Effect of thin-walled workpiece dynamics on milling stability: a 3D spectral element method-based study

Chatter stability is a major challenge in milling thin-walled components due to their evolving dynamics during machining. In this study, we predicted the workpiece dynamics along the tool path using a three-dimensional spectral element method (3D-SEM) based on a spectral- Chebyshev formulation. The workpiece was discretized into coarse brick elements, the elemental mass and stiffness matrices were computed spectrally, and at each material-removal step an eigenvalue problem was solved to obtain the instantaneous natural frequencies and mode shapes. The corresponding frequency-response functions (FRFs) at the tool–workpiece interface were determined, capturing the dynamic changes due to tool position and progressive material removal. Using these FRFs, we constructed 3D stability-lobe diagrams for each milling pass and identified chatter-free cutting parameters, which were validated by time-domain simulations and showed excellent agreement. The results demonstrate that the 3D-SEM accurately and efficiently captures the variations in workpiece dynamics and provides a robust tool for reliable chatter-stability prediction in the milling of thin-walled structures.