Nonlinear Stability Analysis of Chatter in Metal Cutting

The occurrence of machine-tool chatter is usually undesirable as it gives rise to severe production problems. The existing theoretical and experimental studies on dynamic cutting indicate that the chip thickness and forces in cutting are related by a nonlinear equation. But the existing studies on chatter stability employ a linear relationship between these variables. In this paper, a relationship is developed between the chip thickness and forces in cutting under dynamic conditions. This relationship is based on existing experimental results and it exhibits active hysteresis. Hence, the oscillations in chip thickness lead the oscillations in cutting forces for all frequencies. A nonlinear theory is developed based on the describing function approach. An example is given of computing a stability chart giving the width of cut, frequency of chatter, and critical cutting speeds for regenerative chatter. In contrast to the linear stability analysis, the nonlinear theory can better explain the experimentally observed phenomena as well as give better correlation with the theoretical analysis of dynamic cutting.