An Integrated Model to Characterize Comprehensive Stiffness of Angular Contact Ball Bearings

The bearing dynamic behaviors will be complicated due to the changes in the geometric sizes and relative positions of the bearing components at high speed. In this paper, based on the Hertz contact theory, elastohydrodynamic lubrication (EHL) model, and Jones’ bearing theory, the comprehensive stiffness model of the angular contact ball bearing is proposed in consideration of the effects of elastic deformation, centrifugal deformation, thermal deformation, and the ball spinning motion. The influences of these factors on bearing dynamic stiffness are investigated in detail. The calculation results show that the centrifugal deformation and thermal deformation increase with the increase in rotation speed. When the centrifugal deformation and thermal deformation are considered, the bearing radial contact stiffness increases as the speed increases, whereas the axial contact stiffness and the angular contact stiffness decrease. When the deformations and the EHL are all considered, the comprehensive bearing stiffness decreases with the increasing speed. It is also found that the spinning motion of the ball causes the comprehensive bearing stiffness to increase.

Three-directional contact force model for the ball spinning of a thin-walled tube

This paper provides a computational model for calculating three-directional ball spinning force in accordance with the theory of space analytic geometry. The contact boundary equation of the ball and tube is obtained. By projection, the two-dimensional curve in each coordinate plane is acquired. The projected area of the contact zone in the coordinate plane is calculated through the curve integral. It is assumed that the average pressure of the forming region is nearly equal to that when the steel ball is pressed into the tube. Hence, the unit pressure of the deformation zone is obtained. Then, the spinning component force and total spinning force are calculated. Using a Tu1 thin-walled tube of oxygen-free copper as experimental object, a ball spinning experiment is conducted, the axial spinning components force are tested and the ball spinning force calculation model is verified. Based on deformation rate, backward sliding accumulation and extension and frictional heating, the factors influencing calculation error are analysed at the end of this paper.