摩擦学中的接触力学 扫描版

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中文名: 摩擦学中的接触力学

原名: Contact Mechanics in Tribology

作者: I. G. GORYACHEVA

图书分类: 科技

资源格式: PDF

版本: 扫描版

出版社: I. G. GORYACHEVA

书号: ISBN 0-7923-5257-2

发行时间: 1998年01月01日

简介: 

目录:

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
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

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