Contact Mechanics in Tribology

cover.jpg......Page 1
Front Matter......Page 2
Preface......Page 6
Table of Contents......Page 0
Table of Contents......Page 7
1. Introduction......Page 14
1.1 Friction Contact from the Standpoint of Mechanics......Page 15
1.2 Previous Studies and the Book Outline......Page 17
1.2.2 Friction......Page 18
1.2.3 Imperfect Elasticity......Page 19
1.2.4 Inhomogeneous Bodies......Page 21
1.2.6 Wear Contact Problems......Page 22
2.1.1 Surface Macro- and Micro- Geometry......Page 24
2.1.2 Problem Formulation......Page 25
2.1.3 Previous Studies......Page 26
2.2.1 One-Level Model......Page 28
2.2.2 Principle of Localization......Page 31
2.2.3 System of Indenters of Various Heights......Page 34
2.2.4 Stress Field Analysis......Page 36
2.3.1 Problem Formulation......Page 43
2.3.2 A System of Cylindrical Punches......Page 47
2.3.3 A System of Spherical Punches......Page 53
2.4.1 The Function Definition......Page 55
2.4.2 Some Particular Cases......Page 58
2.4.3 Properties of the Function......Page 60
2.5.1 The Problem of Continuous Contact......Page 62
2.5.2 Plane Contact Problem......Page 63
2.5.3 Axisymmetric Contact Problem......Page 68
2.5.4 Characteristics of the Discrete Contact......Page 69
3.1 Mechanism of Friction......Page 74
3.2.1 Problem Formulation......Page 76
3.2.2 Contact Problem for a Cylinder......Page 78
3.2.3 Contact Problem for a Flat Punch......Page 81
3.3.1 The Friction Law Has the Form {tau(xz) = µ*p}......Page 86
3.3.2 The Friction Law Has the Form {tau(xz) = tau(0) + µ*p}......Page 90
3.4 Sliding Contact of Viscoelastic Bodies......Page 92
3.4.1 Constitutive Equations for the Viscoelastic Body......Page 93
3.4.2 Problem Formulation......Page 94
3.4.3 Analytical Results......Page 95
3.4.4 Some Special Cases......Page 97
3.5.1 Problem Formulation......Page 100
3.5.2 Solution......Page 101
3.5.4 Rolling Friction Analysis......Page 104
3.5.5 Some Special Cases......Page 107
3.6 Mechanical Component of Friction Force......Page 108
4.1 Bodies with Internal Defects......Page 114
4.1.1 Boundary Problem for Elastic Bodies with an Internal System of Defects......Page 115
4.1.2 The Tensor of Influence......Page 116
4.1.3 The Auxiliary Problem......Page 118
4.1.4 A Special Case of a System of Defects......Page 119
4.1.5 Half-Plane Weakened by a System of Defects......Page 120
4.1.6 Influence of Defects on Contact Characteristics and Internal Stresses......Page 122
4.2 Coated Elastic Bodies......Page 123
4.2.1 Periodic Contact Problem......Page 125
4.2.2 Method of Solution......Page 126
4.2.3 The Analysis of Contact Characteristics and Internal Stresses......Page 130
4.3 Viscoelastic Layered Elastic Bodies......Page 135
4.3.1 Model of the Contact......Page 136
4.3.2 Normal Stress Analysis......Page 138
4.3.3 Tangential Stress Analysis......Page 141
4.3.4 Rolling Friction Analysis......Page 144
4.3.5 The Effect of Viscoelastic Layer in Sliding and Rolling Contact......Page 145
5.1.1 Wear and Its Causes......Page 151
5.1.2 Active Layer......Page 152
5.1.3 Types of Wear in Sliding Contact......Page 154
5.1.5 Detached and Loose Particles......Page 155
5.2.1 The Main Stages in Wear Modeling......Page 156
5.2.2 Fatigue Wear......Page 157
5.3.1 The Model Formulation......Page 158
5.3.2 Surface Wear Rate......Page 159
5.3.3 Wear Kinetics in the Case {q(z,P) = K*tau(N,max)}, P = const......Page 161
5.3.4 Influence of the Load Variations P(t) on Wear Kinetics......Page 163
5.3.5 Steady-State Stage Characteristics......Page 168
5.3.6 Experimental Determination of the Frictional Fatigue Parameters......Page 169
5.4 Fatigue Wear of Rough Surfaces......Page 170
5.4.1 The Calculation of Damage Accumulation on the Basis of a Thermokinetic Model......Page 171
5.4.2 Particle Detachment......Page 174
5.4.3 The Analysis of the Model......Page 177
6.1.1 Characteristics of the Wear Process......Page 179
6.1.2 Experimental and Theoretical Study of the Wear Characteristics......Page 181
6.2.1 The Relation between Elastic Displacement and Contact Pressure......Page 186
6.2.2 Contact Condition......Page 187
6.3.1 Steady-State Wear for the Problems of Type A......Page 189
6.3.2 Asymptotic Stability of the Steady-State Solution......Page 190
6.4.1 Problem Formulation......Page 192
6.4.2 Solution......Page 194
6.5.1 Problem Formulation......Page 198
6.5.2 Axisymmetric Contact Problem......Page 200
6.5.3 The Case V(x,y) = V{(infinity)}......Page 207
6.6.1 The Wear of an Elastic Half-Space by a Punch Moving Translationally......Page 209
6.6.2 Wear of a Half-Plane by a Disk Executing Translational and Rotational Motion......Page 213
6.7 Wear of a Thin Elastic Layer......Page 216
6.7.1 Problem Formulation......Page 217
6.7.3 Calculation Techniques and Numerical Results......Page 220
6.8.1 Problem Formulation......Page 222
6.8.2 The Cases of Increasing, Decreasing and Constant Contact Region......Page 223
7.1.1 Problem Formulation......Page 226
7.1.2 Steady-State Wear Stage for the Surface Hardened Inside Strips......Page 229
7.1.3 Steady-State Wear Stage for a Surface Hardened Inside Circles......Page 235
7.1.4 The Shape of the Worn Surface of an Annular Punch for Various Arrangements of Hardened Domains......Page 238
7.2.1 Mathematical Model......Page 242
7.2.2 Model Analysis......Page 243
7.2.3 Running-in Stage of Wear Process......Page 246
7.2.4 Steady-State Stage of Wear Process......Page 248
7.2.5 Model of Equilibrium Roughness Formation......Page 251
7.2.6 Complex Model of Wear of a Rough Surface......Page 253
7.3.1 Problem Formulation......Page 256
7.3.2 Hardened Surface with Variable Wear Coefficient......Page 258
7.3.3 Abrasive Tool Surface with Variable Inclusion Density......Page 260
8. Wear of Components......Page 263
8.1.1 Model Assumptions......Page 264
8.1.2 Problem Formulation......Page 265
8.1.3 Method of Solution......Page 267
8.1.4 Wear Kinetics......Page 268
8.1.5 Steady-State Stage of Wear Process......Page 270
8.2.1 Contact Problem Formulation......Page 272
8.2.2 The Main Integro-Differential Equation......Page 274
8.2.3 Method of Solution......Page 276
8.2.4 Contact Characteristics Analysis......Page 278
8.2.5 Wear Analysis......Page 280
8.3 Comparison of Two Types of Bearings......Page 283
8.4 Wheel/Rail Interaction......Page 285
8.4.1 Parameters and the Structure of the Model......Page 286
8.4.2 Contact Characteristics Analysis......Page 287
8.4.3 Wear Analysis......Page 290
8.4.4 Fatigue Damage Accumulation Process......Page 292
8.4.5 Analysis of the Results......Page 293
8.5 A Model for Tool Wear in Rock Cutting......Page 299
8.5.1 The Model Description......Page 300
8.5.2 Stationary Process without Chip Formation and Tool Wear......Page 304
8.5.3 Analysis of the Cutting Process......Page 305
8.5.4 Influence of Tool Wear on the Cutting Process......Page 308
9. Conclusion......Page 311
10. References......Page 313
B......Page 329
C......Page 330
E......Page 332
G......Page 333
L......Page 334
M......Page 335
R......Page 336
S......Page 337
V......Page 339
W......Page 340
Y......Page 341