Nonlinear regenerative chatter in turning

Chatter is a topic of immense engineering importance because its occurrence in machining results in poor surface finish, promotes tool wear and hampers productivity. In this paper, a single degree of freedom, delay differential equation model is presented. The central idea of the model is the study of regenerative chatter effect, which qualitatively explains the nonlinear dynamics in machining. Stability charts are derived for the linearized case in a two dimensional phase plane (mu,Omega) with the bifurcation parameter mu representing the dynamic variation of the chip thickness, and the critical rotational speed Omega. The governing nonlinear equations are integrated in time by Adams Predictor corrector Method. Phase portraits are drawn between the instantaneous tool position x(1) and the relative tangential velocity x(2). It has been shown that in the absence of a cubic nonlinearity, the chatter response appears to be more chaotic. (C) 2001 Published by Elsevier Science Ltd.