The introduction of active magnetic bearings (AMBs) has enabled turbomachinery to increase power density, controllability, and general resilience to external disturbances. However, because of the limited load capacity of AMBs, the base shock condition that "on-board" machines often encounter may result in contact between the rotor and the touchdown bearings (TDBs), which can seriously damage the machine. A challenge in AMB applications is to alleviate this problem. This study presents a dynamic analysis of a rotor-AMB-TDB system under strong base shocks while the AMBs are operating. Detailed TDB and contact models are presented using Hertzian contact theory. A PD controller was then designed considering system saturation and friction, based on the Coulomb model and the effect of lubrication. The dynamic equations were solved for the dynamic trajectory and FFT spectra, STFT spectra, Poincaré maps and bifurcation diagrams were used for the parametric analysis. The results show that the rotor had three motion modes. System parameters, including unbalance eccentricity, magnetic gap clearance and equivalent stiffness and damping ratio, may lead to complex nonlinear dynamic behavior including periodic, KT-periodic, and quasi-periodic responses and jump phenomenon. Suitable designs that consider these parameters may avoid undesirable rotor dynamic behavior. This study reveals the mechanism for nonlinear response, providing a method for its prediction, and core controller parameter designs for rotor re-levitation
