Dynamics of 2-dof regenerative chatter during turning

A two-degree-of-freedom (2-dof) model comprising nonlinear delay differential equations (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 flank interference), ploughing force, and variations in shear angle and friction angle. Assuming a two-period delay at most, an algorithm based on an existing shooting method for DDEs is developed to simulate tool dynamics and seek periodic solutions. The multiple-regenerative and tool-leaving-cut effects for 2-dof chatter are simulated via an equivalent 1-dof analysis by introducing a time shift. Thus, the cut profile and instantaneous chip thickness are obtained by accounting for chatter motions along both axes. While the amplitude and minimum period of limit cycles computed via shooting and via direct numerical integration compare well, the shooting method converges much faster. Numerical studies involving machining parameters reveal period-1 motion only, for the range of cutting parameters considered here. The possibility of subcritical instability, characterized by the sudden onset of finite-amplitude chatter, is displayed. Additional process damping causes a reduction in chatter amplitudes as well as the subcritical instability to occur at a larger width of cut. An increase in the width of cut causes frequent tool-leaving-cut events and increased chatter amplitudes. The frequency of tool disengagement increases with cutting velocity, despite cutting force in the shank direction remaining constant over a certain velocity range. The chatter amplitude increases and then decreases when the cutting velocity or the uncut chip thickness is increased. The present plant model and dynamics would be useful for state estimator design in active control of tool chatter.