A New Microcontact Model Developed for Variable Fractal Dimension, Topothesy, Density of Asperity, and Probability Density Function of Asperity Heights
A New Microcontact Model Developed for Variable Fractal Dimension, Topothesy, Density of Asperity, and Probability Density Function of Asperity Heights
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DOI：
10.1115/1.2338059
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发表时间：
2007-07
期刊：
影响因子：
--
通讯作者：
J. Liou;J. Lin
中科院分区：
文献类型：
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作者：
J. Liou;J. Lin
本文应用分形理论对传统的以统计形式建立的接触表面微接触模型（Greenwood和威廉姆森模型）进行了修正。平均曲率半径（R）和微凸体密度（η）不再被视为常数，而是被视为相关参数（包括分形维数（D）、拓扑性（G）和两个接触表面的平均间距）的函数。从理论模型中得到了不同接触面平均间距下的分形维数和拓扑结构。然后，平均曲率半径和粗糙体的密度也通过不同的平均间隔而变化。因此，一个数值计划，以确定相应的平均分离的分形维数和拓扑的收敛值。由不同分离度的理论预测得到的表面形貌表明，微凸体高度的概率密度函数不再是高斯分布。随着平均间距的增大，分形维数和拓扑性都得到了提高。通过减小平均间距来减小微凸体的密度。采用变量D、G* 和η以及非高斯分布预测的接触载荷和总接触面积结果始终高于采用常数D、G*、η以及高斯分布预测的结果。
In the present study, the fractal theory is applied to modify the conventional model (the Greenwood and Williamson model) established in the statistical form for the microcontacts of two contact surfaces. The mean radius of curvature (R) and the density of asperities (η) are no longer taken as constants, but taken as variables as functions of the related parameters including the fractal dimension (D), the topothesy (G), and the mean separation of two contact surfaces. The fractal dimension and the topothesy varied by differing the mean separation of two contact surfaces are completely obtained from the theoretical model. Then the mean radius of curvature and the density of asperities are also varied by differing the mean separation. A numerical scheme is thus developed to determine the convergent values of the fractal dimension and topothesy corresponding to a given mean separation. The topographies of a surface obtained from the theoretical prediction of different separations show the probability density function of asperity heights to be no longer the Gaussian distribution. Both the fractal dimension and the topothesy are elevated by increasing the mean separation. The density of asperities is reduced by decreasing the mean separation. The contact load and the total contact area results predicted by variable D, G*, and η as well as non-Gaussian distribution are always higher than those forecast with constant D, G*, η, and Gaussian distribution.