A predictor-corrector-based holistic-discretization method for accurate and efficient milling stability analysis

Chatter vibration in milling has been one crucial factor hindering the realization of high-performance machining. The corresponding stability analysis is of great significance for obtaining chatter-free machining parameters. Based on the predictor-corrector scheme, this paper develops an accurate and efficient holistic-discretization method for the stability analysis of milling processes. According to the system state equation, the period of the time-periodic coefficient matrix is divided into two time intervals. The forced vibration time period is then equidistantly discretized. Working as a holistic unit, the time-periodic parameter matrix, the state term, and the delay term are approximated over two different subintervals by the second-order Lagrange interpolations. Finally, the Floquet transition matrix can be constructed by taking advantage of the predictor-corrector scheme, and the milling stability can be semi-analytically determined by utilizing the Floquet theory. The computational accuracy of the proposed method is analyzed theoretically and illustrated by making comparisons with the first-order semi-discretization method (1st SDM), the second-order, and the third-order updated full-discretization methods (2nd UFDM and 3rd UFDM). The stability lobes for two benchmark milling models and the computational efficiency of these methods are presented to further verify the effectiveness of the proposed method. Theoretical analysis and numerical results validate that the proposed predictor-corrector-based holistic-discretization method achieves both high computational accuracy and efficiency for milling stability analysis. In conclusion, the proposed semi-analytical algorithm has a high potential for industrial applications.

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