A multiscale method for optimising surface topography in elastohydrodynamic lubrication (EHL) using metamodels

The frictional performance of a bearing is of significant interest in any mechanical system where there are lubricated surfaces under load and in relative motion. Surface topography plays a major role in determining the coefficient of friction for the bearing because the size of the fluid film and topography are of a comparable order. The problem of optimising topography for such a system is complicated by the separation in scales between the size of the lubricated domain and that of the topography, which is of at least one order of magnitude or more smaller. This paper introduces a multiscale method for optimising the small scale topography for improved frictional performance of the large scale bearing. The approach fully couples the elastohydrodynamic lubrication at both scales between pressure generated in the lubricant and deformation of the bounding surfaces. Homogenised small scale data is used to inform the large scale model and is represented using Moving Least Squares metamodels calibrated by cross validation. An optimal topography for a minimum coefficient of friction for the bearing is identified and comparisons made of local minima in the response, where very different topographies with similar frictional performance are observed. Comparisons of the optimal topography with the smooth surface model demonstrated the complexity of capturing the non-linear effect of topography and the necessity of the multiscale method in capturing this. Deviations from the smooth surface model were quantified by the metamodel coefficients and showed how topographies with a similar frictional performance have very different characteristics.