考虑微凸体基体变形和相互作用的结合面法向接触刚度模型

A Normal Contact Stiffness Model of Joint Surfaces Considering Interaction of Deformations of Substrate and Asperity

针对以经典Greenwood-Willamson(GW)统计模型为基础建立的结合面法向接触刚度计算模型忽略微凸体基体变形和相互作用而导致的结合面刚度计算值增大的问题,建立了一种综合考虑微凸体基体变形和相互作用的结合面法向接触刚度模型。该模型以GW统计模型计算刚度的方法为基础,根据经典赫兹接触理论和弹性理论,在微凸体的总变形量中引入单个微凸体受法向载荷作用时基体的变形函数和周围区域的变形函数,采用不动点迭代法先后推导出单独考虑微凸体基体变形或相互作用时结合面法向接触载荷和刚度的表达式。对两种变形函数进行叠加给出了含微凸体基体变形和相互作用的结合面法向载荷和刚度的表达式,进而建立了结合面法向接触刚度模型。与GW统计模型进行了对比,仿真结果表明:考虑微凸体基体变形或相互作用的结合面法向接触刚度小于GW统计模型的法向接触刚度,在微凸体高度标准偏差为0.05μm时,最小结合面平均分离距离下考虑基体变形后结合面法向接触刚度下降9.8%,考虑微凸体相互作用后结合面法向接触刚度下降23.2%,此时微凸体相互作用比基体变形对系统的总刚度影响大。随着微凸体高度标准偏差的增大,前述两因素对结合面法向接触刚度的影响规律呈现相反的趋势。

A normal contact stiffness model of joint surface considering interaction of deformations of substrate deformation and asperity is proposed to solve the problem that the normal contact stiffness calculation model based on classical Greenwood-Willamson(GW)statistical model ignores the deformation and interaction of the micro-convex substrate and results an increase of the calculated value of the joint surface stiffness.The model bases on the method of calculating the stiffness of the GW statistical model.According to the classic Hertzian contact theory and elasticity theory,a deformation function of the base body and a deformation function of the surrounding area when a single micro convex body is subjected to a normal load are introduced into the total deformation of the micro convex body.Expressions of the normal contact load and stiffness of the combined surface are derived by using the fixed point iterative method when the deformation or interaction of the microconvex substrate is separately considered.Finally,the two deformation functions are superimposed to give the expressions of the normal load and stiffness of the joint surface containing interaction of deformations of substrate deformation and asperity,and furthermore,the normal contact stiffness model of the joint surface is established.A comparison with the GW statistical model is performed.Simulation results show that the normal contact stiffness of the joint surfaces considering interaction of deformations of substrate deformation and asperity is smaller than that of the GW statistical model.When the standard deviation of the height of the micro-convex is 0.05 microns,considering the average separation distance of the minimum joint surface,the normal contact stiffness of the joint surface is reduced by 9.8%after considering the deformation of the substrate,and the normal contact stiffness of the joint surface is reduced by 23.2%after considering the microprojection interaction.With the increase of the standard deviation of the height of the micro-convex body,the influence of these two factors on the normal contact stiffness of the joint surface shows an opposite trend.