基于泛形理论的粗糙表面法向接触刚度研究

Research on the Normal Contact Stiffness of Rough Surfaces Based on the Ubiquitiform Theory

基于泛形理论和赫兹接触理论,通过泛形海岛分布描述粗糙表面的形貌从而建立结合面弹性接触模型,求解结合面的法向接触刚度.假设粗糙接触表面微凸体的高度满足高斯分布,通过赫兹接触理论建立单个微凸体的微观接触模型,利用粗糙表面的泛形复杂度D与面积度量尺码的最小下确界a;确定表面形貌.泛形复杂度反映微凸体在粗糙表面上占据的空间大小程度;度量尺码下确界是接触过程中的最小接触面积.通过泛形复杂度和面积最小下确界推导出粗糙表面法向接触刚度的解析表达式.数值算例结果表明:在相同的面积尺度区间内,粗糙表面的法向接触刚度随着泛形复杂度的增加而增加,反之减小.当接触表面的泛形复杂度不变时,粗糙表面的法向接触刚度随最小下确界的减小而增大.泛形复杂度的较大时,最小下确界的变化对于接触刚度的影响更加明显.通过与已发表的文献结果对比分析之后,发现采用泛形海岛模型所得到的结合面接触刚度与文献中实验结果吻合较好.

Based on the ubiquitiform theory and Hertzian contact theory,the morphology of the rough surface is described by the ubiquitiformal islands to establish the elastic contact model of the joint surface,which characterizes the normal contact stiffness of the joint surface.Assuming that the height of the asperity of the rough contact surface satisfies the Gaussian distribution,by establishing the asperity micro-contact model,the ubiquitiformal complexity D of the rough surface and the minimum infimum of measurement sizeδ;are introduced.Then the normal contact stiffness of the rough surface is derived based on the ubiquitiformal model.Different from the fractal model,the limited self-similar or self-affine structures only have integer dimensions.The ubiquitiformal complexity shows the complexity of the surface topography.The infimum of measurement size can reflect the details of the surface topography,and the surface topography is determined by the ubiquitiformal complexity and the minimum infimum of the area.After comparing with and analyzing the results from literature,it is found that the contact stiffness of the joint surface obtained by using the ubiquitiform island model is more consistent with the experimental results than the fractal model.Numerical results are obtained for the normal contact stiffness of rough surfaces with different values of ubiquitiformal complexity D and minimum infimum of measurement sizeδ;.It shows that in the same area scale interval,the normal contact stiffness of rough surfaces increases with the increase of ubiquitiformal complexity,and vice versa;when other conditions remain unchanged,the normal contact stiffness of rough surface increases with the decrease of the minimum infimum.When the ubiquitiformal complexity is larger,the change of the minimum infimum has a more obvious influence on the contact stiffness.These results can provide theoretical guidance for evaluating the normal contact stiffness of rough surfaces and improving accuracy of contact machine in engineering application.