Modeling and vibration mode analysis of a ball screw drive

Positioning systems for machine tools are generally driven by ball screws due to their high stiffness and low sensitivity to external perturbations. However, as modern machine tools increase their velocity and acceleration of positioning, the resonant modes of these systems could be excited degrading the trajectory tracking accuracy. Therefore, a dynamic model including the vibration modes is required for machine design as well as for controller selection and tuning. This work presents a high-frequency dynamic model of a ball screw drive. The analytical formulation follows a comprehensive approach, where the screw is modeled as a continuous subsystem, using Ritz series approximation to obtain an approximate N-degree-of-freedom model. Based on this model, the axial and angular components of each mode function are studied for different transmission ratios to determine the degree of coupling between them. After that, the frequency variation of each mode was studied for different carriage positions and different moving masses. Finally, an analysis of these results applied to controller design and parameter estimation is also presented.