Study on static load distribution of ball screw with gothic arc groove

Ball screws offer many specific features, such as high mechanical performance, high accuracy, long-term stability, and suitability to a wide range of loads and speeds. Therefore, they are used as central elements in driving and transmission mechanisms. In a ball screw, the ball load distribution is an important factor for fatigue life, torque loss, and lubricating condition of the ball screw. A new analytical method, presented by this paper, can be used to determine the ball load distribution including the effect on a given ball screw geometry and arbitrary load conditions such as axial force, radial force, and moment. This method is an expansion of the analytical method of ball bearing described by JONES and includes the change of contact angle, contact deformation between the ball and raceway, as well as stiffness of the shaft and nut. A parametric study on a ball screw is carried out to estimate the effectiveness of the method as a design tool.