Stability Prediction of Multi-Factor Coupled Cast Iron Milling System Based on an Improved Full-Discretization Method

Cast iron components are indispensable in aerospace and automotive systems, yet their milling operations are severely affected by regenerative chatter, which degrades machining quality and damages equipment. Although various chatter prediction methods have been reported, the optimal interpolation strategy of full-discretization methods (FDMs) for multi-factor coupled dynamic systems remains unclear. This study proposes an enhanced FDM to fill this research gap. A dynamic milling model accounting for regenerative effects, modal coupling and process damping is established, and an improved FDM based on Lagrange interpolation is further developed. A systematic single-factor analysis is carried out to examine the performance of 1st–4th-order interpolation for state, delay and periodic terms. Counter-intuitively, convergence analysis and stability lobe diagram (SLD) verification reveal that higher-order interpolation does not guarantee better performance. The optimal orders are identified as 2nd/3rd for state terms, 3rd for delay terms and 1st for periodic terms. Accordingly, the proposed 321-FDM (3rd-order state, 2nd-order delay, 1st-order periodic) exhibits higher accuracy and computational efficiency compared with benchmark methods, namely the semi-discretization method and Hermite-based 3rd-order FDM. Milling experiments on cast iron workpieces validate the established model and the 321-FDM, and the experimental stability thresholds agree well with numerical predictions. This work presents a validated, high-performance stability prediction tool for chatter avoidance in cast iron machining.