Fractals and Surface Rroughness in EHL
 F. M. Borodich
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Abstract
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 noncritical 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 parametrichomogeneous (PH) surfaces, are discussed. The wellknown WeierstrassMandelbrot (WM) profile is a particular case of PHprofiles. 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 onelevel 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.
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 Title
 Fractals and Surface Rroughness in EHL
 Book Title
 IUTAM Symposium on Elastohydrodynamics and Microelastohydrodynamics
 Book Subtitle
 Proceedings of the IUTAM Symposium held in Cardiff, UK, 1–3 September 2004
 Pages
 pp 397408
 Copyright
 2006
 DOI
 10.1007/1402045336_29
 Print ISBN
 9781402045325
 Online ISBN
 9781402045332
 Series Title
 Solid Mechanics and Its Applications
 Series Volume
 134
 Series ISSN
 09250042
 Publisher
 Springer Netherlands
 Copyright Holder
 Springer
 Additional Links
 Topics
 Keywords

 roughness
 fractal
 parametrichomogeneous surfaces
 multilevel prefractal model
 Industry Sectors
 eBook Packages
 Editors

 R. W. Snidle ^{(2)}
 H. P. Evans ^{(2)}
 Editor Affiliations

 2. University of Cardiff
 Authors

 F. M. Borodich ^{(3)}
 Author Affiliations

 3. School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK
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