An updated full-discretization milling stability prediction method based on the higher-order Hermite-Newton interpolation polynomial

Chatter is undesirable self-excited vibrations, which always lead to adverse effects during milling process. Selecting a reasonable combination of cutting parameters is an effective way to avoid chatter. Based on the mathematical model of milling process and the Floquet theory, the stable cutting area can be determined. The stability lobe diagrams (SLD) could be obtained by different interpolation methods. To study the effect of higher order interpolation methods on the accuracy and efficiency of milling stability prediction, the state item, the time-delayed item, and the periodic-coefficient item of the state-space equation are approximated by different higher order interpolation methods, respectively. The calculations show that when the state item is approximated by the third-order Hermite interpolation polynomial, third-order Newton interpolation of the time-delayed item can improve the accuracy of SLD, while higher order interpolation of periodic-coefficient item has negative effect on improving effectiveness and efficiency compared to high-order interpolation of the state item and the time-delayed item. In order to obtain the SLD of milling process more accurately, an updated full-discretization milling stability prediction method which based on the third-order Hermite-Newton interpolation polynomial approximation is proposed in this paper. By dividing the tooth passing period equally into a finite set of time intervals, the third-order Hermite interpolation polynomial and the third-order Newton interpolation polynomial are utilized in each time interval to estimate the state item and the time-delayed item, respectively. The comparison of convergence rate of the critical eigenvalues and the SLD of the proposed method between the existing methods is carried out. The results indicate that the proposed method show a faster convergence rate than that of other methods, and its SLD is more close to the ideal ones with small number of time intervals.