A Multiscale Statistical Analysis of Rough Surfaces and Applications to Tribology

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 th...

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Bibliographic Details
Published inMathematics (Basel) Vol. 12; no. 12; p. 1804
Main Authors Borodich, Feodor M, Pepelyshev, Andrey, Jin, Xiaoqing
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.06.2024
Subjects
fractal
Fractal geometry
Fractals
Friction
Influence
Lubricants & lubrication
multiscale
Power spectral density
roughness
Statistical analysis
statistics
surface
Surface roughness
Technology application
Topography
Tribology
Canada
United Kingdom
Germany
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12121804