A general elastic-plastic approach to impact analysis for stress state limit evaluation in ball screw bearings return system

A methodology for stress state limit recovering in ball screws return system is presented in this paper. A lot of different researches and standards have been already performed for rolling bearings load static and dynamic rating (ISO 76, ISO 281), but nothing has been said for ball screws except in some drafting standards (Draft standard DIN 69051-4). Also the overall stress limits introduced for rolling bearings in ISO standards are not valid for ball screws bearing because of their different contact geometry. Moreover, the plastic contact due to impact between the spheres and the ball return system, very important for ball screw bearing life determination, has been investigated in very recent works only for nominal impacts by Hung et al. [Impact failure analysis of re-circulating mechanism in ball screw. Eng Failure Anal 2004;11:561–73]. A general model for the elastic–plastic contact between two curved bodies, derived from the models introduced by Thornton [Coefficient of restitution for collinear collisions of elastic perfectly plastic spheres. ASME J Appl Mech 1997;64:383], and Thornton and Zemin Ning [A theoretical model for the stick/bounce behaviour of adhesive, elastic–plastic spheres. Powder Technol 1998;99:154–62], is introduced in this paper to describe the elastic–plastic impact behaviour of two general curved bodies. By using this approach the influence on the stress state due to geometric properties, materials and impact velocities is established using an experimental plastic deformation limit. So one can finally estimate an equivalent elastic Hertz stress limit (EHSL) useful for ball screw bearing design through the typical elastic Hertz formulas. Finally the optimal correlation between the EHSL and the experimental results for ‘‘conventional’’ ball bearings is recovered, moreover the EHSL for a lot of different ball screw return systems are evaluated