Analytical Prediction of Chatter Stability in Milling: Part I — General Formulation

A new analytical method of chatter prediction in milling is presented. A general formulation is developed by modeling the cutter and workpiece as multi degree-of-freedom structures with 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 limit in milling. The model can be used to determine the chatter free axial and radial depth of cuts without resorting to the time domain simulations.