The analytical model of ball-spinning force for processing an annular groove on the inner wall of a steel tube

This paper presents a method for machining an annular groove on the inner wall of a steel tube by ball spinning. Based on spatial analytic geometry theory and assumptions about radial helical feed, the process utilizes a simplified expression of boundary curves of radial and tangential contact area between ball and workpiece. Through curve integration, the equations of radial and tangential contact areas for calculating ball-spinning force have been obtained. Based on results from calculation examples, this paper discusses the relationships between spinning depth, ball diameter, spinning feed, and ball-spinning force. The comparison of calculation results between the analytical model and the finite element method has been supplied, and the validity of the model has been certified.