基于三维各向异性分形理论的固定机械结合面法向接触刚度建模研究

Research on Modeling of Normal Contact Stiffness of Joint Surface of Fixed Machinery Interface Based on Three-dimensional Anisotropic Fractal Theory

将结合面接触点拓展为椭圆形,基于KE有限元模型,类比球形微凸体在弹塑性接触变形阶段法向载荷、接触面积以及变形量之间的关系,采用代入法得到了表征椭圆抛物面形微凸体弹塑性接触变形机制的对应关系式.假设结合面接触点离心率分布与接触点面积分布相互独立,根据概率论以及接触点的面积大小分布函数,获得了关于结合面接触点面积与离心率的二维联合分布密度函数,进而依据三维各向异性分形几何理论建立了包含微凸体完全弹性、弹塑性以及完全塑性三种变形机制的结合面法向接触刚度分形模型.所建模型理论刚度与实验数据的对比结果,表明了模型的正确性及有效性,能较好的预测在轻载状态下的固定结合面法向接触刚度.

In this study,the contact point of the mechanical joint is expanded into an ellipse.According to the relationship between the normal load,contact area and deformation of the spherical asperity in the elastoplastic contact deformation stage,the corresponding elliptical paraboloid asperity relation is obtained by the substitution method.Assuming that the eccentricity distribution and area distribution of the contact points of the mechanical joint are independent of one another,according to the probability theory and the area distribution function of the contact points,the two-dimensional joint distribution density function of the area and the eccentricity of the mechanical joint surface contact points is obtained.Finally,according to the three-dimensional anisotropic fractal geometry theory,a fractal model of the normal contact stiffness of the mechanical joint surface including the three deformation mechanisms of asperity elasticity,elastoplasticity and plasticity is established.The comparison between the theoretical stiffness of the model in this study and the experimental data shows that the model is correct and effective,and can well predict the normal contact stiffness of the fixed mechanical joint under light load.