New concepts of homogenization applied in rough surface hydrodynamic lubrication

Abstract This work introduces a new concept of homogenization that enables efficient analysis of the effects of surface roughness representations obtained by measurements in applications modeled by the Reynolds equation. Examples of such applications are trust- and journal-bearings. The numerical analysis of these types of applications requires an extremely dense computational mesh in order to resolve the surface roughness, suggesting some type of averaging. One such method is homogenization, which has been applied to Reynolds type equations with success recently. This approach is similar to the technique proposed by Patir and Cheng, who introduced flow factors determining the hydrodynamic action due to surface roughness. The difference is, however, that the present technique has a rigorous mathematical support. Moreover, the recipe to compute the averaged coefficients is simple without any ambiguities. Using either the technique proposed by Patir and Cheng or homogenization, the coefficients determining the averaged Reynolds equation are obtained by solving differential equations on a local scale. Unfortunately, this is detrimental when investigating the effects induced by real, measured, surface roughness, even though these local problems may be solved in parallel. The present work presents a solution by applying the technique based on bounds. This technique transforms the stationary Reynolds equation into two computationally feasible forms, one for the upper bound and one for the lower bound, where the flow factors are obtained by straightforward integration. Together with the preciseness of these bounds, the bounds approach becomes an eminent tool suitable for investigating the effect of real, measured, surface roughness on hydrodynamic performance.