Prediction of Parameters of Equivalent Sum Rough Surfaces

Abstract

In statistical models, the contact of two surfaces is typically replaced by the contact of a smooth, flat, and an equivalent rough sum surface. For the sum surface, the zeroth, second, and fourth moments of the power spectral density m0, m2, and m4 respectively, are the sum of spectral moments of two contacted surfaces. In this work, the selected parameters of the sum surfaces were predicted when the parameters of individual surfaces are known. During parameters selection, it was found that the pair of parameters: Sp/Sz (the emptiness coefficient) and Sq/Sa, better described the shape of the probability ordinate distribution of the analyzed textures than the frequently applied pair: the skewness Ssk and the kurtosis Sku. It was found that the RMS height Sq and the RMS slope Sdq were predicted with very high accuracy. The accuracy of prediction of the average summit curvature Ssc, the areal density of summits Sds, and parameters characterizing the shape of the ordinate distribution Sp/Sz and Sq/Sa was also good (the maximum relative errors were typically smaller than 10%).