Stochastic models and statistical methods for analysing roughness of plateau-honed surfaces

Plateau honing is a way of enhancing the lubricant retention qualities of interfacing surfaces which are in relative motion. Surfaces prepared in this way enjoy two levels of roughness, which broadly correspond to a sequence of smooth plateaus at which they touch, and a series of rough crevices honed into one or both of the surfaces for the purpose of retaining lubricant. In the present paper we suggest a stochastic model for a class of such surfaces, based on an alternating sequence of segments of two processes of quite different roughness. Statistical methods are proposed for estimating the principal parameters of these processes, and their performance is studied both theoretically and numerically. We describe roughness in terms of a scale-free quantity, which may be taken equal to either fractal dimension or fractal index, and a measure of scale, the topothesy.