Este trabalho versa sobre a análise teórica do desempenho da regulação sincronizada aplicada na redução de vibrações de rotores utilizando mancais magnéticos. Originalmente apresentado na dissertação \\Regulação sincronizada de distúrbios senoidais\", de Vaydia I. C. Segura, o regulador teve o seu módulo de regulação modificado para trabalhar com múltiplas entradas e saídas, além de permitir a estimação em tempo real da matriz de influência. O desempenho e a robustez do regulador foram analisados em função de seus parâmetros. A regulação sincronizada foi aplicada a um modelo teórico de rotor desenvolvido pelo método dos elementos finitos e simulado em computador. / This work discusses about the theoretical analysis of the performance of synchronized regulation applied in reduction of rotor vibrations using magnetic bearings. Originally presented in the dissertation \\Synchronized regulation of sinoidal disturbing\", of Vaydia I. C. Segura, the regulator had its regulation module changed to work with multiple inputs and outputs, in addition to enabling real-time estimation of the influence matrix. The performance and robustness of the regulator were analyzed as a function of the parameters. The synchronized regulation was applied to the theoretical model developed by the finite elements method and simulated in a computer.

Thesis (Ph. D.)--University of California, San Diego, 2001. / Vita. Includes bibliographical references.

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

Este trabalho versa sobre a análise teórica do desempenho da regulação sincronizada aplicada na redução de vibrações de rotores utilizando mancais magnéticos. Originalmente apresentado na dissertação \\Regulação sincronizada de distúrbios senoidais\", de Vaydia I. C. Segura, o regulador teve o seu módulo de regulação modificado para trabalhar com múltiplas entradas e saídas, além de permitir a estimação em tempo real da matriz de influência. O desempenho e a robustez do regulador foram analisados em função de seus parâmetros. A regulação sincronizada foi aplicada a um modelo teórico de rotor desenvolvido pelo método dos elementos finitos e simulado em computador. / This work discusses about the theoretical analysis of the performance of synchronized regulation applied in reduction of rotor vibrations using magnetic bearings. Originally presented in the dissertation \\Synchronized regulation of sinoidal disturbing\", of Vaydia I. C. Segura, the regulator had its regulation module changed to work with multiple inputs and outputs, in addition to enabling real-time estimation of the influence matrix. The performance and robustness of the regulator were analyzed as a function of the parameters. The synchronized regulation was applied to the theoretical model developed by the finite elements method and simulated in a computer.

Die Kenntnis der dynamischen Eigenschaften von Turbomaschinenrotoren sind bei magnetgelagerten Maschinen von entscheidender Bedeutung für den sicheren Betrieb und die Regelung. Besonders der Temperatureinfluss auf die Materialien und die Eigenformen müssen dabei berücksichtigt werden. In diesem Beitrag wird ein MATLAB-Tool vorgestellt mit dem es möglich ist, die Eigenfrequenzen und -formen für magnetgelagerte Turbomaschinen zu berechnen und das Rotormodell für dynamische Simulationen zu erstellen. Es wird auf die zu Grunde liegende Mathematik eingegangen und die Implementierung vorgestellt. Die bisher erreichten Ergebnisse und die Implementierung in ein Simulationsmodell für eine magnetgelagerte Maschine werden gezeigt. / Knowledge of the dynamic properties of turbomachinery rotors is of crucial importance for safe operation and control in machines with magnetic bearings. Especially the temperature influence on the materials and the eigenmodes have to be considered. In this paper, a MATLAB tool is presented with which it is possible to calculate the natural frequencies and shapes for magnetically levitated turbomachinery and to create the rotor model for dynamic simulations. The underlying mathematics is discussed and the implementation is presented. The results achieved so far and the implementation in a simulation model for a machine with magnetic bearings are shown.

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

Magnetic bearings support turbomachinery by regulating their forces exerted in relation to the displacement of the machine supported. The regulating control system must be tuned for stable and safe operation of the rotor. The ultimate goal of this study is to determine the effects of changing controller gains on the behavior of the rotor during operation in its normal speed range with a known unbalance load. We also endeavor to confirm the model of the rotor supported the magnetic bearings, as an additional goal. We first investigate the modelling of rotors supported by magnetic bearings, including the model of the control system. We present a finite element model of a magnetic bearing supported rotor, and perform experiments to determine the characteristics of the control system which governs the magnetic forces on the rotor. The experimental control system characteristics confirm the expected characteristics from theory. With this knowledge, we perform simulations and experiments under the same forcing conditions to determine the accuracy of the model in predicting the experimental behavior of an unbalanced rotor. The model exhibits satisfactory ability in predicting the experimental behavior of the rotor under this loading. Our next step is to determine the effects of variation of proportional and integral controller gains on the behavior of the rotor. Both simulations and experiments show that an increase in the proportional controller gain results in an increase in the rotor’s first critical speed. An increase in the integral gain results in a small decrease in the location of the peak response speed in the speed range tested, while leaving the peak amplitude insignificantly changed. Again, simulations and experiments predict this result. We reach the following three conclusions from this study. First, the finite element model of the rotor/bearing system is a viable model for predicting the behavior of the experimental system. Second, tuning of the proportional gain shows a significant effect on the behavior of the rotor during unbalance loading across its speed range, due to considerable change in bearing stiffness caused by the tuning of this gain. Last, tuning of the integral gain has a small effect on the behavior of the rotor due to the change in bearing damping, too small to be considered significant. / Master of Science

In Vakuumanwendungen, wie Molekularpumpen oder Schwungradenergiespeichern, treffen oftmals hohe Drehzahlen auf schwierige Kühlbedingungen. Es besteht daher der Bedarf nach aktiven Magnetlagern mit einem besonders geringem Leistungsbedarf sowie geringen Ummagnetisierungsverlusten im Rotor. Die zur Verlustminimierung prädestinierten Pulververbundwerkstoffe (SMC - Soft Magnetic Composites) finden aufgrund ihrer geringen mechanischen Festigkeit bisher keine Anwendung in industriellen Hochgeschwindigkeitsanwendungen. In diesem Artikel wird das DFG-Projekt „Verlustarme magnetische Radial-/Axiallagerung unter Verwendung von Pulververbundwerkstoffen“ zusammengefasst sowie abschließend der experimentelle Nachweis erbracht, dass die neu entwickelte dreipolige Lagerstruktur mit kombiniertem Radial- und Axiallager den Einsatz von SMC auch bei Drehzahlen von bis zu 30 000 U/min erlaubt. Eine Projizierung der Messergebnisse auf verlustoptimierte industrielle SMC-Sorten verspricht zudem ein Reduzierungspotential der Ummagnetisierungsverluste von mindestens 23 – 44%, wobei insbesondere kompakte und hochausgenutzte Geometrien im Vorteil sind.

Orientador: Robson Pederiva / Dissertação (mestrado) - Universidade Estadual de Campinas. Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-07T00:56:52Z (GMT). No. of bitstreams: 1 Silva_GilbertoMachadoda_M.pdf: 1128289 bytes, checksum: e5a6e2d7aeb16be17a0a3d45dd834193 (MD5) Previous issue date: 2006 / Resumo: Aplica-se neste trabalho a metodologia de diagnóstico de falhas em sistemas mecânicos rotativos sustentados por mancais magnéticos ativos em conjunto com um sistema de controle ativo de vibração, excitados por forças de desbalanço e ruído branco. Este diagnóstico baseia-se no emprego das equações de correlações, através da formulação matricial de Ljapunov, para sistemas lineares estacionários juntamente com redes neurais artificiais. Este procedimento utiliza apenas as variáveis de estado medidas, através da correlação das variáveis de saída. É gerado um conjunto de relações envolvendo os parâmetros físicos do sistema juntamente com as matrizes de correlações das variáveis medidas. As falhas no sistema são detectadas através do monitoramento da variação dos parâmetros físicos e da comparação das funções de correlação teóricas e estimadas. As redes neurais artificiais são usadas para mapear as correlações que envolvem estados que não são medidos. Dado ao grande número de equações de compatibilidade resultantes, é proposta uma metodologia para selecionar as equações relacionadas com as falhas propostas. Com o método de diagnóstico de falhas proposto é possível detectar e discernir as falhas tanto mecânicas quanto elétricas, bem como sua localização no sistema / Abstract: This work applies the methodology of fault diagnosis in rotating machinery supported by active magnetic bearings and active con1rol systems, excited by unbalance and white noise. This diagnostic applies the correlation matrices based on the Ljapunov matrix formulation and artificial neural network for linear stationary systems. The procedure uses only measured state variables, computing the correlation between the output variables. It is possible to derive specific relations involving the physical parameter of the system and the correlation matrices of the measured variables. Faults in the system can be detected by monitoring the variation of the physical parameter through a comparison of theoretical and estimated correlation functions. Artificial neural networks are used to map the correlations involving the variables, which are difficult to be measured. There is a large number of resultant compatibility equations and it is proposed a methodology to select the equations that establish relationships with the faults. The proposed fault diagnosis method can detect the fault present in the system and it is also possible to distinguish between mechanical and electrical fault as well as their location in the system / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica