针对精密丝杠直线进给系统在低频伺服力激励下产生动态响应的原因及机理进行了建模研究，提出了一种进给系统动力学模型。其特色在于不同于伺服输出力高频成分或其他方向高频激励可能会引起机械系统共振的建模分析，描述了伺服电动机的伺服输出力的低频谐波成分对进给系统动态响应的影响。采用集中参数法建立了进给系统的动力学模型，利用拉格朗日方法，推导了精密车床进给系统的运动方程。仿真和试验结果表明：① 伺服力矩中存在着众多的谐波成分，频率数值远远低于进给系统的第一阶固有频率66 Hz，而且随着速度的增大，频率分量增大；② 刀尖点在z轴进给方向振型所对应的第一个固有频率，仿真与试验结果误差在5%之内，验证了所建动力学模型的有效性；③ 与测量的匀速运动下刀塔运动速度响应对比，所建模型能有效地反映伺服输出力低频谐波成分对机械系统动态响应的影响；响应的幅值变化量15%左右。最后指出，在精密机床进给系统设计中，必须考虑伺服激励的低频谐波成分带来机械系统的微小强迫振动。

A feed system dynamics model is proposed to study the reasons and mechanism that cause the precision lathe dynamic response in the excitation of low frequency servo force. The proposed modeling is based on dynamics theory analysis, from which the influence of low frequency harmonic components of servo force and the mechanical friction characteristics on the dynamic response of the feed system can be described. A classic z axis of lathe tool is taken as an example, lumped-parameter method is used to set up the dynamic model of machine tool and the dynamic equation is derived by Lagrange method. The displacement response of knife tower are measured when the z axis moves at a uniform velocity, and compared with the simulation results to validate the accuracy of the model. The simulation and experimental results show that: ① there are many harmonic components of the servo torque, frequency is far lower than the first order natural frequency (66 Hz)of the feed system, and with the increase of the speed, the frequency components increase; ② the first natural frequency of simulation and experimental results are within 5%, validate the dynamics model; ③ with the test results comparison under the uniform motion velocity, the model can effectively reflect the low frequency harmonic components of servo force on the effect on the dynamic response of the mechanical system, the amplitude variation of about 15%. And also it points out that the low frequency harmonic component of servo force is un-ignorable factor to solve precision displacement response of feeding system movement.