Abstract: Chatter is one of the major limitation factors in the machining process, which affects milling quality and efficiency. In order to improve the prediction accuracy of milling chatter, an updated complete discretization method (U-FDM) is proposed. Based on the second-order Lagrange polynomials, the delay term and state term of the delay differential equation of milling dynamic system are numerically iterated, and the high-precision lobe diagram of chatter stability region is constructed by using Floquet principle. The convergence rate of the second order complete discretization method is almost the same as that of the first order complete discretization method when the number of discretization interval is more than 50. The convergence analysis of eigenvalue for single degree of freedom shows that the U-FDM has the best convergence characteristics. The comparisons of single and two degree of freedom lobes show that the U-FDM algorithm has high fitting accuracy. Compared with semi-discretization method, the computational efficiency is improved by 70.6% and 64.9% respectively. The force response signal of milling process is analyzed in time domain, frequency domain and synchronous sampling. The results prove that the proposed milling dynamic model and U-FDM algorithm are effective, which can give a help for the practical machining.

Key words: milling dynamics, chatter, time delay, complete discrete method, stability lobe diagram