The kinematics of ball-screw mechanisms via the slide–roll ratio

• Five possible relative motion states exist between the balls and the raceways.
• The slide–roll ratios at the contact points are numerically calculated.
• Pure rolling in the tangential direction of the helix path can be realized.
• The wear speed of the ball screw mechanism decreases at small slide–roll ratios.

The motion state of balls in the ball screw mechanism is hard to observed or measured because of the complexity of the mechanism consisting of three main components: screw, nut and balls. In this paper, a kinematic model for the basic single arc ball screw mechanism driven by the rotation of the screw is established using the homogenous transformation matrix, and the kinematic characteristics and slide–roll ratios at contact points of the raceways are analyzed. There are five possible relative motion states: a) screw pure rolling and nut rolling–sliding mixed motion, b) nut pure rolling and screw rolling–sliding mixed motion, c) screw pure sliding and nut no relative motion, d) nut pure sliding and screw no relative motion, and e) both rolling–sliding mixed motion between the balls and the raceways of the screw and nut in the tangential direction of the helix path. A parametric study is also carried out to evaluate the effect of motion velocity on the slide–roll ratio based on the numerical calculations of the slide–roll ratio at the contact points.