure 2.8 (below) show the dissipation of the stresses along the
length of the shell, and related to shell thickness. Complete decay is only achieved for
a few thicknesses.

38
Figure 2.7 : Large heavy shell rim bending decay [6]
Figure 2.8 : Small thin shell rim bending decay [6]
Summary of the behaviour of Turbine end-disk type:
 Beneficial for use in light to medium-duty. It has similar characteristics to the T-bottom
type end-disk, except that the top of the end-disk is welded to the inside diameter of
the shell and it uses a different locking element (see Figure 2.9) .
 The weld is positioned in a high stress zone. However, because this type of pulley is
subjected to lighter loads, as long as the connection is performed with a full
penetration weld with no lack of fusion and a inner fillet, for reducing the possibility of
cracking through the throat of the weld, then this design is far more affordable than
the T-bottom type of end-disk.

39
Figure 2.9 : Inside fillet and full penetration weld of Turbine-type pulley [11]
 The limited machining required for this type of end-disk, and the implementation of
suitable welding practices renders this configuration the most suitable for a wide
range of applications.
2.2.2.6 Types of locking elements
Over the last 30 years, the keyless connection of the end-disk to shaft, made by virtue of
locking elements, has become the most popular connection method. The locking element
works based on a similar concept to that of a cone clutch with the addition of the inner and
outer rings being split to eliminate shearing loads on the bolts. The inner ring (inner segment)
contracts while the outer ring (outer segment) expands, upon tightening of the bolts. The
locking elements facilitate the removal of the shaft. Additional advantageous characteristics
are:
 The torque applied to bolts induces a expansion of the outer ring and contraction of
the inner ring thus inducing controlled pressure on the hub portion of the end-disk and
shaft respectively. This allows determination of fairly accurate sizing of the hub
portion of the end-disk, with thick-walled cylinder theory. This eliminates unnecessary
end-disk material.
 The torque transmission capacity of the locking element is determined by the torque
applied to the bolts thus eliminating the need for keys and keyways. Thus additional
stress concentrations are avoided.
 The locking element can withstand high axial thrust, virtually eliminating the possibility
of the pulley moving axially on the shaft. If the pulley were to move on the shaft, the
locking elements could be loosened and the pulley re-positioned and then re-
tightened once in position. A similar event with a shrink-fit or key-way would cause
the bore to be worn rendering the entire pulley redundant.

40
The different locking element configurations are:
Locking Element Type "A"
Locking element type "A" was used by the South African market about 20 years ago and was
the most common locking element used in conveyor pulleys at the time. In the unloaded
condition, it had the best stress pattern of the three locking elements to be discussed.
However, when load is applied to the shell and the shaft deflects, the stress pattern changes.
In this configuration. because of the angle of the tapered segments, it is neither self-centering
nor self-locking. Thus, at all times the securing bolts are in tension, and it becomes necessary
to use a centralising ring as shown in Figure 2.10 (below), as well as having to limit the
deflection of the shaft to ensure that the bolts do not exceed the elastic limit.
The acceptable level of deflection for this type of locking element is about 1/2500 of the
bearing centers or a slope of 0.05 degrees. Although this deflection restriction is not totally
unfavourable, it often forced the designer to use a bigger shaft than usual, in order to limit
deflection of the shaft. The most unfavourable characteristic of this type of locking element is
that it is virtually impossible to control the mating surfaces of the segments. This can result in
high point loads initially, and also make it necessary to re-torque the bolts after the initial
running in period, after the segments have settled.
Figure 2.10 : Locking element Type "A" [11]
Locking Element Type "B"
This configuration type (Figure 2.11, below) is used with medium duty pulleys, such as the
turbine or flat bottom design. The reason for using this type of locking element and not type
"A", is that it has the following advantages:

41
 Due to the angle of the tapers on the segments, these elements are both, self-
centering and self-locking. Therefore they do not require a centralising ring behind the
end-disk. Because of the elimination of this ring, it is always possible to withdraw the
shaft from the drum, because the inevitable build-up of rust between the centralising
ring and the shaft does not occur.
 Due to the self-locking tapers, the bolts are not in tension to the same extent as type
"A". Hence greater shaft deflections are possible in the order of 1/1800 to 1/2000 of
the bearing centers or a slope of 0.06 degrees.
 Unlike locking element type "A" it is not so critical that the locking element bolts are
tightened in sequence. This is because of the tapers it is impossible to tighten this
element unsymmetrically.
 The major disadvantage of this type of locking element, is that it cannot transmit the
same torque as type "A". However, on conventional pulleys this seldom causes a
problem as the torque to be transmitted by the shaft is usually well within the
capabilities of the chosen locking element.
Figure 2.11 : Locking element Type "B" [11]

42
Locking Element Type "C"
This configuration (Figure 2.12, below) was specifically designed for conveyor pulleys. It has
all the advantages of types "A" and "B", although with far lower surface pressures. At the
same time being able to transmit between 2 to 3 times the torque of type "A" or "B".
Figure 2.12 : Locking element Type "C" [11]
Summary of end-disk considerations for locking elements:
 The hub portion of the end-disk must be sized correctly, in order to avoid cracking
due to excessive pressure induced by the locking element.
 The hub diameter should not be too large to accommodate the locking element
pressure, as this could limit the degree of flexibility of the end-disk at the shell
connection. In addition, this would cause cracking of the weld, particularly with the
turbine type of end-disk.
2.2.3 Design procedure according to King
This procedure was developed for use at drawing offices, and is based on the superposition
of the individual effects of the pulley shell under the static and fatigue loadings in service [6].
The calculations are typically preformed for the "unworn" and "worn" condition of the shell,
based on reduction of the shell thickness due to wear caused by the conveyor belt.
Hub

43
The static and fatigue stress model proposed by King is shown in the Figure 2.13 (below):
Figure 2.13 : Static and fatigue stress model [6]
2.2.3.1 Belt pressure - fatigue loading
The belt pressure on the surface can be shown from first principles to behave as shown in
Figure 2.14 (below). This is where pressure is solely a function of curvature and
instantaneous belt tension (T).
Figure 2.14 : Belt loading on the pulley diameter [6]

44
Belt tension for a non-drive pulley:
Eq. 2-1
Belt tension for a drive pulley:
Where the belt tension is asymmetrical, an equivalent tension (Te) is found, and assumed to
act evenly over the belt lap. The active drive arc [3] is determined for the highest probable
coefficient of friction.
. /
Eq. 2-2
( )
( * Eq. 2-3
The equivalent belt tension (Te) is used instead of the instantaneous belt tension (T) to find
the belt pressure and hoop stress for position "B" - the center of the shell.
Belt pressure on the shell:
Eq. 2-4
Hoop stress due to the belt pressure on the shell:
Eq. 2-5
2.2.3.2 Shaft connection induced expansion - Static Loading
The Lame's equation [12] for determination of the variation of the stresses through thickness
of a thick cylinder, is used to determine the hoop stress induced at the shell inside diameter,
or end-disk outside diameter. This equation can be used directly to approximate the stress
variation in the turbine type of end-disk. A T-bottom type of end-disk requires an iterative
approach, to accurately assess the variation of the stress through the thickness of the end-
disk. This iterative method is discussed in the subsequent design procedure by Perry.
( )
( )
Eq. 2-6

45
2.2.3.3 Rim bending due to the belt pressure - Fatigue Loading
In modern pulleys, this is often the dominant effect. It describes the stress caused when two
adjacent sections of a plate deflect to different positions (Figure 2.15, below). Schorer [13]
studied local rim-bending in large pipelines with hoop stiffeners. This behaviour was not
previously assessed for pulleys.
Figure 2.15 : Rim bending of the shell [6]
The radial deflection due to the belt pressure is determined as follows:
. / Eq. 2-7
For the rim-bending section moment:
( * Eq. 2-8
Eq. 2-9
For the rim section force:
Eq. 2-10
For the axial rim stress:
Eq. 2-11
Hoop rim stress:

46
( * Eq. 2-12
2.2.3.4 Rim bending due to the shaft connection induced expansion - Static Loading
The radial expansion is determined using Lame's equation for thick cylinders, pertaining
particularly to the turbine type of end-disk. T-bottom type of end-disks require an iterative
process to determine the radial expansion.
The radial expansion due to the locking element pressure is determined as follows:
( )
Eq. 2-13
The determination of Mb1, Hb1, σa1 and σh1 is performed based on the above formulae.
2.2.3.5 Shell bending due to the shaft - fatigue loading
Hartenburg [14] found that when acting in isolation, bending closely followed conventional
engineer's bending theory.
For Shaft bending moment:
( )
Eq. 2-14
For Axial bending stress:
( ( ) )
Eq. 2-15
The above formulation can result in an overly-conservative estimation of the bending stress in
the end-disk-to-shell interface. This is because it is assumed that the shell experiences the
full bending moment of the shaft. King [5] notes that the end-disk bending moment is
determined by the ratio of the inner and outer diameter of the end-disk and the thickness
thereof. A relative stiffness of the shaft and shell are established, thus allowing the end-disk-
to-shell bending moment to be reduced compared to the shaft bending moment. This is then
re-entered into the above axial bending stress equation, in order to determine a less
conservative bending stress in the end-disk-to-shell interface.
For the end-disk-to-shell bending moment:
Firstly, relative stiffness of the shaft and shell are established.

47
For the shaft stiffness constant:
( )
Eq. 2-16
For the end-disk stiffness constant:
Eq. 2-17
( ( )) Eq. 2-18
A suitable end-disk thickness is selected, by setting the radial direct stress to a third of the
allowable fatigue stress, and finding an estimated value for the end-disk thickness from the
equation to follow. The end-disk stiffness is then determined, based on this estimated value.
For radial direct stress:
Eq. 2-19
For end-disk stiffness:
Eq. 2-20
If the shell is then assumed infinitely stiff compared with the shaft and end-disk, which is
reasonable because the stiffness is the fourth power of the diameter, as supported by
Schmoltzi's experimental work [4]. The bending moment is then distributed in the end-disk
and shaft in the proportion to stiffness, as follows:
For the end-disk bending moment:
Eq. 2-21
The axial bending stress for the end-disk-to-shell interface, is then calculated as follows:
( ( ) )
Eq. 2-22

48
2.2.3.6 Total stress
The total stress is determined as the superposition of the static and fatigue stress for both the
axial and hoop components at position "A" and "B".
The axial stress at position "A" is determined as follows:
Eq. 2-23
The hoop stress at position "A" is determined as follows:
Eq. 2-24
2.2.4 Design procedure according to Perry
2.2.4.1 Fatigue considerations
Typically a pulley rotates 35 million times per year [7]. All major pulley components should
therefore be designed for infinite fatigue life. Infinite fatigue life means that the actual stress
must be less than the endurance limit of the steel for a parent material (Figure 2.16, below).
Figure 2.16 : S-N Curve for steel [15]
Actual stress implies that geometrical stress concentration factors, surface finish factors and
size factors have been considered for the stress calculation. Figure 2.17 illustrates the effect
of reduced bearing diameters on shaft stress and Figure 2.18 indicates the effect of surface
finish.

49
Figure 2.17 : Stress concentration factors for filleted shafts in bending [16]
Figure 2.18 : Surface finish modification factors for steel [7]
Fatigue failure is prevented by keeping the fatigue reserve factor (FRF) above 1.3. Figure
2.19 (below) illustrates the meaning of the term fatigue reserve factor.

50
Figure 2.19 : Modified Goodman diagram [7]
2.2.4.2 Shell
As previously stated the shell is more rigid, typically 10 times more rigid than the shaft and
end-disk assembly. The shell is assumed to be a simply supported tube as shown in Figure
2.20 (below). The figure also shows the sinusoidal load distribution assumed along the length
of the shell, for this design procedure.
Figure 2.20 : Support and load distribution assumption for the shell [3]
For the sinusoidal load distribution:
( * Eq. 2-25
For drive pulleys, the load distribution along the circumference is assumed to be linear, as
shown in Figure 2.21 (below).

51
Figure 2.21 : Circumferential load distribution assumption shell [3]
Lange found that maximum axial and hoop stress ranges occur at the center of the shell and
3 stress reversals occur per revolution for a drive pulley with an angle of wrap of 180 degrees.
This is seen in Figure 2.22 (below) where Lange compared calculated data versus measured
data:
Figure 2.22 : Calculated and measured axial stresses in the pulley shell [3]
From these loading conditions the stresses at any point can be determined, and are as
follows:
Eq. 2-26
Eq. 2-27
* ,( ) ( ) ( )
( )*( ) +- ,( )
( )*( ) - + ,( ) ( ) -
Eq. 2-28
In the longitudinal direction:
[ ] ( * Eq. 2-29

52
In the circumferential direction:
[ ] ( * Eq. 2-30
Shear stress:
[ ] ( * Eq. 2-31
Due to the many iterations required, these calculations should not be attempted without the
use of a computer.
The maximum values of these stresses are used to calculate the Fatigue Reserve Factor of
the shell. BS 5400 [17] was used for the fatigue assessment of the circumferential and
longitudinal welds in the shell. The code is used to assess if the calculated stress range is
below the non-propagating stress range (endurance limit) at 1x10
7
cycles, for the particular
class of weld. If this criterion is met then fatigue need not be considered as theoretically
infinite fatigue life should be achieved as long as the weld is sound with no defects.
The following classes of weld are used for the detail of concern according to BS 5400, under
this design criterion:
 Class C is used for the classification of the longitudinal weld of the shell. This is then
compared with the corrected hoop stress range of the shell. A correction factor of
43/59, as observed by the experimental and numerical work conducted by Lange, is
applied to the stress range before the fatigue assessment. This is based on the initial
assumption that the shell is simply-supported. The mean minus two standard
deviation S-N curve, is used for this assessment (Figure 2.23, below).
Figure 2.23 : Mean - 2 standard deviation S-N curve [17]

53
 Class F is used for the classification of the circumferential full penetration T-weld for
the end-disk-to-inside shell of the turbine type of end-disk. The axial and radial stress
range is used for the fatigue assessment.
 Class C is used for the classification of the circumferential full penetration butt-weld
for the end-disk-to-shell of the T-Bottom type of end-disk. Lange determined by strain
gauge measurement that the axial stress range perpendicular to the circumferential
weld is 65% of the maximum axial stress range in the shell, for a pulley with an angle
of wrap of 180 degrees. This reduction is used as the axial stress range at the weld in
this design criterion.
2.2.4.3 Shaft
Two criteria determine shaft size, namely deflection angle at locking element, and fatigue
failure at the location of maximum stress.
Deflection angle:
The shaft and end-disk share the imposed bending moment. The portion carried by each is
directly proportional to its rigidity. The locking element and hub part of the turbine-shaped
end-disks are assumed to be inflexible, provided that the hub diameter is less than one half of
the pulley diameter.
The deflection angle is calculated (for turbine shaped end-disk pulleys) from:
( )( ) ( )( )
( )
Eq. 2-32
( )( ) Eq. 2-33
The maximum allowable shaft deflection angle at the locking element depends on the type of
locking element and is specified by the manufacturers thereof. A typical figure is 5 minutes.
Fatigue failure:
For stepped shafts, the most probable location of failure is in the fillet or at the edge of the
locking element. For straight shafts, it is at the edge of the locking element.
⁄ ( ⁄ ) Eq. 2-34

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