Analysis of non-Hertz contact stress and bearing capacity on meshing pairs in a real-time non-clearance precision ball transmission

Abstract

Considering the friction on meshing pairs in a real-time non-clearance precision ball transmission, a modified meshing mechanical analysis model was established, and the normal meshing force and tangential friction acting on each meshing pair were calculated accurately via the contact stiffness coefficient method. The ball–tooth contact was equivalent to the contact model of an ellipsoid and semi-infinite elastic solid according to non-Hertzian theory, and the contact stress of meshing pairs was analyzed by the discrete convolution and fast Fourier transform (DC-FFT) technique. Furthermore, the bearing-capacity estimation method for a transmission system was established based on the Mises yield criterion. The results show that the tangential distribution force has a significant effect on the contact stress field of a meshing pair, with the maximum Mises equivalent stress being approximately 0.621 times the central contact pressure at different meshing positions. Moreover, the bearing capacity of the planetary plate is weaker than that of the center plate; hence, the bearing capacity of a transmission system should be determined by the planetary plate.