<p>In order to design a power transformer it is important to understand its internal electromagnetic behaviour. That can be obtained by measurements on physical transformers, analytical expressions and computer simulations. One benefit with simulations is that the transformer can be studied before it is built physically and that the consequences of changing dimensions and parameters easily can be tested.</p><p>In this thesis a time-domain transformer model is presented. The model includes core losses as magnetic static hysteresis, eddy current and excess eddy current losses. Moreover, the model comprises winding losses including eddy currents, capacitive effects and leakage flux. The core and windings are first modelled separately and then connected together in a total transformer model. This results in a detailed transformer model.</p><p>One important result of the thesis is the possibility to simulate dynamic hysteresis including the eddy current shielding in the magnetic core material. This is achieved by using Cauer circuit combined with analytical expression for static and dynamic hysteresis. Thereby, all magnetic loss components in the material can be simulated accurately. This dynamic hysteresis model is verified through experiments showing very good agreement.</p>

Thesis (PhD (Electrical and Electronic Engineering))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Certain types of electric machines are particularly susceptible to the proliferation of eddy currents flowing within the solid conducting regions in the rotor. Single-layer, non-overlapping windings within uneven open slots are some stator properties that can produce damaging, asynchronous magnetic field harmonics which manifest in the rotor as eddy currents. The ohmic losses caused by these eddy currents are a source of inefficiency and can cause a marked increase in the temperature of the rotor. This temperature rise can be dangerous for the magnets, which have to be kept within temperature limits to avoid partial or full demagnetization. The research work presented here is concerned with reducing the effect of eddy currents in the rotor magnets and solid rotor yoke of an electric machine. The work presents analytical methods to calculate the magnetic fields, eddy currents and solid loss in an electric machine due to current in the winding and due to the interaction of the permeance variation in the stator with the magnets in the rotor. A method is also suggested where the analytical theory can be used with a magnetostatic finite element solution to produce a transient solid loss result. The research work also investigates a method for optimal segmentation in both level and penetration, and provides some design suggestions. The work presents the method of partial magnet segmentation, which is a technique whereby thin incisions are made into the magnet material from one or both sides. Another method of partial rotor segmentation is also presented where the incisions are made into a portion of the magnet-facing solid yoke. These methods attempt to interrupt the flow of eddy currents and increase the resistance ‘seen’ by the eddy currents, while also keeping construction difficulty and cost to a minimum. The methods are verified using finite element calculations which are compared to measured results. The result is that partial magnet segmentation is a very useful, effective and practical method of segmenting magnets. The loss reduction profile can be similar to that of traditional full segmentation. The method of partial rotor segmentation also shows a large reduction in rotor power loss. With implementation of these methods on a test machine, one can expect an efficiency increase of more than 4 % / AFRIKAANSE OPSOMMING: Sekere tipes van elektriese masjiene is veral sensitief vir die vloei van werwelstrome in solied geleidende gebiede in die rotor. Enkellaag, nie-oorvleuelende wikkelings in oneweredige oop gleuwe is enkele stator eienskappe wat skadelike, asinchrone magneetveld harmonieke tot gevolg kan hê, wat as werwelstrome in die rotor manifesteer. Die ohmiese verliese wat deur hierdie werwelstrome teweeg gebring word is 'n bron van ondoeltreffendheid en kan lei tot 'n merkbare toename in die temperatuur van die rotor. Hierdie temperatuur styging hou gevaar in vir die magnete en moet binne temperatuur limiete gehou word om gedeeltlike of self volle demagnetisering te vermy. Die navorsing vervat in hierdie document is gemoeid met die vermindering van die effek van werwelstrome in die rotor magnete en in die soliede rotor juk van 'n elektriese masjien. Die werk bied analitiese metodes aan vir die berekening van die magneetvelde, werwelstrome en soliede verliese in ’n elektriese masjien as gevolg van strome in die wikkelings en die interaksie van die permeansie variasie van die stator met die magnete in die rotor. ’n Metode word ook voorgestel waar die analitiese teorie saam met ’n magnetostatiese eindige element oplossing gebruik word om ’n resultaat vir die oorgang soliede verliese te verkry. Die navorsingswerk ondersoek ook ’n metode vir die optimale segmentering in beide vlak sowel as penetrasie, en verskaf sekere ontwerp voorstelle. Die werk bied die metode aan van gedeeltelike magneet segmentering, wat 'n tegniek is waarvolgens dun insnydings gemaak word aan een of beide kante van die magneet materiaal. Nog ’n metode van gedeeltelike rotor segmentering word beskou waar die insnydings in in ’n gedeelte aan die magneetkant van die soliede rotor juk gemaak word. Hierdie metodes poog om die vloei van werwelstrome te onderbreek en die weerstand soos "gesien" deur die werwelstrome te verhoog, terwyl konstruksie kompleksiteit en koste tot ’n minimum beperk word. Die metodes word bevestig deur eindige element berekeninge wat met gemete resultate vergelyk word. Die gevolg is dat gedeeltelike magneet segmentering 'n baie nuttige, doeltreffende en praktiese metode van die segmentering van magnete is. Die verliesverminderingsprofiel van gedeeltelike segmentering kan soortgelyk wees aan dit van tradisionele volle segmentering. Die metode van gedeeltelike rotor segmentering toon ook 'n groot afname in rotor drywingsverlies. Met die implementering van hierdie metodes op ’n toetsmasjien, kan ’n mens ’n verhoging in benuttingsgraad verwag van meer as 4 %

Le vieillissement du parc aéronautique, mais aussi la volonté de prolonger le cycle de vie des appareils, impose aux techniques de maintenance des exigences de contrôle accrues en termes de fiabilité et de rapidité. Les principaux enjeux étant la détection, et surtout la caractérisation des micro-fissures pouvant apparaitre dans les pièces sensibles des appareils. Cette caractérisation pouvant aller jusqu'à la reconstruction qualitative, voire quantitative du profil des fissures, ce qui suppose la résolution du problème inverse consistant, à partir des signaux mesurés, à remonter à certaines caractéristiques de la pièce inspectée, notamment géométriques, qui en sont en partie la cause.Ce manuscrit présente une approche originale de conception de sonde d'imagerie par courants de Foucault. Cette approche, ici appliquée à l'imagerie de pièces aéronautiques cylindriques, consiste à concevoir la sonde de façon à satisfaire la double contrainte d'une instrumentation performante et d'une résolution possible du problème inverse. Ainsi, la conception de la sonde est-elle faite de manière à ce que d'une part les signaux mesurés, résultant de ses interactions avec la pièce contrôlée, soient d'amplitude la plus élevée possible, et d'autre part, a n que ces interactions soient modélisables au moyen d'un modèle qui se prête bien à l'inversion.Dans un premier temps, une méthodologie de conception de sonde est présentée, qui vise à optimiser le dimensionnement et l'agencement de ses éléments en se fixant des contraintes de sensibilité et de résolution. Un prototype, conçu d'après cette méthodologie, est réalisé, mis en œuvre et caractérisé. Les résultats expérimentaux obtenus, qui s'avèrent en accord avec une modélisation par éléments finis, offrent une validation du fonctionnement de la sonde, celle-ci permettant effectivement de mettre en évidence les défauts types (micro-fissures) recherchés dans la pièce inspectée. Dans un second temps, la configuration des interactions sonde-pièce inspectée, choisie à dessein, est mise à profit pour élaborer un modèle direct. Celui-ci repose sur l'hypothèse selon laquelle, les défauts étant de faibles dimensions, il est possible de considérer que la perturbation de signal qu'ils engendrent est équivalente à celle que génèreraient des sources virtuelles de courants localisées uniquement dans le volume du défaut. Outre sa simplicité, cette modélisation offre l'avantage d'être adaptée à une mise en œuvre au moyen de la méthode des points sources distribués. Or celle-ci permet de formuler le problème direct sous forme matricielle ce qui constitue une base de nature à faciliter la résolution du problème inverse.C'est à ce problème qu'est consacrée la dernière partie du mémoire. Des méthodes d'inversion y sont proposées, visant à traiter progressivement la complexité du problème. Ainsi un algorithme d'inversion mono-fréquence est-il proposé, qui se montre efficace pour reconstruire des défauts sur de faibles profondeurs. Pour une meilleure reconstruction en profondeur, des algorithmes multifréquence faisant appel à des méthodes de régularisation sont ensuite conçus et appliqués à des signaux correspondant à des défauts de géométries diverses. / The ageing of the aeronautical fleet and the will to increase the aircrafts lifetime require the maintenance techniques to be made always more reliable and fast. In this context, the detection and characterization of the microscopic cracks likely to appear in some sensitive parts of the aircrafts is an important issue to be faced.This work deals with an original approach for the design of an eddy current imaging probe dedicated to the non destructive evaluation of cylindrical fastener parts. This approach consists in designing the probe in such a way that it both satisfies the constraint of an efficient sensing and that of enabling the inverse problem to be solved with a view to the defects reconstruction.Firstly, a probe design methodology is presented that optimizes the emission/reception topology, the choice of the probe elements and their arrangement according to sensitivity and resolution constraints. A prototype is built, implemented and characterized and validation of the design is obtained as the researched defects are displayed with experimental performances that agree with finite elements modelling simulations.Secondly, since the probe relies on a uniform eddy current flow interacting with small defects, a rather simple forward model is proposed based on virtual defect current sources (VDCS). The model implementation is carried out using the distributed point source method leading to a matrix formulation that can facilitate the resolution of the inverse problem.Finally, mono-frequency and multi-frequency methods are proposed for inverting the VDCS forward model and promising defect reconstruction results are obtained.

Este trabalho apresenta o estudo de um sistema genérico de medição que utiliza o princípio das correntes de Foucault, comumente conhecidas como correntes parasitas. O modelo do sistema é representado como um circuito elétrico equivalente composto por R1 e L1, respectivamente caracterizando a resistência e a indutância do circuito primário, as quais são conhecidas por uma bobina de excitação. Já no secundário, R2 e L2, estão representando a perda ôhmica e a indutância da amostra no qual as correntes parasitas são induzidas, além de outros dois componentes, M indutância mútua dos indutores acoplados e k, coeficiente relacionado ao acoplamento magnético entre os circuitos primário e secundário. A análise tradicionalmente utilizada para este tipo de medição é a avaliação da reflexão da impedância equivalente do circuito secundário representando a amostra no circuito primário. O trabalho analisa as equações de malha do circuito equivalente no domínio da frequência e identifica os parâmetros do modelo. A partir da identificação do sistema realizada com os ensaios experimentais, foi possível descobrir a constante de tempo indutiva τL do sistema. A partir dessa constante, observou-se a variação acentuada da mesma em relação a variação da impedância equivalente. Ainda é apresentada uma estimativa dos valores de R2 e L2 realizada por meio da unificação das informações obtidas com a identificação, aliada com as informações de campo magnético obtidas a partir de um sensor do tipo GMR e pela simulação em um software de elementos finitos COMSOL Multiphysics. / This work presents the study of a generic measurement system that uses the prin- ciple of eddy currents. The system model is represented as an equivalent electric circuit composed of R1 and L1 respectively characterizing the resistance and induc- tance of primary circuit, which are known by an excitation coil. In the secondary, R2 and L2 are representing the ohmic loss and the inductance of the sample in which the eddy currents are induced, in addition two other components, the mutual induc- tance of the coupled inductors and k, coefficient related to the magnetic coupling between the primary and secondary circuits. The analysis traditionally used for this type of measurement is the reflection evaluation of the equivalent impedance of the secondary circuit representing the sample in the primary circuit. The work analyzes the mesh equations of the equivalent circuit in the frequency domain and identifies the parameters of the model. From the identification of the system performed with the experimental tests, it was possible to discover the inductive time constant τL of the system. From this constant, it was observed the sharp variation of the same in relation to the variation of equivalent impedance. An estimate values, R2 and L2 performed by unification of the information obtained with the identification, to- gether with the magnetic field information obtained from a GMR type sensor and by simulation in a finite element software COMSOL Multiphysics.

Made available in DSpace on 2017-07-10T15:14:23Z (GMT). No. of bitstreams: 1 DissertacaoMarcosVSchlichting.pdf: 1630212 bytes, checksum: ac35da2426e86a1f7ad159d82eaf4416 (MD5) Previous issue date: 2015-03-12 / This study evaluated a prototype for heating water for use in the agricultural industry, based on the principle of magnetic induction to generate thermal energy through the eddy currents associated with a mechanical energy source for variation of magnetic flux produced by permanent magnets, configured with four six magnets with and without pole reversal, as compared with the water heating done through a resistive system. Induced systems obtained yield 64.74%, 65.13% and 64.48% for six magnets without inversion (6ISI), four magnets with reverse (4ICI) and four magnets without inversion (4ISI) respectively. The resistive system showed 89.21% efficiency, demonstrating greater viability in the study conditions. / O presente trabalho avaliou um protótipo para aquecimento de água para uso na agroindústria, baseado no princípio da indução magnética para geração de energia térmica através das correntes de Foucault associado a uma fonte de energia mecânica para variação do fluxo magnético produzido por imãs permanentes, configurado com quatro e seis imãs com e sem inversão de polos, em comparação com o aquecimento de água feito através de um sistema resistivo. Os sistemas induzidos obtiveram rendimento de 64,74 %, 65,13 % e 64,48 % para seis imãs sem inversão (6ISI), quatro imãs com inversão (4ICI) e quatro imãs sem inversão (4ISI) respectivamente. O sistemas resistivo apresentou eficiência de 89,21%, demonstrando maior viabilidade nas condições do estudo

<p>A magnetostrictive material elongates when it is subjected to a magnetic field. This effect can then be used to design powerful actuators. The department of electromagnetic engineering has been working with magnetostricitve material and their applications since the 1980s and is presently engaged in a project focusing on magnetostrictive transducer utilisation for the aeronautic field.</p><p>The focus of the presented work has been to develop and improve methods and tools supporting the development of magnetostrictive actuators.</p><p>The axial-radial model was previously developed at the department and is well suited for circular cross sections of magnetostrictive rods. It is, however, common to laminate the magnetostrictive rods resulting in rectangular cross sections. The use of Cauer circuits allows modelling of the shielding effect. This shielding effect results in non-homogenous magnetisation and stress in both rectangular and circular cross sections of the rod. A model based on Cauer circuits, including a hysteresis model based on experimental data, was developed during the project. Furthermore, it is demonstrated how figures of merit and the use of finite element methods can be used to find optimised designs in a systematic and computational efficient way. The<i> modified generalised Fabry factor</i> <i>and the magnetisation inhomogeneity coefficient</i> are two proposed new figures of merit.</p><p>A Magnetostricitve material is characterised through an experimental procedure. Usually, magnetostrictive material exhibit large hysteresis. An important part of the material characterisation is the post-processing of the measurement data, including a de-hysterisation procedure. In the thesis, a de-hysterisation method which ensures energy consistent data is presented. Energy consistent material data is essential to achieve energy consistent simulations of magnetostrictive systems.</p><p>It is also demonstrated how the knowledge at the department can be utilised in international projects. In an ongoing project, the department is engaged in two sub tasks. In one of these sub tasks a high torque actuator is to be developed for the helicopter industry. The developed magnetostrictive models are used to perform system simulations of such actuator systems. In the other sub task a device for power harvesting from vibrations is analysed. It has now been shown how to adapt the load impedance in order to extract maximal electric power from the device.</p>

The issue of eddy currents induced by the rapid switching of magnetic field gradients is a long-standing problem in magnetic resonance imaging. A new method for dealing with this problem is presented whereby spatial harmonic components of the magnetic field are continuously sensed, through their temporal rates of change, and corrected. In this way, the effects of the eddy currents on multiple spatial harmonic components of the magnetic field can be detected and corrections applied during the rise time of the gradients. Sensing the temporal changes in each spatial harmonic is made possible with specially designed detection coils. However to make the design of these coils possible, general relationships between the spatial harmonics of the field, scalar potential, and vector potential are found within the quasi-static approximation. These relationships allow the vector potential to be found from the field – an inverse curl operation – and may be of use beyond the specific problem of detection coil design. Using the detection coils as sensors, methods are developed for designing a negative feedback system to control the eddy current effects and optimizing that system with respect to image noise and distortion. The design methods are successfully tested in a series of proof-of-principle experiments which lead to a discussion of how to incorporate similar designs into an operational MRI.

The issue of eddy currents induced by the rapid switching of magnetic field gradients is a long-standing problem in magnetic resonance imaging. A new method for dealing with this problem is presented whereby spatial harmonic components of the magnetic field are continuously sensed, through their temporal rates of change, and corrected. In this way, the effects of the eddy currents on multiple spatial harmonic components of the magnetic field can be detected and corrections applied during the rise time of the gradients. Sensing the temporal changes in each spatial harmonic is made possible with specially designed detection coils. However to make the design of these coils possible, general relationships between the spatial harmonics of the field, scalar potential, and vector potential are found within the quasi-static approximation. These relationships allow the vector potential to be found from the field – an inverse curl operation – and may be of use beyond the specific problem of detection coil design. Using the detection coils as sensors, methods are developed for designing a negative feedback system to control the eddy current effects and optimizing that system with respect to image noise and distortion. The design methods are successfully tested in a series of proof-of-principle experiments which lead to a discussion of how to incorporate similar designs into an operational MRI.

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Este trabalho apresenta o estudo de um sistema genérico de medição que utiliza o princípio das correntes de Foucault, comumente conhecidas como correntes parasitas. O modelo do sistema é representado como um circuito elétrico equivalente composto por R1 e L1, respectivamente caracterizando a resistência e a indutância do circuito primário, as quais são conhecidas por uma bobina de excitação. Já no secundário, R2 e L2, estão representando a perda ôhmica e a indutância da amostra no qual as correntes parasitas são induzidas, além de outros dois componentes, M indutância mútua dos indutores acoplados e k, coeficiente relacionado ao acoplamento magnético entre os circuitos primário e secundário. A análise tradicionalmente utilizada para este tipo de medição é a avaliação da reflexão da impedância equivalente do circuito secundário representando a amostra no circuito primário. O trabalho analisa as equações de malha do circuito equivalente no domínio da frequência e identifica os parâmetros do modelo. A partir da identificação do sistema realizada com os ensaios experimentais, foi possível descobrir a constante de tempo indutiva τL do sistema. A partir dessa constante, observou-se a variação acentuada da mesma em relação a variação da impedância equivalente. Ainda é apresentada uma estimativa dos valores de R2 e L2 realizada por meio da unificação das informações obtidas com a identificação, aliada com as informações de campo magnético obtidas a partir de um sensor do tipo GMR e pela simulação em um software de elementos finitos COMSOL Multiphysics. / This work presents the study of a generic measurement system that uses the prin- ciple of eddy currents. The system model is represented as an equivalent electric circuit composed of R1 and L1 respectively characterizing the resistance and induc- tance of primary circuit, which are known by an excitation coil. In the secondary, R2 and L2 are representing the ohmic loss and the inductance of the sample in which the eddy currents are induced, in addition two other components, the mutual induc- tance of the coupled inductors and k, coefficient related to the magnetic coupling between the primary and secondary circuits. The analysis traditionally used for this type of measurement is the reflection evaluation of the equivalent impedance of the secondary circuit representing the sample in the primary circuit. The work analyzes the mesh equations of the equivalent circuit in the frequency domain and identifies the parameters of the model. From the identification of the system performed with the experimental tests, it was possible to discover the inductive time constant τL of the system. From this constant, it was observed the sharp variation of the same in relation to the variation of equivalent impedance. An estimate values, R2 and L2 performed by unification of the information obtained with the identification, to- gether with the magnetic field information obtained from a GMR type sensor and by simulation in a finite element software COMSOL Multiphysics.