Interfacial Mechanics Theories and Methods for Contact and Lubrication

Understanding the characteristics of material contact and lubrication at tribological interfaces is of great importance to engineering researchers and machine designers. Traditionally, contact and lubrication are separately studied due to technical difficulties, although they often coexist in reality and they are actually on the same physical ground. Fast research advancements in recent years have enabled the development and application of unified models and numerical approaches to simulate contact and lubrication, merging their studies into the domain of Interfacial Mechanics. This book provides updated information based on recent research progresses in related areas, which includes new concepts, theories, methods, and results for contact and lubrication problems involving elastic or inelastic materials, homogeneous or inhomogeneous contacting bodies, using stochastic or deterministic models for dealing with rough surfaces. It also contains unified models and numerical methods for mixed lubrication studies, analyses of interfacial frictional and thermal behaviors, as well as theories for studying the effects of multiple fields on interfacial characteristics. The book intends to reflect the recent trends of research by focusing on numerical simulation and problem solving techniques for practical interfaces of engineered surfaces and materials. This book is written primarily for graduate and senior undergraduate students, engineers, and researchers in the fields of tribology, lubrication, surface engineering, materials science and engineering, and mechanical engineering.

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 Solutio

Q. Jane Wang received her Ph. D. in mechanical engineering from Northwestern University, IL, USA, in 1993. She taught for five years at Florida International University, Miami, FL, USA, and is now a Professor in the Mechanical Engineering Department at Northwestern University, USA. She was elected Fellow of the American Society of Mechanical Engineers (ASME) in 2009 and Society of Tribologists and Lubrication Engineers (STLE) in 2007. Her research interests are mainly in the areas of contact and interfacial mechanics and tribology of advanced materials and novel lubricants. Dong Zhu received his Ph. D. in mechanical engineering from Tsinghua University of China in April of 1984. He started to work at the Center for Engineering Tribology, Northwestern University, USA, as a Research Fellow in January of 1986. He joined the Technical Center of Aluminum Company of America in the beginning of 1991 then Eaton Innovation Center in 1994, doing tribology and surface engineering related research and product development. After his retirement from Eaton, he was appointed to a Professor position at Sichuan University of China and Adjunct Professor at Tsinghua University. He is now an Adjunct Professor at Harbin Engineering University. He was elected Fellow of the American Society of Mechanical Engineers (ASME) in 2007 and Society of Tribologists and Lubrication Engineers (STLE) in 2006. His research interests mainly include elastohydrodynamic lubrication (EHL), mixed lubrication, surface engineering and tribological testing.