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

Abstract

The growth of doubly regenerative chatter in a typical plunge cylindrical grinder is analyzed. The work is based on the mathematical method developed in reference [1]. Throughout, the physics of double regeneration is explained: (a) the individual contribution to chatter of wheel and workpiece regeneration is illustrated; (b) the wear resistant Borazon* wheel, although slightly more chatter prone, is shown to have an advantage over alumina because it requires less frequent dressing; and (c) the best in-process measure of grinding stability is shown to be wheel and workpiece lobe precession. The paper is concluded by showing how the optimum wheel and workpiece speeds are chosen. Under optimum conditions part tolerance and machine noise limit the maximum allowable grinding time and wheel wear establishes the dressing schedule.