Two-scale EHL: Three-dimensional topography in tilted-pad bearings

• Two-scale method derived for EHL and micro-EHL in textured tilted-pad bearings.
• Moving Least Squares used to couple simulations at the different scales.
• Compressibility and piezoviscosity significantly affect bearing performance.
• Increasing the size of topography increased the coefficient of friction.
• Increasing the size of topography reduced the minimum film thickness.

Derived from the Heterogeneous Multiscale Methods (HMM), a two-scale method is developed 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 describing the Fluid Structure Interaction (FSI) of topographical features. 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.