Modeling and analysis for time-varying dynamics of thin-walled workpieces in mirror milling considering material removal

To reduce the vibration and deformation of large thin-walled workpieces during the milling process, mirror milling is widely used due to its point-to-point support and strong applicability. The influence of the support head on the workpiece’s dynamic characteristics is crucial in determining whether the mirror milling process is reliable and effective. Therefore, this study establishes a time-varying dynamic model for mirror milling of thin-walled workpieces with various boundary conditions to accurately analyze and predict the dynamic characteristics and response of the workpiece. First, a new analytical method for material removal with extensive applicability and high precision is proposed. In this method, the Ritz mode shape is used to approximate the workpiece’s mode shape as it changes during material removal. Next, the Hertz contact theory is adopted to establish a tool-workpiece-support head coupling model, which considers the jump-off phenomenon between them. Subsequently, the dynamic model is solved using the Newmark-β numerical integration method to obtain the workpiece’s time-domain acceleration and displacement responses under the forced vibration. Finally, the measured frequency response function (FRF) and vibration signals of workpieces verify the correctness of the proposed mirror milling model for thin-walled workpieces considering material removal. In addition, this paper analyzes the dynamic characteristics and forced vibration law of workpieces in mirror milling, which lays the foundation for high precision mirror milling.