Thermo-hydrodynamic Lubrication in Hydrodynamic Bearings

Dominique Bonneau is Professor Emeritus specializing in the numerical modelization of lubrication problems who has worked as a teacher-researcher at the IUT of Angoulême and at the Institute PPRIME (Laboratory of Mechanics of Solids) of the University of Poitiers-CNRS-ENSMA in France.Aurelian Fatu is Professor and a researcher at the Institute PPRIME specializing in the modeling of problems of lubrication for engine bearings and for systems' sealing devices.Dominique Souchet specializes in the modeling of thermo-hydrodynamic lubrication of journal and thrust bearings with Newtonian or non-Newtonian fluids. He is a university lecturer and researcher at the Institute PPRIME.

• PERFACE ixNOMENCLATURE xiCHAPTER 1. THERMO-HYDRODYNAMIC LUBRICATION 11.1. Global thermal balance 11.2. Energy equation for the lubricant film 41.2.1. Particular case of non-filled film zones 51.3. Fourier equation inside the solids 61.4. Boundary conditions 71.4.1. Supply ducts 71.4.2. External walls of solids 81.4.3. Surfaces at solid truncations 91.4.4. Interfaces between film and solids 91.4.5. Supply orifices and grooves 111.4.6. Axial extremities of the lubricant film 171.5. Bibliography 17CHAPTER 2. THREE-DIMENSIONAL THERMO-HYDRODYNAMIC MODEL 192.1. Model description 192.2. Discretization of the film energy equation 202.2.1. Stationary case 202.2.2. Transient case 272.3. Discretization of Fourier equation in the solids 382.4. Assembly of discretized equations for the film and the solids 402.5. Numerical behavior of the THD finite element model 432.5.1. Definition of reference problems 432.5.2. Behavior for a stationary case 452.5.3. Behavior for a transient case 572.5.4. Behavior in the case of a variation in the axial direction of the film thickness 692.5.5. Evaluation of the global thermal method (GTM) 702.6. Bibliography 71CHAPTER 3. SIMPLIFIED THERMO-HYDRODYNAMIC MODELS 733.1. Simplified THD model based on the Rhode and Li assumptions 733.1.1. Expression of the pressure and reduced Reynolds equation 733.1.2. Velocity components 753.1.3. Energy and Fourier equations 763.1.4. Discretization of equations 773.1.5. Evaluation of the method based on Rhode and Li assumptions 823.2. Simplified models for cyclic regimes 853.2.1. Model with the temperature averaged on the film thickness (ATM) 873.2.2. Model with a parabolic temperature profile across the film thickness (PTM) 953.3. Bibliography 101CHAPTER 4. COMPUTING THE THERMOELASTIC DEPENDENCY MATRICES 1034.1. Computing the thermoelastic dependency matrices to be used for the three-dimensional and Rhode and Li models 1044.2. Computing the thermoelastic dependency matrices to be used for the simplified models 1054.2.1. Equation setting for compliance matrices when the thermal boundary layer is modeled by a transfer coefficient 1064.2.2. Equation setting for compliance matrices when the thermal boundary layer is modeled by a Fourier series 1074.3. Bibliography 110CHAPTER 5. GENERAL ALGORITHM AND SOFTWARE FOR SOLVING BEARING LUBRICATION PROBLEMS  1115.1. Parameters and equations 1115.1.1. The parameters that must be known before computing 1115.1.2. The unknown parameters, objective of the computation 1135.1.3. The equations to be solved 1145.2. General algorithm 1155.3. Solving finite element discretized EHD problem with the Newton–Raphson method 1175.3.1. Constitutive equations for the EHD problem 1175.3.2. Discretized equations for the EHD problem 1195.3.3. Solving algorithm for the EHD problem 1295.4. Techniques for reducing the computation time 1315.4.1. Non-systematic evaluation of the Jacobian matrix 1315.4.2. Decomposition of the hydrodynamic pressure 1325.5. Mesh refinement 1385.5.1. Principle of the refinement method 1385.5.2. Computation of the local compliance matrix 1405.5.3. Expression of the shell surface deformation 1415.6. Architecture of software for bearing lubrication computation 1435.7. An example of TEHD computation software: ACCEL 1455.8. Bibliography 147APPENDIX 149INDEX 153