Topography Analysis of Random Anisotropic Gaussian Rough Surfaces

Engineered surfaces (ground and similarly structured rough surfaces) show anisotropic characteristics and their topography parameters are direction dependent. Statistical characterization of these surfaces is still complex because of directional nature of surfaces. In this technical brief, an attempt is made to simulate anisotropic surfaces through use of topography parameters (three-dimensional (3D) surface parameters). First, 3D anisotropic random Gaussian rough surface is generated numerically with fast Fourier transform (FFT). Numerically generated anisotropic random Gaussian rough surface shows statistical properties (texture direction, texture ratio) similar to ground and similarly directional anisotropic rough surfaces. For numerically generated anisotropic Gaussian rough surface, important 3D roughness parameters are determined. Sayles and Thomas' (1976, “Thermal Conductance of Rough Elastic Contact,” Appl. Energy, 2(4), pp. 249–267.) theoretical model for directional anisotropic rough surface is adopted here for calculating the summit parameters, i.e., equivalent bandwidth parameter, mean summit curvature, skewness of summit height, standard deviation of summit height, and equivalent spectral moments. This work demonstrates the variation of spectral moments in both across and parallel to the lay directions with pattern ratio (⁠$γ=βx/βy$⁠). Correlation length (β_x) is fixed $10μm$ and correlation length (β_y) is varied from 100 to 10 $μm$⁠. Variation of summit parameters with pattern ratio is also discussed in detail. Results shows that mean summit curvature and skewness of summit heights increase with increase in pattern ratio, whereas standard deviation of summit heights and equivalent bandwidth parameter (α_e) decreases with pattern ratio. A significant difference is found in “Abbott-Firestone” parameters when calculated in both perpendicular and parallel to lay directions. Effect of these parameters on wear process is discussed in brief.