Chatter in low immersion milling behaves differently from that in full immersion milling, mainly because of the non-negligible time-variant dynamics and the occurrence of period doubling bifurcation. The intermittent and time-variant characteristics make the active chatter suppression based on Lyaponov theorem a non-trivial problem. The main challenges lie in how to deal with the time-variant directional coefficient and how to construct a suitable Lyaponov function so as to alleviate the conservation, as well as the saturation of the controller. Generally, the Lyaponov stability of time-invariant dynamics is more tractable. Hence, in our paper, a first-order piecewise model is proposed to approximate the low immersion milling system as two time-invariant sub-ones that are cyclically switched. To alleviate the conservation, a novel piecewise Lyaponov function is constructed to determine the stability of each subsystem independently. The inequality conditions for determining the stability and stabilization are derived. The validity of the proposed stabilization algorithm to suppress both the hopf and period doubling bifurcation, as well as to reduce the conservation of the controller parameters have been verified.

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