Period-n bifurcations in milling operations are studied in this dissertation. Period-n bifurcations represent a special type of unstable dynamic behavior because they have a response period that is an integer multiple (n) of the forcing period. The existence of period-n bifurcations is demonstrated both through numerical simulation and experimental validation. Period-2, -3, -6, -7, -8, and -15 bifurcations are identified and verified by using once-per-tooth sampling (i.e. synchronous sampling) of in-process dynamic signals (time-varying system displacement and velocity) and the corresponding Poincaré maps. The sensitivity of period-n bifurcations to variations in the dynamic system’s natural frequency and damping ratio is also studied both through numerical simulation and experiments. A milling time domain simulation is presented that is capable of automatically detecting stable, unstable, and period-n behavior. This enhanced simulation allows the global existence of period-n bifurcations to be studied. Surface location error (SLE), or the difference between the commanded and actual surface locations due to milling dynamic behavior, and surface roughness is predicted and verified for period-2 and stable milling conditions.
