Experimental Validation of Period-n Bifurcations in Milling

This paper describes numerical and experimental analyses of milling bifurcations, or instabilities. The time-delay equations of motions that describe milling behavior are solved numerically for low radial immersion conditions and Poincaré maps are used to study the stability behavior, including secondary Hopf and period-n bifurcations. The numerical studies are complemented by experiments where milling vibration amplitudes are measured under both stable and unstable conditions. The vibration signals are sampled once per tooth period to construct experimental Poincaré maps. The results are compared to numerical stability predictions. The sensitivity of milling bifurcations to changes in natural frequency is also predicted and observed.