Friction-induced vibrations and self-organization : mechanics and non-equilibrium thermodynamics of sliding contact / Michael Nosonovsky, Vahid Mortazavi.

Format:

Book

Author/Creator:

Nosonovsky, Michael.

Contributor:

Mortazavi, Vahid.

Emma Louise McClellan Fund.

Language:

English

Subjects (All):

Nonequilibrium thermodynamics.

Sliding friction.

Vibration.

Physical Description:

xiv, 313 pages : illustrations ; 24 cm

Place of Publication:

Boca Raton : CRC Press, Taylor & Francis Group, 2013.

Summary:

"Friction induced instabilities can lead to vibrations, which are often undesirable (e.g., car brake squeal). On the other hand, they may be useful (e.g., music sound generation). New materials capable to resist wear and heal minor damage (self-healing) in themselves can be developed if the ability for self-organization is embedded into the material. This book emphasizes thermodynamic analysis of friction-induced instabilities, vibrations, and self-organization as well as fundamental properties of friction and wear related to these"-- Provided by publisher.

"This book is different from numerous other textbooks and monographs about friction. In this work we study various effects and manifestations of friction in order to identify those properties of friction that are invariant for different friction mechanisms and thus constitute the very essence of friction as a physical phenomenon. By doing that we are making the case that friction is a fundamental force of nature whose properties can be deduced directly from the second law of thermodynamics, rather than treated as a collection of phenomenological unrelated effects and empirical facts"-- Provided by publisher.

Contents:

1 Introduction: Friction as a Fundamental Force of Nature in the History of Mechanics 1

1.1 Historical Background 1

1.2 Certain Philosophical Concepts of Mechanics 9

1.2.1 Discrete versus Continuum 9

1.2.2 Rest versus Motion 9

1.2.3 Terrestrial versus Celestial Motion 10

1.2.4 Translational versus Rotational Motion 10

1.2.5 Empty versus Occupied Space 11

1.2.6 What Is Force? 11

1.2.7 The Law of Identity 11

1.3 Hilbert's Sixth Problem 12

1.4 Noll's Axiomatic Mechanics 14

1.4.1 The Laws of Mechanics 15

1.4.2 Space and Frame of Reference 15

1.4.3 Forces 16

1.4.4 Logic and Mathematical Notation 17

1.5 P. Zhilin's Approach 17

1.5.1 Time, Space, and Coordinates 17

1.5.2 Fundamental Laws as Definitions 18

1.5.3 Force versus Torque; Linear versus Rotational Motion 19

1.5.4 Thermodynamic Quantities: Temperature and Entropy 20

1.6 The Study of Friction 20

1.7 Summary 22

References 22

2 Vibrations and Stability at the Bulk and at the Interface 25

2.1 Linear Vibrations in Systems with Single, Multiple, and Infinite Number of Degrees of Freedom 25

2.2 Stability Analysis 28

2.3 Non-Linear Vibration and Stability Analysis 32

2.4 Bifurcations, Catastrophes, and Chaos 35

2.5 Multi-Scale Systems 36

2.6 Self-Organization: Different Types 40

2.7 Example: Benard Cells 43

2.8 Self-Organization in Tribology 45

2.9 Asymptotic Transition from a 3D (Bulk) to a 2D (Interface) System 47

2.10 Summary 49

References 50

3 Principles of Non-Equilibrium Thermodynamics and Friction 53

3.1 Thermodynamic Potentials and Equations 53

3.2 Irreversible Processes and Non-Equilibrium 59

3.3 Extremal Principles and Stability of Frictional Motion 63

3.4 Stability Criterion for Frictional Sliding 65

3.4.1 Stability Criterion for the Stationary Regime δ²S > 0 65

3.4.2 Instabilities during Velocity-Dependent Friction 67

3.4.3 Friction-Induced Instabilities in Deformable Bodies 67

3.4.4 Instability during Friction Heat Conduction 68

3.4.5 Diffusion, Mass Transfer, and Wear during Friction 70

3.4.6 Tribochemical Reactions 71

3.4.7 Electrical Contact and Other Effects 71

3.5 Summary 74

References 75

Bibliography 76

4 Fundamentals of Friction 79

4.1 Empirical Laws of Friction 79

4.2 Mechanisms of Friction 82

4.2.1 Adhesive Friction and Surface Roughness 83

4.2.1.1 Adhesive Contact 83

4.2.1.2 Greenwood-Williamson Approach to Surface Roughness 83

4.2.1.3 Statistical Models of Contact of Rough Surfaces 85

4.2.1.4 Fractal and Hierarchical Roughness 88

4.2.1.5 Adhesion Hysteresis and Dissipation 89

4.2.2 Deformation of Asperities 89

4.2.3 Plastic Yield 91

4.2.4 Fracture 91

4.2.5 Ratchet and Cobblestone Mechanisms 92

4.2.6 "Third Body" Mechanism 92

4.2.7 Note on the Linearity of the Amontons-Coulomb Law 92

4.2.8 Linearity and the "Small Parameter" 94

4.3 Non-Linear Character of Friction 95

4.3.1 Friction and Reduction of Degrees of Freedom 96

4.3.2 Stick-Slip Friction Phases 96

4.3.3 Running-in and "Shakedown" 97

4.3.4 Dynamic Friction: State-and-Rate Models 98

4.3.5 Modeling Dynamic Friction for Control 99

4.3.6 Atomic Friction and Kinetics 102

4.3.7 Paradoxes: Is Friction Compatible with Elasticity? 104

4.3.8 Friction and Fracture: The Role of Heterogeneity 104

4.4 Thermodynamics of Friction 107

4.5 Summary 111

References 112

5 Wear and Lubrication 117

5.1 Mechanisms of Wear 117

5.2 Empirical Laws of Wear 120

5.3 Thermodynamics of Wear: Entropy Generation and Degradation 121

5.4 Lubricated Contact 124

5.5 Summary 125

References 125

Bibliography 126

6 Friction-Induced Instabilities and Vibrations 129

6.1 Mechanics of Elastic Contact and Stability of Frictional Sliding 129

6.1.1 Static Problems of Contact Mechanics 129

6.1.2 Elastodynamic Problems 133

6.1.3 Elastodynamics with Friction: Paradoxes and Instabilities 137

6.2 Velocity Dependency of Coefficient of Friction and Stability Criterion 139

6.3 Thermoelastic Instabilities 142

6.3.1 Barber's Experiment 143

6.3.2 Extension of Barber's Work 145

6.3.3 TEI in a Generalized System with Liquid Lubricant 148

6.3.4 Sliding Thermoelastodynamic Instability 149

6.4 Adams-Martins Instabilities 151

6.4.1 Stability Analysis 151

6.4.2 Adams's Simple Dynamic Model of a Beam on an Elastic Foundation 161

6.4.3 Dynamic Instabilities during Sliding of Rough Surfaces 166

6.4.3.1 Formulation of the Problem 166

6.4.3.2 The Steady-State Solution 168

6.4.3.3 Steady State: Analytical Solution 170

6.4.3.4 Steady State: Results and Discussion 175

6.4.3.5 Small Vibrations near the Steady-State Solution 175

6.4.3.6 Formulation in Integral Equation Form 178

6.4.3.7 Special Solutions for Limiting and Resonance Cases 184

6.4.3.8 Numerical Analysis of the Integral Equation 186

6.4.3.9 Discussion 189

6.4.4 Ill Posedness and Regularization 190

6.5 Radiation of Elastic Waves by Friction 192

6.5.1 Formulation of the Problem 194

6.5.2 Steady Sliding with Radiated Waves 196

6.5.3 A Slip Pulse 199

6.5.4 Discussion 200

6.6 Interaction of Elastic Waves with Friction 201

6.6.1 Incoming Dilatational Wave 202

6.6.2 Incoming Shear Wave 205

6.6.3 Discussion 207

6.7 Friction Reduction and Self-Organized Patterns due to Friction-Induced Vibrations 207

6.8 Summary 208

References 208

Bibliography 213

7 Friction-Induced Vibrations and Their Applications 215

7.1 Brakes and Vehicles 215

7.2 Music and Sound Generation 219

7.3 Nature 220

7.4 Summary 221

References 222

8 From Frictional Instabilities to Friction-Induced Self-Organization 225

8.1 Self-Organization, Instabilities, and Friction 225

8.2 Stability of Frictional Sliding with Coefficient of Friction Dependent on Temperature 229

8.2.1 Introduction 229

8.2.2 Mathematical Modeling 230

8.2.3 Reproducibility of Disk Brake Test Results 236

8.2.3.1 Numerical Model 236

8.2.3.2 Stability Analysis 239

8.2.4 Results and Discussion 241

8.3 Running-In as a Self-Organized Process 245

8.3.1 Introduction 245

8.3.2 Shannon Entropy as a Characteristic of a Rough Surface 246

8.3.3 Thermodynamic Model for Surface Roughness Kinetics 248

8.3.4 Experimental Study 251

8.3.5 Results 252

8.3.6 Discussion 256

8.4 Frictional Turing Systems 256

8.4.1 Introduction 256

8.4.2 Turing Systems and Self-Organization 257

8.4.3 Numerical Simulation of Frictional Turing Systems 258

8.4.4 Results 260

8.4.5 Discussion 266

8.5 Modeling of the Formation of Tribofilms 269

8.5.1 Introduction 269

8.5.2 Criterion for Self-Organization 270

8.5.3 Formation of a Tribofilm 271

8.5.4 A Cellular Potts Model for Formation of a Tribofilm 273

8.5.4.1 Cellular Potts Modeling 273

8.5.4.2 Simulation and Results 275

8.5.5 Discussion 280

8.6 Stick-Slip Motion and Self-Organization 280

8.6.1 Introduction 280

8.6.2 Self-Organized Criticality and Stick-Slip Motion 281

8.6.3 Different Models of Stick-Slip Motion 282

8.7 Summary 285

References 285

9 Self-Lubrication 291

9.1 Principles of Self-Healing and Self-Lubricating Materials 291

9.2 Various Approaches to Self-Lubrication 294

9.3 Summary 300

References 301

10 Outlook 305.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Emma Louise McClellan Fund.

ISBN:

1466504013

9781466504011

OCLC:

754730214

Publisher Number:

99956201964