Accurate and efficient prediction of milling stability with updated full-discretization method

The study of the time domain method for milling stability prediction mainly focuses on the prediction accuracy and efficiency. The state item of the full-discretization formulations is usually approximated through the higher-order Lagrange polynomial interpolation for the higher prediction accuracy of milling stability. However, the time-delay term has not been considered. This paper proposes an updated full-discretization method for milling stability prediction based on the high-order interpolation of both the state item and the time-delay term and investigates the effect of the high-order interpolation of the time-delay term on accuracy of milling stability prediction. The state transition matrix on one time period is established directly to compensate the computational time expense of the high-order interpolation. By analyzing the convergence feature and lobes of benchmark examples, the high-order interpolation of both the state item and the time-delay term is proven to be more effective than only the higher-order interpolation of the state item, and the direct establishment of the state transition matrix can achieve the purpose of saving computational time.