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Probabilistic, fractal, and related techniques for analysis of engineering surfaces

Borodich, Feodor ORCID:, Jin, Xiaoqing and Pepelyshev, Andrey ORCID: 2020. Probabilistic, fractal, and related techniques for analysis of engineering surfaces. Frontiers in Mechanical Engineering 6 , 64. 10.3389/fmech.2020.00064

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n many engineering fields surface topography is of crucial importance solving problems offriction and other problems of tribology. A review of mathematical approaches for descriptionof topography of engineering surfaces is presented. Firstly, we give a brief introduction to someof statistical parameters used for description of surface roughness. It is argued that althoughsome of these parameters may be quite useful for specific engineering problems, a set of finitenumbers of parameters cannot describe contact properties of rough surfaces. Then we discussvarious 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 thedistribution of the asperity heights is Gaussian, are presented. Further fractal models of rough-ness are discussed. Using fractal parametric-homogeneous (PH) surfaces, it is demonstratedthat tribological properties of a rough surface cannot be characterized just by the fractaldimension of the surface. It is also shown that models based solely on the power-spectraldensity function (PSDF) are quite similar to fractal models and these models do not reflecttribological properties of surfaces. In particular, it is demonstrated that different profiles mayhave the same PSDF.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Additional Information: This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY)
ISSN: 2297-3079
Date of First Compliant Deposit: 4 July 2020
Date of Acceptance: 2 July 2020
Last Modified: 05 May 2023 13:30

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