Fractal analysis of height distributions of anisotropic rough surfaces

A general distribution function for the heights of anisotropic engineering surfaces is obtained by extending earlier work on surface profiles. The derivation starts from a functional description of surface heights that involves fractal quantities and is comprehensive enough to include almost all of the mathematical models for surface topography that have appeared in the literature. It is found that the distribution is 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 predict the dependence of bearing-area on fractal parameters, and is compared with other approaches to anisotropic surfaces in the literature. Two truncated approximate versions of the distribution function are introduced in order to test the theoretical model against experimentally obtained distributions of engineering surfaces; the results show good agreement between theory and experiment.