Probability and statistic model of tangential contact stiffness of joint surfaces

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.