• CN:11-2187/TH
  • ISSN:0577-6686

›› 2006, Vol. 42 ›› Issue (9): 219-223.

• 论文 • 上一篇    下一篇



  1. 清华大学摩擦学国家重点实验室
  • 发布日期:2006-09-15


CHEN Hui;HU Yuanzhong;WANG Hui;WANG Wenzhong   

  1. State Key Laboratory of Tribology, Tsinghua University
  • Published:2006-09-15

摘要: 为了研究工程表面具有分形的特性,即在不同尺度下具有统计自相似性,探讨粗糙表面的分形特征,用随机中点位移和Weierstrass-Mandelbrot函数两种方法对轮廓和表面进行模拟,并对表面轮廓进行幂率谱分析,建立分形维数和幂率谱的关系,检验计算表明模拟表面的分形维数和指定值吻合良好。讨论分形参数的尺寸独立性和分形表面的统计特征,从幂率谱图可以看出,单分形的幂率谱图为一个区段,而双分形表面的幂率谱呈现明显的两个区段,不同尺度下的分形维数体现在其幂率谱图形上。与传统的统计参数相比,分形维数和特征尺度具有一定程度尺寸独立性。统计检验表明两种方法模拟的表面均符合近似的高斯分布。指出粗糙表面完整的描述和表征应兼顾分形和统计特征两个方面。

关键词: 粗糙表面, 分形, 计算机模拟

Abstract: In order to investigate the fractal characterization, namely the statistically self-affine of the engineering surfaces in different scale, two methods, the random-mid-displacements method and Weierstrass-Mandelbrot function method, are employed to simulate the profiles and 3D topography of rough surfaces. The power spectra of the surface profile is analyzed and the rela-tionship of fractal dimension and its power spectra is built. From the graph of the power spectrum, the power spectrum of single fractal surface only has one segment, but the power spec-trum of bifractal surface has two distinct segments, the different fractal dimensions are shown on the spectra graph. It is verified by calculation that fractal dimensions of the generated surfaces are in good agreement with the specified values. To compare with the traditional statistic parameters, the fractal dimensions and characteristic scale are scale independence to some extent. According to statistics, the two generated surfaces both have the character of the Gauss distribution. The scale independence of fractal characterization and statistical properties of the generated surfaces are discussed, through which it is concluded that a sophisticated description of rough surfaces should include both fractal and statistic features.

Key words: Computer simulation, Fractal Rough, surfaces