中文摘要：

在铣削过程中，颤振的发生通常会导致被加工工件表面粗糙、刀具快速磨损，甚至会损坏主轴系统，严重影响机床生产效率和产品精度。其中，再生颤振在实际铣削过程中最为普遍。基于再生颤振原理和离散算法进行颤振预测，针对变速铣削中的周期较长、系数变化明显等问题，提出一种应用于变速铣削过程的整体逼近的离散化算法，并分析算法收敛性。结果证明，此方法可提高计算效率和精度。

英文摘要：

In the milling process, chatter always results in poor workpiece surface smoothness, tool wear, and other potential damage which reduce the productive efficiency and the accuracy of the workpiece processing. The regenerative chatter is the most common chatter in the actual milling process. An effective method to avoid the chatter is to change the spindle speed periodically. In this paper, a novel discretization method based on the regenerative principle is proposed to predict the stability of the variable speed milling. The differential terms of the solution is used through the matrix reconstruction. The results show that the proposed method can reduce the computation time and improve the accuracy of the solution.