Parametric modeling of ball screw spindles

In the product development process numerical optimization can successfully be applied in the early product design stages. In the very common case of ball screw drives, the dynamical behavior is most depending on the geometrical shape of the ball screw itself. Properties like axial and torsional stiffness, moment of inertia, maximum velocity and acceleration are determined not only by the servo motor but also by screw diameter, slope and ball groove radius. Furthermore coupling effects between the design variables make the optimization task even more difficult. In order to capture these effects, efficient numerical (usually FEM or MBS) models are needed. In this work a new more accurate and efficient method of computing the axial and torsional stiffness of ball screw spindles is presented. We analytically derive parametric equations which depicts most of the dependencies of stiffness on geometrical parameters of the screw. Furthermore, we enhance the analytical model with an identified function, which increase the accuracy even more. The presented analytical model is validated against FEM model and catalog data with the help of numerous examples.