粗糙表面接触的层级模型

A hierarchical contact model for rough surface

真实的材料加工表面的粗糙度往往跨越了多个尺度。本研究建立了一种新的粗糙表面层级接触模型。对于较大尺度部分,截断过滤短波长的粗糙度,然后运用连续介质力学的方法计算出相应的近似接触面积和局部压力的分布;对于较小尺度部分,本研究基于分形理论,利用二维Cantor集来描述层叠的短波长微凸峰,然后对在较大尺度得到的近似接触面积进行细化修正,计算出了最终的接触面积。为了验证所建立的模型,将得到的整体接触响应与有限元法计算结果进行了比较。结果表明,该模型能够充分预测粗糙表面的弹性接触响应,而且大大降低了多尺度粗糙表面接触力学建模的计算规模。这对进一步研究跨尺度粗糙表面之间的接触和摩擦具有重要意义。

Real machined surfaces are always rough across a wide range of length scales.This paper develops a hierarchical contact model,in which surface power spectrum density function is employed to divide roughness into two parts.In the macroscopic part,by cutting off short-wavelength roughness,the approximate contact area and the distribution of normal force are obtained adopting the continuum mechanics solution.In the microscopic part,the superposition of asperities for short wavelength is transformed into a two dimensional Cantor set based on fractal theory,and the approximate contact area is further refined based on the local pressure and geometric parameters.The contact response of the whole surface is thus obtained by adding the modification of the microscopic part into the macroscopic part.For verification,FEM is adopted to calculate the response of the fractal rough surfaces.The results demonstrate that our model can adequately predict the contact response of the multi-scale rough surface.The current study reduces the computing scale of the mechanical model of rough surfaces and thus provides a new method modeling rough surfaces in a larger scale span.This may have significant implications for further research on contact and friction between multi-scale rough surfaces.