A Multiscale Statistical Analysis of Rough Surfaces and Applications to Tribology

Feodor M. Borodich (), Andrey Pepelyshev and Xiaoqing Jin
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Feodor M. Borodich: College of Aerospace Engineering, Chongqing University, Chongqing 400044, China
Andrey Pepelyshev: School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK
Xiaoqing Jin: College of Aerospace Engineering, Chongqing University, Chongqing 400044, China

Mathematics, 2024, vol. 12, issue 12, 1-19

Abstract: Mathematical modelling of surface roughness is of significant interest for a variety of modern applications, including, but not limited to, tribology and optics. The most popular approaches to modelling rough surfaces are reviewed and critically examined. By providing counterexamples, it is shown that approaches based solely on the use of the fractal geometry or power spectral density have many drawbacks. It is recommended to avoid these approaches. It is argued that the surfaces that cannot be distinguished from the original rough surfaces can be synthesised by employing the concept of the representative elementary pattern of roughness (REPR), i.e., the smallest interval (or area) of a rough surface that statistically represents the whole surface. The REPR may be extracted from surface measurement data by the use of the “moving window” technique in combination with the Kolmogorov–Smirnov statistic.

Keywords: roughness; statistics; fractal; multiscale; surface; tribology; friction; multilevel (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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