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 a key factor in determining successful component performance especially in tribological applications. 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 assumption of normality of the asperity heights or similar assumptions that involve Gaussian distributions. The results of application of various modern tests of normality for checking whether the assumption of the normal distribution for the roughness heights is valid, are presented. Further models based on assumption of fractal character of roughness are discussed. Using fractal parametric-homogeneous (PH) surfaces, it is demonstrated that fractal dimension alone cannot characterize the contact features of rough surfaces. It is also shown that models based solely on properties of the auto-correlation function or its Fourier transform, i.e. 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.