Combining and Contacting of Two Rough Surfaces with Asymmetric Distribution of Asperity Heights

The statistical approach of describing rough surfaces is extended to include the contact of two rough surfaces in which their distribution of asperity heights can either be symmetric or asymmetric, and the asymmetry is modeled using the normalized Weibull distribution. In considering the contact between two rough surfaces, as in most practical applications, the contact can be approximated by an equivalent rough surface in contact with a smooth plane. The roughness parameters of the equivalent surface are obtained using the spectral moment method, and its validity is verified using realistic surface roughness measurements. This paper presents a method to obtain the equivalent rough surface with a Weibull distribution of asperity heights, in which the standard deviation and skewness parameters of asperity heights of the actual contacting surfaces are preserved. The advantages of this method are demonstrated via direct comparisons with a previously proposed method as well as with exact numerical simulation of the contact parameters of several different actual surfaces from magnetic storage and MEMS applications. For practical engineering applications, where the roughness parameters of each individual surface are known, contour plots for the skewness value of the equivalent rough surface are provided for practical ranges of combinations of standard deviation ratios and skewness values. As expected when the roughness of one of the contacting surfaces dominates, the skewness is solely determined by the rougher surface.