粗糙表面接触分形模型的提出与发展

Fractal Model for Contact of Rough Surfaces

自表面接触塑性变形模型问世以来，经过近４０年的发展，已经形成以分形几何理论为基础的Ｍ－Ｂ粗糙表面接触分形模型．Ｍ－Ｂ模型以分形参数代替统计学参数表征粗糙表面，推导出了实际接触面积与载荷的关系，以及实际弹性接触面积和实际塑性接触面积的计算公式，指出了影响接触面变形性质的因素与规律．由于分形参数的尺度独立性，可望利用Ｍ－Ｂ模型对接触面积的预测不受测量仪器分辨率和取样长度等因素的影响，故其比基于统计分析的Ｇ－Ｗ接触模型更为合理．尽管如此，Ｍ－Ｂ模型还有待完善。

The plastic deformation model for contact of rough surfaces has been developing for about 40 years since it was proposed.M B fractal model for contact of rough surfaces has been formed recently,which is based on fractal geometry.M B model characterized rough surfaces using fractal parameters instead of statistical parameters.The relation between real contact area and applying load and the calculating formulas of real elastic and plastic contact area were derived from this model,the factors affecting the deforming property of contact surfaces and their changing tendency were also indicated.The prediction of contact area using this model would not change with the resolution of roughness measuring instrument and the length of sample because of the scale independence of fractal parameters,so this model is more reasonable than G W contact model which was based on statistical analysis.However,M B model needs further improvement and there are still some problems to be deeply investigated later.