A fractal dimension and a fractal roughness parameter are usually used to characterize a fractal surface. For a fractal-regular surface, a fractal domain length is also included. Such a formulation is based on an approximation using a constant value of the fractal scaling parameter that represents the ratio of the spatial frequencies of adjacent harmonic components in the Weierstrass-Mandelbrot (W-M) function. Although there were some reasons for assuming a constant value of 1.5 for the fractal scaling parameter, it is still left more or less arbitrary to adopt this assumption in fractal modeling of solid contact. In the present study, the fractal scaling parameter was treated as a variable rather than a constant by using a form of the W-M function with randomized phases based on a random walk formulation. A new scheme with clear graphical interpretation was developed to determine the value of the fractal scaling parameter. The fractal dimension, fractal roughness parameter, and fractal scaling parameter were all recovered with reasonable accuracy from numerically generated surface profiles.
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STLE/ASME 2006 International Joint Tribology Conference
October 23–25, 2006
San Antonio, Texas, USA
Conference Sponsors:
- Tribology Division
ISBN:
0-7918-4259-2
PROCEEDINGS PAPER
Determination of the Fractal Scaling Parameter From Simulated Fractal-Regular Surface Profiles Based on the Weierstrass-Mandelbrot Function
Shao Wang,
Shao Wang
Nanyang Technological University, Singapore
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Ji Shen,
Ji Shen
Nanyang Technological University, Singapore
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Wai Kin Chan
Wai Kin Chan
Nanyang Technological University, Singapore
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Shao Wang
Nanyang Technological University, Singapore
Ji Shen
Nanyang Technological University, Singapore
Wai Kin Chan
Nanyang Technological University, Singapore
Paper No:
IJTC2006-12068, pp. 713-719; 7 pages
Published Online:
October 2, 2008
Citation
Wang, S, Shen, J, & Chan, WK. "Determination of the Fractal Scaling Parameter From Simulated Fractal-Regular Surface Profiles Based on the Weierstrass-Mandelbrot Function." Proceedings of the STLE/ASME 2006 International Joint Tribology Conference. Part A: Tribomaterials; Lubricants and Additives; Elastohydrodynamic Lubrication; Hydrodynamic Lubrication and Fluid Film Bearings; Rolling Element Bearings; Engine Tribology; Machine Components Tribology; Contact Mechanics. San Antonio, Texas, USA. October 23–25, 2006. pp. 713-719. ASME. https://doi.org/10.1115/IJTC2006-12068
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