Subsynchronous vibrations such as those caused by rotor instability represent one of the most harrowing scenarios of rotor vibration. They are related to a great diversity of destabilizing forces and some of them are not well understood yet. Therefore, special attention must be paid to this type of vibration. Active Magnetic Bearings (AMBs) monitor the position of the shaft and change the dynamics of the system accordingly to keep the rotor in a desired position, offering the possibility of being used as dampers for vibration control. In the present work, a single-disk and a three-disk rotor were built to evaluate the effectiveness of an Active Magnetic Damper (AMD) in damping subsynchronous vibrations. An AMD was used to inject a signal simulating a subsynchronous vibration in the rotor, as another AMD was used to perform active control. Two locations of the AMD were considered for each rotor. For the single-disk rotor, experimental data was taken with the AMD located at three-quarters of the rotor-span and with the AMD located at midspan. For the three-disk rotor, experimental data was taken with the AMD located at a quarter-span and with the AMD at two-thirds of the rotor span. An undamped critical speed and a forced response analysis were performed on the rotors in order to predict the dynamic characteristics of the rotors with and without the AMD. It was demonstrated that an AMD is effective in damping subsynchronous vibrations. The addition of an AMD introduces damping and stiffness to the rotor-bearing system resulting in a change in the synchronous response and a consequent increase of the amplitude of vibrations at synchronous frequencies. This effect must be carefully considered when designing a system with an AMD. / Master of Science

O Motor Assíncrono Tubular para Aplicação na Extração de Óleo do Subsolo MATÆOS foi desenvolvido na Escola Politécnica da Universidade de São Paulo (EPUSP) com a função de acionar diretamente uma bomba de sucção, instalada no fundo de um poço de petróleo em terra. Dando continuidade aos trabalhos realizados na EPUSP envolvendo sistemas de levitação magnética, foi desenvolvido um mancal magnético ativo (AMB - Active Magnetic Bearing), aplicado ao protótipo do motor em substituição ao mancal mecânico tradicional existente. O projeto abrange a construção de um protótipo de mancal magnético composto das partes mecânicas, elétricas e de software necessárias ao funcionamento do sistema. O projeto do eletroímã foi realizado por meio do método dos elementos finitos (MEF), para análise da densidade de fluxo e da relação entre a força radial e a corrente elétrica nas bobinas. O controle da levitação do mancal é realizado por meio de controlador digital com placas conversoras AD/DA e algoritmo de controle implementado em hardware FPGA. Utilizando o modelo do sistema, os controladores são sintonizados para atender aos requisitos de estabilidade e rejeição de perturbações, que desviem o entreferro do seu valor nominal. Na configuração do AMB, ao invés do sistema tradicional com oito pólos, um conceito diferente é adotado. Neste, uma máquina primitiva bearingless é excitada com corrente contínua e usada como mancal magnético. Os resultados experimentais obtidos com o protótipo em funcionamento mostram que o sistema em malha fechada é estável e apresenta uma resposta transitória satisfatória. / A tubular linear induction motor applied to onshore oil exploitation, named MATÆOS (which is in the Portuguese acronym for Tubular Asynchronous Motor for Onshore Oil Exploitation) was built at Escola Politécnica da Universidade de São Paulo (EPUSP). Its purpose is to directly drive the sucker-rod pump installed in the down hole of the oil well. In continuing the research accomplished at EPUSP concerning magnetic levitation systems, an Active Magnetic Bearing (AMB) was developed and applied to the prototype of the motor in substitution to the existing traditional bearing. The design includes the construction of the magnetic bearing prototype composed of mechanical, electric and software components required to the operation of the system. The electromagnet design was accomplished using the Finite Element Method (FEM) in the analysis of both the flux density and the relationship between the radial force and the suspension winding current. The magnetic bearing levitation control is executed by a digital controller using an AD/DA converter and a control algorithm implemented in FPGA hardware. Using the system model, the controllers are tuned to provide both stability and rejection of disturbances that tend to move the air gap from its nominal value. Instead of the usual eight-pole AMB, a different concept is adopted where a DC-excited primitive bearingless machine is used as a magnetic bearing. The experimental results obtained with the prototype in operation show that the closed-loop system is stable and exhibits a satisfactory transient response.

Esta dissertação tem como objetivo o projeto de um mancal magnético para rodas de reação com aplicação na malha de controle de atitude de satélites. Mancais magnéticos são alternativas aos mancais tradicionais tais como os de esferas ou de lubrificação seco pois trabalham sem contato mecânico entre o rotor e o estator, minimizando assim a fricção entre ambas as partes. Além da minimização do atrito, o ganho em confiabilidade e vida útil da roda de reação é considerável por não apresentar desgastes mecânicos. Devido às consequências de qualquer fricção no movimento relativo entre a inércia (parte rotativa da roda de reação) e o satélite, o mancal torna-se um componente crítico da roda de reação. A fricção se traduz não apenas num maior consumo de potência elétrica, como também na introdução de uma zona morta de atuação em torque, bem como na limitação da vida útil da roda de reação devido ao gradual desgaste do mancal. O mancal proposto possui dois graus de liberdade axiais ativamente controlados e faz uso de ímãs para a estabilização passiva dos demais graus de liberdade. Ao longo do desenvolvimento são apresentados modelos não lineares dos campos magnéticos e das forças atuantes no mancal são encontrados. Com esses modelos, uma otimização é realizada a fim de encontrar melhores características. Um modelo não linear da dinâmica do rotor é desenvolvido e um controle PID capaz de estabilizar o rotor em seu ponto de equilíbrio é apresentado com o objetivo de demonstrar a viabilidade da topologia proposta. / The main objective of this work is to project a magnetic bearing for reaction wheels with application in satellite attitude control. Magnetic bearings are alternatives to traditional bearings such as ball or dry lubrication because they work without mechanical contact between the rotor and the stator thereby minimizing friction between both parts. In addition to minimizing friction, the gain in reliability and lifetime of the reaction wheel is considerable as a consequence of the absence of wear. Because of the consequences of any friction in the relative movement between the inertia (of the reaction wheel) and the satellite ( which is rigidly connected to the satellite body), the bearing becomes a critical component of the reaction wheel. The friction gives rise not only to a greater consumption of electric power, as well as the introduction of a torque dead zone operation, in a reduced lifetime of the reaction wheel due to gradual wear of the bearing. The proposed bearing has two axial degrees of freedom actively controlled and makes use of magnets for the passive stabilization of other degrees of freedom. Nonlinear models of magnetic fields and forces acting on the bearing are presented. With these models, an optimization is performed to find the best bearing characteristics. A nonlinear model rotor dynamics is developed and a PID control capable of stabilizing the active degrees of freedom presented.

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.

Made available in DSpace on 2014-06-11T19:27:14Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-03-03Bitstream added on 2014-06-13T18:31:08Z : No. of bitstreams: 1 goncalvesjr_r_me_ilha.pdf: 1793490 bytes, checksum: 31bd12dfbef20fead2490b33aa2d1148 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho apresenta uma análise teórica do desempenho de um sistema de controle ativo de vibração de rotores utilizando mancais magnéticos. O esquema de controle ativo proposto utiliza a estratégia de controle ativo feedforward sobreposta ao sistema de controle feedback dos mancais magnéticos. O desempenho desse sistema de controle foi analisado em função da flexibilidade dos rotores considerando o impacto do número e da localização dos atuadores e dos sensores de erro sobre a redução dos níveis de vibração desses rotores, tanto em termos de vibração global quanto em termos de vibração local. O sistema de controle foi aplicado em um modelo teórico de rotor desenvolvido através do método da matriz de impedância. / This work presents a theoretical analysis of the performance of a system of active control of rotor vibrations using magnetic bearings. The proposed scheme of active control uses a feedforward active control strategy superimposed on the feedback control system of the magnetic bearings. The performance of this control system was analyzed as a function of the rotor flexibility considering the impact and optimization of the actuators and error sensors placement on the reduction of vibration levels of these rotors, in terms of global vibration as well as in terms of local vibration of the rotor. The control system was applied to a theoretical rotor model developed by the matrix impedance method.

Esta dissertação tem como objetivo o projeto de um mancal magnético para rodas de reação com aplicação na malha de controle de atitude de satélites. Mancais magnéticos são alternativas aos mancais tradicionais tais como os de esferas ou de lubrificação seco pois trabalham sem contato mecânico entre o rotor e o estator, minimizando assim a fricção entre ambas as partes. Além da minimização do atrito, o ganho em confiabilidade e vida útil da roda de reação é considerável por não apresentar desgastes mecânicos. Devido às consequências de qualquer fricção no movimento relativo entre a inércia (parte rotativa da roda de reação) e o satélite, o mancal torna-se um componente crítico da roda de reação. A fricção se traduz não apenas num maior consumo de potência elétrica, como também na introdução de uma zona morta de atuação em torque, bem como na limitação da vida útil da roda de reação devido ao gradual desgaste do mancal. O mancal proposto possui dois graus de liberdade axiais ativamente controlados e faz uso de ímãs para a estabilização passiva dos demais graus de liberdade. Ao longo do desenvolvimento são apresentados modelos não lineares dos campos magnéticos e das forças atuantes no mancal são encontrados. Com esses modelos, uma otimização é realizada a fim de encontrar melhores características. Um modelo não linear da dinâmica do rotor é desenvolvido e um controle PID capaz de estabilizar o rotor em seu ponto de equilíbrio é apresentado com o objetivo de demonstrar a viabilidade da topologia proposta. / The main objective of this work is to project a magnetic bearing for reaction wheels with application in satellite attitude control. Magnetic bearings are alternatives to traditional bearings such as ball or dry lubrication because they work without mechanical contact between the rotor and the stator thereby minimizing friction between both parts. In addition to minimizing friction, the gain in reliability and lifetime of the reaction wheel is considerable as a consequence of the absence of wear. Because of the consequences of any friction in the relative movement between the inertia (of the reaction wheel) and the satellite ( which is rigidly connected to the satellite body), the bearing becomes a critical component of the reaction wheel. The friction gives rise not only to a greater consumption of electric power, as well as the introduction of a torque dead zone operation, in a reduced lifetime of the reaction wheel due to gradual wear of the bearing. The proposed bearing has two axial degrees of freedom actively controlled and makes use of magnets for the passive stabilization of other degrees of freedom. Nonlinear models of magnetic fields and forces acting on the bearing are presented. With these models, an optimization is performed to find the best bearing characteristics. A nonlinear model rotor dynamics is developed and a PID control capable of stabilizing the active degrees of freedom presented.

O Motor Assíncrono Tubular para Aplicação na Extração de Óleo do Subsolo MATÆOS foi desenvolvido na Escola Politécnica da Universidade de São Paulo (EPUSP) com a função de acionar diretamente uma bomba de sucção, instalada no fundo de um poço de petróleo em terra. Dando continuidade aos trabalhos realizados na EPUSP envolvendo sistemas de levitação magnética, foi desenvolvido um mancal magnético ativo (AMB - Active Magnetic Bearing), aplicado ao protótipo do motor em substituição ao mancal mecânico tradicional existente. O projeto abrange a construção de um protótipo de mancal magnético composto das partes mecânicas, elétricas e de software necessárias ao funcionamento do sistema. O projeto do eletroímã foi realizado por meio do método dos elementos finitos (MEF), para análise da densidade de fluxo e da relação entre a força radial e a corrente elétrica nas bobinas. O controle da levitação do mancal é realizado por meio de controlador digital com placas conversoras AD/DA e algoritmo de controle implementado em hardware FPGA. Utilizando o modelo do sistema, os controladores são sintonizados para atender aos requisitos de estabilidade e rejeição de perturbações, que desviem o entreferro do seu valor nominal. Na configuração do AMB, ao invés do sistema tradicional com oito pólos, um conceito diferente é adotado. Neste, uma máquina primitiva bearingless é excitada com corrente contínua e usada como mancal magnético. Os resultados experimentais obtidos com o protótipo em funcionamento mostram que o sistema em malha fechada é estável e apresenta uma resposta transitória satisfatória. / A tubular linear induction motor applied to onshore oil exploitation, named MATÆOS (which is in the Portuguese acronym for Tubular Asynchronous Motor for Onshore Oil Exploitation) was built at Escola Politécnica da Universidade de São Paulo (EPUSP). Its purpose is to directly drive the sucker-rod pump installed in the down hole of the oil well. In continuing the research accomplished at EPUSP concerning magnetic levitation systems, an Active Magnetic Bearing (AMB) was developed and applied to the prototype of the motor in substitution to the existing traditional bearing. The design includes the construction of the magnetic bearing prototype composed of mechanical, electric and software components required to the operation of the system. The electromagnet design was accomplished using the Finite Element Method (FEM) in the analysis of both the flux density and the relationship between the radial force and the suspension winding current. The magnetic bearing levitation control is executed by a digital controller using an AD/DA converter and a control algorithm implemented in FPGA hardware. Using the system model, the controllers are tuned to provide both stability and rejection of disturbances that tend to move the air gap from its nominal value. Instead of the usual eight-pole AMB, a different concept is adopted where a DC-excited primitive bearingless machine is used as a magnetic bearing. The experimental results obtained with the prototype in operation show that the closed-loop system is stable and exhibits a satisfactory transient response.

Hochtemperaturmagnetlager in Turbomaschinen erfordern Lagesensoren, die den Umgebungsbedingungen ebenfalls dauerhaft standhalten und den Lagereglern hinreichend genaue und störungsfreie Informationen über die Rotorpositionen kontinuierlich zur Verfügung stellen. Ausgehend von den Einsatzbedingungen wurden mögliche Messprinzipien untersucht. In einem zweiten Schritt erfolgte die Recherche zu temperaturbeständigen Werkstoffen für die Sensorkomponenten und auf Basis einer Marktanalyse wurde deren Verfügbarkeit geprüft. Im Anschluss wurde ein kombinierter induktiver Radial-Axial-Lagesensor als Prototyp für den Einsatz am Magnet- und Fanglagerprüfstand MFLP ausgelegt. Dazu wurde ein analytischer Auslegungsalgorithmus für schnelle Auslegungsrechnungen erstellt und in MATLAB umgesetzt. Aufbauend auf den Ergebnissen der Auslegung wurde der Sensor konstruiert und gefertigt. Parallel dazu wurde eine Sensorelektronik entwickelt. Das Paper beschreibt die Auslegung und Konstruktion des Sensors und die Entwicklung der dazugehörigen Elektronik. / High-temperature magnetic bearings in turbomachinery require position sensors that can also withstand the ambient conditions permanently. This measurement system continuously provide the position controllers with sufficiently accurate and interference-free information about the rotor positions. Based on the operating conditions, suitable measurement principles were investigated. Furthermore suitable temperature-resistant materials for the sensor components were identified and their availability was checked based on a market analysis. Subsequently, a combined inductive radial-axial position sensor was developed. The demonstrator was designed for air gap measurements at the MFLP - a test rig for magnetic and backup bearings. For this purpose, an analytical design algorithm for fast design calculations was created and implemented in MATLAB. Based on the design results, the sensor was designed and manufactured. In parallel, sensor electronics were developed. The paper describes the design and construction of the sensor and the development of the associated electronics.

No description available.