Variable-Coefficient Dynamic Modeling Method for a Ball Screw Feed System in the No-Extra-Load Running State

Abstract

In a ball screw feed system of high-speed/high-acceleration machine tools, large frictional and inertial forces may change the real contact state of the kinematic joints, resulting in changes in the contact and transmission stiffnesses and, hence, changes in the dynamic characteristics of the system. In this study, a variable–coefficient dynamic modeling method for a ball screw feed system is proposed, considering the influence of changes in the no-extra-load running states, such as position, speed, and acceleration. Based on Timoshenko beam elements with two nodes and four DOFs, an equivalent dynamic model of a ball screw feed system is established using the hybrid element method. The expression for the equivalent axial stiffness of individual kinematic joints is derived, considering the influence of the feed speed/acceleration under the no-extra-load running state of the system. In addition, the stiffness and mass of the screw shafts on both sides of the screw nut are calculated, considering the influence of the system’s feed position. Hence, we obtain the total stiffness and mass of the system in the no-extra-load running state and analyze the natural frequency. Finally, we conduct validation experiments on a ball screw feed system of a large gantry-type machine tool with different no-extra-load running states.