Abstract: Using the Chebyshev segmentation method to discrete the time period contained in delay differential equation， the Newton second-order difference quotient method was used to calculate the motion vector of cutter at each time endpoint， then the transfer matrix of milling system was obtained， and the system stability was determined by the Floquet theory. Using the above methods， a two-degrees of freedom milling system stability issues was investigated to get system stability lobe diagrams. The results showed that under the same calculation accuracy， the points needed to cut the time period by the Chebyshev segmentation are less than those by the average segmentation， and the computational efficiency of the Chebyshev segmentation is higher. When the time period is divided into the same parts， the stability lobe diagrams gotten by the Chebyshev segmentation method are more accurate than that of the other.

Key words: milling, Chebyshev segmentation, transfer matrix, Newton second-order difference quotient method, stability lobe diagram