The productivity of many industrial cutting processes is limited by high amplitude chatter vibrations. An optimization technique based on the use of the stability lobes helps to increase the productivity of these processes, improving the life of machine elements and reducing the tool wear as well. The best-known lobes correspond to Hopf bifurcations. However, in case of interrupted cutting, additional lobes appear due to period doubling or flip bifurcation. When the system has more than one dominant vibration mode, important variations can appear in stability due to interaction between modes.
The basic mathematics for the appearance of these new lobes are shown in this article. The frequency domain study shows that lobes related to flip bifurcation are a special case of the interaction between modes. The results of these interactions are verified by comparison with semi-discretization method and time domain simulations, respectively.
