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.