Weakly rigid thin-walled components exhibit excellent lightweight performance and are widely used in aerospace and other fields. However

chatter is highly prone to occur during their milling process

which severely impairs machining quality and efficiency. Existing models mostly focus on the dynamic characteristics of the system

while neglecting the dynamic time-varying effect on radial cutting depth induced by the workpiece–tool elastic deformation caused by cutting forces under the combined action of different cutting positions of the workpiece and machining parameters. To address this problem

a time-varying prediction method for milling stability of weakly rigid thin-walled components is proposed

which takes into account the effect of machining-induced elastic deformation. First

an efficient iterative prediction model for continuous machining elastic deformation is established based on stiffness matrix reconstruction and the element birth and death method

enabling the rapid calculation of deformation along the tool path and the dynamic update of cutting parameters. Second

a tool–workpiece multi-point contact milling dynamic model coupled with the elastic deformation effect is constructed

revealing the time-varying dynamic coupling mechanism. Third

a high-precision and efficient solution algorithm is developed based on the extended Newton – Cotes rule (O(τ7))

which significantly improves the solution efficiency of the complex dynamic model. Finally

systematic milling experiments are carried out to verify the accuracy and efficiency of the proposed method in predicting the machining stability domain. The results show that the proposed method can effectively predict the stable cutting parameter domain considering the influence of deformation

providing theoretical support for the high-efficiency and high-quality machining of weakly rigid thin-walled components.