Finite Element Formulation of Pre-Stressed Ball Screw Drives

In this paper a stiffness matrix of the ball screw drive element is formulated as an approach for substitute modeling of the stiffness conditions at the ball-groove contacts in the engagement region of the ball screw and the nut. A scalar spring model is proposed, for the coupling between the ball screw and the nut with respect to both the stiffness properties and the screw degree of freedom of the ball screw drive. This permits combined modelling and vibration analysis of entire frame structures including ball screw feed drive systems by means of integral finite element models. The feed axis of a feed drives test station serves here as an example for demonstration and for verification of the modelling approach. A reduced order representation of the finite element model is used for simulation of the feed axis in control, the results of which match corresponding measurement results obtained from the test station.