Active magnetic bearings (AMBs) have the ability to act concurrently as support bearings and as load sensing measurement tools. Previous work in the area of AMB force measurement has relied upon basic magnetic equations requiring knowledge of coil currents and air gap lengths. Some researchers have utilized magnetic flux probes to eliminate the need for air gap measurements, but these are limited by physical size constraints and require complex hardware. This thesis presents a new method for measuring forces with AMBs that utilizes multiple current pairs with no gap measurement to provide accurate and precise force predictions. Previous methods for force measurement with AMBs rely on the controlled environment of a laboratory setting for accurate measurements. The goal of this work is to develop a robust force measurement procedure for use in industrial and field applications, as well as the laboratory. The harsh environment of a factory floor makes air gap measurements difficult, which limits the use of current-based force equations. Additionally, the flexibility of AMB-equipped thrust measurement systems (TMSs) to measure many types of forces with little to no reconfiguration or calibration makes them appealing. The multi-point method provides predictions of both shaft force and rotor position using only current pairs without air gap measurements. Static and dynamic load scenarios were investigated to determine the feasibility of this new approach to force measurement. For both, the effects of bearing load and rotor position within the bearing were analyzed. Under dynamic loading, different amounts of unbalance as well as various rotor speeds were used to provide multiple test cases. The multi-point predictions of rotor position were analyzed and compared with the measured rotor positions. It was shown that this new multiple-point method for measuring bearing loads with AMBs provides equivalent or better force predictions to analogous single-point methods for static loads while eliminating the need for measuring rotor position. / Master of Science

The McTronX Research group at the Potchefstroom campus of the North-West University, aims to establish a knowledge base on active magnetic bearing (AMB) systems. Up to date, the group has established a firm knowledge base on various topics related to AMB systems. A recent focus was the design and development of a high speed AMB supported rotor system called the rotor delevitation system (RDS) to analyse rotor drops. During the testing phase of the RDS, the machine exhibited vibrations, of which the origins were unknown. The research presented in this dissertation sets out to characterize the vibrations of the RDS, which is the group’s first attempt to fulfil the need for characterizing vibrations in an AMB supported rotor. Emphasis is placed on characterizing the natural response of the RDS rotor, stator and integrated system. The research project is defined in terms of four main objectives: rotor and stator characterization, modelling, system characterization and rotor dynamic diagnostics. A comprehensive literature study introduces the fundamental concepts regarding vibrations of single and multiple degree of freedom systems. These concepts include; natural frequencies, damping, machine vibrations, rotor dynamics and modelling techniques. These modelling techniques are introduced to verify the experimental methodology used to determine the natural frequencies. A critical overview of the literature contextualises the theory with the research investigation. For the RDS rotor and stator characterization, a modal analysis process also known as the “bump test” is implemented in order to validate the bending natural frequencies of the rotor and stator. A simulation model of the RDS is constructed in the finite element (FE) package DyRoBeS®. The model is verified with a numerical and an analytical model and validated with the measured bending natural frequencies of the RDS rotor. For the system characterization, a number of modal analysis processes are implemented, which validates the rigid body natural frequencies of the RDS. These frequencies are also used to validate the FE simulation. The origins of the synchronous vibration harmonics are verified by formulating and evaluating hypotheses according to different modal analysis processes. From the RDS rotor modal analysis it was identified that a bending natural frequency of the rotor is situated at approximately 443.33 Hz. This was verified using the FE simulation model. During the system modal analyses, it was identified that only one rigid body natural frequency, situated at approximately 62 Hz, is excited. This frequency increases with the differential gain control parameter of the system up to approximately 140 Hz. After evaluating two hypotheses regarding the origins of the synchronous vibrations harmonics, it was verified that non-circularity of the rotor at the measuring positions is the cause. Overall the objectives of the study were addressed by characterizing the natural frequencies of the rotor, stator and RDS system. This include the mode forms of the rigid body and bending natural frequencies of the system. The results of the verification and validation methods correlated, which imply these methods are reliable to identify the origins of vibrations in rotor-bearing systems. The differential gain control parameter of the AMBs control the equivalent damping in the RDS. An increase in this parameter should lead to a decrease in amplitude and frequency of the maximum vibration, and vice versa. However, it was noted that an increase in this parameter caused a linear increase in the rigid body natural frequency. The literature indicates that this effect can only be caused by an increase in system stiffness. It is therefore recommended to evaluate the stiffness of the system as a function of the differential gain control parameter. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2012.

The McTronX Research group at the Potchefstroom campus of the North-West University, aims to establish a knowledge base on active magnetic bearing (AMB) systems. Up to date, the group has established a firm knowledge base on various topics related to AMB systems. A recent focus was the design and development of a high speed AMB supported rotor system called the rotor delevitation system (RDS) to analyse rotor drops. During the testing phase of the RDS, the machine exhibited vibrations, of which the origins were unknown. The research presented in this dissertation sets out to characterize the vibrations of the RDS, which is the group’s first attempt to fulfil the need for characterizing vibrations in an AMB supported rotor. Emphasis is placed on characterizing the natural response of the RDS rotor, stator and integrated system. The research project is defined in terms of four main objectives: rotor and stator characterization, modelling, system characterization and rotor dynamic diagnostics. A comprehensive literature study introduces the fundamental concepts regarding vibrations of single and multiple degree of freedom systems. These concepts include; natural frequencies, damping, machine vibrations, rotor dynamics and modelling techniques. These modelling techniques are introduced to verify the experimental methodology used to determine the natural frequencies. A critical overview of the literature contextualises the theory with the research investigation. For the RDS rotor and stator characterization, a modal analysis process also known as the “bump test” is implemented in order to validate the bending natural frequencies of the rotor and stator. A simulation model of the RDS is constructed in the finite element (FE) package DyRoBeS®. The model is verified with a numerical and an analytical model and validated with the measured bending natural frequencies of the RDS rotor. For the system characterization, a number of modal analysis processes are implemented, which validates the rigid body natural frequencies of the RDS. These frequencies are also used to validate the FE simulation. The origins of the synchronous vibration harmonics are verified by formulating and evaluating hypotheses according to different modal analysis processes. From the RDS rotor modal analysis it was identified that a bending natural frequency of the rotor is situated at approximately 443.33 Hz. This was verified using the FE simulation model. During the system modal analyses, it was identified that only one rigid body natural frequency, situated at approximately 62 Hz, is excited. This frequency increases with the differential gain control parameter of the system up to approximately 140 Hz. After evaluating two hypotheses regarding the origins of the synchronous vibrations harmonics, it was verified that non-circularity of the rotor at the measuring positions is the cause. Overall the objectives of the study were addressed by characterizing the natural frequencies of the rotor, stator and RDS system. This include the mode forms of the rigid body and bending natural frequencies of the system. The results of the verification and validation methods correlated, which imply these methods are reliable to identify the origins of vibrations in rotor-bearing systems. The differential gain control parameter of the AMBs control the equivalent damping in the RDS. An increase in this parameter should lead to a decrease in amplitude and frequency of the maximum vibration, and vice versa. However, it was noted that an increase in this parameter caused a linear increase in the rigid body natural frequency. The literature indicates that this effect can only be caused by an increase in system stiffness. It is therefore recommended to evaluate the stiffness of the system as a function of the differential gain control parameter. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2012.

Existing thrust measurement systems (TMSs) at NASA Stennis Space Center use strain gauges and flux plates to measure forces produced by a test article. Alignment and calibration can take two weeks or more every time a piece of hardware or test article is changed. Cross axis loading is also problematic because it is impossible to perfectly align the flex plates and strain gauges in the thrust direction. In response to these problems, a magnetically levitated thrust measurement system has been proposed and a 300lb capacity demonstrator has been designed and built. In this design, the magnetic bearings work concurrently as support bearings and force measurement devices. The demonstrator consists of a floating frame that is completely levitated within a fixed frame by four support bearings carrying loads in the x- and y-direction and seven thrust bearings carrying loads in the z- or thrust direction. Joe Imlach of Imlach Consulting Engineering designed the demonstrator and magnetic bearing components, while Virginia Tech's role has been the application of the multipoint calibration technique including code development, the implementation of a 128-channel data acquisition system, and the overall test verification of the TMS demonstrator.A turnbuckle assembly and magnetostrictive actuator are used in series with a conventional load cell for static and dynamic testing, respectively. Both current based and flux based force equations were used to measure the reaction forces at the bearings. The static results using the current based equations including the current based fringing equations resulted in accuracies of 93% of full load, while the static results using the flux based equations including the flux based fringing equations resulted in accuracies of 99.5% of full load. These accuracies can be compared to accuracies of 83-90% seen in previous work using magnetic bearings to measure forces by monitoring currents and to accuracies of about 99% in previous work using magnetic bearings to measure forces by monitoring fluxes. All of the improved accuracies were made possible through the implementation of a calibration technique known as the multipoint method and the implementation of a gap dependent fringing correction factor developed by Joe Imlach. The demonstrator was not outfitted with accelerometers so the inertia of the floating frame could not be accounted for, limiting the scope of dynamic testing. However, the tests confirmed the ability of the demonstrator to measure dynamic loads in general. / Master of Science

Active magnetic bearings have several potential applications in spacecraft design. Based on the gyrostat model, we develop equations that describe the internal torques and forces that occur between the body and one of the attached wheels. We evaluate the transverse torques for the torque--free gyrostat and a gyrostat undergoing attitude maneuvers using momentum wheels and external torques. We then apply these internal forces to a model of an active magnetic bearing system and discuss their effects on the force limit, the actuator slew rate and the equivalent stiffness and damping parameters. As a basis for this study we use the Distributed Spacecraft Attitude Control System Simulator (DSACSS) with a Revolve MBRotor active magnetic bearing system. The results of several numerical simulations show that the magnitude and frequency of the internal torques remain small over the estimated range of motion of the DSACSS--MBRotor gyrostat. As such, the transverse torques caused by the rotational motion remain less than the discussed performance limits. We show that the magnitude of the internal torques can also be minimized by reducing the axial moment of inertia of the wheel. Furthermore, we discuss the equivalent Jeffcott model. By applying a standard Proportional--Integral--Derivative controller to the active magnetic bearing both the equivalent stiffness and damping parameters remain constant. / Master of Science

Due to their frictionless operation active magnetic bearings (AMBs) are essential components in high-speed rotating machinery. Active magnetic control of a high speed rotating rotor requires precise knowledge of its position. Self-sensing endeavours to eliminate the required position sensors by deducing the rotor’s position from the voltages and currents with which it is levitated. For self-sensing AMBs to be of practical worth, they have to be robust. Robustness analysis aims to quantify a control system’s tolerance for uncertainty. In this study the stability margin of a two degree-of-freedom self-sensing AMB is estimated by means of μ-analysis. Detailed black-box models are developed for the main subsystems in the AMB by means of discrete-time system identification. Suitable excitation signals are generated for system identification in cognisance of frequency induced nonlinear behaviour of the AMB. Novel graphs that characterize an AMB’s behaviour for input signals of different amplitudes and frequency content are quite useful in this regard. In order to obtain models for dynamic uncertainty in the various subsystems (namely the power amplifier, self-sensing module and AMB plant), the identified models are combined to form a closed-loop model for the self-sensing AMB. The response of this closed-loop model is compared to the original AMB’s response and models for the dynamic uncertainty are empirically deduced. Finally, the system’s stability margin for the modelled uncertainty is estimated by means of μ-analysis. The potentially destabilizing effects of parametric uncertainty in the controller coefficients as well as dynamic uncertainty in the AMB plant and self-sensing module are examined. The resultant μ-analyses show that selfsensing AMBs are much less robust for parametric uncertainty in the controller than AMBs equipped with sensors. The μ-analyses for dynamic uncertainty confirm that self-sensing AMBs are rather sensitive for variations in the plant or the self-sensing algorithm. Validation of the stability margins estimated by μ-analysis reveal that μ-analysis is overoptimistic for parametric uncertainty on the controller and conservative for dynamic uncertainty. (Validation is performed by means of Monte Carlo simulations.) The accuracy of μ-analysis is critically dependent on the accuracy of the uncertainty model and the degree to which the system is linear or not. If either of these conditions are violated, μ-analysis is essentially worthless. / Thesis (Ph.D. (Electronical Engineering))--North-West University, Potchefstroom Campus, 2010

Due to their frictionless operation active magnetic bearings (AMBs) are essential components in high-speed rotating machinery. Active magnetic control of a high speed rotating rotor requires precise knowledge of its position. Self-sensing endeavours to eliminate the required position sensors by deducing the rotor’s position from the voltages and currents with which it is levitated. For self-sensing AMBs to be of practical worth, they have to be robust. Robustness analysis aims to quantify a control system’s tolerance for uncertainty. In this study the stability margin of a two degree-of-freedom self-sensing AMB is estimated by means of μ-analysis. Detailed black-box models are developed for the main subsystems in the AMB by means of discrete-time system identification. Suitable excitation signals are generated for system identification in cognisance of frequency induced nonlinear behaviour of the AMB. Novel graphs that characterize an AMB’s behaviour for input signals of different amplitudes and frequency content are quite useful in this regard. In order to obtain models for dynamic uncertainty in the various subsystems (namely the power amplifier, self-sensing module and AMB plant), the identified models are combined to form a closed-loop model for the self-sensing AMB. The response of this closed-loop model is compared to the original AMB’s response and models for the dynamic uncertainty are empirically deduced. Finally, the system’s stability margin for the modelled uncertainty is estimated by means of μ-analysis. The potentially destabilizing effects of parametric uncertainty in the controller coefficients as well as dynamic uncertainty in the AMB plant and self-sensing module are examined. The resultant μ-analyses show that selfsensing AMBs are much less robust for parametric uncertainty in the controller than AMBs equipped with sensors. The μ-analyses for dynamic uncertainty confirm that self-sensing AMBs are rather sensitive for variations in the plant or the self-sensing algorithm. Validation of the stability margins estimated by μ-analysis reveal that μ-analysis is overoptimistic for parametric uncertainty on the controller and conservative for dynamic uncertainty. (Validation is performed by means of Monte Carlo simulations.) The accuracy of μ-analysis is critically dependent on the accuracy of the uncertainty model and the degree to which the system is linear or not. If either of these conditions are violated, μ-analysis is essentially worthless. / Thesis (Ph.D. (Electronical Engineering))--North-West University, Potchefstroom Campus, 2010

The current development in the field of electric machinery is focusing on high-speed electric machines. This opens also other fields related to high-speed machines. One of them are magnetic bearing systems. Tradition approach of using ball bearing brings a few problems in design dealing with friction at high speeds. Together with magnetic bearings, development is their control. Faster chips opened a new way of thinking of control and helped to evolve robust control loops. The biggest advantage of magnetic bearing is non-friction run and almost no maintenance. Compare to traditional ball bearing, a magnetic bearing system needs more space and in some applications could happen that the shaft will be twice as long. This problem can be solved designing complex system with motor and integrated magnetic bearing what leads to downsizing. In this master thesis, the design of magnetic bearing for 12kw, 45000rpm is discussed. It focuses on practical design and correlations between parameter selection. The analytical approach is used to sketch the design and optimization is done afterwards. Problem with an analytical design is that it doesn't cover all parasitic phenomenae and thus numerical modelling snd optimization are demanded. Also, the critical speed analyze is included in this thesis. The results of the work will be used for manufacturing prototype as an extension to the existing high-speed machine.

This thesis describes the test rig and results from a project expanding the field of rotor health monitoring by using Active Magnetic Bearings (AMBs) as actuators for applying a variety of known force inputs to a spinning. Similar to modal analysis and other nondestructive evaluation (NDE) techniques which apply input signals to static structures in order to monitor responses; this approach allows for the measurement of both input and output response in a rotating system for evaluation. However, unlike these techniques, the new procedure allows for multiple forms of force input signals to be applied to a rotating structure. This technique is used on a rotating shaft supported in conventional bearings with an AMB actuator added to the system. This paper presents the results from this project including shaft rub and notch. An EDM notch was also tested to attempt a breathing scenario similar to breathing cracks. / Master of Science

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