Numerical integration scheme–based semi-discretization methods for stability prediction in milling

Abstract

Chatter is not conducive to machining efficiency and surface quality. One of the essential types of chatter in the machining process is regenerative chatter. This study presents the numerical integration scheme–based semi-discretization methods (NISDMs) for milling stability prediction. Firstly, the dynamic model of the milling process is represented by the delay differential equation (DDE). The forced vibration period is discretized into many small-time intervals. After integrating on the small-time interval, only the time-delay term–related part is approximated by different order numerical integration schemes. Both the free and forced vibration processes are considered in the derivation process. The state transition matrix is constructed by mapping the dynamic displacement between the current and previous time periods. The NISDMs are compared with the benchmark methods in terms of the rate of convergence and computational time. The comparison results show that the NISDMs converge faster than the benchmark methods. To improve the computational efficiency of the NISDMs, the precise integration method is used in the calculation process. The computational time consumed by the NISDMs is much less than that consumed by the benchmark methods. The NISDMs are proved to be more accurate and efficient methods for stability prediction in milling than the other considered methods.