Comparison of Homogenization and Direct Techniques for the Treatment of Roughness in Incompressible Lubrication

Abstract

Homogenization is a formal mathematical two-scale averaging process that can be applied to roughness problems and can replace previous heuristic averaging procedures, which have sometimes led to ambiguous results. This procedure was previously mathematically developed and applied to compressible flow problems. The purpose of this paper is the development of a special form of Reynolds equation for such homogenized conditions applied to the incompressible Newtonian case. The equation allows the calculation of the operating characteristics of a contact by taking into account the local geometry of surfaces while making a substantial improvement in computing time. The method allows for the study of rough surfaces, but requires considerably fewer calculated points than for traditional deterministic discretization methods.