Generalization of Geometrical Rounding Mechanism in Regenerative Centerless Supports

This paper generalizes the geometrical rounding mechanism of regenerative centerless supports as applied to centerless grinding, shoe centerless grinding, and centerless support superfinishing. Relationships between support conditions and rounding stability are analyzed using a newly introduced parameter, the generalized center height angle. The effects of roundness errors at the support points on the depth of cut are clarified, and the rounding stability for each undulation on the workpiece is examined. Additionally, the geometrical filter effects caused by interference and the contact length with abrasive wheels are depicted, showing a significant reduction in roundness components for undulations above the cutoff threshold. The proposed rounding mechanism, based on the generalized center height angle, accurately predicts unstable undulations, a finding that is experimentally verified through tests on both centerless grinding and shoe centerless grinding setups.