Finite element modeling of elastohydrodynamic lubrication problems. (2018)

• Record Type: Book
• Further Information: Note: Wassim Habchi.
• Authors: Habchi, Wassim, 1982-
• Contents: Preface xiii Nomenclature xvii About the CompanionWebsite xxv Part I Introduction 1 1 Elastohydrodynamic Lubrication (EHL) 3 1.1 EHL Regime 3 1.2 Governing Equations in Dimensional Form 7 1.2.1 Generalized Reynolds Equation 9 1.2.2 FilmThickness Equation 15 1.2.3 Linear Elasticity Equations 18 1.2.4 Load Balance Equation 24 1.2.5 Energy Equations 24 1.2.6 Shear Stress Equations 28 1.3 Governing Equations in Dimensionless Form 28 1.3.1 Dimensionless Parameters 29 1.3.2 Generalized Reynolds Equation 31 1.3.3 FilmThickness Equation 32 1.3.4 Linear Elasticity Equations 33 1.3.5 Load Balance Equation 34 1.3.6 Energy Equations 34 1.3.7 Shear Stress Equations 36 1.4 Lubricant Constitutive Behavior 36 1.4.1 Pressure and Temperature Dependence 37 1.4.1.1 Density 37 1.4.1.2 Viscosity 39 1.4.1.3 Thermal Conductivity and Heat Capacity 41 1.4.2 Shear Dependence of Viscosity 41 1.4.3 Limiting Shear Stress 43 1.5 Dimensionless Groups 44 1.6 Review of EHL Numerical Modeling Techniques 46 1.7 Conclusion 52 References 52 2 Finite ElementMethod (FEM) 59 2.1 FEM:The Basic Idea 59 2.2 Model PDE 61 2.3 Steady-State Linear FEM Analysis 63 2.3.1 Elementary Integral Formulations 64 2.3.1.1 Weighted-Residual Form 64 2.3.1.2 Weak Form 65 2.3.2 Solution Approximation 66 2.3.2.1 Meshing and Discretization 67 2.3.2.2 Lagrange Linear Elements 69 2.3.2.3 Lagrange Quadratic Elements 73 2.3.3 Galerkin Formulation 75 2.3.4 Integral Evaluations: Mapping between Reference and Actual Elements 78 2.3.5 Connectivity of Elements 85 2.3.6 Assembly Process and Treatment of B.C.’s 86 2.3.7 Resolution Process 90 2.3.8 Post-Processing of the Solution 91 2.3.9 One-Dimensional Example 92 2.4 Steady-State Nonlinear FEM Analysis 99 2.4.1 Newton Methods for Nonlinear Systems of Equations 99 2.4.1.1 Newton Method 100 2.4.1.2 Damped-NewtonMethod 102 2.4.2 Nonlinear FEM Formulation 105 2.5 Transient FEM Analysis 109 2.5.1 Space-Time Discretization 110 2.5.2 Time-Dependent FEM Formulation 111 2.6 Multi-Physical FEM Analysis 112 2.6.1 Multi-Physical FEM Formulation 113 2.6.2 Assembly Process 115 2.6.3 Coupling Strategies 116 2.6.3.1 Weak Coupling 117 2.6.3.2 Full/Strong Coupling 117 2.7 Stabilized FEM Formulations 118 2.7.1 Isotropic Diffusion 120 2.7.2 Streamline Upwind Petrov–Galerkin 121 2.7.3 Galerkin Least Squares 121 2.8 Conclusion 123 References 123 Part II Finite ElementModeling Techniques 125 3 Steady-State Isothermal Newtonian Line Contacts 127 3.1 Contact Configuration 127 3.2 Geometry, Computational Domains, and Meshing 128 3.2.1 Geometry 128 3.2.2 Computational Domains 128 3.2.3 Meshing and Discretization 130 3.3 Governing Equations and Boundary Conditions 132 3.3.1 Reynolds Equation 133 3.3.2 Linear Elasticity Equations 136 3.3.3 Load Balance Equation 138 3.4 FEM Model 138 3.4.1 Connectivity of Elements 139 3.4.2 Weak Form Formulation 139 3.4.3 Elementary Matrix Formulations 141 3.4.3.1 Elastic Part 142 3.4.3.2 Hydrodynamic Part 144 3.4.3.3 Load Balance Part 145 3.4.4 Stabilized Formulations 146 3.5 Overall Solution Procedure 150 3.6 Model Calibration and Preliminary Results 153 3.6.1 Mesh Sensitivity Analysis 153 3.6.2 Penalty Term Tuning 153 3.6.3 Solid Domain Size Calibration 156 3.6.4 Preliminary Results 157 3.7 Conclusion 161 References 161 4 Steady-State Isothermal Newtonian Point Contacts 165 4.1 Contact Configuration 165 4.2 Geometry, Computational Domains, and Meshing 166 4.2.1 Geometry 166 4.2.2 Computational Domains 166 4.2.3 Meshing and Discretization 169 4.3 Governing Equations and Boundary Conditions 170 4.3.1 Reynolds Equation 171 4.3.2 Linear Elasticity Equations 173 4.3.3 Load Balance Equation 174 4.4 FEM Model 175 4.4.1 Connectivity of Elements 175 4.4.2 Weak Form Formulation 176 4.4.3 Elementary Matrix Formulations 177 4.4.3.1 Elastic Part 178 4.4.3.2 Hydrodynamic Part 180 4.4.3.3 Load Balance Part 182 4.4.4 Stabilized Formulations 183 4.5 Overall Solution Procedure 187 4.6 Model Calibration and Preliminary Results 190 4.6.1 Mesh Sensitivity Analysis 190 4.6.2 Penalty Term Tuning 191 4.6.3 Preliminary Results 192 4.7 Conclusion 196 References 196 5 Steady-State Thermal Non-Newtonian Line Contacts 199 5.1 Contact Configuration 199 5.2 Geometry, Computational Domains, and Meshing 200 5.2.1 Geometry 200 5.2.2 Computational Domains 200 5.2.3 Meshing and Discretization 201 5.3 Governing Equations and Boundary Conditions 203 5.3.1 Generalized Reynolds Equation 204 5.3.2 Linear Elasticity Equations 205 5.3.3 Load Balance Equation 205 5.3.4 Energy Equations 205 5.3.5 Shear Stress Equation 207 5.4 FEM Model 208 5.4.1 Connectivity of Elements 208 5.4.2 Weak Form Formulation 210 5.4.3 Elementary Matrix Formulations 213 5.4.3.1 Elastic Part 215 5.4.3.2 Hydrodynamic Part 215 5.4.3.3 Load Balance Part 218 5.4.3.4 Thermal Part 219 5.4.3.5 Shear Stress Part 224 5.4.4 Stabilized Formulations 225 5.5 Overall Solution Procedure 227 5.6 Model Calibration and Preliminary Results 228 5.6.1 Mesh Sensitivity Analysis 230 5.6.2 Full versusWeak Coupling 230 5.6.3 Preliminary Results 239 5.7 Conclusion 240 References 241 6 Steady-State Thermal Non-Newtonian Point Contacts 243 6.1 Contact Configuration 243 6.2 Geometry, Computational Domains, and Meshing 244 6.2.1 Geometry 244 6.2.2 Computational Domains 244 6.2.3 Meshing and Discretization 245 6.3 Governing Equations and Boundary Conditions 247 6.3.1 Generalized Reynolds Equation 248 6.3.2 Linear Elasticity Equations 249 6.3.3 Load Balance Equation 249 6.3.4 Energy Equations 249 6.3.5 Shear Stress Equations 252 6.4 FEM Model 252 6.4.1 Connectivity of Elements 253 6.4.2 Weak Form Formulation 255 6.4.3 Elementary Matrix Formulations 258 6.4.3.1 Elastic Part 260 6.4.3.2 Hydrodynamic Part 261 6.4.3.3 Load Balance Part 264 6.4.3.4 Thermal Part 264 6.4.3.5 Shear Stress Part 270 6.4.4 Stabilized Formulations 273 6.5 Overall Solution Procedure 274 6.6 Model Calibration and Preliminary Results 275 6.6.1 Mesh Sensitivity Analysis 276 6.6.2 Preliminary Results 276 6.7 Conclusion 280 References 280 7 Transient Effects 281 7.1 Contact Configuration 281 7.2 Geometry, Computational Domains, and Meshing 281 7.3 Governing Equations, Boundary, and Initial Conditions 282 7.3.1 Reynolds Equation 282 7.3.2 Linear Elasticity Equations 284 7.3.3 Load Balance Equation 284 7.4 FEM Model
• Edition: 1st
• Publisher Details: Hoboken, New Jersey : John Wiley & Sons, Inc
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 621.89; Elastohydrodynamic lubrication; Finite element method
• Languages: English
• ISBNs: 9781119225140; 9781119225157
• Related ISBNs: 9781119225126
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