On the Doubly Regenerative Stability of a Grinder: The Theory of Chatter Growth

Abstract

A mathematical method is devised to solve for the growth of chatter in grinders. The chatter growth rate is important because the grinding process is generally unstable. As such there is a need to find the conditions which minimize wheel and workpiece wave growth and optimize, the time between wheel dressing cycles. The analysis of grinding is complicated by the fact that regenerative feedback from both the wheel and workpiece drive the system. The treatment of this complication follows the author’s past work [1–3], but here, instead of assuming a constant chatter amplitude, the amplitude is allowed to vary according to the law, F = F0 eαt , and the objective is to solve for α.