Some problems in hydrodynamic lubrication

Several computational and mathematical modelling problems in the areas of compressible and incompressible hydrodynamic lubrication are addressed. The first problem involves application of the collocation method for static and dynamic analyses of finite-length gas journal bearings. The method is shown to be an order of magnitude computationally faster than the finite difference method. Transient and steady-state unbalance response of the journal center is obtained for finite-length gas-journal bearings by solving the compressible Reynolds equation for journal bearings. The technique, in principle, can also be extended to slider and tilting-pad bearings.; Squeeze-film dampers of finite-length with variable clearance is next investigated using the collocation method. It is shown that by suitably varying the two parameters that control the nature of axial clearance variation, the secant stiffness and damping coefficient variation with journal eccentricity ratio can be altered to better suit specific design needs. The collocation method is shown to be a viable and efficient method for static and dynamic analyses of the incompressible lubrication of squeeze-film dampers.; Surface roughness effects on the hydrodynamic lubrication characteristics of finite-length gas journal bearings is studied next by numerically solving the ensemble averaged compressible Reynolds equation. Load capacities and viscous friction losses for bearings with longitudinal and transverse roughness patterns are compared with smooth bearings for various eccentricity ratios, L/D ratios and compressibility numbers. Nonlinear transient unbalance response of finite-length rough bearings is also compared with smooth bearing results.; The last problem deals with gas-lubricated finite-length foil-journal bearings. An elasticity solution which solves for the deflection of the compliant foil bearing surface for applied loads is first developed, and used for the study of load-deflection characteristics of the foil bearing with a non-rotating journal. The analytical load-displacement curves show good agreement with experimental results. Next, the computationally intensive elasto-hydro-dynamic (EHD) problem involving the simultaneous solution of the elasticity and compressible hydrodynamic problems is attempted using an iterative technique. Pressure distributions and load capacities for various journal eccentricities and speeds are presented.