A Spectral-Integral-Formula-Based Method for Fast and Matrix Exponentials Free Milling Stability Prediction

Efficient and accurate prediction of milling stability is an enduring and important issue in the field of machining. In this article, a highly efficient and accurate semi-analytic milling stability prediction method based on the spectral integral formula (SIM) is presented. The governing equation is transferred into direct integral form to avoid the calculation of matrix exponentials, and the tool passing time interval is divided to satisfy the smoothness criteria of the spectral method. An analytic solution for the free vibration time interval is used to improve computational efficiency for low immersion ratio cutting. The monodromy matrix for the stability analysis is approximately constructed by Lagrange interpolation on each forced vibration interval. The milling stability is determined by the spectral radius of the monodromy matrix. The exponential convergence property of the proposed SIM is confirmed through theoretical analysis and numerical simulations, demonstrating superiority over the three benchmark methods. Moreover, a milling experiment was conducted on a five-axis computer numerical control (CNC) machine tool to validate the correctness of the proposed SIM.