Probabilistic, Fractal, and Related Techniques for Analysis of Engineering Surfaces - Borodich, Feodor M.; Jin, Xiaoqing; Pepelyshev, Andrey (Frontiers in Mechanical Engineering, 2020)
In many engineering fields surface topography is of crucial importance solving problems of friction and other problems of tribology. A review of mathematical approaches for description of topography of engineering surfaces is presented. Firstly, we give a brief introduction to some of statistical parameters used for description of surface roughness. It is argued that although some of these parameters may be quite useful for specific engineering problems, a set of finite numbers of parameters cannot describe contact properties of rough surfaces. Then we discuss various models of surface roughness based on Gaussian models of the asperity heights. The results of application of various modern tests of normality for checking whether the distribution of the asperity heights is Gaussian, are presented. Further fractal models of roughness are discussed. Using fractal parametric-homogeneous (PH) surfaces, it is demonstrated that tribological properties of a rough surface cannot be characterized just by the fractal dimension of the surface. It is also shown that models based solely on the power-spectral density function (PSDF) are quite similar to fractal models and these models do not reflect tribological properties of surfaces. In particular, it is demonstrated that different profiles may have the same PSDF.