Accurate Stability Prediction of Milling Operations Based on Adams–Simpson’s 3/8-Based Predictor–Corrector Methods

Machining chatter acts as a major obstacle in milling operations, which degrades surface finish quality, accelerates tool wear, and restricts production efficiency. Reliable stability prediction is therefore fundamental to chatter suppression and rational parameter configuration. To efficiently balance prediction accuracy and computational cost, this paper develops the Adams–Simpson’s 3/8-based predictor–corrector methods (ASPCMs) for the precise prediction of milling stability. Firstly, delay differential equations (DDEs) are utilized to mathematically formulate the milling dynamic models. According to the values of the coefficient matrix, the tooth passing period is further partitioned into two unequal subintervals. Relying on the predictor–corrector strategy, the two-step, three-step, and four-step Adams–Moulton formulas are respectively applied to predict the state term, while Simpson’s 3/8 formula is utilized for the state term correction. The combination of the Adams–Moulton and Simpson’s 3/8 formulas further enables the efficient construction of the Floquet transition matrix. Subsequently, the representative existing methods are introduced to comprehensively evaluate the effectiveness and superiority of the proposed ASPCMs. The comparison results demonstrate that the ASPCMs achieve superior prediction performance without sacrificing computational cost. Compared with the second-order semi-discretization method, the computation time of the second-order, third-order, and fourth-order ASPCMs can be saved by approximately 48%, 47%, and 43%, respectively. Finally, comprehensive experimental verifications considering regenerative effect, multiple modes and helix angle are performed to further evaluate the feasibility and applicability of the ASPCMs. Experimental results indicate that the stability boundaries predicted by the third-order ASPCM are in excellent agreement with the measured cutting data. This consistent correspondence demonstrates that the ASPCMs offer better prediction capability for practical milling scenarios.