Parametric Study of Simulated Randomly Rough Surfaces Used in Contact Mechanics

The study and numerical simulation of randomly rough surfaces is a fundamental topic in contact mechanics. Existing theory permits calculating the distributions of values such as height, slopes and gradients based on the power spectrum of the surface. Determination of derived quantities like summit height or radius distribution tends to become mathematically intractable. An alternative approximation is then to simulate the random surfaces to obtain these distributions empirically. Here, a direct Monte-Carlo approach is presented in which distributions of summit heights and curvatures are obtained directly from the theoretical formulae. Results are compared to distributions calculated from simulated surfaces, over a wide range simulation parameters. The latter approach induces significant statistical dispersion as compared to the former. The summit radius distribution is narrower for the simulated surfaces than predicted by theory.