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

摘要：将结合面微凸体拓展为椭球体，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，根据椭球体的弹性接触理论，采用代入法得到了表征椭球形微凸体弹塑性接触变形机制的对应关系式。结合三维各向异性分形几何理论得到了结合面接触点离心率的有效区间为0,0.7374]，在此基础上，假设结合面接触点离心率分布在有效区间内，在该区间上服从指数分布，且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，进而建立了包含椭球形微凸体完全弹性、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，能较好的预测固定结合面在轻载状态下的法向接触刚度。

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

Abstract: In this article, the asperity of joint surface is equivalent to the micro ellipsoid. According to the KE finite element model and the elastic Hertz contact theory of ellipsoid, the relationship between normal load, contact area and deformation was obtained by analogy with the elastoplastic contact deformation mechanism of the spherical asperity. Combined with the theory of three-dimensional anisotropic fractal geometry, the strict effective interval of the eccentricity of the contact point of the joint surface is 0,0.7374]. Assuming that the eccentricity of the contact point of the joint surface obeys the exponential distribution in the effective range, and is independent with the area distribution, Using probability theory and the area size distribution function of the contact point, the two-dimensional joint distribution density function of the area of the contact point and the eccentricity of the joint surface was obtained. Furthermore, the fractal model of the normal contact stiffness of the joint surface including the complete elasticity, elastoplasticity and complete plasticity of the ellipsoidal asperities was established. The comparison between the theoretical stiffness of the model and the experimental data shows that: the model can better predict the normal contact stiffness of the joint surface. Especially under light load conditions, the model has a higher prediction accuracy.