Extracting Summit Roughness Parameters From Random Gaussian Surfaces Accounting for Asymmetry of the Summit Heights Available to Purchase

The random Gaussian surface model proposed by Nayak is important to many statistical summit-based micro contact models. A Gaussian distribution is usually assumed for the summit heights as many surfaces have a Gaussian distribution of surface heights. In this work, based on Nayak’s models the skewness and kurtosis of the summit heights distribution are derived as a function of the bandwidth parameter α. The correctness of these two equations verified using a numerical scheme that generates random Gaussian surfaces with various α values. Also, practical contact simulations are performed to demonstrate the significance of the proposed equations and also to show the error of using a Gaussian distribution versus a correct asymmetric distribution for the summit heights.