Non-Hertzian Elastohydrodynamic Contact Stress Calculation of High-Speed Ball Screws

Abstract

In order to eliminate the calculation error of the Hertzian elastohydrodynamic contact stress due to the asymmetry of the contact region of the helix raceway, a non-Hertzian elastohydrodynamic contact stress calculation method based on the minimum excess principle was proposed. Firstly, the normal contact stresses of the screw raceway and the nut raceway were calculated by the Hertzian contact theory and the minimum excess principle, respectively. Subsequently, the Hertzian solution and the non-Hertzian solution of the elastohydrodynamic contact stress could be determined by the Reynolds equation under different helix angles and screw speeds. Finally, the friction torque test of the double-nut ball screws was designed and implemented on a self-designed bed for validation of the proposed method. The comparison showed that the experimental friction torque was the good agreement with the simulated friction torque, which verified the effectiveness and correctness of the non-Hertzian elastohydrodynamic contact stress calculation method. Under the large helix angle, the calculation accuracy of asperity contact stress for the non-Hertzian solution was more accurate than that of the Hertzian solution at the contact region of ball screws. Therefore, the non-Hertzian elastohydrodynamic contact stress considering the asymmetry of the raceway contact region could more accurately analyze the wear depth of the high-speed ball screws.