Redefining ball screw kinematics: Analysing the limitations of traditional formulations for orbital and angular speed

Abstract

The orbital and angular speeds of the balls are fundamental kinematic variables for predicting the dynamic performance of ball screws, including power losses, vibration analysis, ball passing frequency, and wear phenomena. However, the theoretical formulation employed in the literature to calculate these variables does not account for the effect of transversal velocity component introduced by the helix angle. The present work introduces a new formulation that fully incorporates this effect, demonstrating substantial differences between the two approaches, especially at high helix angles. Additionally, a novel experimental methodology is presented to measure the orbital speed by calculating the ratio between the orbital rotation of the ball and the angular displacement of the screw. The experimental results show strong agreement with the predictions of the proposed formulation, offering more accurate results than existing models in the literature. A detailed analysis of the error is conducted, comparing the proposed formulation with traditional literature models across various ball screw geometries. Finally, an analysis of the rolling and sliding state of the contact on the kinematics of the ball is conducted, by studying the impact of the slide-to-roll ratio.