《摩擦學中的接觸力學》是 1998年 I. G. GORYACHEVA出版的圖書，作者是I. G. GORYACHEVA。
基本介紹
- 書名：摩擦學中的接觸力學
- 類別：科技
- 出版社：I. G. GORYACHEVA
- 出版時間：1998年01月01日
簡介,內容簡介,目錄,
簡介
中文名:摩擦學中的接觸力學
原名:Contact Mechanics in Tribology
作者:I. G. GORYACHEVA
圖書分類:科技
資源格式:PDF
版本:掃描版
出版社:I. G. GORYACHEVA
書號:ISBN 0-7923-5257-2
發行時間:1998年01月01日
地區:美國
語言:英文
內容簡介
Tribology is the science of friction, lubrication and wear of moving components. Results obtained from tribology are used to reduce energy losses in friction processes, to reduce material losses due to wear, and to increase the service life of components. Contact Mechanics plays an important role in Tribology. Contact Mechanics studies the stress and strain states of bodies in contact; it is contact that leads to friction interaction and wear. This book investigates a variety of contact problems: discrete contact of rough surfaces, the effect of imperfect elasticity and mechanical inhomogeneity of contacting bodies, models of friction and wear, changes in contact characteristics during the wear process, etc. The results presented in this book were obtained during my work at the Institute for Problems in Mechanics of the Russian Academy of Sciences. The first steps of this research were carried out under the supervision of Professor L.A.Galin who taught me and showed me the beauty of scientific research and solutions. Some of the problems included in the book were investigated together with my colleagues Dr.M.N.Dobychin, Dr.O.G.Chekina, Dr.I.A.Soldatenkov, and Dr.E.V.Torskaya from the Laboratory of Friction and Wear (IPM RAS) and Prof. F.Sadeghi from Purdue University (West Lafayette, USA). I would like to express my thanks to them. I am very grateful to Professor G. M. L. Glad well who edited my book, helped me to improve the text and inspired me to this very interesting and hard work. Finally, I would like to thank Ekaterina and Alexandre Goryachev for their help in preparation of this manuscript. I hope that this book will be useful for specialists in both contact
目錄
Preface ......................................................................................... xiii
1. Introduction .......................................................................... 1
1.1 Friction Contact from the Standpoint of Mechanics .................. 2
1.2 Previous Studies and the Book Outline ..................................... 4
1.2.1 Surface Microstructure ............................................. 5
1.2.2 Friction ..................................................................... 5
1.2.3 Imperfect Elasticity .................................................. 6
1.2.4 Inhomogeneous Bodies ........................................... 8
1.2.5 Surface Fracture ...................................................... 9
1.2.6 Wear Contact Problems ........................................... 9
2. Mechanics of Discrete Contact ........................................... 11
2.1 Multiple Contact Problem ........................................................... 11
2.1.1 Surface Macro- and Micro- Geometry ...................... 11
2.1.2 Problem Formulation ............................................... 12
2.1.3 Previous Studies ...................................................... 13
2.2 Periodic Contact Problem .......................................................... 15
2.2.1 One-Level Model ..................................................... 15
2.2.2 Principle of Localization ........................................... 18
2.2.3 System of Indenters of Various Heights ................... 21
2.2.4 Stress Field Analysis ............................................... 23
2.3 Problem with a Bounded Nominal Contact Region ................... 30
2.3.1 Problem Formulation ............................................... 30
2.3.2 A System of Cylindrical Punches ............................. 34
2.3.3 A System of Spherical Punches ............................... 40
2.4 The Additional Displacement Function ...................................... 42
2.4.1 The Function Definition ............................................ 42
2.4.2 Some Particular Cases ............................................ 45
2.4.3 Properties of the Function ........................................ 47
2.5 Calculation of Contact Characteristics ....................................... 49
2.5.1 The Problem of Continuous Contact ........................ 49
2.5.2 Plane Contact Problem ............................................ 50
2.5.3 Axisymmetric Contact Problem ................................ 55
2.5.4 Characteristics of the Discrete Contact .................... 56
3. Friction in Sliding/Rolling Contact ..................................... 61
3.1 Mechanism of Friction ................................................................ 61
3.2 Two-Dimensional Sliding Contact of Elastic Bodies .................. 63
3.2.1 Problem Formulation ............................................... 63
3.2.2 Contact Problem for a Cylinder ................................ 65
3.2.3 Contact Problem for a Flat Punch ............................ 68
3.3 Sliding Contact of Elastic Bodies (3-D) ...................................... 73
3.3.1 The Friction Law Has the Form τxz = μp ................... 73
3.3.2 The Friction Law Has the Form τxz = τ0 + μp ............ 77
3.4 Sliding Contact of Viscoelastic Bodies ...................................... 79
3.4.1 Constitutive Equations for the Viscoelastic
Body ........................................................................ 80
3.4.2 Problem Formulation ............................................... 81
3.4.3 Analytical Results .................................................... 82
3.4.4 Some Special Cases ............................................... 84
3.5 Rolling Contact ........................................................................... 87
3.5.1 Problem Formulation ............................................... 87
3.5.2 Solution ................................................................... 88
3.5.3 The Contact Width and the Relation between
the Slip and Stick Zones .......................................... 91
3.5.4 Rolling Friction Analysis ........................................... 91
3.5.5 Some Special Cases ............................................... 94
3.6 Mechanical Component of Friction Force .................................. 95
4. Contact of Inhomogeneous Bodies ................................... 101
4.1 Bodies with Internal Defects ...................................................... 101
4.1.1 Boundary Problem for Elastic Bodies with an
Internal System of Defects ....................................... 102
4.1.2 The Tensor of Influence ........................................... 103
4.1.3 The Auxiliary Problem .............................................. 105
4.1.4 A Special Case of a System of Defects .................... 106
4.1.5 Half-Plane Weakened by a System of
Defects .................................................................... 107
4.1.6 Influence of Defects on Contact Characteristics
and Internal Stresses ............................................... 109
4.2 Coated Elastic Bodies ................................................................ 110
4.2.1 Periodic Contact Problem ........................................ 112
4.2.2 Method of Solution ................................................... 113
4.2.3 The Analysis of Contact Characteristics and
Internal Stresses ...................................................... 117
4.3 Viscoelastic Layered Elastic Bodies .......................................... 122
4.3.1 Model of the Contact ................................................ 123
4.3.2 Normal Stress Analysis ............................................ 125
4.3.3 Tangential Stress Analysis ....................................... 128
4.3.4 Rolling Friction Analysis ........................................... 131
4.3.5 The Effect of Viscoelastic Layer in Sliding and
Rolling Contact ........................................................ 132
4.4 The Effect of Roughness and Viscoelastic Layer ...................... 137
4.4.1 Model of the Contact and its Analysis ...................... 138
4.4.2 The Method of Determination of Internal
Stresses .................................................................. 143
4.4.3 Contact Characteristics ............................................ 145
4.4.4 Internal Stresses ...................................................... 150
4.5 Viscoelastic Layer Effect in Lubricated Contact ........................ 152
4.5.1 Problem Formulation ............................................... 153
4.5.2 Method of Solution of the Main System of
Equations ................................................................ 154
4.5.3 Film Profile and Contact Pressure Analysis ............. 157
4.5.4 Rolling Friction and Traction Analysis ...................... 160
5. Wear Models ......................................................................... 163
5.1 Mechanisms of Surface Fracture ............................................... 163
5.1.1 Wear and Its Causes ............................................... 163
5.1.2 Active Layer ............................................................. 164
5.1.3 Types of Wear in Sliding Contact ............................. 166
5.1.4 Specific Features of Surface Fracture ...................... 167
5.1.5 Detached and Loose Particles ................................. 167
5.2 Approaches to Wear Modeling .................................................. 168
5.2.1 The Main Stages in Wear Modeling ......................... 168
5.2.2 Fatigue Wear ........................................................... 169
5.3 Delamination in Fatigue Wear ................................................... 170
5.3.1 The Model Formulation ............................................ 170
5.3.2 Surface Wear Rate .................................................. 171
5.3.3 Wear Kinetics in the Case q(z,P) ~ τN
max,
P = const ................................................................. 173
5.3.4 Influence of the Load Variations P(t) on Wear
Kinetics .................................................................... 175
5.3.5 Steady-State Stage Characteristics ......................... 180
5.3.6 Experimental Determination of the Frictional
Fatigue Parameters ................................................. 181
5.4 Fatigue Wear of Rough Surfaces .............................................. 182
5.4.1 The Calculation of Damage Accumulation on
the Basis of a Thermokinetic Model ......................... 183
5.4.2 Particle Detachment ................................................ 186
5.4.3 The Analysis of the Model ........................................ 189
6. Wear Contact Problems ...................................................... 191
6.1 Wear Equation ........................................................................... 191
6.1.1 Characteristics of the Wear Process ........................ 191
6.1.2 Experimental and Theoretical Study of the
Wear Characteristics ............................................... 193
6.2 Formulation of Wear Contact Problems .................................... 198
6.2.1 The Relation between Elastic Displacement and
Contact Pressure ..................................................... 198
6.2.2 Contact Condition .................................................... 199
6.3 Wear Contact Problems of Type A ............................................ 201
6.3.1 Steady-State Wear for the Problems of Type A ....... 201
6.3.2 Asymptotic Stability of the Steady-State
Solution ................................................................... 202
6.3.3 General Form of the Solution ................................... 204
6.4 Contact of a Circular Beam and a Cylinder ............................... 204
6.4.1 Problem Formulation ............................................... 204
6.4.2 Solution ................................................................... 206
6.5 Contact Problem for an Elastic Half-Space ............................... 210
6.5.1 Problem Formulation ............................................... 210
6.5.2 Axisymmetric Contact Problem ................................ 212
6.5.3 The Case V(x,y) = V∞ ............................................... 219
6.6 Contact Problems of Type B ...................................................... 221
6.6.1 The Wear of an Elastic Half-Space by a Punch
Moving Translationally ............................................. 221
6.6.2 Wear of a Half-Plane by a Disk Executing
Translational and Rotational Motion ......................... 225
6.7 Wear of a Thin Elastic Layer ...................................................... 228
6.7.1 Problem Formulation ............................................... 229
6.7.2 The Dimensionless Analysis .................................... 232
6.7.3 Calculation Techniques and Numerical
Results .................................................................... 232
6.8 Problems with a Time-Dependent Contact Region ................... 234
6.8.1 Problem Formulation ............................................... 234
6.8.2 The Cases of Increasing, Decreasing and
Constant Contact Region ......................................... 235
7. Wear of Inhomogeneous Bodies ........................................ 239
7.1 Variable Wear Coefficient .......................................................... 239
7.1.1 Problem Formulation ............................................... 239
7.1.2 Steady-State Wear Stage for the Surface
Hardened Inside Strips ............................................ 242
7.1.3 Steady-State Wear Stage for a Surface
Hardened Inside Circles .......................................... 248
7.1.4 The Shape of the Worn Surface of an Annular
Punch for Various Arrangements of Hardened
Domains .................................................................. 251
7.2 Wear in Discrete Contact ........................................................... 255
7.2.1 Mathematical Model ................................................. 255
7.2.2 Model Analysis ........................................................ 256
7.2.3 Running-in Stage of Wear Process .......................... 259
7.2.4 Steady-State Stage of Wear Process ....................... 261
7.2.5 Model of Equilibrium Roughness Formation ............. 264
7.2.6 Complex Model of Wear of a Rough Surface ........... 266
7.3 Control of Inhomogeneous Surface Wear ................................. 269
7.3.1 Problem Formulation ............................................... 269
7.3.2 Hardened Surface with Variable Wear
Coefficient ............................................................... 271
7.3.3 Abrasive Tool Surface with Variable Inclusion
Density .................................................................... 273
8. Wear of Components ........................................................... 277
8.1 Plain Journal Bearing with Coating at the Bush ........................ 278
8.1.1 Model Assumptions ................................................. 278
8.1.2 Problem Formulation ............................................... 279
8.1.3 Method of Solution ................................................... 281
8.1.4 Wear Kinetics .......................................................... 282
8.1.5 Steady-State Stage of Wear Process ....................... 284
8.2 Plain Journal Bearing with Coating at the Shaft ........................ 286
8.2.1 Contact Problem Formulation .................................. 286
8.2.2 The Main Integro-Differential Equation .................... 288
8.2.3 Method of Solution ................................................... 290
8.2.4 Contact Characteristics Analysis ............................. 292
8.2.5 Wear Analysis .......................................................... 294
8.3 Comparison of Two Types of Bearings ..................................... 297
8.4 Wheel/Rail Interaction ................................................................ 299
8.4.1 Parameters and the Structure of the Model ............. 300
8.4.2 Contact Characteristics Analysis ............................. 301
8.4.3 Wear Analysis .......................................................... 304
8.4.4 Fatigue Damage Accumulation Process .................. 306
8.4.5 Analysis of the Results ............................................ 307
8.5 A Model for Tool Wear in Rock Cutting ..................................... 313
8.5.1 The Model Description ............................................. 314
8.5.2 Stationary Process without Chip Formation and
Tool Wear ................................................................ 318
8.5.3 Analysis of the Cutting Process ............................... 319
8.5.4 Influence of Tool Wear on the Cutting Process ........ 322
9. Conclusion ........................................................................... 325
10. References ........................................................................... 327
Index ............................................................................................ 343
1. Introduction .......................................................................... 1
1.1 Friction Contact from the Standpoint of Mechanics .................. 2
1.2 Previous Studies and the Book Outline ..................................... 4
1.2.1 Surface Microstructure ............................................. 5
1.2.2 Friction ..................................................................... 5
1.2.3 Imperfect Elasticity .................................................. 6
1.2.4 Inhomogeneous Bodies ........................................... 8
1.2.5 Surface Fracture ...................................................... 9
1.2.6 Wear Contact Problems ........................................... 9
2. Mechanics of Discrete Contact ........................................... 11
2.1 Multiple Contact Problem ........................................................... 11
2.1.1 Surface Macro- and Micro- Geometry ...................... 11
2.1.2 Problem Formulation ............................................... 12
2.1.3 Previous Studies ...................................................... 13
2.2 Periodic Contact Problem .......................................................... 15
2.2.1 One-Level Model ..................................................... 15
2.2.2 Principle of Localization ........................................... 18
2.2.3 System of Indenters of Various Heights ................... 21
2.2.4 Stress Field Analysis ............................................... 23
2.3 Problem with a Bounded Nominal Contact Region ................... 30
2.3.1 Problem Formulation ............................................... 30
2.3.2 A System of Cylindrical Punches ............................. 34
2.3.3 A System of Spherical Punches ............................... 40
2.4 The Additional Displacement Function ...................................... 42
2.4.1 The Function Definition ............................................ 42
2.4.2 Some Particular Cases ............................................ 45
2.4.3 Properties of the Function ........................................ 47
2.5 Calculation of Contact Characteristics ....................................... 49
2.5.1 The Problem of Continuous Contact ........................ 49
2.5.2 Plane Contact Problem ............................................ 50
2.5.3 Axisymmetric Contact Problem ................................ 55
2.5.4 Characteristics of the Discrete Contact .................... 56
3. Friction in Sliding/Rolling Contact ..................................... 61
3.1 Mechanism of Friction ................................................................ 61
3.2 Two-Dimensional Sliding Contact of Elastic Bodies .................. 63
3.2.1 Problem Formulation ............................................... 63
3.2.2 Contact Problem for a Cylinder ................................ 65
3.2.3 Contact Problem for a Flat Punch ............................ 68
3.3 Sliding Contact of Elastic Bodies (3-D) ...................................... 73
3.3.1 The Friction Law Has the Form τxz = μp ................... 73
3.3.2 The Friction Law Has the Form τxz = τ0 + μp ............ 77
3.4 Sliding Contact of Viscoelastic Bodies ...................................... 79
3.4.1 Constitutive Equations for the Viscoelastic
Body ........................................................................ 80
3.4.2 Problem Formulation ............................................... 81
3.4.3 Analytical Results .................................................... 82
3.4.4 Some Special Cases ............................................... 84
3.5 Rolling Contact ........................................................................... 87
3.5.1 Problem Formulation ............................................... 87
3.5.2 Solution ................................................................... 88
3.5.3 The Contact Width and the Relation between
the Slip and Stick Zones .......................................... 91
3.5.4 Rolling Friction Analysis ........................................... 91
3.5.5 Some Special Cases ............................................... 94
3.6 Mechanical Component of Friction Force .................................. 95
4. Contact of Inhomogeneous Bodies ................................... 101
4.1 Bodies with Internal Defects ...................................................... 101
4.1.1 Boundary Problem for Elastic Bodies with an
Internal System of Defects ....................................... 102
4.1.2 The Tensor of Influence ........................................... 103
4.1.3 The Auxiliary Problem .............................................. 105
4.1.4 A Special Case of a System of Defects .................... 106
4.1.5 Half-Plane Weakened by a System of
Defects .................................................................... 107
4.1.6 Influence of Defects on Contact Characteristics
and Internal Stresses ............................................... 109
4.2 Coated Elastic Bodies ................................................................ 110
4.2.1 Periodic Contact Problem ........................................ 112
4.2.2 Method of Solution ................................................... 113
4.2.3 The Analysis of Contact Characteristics and
Internal Stresses ...................................................... 117
4.3 Viscoelastic Layered Elastic Bodies .......................................... 122
4.3.1 Model of the Contact ................................................ 123
4.3.2 Normal Stress Analysis ............................................ 125
4.3.3 Tangential Stress Analysis ....................................... 128
4.3.4 Rolling Friction Analysis ........................................... 131
4.3.5 The Effect of Viscoelastic Layer in Sliding and
Rolling Contact ........................................................ 132
4.4 The Effect of Roughness and Viscoelastic Layer ...................... 137
4.4.1 Model of the Contact and its Analysis ...................... 138
4.4.2 The Method of Determination of Internal
Stresses .................................................................. 143
4.4.3 Contact Characteristics ............................................ 145
4.4.4 Internal Stresses ...................................................... 150
4.5 Viscoelastic Layer Effect in Lubricated Contact ........................ 152
4.5.1 Problem Formulation ............................................... 153
4.5.2 Method of Solution of the Main System of
Equations ................................................................ 154
4.5.3 Film Profile and Contact Pressure Analysis ............. 157
4.5.4 Rolling Friction and Traction Analysis ...................... 160
5. Wear Models ......................................................................... 163
5.1 Mechanisms of Surface Fracture ............................................... 163
5.1.1 Wear and Its Causes ............................................... 163
5.1.2 Active Layer ............................................................. 164
5.1.3 Types of Wear in Sliding Contact ............................. 166
5.1.4 Specific Features of Surface Fracture ...................... 167
5.1.5 Detached and Loose Particles ................................. 167
5.2 Approaches to Wear Modeling .................................................. 168
5.2.1 The Main Stages in Wear Modeling ......................... 168
5.2.2 Fatigue Wear ........................................................... 169
5.3 Delamination in Fatigue Wear ................................................... 170
5.3.1 The Model Formulation ............................................ 170
5.3.2 Surface Wear Rate .................................................. 171
5.3.3 Wear Kinetics in the Case q(z,P) ~ τN
max,
P = const ................................................................. 173
5.3.4 Influence of the Load Variations P(t) on Wear
Kinetics .................................................................... 175
5.3.5 Steady-State Stage Characteristics ......................... 180
5.3.6 Experimental Determination of the Frictional
Fatigue Parameters ................................................. 181
5.4 Fatigue Wear of Rough Surfaces .............................................. 182
5.4.1 The Calculation of Damage Accumulation on
the Basis of a Thermokinetic Model ......................... 183
5.4.2 Particle Detachment ................................................ 186
5.4.3 The Analysis of the Model ........................................ 189
6. Wear Contact Problems ...................................................... 191
6.1 Wear Equation ........................................................................... 191
6.1.1 Characteristics of the Wear Process ........................ 191
6.1.2 Experimental and Theoretical Study of the
Wear Characteristics ............................................... 193
6.2 Formulation of Wear Contact Problems .................................... 198
6.2.1 The Relation between Elastic Displacement and
Contact Pressure ..................................................... 198
6.2.2 Contact Condition .................................................... 199
6.3 Wear Contact Problems of Type A ............................................ 201
6.3.1 Steady-State Wear for the Problems of Type A ....... 201
6.3.2 Asymptotic Stability of the Steady-State
Solution ................................................................... 202
6.3.3 General Form of the Solution ................................... 204
6.4 Contact of a Circular Beam and a Cylinder ............................... 204
6.4.1 Problem Formulation ............................................... 204
6.4.2 Solution ................................................................... 206
6.5 Contact Problem for an Elastic Half-Space ............................... 210
6.5.1 Problem Formulation ............................................... 210
6.5.2 Axisymmetric Contact Problem ................................ 212
6.5.3 The Case V(x,y) = V∞ ............................................... 219
6.6 Contact Problems of Type B ...................................................... 221
6.6.1 The Wear of an Elastic Half-Space by a Punch
Moving Translationally ............................................. 221
6.6.2 Wear of a Half-Plane by a Disk Executing
Translational and Rotational Motion ......................... 225
6.7 Wear of a Thin Elastic Layer ...................................................... 228
6.7.1 Problem Formulation ............................................... 229
6.7.2 The Dimensionless Analysis .................................... 232
6.7.3 Calculation Techniques and Numerical
Results .................................................................... 232
6.8 Problems with a Time-Dependent Contact Region ................... 234
6.8.1 Problem Formulation ............................................... 234
6.8.2 The Cases of Increasing, Decreasing and
Constant Contact Region ......................................... 235
7. Wear of Inhomogeneous Bodies ........................................ 239
7.1 Variable Wear Coefficient .......................................................... 239
7.1.1 Problem Formulation ............................................... 239
7.1.2 Steady-State Wear Stage for the Surface
Hardened Inside Strips ............................................ 242
7.1.3 Steady-State Wear Stage for a Surface
Hardened Inside Circles .......................................... 248
7.1.4 The Shape of the Worn Surface of an Annular
Punch for Various Arrangements of Hardened
Domains .................................................................. 251
7.2 Wear in Discrete Contact ........................................................... 255
7.2.1 Mathematical Model ................................................. 255
7.2.2 Model Analysis ........................................................ 256
7.2.3 Running-in Stage of Wear Process .......................... 259
7.2.4 Steady-State Stage of Wear Process ....................... 261
7.2.5 Model of Equilibrium Roughness Formation ............. 264
7.2.6 Complex Model of Wear of a Rough Surface ........... 266
7.3 Control of Inhomogeneous Surface Wear ................................. 269
7.3.1 Problem Formulation ............................................... 269
7.3.2 Hardened Surface with Variable Wear
Coefficient ............................................................... 271
7.3.3 Abrasive Tool Surface with Variable Inclusion
Density .................................................................... 273
8. Wear of Components ........................................................... 277
8.1 Plain Journal Bearing with Coating at the Bush ........................ 278
8.1.1 Model Assumptions ................................................. 278
8.1.2 Problem Formulation ............................................... 279
8.1.3 Method of Solution ................................................... 281
8.1.4 Wear Kinetics .......................................................... 282
8.1.5 Steady-State Stage of Wear Process ....................... 284
8.2 Plain Journal Bearing with Coating at the Shaft ........................ 286
8.2.1 Contact Problem Formulation .................................. 286
8.2.2 The Main Integro-Differential Equation .................... 288
8.2.3 Method of Solution ................................................... 290
8.2.4 Contact Characteristics Analysis ............................. 292
8.2.5 Wear Analysis .......................................................... 294
8.3 Comparison of Two Types of Bearings ..................................... 297
8.4 Wheel/Rail Interaction ................................................................ 299
8.4.1 Parameters and the Structure of the Model ............. 300
8.4.2 Contact Characteristics Analysis ............................. 301
8.4.3 Wear Analysis .......................................................... 304
8.4.4 Fatigue Damage Accumulation Process .................. 306
8.4.5 Analysis of the Results ............................................ 307
8.5 A Model for Tool Wear in Rock Cutting ..................................... 313
8.5.1 The Model Description ............................................. 314
8.5.2 Stationary Process without Chip Formation and
Tool Wear ................................................................ 318
8.5.3 Analysis of the Cutting Process ............................... 319
8.5.4 Influence of Tool Wear on the Cutting Process ........ 322
9. Conclusion ........................................................................... 325
10. References ........................................................................... 327
Index ............................................................................................ 343
