Finite element modeling and stability analysis of chatter in end milling machining

In this paper, chatter in end milling machine tools is investigated using a Timoshenko beam model and finite element analysis. The model is developed for the cases where the slender machining cutters are flexible along the axial direction. A closed form solution for obtaining the stability lobes is derived assuming cutting forces as point loads applied to the end of the tool. It is shown that the stability lobes converge as the number of elements increase. The results indicate that using a single mass model used in the literature predict a more conservative chatter stability compared to the more accurate model using finite element and Timoshenko beam model.