On the effects of the Reynolds and Stokes surface roughnesses in a two-dimensional slider bearing

Abstract

Perturbation solutions are presented to the Reynolds and the Stokes equations for a two-dimensional slider bearing with homogeneous surface roughness. In the Reynolds equation the surface roughness has a general two-dimensional form, and in the Stokes equation the surface roughness is parallel to the flow direction. For the parallel surface roughness, if the surface corrugations on two bearing plates are uncorrelated then an error of order 10% is made when using the Reynolds equation to correct for the surface roughness provided that λh ≼ 0.5. Here λ is a characteristic frequency of the corrugation and h is the mean film thickness. Furthermore, if λh ≽ 1.91 then the Stokes solution demands a positive load enhancement, whereas the Reynolds equation predicts a negative load enhancement that depends on λ through terms of order O ( h / L ), where 2 L is the bearing length.