Determination of the fractal scaling parameter from simulated fractal-regular surface profiles based on the Weierstrass-Mandelbrot function
Determination of the fractal scaling parameter from simulated fractal-regular surface profiles based on the Weierstrass-Mandelbrot function
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DOI：
10.1115/1.2768617
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发表时间：
2007-10-01
影响因子：
2.5
通讯作者：
Chan, Wai Kin
中科院分区：
文献类型：
--
作者：
Wang, Shao;Shen, Ji;Chan, Wai Kin
分形维数和分形粗糙度参数通常用来表征分形表面。对于分形规则曲面，还包括分形域长度。这样的公式基于使用分形标度参数的常数值的近似，该参数表示 Weierstrass-Mandelbrot (W-M) 函数中相邻谐波分量的空间频率的比率。尽管有一些理由假设分形标度参数的常数值为 1.5，但在固体接触的分形建模中采用此假设仍然或多或少是任意的。在本研究中，通过使用基于随机游走公式的具有随机相位的 W-M 函数形式，将分形标度参数视为变量而不是常数。开发了具有清晰图形解释的简单数值方案来确定分形标度参数的值。分形维数、分形粗糙度参数和分形标度参数均以合理的精度从数值生成的表面轮廓中恢复。
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 simple numerical 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.