On the Doubly Regenerative Stability of a Grinder: The Effect of Contact Stiffness and Wave Filtering

In the interest of acquiring a physical understanding of the causes and growth of chatter in grinders, past studies of doubly regenerative stability by the author (Thompson, 1974, 1977; Hahn and Thompson, 1977) looked at unnaturally high workpiece rotational speeds, excluded the contribution of cutting zone contact stiffness, and did not consider the effect of workpiece wave filtering. By incorporating these effects into the past referenced work, this paper attempts to close the gap between basic understanding and actual grinder behavior. It is known that at low speeds chatter involving large numbers of lobe pairs is excited. This leads to a diffuse frequency spectrum. It is further shown that the effect of finite contact stiffness is to improve stability and that workpiece wave filtering has no effect on basic stability, but leads to self-limiting chatter. The approach to wave filtered quasistability is accompanied by a lowering of chatter frequency.