An efficient full-discretization method for milling stability prediction

To address the vibration phenomenon in the milling process, this study proposed an implicit Adams method (IAM) to predict the stability of the milling process. The dynamic equation of milling process with regenerative chatter can be expressed as a delay linear differential equation. The cutter tooth cycle can be divided into the forced and free vibration stages. The forced vibration stage is discretized and IAM is used to construct state transition matrix. The stability of the system is determined based on Floquet theory and the stability lobe diagrams are obtained. Matlab simulation and experiment results show that IAM is an effective method to predict the stability of milling. First, compared with the typical discretization methods, the IAM method indicates a faster convergence rate. Next, in one- and two-degree freedom dynamic model, the stability lobe diagrams show that the prediction accuracy and computation efficiency of IAM are better than that of the first-order semi-discretization method (1st-SDM), second-order full discretization method (2nd-FDM), and the Simpson method (SIM). Finally, acceleration signals collected from cutting experiments are analyzed by mathematical statistics, time-domain method, and frequency-domain method. It is concluded that the simulation results are consistent with the experimental analysis results which verifies the effectiveness of IAM.