On the Doubly Regenerative Stability of a Grinder

Abstract

Traditionally, grinder stability analyses have been based on Laplace Transform techniques. In this paper an alternative approach is developed which takes into account the wear and speed of both the wheel and workpiece. Starting with the steady-state response of a grinder, the damping c, for quasi-stability, is expressed in terms of the fundamental dynamic parameters of the grinder and cutting process. The requirements for speed independent or unconditional stability are found by maximizing the pression for c. They are valid for both surface and cylindrical grinding, and reduce to those derived by Hahn in the special case of a nonwearing wheel. The requirements for conditional stability are found. The importance of wheel dress and extraneous forces is emphasized, and it is shown that conditional stability is dependent on lobe precession rates. The effect of wheel speed on conditional stability is questioned.