“Bi-Gaussian” representation of worn surface topography in elastic contact problems

Abstract

Machine elements such as seals, piston rings and bearings commonly operate in the mixed friction regime. Here, lubrication leakage and friction depend on surface roughness. Previous authors have described how “two process” preparations such as grinding followed by honing, result in a beneficial surface texture characterised by plateau regions interspersed by deeper pockets and channels. (For reasons explained in this paper, such surfaces are herein described as “bi-Gaussian”.) However, in applications such as mechanical seals, a very similar surface topography is exhibited after wear, sometimes in excess of 1 mm. This means that the texture must be self-replicating and not simply the result of “wearing-in” by truncation of larger-scale roughness asperities left by the preparation process. This suggests that a combination of the wear process and the material microstructure is responsible for the worn surface texture. Thus a given microstructure would result in a particular self-replicating “bi-Gaussian” surface texture. Characterising such surfaces with simple parameters and understanding how they behave in sliding contact, makes it possible to optimise the texture for given operating conditions. It is then possible, in principle, to specify a microstructure to produce the in-service surface texture for optimum functional performance in a given duty. This paper presents the mathematical description of the “bi-Gaussian” surface and considers its elastic contact with a smooth plain counterface in terms of plateau-top asperity characteristics obtained using low-cost profilometry equipment. The validity of an elastic contact model is discussed. Finally an outline of the application of the contact model to a particular case of mixed friction sliding is outlined, to illustrate the potential for surface texture optimisation.