Analytical Prediction of Chatter Stability in Milling: Part II — Application of the General Formulation to Common Milling Systems

The general formulation for the milling chatter prediction developed in Part I of the paper is applied to common milling systems. Three cases are considered: a workpiece with single degree-of-freedom, a face milling cutter with two degrees-of-freedom, and peripheral milling of flexible cantilevered thin web. The general milling stability formulation is further simplified for the less complicated models which do not have varying dynamics in the axial direction. For each case, an analytical expression which explicitly relate the chatter limit to the milling conditions and tool-workpiece dynamics are derived. The analytical predictions are compared with numerical and time domain solutions proposed by previous research. It is shown that the proposed method can accurately predict the chatter limits in milling and thus eliminates the time consuming numerical solutions.