The effect of the lead error on the load distribution and no-load drag torque in a double-nut ball screw

In a ball screw mechanism, the lead error is not only the key parameter to evaluate the precision, but also an important parameter to determine the load distribution. In this paper, a model is proposed to predict the load distribution related to the lead errors. The mechanical analysis of a double-nut ball screw is conducted to investigate the effect of the lead errors on the balls’ contact deformations and contact angles. Based on the Hertz contact theory, the equations to predict the preload and no-load drag torque are established, and the amplitude of the preload is obtained when the rotational speed is low. To verify the model, various experiments are conducted to measure the lead errors and the no-load drag torques of the ball screw by changing the screws with different accuracy levels. The experimental results show that the preload and no-load drag torque rise when the lead error increases in a double-nut ball screw. Besides, the relative errors between the experimental value and the theoretical value are less than 10%. This proves that the model can predict the preload and the no-load drag torque influenced by the lead error well, which is beneficial to the design of the double-nut ball screw for a certain preload.