Nonlinear regenerative chatter in turning

Abstract 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 (μ, Ω) with the bifurcation parameter μ representing the dynamic variation of the chip thickness, and the critical rotational speed Ω. The governing nonlinear equations are integrated in time by Adams Predictor corrector Method. Phase portraits are drawn between the instantaneous tool position x1 and the relative tangential velocity x2. It has been shown that in the absence of a cubic nonlinearity, the chatter response appears to be more chaotic.