椭圆抛物体形微凸体弹性接触力学模型

Elastic Contact Model of Elliptical Parabolic Asperity

为了更准确地描述粗糙结合面的微观接触特性,构建了一种椭圆抛物体形微凸体曲面弹性接触模型。该模型同时考虑了微凸体正接触与侧接触的情形,采用了Weingarten映射的方法来求解接触点处的曲率,并结合赫兹曲面接触理论进行求解,得出椭圆抛物体在弹性侧接触时的接触面积与接触位移的解析公式。讨论了微凸体在不同相对位置下及不同椭圆率的情况下接触面积与接触位移的变化,并通过有限元仿真与该模型进行了对比计算,结果表明:椭圆率对接触面积、接触位移的计算结果影响较大,当椭圆率在超过0.9后,两微凸体接触面积迅速减小,接触位移迅速增大;提出的模型与有限元模型结果相比,两微凸体接触位移计算结果差异最大为10%,接触面积结果差异最大为6.2%。该模型同样适用于求解几何模型具有二阶连续偏导数的微凸体弹性接触问题,为研究形状更为复杂的微凸体接触奠定了基础。

To precisely describe the contact mechanics between two solid rough surfaces, a kind of el shou iptical parabolic elastic asperity contact model was proposed. Both top-top contact and der-shoulder contact were considered in this model. Weingarten map was adopted to obtain the curvature of contact point, and Hertz surface contact theory was used to solve this model. Analytic formula was deduced to get contact displacement and contact area for shoulder-shoulder contact. The influence of relative location and ellipticity on contact area and contact displacement was discussed. Finite element model and the proposed model were compared. The result shows that the ellipticity exerts an obvious influence on the contact area and contact displacement～ when ellipticity exceeds 0.9, the contact area and contact displacement of two asperities change drastically; the largest contact displacement error reaches 10 %, and the largest contact area error reaches 6.2 %. The proposed model is suitable for the other asperity models with second-order continuous partial derivatives.