Contact Mechanics and Friction (eBook)

Preface to the English Edition 8
Preface to the German Edition 10
Table of Contents 12
1 Introduction 17
1.1 Contact and Friction Phenomena and their Applications 17
1.2 History of Contact Mechanics and the Physics of Friction 19
1.3 Structure of the Book 23
2 Qualitative Treatment of Contact Problems – Normal Contact without Adhesion 24
2.1 Material Properties 25
2.2 Simple Contact Problems 28
2.3 Estimation Method for Contacts with a Three-Dimensional, Elastic Continuum 31
3 Qualitative Treatment of Adhesive Contacts 39
4 Capillary Forces 55
4.1 Surface Tension and Contact Angles 55
4.2 Hysteresis of Contact Angles 59
4.3 Pressure and the Radius of Curvature 59
4.4 Capillary Bridges 60
4.5 Capillary Force between a Rigid Plane and a Rigid Sphere 61
4.6 Liquids on Rough Surfaces 62
4.7 Capillary Forces and Tribology 63
Problems 64
5 Rigorous Treatment of Contact Problems – Hertzian Contact 69
5.1 Deformation of an Elastic Half-Space being Acted upon by Surface Forces 70
5.2 Hertzian Contact Theory 73
5.3 Contact between Two Elastic Bodies with Curved Surfaces 74
5.4 Contact between a Rigid Cone-Shaped Indenter and an Elastic Half- Space Space Space 77
5.5 Internal Stresses in Hertzian Contacts 78
Problems 81
6 Rigorous Treatment of Contact Problems – Adhesive Contact 85
7 Contact between Rough Surfaces 94
7.1 Model from Greenwood and Williamson 95
7.2 Plastic Deformation of Asperities Asperities Asperities 101
7.3 Electrical Contacts 102
7.4 Thermal Contacts 105
7.5 Mechanical Stiffness of Contacts 106
7.6 Seals 106
7.7 Roughness and Adhesion 107
Problems Problems Problems 108
8 Tangential Contact Problems 117
8.1 Deformation of an Elastic Half-Space being Acted upon by Tangential Forces 118
8.2 Deformation of an Elastic Half-Space being Acted upon by a Tangential Stress Distribution Distribution Distribution 119
8.3 Tangential Contact Problems without Slip Slip Slip 121
8.4 Tangential Contact Problems Accounting for Slip 122
8.5 Absence of Slip for a Rigid Cylindrical Indenter Indenter Indenter Indenter 126
Problems 126
9 Rolling Contact 130
9.1 Qualitative Discussion of the Processes in a Rolling Contact 131
9.2 Stress Distribution in a Stationary Rolling Contact 133
Problems 139
10 Coulomb’s Law of Friction 144
10.1 Introduction 144
10.2 Static and Kinetic Friction 145
10.3 Angle of Friction 146
10.4 Dependence of the Coefficient of Friction on the Contact Time3 147
10.5 Dependence of the Coefficient of Friction on the Normal Force 148
10.6 Dependence of the Coefficient of Friction on Sliding Speed5 150
10.7 Dependence of the Coefficient of Friction on the Surface Roughness 150
10.8 Coulomb’s View on the Origin of the Law of Friction 151
10.9 Theory of Bowden and Tabor 153
10.10 Dependence of the Coefficient of Friction on Temperature 156
Problems 157
11 The Prandtl-Tomlinson Model for Dry Friction 166
11.1 Introduction 166
11.2 Basic Properties of the Prandtl-Tomlinson Model 168
11.3 Elastic Instability 172
11.4 Superlubricity 176
11.5 Nanomachines: Concepts for Micro and Nano-Actuators 177
Problems 181
12 Frictionally Induced Vibrations 186
12.1 Frictional Instabilities at Decreasing Dependence of the Frictional Force on the Velocity 187
12.2 Instability in a System with Distributed Elasticity 189
12.3 Critical Damping and Optimal Suppression of Squeal 192
12.4 Active Suppression of Squeal 194
12.5 Strength Aspects during Squeal 196
12.6 Dependence of the Stability Criteria on the Stiffness of the System 197
12.7 Sprag-Slip 202
Problems 204
13 Thermal Effects in Contacts 209
13.1 Introduction 210
13.2 Flash Temperatures in Micro-Contacts 210
13.3 Thermo-Mechanical Instability 212
Problems 213
14 Lubricated Systems 216
14.1 Flow between two parallel plates 217
14.2 Hydrodynamic Lubrication 218
14.3 “Viscous Adhesion” 222
14.4 Rheology of Lubricants 225
14.5 Boundary Layer Lubrication 227
14.6 Elastohydrodynamics Elastohydrodynamics Elastohydrodynamics 228
14.7 Solid Lubricants 231
Problems 232
15 Viscoelastic Properties of Elastomers 239
15.1 Introduction 239
15.2 Stress-Relaxation 240
15.3 Complex, Frequency-Dependent Shear Moduli Moduli 242
15.4 Properties of Complex Moduli 244
15.5 Energy Dissipation in a Viscoelastic Material 245
15.6 Measuring Complex Moduli 246
15.7 Rheological Models 247
15.8 A Simple Rheological Model for Rubber (“Standard Model”) 250
15.9 Influence of Temperature on Rheological Properties Properties Properties 252
15.10 Master Curves 253
15.11 Prony Series 254
Problems Problems 258
16 Rubber Friction and Contact Mechanics of Rubber 262
16.1 Friction between an Elastomer and a Rigid Rough Surface 262
16.2 Rolling Resistance 268
16.3 Adhesive Contact with Elastomers 270
Problems 272
17 Wear 278
17.1 Introduction 278
17.2 Abrasive Wear 279
17.3 Adhesive Wear 282
17.4 Conditions for Low-Wear Friction 285
17.5 Wear as the Transportation of Material from the Friction Zone 286
17.6 Wear of Elastomers 287
Problems 290
18 Friction Under the Influence of Ultrasonic Vibrations 292
18.1 Influence of Ultrasonic Vibrations on Friction from a Macroscopic Point of View 293
18.2 Influence of Ultrasonic Vibrations on Friction from a Microscopic Point of View 298
18.3 Experimental Investigations of the Force of Static Friction as a Function of the Oscillation Amplitude 300
18.4 Experimental Investigations of Kinetic Friction as a Function of Oscillation Amplitude 302
Problems 304
19 Numerical Simulation Methods in Friction Physics 307
19.1 Simulation Methods for Contact and Frictional Problems: An Overview 19.1.1 Many- Body Systems 308
19.1.2 Finite Element Methods 309
19.1.3 Boundary Element Method 310
19.1.4 Particle Methods 311
19.2 Reduction of Contact Problems from Three Dimensions to One Dimension 312
19.3 Contact in a Macroscopic Tribological System 313
19.4 Reduction Method for a Multi-Contact Problem 317
19.5 Dimension Reduction and Viscoelastic Properties 321
19.6 Representation of Stress in the Reduction Model 322
19.7 The Calculation Procedure in the Framework of the Reduction Method 323
19.8 Adhesion, Lubrication, Cavitation, and Plastic Deformations in the Framework of the Reduction Method 324
Problems 324
20 Earthquakes and Friction 329
20.1 Introduction 330
20.2 Quantification of Earthquakes 331
20.2.1 Gutenberg-Richter Law 332
20.3 Laws of Friction for Rocks 333
20.4 Stability during Sliding with Rate- and State-Dependent Friction 337
20.5 Nucleation of Earthquakes and Post-Sliding 340
20.6 Foreshocks and Aftershocks 343
20.7 Continuum Mechanics of Block Media and the Structure of Faults 344
20.8 Is it Possible to Predict Earthquakes? 348
Problems 349
Appendix Appendix Appendix 352
Further Reading 356
Figure Reference 362
Index 364