中文摘要：

以数控机床进给系统为研究对象,运用第二类拉格朗日方程理论建立了系统扭转-纵向的耦合动力学模型,并利用四阶龙格-库塔法对方程进行了数值求解。采用等倍数法增加各参数值,进而求取了不同参数下的工作台速度最大振动幅值。在此基础上,分析了丝杠与螺母结合部轴向刚度、联轴器刚度、轴承刚度三个因素对进给系统工作台轴向振动的影响,并分析了在变导程下增加结合部等效扭转刚度对工作台扭转振动的影响。研究结果表明,随轴向刚度的增加工作台轴向振动幅值都呈减弱的趋势,螺母结合部轴向刚度是影响工作台轴向振动最大的因素,联轴器刚度是影响最小的因素。导程越大,工作台扭转振动幅值越大,等效扭转刚度对工作台扭转振动的影响率越明显。为进给系统的研究提供了理论参考,并为机床减振和结构优化提供理论依据。

英文摘要：

By taking numerical control machine feed system as the research subject, a axial-torsional cou- pling dynamic model of feed system has been established using the second theory of Lagrange equation, and the model has also been numerically solved by the four-order Runge-Kutta method. Increasing the various parameter values of feed system by equimultiple, the maximum velocity amplitude of workbench vibration under the different parameters has been obtained. Influence of the axial stiffness of nut integration, the cou- pling stiffness and the beating stiffness on workbench axial vibration has been analyzed, and under the changeable lead, the influence of increasing the integration equivalent torsional stiffness on workbench tor- sional vibration has also been analyzed. It turns out that when increasing the three axial stiffness, vibration amplitude of the workbench axial decreases. The axial stiffness of nut integration is taken as the major factor of the workbench axial vibration, and the coupling stiffness as the minimum factor. The bigger the screw lead, the greater the torsional vibration, and the influence ratio of equivalent torsional stiffness on workbench torsional vibration become more obvious. The discovery can be served as theory reference of feed system re- search, and provides theoretical basis for the vibration absorption and structure optimization of machine tool.