包含几何误差的机械结合面法向刚度研究

Study of normal stiffness of machine joint surface involving geometric errors

对包含几何误差的机械结合面进行离散化,离散后的微表面的基准平面高度满足结合面几何误差分布。每个微表面内,微凸体的高度只受粗糙度的影响。基于接触理论建立了微表面的法向刚度模型,通过对微表面模型集成获得了结合面的法向刚度模型。通过对所建模型的数值仿真,揭示了结合面法向刚度与间隙的非线性关系,几何误差的幅值和波长对法向刚度的影响以及非线性刚度对结合面振动特性的影响。计算结果表明:法向刚度随着间隙的减少而迅速增加,几何误差会导致结合面宏观上的局部接触和应力集中;在相同干涉量下,法向刚度随着几何误差幅值的增加而增加,但与结合面的波长没有关系;非线性刚度会导致结合面固有频率的下降和振动位移的不对称。

The machine joint surface including geometric errors was discretized into mini interfaces, to make their base planes well satisfied the geometric error distribution of the joint interface. For each mini surface, the height of micro-peaks only depended on the surface roughness. The normal stiffness model of mini interfaces was proposed based on the contact mechanics, and then the normal stiffness model of the whole joint interface was obtained through combing the models of mini interfaces. By numerical simula- tion,it revealed the nonlinear relationship between the normal stiffness and clearance of interfaces, the effects of amplitude and wavelength of geometric errors on normal contact stiffness, and the influence of nonlinear stiffness on vibration. The result showed that the normal stiffness rapidly increased with the decrease of clearance. As a result of geometric errors,there would be local contact and stress concentra- tion of joint surface in macroscopical. With the same interference value, the normal contact stiffness increased with the amplitude of geometric errors increasing, which was independent on the wavelength of geometric errors. The nonlinear stiffness can lead to the decrease of the natural frequency of joint surface and asymmetry of the vibrating displacement.