Thermo-hydrodynamic Lubrication in Hydrodynamic Bearings

This Series provides the necessary elements to the development and validation of numerical prediction models for hydrodynamic bearings. This book describes the thermo-hydrodynamic and the thermo-elasto-hydrodynamic lubrication. The algorithms are methodically detailed and each section is thoroughly illustrated.

This Series provides the necessary elements to the development and validation of numerical prediction models for hydrodynamic bearings. This book describes the thermo-hydrodynamic and the thermo-elasto-hydrodynamic lubrication. The algorithms are methodically detailed and each section is thoroughly illustrated.

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 MODEL192.1. 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 thesolids 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 axialdirection 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 assumptions733.1.1. Expression of the pressure and reduced Reynolds equation733.1.2. 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 Liassumptions 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 thefilm thickness (PTM) 953.3. Bibliography 101CHAPTER 4. COMPUTING THE THERMOELASTIC DEPENDENCY MATRICES1034.1. Computing the thermoelastic dependency matrices to be usedfor the three-dimensional and Rhode and Li models 1044.2. Computing the thermoelastic dependency matrices to be usedfor the simplified models 1054.2.1. Equation setting for compliance matrices when the thermalboundary layer is modeled by a transfer coefficient 1064.2.2. Equation setting for compliance matrices when the thermalboundary layer is modeled by a Fourier series 1074.3. Bibliography 110CHAPTER 5. GENERAL ALGORITHM AND SOFTWARE FOR SOLVING BEARINGLUBRICATION PROBLEMS 1115.1. Parameters and equations 1115.1.1. The parameters that must be known before computing1115.1.2. The unknown parameters, objective of the computation1135.1.3. The equations to be solved 1145.2. General algorithm 1155.3. Solving finite element discretized EHD problem with theNewton-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 lubricationcomputation 1435.7. An example of TEHD computation software: ACCEL 1455.8. Bibliography 147APPENDIX 149INDEX 153