多重分形表面的弹塑性接触模型研究

Research on the Elastic-Plastic Contact Model for Multi-Fractal Surfaces

提出了在多重分形接触表面的最大接触长度范围内接触点尺寸分布数、频率分布函数和实际接触面积的普遍表达式 .这些表达式建立在对该类表面在不同临界频率范围内弹塑性接触变形方式的分析基础上 ,是研究多重分形接触表面的有关分形性质所必需的 .当给定这些表面的诸如分维数和特征长度等分形参数时 ,利用这些表达式 ,可实现对任意多重分形表面诸如磨损等接触性质的研究 ,使对复杂的多重分形接触表面的研究变得相对容易进行 .据此 ,以双分形表面为例 ,研究了其分形参数与磨损的关系 .计算结果表明 ,双分形表面的磨损率会随着表面最大接触尺寸和分形区域界限频率的增加而增加 .

Generalized multi-fractal contacted surface equations for size distributions, frequency distributions and real contact areas are presented in different ranges within the largest contact length. Based on the analysis of elastic-plastic deformation mechanism of these surfaces in different ranges of critical frequencies, these equations are necessary to research into the some properties concerning the fractal of these surfaces. When fractal parameters, such as fractal dimensions and characteristic lengths of the surfaces, are given, with the use of equations, researches on some properties, like wear, of these complex surfaces appear easier to carry out. The relationship between fractal parameters and wear of bi-fractal surfaces is emphatically discussed as an example. The calculation result shows that the wear rate of bi-fractal surfaces increases with the increase of the largest contact area and demarcation frequency.