A novel approximate-analytical method for prediction of milling stability

Accurate prediction of stability lobe diagrams (SLDs) is essential for chatter suppression and productivity enhancement in milling. Existing approaches are typically analytical or discretization-based: the widely used zero-order approximation (ZOA) is computationally efficient but may suffer from non-negligible prediction errors, whereas discretization-based methods improve accuracy at the expense of high computational cost. To address this trade-off, this paper proposes a novel approximate-analytical method (AAM) for efficient and accurate milling stability prediction. Based on nonlinear dynamic theory, an implicit analytical condition for the milling stability boundary is derived by incorporating higher-order harmonics of the directional coefficients, in which the stability limit is defined as the solution of a closed-form algebraic equation and traced directly without exhaustive parameter-space scanning. A numerical continuation scheme is then employed to efficiently construct SLDs, and a dedicated strategy is developed to robustly handle initial-point selection and lobe transitions. The proposed formulation provides a unified treatment of stability limits associated with both Neimark–Sacker and period-doubling bifurcations within a unified framework. Benchmark comparisons with ZOA, SDM, E-FDM, and FDM demonstrate that AAM achieves comparable prediction accuracy while significantly improving computational efficiency.