The Hydrodynamic Lubrication of Rough Surfaces Based on a New Perturbation Approach

Abstract

A new method for treating roughness problems in hydrodynamic lubrication is presented. The approach consists of an expansion of the pressure by means of the perturbation parameter ε which is the ratio of the characteristic wavelengths across and along the direction of motion, respectively. This parameter may also be interpreted as the inverse of the Peklenik number of the surface texture. It is found that the zeroth components are those of To̸nder’s approximate theory. The terms are modified so as to remain finite at infinite ε. It is demonstrated that the corrections thus obtained are very accurate for configurations which are not disconnected pockets, even for very large roughness amplitudes. Such pockets are well treated, however, for moderate roughnesses. The method is applicable to statistically symmetric cases and may be easily extended to two-sided roughness. The application of the approach is quite straightforward numerically and does not require the boundary conditions of sample roughnesses to be known.