The problem addressed in this thesis is the delevitation modelling of an active magnetic bearing (AMB) supported rotor. A system model needs to be developed that models the highly non-linear interaction of the rotor with the backup bearings (BBs) during a delevitation event. The model should accurately predict forward and backward whirl as well as the system forces experienced. To this end, the severity of rotor delevitation events should be characterised. The contributions of the research include a more comprehensive model of a cross-coupled flexible rotor-AMB-BB system, a method to obtain repeatable experimental results, two methods for quantifying the severity of a rotor-drop (RDQ and Vval) and the simulation of forward whirl. A simulation model (BBSim) was developed to predict the behaviour of a rotor in rolling element BBs in an AMB system during a rotor delevitation event. The model was validated using a novel rotor delevitation severity quantification method (Vval) to compare experimental and simulated results. In this study the force impulse values as the rotor impacts the BBs are seen as critical to monitor, as an indication of rotor drop severity. The novel quantification method was verified by comparing the impulse values of delevitation events to the values obtained for the same delevitation events using the novel quantification method. The simulation model (BBSim) was developed by integrating and cross coupling various simpler models to obtain a model that could accurately predict the behaviour of a rotor during a delevitation event. A plethora of simulation results were generated for various initial conditions. The simulation results were used to perform a parametric study, from which the effects that certain design parameters have on the severity of rotor delevitation events are determined. The novel quantification method results presented in this research compared well to the impulse values. Since most AMB systems that have BBs do not have force measurement capabilities, the development of the novel quantification method enables the quantification of rotor drop severity solely based on position data. The simulation model BBSim was found to accurately predict the behaviour of a rotor during a delevitation event. The parametric study completed using BBSim revealed that the severity of rotor delevitation events is less sensitive to the bearing stiffness than the bearing damping. The parametric study also found that the severity of a delevitation event is slightly sensitive to the angle of delevitation. The friction factor between the rotor and the inner-race of the rolling element bearings moderately influences the severity of the rotor delevitation event. The inertia of the rolling element bearing’s inner-race and balls influences the behaviour in a complex manner, where the inertia should be kept as low as possible for actively braked rotors, and should be higher for free running rotors. The unbalance of the rotor plays a major role in the severity of rotor delevitation events. A rotor with a high unbalance usually tends to go into forward whirl, whereas low unbalance could promote the development of backward whirl if the inertia of the inner-race and the friction factor between the inner-race and the rotor are excessively large. Some of the recommended future work to be done on BBSim Include investigations into load sharing, various failure modes of AMBs, the effect that rotor circularity has on the stability of AMB control and an investigation into forward whirl. Envisaged improvements that can be made to BBSim are the inclusion of an axial rotor AMB and BB model, cross-coupled with the existing BBSim model. Other improvements could be the inclusion of thermal modelling and the ability to simulate other types of BBs. Future experimental work could include a comparison of simulated and experimental results of larger systems and using the developed quantification methods to refine the defined threshold values for the safe operation of AMB systems. / PhD, North-West University, Potchefstroom Campus, 2014 / Appendix C is attached seperately because of the size of the pdf (920 MB). If it is too large to download, please loan the hardcopy with the CD from the Loan desk in the Ferdinand Postma Library.

The problem addressed in this thesis is the delevitation modelling of an active magnetic bearing (AMB) supported rotor. A system model needs to be developed that models the highly non-linear interaction of the rotor with the backup bearings (BBs) during a delevitation event. The model should accurately predict forward and backward whirl as well as the system forces experienced. To this end, the severity of rotor delevitation events should be characterised. The contributions of the research include a more comprehensive model of a cross-coupled flexible rotor-AMB-BB system, a method to obtain repeatable experimental results, two methods for quantifying the severity of a rotor-drop (RDQ and Vval) and the simulation of forward whirl. A simulation model (BBSim) was developed to predict the behaviour of a rotor in rolling element BBs in an AMB system during a rotor delevitation event. The model was validated using a novel rotor delevitation severity quantification method (Vval) to compare experimental and simulated results. In this study the force impulse values as the rotor impacts the BBs are seen as critical to monitor, as an indication of rotor drop severity. The novel quantification method was verified by comparing the impulse values of delevitation events to the values obtained for the same delevitation events using the novel quantification method. The simulation model (BBSim) was developed by integrating and cross coupling various simpler models to obtain a model that could accurately predict the behaviour of a rotor during a delevitation event. A plethora of simulation results were generated for various initial conditions. The simulation results were used to perform a parametric study, from which the effects that certain design parameters have on the severity of rotor delevitation events are determined. The novel quantification method results presented in this research compared well to the impulse values. Since most AMB systems that have BBs do not have force measurement capabilities, the development of the novel quantification method enables the quantification of rotor drop severity solely based on position data. The simulation model BBSim was found to accurately predict the behaviour of a rotor during a delevitation event. The parametric study completed using BBSim revealed that the severity of rotor delevitation events is less sensitive to the bearing stiffness than the bearing damping. The parametric study also found that the severity of a delevitation event is slightly sensitive to the angle of delevitation. The friction factor between the rotor and the inner-race of the rolling element bearings moderately influences the severity of the rotor delevitation event. The inertia of the rolling element bearing’s inner-race and balls influences the behaviour in a complex manner, where the inertia should be kept as low as possible for actively braked rotors, and should be higher for free running rotors. The unbalance of the rotor plays a major role in the severity of rotor delevitation events. A rotor with a high unbalance usually tends to go into forward whirl, whereas low unbalance could promote the development of backward whirl if the inertia of the inner-race and the friction factor between the inner-race and the rotor are excessively large. Some of the recommended future work to be done on BBSim Include investigations into load sharing, various failure modes of AMBs, the effect that rotor circularity has on the stability of AMB control and an investigation into forward whirl. Envisaged improvements that can be made to BBSim are the inclusion of an axial rotor AMB and BB model, cross-coupled with the existing BBSim model. Other improvements could be the inclusion of thermal modelling and the ability to simulate other types of BBs. Future experimental work could include a comparison of simulated and experimental results of larger systems and using the developed quantification methods to refine the defined threshold values for the safe operation of AMB systems. / PhD, North-West University, Potchefstroom Campus, 2014 / Appendix C is attached seperately because of the size of the pdf (920 MB). If it is too large to download, please loan the hardcopy with the CD from the Loan desk in the Ferdinand Postma Library.