结合面切向接触刚度的概率统计模型

PROBABILITY AND STATISTIC MODEL OF TANGENTIAL CONTACT STIFFNESS OF JOINT SURFACES

该文考虑结合面上微凸体接触为椭圆形接触,运用弹性力学空间半无限体受载荷变形理论,并根据椭圆形接触面上压力分布的Hertz理论,推导出椭圆形接触面的长、短半轴计算式和单个微凸体接触时的切向接触刚度表达式。建立了结合面上微凸体椭圆形接触面的长、短半轴呈二维正态分布、高度呈正态分布情况下的宏观切向接触刚度模型,得到了相应的宏观切向接触刚度表达式。通过数值计算给出了切向接触刚度随结合面的法向载荷、切向载荷、椭圆微凸体的离心率、微凸体分布的相关系数、微凸体测量高度和微凸体分布的标准方差等各影响因素的变化情况,增大法向载荷可以提高结合面的切向接触刚度,而切向载荷的增大会导致切向接触刚度的减小。

Considering that the asperity contact region is elliptical, we derive the governing formulae for the tangential contact stiffness of a single asperity contact based on the elastic deformation theory of a semi-infinite body under loads and Hertzian pressure distribution. The macro-model and corresponding formulae for obtaining the tangential contact stiffness are created for the elliptical contact surface of the asperity on the joint surface,where the major and minor axes show a two-dimensional normal distribution and the height shows a normal distribution. The influence of normal and tangential loads, the eccentricity of the elliptical asperity, the standard deviation and the correlation coefficient of the asperity's distribution, and the asperity measuring height on the tangential contact stiffness are evaluated by using the numerical simulation. The results reveal that the tangential contact stiffness of a joint surface can be improved by increasing its normal load. However, the decrease of the tangential load leads to the reduction of tangential contact stiffness.