Analysis of steel ball’s motion inside a ball screw (1st report: Contact forms ruled by geometric condition, external load and friction force)

Abstract

Ball screws and ball bearings are important mechanical elements in automobiles and machine tools due to their high mechanical transmission efficiency. However, with the spread of electric vehicles, the designs that ensure low noise and high durability are required. Currently, numerical analysis is mainly used to clarify the inner balls motion, but it is necessary to tune simulation models based on knowledge obtained from experiments in order to reproduce the behavior of experimental systems. Moreover, while there are the quantification methods of contact states and rolling motion of steel balls inside the ball screw using mathematical methods, the contact state and the ball motion are only considered in limited circumstances. Therefore, this study aims to extend mathematical methods to clarify the contact state and rolling motion of steel balls and guide grooves inside ball screws in order to contribute to noise reduction and longevity of ball screws. Four arc shapes of a Gothic arc, considering the helix orbit of steel balls and the position and dimensional errors of the steel balls in the contact plane under non-driven and non-loaded conditions of the ball screw, are given as geometric shapes, and the balance and rolling motion of steel balls during ball screw drive are calculated. Next, numerical examples are presented to examine the effects of changes in the arc shape on the revolution and rotation of steel balls and the impact on noise, wear, and lost motion inside the ball screw. Finally, the validity of the mathematical model is demonstrated by comparing the measured values with the theoretical values using a device composed of intersecting straight grooves with a crossing angle.

Keywords

• ball screw
• ball bearing
• contact condition
• ball motion
• rolling groove