垂直轴滚珠丝杠进给系统动力学建模研究

Huijie Zhang, Wanhua Zhao, Jun Zhang, Haitao Liu
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引用次数: 3

摘要

机床进给系统的运动关节是动力学建模的关键。它影响着机床进给系统的动态特性,进而对工件的加工质量产生重大影响。考虑主轴箱部件的重力作用,采用集总参数法建立了垂直轴进给系统的动力学模型。基于动力学模型计算了螺杆螺母和上下轴承的轴向刚度。当螺母移动到螺杆中间时,得到进给系统的传动刚度。进一步分析了进给系统在传动方向上的固有频率和加速度振动响应。以三轴高速立式加工中心的立轴滚珠丝杠主轴箱进给系统为例进行分析,结果表明:螺杆螺母刚度、上、下轴承刚度、进给系统的传动刚度在34左右变化。与不考虑重力效应的情况相比,分别为8%、10.0%、-12.5%、12.5%。加速度振动响应的固有频率和幅值变化幅度分别为6.3%和7.0%。固有频率的理论值与实验值的差异约为4.7%,而加速度振动响应幅值与实验值的差异约为18.0%。忽略重力效应时,固有频率解析值比实验值变化约10.4%,加速度振动响应解析幅值比实验值下降约23.4%。因此,考虑重力效应的垂直轴进给系统动力学模型具有较高的分析精度。
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Research on the modeling of dynamics for vertical axis ball screw feed system
The kinematic joints of machine tool feed system are crucial for the dynamics modeling. It affects the dynamic characteristics of machine tool feed system, and then there will be a significant influence on machining quality of workpieces. Considering the gravity of spindle box components, a dynamic model of vertical axis feed system was established using lumped parameter method in this paper. The axial stiffness of the screw-nut and up/down bearings was calculated based on the dynamics model. The transmission stiffness of the feed system was obtained when the nut moved to the middle of the screw. Furthermore, the feed system's natural frequency and acceleration vibration response in transmission direction were analyzed. Taking the vertical axis ball screw spindle box feed system of a three-axis high-speed vertical machining center as an example for analysis, the results show that the stiffness of the screw-nut, the stiifness of the up bearing and the down bearing, the transmission stiffness of the feed system varied about 34. 8%, 10.0%, -12.5%, 12.5% respectively compared with the situation ignoring gravity effect. The natural frequency and the amplitude of acceleration vibration response varied about 6.3% and 7.0% respectively. The theoretical data of natural frequency varies about 4.7% compared with the experimental data while that of the amplitude of acceleration vibration response is about 18.0% lower than the experimental data. When the gravity effect is ignored, the analytic value of natural frequency changes about 10.4% compared with the experiemental value, while the analytic amplitude of acceleration vibration response drops about 23.4% than the experimental one. Thus, the dynamic model of vertical axis feed system considering the gravity effect presents higher analytical accuracy.
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