Regenerative chatter is the main factor affecting the stability of milling process. The reasonable prediction of milling stability lobe diagram (SLD) is the core to controlling chatter and improving production efficiency. Therefore, a milling system with consideration of the regenerative effect is formulized as the delay differential equation (DDE). By uniformly discretizing the part of the forced vibration in the tooth passing period, the state transition matrix can be achieved by sophisticatedly adopting the Cotes formula for the fit value of the DDE at every discretized point. And then, the judgment criterion of milling stability that the eigenvalues of the state transition matrix are not more than 1 is suggested by using Floquet theory. Compared with the first-order semi-discretization method (SDM), the first-order full-discretization method (FDM) and second-order FDM, the results show that the proposed method has an advantage over the first-order SDM and the FDM whether in the computational accuracy or the computational efficiency. Finally, some group of milling experiments were done to validate the proposed method. The morphology of machined surface shows the predicted SLD results are highly consistent with the experimental values. Therefore, the proposed method has a good industrial application value in determining the optimal chatter-free cutting conditions.

再生颤动是影响铣削过程稳定性的主要因素。铣削稳定凸角图（SLD）的合理预测是控制颤振和提高生产效率的核心。因此，考虑了再生效果的铣削系统被制定为延迟微分方程（DDE）。通过均匀地离散在牙齿经过期间的部分强迫振动，可以通过在每个离散点上采用D的拟合值的Cotes公式来精细地获得状态转换矩阵。然后，利用Floquet理论提出了铣削稳定性的判断标准，即状态转移矩阵的特征值不大于1。与一阶半离散化方法（SDM）相比，结果表明，该方法在计算精度或计算效率上均优于一阶SDM和FDM。最后，进行了一些铣削实验以验证所提出的方法。加工表面的形态表明，预测的SLD结果与实验值高度一致。因此，该方法在确定最佳无颤动切削条件方面具有良好的工业应用价值。加工表面的形态表明，预测的SLD结果与实验值高度一致。因此，该方法在确定最佳无颤动切削条件方面具有良好的工业应用价值。加工表面的形态表明，预测的SLD结果与实验值高度一致。因此，该方法在确定最佳无颤动切削条件方面具有良好的工业应用价值。