FRACTAL ANALYSIS OF HEIGHT DISTRIBUTIONS OF ANISOTROPIC ROUGH SURFACES

A general distribution function for the heights of anisotropic enginee ring surfaces is obtained by extending earlier work on surface profile s. The derivation starts from a functional description of surface heig hts that involves fractal quantities and is comprehensive enough to in clude almost all of the mathematical models for surface topography tha t have appeared in the literature. It is found that the distribution i s in the form of a Gaussian function multiplied by a convergent power series, and the terms in the series depend in a fundamental way on the fractal parameters of the surface. This distribution is used to predi ct the dependence of bearing-area on fractal parameters, and is compar ed with other approaches to anisotropic surfaces in the literature. Tw o truncated approximate versions of the distribution function are intr oduced in order to test the theoretical model against experimentally o btained distributions of engineering surfaces; the results show good a greement between theory and experiment.