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基于Hertz接触理论推导了两个微凸体之间互相作用的法向接触静弹性刚度。根据修正后的一个微接触点的平截面积尺寸分布,给出了界面的总法向接触静弹性条件刚度、总条件载荷的解析解。将法向静弹性刚度的解析解嵌入到有限元软件中,获得整机的理论模态。通过实验对解析解进行了定量验证。以机床结合部为研究对象,在理论振型与实验振型一致的条件下,模型的相对误差在-17.8%~17.3%之间。
Based on Hertz contact theory, the static contact stiffness of normal contact between two asperities was deduced. According to the corrected cross-sectional area distribution of a micro-contact point, the analytical solution of the total normal contact static elastic stiffness and the total conditional load of the interface are given. The analytical solution of normal static elastic stiffness is embedded into the finite element software to obtain the theoretical modal of the whole machine. The analytical solution is quantitatively verified through experiments. Taking the machine tool joint as the research object, the relative error of the model is between -17.8% and 17.3% under the condition that the theoretical vibration mode and the experimental mode are the same.