umesNumerical Modelling of the Effect of Fretting Wear on Fretting Fatigue

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Contents
Abstract…………………………………………………………………………. v
Publications ……………………………………………………………………. vi
Acknowledgements…………………………………………………………… vii
Nomenclature………………………………………………………………...… viii
Chapter 1 Introduction
1.1 Air Travel………………………………………………………………. 1
1.2 Socio-Economic Drivers for Efficient Engine Design .……………. 2
1.3 A Future Perspective ………………………………………………… 2
1.4 Spline couplings……………………………………………………….. 3
1.5 Aims…………………………………………………………………….. 6
1.6 Thesis scope…………………………………………………………… 6
Chapter 2 Literature Review
2.1 Introduction……………………………………………………………... 8
2.2 Contact mechanics……………………………………..……………… 8
2.3 Tribology.……………………………………………………………… 16
2.3.1 Introduction……………………………………………………….. 16
2.3.2 Friction…………………………………………………………….. 16
2.3.3 Wear……………………………………………………………..... 18
2.4 Fatigue of Metals……………………………………………………... 19
2.4.1 General………….………………………………………………… 19
2.4.2 Fatigue Mechanisms…………………………………………….. 20
2.4.3 Relating Stress and Fatigue Life……………………………….. 21
2.4.4 Damage Models………………………………………………….. 24
2.4.5 Fracture Mechanics…………………………………………….... 27
2.5 Fretting…………………………………………………………….... 32
2.5.1 General…………………………………………………………...... 32
2.5.2 Multiaxial fatigue parameters in fretting…………………........... 36
2.5.3 Fracture mechanics in fretting……………………….................. 38
2.5.4 Numerical modelling of fretting contact………………………… 40
2.5.5 Wear modelling in fretting……………………….................. 42
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2.6 Summary of literature review ……………………….................. 44
Chapter 3 Methodology Description
3.1 Overview………………………........................................................ 46
3.2 A new fretting fatigue modelling approach………………............... 46
3.3 Wear model development……………………….............................. 48
3.3.1 Introduction………..…………................................................. 48
3.3.2 Validation of the AMC approach…………............................... 51
3.3.3 Friction model………..………….............................................. 54
3.4 Critical plane fatigue damage model………………………............... 56
3.5 Combining fretting fatigue and fretting wear modelling ................... 57
3.5.1 General………..…………......................................................... 57
3.5.2 Damage accumulation framework……………………………… 59
3.5.3 Material point mesh……………………………………............... 61
3.5.4 Damage anisotropy……………………………………............... 62
3.6 Numerical Aspects………………………........................................... 63
Chapter 4 Analysis of Hertzian Fretting Fatigue
4.1. Overview……………………….………………………….................... 64
4.2. Model description………..…….………………………....................... 64
4.3. Load history………..…….………………………................................ 65
4.4. Contact formulation………..…….……………................................... 67
4.5. Validation of FE model against theory………..…….......................... 67
4.6. Results…….…….…………………………….…................................. 73
4.7. Discussion of results………..………………………………................ 86
4.8. Conclusions………..………………………………............................. 91
Chapter 5 Analysis of nearly complete fretting fatigue
5.1 Overview………..……………………………….................................. 93
5.2 Model description………..…………………………………................. 93
5.2.1 Test Geometry………..………………………………................. 93
5.2.2 FE Model………..…………………...…………………................ 94
5.2.3 Variation of k ………..………………………………................. 96
5.3 Results and Discussion………..………………………… .................. 97
5.3.1 Model Validation and geometry study……………...… ............ 97
5.3.2 Effect of rig compliance………………………........................... 101
5.3.3 Effect of slip amplitude………………………............................ 102
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5.3.4 Effect of wear: Gross sliding……………….….......................... 104
5.3.5 Effect of wear: Partial slip…………………..….......................... 106
5.3.6 Effect of wear coefficient on fretting fatigue behaviour …........ 109
5.4 Conclusions………..……………….................................................... 113
Chapter 6 A Combined Fracture Mechanics and Wear Modelling Method
6.1 Introduction………..……………........................................................ 115
6.2 Damage tolerant approach…………………..…................................ 115
6.3 Methodology………..….………......................................................... 118
6.4 Crack growth………..….………........................................................ 119
6.5 Finite element modelling………........................................................ 122
6.5.1 Global-sub model approach…………………..…...................... 122
6.5.2 Mesh generation ………………………..……..…...................... 125
6.5.3 Stress intensity factor determination……………………........... 125
6.6 Combining critical plane and LEFM approaches……………............ 130
6.7 Contact stress evolution treatment…………………………............... 131
Chapter 7 Effect of wear on crack growth behaviour
7.1 Introduction………..….………........................................................... 133
7.2 Results………..….……….................................................................. 133
7.2.1 Comparison with test data…………………….………............... 133
7.2.2 Effect of nucleation period…………………….………............... 134
7.2.3 Effect of bulk stress: crack arrest…………………….…............ 139
7.3 Discussion …………………….…………………………….................. 143
7.4 Conclusions …………………………………………….…................... 148
Chapter 8 Fretting analysis of a tapered rotor joint
8.1 Overview ………………………………………….….…....................... 151
8.2 Torque couplings……………………………………….…................... 151
8.2.1 Taper couplings ……………………………………….…............ 151
8.2.2 Conic Coupling …………………………………………………… 152
8.3 Model description ………………………………………………………. 153
8.4 Results …………………………………………………………………... 157
8.4.1 Fretting wear study ………………………………………………. 157
8.4.2 Design optimisation ……………………………………………… 159
8.5 Conclusions ………………………………………………………….…. 161
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Chapter 9
9.1 Conclusions……………………………………………………………… 162
Chapter 10 Recommendations and further work
10.1 Overview ………………………………………………………..……... 164
10.2 Method improvements ……………………………………………….. 164
10.2.1 Tribology Model .……………………………………………..…. 164
10.2.2 Friction Model Improvements …………………………………. 165
10.2.3 Wear Model Improvements ……………………………………..165
10.3 Fatigue Model ……………………………………………………….....167
10.3.1 General …………………………………………………….......…167
10.3.2 Damage accumulation assumption ……………….......……... 168
10.4 Other areas of application .……………….............................……... 169
10.4.1 Engineering assemblies ……………………………......……... 169
10.4.2 Materials ……………….......……... ……………….......…….....169
10.4.3 Coatings ……………………………......……………………….. 170
Appendix A1 Abaqus Subroutine
A1.1 Overview …………………………….....……………………………... 171
A1.2 Code ………………………......……...……………………………..... 172
Appendix A2 Verification of Numerical Aspects
A2.1 Overview ………………….....……………………………................. 176
A2.2 Effect of cycle jumping ………………….....……………………...…. 176
A2.3 Effect of increment size ………………….....…..…………….……... 181
A2.4 Mesh refinement ………………….....……………...…………..……. 185
A2.5 Stress reporting location …………………..………...………………. 189
Appendix A3 Effect of rig compliance
A3.1 Overview ………………….....………………………...….………... 192
A3.2 Initial geometry …………….....……………………….………….... 192
References...……………………….....………………………..…..…………... 198