Vibration frequencies in high-speed milling processes or a positive answer to Davies, Pratt, Dutterer, and Burns

The stability charts of high-speed milling are constructed. New unstable regions and vibration frequencies are identified. These are related to flip bifurcation, i.e. period doubling vibrations occur apart of the conventional self-excited vibrations well-known for turning or low-speed milling with multiple active teeth. The Semi-Discretization method is applied for the delayed parametric excitation model of milling providing the connection of the two existing and experimentally verified results of machine toot chatter research. The two extreme models in question, that is, the traditional autonomous delayed model of time- independent turning, and the recently introduced discrete map model of timedependent highly interrupted machining, are both involved as special cases in the universal approach presented in this study.