Static and dynamic stabilities of self-excited random vibrations are investigated in terms of the differential equation and time series model for the vibrational signal. Various instabilities are demarcated in the parameter space of the time series model, so that the stability of random vibrations can be ascertained by locating the parameters obtained from the vibration data. These results are applied to machine tool chatter by analyzing tool point vibrations in a turning operation under different degrees of chatter. This analysis substantiates the theoretical investigation, which is further confirmed by resonance curves obtained for the workpiece and cutting tool.

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