Ball Screw Drive Systems: Evaluation of Axial and Torsional Deformations

Abstract

The ball screw drives are among the most commonly mechanisms used to provide motion in high speed machine tools. The most important factor that affects high speed positioning accuracy is the closed loop bandwidth, which in turn is affected by the structural vibration modes. In recent years, newer strategies have emerged achieving higher control bandwidth, but requiring higher order plant models as well as a better understanding of the system dynamics. This work presents a dynamic model of a lead screw drive accounting for high frequency modes. The analytical formulation follows a comprehensive approach, where the screw was modeled as a continuous subsystem. The axial and angular displacement fields for this continuous screw were approximated by Ritz series to obtain an approximate N-degree-of-freedom model. Furthermore, it is discussed how to decouple the damping matrix to transform an N-degree-of-freedom system into N one-degree-of-freedom systems, because the advantages that this implies when numerical solution is required. Then, expressions for the displacement fields in terms of modal coordinates are found and a procedure to compute the axial and angular components of the mode functions is discussed, as well as a numerical procedure to compute the system deformation. In order to obtain conclusions about the system behavior in the first modes, the axial an angular components of the mode functions are plotted. Then, an analysis based on a comparison with results from others works is presented.