Rough surface flow factors in full film lubrication based on a homogenization technique

This paper describes a method to compute the flow factors that compensate for an arbitrary surface roughness in a compressible hydrodynamic lubrication based on a homogenization technique. The Reynolds equation is used as the governing equation and the two-scale expansion involved in the homogenization process enables the local roughness scale to be treated separately from the global geometry scale. With this method, it is possible to compute the flow factors for any deterministic roughness. Measured two-dimensional surface profiles are used as examples. Profiles having the same Abbot curve are also shown to have the same flow factors, providing an efficient classification of surfaces in hydrodynamic two-dimensional contacts. Flow factors are computed for the rough surface profiles, and solutions for global bearing geometry are obtained and compared with the corresponding solutions from a smooth geometry.