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A new analytical method of chatter stability prediction in milling is presented. A general formulation for the dynamic milling system is developed by modeling the cutter and workpiece as multi-degree-of-freedom structures. The dynamic interaction between the milling cutter and workpiece is modeled considering the varying dynamics in the axial direction. The dynamic milling forces are governed by a system of periodic differential equations with delay whose stability analysis leads to an analytical relation for chatter stability limit in milling. The model can be used to determine the chatter free axial and radial depth of cuts without resorting to time domain simulations.
Budak et al. (Sun,) studied this question.