The chaotic oscillations of high-speed milling

In case of highly interrupted machining, the ratio of time spent cutting to not cutting can be considered as a small parameter. In these cases, the classical regenerative vibration model playing an essential role in machine tool vibrations breaks down to a simplified discrete mathematical model. The linear analysis of this discrete model leads to the recognition of the doubling of the so-called instability lobes in the stability charts of the machining parameters. This kind of lobe doubling is related to the appearance of period doubling vibration or flip bifurcation. This is a new phenomenon occurring primarily in low-immersion high-speed milling along with the classical self-excited vibrations or secondary Hopf bifurcations. The present work investigates the nonlinear vibrations in case of period doubling and compares this to the well-known subcritical nature of the Hopf bifurcations in turning processes. Also, the appearance of chaotic oscillation 'outside' the unstable period-two oscillation is proved for low-immersion high-speed milling processes.