A Numerical and Experimental Investigation of Period-n Bifurcations in Milling

Abstract

Numerical and experimental analyses of milling bifurcations, or instabilities, are detailed. The time-delay equations of motions that describe milling behavior are solved numerically and once-per-tooth period sampling is used to generate Poincaré maps. These maps are subsequently used to study the stability behavior, including period-n bifurcations. Once-per-tooth period sampling is also used to generate bifurcation diagrams and stability maps. The numerical studies are combined with experiments, where milling vibration amplitudes are measured for both stable and unstable conditions. The vibration signals are sampled once-per-tooth period to construct experimental Poincaré maps and bifurcation diagrams. The results are compared to numerical stability predictions. The sensitivity of milling bifurcations to changes in natural frequency and damping is also predicted and observed.