Hybrid Modeling of Ball Screw Drives With Coupled Axial, Torsional, and Lateral Dynamics

It has been a common practice to assume that the torsional and axial dynamics are totally decoupled from the lateral dynamics of the screw when modeling ball screw drives. However, experiments show that there is a considerable coupling between them, which could adversely affect the positioning accuracy and fatigue life of the drive. In this paper, the lateral dynamics of the screw is explicitly incorporated into the hybrid finite element model of ball screw drives. The ball screw is modeled by Timoshenko beam elements, and the balls, joints, bearings, and fasteners are modeled as pure springs. Rigid components are modeled as lumped masses. The proposed screw-nut interface model, which includes the effects of lateral vibrations, is shown to predict the coupling between axial, torsional, and lateral dynamics of ball screw drives. The effects of this dynamic coupling on the positioning accuracy of the drive are also presented with experimental proof. The proposed model provides a more realistic platform for a designer to optimize the drive parameters for high speed-high acceleration machine tool applications, where the ball screw vibrations limit the fatigue life of the mechanism, bandwidth of the servo systems, and positioning accuracy of the machine.