$n$-Point Asperity Model for Contact Between Nominally Flat Surfaces

For several decades, asperities of nominally flat rough surfaces were considered to be points higher than their immediate neighbors. Recently, it has been recognized that this model is incorrect. To address the issue, a new multiple-point asperity model, called the $n$-point asperity model, is introduced in this paper. In the new model, asperities are composed of $n$ neighboring sampled points with $n-2$ middle points being above a certain level. When the separation between two surfaces decreases, new asperities with higher number of sample points, $n$⁠, will come into existence. Based on the above model, the height and curvature of $n$-point asperities are defined and their distributions are found. The model is developed for Gaussian surfaces and for the general case of an autocorrelation function (ACF). As a case study, the exponential ACF is applied to the new model, which is shown to produce remarkably good agreement with measurements from real and simulated surfaces.