In a high speed ball screw, the spin motion of the ball, which results from elastic deformation at the ball-raceway contact, is an important factor in the friction heat and wear of the ball screw. A new analytical method which is presented by this paper can be used to determine the motion of the ball and the ball load distribution including the effect of the motion for a given ball screw geometry and operating condition. The method is an expansion of the analytical method of ball bearings described by JONES and includes the centrifugal force acting on the ball, change of the contact angle, contact deformation between the ball and raceway as well as stiffness of the shaft and nut. A force generated by contact between the balls is neglected. The motion of the ball is based on raceway control theory introduced by JONES. A parametric study on a ball screw is carried out to estimate the effectiveness of the method as a design tool.
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