Efficiency analysis of sinusoidal stiffness variation method for chatter suppression

Chatter known as an unstable state, is a self-excite vibration which limits productivity of machining processes. To achieve stable machining and high productivity, chatter should be suppressed before it is fully developed. Sinusoids stiffness variation is an efficient method of chatter suppression that continuously varies the stiffness of the tool post. The frequency and the amplitude of sinusoids naturally play a critical role in the performance of chatter suppression. However, previous researches on stiffness variation are mostly qualitative based on experimental tests. Thus, this paper quantitatively investigates the effects of the frequency and the amplitude on chatter suppression from theoretical point of view. Both joint and individual effects of the frequency and the amplitude on the control efficiency are explored using semi-discretization method. The improvement of the stability limit is verified by the time response using Simulink. Moreover, the influence of the initial phase is studied and suggests the sinusoidal stiffness variation is dependent on the initial phase when the frequency is larger than 0.25 Hz.