Three degrees of freedom stability analysis in the milling with bull-nosed end mills

When bull-nosed end mills are applied to machine the eccentric brackets of special-shaped parts, the chip regeneration mechanism is influenced by relative vibrations between the cutter and the workpiece in three directions. Three degrees of freedom stability is modeled analytically in this paper, in which dynamics of the cutter and the workpiece are both taken into consideration. In order to obtain the dynamic equation, a universal vector method is proposed to calculate dynamic chip thickness of the infinitesimal cutting flute in three directions based on the characteristics of relative vibrations between the cutter and the workpiece. A checking value point-by-point method is introduced to determine whether the infinitesimal cutting flute is in cutting or not. The full-discretization method is adopted to solve the dynamic equation. Since the dynamics of the thin walls is varied with the position, there exists a significant difference in the stability lobes at different positions. The stability lobes show that the stability limit at the end of the thin walls is lower than that in the middle of the thin walls. The verification experiments of three degrees of freedom stability were conducted in milling thin walls with the bull-nosed end mills on the five-axis machining center GMC 1600 H/2. The predicted three degrees of freedom stability lobes agree well with the experimental results. For comparison, the viability of the two degrees of freedom stability is proven in milling the plate with the same cutters.