Calculation boundary vulnerability of numerical algorithm in milling stability prediction

Though considerable efforts have been made to improve the precision of numerical algorithms for obtaining more accurate chatter stability prediction in milling process, a calculation boundary vulnerability, existing generally in numerical predictive methods, is usually ignored, which can significantly reduce accuracy of chatter stability prediction in certain calculated step lengths. Starting from the numerical solution of delay differential equation, this paper first gives a detailed mathematical derivation to demonstrate the beingness of the numerical calculation errors at the crucial step for two equal interval calculation methods of cutting force coefficients, and then discusses the impact of the errors on the convergence effect and prediction accuracy. Afterwards, the methods seeking and repairing the discrete number of time period with vulnerability are proposed, which are verified by the classic milling models. The presented technique could prevent this undesirable boundary vulnerability happening in numerical prediction of milling stability, and help the path planers obtain more accurate parameters which can achieve chatter free in the manufacturing process.