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.