Multiple regenerative effect governing chatter behaviour after onset

Chatter is the self-excited vibration that occurs during cutting. The entire structure of a self-excited vibration comprises two core mechanisms, i.e., stability limit and sustained vibration with finite amplitude after onset. The latter mechanism remained unnoticed until the discovery of the multiple regenerative effect (MRE) in 1980. However, its effects have not yet been recognized correctly. This paper summarizes the problems that could be resolved by considering the MRE in the analysis from the theoretical and practical viewpoints. In conventional stability limit analyses,tool traces never intersect; however, after the onset of chatter in an actual system, traces immediately intersect. This resultsin tool-workpiece separation, chip thickness variation during the separation period, and chip breakage. A solution for equation of motion considering the MRE agrees well with chatter behaviour in actual applications. In addition, the solution yields the phase relationship between the displacement of work motion and the cutting force, although this relationship is not considered in the equation of motion. Further, the relationship between the penetrating cutting speed and the resistive force, confirmed experimentally, is introduced in equation of motion, which verifies the widening of the stability region at low cutting speeds.