机床结合部特性的理论解析及应用

对机械结构的结合部特性进行了理论解析，从基本的动力学方程出发，推导出单平面结合部静位移与结合部受力之间的关系，进而转换为静刚度的表达式；并基于一个振动周期中某方向的输入能量与阻尼消耗的能量相等的概念，推导出单平面结合部阻尼的表达式。将机械结构中的多平面结合部，看成是多个单平面结合部的组合，而将回转结构等效为正多面体。由此，在机床结合部结构形式、受力大小确定的条件下，可以计算出结合部的等效结合刚度和阻尼。为了在机床整机动力学建模中融合结合部的特性，给出刚性结合和柔性结合两种情况下的协调方程。通过对XK712B立式镗铣床的整机建模和计算，并与试验结果进行比较，结果表明，综合静刚度相对误差的绝对值小于5%，固有频率相对误差的绝对值小于9%。将结合部特性融合到机床整机模型中，可以更精确地预测机床整机的综合静动态特性。

Theoretic Analysis on and Application of Behaviors of Machine Tool Joints

Theoretic analysis on the behaviors of mechanical structure joints is presented. Starting from a basic dynamics equation, the relationship between the static displacement and the load on the joint of a single plane is derived, which is further converted into an expression of the static rigidity. And the expression of damp at the joint of a single plane is derived on the basis of the concept that the input energy is equal to the damp consumption in some direction in a vibration cycle. A rotary structure is equivalent to a multi-plane solid by regarding the multiple joints in a mechanical structure as the combination of joints of multiple single planes. The equivalent joining rigidity and damp at the joint of a machine tool with given structural form and defined load thus can be calculated. Compatibility equations for rigid and flexible joining are given to integrate the behaviors of joints in the overall dynamics modeling of a machine tool. The overall modeling and calculation of the XK712B vertical boring and milling machine as well as the comparison with the test results show that the absolute relative error of comprehensive rigidity is less than 5% and the absolute relative error of natural frequency is less than 9%. By integrating the behavior of joints into the complete machine model, the comprehensive static and dynamic behaviors of the machine as a whole can be predicted more accurately.