In this thesis, two selected topics in magnetism are studied using theoretical modelling and computational methods. The first of these is the magnetocrystalline anisotropy energy (MAE) of transition metal based magnets. In particular, ways of finding 3d transition metal based materials with large MAE are considered. This is motivated by the need for new permanent magnet materials, not containing rare-earth elements, but is also of interest for other technological applications, where the MAE is a key quantity. The mechanisms of the MAE in the relevant materials are reviewed and approaches to increasing this quantity are discussed. Computational methods, largely based on density functional theory (DFT), are applied to guide the search for relevant materials. The computational work suggests that the MAE of Fe1-xCox alloys can be significantly enhanced by introducing a tetragonality with interstitial B or C impurities. This is also experimentally corroborated. Alloying is considered as a method of tuning the electronic structure around the Fermi energy and thus also the MAE, for example in the tetragonal compound (Fe1-xCox)2B. Additionally, it is shown that small amounts (2.5-5 at.%) of various 5d dopants on the Fe/Co-site can enhance the MAE of this material with as much as 70%. The magnetic properties of several technologically interesting, chemically ordered, L10 structured binary compounds, tetragonal Fe5Si1-xPxB2 and Hexagonal Laves phase Fe2Ta1-xWx are also investigated. The second topic studied is that of magnetic effects on the elastic scattering of fast electrons, in the context of transmission electron microscopy (TEM). A multislice solution is implemented for a paraxial version of the Pauli equation. Simulations require the magnetic fields in the sample as input. A realistic description of magnetism in a solid, for this purpose, is derived in a scheme starting from a DFT calculation of the spin density or density matrix. Calculations are performed for electron vortex beams passing through magnetic solids and a magnetic signal, defined as a difference in intensity for opposite orbital angular momentum beams, integrated over a disk in the diffraction plane, is observed. For nanometer sized electron vortex beams carrying orbital angular momentum of a few tens of ħ, a relative magnetic signal of order 10-3 is found. This is considered realistic to be observed in experiments. In addition to electron vortex beams, spin polarised and phase aberrated electron beams are considered and also for these a magnetic signal, albeit weaker than that of the vortex beams, can be obtained. / <p>Felaktigt ISBN i den tryckta versionen: 9789155497149</p><p></p>

Many physical properties, for example structural or magnetic, of a material are directly dependent on elemental composition. Tailoring of properties through highly accurate composition control is possible in thin films. This work exemplifies such tailoring. A short review is given of the current status for research in the area of permanent magnets, focusing on rare earth element free alternatives, where FeNi in the L10 phase is a possible candidate. Epitaxial FeNi L10 thin films were successfully synthesized by magnetron sputtering deposition of monoatomic layers of Fe and Ni on HF-etched Si(001) substrates with Cu or Cu100-xNix/Cu buffers. The in-plane lattice parameter aCuNi of the Cu100-xNix buffer layer was tuned by the Ni content. Through matching of aFeNi to aCuNi, the strain state (c/a)FeNi was controlled, where c is the out-of-plane lattice parameter. The 001 reflection indicative of chemical order, as measured by resonant x-ray diffraction, was in most cases split in two peaks due to a composition modulation of Fe and Ni. This chemical disorder contributed to that the uniaxial magnetocrystalline anisotropy energy, KU≈0.35 MJ/m3, was smaller than predicted. In later experiments the composition modulation could partly be compensated for. Remaining discrepancies with respect to predicted KU values were attributed to additional disorder induced by surface roughness of the buffer layer. The interface sharpness between Fe and Ni was explored by producing epitaxial symmetric multilayers with individual layer thicknesses n = 4-48 monolayers (ML). For n ≤ 8 ML the films had pure fcc structure, with antiferromagnetic Fe layers. For n ≥ 8 ML the Fe layers relaxed to bcc structure. A combinatorial sputter chamber, which has the capability to deposit samples with composition and thickness gradients, was assembled. A model for simulation of composition and thickness across large substrates, for the conditions in this chamber, is presented. The model is verified by comparison to experimental data. Some challenges inherent in combinatorial sputtering are discussed, and two experimental studies employing the technique are presented as examples. These investigated magnetic and structural properties of Tb-Co films, with 7-95 at.% Tb, and of amorphous and crystalline ternary gradient Co-Fe-Zr films, respectively.

Pós magnéticos foram produzidos utilizando o processo de hidrogenação, desproporção, dessorção e recombinação (HDDR). A primeira parte deste trabalho envolveu o estudo do efeito da adição de Co na liga Pr14FebalCoxB6Nb0.1 (x= 0, 4, 8, 10, 12, 16) variando a de temperatura de dessorção/ recombinação de 800° a 900°C, com o objetivo de otimização do tratamento HDDR. A liga Pr14Fe80B6 foi utilizada como padrão. As ligas foram tratadas termicamente a 1100°C por 20 horas para eliminação do Fe- exixtente na liga em estado bruto de fusão. A temperatura de dessorção/ recombinação afetou a microestrutura e as propriedades magnéticas dos ímãs moldados com polímeros. A liga com baixa adição de cobalto (4 at.%) exigiu a temperatura de reação mais alta (880°C) entre os demais ímãs. As temperaturas ótimas para as ligas com 8 at.% Co e 10 at.% Co foram 840°C e 820°C, respectivamente. Ligas com altas concentrações de cobalto (12 at.% and 16 at.%) foram processadas a 840°C. A temperatura de dessorção/ recombinação que apresentou alta anisotropia nas ligas Pr14Fe80B6 e Pr14Fe79,9B6Nb0,1 foi de 820°C. O ímã que apresentou melhor remanência (862mT) foi processado com a liga Pr14Fe67,9Co12B6Nb0,1. Cada liga apresentou uma temperatura de reação otimizada e exibiu uma microestrutura particular, de acordo com a composição. A segunda parte deste trabalho envolveu a caracterização, dos pós HDDR de Pr14Fe80B6, que foram analisadas por difração de raios X com fonte síncrotron para a identificação e quantificação de fases cristalinas, e ainda para a determinação do tamanho médio de cristalitos da fase principal. A microscopia eletrônica de varredura (MEV) foi utilizada para revelar a morfologia dos pós HDDR. / Fine magnetic powders were produced using the hydrogenation disproportionation desorption and recombination (HDDR) process. The first stage in this work involved an investigation of the effect of the Co content and range of desorption/ recombination temperatures between 800 and 900°C with the purpose of optimizing the HDDR treatment for Pr14Fe80B6 and Pr14FebalCoxB6Nb0,1 (x= 0, 4, 8, 10, 12, 16) alloys. The cast alloys were annealed at 1100°C for 20 hours for homogenization. The processing temperature (desorption/ recombination) affected the microstructure and magnetic properties of the bonded magnets. The alloy with low cobalt content (4 at.%) required the highest reaction temperature (880°C) to yield anisotropic bonded magnets. The optimum temperature for alloys with 8 at.% Co and 10 at.% Co were 840°C and 820°C, respectively. Alloys with high cobalt content (12 at.% and 16 at.%) were processed at 840°C. The optimum desorption temperature for achieving high anisotropy for Pr14Fe80B6 and Pr14Fe79,9B6Nb0,1 was 820°C. The best remanence (862mT) was achieved with the Pr14Fe67,9B6Co12Nb0,1 magnet, processed at 840°C. Each alloy required an optimum reaction temperature and exhibited a particular microstructure according to the composition. The second stage of the work involved the characterization, for each temperature, of the Pr14Fe80B6 HDDR powder processed using X-ray diffraction analysis. The samples of the HDDR material were studied by synchrotron radiation powder diffraction using the Rietveld method for cell refinement, phase quantification and crystallite sizes determination. Scanning electron microscopy (SEM) has also been employed to reveal the morphology of the HDDR powder.

Este trabalho propõe uma investigação sobre a influência da alocação da área de mancal em compressores herméticos para a refrigeração, considerando um motor Síncrono de Ímãs Permanentes com Partida Direta na Rede (LSPMSM) monofásico, e utilizando cálculos analíticos convencionais e o Método de Elementos Finitos (MEF). O recente aumento da preocupação com a eficiência energética tem levado muitos países a implantarem legislações que impõem necessidades de aumento de eficiência de motores elétricos. Neste contexto, o motor LSPMSM se apresenta como alternativa aos motores de indução convencionais visando à diminuição do consumo de energia elétrica, por exemplo, em refrigeradores. No entanto, a exigência de alocação de uma grande área para o mancal e por consequência a retirada de materiais ferromagnéticos do rotor pode diminuir o desempenho do motor LSPMSM inviabilizando assim sua aplicação. Para a realização deste estudo, foi adotada uma metodologia de projeto disponível na literatura para estabelecer as etapas do projeto a ser realizado. Tal referência de projeto, embora elaborada para ser utilizada em um motor LSPMSM trifásico, foi utilizada em um projeto de motor monofásico. Os resultados do ensaio foram comparados com os dados obtidos via simulações computacionais de tal forma a validar o método proposto e também avaliar o impacto da retirada de material do rotor no desempenho final do motor. Os resultados práticos ficaram próximos aos resultados obtidos em simulação validando a utilização da metodologia também em motores monofásicos. Desta forma foi possível visualizar o efeito da área de mancal no rotor que devido ao aumento da relutância do circuito magnético alterou os resultados do valor da tensão induzida dos ímãs. / This work proposes a study about the influence of the bearing area allocation in hermetic compressors for refrigeration, considering a single phase Line Start Permanent Magnets Synchronous Motor, and employing conventional analytical calculations and the Finite Element Method (MEF). Recent increase in concern about energy efficiency has led many countries to roll out laws that impose requirements to raise the electric motor efficiency. In this context the LSPMSM motor is an alternative over conventional induction motors for the purpose of seeking power consumption reduction. However, the requirement to allocate a large area for the bearing and thus removal of ferromagnetic materials of the rotor can reduce LSPMSM motor performance what may impede its implementation. For the accomplishment of this study it was adopted a methodology of design available in the literature to set up the steps to be followed. Such design reference was at first described to be applied in three phase LSPMSM, however in this work it was applied in a single phase motor. Tests results were compared with data obtained via computer simulations in a way to validate the proposed method and to assess the impact of material removal from de rotor on the motor performance. The obtained bench test results were close to those simulated ones validating the methodology to be used in single phase motors too. Therefore, it was feasible to notice the influence of the counterbore area in the rotor, which, due to the increased value of the circuit reluctance, changed induced voltage values related to the magnets.

O objetivo deste trabalho foi tentar correlacionar microestrutura e propriedades magnéticas de ímãs permanentes de alta energia do tipo Sm(CoFeCuZr)z para aplicações em temperaturas acima de 300°C. Avaliou-se a possibilidade de que o constituinte matriz da microestrutura dos ímãs para altas temperaturas fosse diferente do constituinte matriz dos ímãs convencionais. Com este propósito foram estudados três conjuntos de amostras: i) Dois ímãs comerciais para aplicações na temperatura ambiente, um da Electron Energy e outro da Vacuumschmelze. Eles foram caracterizados magneticamente e a sua microestrutura foi analisada por microscópio eletrônico de varredura dotado de análise química, com o objetivo de avaliar se os mesmos apresentavam dois microconstituintes presentes em algumas ligas de Sm(CoFeCuZr)z. ii) Uma liga comercial da Johnson Matthey (JM) que é utilizada para produzir ímãs permanentes de Sm(CoFeCuZr)z. Essa liga foi utilizada para o estudo e avaliação de ciclos térmicos como solubilização, tratamento isotérmico, rampa de resfriamento lento e tratamento térmico a 400°C, e o seu efeito nas propriedades magnéticas e na micro e nano estruturas. iii) Duas séries de ligas com seis amostras cada série produzidas em forno a arco voltaico no LMM-IFUSP, com o propósito de estudar o efeito do teor de cobre e samário nas propriedades magnéticas, na microestrutura e na nanoestrutura dessas ligas. A caracterização magnética em campo de 9T permitiu determinar a polarização máxima e o campo coercivo das amostras. A caracterização magnética em campos de até 2T permitiu determinar o campo coercivo e a polarização remanente das amostras em temperaturas na faixa de 200 a 500°C. Três ligas resultaram em campo coercivo Hci > 398kA/m (Hci > 5kOe) a 450°C, que segundo a literatura, podem ser utilizadas em aplicações em temperaturas elevadas. Uma caracterização detalhada da microestrutura e da composição química foi feita utilizando-se Microscopia Eletrônica de Varredura (MEV) com VI análise química de praticamente todas as amostras. No diagrama de fases pseudo-ternário foi possível definir o campo de fases das composições 2:17R com baixo e alto Sm. As amostras da liga comercial JM e três das doze ligas produzidas em forno a arco voltaico apresentaram os microconstituintes claro e escuro e estes parecem não afetar as propriedades magnéticas das amostras. Foi observado que com o aumento do teor de Sm na liga a polarização máxima diminui. A polarização máxima Jmáx também diminui com o aumento do teor de Cu na liga, porém de forma menos acentuada. Foi possível observar a estrutura nanométrica, bem como a presença e a formação das nanocélulas nessas ligas nanocristalinas com elétrons secundários via microscopia eletrônica de varredura com fonte de emissão de campo MEV/FEG, que é um diferencial neste trabalho uma vez que essas análises são típicas em microscopia eletrônica de transmissão. Verificou-se que as nanocélulas são observáveis com FEG em amostras cuja coercividade são superiores a 159 kA/m (2kOe). Foi possível aplicar o modelo de Stoner-Wohlfarth modificado por Callen Liu e Cullen à curva de histerese para determinar o campo de anisotropia magnetocristalina, a magnetização de saturação e o coeficiente de interação de campo médio 1/d. A difração de Raios-X aliada ao refinamento Rietveld permitiram determinar as fases formadas em altas temperaturas após o tratamento de homogeneização a 1175°C/4h. Verificou-se que há a formação de duas fases romboédricas, uma rica em cobre e a outra rica em ferro. Este dado é inédito na literatura. / The main objective of this study was to correlate microstructure and magnetic properties of high-energy permanent magnets of the Sm(CoFeCuZr)z type for applications at temperatures above 300°C. The possibility that the matrix constituents of the microstructure of high temperature magnets are different from the matrix constituents of the conventional magnets is investigated with three sets of samples: i) Two magnets for commercial applications at room temperature, one produced by Electron Energy and the other by Vacuumschmelze. ii) A Sm(CoFeCuZr)z as-cast alloy synthesized by Johnson Matthey (JM) for permanent magnets production was used to study the effect of heat treatment steps as follows: (a) solutionizing at 1175°C for 4h, b) followed by quenching in water, (c) reheating at 820°C for 7h, d) followed by slow cooling down at 1°C/min to 400°C, and (e) heat treatment at 400°C for different durations and their effects on its magnetic properties and its micro and nanostructure. iii) Two series of Sm(CobalFe0.15CuxZr0.023)7 and Sm(CobalFe0.15CuxZr0.023)8.5 alloys with x=0.058, 0.088, 0.108 were prepared by arc melting technique, in order to study the effect of Copper and Samarium contents on its microstructure and magnetic properties. The characterization in magnetic fields up to 9T allowed to determine the maximum polarization and the intrinsic coercivity of the samples. The characterization in magnetic field up 2T allowed to determine the coercive field and remanence of the samples at temperatures between 200°C and 500°C. Three alloys resulted in coercive field Hci > 398kA/m (Hci > 5kOe) at 450°C, which according to the literature, can be used in applications at elevated temperatures. A detailed characterization of the microstructure and chemical composition was performed using scanning electron microscopy (SEM) with EDAX chemical analysis of virtually all samples. The JM samples and three of the twelve alloys produced in the electric arc furnace showed the light and dark microconstituents, here identified as two 2:17 rombohedral phases with low and VIII high Sm. In a pseudo-ternary phase diagram it was possible to define the two phase field of 2:17R with low and high Sm. No correlation could be found with the magnetic properties of the samples. It was observed that by increasing the Sm content in the alloy the maximum induction Jmax decreases. The maximum induction Jmax also decreases with increasing Cu content in the alloy, but to a lesser extent. It was possible to observe the nanocrystalline microstructure as well as the presence and formation of nanocrystalline cells with scanning electron microscopy with field emission source SEM-FEG. Those characteristics are usually only observed by transmission electron microscopy. It was found that the nanocrystalline cells are observable with SEM-FEG on samples whose coercivity is above 159 kA/m (2kOe). It was possible to apply the Stoner-Wohlfarth model modified by Callen Liu and Cullen in the hysteresis loop to determine the magnetocrystalline anisotropy field, the saturation magnetization and the mean field interaction 1/d. The X-ray diffraction coupled with a Rietveld refinement were used to determine the phases formed at high temperatures after the solutinizing heat treatment at 1175°C/4h. It was found that there are two kinds of 2:17 rhombohedral phases formation. One is rich in copper and the other rich in iron.

Les accouplements (ou coupleurs) magnétiques servent à transmettre le couple d'un moteur vers sa charge sans contact mécanique. La suppression de ces contacts permet de réduire les bruits et vibrations, d'augmenter la fiabilité et d'assurer l'étanchéité dans des environnements difficiles. Dans le cas des moteurs supraconducteurs, un accouplement utilisant des matériaux supraconducteurs permet une nette augmentation des performances tout en transmettant le couple entre un environnement cryogénique (cryostat) et la température ambiante. Ce mémoire porte sur l'étude de coupleurs magnétiques à base de supraconducteurs à haute température critique (HTC) et d'aimants permanents. Deux topologies sont proposées, l'une à flux radial et l'autre à flux axial. Des outils analytiques et numériques sont développés pour le dimensionnement des accouplements étudiés. Un modèle analytique 2D de calcul du champ magnétique dans un accouplement supraconducteur à flux radial est développé et validé par éléments finis. Ce modèle est par la suite utilisé dans une procédure d'optimisation par algorithmes génétiques. L'objectif étant de rechercher les dimensions de l'accouplement qui maximisent le couple et minimisent la longueur du fil supraconducteur. Un prototype d'accouplement à flux axial est aussi réalisé. Plusieurs essais de caractérisation des bobines HTC sont menés. Des résultats de mesure de champ magnétique, de courant critique et de couple sont présentés / Magnetic couplings (or couplers) are used to transmit torque from a prime mover to its load without mechanical contact. This contactless transmission allows to reduce noise and vibration, to increase reliability and ensure hermetic isolation in severe environments. When the prime mover is a superconducting motor, a coupler which uses superconducting materials has more torque transmission capabilities and enables to transmit torque between a cryogenic media (cryostat) and the ambient temperature. This work focuses on the study of magnetic couplers using high temperature superconductors (HTS) and permanent magnets. Radial and axial field magnetic couplings, for which we developed analytical and numerical design tools, are proposed. A 2D analytical model for calculating the magnetic field distribution in a flux focusing HTS coupling is developed and validated by finite element computations. This model is then embedded in a genetic algorithms optimization procedure. The aim is to find the dimensions of the coupling that maximize torque and minimize the overall length of the HTS wires. A prototype axial field HTS coupler has been also designed, constructed and tested. Several tests have been conducted to characterize the HTS coils. Results of magnetic field, critical current and torque measurements are presented

Nous proposons l’étude d’une machine supraconductrice à flux axial composée d’un stator bobiné en cuivre et d’un inducteur avec des solénoïdes supraconducteurs à hautes températures critiques (HTc). Ce type de machine est adapté pour des applications de fortes puissances (plusieurs MW) avec de faibles vitesses de rotation (quelques centaines de tr/min), comme la propulsion de navire. Un accouplement magnétique, intégré au moteur, est utilisé pour transmettre le couple de l’inducteur supraconducteur vers la charge à température ambiante sans contact. On peut ainsi se passer des « torques tubes » qui sont habituellement présents dans les moteurs supraconducteurs pour relier mécaniquement l’inducteur à la charge et ainsi réduire les pertes thermiques par conduction. De plus, les accouplements magnétiques offrent une protection naturelle contre les surcharges mécaniques. Pour évaluer les performances de la solution proposée, nous avons développé un modèle analytique en 3D prenant en compte le comportement non linéaire des supraconducteurs en fonction du champ magnétique appliqué et de la température de fonctionnement. Ce modèle est ensuite intégré dans un processus de dimensionnement utilisant un algorithme génétique multi objectifs. Les résultats de cette optimisation montrent un gain en compacité (machine avec accouplement magnétique) 2 à 3,5 fois plus importants par rapport à des machines conventionnelles. Un prototype de machine supraconductrice à flux axial avec accouplement magnétique intégré est aussi réalisé. La conception, la fabrication et les tests sont présentés dans ce manuscrit. Tous les résultats sont validés par des calculs par éléments finis. / The study of an axial-field high temperature superconducting (HTS) motor for applications requiring high torque densities is proposed. The HTS motor consists of a stator with copper winding and an inductor with superconducting coils. A HTS magnetic coupler is used as a part of the system, to transmit the torque from the HTS motor to the load. This solution is a good alternative to the usually used torques tubes as it results in the reduction of conduction thermal losses and offers an intrinsic protection against overloads. To evaluate the performance of the studied device, a 3D electromagnetic analytical model has been developed. This model takes into account the dependence on the applied magnetic field and temperature of the HTS material. Finally, a genetic algorithms optimization of the studied device is carried out to find the optimum geometric dimensions. The results show that the proposed solution (machine with magnetic coupling) is about 2 to 3,5 times more compact than a conventional machine drive solution. An axial-field HTS motor with integrated magnetic coupling has been also designed, constructed and tested. The test results have been checked by 3D finite element computations.

Este trabalho propõe uma investigação sobre a influência da alocação da área de mancal em compressores herméticos para a refrigeração, considerando um motor Síncrono de Ímãs Permanentes com Partida Direta na Rede (LSPMSM) monofásico, e utilizando cálculos analíticos convencionais e o Método de Elementos Finitos (MEF). O recente aumento da preocupação com a eficiência energética tem levado muitos países a implantarem legislações que impõem necessidades de aumento de eficiência de motores elétricos. Neste contexto, o motor LSPMSM se apresenta como alternativa aos motores de indução convencionais visando à diminuição do consumo de energia elétrica, por exemplo, em refrigeradores. No entanto, a exigência de alocação de uma grande área para o mancal e por consequência a retirada de materiais ferromagnéticos do rotor pode diminuir o desempenho do motor LSPMSM inviabilizando assim sua aplicação. Para a realização deste estudo, foi adotada uma metodologia de projeto disponível na literatura para estabelecer as etapas do projeto a ser realizado. Tal referência de projeto, embora elaborada para ser utilizada em um motor LSPMSM trifásico, foi utilizada em um projeto de motor monofásico. Os resultados do ensaio foram comparados com os dados obtidos via simulações computacionais de tal forma a validar o método proposto e também avaliar o impacto da retirada de material do rotor no desempenho final do motor. Os resultados práticos ficaram próximos aos resultados obtidos em simulação validando a utilização da metodologia também em motores monofásicos. Desta forma foi possível visualizar o efeito da área de mancal no rotor que devido ao aumento da relutância do circuito magnético alterou os resultados do valor da tensão induzida dos ímãs. / This work proposes a study about the influence of the bearing area allocation in hermetic compressors for refrigeration, considering a single phase Line Start Permanent Magnets Synchronous Motor, and employing conventional analytical calculations and the Finite Element Method (MEF). Recent increase in concern about energy efficiency has led many countries to roll out laws that impose requirements to raise the electric motor efficiency. In this context the LSPMSM motor is an alternative over conventional induction motors for the purpose of seeking power consumption reduction. However, the requirement to allocate a large area for the bearing and thus removal of ferromagnetic materials of the rotor can reduce LSPMSM motor performance what may impede its implementation. For the accomplishment of this study it was adopted a methodology of design available in the literature to set up the steps to be followed. Such design reference was at first described to be applied in three phase LSPMSM, however in this work it was applied in a single phase motor. Tests results were compared with data obtained via computer simulations in a way to validate the proposed method and to assess the impact of material removal from de rotor on the motor performance. The obtained bench test results were close to those simulated ones validating the methodology to be used in single phase motors too. Therefore, it was feasible to notice the influence of the counterbore area in the rotor, which, due to the increased value of the circuit reluctance, changed induced voltage values related to the magnets.

De nombreux systèmes utilisent des convertisseurs électroniques de puissance fonctionnant en modulation de largeur d'impulsions (MLI) comme organe de réglage ou de commande. On peut en particulier citer les entraînements à vitesse variable, les alimentations à découpage ou les filtres actifs. L'objectif du travail est de contribuer à l'étude en temps discret du fonctionnement de ces systèmes lorsqu'ils sont munis d'une commande numérique dont la période d'échantillonnage est synchronisée sur la période de modulation de largeur d'impulsions. Pour cela nous avons développé une méthode originale qui consiste à écrire les équations différentielles qui décrivent la dynamique du système en remplaçant sur chaque période de modulation les fonctions binaires qui représentent les états successifs (ON ou OFF) des semi-conducteurs de puissance par un développement limité en série de Fourier. En introduisant de manière judicieuse dans les équations différentielles du système, des termes harmoniques des fonctions binaires qui décrivent les états des interrupteurs, cette manière de procéder nous a permis de décomposer l'étude en deux étapes : · dans une première étape en limitant le développement en série de Fourier des fonctions binaires décrivant les états des interrupteurs à leur premier terme (c'est-à-dire à leurs valeurs moyennes) nous avons construit un modèle discret d'ordre zéro qui rend compte de l'effet moyen de la découpe MLI, · dans une deuxième étape nous avons construit un modèle dynamique approché de l'écart existant entre le modèle d'ordre zéro et le modèle détaillé du système. Ce modèle fournit une bonne estimation des ondulations induites par la découpe MLI dans les grandeurs du système. Pour le cas des entraînements par moteurs synchrones à aimants permanents alimentés par onduleurs de tension nous avons ainsi pu mettre en évidence que l'étude de la stabilité des boucles des courants du moteur à partir du modèle d'ordre zéro reste valable en présence des ondulations dues à la MLI pour autant qu'on utilise une MLI symétrique avec rafraîchissement des références une fois par période. / Nowadays, a large number of systems are using Pulse Width Modulation (PWM) Power Electronic Converters as control part. These systems can, for example, be variable-speed drives, switching power supplies or active filters. The goal of this work is to contribute to the study of operation of this type of system when they are equipped with a digital control part of which the sampling period is synchronized on the modulation one. After having shown how the equations of these systems can be written down and indicated how their evolution in closed loop operation can be described by using iterative maps, we have tried to develop an approach which allows simplifying this study. The iterative map method has been used in order to take into account the “sequential “character of these systems, i.e. the fact that the control signals are sequences of events which correspond to the changes of the state of the converter semiconductor switches. Therefore we have developed an original method which consists in replacing on each modulation period, in the differential equations describing the system dynamics, the binary functions representing the successive ON or OFF states of the power semiconductors, by a limited Fourier series development of these functions. This method has allowed splitting the study of these systems into two steps: • in the first step a “zero order” model was built. This first model, which provides the average effect of the PWM pulse pattern, has been obtained by limiting the Fourier series development of the binary functions describing the states of the converter switches, to their first term, the one corresponding to their average values on the PWM period, • in the second step we have introduced an approached dynamic model characterising the error between the zero order model and the exact model of the system. This model was built by considering a well chosen number of harmonic terms of the binary functions describing the ON-OFF states of the switches in the differential equations of the system. By combining the error model and the zero order model we have been able to estimate in which measure the ripples induced by the PWM modulation affect the results of the system stability study made by using the zero order model. For the case of Permanent Magnets Synchronous Motors fed by Voltage Source Inverters we have shown that the study of the stability of the motor currents loops made with the zero order model remains valid in the presence of ripples induced by the PWM, as long as a symmetrical modulation is used, with references which are refreshed one time on each switching period.

This thesis is a part of a larger project that focuses on the development of a highspeed, high energy flywheel using both high-tech composites and levitating magneticbearings alongside a custom made, permanent magnetized generator built into theflywheel itself. The goal of the project is then to integrate this flywheel into anelectrical vehicle.The main focus of this thesis is the composite material. The composite is to be usedas a shell around the flywheel rotor. This composite shell fills two purposes. The firstis to act as the main energy carrying material, storing above 75% of the total energy inthe flywheel. The second purpose it to strengthen the machine, holding it together.This so that higher speeds than normally possible can be achieved, with the goal beingset to 30 000rpm.In order to be able to design the composite shell correctly a method of calculating theload stresses had to be developed. This was done by the creation of a Matlabprogram, named Spin2Win, capable of calculating the stresses inside a compositemetal hybrid flywheel. Using said Matlab code, combined with modelling andsimulations from SolidWorks, a fully-fledged flywheel was designed complete withdrawings and material specifications.The composite analysis surprisingly shows that the best combination of compositematerials is a mixture of both high strength carbon fibres alongside softer glass fibrescoupled with the weight of the central core. This allowed for control of the radialstresses which was shown to otherwise be the limiting factor when designing rotatingcomposite materials.One of the most interesting, and perhaps even unique, parts of the design is that theelectrical machine has been integrated into the flywheel’s composite shell. Having thetwo entities working together in order to control the radial stresses in thecomposite, by utilizing the weight of the permanent magnets.