Prediction of chatter stability for milling process using precise integration method

The explicit precise integration method (PIM) is adopted to predict the chatter stability of milling process. To begin with, the dynamic equation with the regenerative effect is established from a simplified 2-DOF milling model. Then, the general solution for Hamilton system of the delay differential equation (DDE) is obtained by ordinary differential theory. To attain time series expression, the nonhomogeneous term is expanded by Taylor formula. Subsequently, the exponential matrix is resolved by 2Nth order algorithm, which achieves complete discretization of iterative formula. Lastly, the stability lobe diagram is constructed by utilizing Floquet theory to judge the eigenvalues of the state transition matrix corresponding to certain cutting conditions. A classic benchmark example is introduced and the comparison results show PIM is valid for prediction of chatter stability.