IUTAM Symposium on Elastohydrodynamics and Micro-elastohydrodynamics

Volume 134 of the series Solid Mechanics and Its Applications pp 397-408

Fractals and Surface Rroughness in EHL

  • F. M. BorodichAffiliated withSchool of Engineering, Cardiff University

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Firstly, a brief introduction to fractals and similarity methods is given. Fractal models of rough surfaces are usually used when the spectral density function of surfaces has the power law character. It is argued that the main source for various misunderstandings in applications of fractals to mechanics is the lack of precise definitions and non-critical repetition of common statements about fractal geometry. Some key papers concerning fractal models of roughness and papers connecting EHL and fractals are reviewed. Two classes of fractal surfaces introduced by the author, namely the Cantor profile models and the parametric-homogeneous (PH) surfaces, are discussed. The well-known Weierstrass-Mandelbrot (W-M) profile is a particular case of PH-profiles. It is shown that only physical fractals (prefractals) should be attributed to real surfaces. It is argued that the Cantor profile is simple for analytical analysis. However, it has a minor drawback: all asperities of the profile have one-level character, while, as Archard showed, real roughness has a hierarchical structure. Finally, it is suggested to model rough surfaces by a multilevel prefractal model introduced by Borodich and Onishchenko.


roughness fractal parametric-homogeneous surfaces multilevel prefractal model