Discussion on Ball Screw Slide–Roll Ratio and Entrainment Velocity Calculation

Abstract

The slide–roll ratio and entrainment velocity are critical parameters in ball screw mechanism tribology investigations and are often determined by Chin-Chung Wei’s approach. Their findings indicated that substantial sliding always occurs between the ball and the raceways, which appears to violate the ball drive principle. We validated Wei’s approach using the Harris method, which is widely used in rolling bearing research. When the helix angle is set to zero, significant differences occur: when the Harris method is utilized, the entrainment velocity at the inner contact points is essentially equal to that at the outer contact points, and the slide–roll ratio is zero for both; however, when Wei’s method is utilized, the entrainment velocity at the inner side is nearly three-times that of the outer side, and the slide–roll ratio at the outer side approaches two—the level of pure sliding—which is clearly incorrect. To overcome this issue, we present an accurate approach for obtaining the slide–roll ratio and entrainment velocity for ball screws by regarding the Frenet frame as a virtual cage, which is particularly applicable to those with a long lead and operating at high speeds. Moreover, we investigated the effect of structural factors on the slide–roll ratio and entrainment velocity utilizing this model.