Influence of anisotropic support of tool for self-excited chatter in end-milling

In end milling, chatter vibration generated during processing becomes a problem in processing accuracy. Chatter vibration is classified into forced chatter and self-excited chatter depending on the cause of the vibration. Especially, stability of self-excited chatter is very important, because it becomes large amplitude vibration if it occurs. Generally, the chatter vibration phenomenon in end milling is modeled as a periodic system with time delay. However, all of the existing stability analysis methods of self-excited chatter are approximate and an accurate analysis method has not been established. In this study, a numerical method to calculate characteristic exponents of a periodic system with time delay equal to the fundamental period accurately using Fourier series is proposed. The proposed method is applied to the stability analysis of the self-excited chatter in end milling. The validity and accuracy of the proposed method is confirmed by comparing the results of the proposed method to well-known real phenomena and the numerical simulation results. Furthermore, the analysis method is applied to the case that the support of the tool is anisotropic, and influence of the anisotropic support for the self-excited vibration is studied.