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Resposta ao desbalanço de rotor com absorvedor dinâmico rotativo com elemento viscoelástico / Unbalance response of rotor with rotating dynamic absorber with viscoelastic elementFontes, Yuri Correa 19 February 2015 (has links)
O presente trabalho consiste no projeto de um modelo em elementos finitos de um absorvedor dinâmico rotativo utilizando-se um material viscoelástico como componente dissipador do sistema. O absorvedor é composto por um anel de material viscoelástico interposto entre dois anéis de aço, o qual é fixado na extremidade livre de um sistema rotativo representado por um eixo flexível, suportado por dois rolamentos, no qual estão fixos dois discos igualmente espaçados do centro entre os dois mancais. O modelo em elementos finitos do sistema rotativo é validado com os dados experimentais do modelo real e suas velocidades críticas são determinadas baseadas no diagrama de Campbell e na resposta ao desbalanço em um dos discos. O modelo inicial do absorvedor dinâmico rotativo é replicado de um modelo da literatura e as respostas a uma excitação na forma de impulso são comparadas. O modelo desenvolvido equipara-se ao da literatura para frequências até 600 Hz, intervalo que compreende as velocidades críticas a serem amortecidas. A otimização do absorvedor é realizada através de variações da geometria do mesmo e são traçadas curvas de influência de cada parâmetro sobre suas frequências naturais. Com base nestas curvas são realizadas análises de influência conjunta dos parâmetros geométricos sobre tais frequências. Pelos resultados obtidos verifica-se a possibilidade da obtenção de um modelo que atue sobre modos de flexão específicos do sistema rotativo, atenuando as amplitudes de vibração das velocidades críticas correspondentes a cada modo. Uma vez obtidos os modelos de absorvedores dinâmicos correspondentes aos dois primeiros modos de flexão do sistema rotativo, ambos são acoplados ao sistema e se observa grande redução dos picos de amplitude do primeiro modo de flexão, enquanto os picos do segundo modo sofrem baixa alteração. / The present work concerns the development, optimization and validation of a finite element model of a dynamic vibration absorber using a viscoelastic material as the damping component. The dynamic absorber consists of a ring of viscoelastic material interposed between two rings of steel, which is fixed to the free end of a rotary system represented by a flexible shaft supported by two bearings, on which are fixed two discs equally spaced in the center of both bearings. The finite element model of the rotating system is validated with experimental data from the actual model and its critical speeds are determined based on the Campbell diagram and in its response to the imbalance. The initial model of the dynamic absorber is replicated from a model of the literature and the responses to an impulse excitation are compared. The developed model matches the literature one for frequencies up to 600 Hz, range comprising the critical speeds to be damped. The absorber\'s optimization is accomplished through variations of its geometry and influence curves of each parameter over its natural frequencies are drawn. Based on these curves, combined influence analyzes of the geometrical parameters over such frequencies are performed. From the results obtained, it can be seen the possibility of achieving a model that acts on specific bending modes of the rotation system, reducing the vibration amplitudes of the critical speeds corresponding to each mode. Once obtained the dynamic absorbers models corresponding to the first two modes of vibration of the rotatative system, both models are coupled to the system and it is observed great reduction of the amplitude of the first bending mode peaks, while the second mode suffer low peaks reduction.
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Etude et optimisation de machines à aimant permanent à démarrage direct sur le réseau / Study and optimization of line-start Permanent Magnet MotorsDing, Tingting 08 April 2011 (has links)
Dans le cadre de la réduction des émissions des gaz à effet de serre, et devant l'augmentation incessante du prix de l'énergie, la course à l'amélioration des performances énergétiques touche tous les secteurs : industriel, tertiaire ou même celui des particuliers. La consommation de l'énergie électrique est due en grande partie aux moteurs électriques, et particulièrement les machines asynchrones, utilisées dans diverses applications telles que le pompage, la ventilation ou la compression. Ces machines sont caractérisées par des rendements relativement faibles et leur remplacement par des machines plus performantes permettrait un gain d'énergie non négligeable. Les machines à aimants permanent ayant pouvoir de démarrage autonome sont de bonnes candidates pour répondre à ce besoin. Elles ont de très bons rendements et les artifices supplémentaires permettant le démarreur automne suppriment la nécessité d'utiliser des convertisseurs statiques comme dans le cas des machines à aimants classiques. Des contraintes spécifiques se posent cependant pour l'utilisation et le dimensionnement de ces machines : en effet, le courant de démarrage ne doit pas être trop important à cause du risque de démagnétiser les aimants et le couple de démarrage doit être suffisamment grand pour assurer un démarrage en charge. Par ailleurs les rendement et facteurs de puissance en pleine charge doivent être assez nettement supérieurs à ceux des machines asynchrones pour les rendre plus compétitives. Dans cette thèse, nous étudions trois structures de rotor permettant de répondre à un cahier des charges donné. Ces trois structures utilisent des aimants en surface, insérés dans un rotor massif ou dans un rotor à cage. Elles ont leurs avantages et leurs inconvénients, que nous avons mis en évidence par une étude comparative assez détaillée. Cette étude comparative n'a pu être mise en oeuvre sans l'établissement de modèles en régime statique ou dynamique de ces machines ou encore de méthodologie de conception. Un prototype à échelle réduite a été dimensionné, réalisé et testé au laboratoire ; il confirme les principes de base de ce type de machines / In the context of reducing emissions of greenhouse effect, and of energy cost, the competition to improve the performances of the equipments affects all the domains. The consumption of electricity is mostly due to the electric motors, and particularly induction machines, used in various devices such as pumps, fans or compressors. These machines are characterized by relatively low efficiencies, and their replacement by more efficient machines should lead to a significant power saving. The Line-Start Permanent Magnet motors are good candidates to achieve this purpose. They have higher efficiencies and the additional devices for self-start eliminates the need of static converters, as it is normally required for conventional permanent magnet motors. Specific constraints arise for the use and the design of these machines: the starting current should not be so high to avoid the risk of the demagnetization of magnets and the starting torque must be large enough to ensure the start under load. Moreover, the efficiency and power factor at full load must be sufficiently higher than those of asynchronous machines in order to make them more competitive. In this thesis, we study three rotor structures to meet a given specification. These three structures use magnets inserted on the surface, embedded in a solid rotor or a cage rotor. They have their advantages and drawbacks that we have shown by a comparative study in some detail. This comparative study could not be implemented without the development of models in both static and dynamic conditions of these machines and a specific design methodology. A small scale of prototype has been designed, built and tested in the laboratory; it confirms the basic principles of such machines
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Comparison of electricity production between semi-submersible and spar-buoy floating offshore wind turbinesSaracevic, Nermina January 2018 (has links)
The paper compares electricity production between the semi-submersible and the spar-buoy floating wind turbine systems under normal, stochastic and extreme wind conditions at Utsira Nord site located on the Norwegian continental shelf in the North Sea. The analysis of complex behavior of the floating wind turbine system and the fluid-structure interaction is performed in aero-servo-hydro-elastic code ASHES. The results indicate a slightly better energy performance of the semi-submersible than the spar in all load cases but one. The pitch and heave degrees of freedom are evaluated as the most relevant for the power output. It is shown that pitch and heave platform motions have smaller displacement in the semi-submersible floater than in the spar under average environmental conditions and at the rated wind speed operating range. The simulation also confirmed that the energy yield is very sensitive to the magnitude of the loads: the spar performed best under mild environmental conditions, while the semi-submersible was better under medium environmental conditions. Small difference in energy yield is attributed to the same baseline blade and external controller properties used for both floaters where generator torque was kept constant to limit the power excursions above the rated power. The method proposed under this paper has demonstrated that a good approximation of the energy performance of the floating wind turbine system can be performed in a fast and effective manner.
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Fast Modelling, Torque-Ripple-Reduction and Fault-Detection Control of Switched Reluctance MotorsPeng, Wei 05 April 2019 (has links) (PDF)
As the world moves towards a cleaner and greener future, electrical machines for various industrial purposes and transport applications have gained a lot of attention. Permanent magnet synchronous machines (PMSMs) are usually the solution for electric vehicle (EV) applications thanks to their high efficiency, compactness and high-power density. On the downside, although the price of rare-earth materials has recovered close to historical levels, concerns still remain and the questions on the environmental sustainability of these materials have also been raised, which has encouraged the researchers to consider rare-earth-free machines.The switched reluctance machine (SRM) is one of the competitive alternatives, thanks to the simple and robust construction, high reliability and inherent fault tolerance capability. However, it has a bad reputation when it comes to torque ripple and acoustic noise. And the highly nonlinear characteristic brings much difficulty to routine design purposes and machine optimisation.Therefore, some of the above mentioned problems are addressed - a torque-ripple-reduction, reliable and low-cost system of SRMs is presented in this thesis. Firstly from the modelling point of view, a combined magnetic equivalent circuit (MEC) and finite element (FE) model of SRMs is developed for fast characterization the nonlinear behavior. Secondly from the control point of view, various torque-ripple reduction techniques are implemented and compared. Moreover, a minimal current sensing strategy with enhanced fault-detection capability is proposed and validated experimentally. It requires two current sensors, to replace the phase current sensors, with no additional devices for fault detection, to achieve a more compact and low-cost drive. Finally from the reliability point of view, an interturn short-circuit fault detection method and a rotor position estimation approach are investigated and validated experimentally, which leads to a more reliable system. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished
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Reducing unbalanced magnetic pull in induction machinesChuan, Haw Wooi January 2018 (has links)
Induction machines are the most widely used type of electrical machines because of their robustness, simplicity, and relatively low cost. However, the small airgap in the induction machine makes them more susceptible to Unbalanced Magnetic Pull (UMP). This is because the magnitude of the UMP is a function of the degree of eccentricity, which is the ratio between the length of misalignment and the mean airgap length. The bearing-related failure accounts for approximately 41% of the total failures of induction machines; the percentages of bearing-related failure would be higher for applications in a harsher environment. In this thesis, the UMP caused by rotor eccentricity is investigated, because a small degree of rotor eccentricity is unavoidable due to the manufacturing tolerance and 80% of the mechanical faults could cause rotor eccentricity in electrical machines. When the rotor is not at the centre of the stator, the eccentric rotor causes an uneven airgap around the rotor, in which the magnetic permeance with the higher harmonics content will be created. The magnetomotive force (MMF) produces additional pole-pair ±1 magnetic flux around the airgap. The interaction between each magnetic flux with its pole pair ±1 magnetic flux produces UMP. As only the magnetic flux that crosses the airgap causes UMP, the magnetic flux is categorised into magnetising flux and airgap leakage flux, because both types of flux possess different characteristics at a different rotor slip. As the airgap leakage flux is difficult to calculate analytically, an empirical method is proposed to estimate the UMP caused by the airgap leakage flux. Then, the UMP caused by the magnetising flux can also be estimated by using the empirical method. The parameters for the empirical method can be found by using either the FEA or the experimental results. The damping effect of the magnetising flux in a parallel connected rotor bar is discussed and a damping coefficient is introduced to explain this scenario. The damping coefficient can also be used to calculate the UMP in a steady state analysis. UMP comparisons between the cage rotor and wound rotor induction machines are made. The wound rotor has a much higher UMP because the pole-specific wound rotor could not damp the additional pole pair ±1 magnetic flux. Therefore, a damper winding at the stator slot is also proposed in order to damp the UMP by producing a counteracting flux. In addition, analytical equations have also been derived for different scenarios, such as static eccentricity, dynamic eccentricity, axial-varying eccentricity, and skew rotor bars. Finite Element Analysis (FEA) and experimental work are used to demonstrate the derived analytical equation. Furthermore, the power losses caused by the rotor eccentricity are investigated. Iron losses, copper losses, and frictional loss are discussed and compared with both the analytical equation and the FEA results. In order to reduce the UMP in the induction machines, the two proposed methods are the slip control method and damper windings topology. The slip control method utilises the non-linearity characteristic of the UMP at different rotor slip. To find the optimum operating slip with the lowest UMP, the UMP/Torque ratio is introduced. The characteristics of the UMP/Torque ratio varies with the type and design of the induction machines. However, this method is only applicable when the machine is lightly loaded, because the magnetising flux is limited by the capped terminal voltage and the core saturation of the machine. For the damper winding topology, a circulating current flowing in the damper winding could produce a counteracting flux to damp the UMP. The proposed damper windings configuration is only suitable for the induction machine with an even pole pair number. Finally, comparisons between both UMP reduction methods are made.
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Modélisation du comportement dynamique couplé rotor-stator d'une turbine en situation accidentelleRoques, Sébastien 17 December 2007 (has links) (PDF)
Pour les groupes turbo-alternateurs du parc nucléaire français, la situation accidentelle de référence lors du dimensionnement est définie par le départ d'une ailette terminale des corps basse pression. Après avoir détecté la perte de l'ailette, la turbine est déconnectée du réseau électrique, et la turbomachine ralentit progressivement sous l'effet de frottements d'origine fluide. Le dimensionnement consiste alors à vérifier que les structures palières sont capables de supporter l'effort résultant du balourd généré par cette perte d'ailette pendant la phase de ralentissement, notamment lors du passage des vitesses pour lequel des contacts rotor-stator peuvent se produire. A cet effet, un modèle éléments finis de turbine a été développé pour simuler des transitoires de vitesse d'un rotor en considérant la vitesse de rotation de l'arbre comme une inconnue, permettant ainsi d'estimer la décélération angulaire due au contact frottant. Trois modèles de stator ont été proposés appréhender le comportement dynamique du carter, et le couplage des structures est réalisé au moyen des forces de contact calculées par la méthode des multiplicateurs de Lagrange. La résolution des équations non-linéaires du mouvement a nécessité le développement d'un algorithme de contact, adapté à la géométrie de chacun des carters. Des simulations réalisées sur un modèle simple de turbine montrent que la vitesse de rotation et les chargements aux paliers sont bien estimés lors de l'interaction rotor-stator. Ainsi l'outil numérique permet d'étudier la réponse couplée rotor-stator et de prédire l'influence de paramètres tels que le coefficient de friction et les propriétés matérielles du stator.
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Instabilité du flottement gyroscopique des convertiblesNaccarato, Gianni 06 June 2003 (has links) (PDF)
En vol de croisière, le convertible (ADAV) est soumis à une instabilité de type aéroélasticité dynamique, appelée flottement gyroscopique. Ce phénomène se caractérise par un mouvement de précession du rotor qui accélère la fatigue et augmente les charges sur la structure, et dont les conséquences peuvent être catastrophiques. Le but de cette étude est de mettre en place un modèle analytique permettant de reproduire avec précision le flottement gyroscopique. Pour cela, un outil de mise en équation a été développé afin de faire évoluer le modèle analytique suivant le choix du système à étudier. Les équations de Lagrange sont utilisées et développées à l'ordre 1. Les efforts aérodynamiques du rotor sont représentés par un modèle quasi statique plan d'ordre 1. Le système final étudié est constitué de l'ensemble isolé aile - mât - rotor du convertible. Le rotor 3 pales avec liaison K, est de type gimbal, et le pas des pales s'adapte automatiquement en fonction de la vitesse d'avancement de l'appareil. Grâce aux données expérimentales obtenues en soufflerie sur une maquette constituée d'une demi - aile, le modèle analytique a été validé pour différentes configurations de vitesse d'avancement et de raideurs de l'aile. Les vitesses critiques d'apparition du flottement gyroscopique sont retrouvées, et des simulations de balayages paramétriques permettent de proposer différentes configurations sur les caractéristiques du système pour repousser la limite de stabilité
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Contribution à la Conception des Machines Electriques à Rotor Passif pour des Applications Critiques : Modélisations Electromagnétiques et Thermiques sur Cycle de Fonctionnement, Etude du Fonctionnement en Mode Dégradé.Li, Guangjin 05 July 2011 (has links) (PDF)
Dans cette thèse, une comparaison entre différentes topologies de machines a été tout d'abord réalisée. Deux machines électriques: Machine à Réluctance Variable (MRV) et Machine à Commutation de Flux (MCF) ont ensuite été choisies pour les études suivantes. Un modèle électromagnétique-thermiquement couplé est mis en ouvre pour ces deux structures. Ce modèle est basé sur une caractérisation préalable par la méthode des éléments finis (EF) 2D via le calcul du couple instantané, des deux composantes de l'induction magnétique (Br et Bθ) de chaque élément du maillage du rotor ainsi que du stator pour différentes densités des courants efficaces et pour différentes positions du rotor. Ces résultats sont ensuite utilisés dans les modèles analytiques de pertes permettant de calculer les pertes Joule et les pertes fer sur un cycle de fonctionnement. Des modèles thermiques transitoires basés sur un réseau de résistances thermiques et l'EF 2D sont réalisés, dans lesquels les pertes instantanées obtenues précédemment sont utilisées comme sources de chaleur pour le calcul des variations des températures dans différents composants d'une machine électrique sur cycle de fonctionnement. Un modèle de défaut couplé avec la thermique pour une MCF triphasée est aussi proposé. Les défauts étudiés dans cette thèse sont principalement dus au court-circuit: le court-circuit entre-spires d'une phase, le court-circuit entre-spires et entre-phase dans une MCF sans redondance, le court-circuit d'une phase ou de trois phases dans une MCF avec redondance. A l'aide de MATLAB/Simulink, les courants sains et les courants de court-circuit sont obtenus, et les pertes instantanées peuvent être calculées en utilisant la méthode mentionnée précédemment. De cette manière, le comportement thermique en cas de défauts peut être prévu. Enfin, des études de défauts pour une MCF hexa-phasée sans redondance sont présentées, et un convertisseur du type pont complet est utilisé pour alimenter la machine. Cela nous permet de contrôler indépendamment chaque phase en cas de défauts. Les défauts sont entre autres le circuit ouvert ou le court-circuit dans une ou plusieurs phases (jusqu'à trois). Certaines méthodes de correction telles que: l'augmentation de l'amplitude du courant dans les phases saines et / ou modifier leurs phases, sont proposées pour maintenir le couple électromagnétique tout en minimisant l'ondulation de couple. Les résultats analytiques et numériques ont montré la bonne efficacité des méthodes proposées, tant dans le cas de l'ouverture des phases que dans le cas d'un court-circuit.
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Aerolastic simulation of wind turbine dynamicsAhlström, Anders January 2005 (has links)
The work in this thesis deals with the development of an aeroelastic simulation tool for horizontal axis wind turbine applications. Horizontal axis wind turbines can experience significant time varying aerodynamic loads, potentially causing adverse effects on structures, mechanical components, and power production. The needs for computational and experimental procedures for investigating aeroelastic stability and dynamic response have increased as wind turbines become lighter and more flexible. A finite element model for simulation of the dynamic response of horizontal axis wind turbines has been developed. The developed model uses the commercial finite element system MSC.Marc, focused on nonlinear design and analysis, to predict the structural response. The aerodynamic model, used to transform the wind flow field to loads on the blades, is a Blade-Element/Momentum model. The aerodynamic code is developed by The Swedish Defence Research Agency (FOI, previously named FFA) and is a state-of-the-art code incorporating a number of extensions to the Blade-Element/Momentum formulation. The software SOSIS-W, developed by Teknikgruppen AB was used to generate wind time series for modelling different wind conditions. The method is general, and different configurations of the structural model and various type of wind conditions can be simulated. The model is primarily intended for use as a research tool when influences of specific dynamic effects are investigated. Verification results are presented and discussed for an extensively tested Danwin 180 kW stall-controlled wind turbine. Code predictions of mechanical loads, fatigue and spectral properties, obtained at different conditions, have been compared with measurements. A comparison is also made between measured and calculated loads for the Tjæreborg 2 MW wind turbine during emergency braking of the rotor. The simulated results correspond well to measured data. / QC 20100826
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Análisis y diseño de volantes de inercia de materiales compuestosRipoll Masferrer, Lluís 11 January 2006 (has links)
Los volantes de inercia superan a las baterías eléctricas por su capacidad de absorber y ceder energía en poco tiempo y, si se fabrican con materiales compuestos, también por su reducido peso. La tesis presenta un estudio sobre los rotores de materiales compuestos aplicados a los acumuladores cinéticos para hacerlos más asequibles a usos industriales baratos. Para ello se proponen dos objetivos: obtener un sistema analítico de cálculo, y mejorar el diseño de rotores de bajo coste.Se desarrolla un sistema analítico de cálculo muy completo, tanto en las cargas como en las tensiones. Se consideran todas las cargas necesarias para el diseño mecánico del rotor: la fuerza centrífuga, la fuerza de aceleración y las tensiones residuales, térmica y de hidratación; y se determinan todas las componentes, normales y cortantes, de la tensión para cada punto del rotor.El cálculo en condiciones de tensión plana, utilizado por la mayoría de autores, se amplía con el cálculo en deformación axial constante, que es una variante mejorada de la deformación plana. Se comprueba que sus resultados son mejores que los de tensión plana cuando se comparan con los obtenidos en modelos de elementos finitos. Paralelamente, como aportación nueva de la tesis, se deducen las funciones de la variación de la tensión axial y de la tensión cortante radial-axial a lo largo del eje longitudinal del rotor. A partir de estos resultados se desarrolla un sistema general de cálculo que, además de unificar los sistemas de tensión plana y deformación axial constante, permite determinar todas las tensiones en cualquier posición radial-axial del rotor.Este sistema unificado de cálculo se amplia con tres particularidades: una aplicación de cálculo para resolver rotores multicapa, las ecuaciones especiales para los materiales singulares no resolubles con las ecuaciones generales, y el cálculo de capas con fibras orientadas axialmente aplicadas para refuerzo en configuraciones especiales.Con el objeto de mejorar las prestaciones del rotor se estudian dos procedimientos para crear tensiones de pretensado: generando tensiones durante el bobinado y utilizando las tensiones residuales térmicas. En el primero se elabora un sistema analítico de cálculo para determinar las tensiones residuales de bobinado y se complementa con una simulación mediante elementos finitos basada en submodelos incrementales. Ambos cálculos son capaces de simular el material no curado aplicando las propiedades viscoelásticas de los ensayos experimentales de otros autores. En el segundo se presenta un sistema nuevo, denominado pretensado térmico, basado en el curado por etapas, que genera tensiones residuales parecidas a las de bobinado pero con menos problemas de fabricación.El diseño de volantes se aplica a tres configuraciones básicas: rotores híbridos multicapa con materiales de rigidez progresiva, rotores de un solo material con anillos de elastómero y rotores con pretensado térmico.Sus prestaciones se valoran con tres variables: la masa, el volumen y el coste del material; de las cuales el coste es la principal y se utiliza para la optimización de la geometría.En cada configuración se determina la energía máxima para distintas relaciones de radios del rotor y se compara con el rotor de un sólo material. Se utilizan los materiales básicos usados en la fabricación de rotores: la fibra de carbono con matriz epoxi, la fibra de vidrio con matriz epoxi, el aluminio y el acero. Los dos materiales compuestos ofrecen mejores resultados que los metales, pero disminuyen sensiblemente en rotores con espesor de pared grande. En estos casos, la energía por unidad de coste mejora aplicando los anillos elásticos y el pretensado térmico. / Flywheels are better than electric batteries in that they absorb and yield energy in shorter time and, if made out of composite materials, also in that they weight less. This thesis presents a study of composite material rotors applied to kinetic accumulators in order to make them usable for low cost general industrial uses. Two objectives are proposed: a) to develop an analytical system for computation and b) to design alternatives in order to improve the performance on low-cost rotors.The analytical system is intended to be very complete, considering all relevant types of external loads and stress components. For the former, centrifugal, acceleration forces and residual, thermal and moisture stresses are included. For the latter, five normal and shear components are computed at each point of the rotor.The usual plane stress condition is expanded with the consideration of constant axial strain, along the lines of the plane strain hypothesis but with greater accuracy. It is shown that the current theory results fit the ones from finite elements much better than those from plain stress. As a new contribution, the functions for the axial stress and the radial-axial stress along the axis of the rotor are developed. From these results, a general system that unifies the plane stress and constant axial strain can compute the stress state at any position.In addition, the unified system includes three novel aspects: an extension of computation for multi-layer rotors, special equations for some materials in which behaviour present singularities and the computation of layers with fibers along the axial direction, which can be useful as a reinforcement for some configurations.Two procedures that can create beneficial residual stresses are studied: generating stresses during the filament winding and using the thermal stresses. For the first, analytical expressions are developed and validated and complemented with especially developed finite elements based on incremental submodels. In both cases the material is characterized by viscoelastic properties taken from the literature. For the second, a new procedure called thermal prestress is based on the accumulation of partial curing processes (by stages), which is able to create residual stresses similar to those of winding but involving simpler manufacturing.Three basic configurations are studied for the design: hybrid rotors with progressive stiffness along the radius, single material rotors with elastomer thin rings and rotors manufactured with thermal prestress, evaluating the performance as a function of the mass, volume and cost of the material. The latter is defined as the most important, and it is used as a reference for the geometry optimization.The maximum energy stored on each of the configurations is compared with that of a single material rotor, using the most common ones: glass and carbon fiber both with epoxy matrix, aluminium and steel. Results show that glass/epoxy has the highest storing capability per unit cost, although the number is greatly reduced when the thickness increases. If this rotor has a thin layer of carbon/epoxy, the capability does not increase, although it does with distributed elastomeric layers. There is also an increase with fabrication based on the thermal prestress technique.
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