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