Interfacial Mechanics-Theories and Methods for Contact and Lubrication

Chapter 1 Introduction 
1.1. Significance of the Topics 
1.2. Tribological Interface Systems 
Interface Systems Defined Based on Geometry 
Interface Systems Defined Based on Relative Motion 
Interface Systems Defined Based on Lubricating Media 
Interface Systems Defined Based on Lubrication Status 
1.3. Brief Historic Review 
1.3.1. Empirical Knowledge Accumulated in Early Years 
1.3.2. Pioneering Studies
1.3.3. Establishment of Contact Mechanics and Lubrication Theory 
1.3.4. Rapid Development Assisted by Digital Computers 
1.3.5. Recent Advancements 
1.3.6. Conclusion Remarks 
1.4. Interfacial Mechanics 
1.5. Coverage of This Book 
Chapter 2 Properties of Engineering Materials and Surfaces 
Mechanical Properties of Typical Solid Materials 
Topographic Properties of Engineering Surfaces 
Engineering Surfaces 
Surface Characterization by Statistic Parameters 
Surface Characterization by Direct Digitization 
Rough Surfaces Generated by Computer 
Lubricant Properties 
Viscosity 
Effect of Temperature on Viscosity 
Effect of Pressure on Viscosity 
Density 
Non-Newtonian Behaviors 
Additives in Lubricants 
Chapter 3 Fundamentals of Contact Mechanics
3.1. Introduction
3.2. Basic Half-Space Elasticity Theories 
3.2.1. Potential Equations 
3.2.2. Displacements Due to Normal Loading 
3.2.3. Displacements Due to Tangential Traction
3.2.4. General Equations for Surface Displacements
3.2.5. Subsurface Stresses 
3.3. Line Contact Hertzian Theory
3.3.1. Basic Model 
3.3.2. Contact Pressure and Surface Deformation 
3.3.3. Subsurface Stresses 
3.4. Point Contact Hertzian Theory 
3.4.1. Basic Model 
3.4.2. Contact Pressure and Surface Deformation 
3.4.3. Subsurface Stresses 
Contact Strength Analysis Based on the Subsurface Stress Field 
Theories for Yield Criteria 
3.5.2. Subsurface Stress Field and Yield Pressure in Line Contacts 
3.5.3. Subsurface Stress Field and Yield Pressure in Circular Contacts 
3.5.4. Subsurface Stress Field in Elliptical Contacts 
3.5.5. Effect of Friction on the Subsurface Stresses 
3.5.6. Contact Yield Initiation in a Case Hardened Solid 
3.5.6.1. Basic Model 
3.5.6.2. Solution for Circular Contacts 
3.5.6.3. Solution for Line Contacts 
3.5.6.4. General Expressions 
3.6. Selected Basic Solutions 
3.6.1. Displacements Due to Concentrated Forces 
3.6.2. Surface Displacements Induced by Uniform Pressure 
3.6.2.1. 2D Plane Strain Problems 
3.6.2.2. 3D Half-Space Problems 
3.6.3. Indentation by a Rigid Punch 
3.6.4. Frictionless Indentation by a Blunt Wedge or Cone 
3.6.5. A Sinusoidal Wavy Surface in Contact with a Flat 
3.6.5.1. 2D Wavy Surface 
3.6.5.2. 3D Wavy Surface 
3.7. Contact with Rough Surfaces 
3.7.1. A Stochastic Model for Rough Surface Contacts 
3.7.2. Empirical Formulae Based on Numerical Solutions for Rough Surface Contacts 
3.7.2.1. Empirical Formulae by Lee and Ren (1996) 
3.7.2.2. Empirical Formulae by Chen et al. (2007) 
3.8. Contact of Multilayer Materials 
3.8.1. Problem Description 
3.8.2. Fourier Transforms of the Governing and Boundary/Interfacial Equations 
3.8.3. Structures of B and AC Matrices 
3.8.3.1. B Matrix and B Matrix Equation 
3.8.3.2. AC Matrix and AC Matrix Equation 
3.8.4. Solutions of Matrix Equations 
3.8.5. Typical Sample Cases 
3.8.6. Solution for Problems with a Single Layer Coating 
3.8.7. Extended Hertzian Theories 
3.9. Closure
Chapter 4 Numerical Methods for Solving Contact Problems
4.1. Introduction
4.1.1. Background
4.1.2. FEM Approach
4.1.3. Stochastic Models
4.1.4. IC Matrix Approach
4.1.5. Quadratic Programming Approach and CGM 
4.1.6. Fast Fourier Transform (FFT) Approaches 
4.1.7. Discrete Convolution and Fast Fourier Transform (DC-FFT) Approach
4.1.8. Contact Problems with Inelastic and Inhomogeneous Materials 
4.2. Discretization with Influence Coefficients 
4.2.1. Basic Concept 
4.2.2. Influence Coefficients for 2D Half-Plane Problems 
4.2.2.1. ICs Based on Zero Order Approximation 
4.2.2.2. ICs Based on First Order Approximation 
4.2.2.3. ICs Based on Second Order Approximation 
4.2.3. Influence Coefficients for 3D Half-Space Problems 
4.2.3.1. ICs Based on Zero Order Approximation 
4.2.3.2. ICs Based on Bilinear Approximation 
4.2.3.3. ICs Based on Biquadratic Approximation 
4.3. Comparative Cases for Deformation Calculation 
4.3.1. Deformation Due to Indentation by a Rigid Punch 
4.3.2. Deformation Due to Cylindrical Contact Hertzian Pressure 
4.3.3. Deformation Due to Point Contact Hertzian Pressure 
4.4. Solution for Contact Pressure Distribution 
4.4.1. Problem Description 
4.4.2. Conjugate Gradient Method for Solving Contact Problems 
4.5. Numerical Examples 
4.6. FFT-Based Methods for Efficient Surface Deformation Calculation 
4.6.1. Background 
4.6.2. Three Types of Convolution 
4.6.3. DC-FFT Algorithm for Non-Periodic Contact Problems 
4.6.3.1. Cyclic Convolution and the DC-FFT Algorithm 
4.6.3.2. DC-FFT Procedure for Point Contacts 
4.6.3.3. Method Comparisons 
4.6.3.4. Numerical Examples 
4.6.4. Continuous Convolution and Fourier Transform (CC-FT) 
4.6.4.1. Description of the CC-FT Approach 
4.6.4.2. Validation and Sample Cases 
4.6.5. DCD-FFT, DCC-FFT, and DCS-FFT Approaches 
4.6.5.1. General Description 
4.6.5.2. DCD-FFT Algorithm 
4.6.5.3. DCC-FFT Algorithm 
4.6.5.4. DCS-FFT Algorithm 
4.7. Calculation of Subsurface Stresses 
4.7.1. General Equations 
4.7.2. Influence Coefficients 
4.7.3. DC-FFT Approach for Stress Calculation 
4.7.4. Additional Numerical Examples 
4.8. Closure 
Chapter 5 Fundamentals of Hydrodynamic Lubrication 
5.1. Introduction 
5.2. Reynolds Equation 
5.2.1. Derivation of Generalized Reynolds Equation 
5.2.2. Simplified Reynolds Equations 
5.2.3. Boundary Conditions for the Reynolds Equation 
5.2.4. Reynolds Equation for Non-Newtonian Lubricants 
5.2.5. Average Reynolds Equation 
5.3. Energy Equations 
5.3.1. Energy Equation for the Lubricant Film 
5.3.2. Heat Transfer Equations for Contacting Bodies 
5.3.3. Surface Temperature Equations 
5.4 Analytical Solutions for Simplified Bearing Problems 
5.4.1. General Description 
5.4.2. Infinitely Long Journal Bearings 
5.4.3. Infinitely Short Journal Bearings 
5.4.4. Infinitely Long Thrust Bearings 
5.5 Closure 
Chapter 6 Numerical Methods for Hydrodynamic Lubrication 
6.1. Finite Length Journal Bearings 
6.1.1. Finite Difference Method (FDM) 
6.1.2. Finite Element Method (FEM) 
6.2. Mixed Thermal Elastohydrodynamic Lubrication (TEHL) Analyses for Journal Bearings
6.2.1. Background 
6.2.2. Hydrodynamic Lubrication Model Considering Roughness Effect 
6.2.3. Asperity Contact Models 
6.2.4. Evaluation of Body Deformations 
6.2.5. Thermal Analysis 
Numerical Procedure 
Typical Sample Results 
Piston Skirts in Mixed Lubrication 
6.3.1. Equation of Motion 
6.3.2. Average Reynolds Equation 
6.3.3. Wavy Surface Contact Pressure 
6.3.4. Deformations of Piston Skirts and Cylinder Bore 
6.3.5. Numerical Procedure 
6.3.6. Typical Sample Results 
Closure 
Chapter 7 Lubrication in Counterformal Contacts – Elastohydrodynamic Lubrication (EHL) 
7.1. Introduction
7.2. Background and Early Studies 
7.2.1. Martin’s Theory (Isoviscous - Rigid)
7.2.2. Blok’s Theory (Piezoviscous - Rigid)
7.2.3. Herrebrugh’s Solution (Isoviscous - Elastic)
7.2.4. Grubin’s Inlet Analysis (Piezoviscous - Elastic)
7.2.5. First Full EHL Solution in Line Contacts by Petrusevich (1951)
7.2.6. Full EHL Solution in Line Contacts by Dowson-Higginson (1959)
7.2.7. First Full EHL Solution in Point Contacts by Ranger et al. (1975) 
7.2.8. Full EHL Solution in Point Contacts by Hamrock & Dowson (1976-77) 
7.2.9. Dimensionless Parameter Groups 
7.2.10. Maps of Lubrication Regimes 
7.3. EHL Numerical Solution Methods
7.3.1. Nonlinearity of EHL Equation Systems 
7.3.2. Straightforward Iterative Method
7.3.3. Inverse Solution 
7.3.4. System Analysis through the Newton-Raphson Procedure
7.3.5. Multi-Grid Method 
7.3.6. Coupled Differential Deflection Method 
7.3.7. Semi-System Approach 
7.3.7.1. Basic Concept 
7.3.7.2. Basic Formulation 
7.3.7.3. Discretization of the Pressure Flow Terms 
7.3.7.4. Discretization of the Entraining Flow Term 
7.3.7.5. Characteristics of the Coefficient Matrix 
7.3.7.6. Sample Mixed EHL Solutions from the Semi-System Approach 
7.3.8. Simulation of Contact by Using EHL Equation System 
7.3.9. Effect of Differential Schemes 
7.3.9.1. General 
7.3.9.2. Differential Schemes for Combined Entraining Flow Term 
7.3.9.3. Differential Schemes for Separate Entraining Flow Terms 
7.3.9.4. Effect of Differential Scheme Arrangement 
7.3.9.5. Schemes for Further Separated Entraining Flow Term 
7.3.9.6. Differential Schemes for Squeeze Flow Term 
7.3.10. Effect of Mesh Density 
7.3.10.1. Background 
7.3.10.2. Dependence of Film Thickness Solution on Mesh Density 
7.3.10.3. Reasonable Mesh Density to be Used in Practice 
7.3.10.4. Limitations of the MG Approach 
7.3.11. Progressive Mesh Densification (PMD) Method 
Experimental Validation of Numerical Solution 
EHL with Arbitrary Entrainment Angle 
7.5.1. Background 
7.5.2. Formulation and Numerical Method 
7.5.3. Typical Results for Validating the Model and Showing Basic Characteristics
7.5.4. Curve-Fitting Formula
7.5.5 Transition of Lubrication Condition with Roughness Considered
Treatments for Starvation and Cavitation 
7.6.1. Background 
7.6.2. Conventional Treatment 
7.6.2.1. Review of Early Studies 
7.6.2.2. Reexamination of the Empirical Formulae 
7.6.2.3. Application 
7.6.3. Updated Treatment Based on JFO and Elrod 
7.6.3.1. Basic Concept and Formulation 
7.6.3.2. Numerical Solution Method 
7.6.3.3. Typical Sample Solutions 
7.6.3.4. Comparison with Conventional Treatment 
Isothermal EHL Behaviors with Smooth Surfaces 
Background 
Entraining Speed Effect 
Load Effect 
Effect of Contact Ellipticity 
Effect of Materials Properties 
7.7.5.1. Effect of Different Viscosity Models 
7.7.5.2. Effect of Lubricant Piezoviscous Property 
7.7.5.3. Effect of Elastic Property of Solids 
7.8. Closure 
Chapter 8 Mixed Lubrication with Rough Surfaces
8.1. Introduction
8.1.1. Background 
8.1.2. Review of Stochastic Models 
8.1.3. Review of Deterministic Models 
8.1.4. Review of Combined Stochastic-Deterministic Approach 
8.1.5. Terminology 
8.2. Stochastic Approach 
8.3. Deterministic Approach for Artificial Roughness 
8.3.1. General 
8.3.2. Calculation Methods for Derivatives ∂H/∂X and ∂H/∂T 
8.3.3. Error Analysis 
8.3.4. Sample Validation Cases 
8.4. Deterministic Approach for Machined Roughness 
8.4.1. Problem Description 
8.4.2. Two Ways to Calculate ∂S/∂X and ∂S/∂T 
8.4.3. Accuracy Comparison Between Methods I+D and D+I 
8.4.4. Sample Rough Surface EHL Solutions 
8.5. Stability of Transient Solution 
8.5.1. Contribution to Coefficient Matrix by Squeeze Flow Term 
8.5.2. Initial Value Problem 
8.5.3. Effect of Time Step Length Employed 
8.5.4. Effect of Convergence Accuracy Requirement 
8.6. 3D Infinitely Long Line Contact Mixed EHL Solution 
8.6.1. Background 
8.6.2. Model Description 
8.6.3. Sample Cases with Smooth Surfaces for Model Verification 
8.6.4. Sample Cases with Machined Surface Roughness 
8.7. 3D Finite Roller Contact Mixed EHL Solution 
8.7.1. Introduction
8.7.2. Roller Contact Geometry
8.7.3. Typical Sample Cases
8.7.4. Simulation of Lubrication Transition with Roughness
8.8. Basic Mixed EHL Characteristics 
8.8.1. Background 
8.8.2. Limitations of Stochastic Mixed Lubrication Models 
8.8.3. Rough Surface Mixed EHL Model Validation 
8.8.4. Transition Characterized by l Ratio 
8.8.5. Effect of Roughness Height on the Mixed EHL Behaviors 
8.9. Effect of Roughness Orientation on Film Thickness 
8.9.1. Background
8.9.2. Case Study with Machined Roughness
8.9.3. Case Study with Sinusoidal Wavy Surfaces 
8.10. Clouse 
Chapter 9 Thermal Behaviors at Counterformal Contact Interfaces 
9.1. Introduction 
9.2. Flash Temperature Calculation 
9.2.1. Three Methods 
9.2.2. Point Heat Source Integration Method
9.2.2.1. Influence Coefficient Algorithm 
9.2.2.2. Calculation of Influence Coefficients 
9.2.2.3. Three Ways to Carry Out Summation Operations
9.2.2.4. Comparative Study via. Numerical Examples 
9.2.3. Simplified Approach for Cases at High Peclet Numbers 
9.3. Full TEHL Solution with Smooth Surfaces 
9.3.1 Line Contact TEHL Solutions 
9.3.1.1. Basic Equations for Line Contact TEHL Problems 
9.3.1.2. Brief Description of Numerical Method 
9.3.1.3. Typical Line Contact TEHL Results 
9.3.2. Point Contact TEHL Solution 
9.3.2.1. Basic TEHL Equations for Point Contact Problems 
9.3.2.2. Solution Domains and Initial/Boundary Conditions 
9.3.2.3. Numerical Solution Methods 
9.3.2.4. Sample Results and Discussions 
9.4. Full Solution of Mixed TEHL with Rough Surfaces
9.4.1. Mixed TEHL Model Description 
9.4.2. Numerical Methods 
9.4.3. Model Validation 
9.4.4. Basic TEHL Characteristics 
9.4.5. TEHL with Surface Roughness 
9.4.6. Transition from Boundary and Mixed to Full-Film Lubrication 
9.4.7. Effect of Lubricant Non-Newtonian Behaviors 
9.5. Thermal Reduction of EHL Film Thickness 
9.6. Bulk Temperature 
9.7. Closure 
Chapter 10 Behaviors of Interfacial Friction 
10.1. Introduction 
10.1.1. Importance of the Topic
10.1.2. Brief Review of Early Studies
10.1.3. Friction in Full-Film EHL 
10.1.4. Friction in Mixed Lubrication
10.1.5. Development of the Stribeck Curves
10.2. Dry Contact Friction 
10.2.1. Basic Model 
10.2.2. Classic Laws of Friction 
10.2.3. Mechanisms of Friction 
10.2.4. Summary to Classic Friction Theories 
10.3. Boundary Lubrication Friction 
10.3.1. General Description 
10.3.2. Formation of Adsorption Film 
10.3.3. Effect of Boundary Additives on Lubrication Performance 
10.4. Rolling Friction 
10.5. Friction in Lubricated Conformal Contacts 
10.6. Friction in Lubricated Counterformal Contacts (EHL Friction) 
10.6.1. Background 
10.6.2. Basic Characteristics of EHL Friction 
10.6.3. Rheological Models 
10.6.4. Calculation of EHL Friction 
10.6.5. Sample Calculation Results 
10.7. Friction in Mixed Lubrication 
10.7.1. Basic Concept 
10.7.2. Mixed Lubrication Friction in Conformal Contacts 
10.7.3. Mixed Lubrication Friction in Counterformal Contacts 
10.7.4. Friction Reduction in Mixed Lubrication 
10.8. The Stribeck Curve 
10.8.1. Calculation of the Stribeck Curves 
10.8.2. Test Apparatus for the Stribeck Curve Measurements 
10.8.3. Sample Stribeck Curves Measured 
10.8.4. Comparison Between Measured and Calculated Stribeck Curves 
10.9. More Friction Reduction Technologies 
10.10 Closure
Chapter 11 Contact of Elastoplastic and Inhomogeneous Materials 
11.1. Introduction 
11.2. Fundamentals of Plasticity Theory 
11.2.1. Plasticity of Materials 
11.2.1.1. Yield Surface 
11.2.1.2. Yield Criteria 
11.2.2. Strain Hardening and Plastic Flow 
11.2.2.1. Yield Initiation and Strain Hardening 
11.2.2.2. Elastic-Perfectly Plastic (EPP) Behavior 
11.2.2.3. Isotropic Hardening Rule 
11.2.2.4. Kinematic Hardening Rule 
11.2.2.5. Combined Isotropic and Kinematic Hardening Rule 
11.2.2.6. Plastic Strain Increment 
11.3. Elastoplastic Contact Modeling
11.3.1. FEM Modeling 
11.3.1.1. Elasto-Perfectly Plastic Contact Analysis Through the FEM 
11.3.1.2. FEM Simulations Considering Strain Hardening 
11.3.2. Method by Jacq et al. 
11.3.2.1. General 
11.3.2.2. Description of the Approach 
11.3.2.3. Typical Examples for a Repeated Rolling/Sliding Contact 
11.4. Inclusion and Equivalent Inclusion Method (EIM) 
11.4.1. Inclusion and Eigenstrain
11.4.2. Inhomogeneity and EIM 
11.4.3. Elastic Fields Caused by Eigenstrains 
11.5. Core Solutions to Eigenstrain-Induced Elastic Fields 
11.5.1. Background 
11.5.2. General Description 
11.5.3. Displacements 
11.5.4. Stress Field Outside 
11.5.5. Stress Field Inside 
11.5.6. Surface Displacement 
11.5.7. Uniform Unit Eigenstrain in a Cuboid and Related Influence Coefficients 
11.5.8. Discrete Correlation and Fast Fourier Transform (DCR-FFT) 
11.6. SAM by Numerical EIM 
11.6.1. General Formulation and Numerical Procedure for Contact Problems 
11.6.2. Traction Cancellation Method (TCM)
11.6.3. Other Enhancement Methods 
11.6.4. Numerical Examples 
11.6.4.1. Stresses Due to a Single Inhomogeneity 
11.6.4.2. Surface Coating as an Inhomogeneity
11.6.4.3. Composites with Distributed Particles 
11.6.4.4. Matrix Material Yield Strength / Hardness 
11.6.4.5. Double Inhomogeneities 
11.6.4.6. Rolling Contact Fatigue of Composite Materials 
11.7. Unified Contact Modeling and Advantages of the SAM 
11.7.1. Unified Framework for Contact Modeling 
11.7.2. SAM with Numerical EIM 
11.8. Closure 
Chapter 12 Plasto-Elastohydrodynamic Lubrication (PEHL) 
12.1. Introduction 
12.1.1. Importance of the Topic 
12.1.2. Brief Review of the Available Studies 
12.2. PEHL Formulation
12.2.1. Problem Description 
12.2.2. Basic Mixed PEHL Equations
12.3. Numerical Procedure for Solving the PEHL Problems
12.4. Smooth Surface PEHL Simulations 
12.4.1. PEHL Model Validation 
12.4.2. Preliminary Sample Cases 
12.4.3. Smooth Surface PEHL Under an Increasing Load 
12.4.4. Effect of Work Hardening Property 
12.5. Rough Surface PEHL Simulations 
12.5.1. PEHL with a Single Surface Asperity 
12.5.1.1. Basic PEHL Phenomena with a Stationary Asperity 
12.5.1.2.Effect of Asperity Height and Radius 
12.5.1.3. PEHL Phenomena with a Moving Surface Asperity 
12.5.2. PEHL with a Single Surface Dent 
12.5.2.1. Basic PEHL Phenomena with a Stationary Dent 
12.5.2.2. Effect of Dent Depth and Radius 
12.5.2.3. PEHL Phenomena with a Moving Surface Dent 
12.5.3. PEHL with Sinusoidal Surfaces 
12.5.3.1. Basic PEHL Characteristics and Comparison with EHL Results 
12.5.3.2.Effect of Material Hardening Property 
12.5.3.3. Effect of Rough Surface Geometric Parameters 
12.5.3.4. Effect of Operating Conditions 
12.5.4. PEHL with Real Machined Rough Surfaces 
12.6. PEHL in Line Contacts of Both Infinite and Finite Lengths 
12.6.1. Background 
12.6.2. Smooth Surface PEHL Solutions 
12.6.3. Rough Surface Mixed PEHL Solutions 
12.7. PEHL in a Rolling Contact 
12.7.1. Basic Model for PEHL in a Rolling Contact 
12.7.2. Numerical Procedure 
12.7.3. Results and Discussions 
12.7.3.1. PEHL Results for the First Rolling Cycle 
12.7.3.2. PEHL Results for the Second Rolling Cycle 
12.7.3.3. Ratcheting and Shakedown 
12.7.3.4. PEHL Phenomena in the First Rolling Cycle 
12.7.3.5. PEHL Phenomena in the Second Rolling Cycle 
12.7.3.6. PEHL Phenomena in the First Five Cycles 
12.7.3.7. Effect of Applied Load on the Shakedown or Ratcheting Behavior 
12.7.3.8. Effect of Material Hardening Law on the Shakedown or Ratcheting Behavior
12.8. Closure 
Chapter 13 EHL of Inhomogeneous Materials
13.1. Introduction
13.2. EHL with a Single Layered Coating 
13.2.1. Background 
13.2.2. Model for Point Contact EHL with Single Layered Coating 
13.2.3. Model Verification 
13.2.4. Influences of Coating Properties on Point Contact EHL 
13.2.5. Influences of Speed, Load and Lubricant Properties 
13.2.6. Curve-Fitting Formulae for Stiff Coating EHL 
13.3. EHL with a Multilayered Coating 
13.3.1. Background 
13.3.2. Theory and Model Description 
13.3.2.1. Equations for Lubrication 
13.3.2.2. Equations for Surface Displacements and Subsurface Stresses 
13.3.2.3. Numerical Solution Procedure 
13.3.3. Typical Sample Results 
13.3.3.1. EHL with a Bi-Layered Coating 
13.3.3.2. EHL with a Multilayered Substrate 
13.3.3.3. EHL with a Functionally Graded Coating 
13.3.4. Remarks 
13.4. EHL with General Inhomogeneities 
13.4.1. Background 
13.4.2. Theory and Model Description 
13.4.2.1. Equations for Point Contact EHL 
13.4.2.2. Equations for Surface Displacement Calculation 
13.4.2.3. Numerical Procedure 
13.4.3. Typical Sample Results and Discussions 
13.4.3.1. Selected Cases and Computational Mesh 
13.4.3.2. A Single Inhomogeneity 
13.4.3.3. Multiple Inhomogeneities 
13.4.3.4. Functionally Graded Coatings 
13.4.4. Computational Efficiency 
13.4.5. Remarks 
13.5. Closure 
Chapter 14 Application Topics
14.1. Introduction 
14.2. Mixed EHL in Gears 
14.2.1. Background 
14.2.2. Mixed EHL in Spur and Helical Gears 
14.2.2.1. Gear Geometry and Kinematics 
14.2.2.2. Simplified Load Distribution 
14.2.2.3. 3D Line Contact Mixed EHL Simulation Model 
14.2.2.4. Results for a Sample Gear Set in Mixed EHL 
14.2.2.5. Gear Tooth Contact Friction 
14.2.2.6. Flash and Bulk Temperatures in Gears 
14.2.3. Mixed EHL in Spiral Bevel and Hypoid Gears 
14.2.3.1. Background 
14.2.3.2. Gearing Geometry and Kinematics 
14.2.3.3. Modified Mixed EHL Model 
14.2.3.4. Interfacial Friction and Flash Temperature Calculations 
14.2.3.5. Sample Results of Calculation 
14.2.3.6. Summary 
14.3. Pitting Life Prediction for Gears 
14.3.1. Problem Description 
14.3.2. Pitting Life Prediction Model 
14.3.3. Gear Pitting Life Prediction Procedure 
14.3.4. Life Prediction Results and Their Comparisons with Testing Data 
14.3.5. Effect of Surface Finish on Predicted Pitting Life 
14.4. Fatigue Life in Rolling-Sliding Contacts
14.4.1. Problem Description 
14.4.2. Asperity Stress Cycle Counting 
14.4.3. Life Prediction Procedure 
14.4.4. Influence of Relative Sliding on Peak Pressure 
14.4.5. Subsurface Stress Variation Due to Sliding 
14.4.6. Influence of Sliding on Fatigue Life 
14.5. Simulation of Sliding Wear in Mixed Lubrication 
14.5.1. Problem Description 
14.5.2. Brief Review of Available Wear Models 
14.5.3. Wear Simulation Procedure 
14.5.4. A Numerical Example 
14.5.5. Phases of Wear 
14.5.6. Wear Coefficient Calibration 
14.6. Surface Design Through Virtual Texturing 
14.6.1. Importance of Surface Texture Design and Optimization 
14.6.2. Virtual Texturing and Its Procedure 
14.6.3. An Application Example
14.6.3.1. Problem Description 
14.6.3.2. Determinations of Dimple/Groove Depth, Size and Density 
14.6.3.3. Texture Distribution Pattern Selection 
14.6.3.4. Bottom Shapes of the Dimples and Grooves 
14.6.3.5. Basic Results of Comparisons 
14.6.3.6. Practical Concerns 
14.6.4. Summary 
14.7. EHL with Emulsion Lubricants 
14.7.1. Background 
14.7.2. Test Apparatus 
14.7.3. Emulsion Lubricants Tested 
14.7.4. Oil Pool Formation and Disappearance 
14.7.5. Results of Measured Film Thickness 
14.7.6. Friction Measurements
14.7.7. Summary 
14.8. Closure 
Chapter 15 Multifield Interfacial Issues and Generalized Contact Modeling 
15.1. Introduction 
15.1.1. Background 
15.1.2. Brief Review of Related Multifield Studies 
15.2. Coupled Mechanical-Electrical-Magnetic-Chemical-Thermal (MEMCT) Theory for Material Systems 
15.2.1. Fundamental Theories and the MEMCT Framework 
15.2.1.1. Multi-Field Coupling and Fundamental Theories 
15.2.1.2. Initial and Boundary Conditions 
15.2.1.3. Generalized MEMCT Constitutive Equations 
15.2.1.4. Evolution Equations 
15.2.2. Generalized MEMCT Theory 
15.2.2.1. A Set of Generalized Solutions 
15.2.2.2. Strategy 
15.3. Generalized Contact Model 
15.3.1. Contact Model Considerations 
15.3.2. Linearized Constitutive Equations and Generalized Boundary Conditions
15.3.3. Generalized Contact and Interfacial Conditions 
15.3.3.1. Generalized Gap, Load, and Surface Flux 
15.3.3.2. Generalized Contact and Interfacial Conditions for Single-Field Cases 
15.3.3.3. Generalized Contact and Interfacial Conditions in Coupled Fields 
15.3.3.4. Contact Conditions 
15.3.3.5. Interfacial Conditions 
15.3.3.6. Other Boundary Conditions 
15.4. Examples of Contact subjected to Coupled Fields 
15.4.1. Sliding Contact Heat Conduction in Homogeneous Materials 
15.4.1.1. Problem Description 
15.4.1.2. Solution Scheme 
15.4.1.3. Different Modeling Considerations 
15.4.1.4. Stress and Temperature Affected by Sliding Velocity 
15.4.2. Contact Heat Conduction with Surface Heat Convection 
15.4.3. Contact Heat Conduction in an Inhomogeneous Half-Space 
15.4.3.1. Problem Description 
15.4.3.2. Analytical Core Solution 
15.4.3.3. Contact and Interfacial Conditions 
15.4.3.4. Numerical Scheme 
15.4.3.5. Disturbed Temperature and Heat Flux Due to Inhomogeneity 
15.4.3.6. Effect of Inhomogeneity Size and Location on Disturbed Temperature 
15.4.3.7. Effect of Inhomogeneity Distance 
15.4.4. Frictional Contact Between Two Multiferroic Materials 
15.4.4.1. Problem Description 
15.4.4.2. Solution Procedure 
15.4.4.3. Indentation of an Smooth MEE Surface 
15.4.4.4. Indentation of a Rough MEE Surface 
15.4.4.5. Parameter Sensitivity 
15.5. Closure 
Appendices
Appendix A: Basic Expressions in Linear Elasticity
Appendix B: Fourier Series, Fourier Transform, Convolution and Correlation
Appendix C: Solutions of the FRFs for Multilayered Materials 
Under Normal and Shear Loadings 
Appendix D: Reference Source Code in FORTRAN for Discrete Convolution 
and Fast Fourier Transform (DC-FFT) 
Appendix E: Basic Equations and Their Discretization Schemes for 
Numerical Solution of Mixed EHL 
Appendix F: Potential Functions, Derivatives and Equations Used in Chapter 11 
Appendix G: Stresses and Surface Displacement Caused by a Cuboidal 
Inclusion with Uniformly D