Accurate and efficient stability prediction for milling operations using the Legendre-Chebyshev-based method

Abstract

Stability prediction with both high computational accuracy and speed is still a challenging issue and has been attracting significant attention from the academia and industry. This study presents a Legendre-Chebyshev-based stability analysis method (LCM) for milling operations. According to the cutting state, it divides the system period of milling model into the free and the forced vibration time periods. By introducing appropriate transformation, the latter time interval is further discretized nonuniformly into the Chebyshev-Gauss-Lobatto points, which has explicit expression. Then, the state term over the discrete time points is approximated with the Legendre expansion, and its corresponding derivative is acquired via a novel and efficient algorithm. Thereafter, Floquet matrix within the system period of milling model can be determined for predicting the system stability via the known Floquet theory. Finally, we validate the effectiveness of the LCM by employing the single and two degrees of freedom (DOF) milling operations and making detailed comparisons with the recent representative algorithms, which indicates that the presented Legendre-Chebyshev-based method has both high prediction accuracy and speed.