Interfacial Mechanics
portes grátis
Interfacial Mechanics
Theories and Methods for Contact and Lubrication
Zhu, Dong; Wang, Jane
Taylor & Francis Inc
12/2019
658
Dura
Inglês
9781439815106
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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 Distributed Eigenstrain Appendix H: Solutions of the FRFs for Multilayered Materials Under Normal and Shear Loadings Appendix I: Frequency Response Functions for Temperature References Subject Index
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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 Distributed Eigenstrain Appendix H: Solutions of the FRFs for Multilayered Materials Under Normal and Shear Loadings Appendix I: Frequency Response Functions for Temperature References Subject Index
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