Simpson’s 3/8–based method stability analysis for milling processes

Chatter stability prediction based on linear time-periodic delay differential equations (DDEs) of the milling dynamic process is an important issue in achieving high-performance processing operations. To obtain efficient and precise regenerative chatter prediction, a novel method for milling stability analysis based on Simpson’s 3/8 rule is proposed. First, the dynamics model of milling processes, considering the regenerative effect, is modeled by an n-dimensional delay differential equation. Second, a set of algebraic equations is obtained to determine the transition matrix by converting and discretizing periodic DDE into a system of integral equations at the neighboring sampling grid points. Then, the eigenvalues of the transition matrix are utilized to determine stability based on Floquet theory. Finally, the comparisons of lobe diagrams calculated by different methods and discretization interval number for one and two degrees of freedom milling models are discussed, and the consistency of the predicted and experimental stability boundaries is analyzed. Results show that the proposed method achieves high computation accuracy with high efficiency.