Abstract: To improve the machining precision and efficiency of machine tools, aiming at the linear rolling guide system with four grooves, the analytic modeling of guide system was completed by using Lagrange equation from rigid body dynamics. Corresponding to different rigid-body modes, the analytical expression of natural frequencies and mode shapes were derived. Based on this expression, the natural frequency values of a rolling guide system were obtained, and compared it with natural frequency values which solved by Vibration module of ADAMS software. The validity of analytic modeling was proved by two solving results which were basically identical. On the basis of analytical model, the effects of design parameters such as contact angle of rolling ball, the length of force area and the distance between contact point and center point of carriage on the dynamics characteristics of guide system were analyzed.

Key words: Lagrange equation, linear rolling guide system, analytical modeling, CNC machine tools, dynamics

摘要： 为提高机床的加工精度和加工效率，从刚体动力学出发，针对具有四排沟槽的直线滚动导轨系统，采用Lagrange方程完成导轨系统的解析建模，推导出对应于导轨各刚体模态的固有频率和振型的解析表达式。基于该表达式获得某滚动导轨系统的固有频率值，将其与利用ADAMS软件Vibration模块求解的固有频率值进行对比，发现两者求解结果基本一致，证明了解析建模的正确性。基于导轨系统的解析模型，分析了接触角、滚珠受力区长度以及滚珠接触点距滑块中心点的水平和垂直距离等设计参数对导轨动力学特性的影响。

关键词: Lagrange方程, 直线滚动导轨系统, 解析建模, 数控机床