A New Method Developed for Fractal Dimension and Topothesy Varying With the Mean Separation of Two Contact Surfaces
A New Method Developed for Fractal Dimension and Topothesy Varying With the Mean Separation of Two Contact Surfaces
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DOI：
10.1115/1.2197839
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发表时间：
2006-07
影响因子：
2.5
通讯作者：
J. Liou;J. Lin
中科院分区：
文献类型：
--
作者：
J. Liou;J. Lin
在表面粗糙度的分形分析中，一般不考虑分形维数（D）和拓扑性（G*）这两个不变量，而是通过改变两个接触表面的平均间距（d*）来改变这两个粗糙度参数。首先建立了分形维数与平均分离度之间的关系。通过将两种不同方法构造的结构函数等效，可以建立功率谱函数中的标度系数、分形维数和微凸体高度拓扑之间的关系。由不同平均间距下的接触点数目和功率谱函数的实验结果，求出分形维数和标度系数，可以确定拓扑性的变化。在这项研究中，发展了一个数值方案，以确定相应于一个给定的平均分离的分形维数和拓扑的收敛值。该模型预测的接触斑点数的理论结果与文献报道的实验结果吻合较好。随着平均间距的增大，分形维数和拓扑性都得到了提高。当平均间距减小到较小值时，在恒定D和G* 与可变D和G* 的模型之间显示出接触载荷或总接触面积的显著差异。
Instead of a general consideration of the fractal dimension (D) and the topothesy (G*) as two invariants in the fractal analysis of surface asperities, these two roughness parameters in the present study are varied by changing the mean separation (d*) of two contact surfaces. The relationship between the fractal dimension and the mean separation is found first. By equating the structure functions developed in two different ways, the relationship among the scaling coefficient in the power spectrum function, the fractal dimension, and topothesy of asperity heights can be established. The variation of topothesy can be determined when the fractal dimension and the scaling coefficient have been obtained from the experimental results of the number of contact spots and the power spectrum function at different mean separations. A numerical scheme is developed in this study to determine the convergent values of fractal dimension and topothesy corresponding to a given mean separation. The theoretical results of the contact spot number predicted by the present model show good agreement with the reported experimental results. Both the fractal dimension and the topothesy are elevated by increasing the mean separation. Significant differences in the contact load or the total contact area are shown between the models of constant D and G* and variable D and G* as the mean separation is reduced to smaller values.