Programmable optimal design of sinusoidal spindle speed variation for regenerative chatter suppression

Continuous spindle speed variation, especially under sinusoidal speed law, is a well-known effective and flexible technique to suppress chatter vibration by disrupting regenerative effect in high-lobe-number zone. In most researches, its optimal design parameters (i.e. amplitude and frequency of spindle speed variation) are selected to maximize cutting depth by using complex stability simulations, which take much time and require machine tool dynamics. In this paper, novel simple criteria, only according to chatter frequency and nominal spindle speed, is proposed to select optimal amplitude and frequency of sinusoidal spindle speed variation (S³V). Under assumption that the variation amplitude and frequency is low in practice, modulation index for S³V can be introduced by analogy between S³V and frequency modulation technique in radio engineering. Then, the proposed formula to select optimal parameters is introduced based on kinematic process energy analysis with modulation index as an argument of Bessel function. Although the proposed method does not give information about stability limit, it has potential to contribute to intelligent active chatter suppression by automatic selection of S³V parameters combined with chatter monitoring system. Some boring tests were conducted to verify the proposed formula.