Research on the Validity of using Nayak's Theory for Summit Parameters of Discrete Isotropic Gaussian Surfaces

Abstract

In this paper, with the aim of more appropriately characterizing surface topography for tribology, the validity of Nayak's theory is assessed through a comparison with direct calculations. The summit parameters examined in this study are the areal density, mean radius of curvature, and standard deviation of height. Functions such as the probability density of summit height and summit height vs. mean radius of curvature are also discussed. Purely homogeneous, isotropic and Gaussian distributed surfaces generated with a stochastic model are used to avoid unpredictable components such as noise and local irregularities. Overall, the estimation showed good qualitative agreement with the direct calculation. The relative discrepancies range from -10 to 20% for density, -20 to -8% for curvature, and -2 to 10% for height.