Heterogeneous Multiscale Methods for modelling surface topography in Elastohydrodynamic Lubrication line contacts

A multiscale method for the Elastohydrodynamic Lubrication (EHL) of line contacts is derived based on the Heterogeneous Multiscale Methods. Periodicity applies to the topographical features and lubricant flow, data is homogenised over a range of variables at a micro-scale and coupled into a macro-scale model. This is achieved using flow factors as calculated from metamodels, which themselves evolve with the solution procedure. Results are given for an idealised topography and illustrate significant deviations from smooth surface assumptions as quantified by the flow factors. Improvements in the accuracy and efficiency with previous work and large fluctuations due to micro-EHL are also presented. Validation of the multiscale method with a deterministic topography is provided demonstrating good accuracy and efficiency.