DYNAMICS OF 2-DOF REGENERATIVE CHATTER DURING TURNING

A two-degree-of-freedom (2-DOF) model comprising nonlinear delay dierential equa-tions (DDEs) is analyzed for self-excited oscillations during orthogonal turning. The model includes multiple time delays, possibility of tool leaving cut, additional process damping (due to ank interference), ploughing force, and shear-angle/friction-angle variation. An algorithm to simulate tool dynamics and seek periodic solutions is developed based on two methods: (i) Direct numerical integration and (ii) Shooting for DDEs. The multiple-regenerative and tool-leaving-cut eects are simulated via an equivalent 1-DOF system by introducing a time shift. The amplitude and minimum-period of limit cycles computed via these two methods compare well. Numerical studies involving the machining parameters are presented. The present plant model and dynamics could be useful for real time active control of tool chatter.