A two-scale approach to elastohydrodynamic lubrication

Derived from the Heterogeneous Multiscale Methods (HMM), a two-scale method is developed in this thesis for the analysis of Elastohydrodynamic Lubrication (EHL) and micro-EHL in tilted-pad bearings with three-dimensional topography. A relationship linking the pressure gradient to mass flow rate is derived and represented in the bearing domain through homogenisation of near-periodic simulations which describe the Fluid Structure Interaction (FSI) of topographical features. This relationship is approximated using Response Surface Methodology (RSM) which allows the scales to be coupled by a Moving Least Squares (MLS) metamodel at a reduced computational effort. For the parameters investigated the influence of compressibility and piezoviscosity was found to be more significant than that of non-Newtonian (shear-thinning) behaviour on textured bearing performance. As the size of topography increased two-scale solutions demonstrated that at constant load the coefficient of friction increased and the minimum film thickness decreased over a range of pad lengths and tilt angles. Through the two-scale method the micro-EHL effect on film thickness was quantified and shown to be at least an order of magnitude or less than that of the total EHL effect. Parameterisation of topography led to an optimisation procedure which aimed to reduce the coefficient of friction in textured bearings as to improve their performance under load. It was shown through this procedure that a transverse topography benefits the performance over a longitudinal one. The best performing topography was found to have a mix of both longitudinal and transverse components, and it was also shown that very different topographies can exhibit similar characteristics. Through the metamodelling process deviation from the smooth surface model was quantified by the constants associated with the MLS approximations.