Sequential Periodic Motions in a Vibration-Assisted, Regenerative, Nonlinear Turning-Tool System

This paper studies the dynamics and bifurcations of a vibration-assisted, regenerative, nonlinear turning-tool system using an implicit mapping method. Machine vibration has been studied for a century for the improvement of machine accuracy and metal removal rate. In fact, this problem is unsolved yet. This is because such dynamical systems are involved in nonlinearity, discontinuity and time-delay. Thus, a comprehensive understanding of nonlinear machining dynamics with time-delay is indispensable. In this paper, period-m motions in the turning machine-tool system are studied through specific mapping structures, and the corresponding stability and bifurcations of the period-m motion are determined through the eigenvalue analysis. The analytical bifurcation scenarios for two sets of sequential period-m motions in a turning-tool system are presented. Numerical simulations of period-m motions are carried out to verify the prediction of periodic motions. The complex dynamics of vibration-assisted machining with strong nonlinearity are presented, which can provide a good overview for nonlinear dynamics of machine-tool systems.