On the Mean Reynolds Equation in the Presence of Surface Roughness: Squeeze-Film Bearing

Abstract

The mean Reynolds equation in the presence of surface roughness is derived using the techniques developed by Keller. This mean equation is nonlocal in the sense that the mean pressure at all points in the flow field has some effect on the mean pressure at any particular point. The performance of a two-dimensional squeeze film bearing with homogeneous surface roughness is considered next showing that the load is enhanced by a factor of 1 + ε2 a2 S/h2 , where εa is the amplitude of the roughness, h is the film thickness, and S varies between −3 〈m2 〉, for parallel surface roughness, to 6 〈m2 〉 for transverse surface roughness. Here, the bearing surfaces are described by εam1 and h + εam2 and m = m2 − m1 .