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.