A Hybrid Integration Approach for Milling Stability Prediction of Regenerative Chatter Using Simpson and Hermite Methods

This paper proposes an enhanced numerical integration technique for predicting milling stability. The underlying milling dynamics model incorporates regenerative chatter effects, formulated as a system of linear time-delay differential equations. The computational methodology begins by dividing the tool engagement period into the free vibration and forced vibration intervals, followed by uniform discretization of the forced vibration interval. A numerical integration method is primarily carried out using Simpson’s and Hermite’s rules. Thus, a discrete dynamic mapping that correlates the system’s current state with its previous state is constructed. Based on this, the milling stability is ultimately determined by applying Floquet theory. Furthermore, the mean squared error metric is introduced to quantify the prediction accuracy of stability lobe diagrams. Through comprehensive comparative analyses, the predicted efficiency and accuracy of the proposed method are systematically benchmarked against the conventional approaches. The simulated and experimental results demonstrate that the proposed method achieves high computational efficiency alongside good accuracy, and its engineering practicality is rigorously validated through milling experiments.