Finite-amplitude stability in regenerative chatter: The effect of process damping nonlinearity and intermittent cutting in turning

The damping forces generated at the tool and workpiece interface, known as process damping, greatly influence the dynamics of regenerative chatter in machining. In addition to the increased stability against chatter at low cutting speeds, which is the well-known effect of process damping, post-chatter dynamics are also affected significantly by process damping nonlinearity, which is the less-studied effect of this phenomenon. Once the process vibrations become unstable after chatter occurrence, the process becomes intermittent in the sense that the tool loses contact with the workpiece and they are no longer in continuous engagement due to large-amplitude chatter vibrations. When vibration amplitudes are relatively large, process damping nonlinearity is shown to create stable limit cycles around which vibrations stabilize at a finite-amplitude. The relationship between the amplitude of the resulting limit cycles and the applied machining parameters is only known approximately from simplified models. Besides, the bifurcation of the resulting limit cycles by machining parameters such as cutting depth and spindle speed has not been studied. In this work, we use numerical continuation to develop the bifurcation diagrams of an SDOF model of regenerative chatter that includes process damping nonlinearity and non-smooth dynamics due to the disengagement of the tool and workpiece in post-chatter large-amplitude oscillations. The developed bifurcation diagrams accurately determine the relationship between the applied machining parameters and the amplitude of the resulting limit cycles. They also show that the stable limit cycles lose their stability by a subcritical non-smooth fold bifurcation when the amplitude is large enough to cause tool-workpiece disengagement. We also show that the static forces in the process, which are normally neglected in existing studies, become dynamic due to the intermittent tool-workpiece disengagement and alter the nature of limit cycle bifurcations. The findings of this study are validated numerically and by comparison to experimental results.