基于分形的表面形貌特征描述与评定参数的研究

运用Ｗｅｉｅｒｓｔｒａｓ－Ｍａｎｄｅｌｂｒｏｔ函数对表面形貌进行描述，并利用结构函数求出表面形貌的分形维数和形貌系数。研究了分形参数与表面支承长度率曲线的关系。理论分析和实验结果表明：支承长度率曲线主要与分形维数有关，而形貌系数对该曲线的影响较小。用分形理论研究表面形貌时，分形维数是主要的评定参数，它能提供表面接触承载能力的单值定量的评估，从而比支承长度率曲线更简洁而实用。

Research of Characterization and Evaluation Parameters for Surface Topography Based on Fractal Theory

Weierstrass-Mandelbrot function is used to introduce a new method for surface topography characterization. Structure function is used to calculate fractal dimension and topothesy. Research of theory and experiment show a primary relationship between fractal dimension and the bearing length ratio curve, while topothesy affects this curve to a smaller degree. So investigation on surface topography by using fractal theory, fractal dimension is a major parameter. Fractal dimension provides a simple quantitative measure of the contact support ability of surface, and it is more concise and practical than bearing length ratio curve.