Distributed Parameter Modeling of Flexible Ball Screw Drives Using Ritz Series Discretization

Ball screw drives are used in automation applications and machine tools to translate rotational motion of an electric motor into translational motion of a slide. Their frequency responses show characteristic torsional and translational resonances. The resonance frequencies vary with the slide position, which is due to the distributed stiffness and inertia of the flexible ball screw. The proposed model treats the ball screw as a flexible element, using Ritz series expansions to obtain a finite approximation of the continuous deformations. The use of problem-specific basis functions allows for a low-order approximation, making the model especially well suited for control design. The model shows excellent validation results and reproduces the variation of the resonance frequencies with high accuracy.