Contents
About the Authors xvii
Second Edition Preface xix
Preface xxi
Introduction xxiii
Part I Lubrication Theory 1
1 Properties of Lubricants 3
1.1 Lubrication States 3
1.2 Density of Lubricant 5
1.3 Viscosity of Lubricant 7
1.3.1 Dynamic Viscosity and Kinematic
Viscosity 7
1.3.1.1 Dynamic Viscosity 7
1.3.1.2 Kinematic Viscosity 8
1.3.2 Relationship between Viscosity and
Temperature 9
1.3.2.1 Viscosity–Temperature Equations 9
1.3.2.2 ASTM Viscosity–Temperature Diagram
9
1.3.2.3 Viscosity Index 10
1.3.3 Relationship between Viscosity and
Pressure 10
1.3.3.1 Relationships between Viscosity,
Temperature and Pressure 11
1.4 Non-Newtonian Behaviors 12
1.4.1 Ree–Eyring Constitutive Equation 12
1.4.2 Visco-Plastic Constitutive Equation
13
1.4.3 Circular Constitutive Equation 13
1.4.4 Temperature-Dependent Constitutive
Equation 13
1.4.5 Visco-Elastic Constitutive Equation
14
1.4.6 Nonlinear Visco-Elastic Constitutive
Equation 14
1.4.7 A Simple Visco-Elastic Constitutive
Equation 15
1.4.7.1 Pseudoplasticity 16
1.4.7.2 Thixotropy 16
1.5 Wettability of Lubricants 16
1.5.1 Wetting and Contact Angle 17
1.5.2 Surface Tension 17
1.6 Measurement and Conversion of Viscosity
19
1.6.1 Rotary Viscometer 19
1.6.2 Off-Body Viscometer 19
1.6.3 Capillary Viscometer 19
References 21
2 Basic Theories of Hydrodynamic
Lubrication 22
2.1 Reynolds Equation 22
2.1.1 Basic Assumptions 22
2.1.2 Derivation of the Reynolds Equation
23
2.1.2.1 Force Balance 23
2.1.2.2 General Reynolds Equation 25
2.2 Hydrodynamic Lubrication 26
2.2.1 Mechanism of Hydrodynamic Lubrication
26
2.2.2 Boundary Conditions and Initial
Conditions of the Reynolds Equation 27
2.2.2.1 Boundary Conditions 27
2.2.2.2 Initial Conditions 28
2.2.3 Calculation of Hydrodynamic
Lubrication 28
2.2.3.1 Load-Carrying CapacityW 28
2.2.3.2 Friction ForceF 28
2.2.3.3 Lubricant FlowQ 29
2.3 Elastic Contact Problems 29
2.3.1 Line Contact 29
2.3.1.1 Geometry and Elasticity Simulations
29
2.3.1.2 Contact Area and Stress 30
2.3.2 Point Contact 31
2.3.2.1 Geometric Relationship 31
2.3.2.2 Contact Area and Stress 32
2.4 Entrance Analysis of EHL 34
2.4.1 Elastic Deformation of Line Contacts
35
2.4.2 Reynolds Equation Considering the
Effect of Pressure-Viscosity 35
2.4.3 Discussion 36
2.4.4 Grubin FilmThickness Formula 37
2.5 Grease Lubrication 38
References 40
3 Numerical Methods of Lubrication
Calculation 41
3.1 Numerical Methods of Lubrication 42
3.1.1 Finite Difference Method 42
3.1.1.1 Hydrostatic Lubrication 44
3.1.1.2 Hydrodynamic Lubrication 44
3.1.2 Finite Element Method and Boundary
Element Method 48
3.1.2.1 Finite Element Method (FEM) 48
3.1.2.2 Boundary Element Method 49
3.1.3 Numerical Techniques 51
3.1.3.1 Parameter Transformation 51
3.1.3.2 Numerical Integration 51
3.1.3.3 Empirical Formula 53
3.1.3.4 SuddenThickness Change 53
3.2 Numerical Solution of the Energy
Equation 54
3.2.1 Conduction and Convection of Heat 55
3.2.1.1 Conduction Heat Hd 55
3.2.1.2 Convection Heat Hv 55
3.2.2 Energy Equation 56
3.2.3 Numerical Solution of Energy Equation
59
3.3 Numerical Solution of
Elastohydrodynamic Lubrication 60
3.3.1 EHL Numerical Solution of Line
Contacts 60
3.3.1.1 Basic Equations 60
3.3.1.2 Solution of the Reynolds Equation
62
3.3.1.3 Calculation of Elastic Deformation
62
3.3.1.4 Dowson–Higginson FilmThickness
Formula of Line Contact EHL 64
3.3.2 EHL Numerical Solution of Point
Contacts 64
3.3.2.1 The Reynolds Equation 65
3.3.2.2 Elastic Deformation Equation 66
3.3.2.3 Hamrock–Dowson FilmThickness
Formula of Point Contact EHL 66
3.4 Multi-Grid Method for Solving EHL
Problems 68
3.4.1 Basic Principles of Multi-Grid Method
68
3.4.1.1 Grid Structure 68
3.4.1.2 Discrete Equation 68
3.4.1.3 Transformation 69
3.4.2 Nonlinear Full Approximation Scheme
for the Multi-Grid Method 69
3.4.3 V andWIterations 71
3.4.4 Multi-Grid Solution of EHL Problems
71
3.4.4.1 Iteration Methods 71
3.4.4.2 Iterative Division 72
3.4.4.3 Relaxation Factors 73
3.4.4.4 Numbers of Iteration Times 73
3.4.5 Multi-Grid Integration Method 73
3.4.5.1 Transfer Pressure Downwards 74
3.4.5.2 Transfer Integral Coefficients
Downwards 74
3.4.5.3 Integration on the Coarser Mesh 74
3.4.5.4 Transfer Back Integration Results
75
3.4.5.5 Modification on the Finer Mesh 75
References 76
4 Lubrication Design of Typical Mechanical
Elements 78
4.1 Slider and Thrust Bearings 78
4.1.1 Basic Equations 78
4.1.1.1 Reynolds Equation 78
4.1.1.2 Boundary Conditions 78
4.1.1.3 Continuous Conditions 79
4.1.2 Solutions of Slider Lubrication 79
4.2 Journal Bearings 81
4.2.1 Axis Position and Clearance Shape 81
4.2.2 Infinitely Narrow Bearings 82
4.2.2.1 Load-Carrying Capacity 83
4.2.2.2 Deviation Angle and Axis Track 83
4.2.2.3 Flow 84
4.2.2.4 Frictional Force and Friction
Coefficient 84
4.2.3 InfinitelyWide Bearings 85
4.3 Hydrostatic Bearings 88
4.3.1 Hydrostatic Thrust Plate 89
4.3.2 Hydrostatic Journal Bearings 90
4.3.3 Bearing Stiffness andThrottle 90
4.3.3.1 Constant Flow Pump 91
4.3.3.2 Capillary Throttle 91
4.3.3.3 Thin-Walled OrificeThrottle 92
4.4 Squeeze Bearings 92
4.4.1 Rectangular Plate Squeeze 93
4.4.2 Disc Squeeze 94
4.4.3 Journal Bearing Squeeze 94
4.5 Dynamic Bearings 96
4.5.1 Reynolds Equation of Dynamic Journal
Bearings 96
4.5.2 Simple Dynamic Bearing Calculation 98
4.5.2.1 A Sudden Load 98
4.5.2.2 Rotating Load 99
4.5.3 General Dynamic Bearings 100
4.5.3.1 Infinitely Narrow Bearings 100
4.5.3.2 Superimposition Method of Pressures
101
4.5.3.3 Superimposition Method of Carrying
Loads 101
4.6 Gas Lubrication Bearings 102
4.6.1 Basic Equations of Gas Lubrication
102
4.6.2 Types of Gas Lubrication Bearings 103
4.7 Rolling Contact Bearings 106
4.7.1 Equivalent Radius R 107
4.7.2 Average Velocity U 107
4.7.3 Carrying Load PerWidthW/b 107
4.8 Gear Lubrication 108
4.8.1 Involute Gear Transmission 109
4.8.1.1 Equivalent Curvature Radius R 110
4.8.1.2 Average Velocity U 111
4.8.1.3 Load PerWidthW/b 112
4.8.2 Arc Gear Transmission EHL 112
4.9 Cam Lubrication 114
References 116
5 Special Fluid Medium Lubrication 118
5.1 Magnetic Hydrodynamic Lubrication 118
5.1.1 Composition and Classification of
Magnetic Fluids 118
5.1.2 Properties of Magnetic Fluids 119
5.1.2.1 Density of Magnetic Fluids 119
5.1.2.2 Viscosity of Magnetic Fluids 119
5.1.2.3 Magnetization Strength of Magnetic
Fluids 120
5.1.2.4 Stability of Magnetic Fluids 120
5.1.3 Basic Equations of Magnetic
Hydrodynamic Lubrication 121
5.1.4 Influence Factors on Magnetic EHL 123
5.2 Micro-Polar Hydrodynamic Lubrication
124
5.2.1 Basic Equations of Micro-Polar Fluid
Lubrication 124
5.2.1.1 Basic Equations of Micro-Polar Fluid
Mechanics 124
5.2.1.2 Reynolds Equation of Micro-Polar
Fluid 125
5.2.2 Influence Factors on Micro-Polar
Fluid Lubrication 128
5.2.2.1 Influence of Load 128
5.2.2.2 Main Influence Parameters of
Micro-Polar Fluid 129
5.3 Liquid Crystal Lubrication 130
5.3.1 Types of Liquid Crystal 130
5.3.1.1 Tribological Properties of
Lyotropic Liquid Crystal 131
5.3.1.2 Tribological Properties
ofThermotropic Liquid Crystal 131
5.3.2 Deformation Analysis of Liquid
Crystal Lubrication 132
5.3.3 Friction Mechanism of Liquid Crystal
as a Lubricant Additive 136
5.3.3.1 Tribological Mechanism of
4-pentyl-4′-cyanobiphenyl 136
5.3.3.2 Tribological Mechanism of
Cholesteryl Oleyl Carbonate 136
5.4 Electric Double Layer Effect inWater
Lubrication 137
5.4.1 Electric Double Layer Hydrodynamic
Lubrication Theory 138
5.4.1.1 Electric Double Layer Structure 138
5.4.1.2 Hydrodynamic Lubrication Theory of
Electric Double Layer 138
5.4.2 Influence of Electric Double Layer on
Lubrication Properties 142
5.4.2.1 Pressure Distribution 142
5.4.2.2 Load-Carrying Capacity 143
5.4.2.3 Friction Coefficient 144
5.4.2.4 An Example 144
References 145
6 Lubrication Transformation and Nanoscale
Thin Film Lubrication 147
6.1 Transformations of Lubrication States
147
6.1.1 Thickness-Roughness Ratio ? 147
6.1.2 Transformation from Hydrodynamic
Lubrication to EHL 148
6.1.3 Transformation from EHL to Thin Film
Lubrication 149
6.2 Thin Film Lubrication 152
6.2.1 Phenomenon ofThin Film Lubrication
153
6.2.2 Time Effect of Thin Film Lubrication
154
6.2.3 Shear Strain Rate Effect onThin Film
Lubrication 157
6.3 Analysis ofThin Film Lubrication 158
6.3.1 Difficulties in Numerical Analysis of
Thin Film Lubrication 158
6.3.2 Tichy’s Thin Film Lubrication Models
160
6.3.2.1 Direction Factor Model 160
6.3.2.2 Surface Layer Model 161
6.3.2.3 Porous Surface Layer Model 161
6.4 Nano-Gas Film Lubrication 161
6.4.1 Rarefied Gas Effect 162
6.4.2 Boundary Slip 163
6.4.2.1 Slip Flow 163
6.4.2.2 Slip Models 163
6.4.2.3 Boltzmann Equation for Rarefied Gas
Lubrication 165
6.4.3 Reynolds Equation Considering the
Rarefied Gas Effect 165
6.4.4 Calculation of Magnetic Head/Disk of
UltraThin Gas Lubrication 166
6.4.4.1 Large Bearing Number Problem 167
6.4.4.2 Sudden Step Change Problem 167
6.4.4.3 Solution of Ultra-Thin Gas
Lubrication of Multi-Track Magnetic Heads 167
References 169
