A systematic and detailed design, building and testing of a high-sensitivity real-time magnetovision imaging system for non-destructive testing (NDT) was the purpose of the research presented here. The magnetic imaging systems developed were all based on an ultra-high sensitivity Quantum Well Hall Effect (QWHE) sensors, denoted as the P2A, which is based on GaAs-InGaAs-AlGaAs 2DEG heterostructures. The research progressed from 0D (single sensor) to 1D (linear array) to 2D (two dimensional arrays) testing modalities. Firstly, the measurement of thermal and shot noises, drift, detection limit, and dynamic offset cancellation of the QWHE sensor were studied in detail to set the framework and limitations of the fundamental QWHE sensors before their eventual use in the imaging systems developed subsequently. The results indicate that the measured data agrees well with calculations for thermal and shot noise when the input bias current is < 3 mA. The measured drift voltages of various QWHE sensors (P2A and P3A) are less than 200 µV when the sensor bias voltage is less than or equal to 2 V. A 4-direction dynamic offset cancellation technique was developed and the results show that the offset equivalent magnetic field of the QWHE sensors can be reduced from ~ 1mT to readings equal to the Earth magnetic field (~ 50 µT). Secondly, a flexible 16 × 1 array and a 32 × 2 staggered array magnetic-field scanners were designed, built, and tested. The QWHE magnetometer had a field strength resolution of 100 nT, and a measurement dynamic range of 138 dB. The flexible 16 × 1 magnetic field scanner can be used to test uneven and/or curved surfaces. This gives the flexible magnetic field scanner better inspection capabilities in both welding hump and circular pipe samples. By the staggered arrangement of two sensor arrays, a 15.4 point per inch horizontal spatial resolution can be achieved for the staggered 32 × 2 magnetic field scanner. Both direct and alternating magnetic flux leakage (DC and AC MFL) tests with the QWHE magnetometer were accomplished to obtain graphical 2-dimensional magnetic field distributions. Both the shape and the location of defects can be identified. The results show that the sensor has high sensitivity and linearity in a wide frequency range which makes it an optimum choice for AC-MFL testing and both ferromagnetic and non-ferromagnetic materials can be investigated. Thirdly, real-time 8 × 8 and 16  16 QWHE array magnetic-field cameras were designed, built, and tested. These prototypes can measure static magnetic field strengths in a 2-dimensional plane. Different shapes of magnets and magnetic field polarities can all be identified by the 8 × 8 magnetic field camera. The camera has a resolution of 3.05 mT, and a dynamic range of 66 dB (the minimum and maximum fields measurable are 3.05 mT and 6.25 mT) and a real time magnetic field measurement rate of 13 frames per second (FPS). By contrast the1616 array magnetic field camera has an improved sampling rate of 600 frame per second and with the use of an interpolation technique, a spatial resolution of 40.6 point per inch can be achieved. The minimum and maximum detectable magnetic field for this magnetic field camera are 1.8 µT and 29.5 mT respectively leading to a record dynamic range of 84 dB for high quality imaging. Finally, a novel, hand held, magnetovision system based on the real-time 16 × 16 QWHE array magnetic-field camera was developed for improved DC and AC electromagnetic NDT testing. The system uses a new super heterodyne technique for data acquisition using the QWHE sensor as a multiplier. This is the first report of such a technique in Hall effect magnetometry. The experimental results of five case studies demonstrate that the defects location and shape can be successfully measured with MFL in DC and AC magnetic field configurations including depth profiling. The major advantages of this real-time magnetic-field camera are: (1) its ease to use as a MFL testing equipment in both DC and AC NDT testing, (2) its ability to provide 2D graphical images similar to Magnetic Particle Inspection (MPI) but without its inherent health and safety drawbacks, (3) its capability to test both ferromagnetic and non-ferromagnetic materials for deep defects below the surface using low frequency alternating magnetic fields, and (4) its ability to identify materials (metals) by alternating external magnetic field illuminations, which has considerable potential in several applications such as security checking and labelling, magnetic markers for analysis, bio-imaging detection, and medical treatments amongst others.

<p> This thesis presents solutions to several inverse problems m electromagnetism and microwave engineering. In general, these inverse problems belong to two applications: breast cancer diagnosis using microwave imaging and defect characterization in metallic structures using magnetic flux leakage (MFL). </p> <p> Our contribution in microwave imaging for breast tumor detection can be divided into three parts. First, we propose a novel ultra-wide band (UWB) antenna that can operate in direct contact with the breast without the need for coupling liquids. This antenna is designed such that more than 90% of the radiated power is directed toward the tissue from its front aperture over the UWB. The performance of the antenna is investigated via simulation and measurement of the following parameters: return loss, near-field directivity, efficiency, fidelity, and group velocity. Overall, the results show that the antenna is a good candidate for frequency and time-domain imaging techniques. </p> <p> Second, we have proposed an aperture raster scanning setup that benefits from the features of our novel antenna. In this scanning setup, the breast tissue is compressed between two rectangular plates (apertures) while two antennas perform two-dimensional (2-D) scan by moving together on both sides of the compressed tissue. For each scanning step, the transmission S-parameter between the two antennas is recorded at several frequencies within UWB. Then, the modulus of the calibrated transmission S-parameter is plotted at each frequency to provide a 2-D image of the interior of the breast. The images are enhanced using a de-blurring technique based on blind de-convolution. This setup provides real time images of strong scatterers inside the normal tissue. </p> <p> Third, we propose 2-D and three-dimensional (3-D) holography algorithms to further improve the quality of the images obtained from the proposed planar scanning setup. These techniques are based on the Fourier transforms of the collected data to provide an image of a 2-D target (when collecting data at a single frequency) or a 3-D target (when collecting wide-band data). These techniques are fast and very robust to noise. The capability of the 2D and 3-D holographic imaging techniques is examined via simulation results. </p> <p> For defect characterization in metallic structures using MFL technique, we propose fast and reliable methodologies to invert the measured MFL response to the defect's shape parameters. First, we present a procedure to estimate the shape parameters of rectangular cracks which are the most common type of defects in the metallic structures. The procedure consists of estimating orientation, length, and depth of the cracks, consecutively. We validate this procedure via estimating the shape parameters of pre-known cracks from the simulated and measured MFL responses. Then, we present a methodology based on space mapping (SM) optimization for defect characterization. We examme the efficiency of this methodology for two types of defects: rectangular cracks and cylindrical pits. </p> / Thesis / Doctor of Philosophy (PhD)

No description available.

Le principe du contrôle non destructif par Flux de Fuite Magnétique (FFM) consiste à magnétiser une pièce à contrôler par un champ magnétique intense et à détecter à l’aide d’un capteur magnétique les fuites des lignes de champ qui résultent de la présence d’un défaut dans la pièce. Les méthodes de contrôle FFM sont très employées notamment lors du processus de fabrication des tubes ferromagnétiques par la société Vallourec, le leader mondial des fabricants de tube. Dans le but d’améliorer les performances des systèmes de contrôle installés en usine, le CEA LIST et le centre de recherches de Vallourec (VRA) collaborent pour développer des outils de simulation rapides dédiés au contrôle virtuel des tubes ferromagnétiques. Le système expérimental existant concerne plus particulièrement la détection des défauts longitudinaux. Le problème de modélisation se pose en termes de modélisation d’un système électromagnétique à géométrie complexe en régime magnétostatique non-linéaire. Les courants de Foucault induits par le mouvement relatif entre la pièce et le circuit magnétique sont négligés. Dans ce contexte, une approche semi-analytique reposant sur le formalisme des équations intégrales (EI) a été choisie. Les travaux effectués dans cette thèse ont pour but de traiter des géométries complexes 3D mais limitées dans une première étape aux matériaux linéaires. Toutefois, le caractère non-linéaire de la relation liant l’induction magnétique et le champ magnétique dans un matériau ferromagnétique doit être envisageable lors du choix de la formulation du problème. Après une étude des paramètres influents du système expérimental existant, menée par des simulations par éléments finis, nous avons considéré deux stratégies de modélisation. La première consiste à proposer un schéma de résolution qui combine un module de calcul 2D et un module d’extension du 2D vers le 3D. Le manque de généralisation de cette première approche simplifiée nous a conduits à proposer une deuxième stratégie qui résout le problème complet de magnétostatique 3D. La formulation par équations intégrales porte sur une quantité scalaire auxiliaire : la densité surfacique de charges magnétiques. Afin de pouvoir résoudre à terme un problème 3D non-linéaire, le schéma numérique proposé considère deux hypothèses : la pièce ferromagnétique est divisée en un ensemble de cellules hexaédriques dans lesquelles la perméabilité magnétique est constante et les inconnues du problème, les densités surfaciques de charge sur les faces de chaque cellule sont projetées sur des fonctions de base d’ordre 0. Le calcul numérique des intégrales singulières s’effectue de manière analytique. Plusieurs résultats de simulation confirment la validité du modèle numérique présenté. Même si le modèle présente encore aujourd’hui quelques limitations notamment sur le manque de précision des calculs en présence de défaut, celui-ci donne satisfaction en absence de défaut. Diverses configurations géométriques ont été traitées grâce à l’emploi du mailleur libre Gmsh. Le travail réalisé débouche sur un modèle 3D linéaire intégrable dans un procédé itératif pour effectuer une simulation en régime non-linéaire. Les inconvénients liés au formalisme des équations intégrales sont aujourd’hui contournables grâce aux méthodes de compression de matrices. Ce modèle est un bon candidat pour servir d’outil de simulation pour le contrôle virtuel des matériaux plans ou cylindriques par flux de fuite. / The principle of Non Destructive Testing (NDT) by using magnetic flux leakage (MFL) consists to magnetize a magnetic component to be inspected by a strong magnetic field and to detect with a magnetic sensor the magnetic flux lines which are leaking from part due to a defect. MFL methods are usually used during the process of manufacture of ferromagnetic pipes by our partner, the Vallourec Group, the leader in the world in manufacturing of pipes. To improve NDT systems in manufacturing plants, the CEA-LIST and the research center of Vallourec are working together to develop fast simulation tools dedicated to virtual testing of ferromagnetic pipes. The main experimental system concerns the detection of longitudinal defect. The modeling problem is to solve an electromagnetism problem with a complex geometry in the magneto-static nonlinear regime. Eddy currents induced by the motion of the pipe with respect to the magnetizing system are neglected.In this context, a semi-analytical approach based on integral equations (IE) has been chosen. The goal of some works which have been carried out in this PHD thesis is to address 3D complex geometries but, in first a step, limited to the linear regime. However, the non-linear behavior of the relationship which links the magnetic flux density and the magnetic field inside a ferromagnetic material must be considered when choosing the 3D formulation of the problem.After a study about influent parameters of the experimental system, carried out by using finite elements computations, we have considered two strategies for modeling. The first one has consisted to build up a strategy which consists to join the 2D numerical model, existing in the laboratory to an extension model from 2D to 3D. This approach was a priori quite simple but the lack of generality of this approach leads us to suggest another strategy which results in solving the complete 3D magneto-static problem. This formulation is based the integral equation formalism implying an auxiliary scalar quantity: the magnetic surface charge density. In order to be able to solve a nonlinear problem in the future, the chosen numerical scheme we have adopted is based on two hypothesis: the ferromagnetic part is firstly divided into a finite number of small hexahedral cells in which the relative magnetic permeability is supposed to be constant and secondly, the unknowns of the problem, the surface charge densities on the facets of each cell are expanded by using basis functions of zero order. Thanks to this limitation, the singular integrals can be analytically computed. Some simulation results confirm the validity of the implemented numerical model. This model presents some limitations at the moment in the cases of a workpiece with a defect but it can provide quite good results without any defect. Several geometries have been addressed by using Gmsh, free meshing software. Moreover, the final numerical model can be included into an iterative process to deal with non-linear cases. The limitations due to the EI formalism can be overcome today by using some compression matrix methods. Presently, this model is a good candidate for virtual NDT for cylindrical and planar geometries by magnetic flux leakage.

[pt] Este trabalho apresenta o desenvolvimento de um sensor inovador combinando três técnicas de inspeção utilizadas nos Pigs Instrumentados Geométrico e Magnético, para a detecção e caracterização de defeitos na geometria em tubulações de aço. O sensor GMD, Geométrico Magnético Discriminador, faz a leitura magnética do duto através da técnica de campo de fuga magnético, com a adição da leitura geométrica além da discriminação de defeitos internos de externos. A combinação dessas três tecnologias habilita a construção de uma ferramenta de inspeção de alta resolução compacta e capaz de identificar e quantificar, com apenas uma coroa de sensores, amassamentos, perdas de espessura e além da sua combinação. Este estudo se apresenta em um momento oportuno, já que a Integração de dados é o ponto fundamental da recente norma de gerenciamento de ricos em dutos, API 1160, na qual combinando os resultados das inspeções de geometria e corrosão, tem-se uma melhor avaliação de risco. Testes foram realizados utilizando um PIG Plano com corpos de prova contendo defeitos variados. Os resultados verificaram que o sensor GMD quantifica e discrimina amassamentos com perda de espessura. Aspectos técnicos do desenvolvimento como os detalhes construtivos do sensor, testes de avaliação a resultados de laboratório são apresentados. / [en] This thesis presents the development of an innovative sensor head for detection and characterization of geometric defects in steel pipes that combines three inspection techniques usually employed separately in Caliper and Magnetic Flux Leakage (MFL) PIGs. The novel Geometric Magnetic Discriminator (GMD) sensor performs high- resolution magnetic pipeline readings using MFL with the addition of internal pipe geometry evaluations and discrimination between internal and external defects. The combination of these technologies in a single sensor facilitates characterization of dents and corrosions, while at the same time optimizing the PIG set-up. According to the repair criteria in the standard API1160, combined defects such as a dent with metal loss, which in the past could only be detected through combined data of two different runs (MFL+ Caliper), must be repaired immediately. The GMD sensor was tested in a linear test rig, known as Flat Pig, and data were taken from different defect sets. Evaluation tests demonstrated that the GMD sensor sizes and discriminates a dent with metal loss. Technical aspects of the development, e.g.: the construction details of the sensor, evaluation tests and laboratory results are presented.

Le principe du contrôle par flux de fuite magnétique (Magnetic Flux Leakage MFL) consiste à aimanter la pièce à contrôler par un champ magnétique et à détecter à l'aide d'un capteur magnétique les fuites des lignes du champ qui résultent de la présence d'un défaut dans la pièce. Dans le but d'améliorer les performances d'un dispositif de détection, le CEA et la société Vallourec collaborent pour développer un modèle numérique dédié au contrôle virtuel des défauts longitudinaux dans les tubes ferromagnétiques. Le dispositif expérimental comprend un circuit magnétique tournant à une vitesse constante autour du tube qui défile. Dans le cadre de cette thèse, on débute le problème de la modélisation sans tenir compte des effets de la vitesse de rotation, il s'agit donc de résoudre un problème d'électromagnétisme en régime magnétostatique.Pour résoudre ce problème, on propose de comparer une approche semi-analytique basée sur le formalisme des équations intégrales (EI) et une approche purement numérique utilisant les éléments finis (EF).Dans la première partie de cette thèse, après avoir établi le formalisme théorique par EI, un premier modèle considérant des matériaux ferromagnétiques à perméabilité magnétique constante (régime linéaire) a été mis en œuvre en 2D. Ce modèle a été appliqué pour un exemple de système extrait de la littérature et validé numériquement par une comparaison des résultats EI/EF. Pour une meilleure détection, il est opportun de saturer magnétiquement la pièce. Le matériau ferromagnétique est alors caractérisé par une courbe B(H) non-linéaire. Par conséquent, la deuxième partie de la thèse a été consacrée à la mise en œuvre du modèle en régime non linéaire qui tient compte de cette caractéristique.Différentes méthodes de discrétisation ont été étudiées afin de réduire le nombre d'inconnues et le temps de calcul. L'originalité de la thèse réside dans l'utilisation des fonctions d'interpolation d'ordre élevé (polynôme de Legendre) pour une discrétisation des équations intégrales par une approche de type Galerkin. Les premiers essais de validation numérique de ce modèle ont été effectués sur un système MFL simplifié. Des premiers essais de validation expérimentale pour des données obtenues par EF ont été effectués en deux phases : La première a consisté à vérifier le distribution du champ magnétique pour un tube sain et en régime magnétostatique. La deuxième phase a consisté à calculer la réponse d'un défaut dans le tube ferromagnétique en tenant en compte les effets éventuels de la rotation du circuit magnétique par rapport au tube. / The principle of the non destructive testing by magnetic flux leakage (MFL) is to magnetize the part to be inspected by a magnetic field and to detect a flaw thanks to magnetic leakage field lines due to the strong decreasing of the magnetic permeability in the flawed region. In order to improve the performance of detection, the CEA and the Vallourec society collaborate to develop a numerical model dedicated to the virtual NDT of longitudinal defects in ferromagnetic tubes. The experimental system includes a magnetic circuit rotating at a constant speed around the tube to be inspected. The modeling task is started without considering the effects of the rotational speed, so the magnetostatic regime is considered to solve the modeling problem. In the framework of this thesis, we propose to compare a semi-analytical approach based on the formalism of integral equations method (IEM) and a purely numerical approach using finite element method (FEM).In the first part of this thesis, the theoretical formalism was established. A first simple discretization scheme is been implemented in the linear regime considering a constant magnetic permeability. This first numerical model has been validated for a simplified MFL configuration extracted and modified from the literature.For better detection, it is wishable to magnetically saturate the piece under-test. The ferromagnetic material is then characterized by a B(H) curve. Therefore, the second part of the thesis was devoted to the implementation of the model in the non-linear regime that takes into account this non-linear characteristic. Different discretization schemes have been studied in order to reduce the number of unknowns and the computational time. The originality of the thesis lies in the use of basis function of high order (Legendre polynomials) associated to a Galerkin approach for the discretization of integral equations. The first numerical result has been validated on a simplified MFL system. The first results of the experimental validation based on simulated data obtain by FEM have been performed in two steps. The first one consists to verify the distribution of the magnetic field for a ferromagnetic tube without any defect and in the magnetostatic regime. The objective of the second one was to compute the response of the flaw and to evaluate the effects of the rotational speed of the magnetic circuit around the tube.

Ermüdungsrissbildung ist ein gefährliches und kostenintensives Phänomen, welches frühzeitig erkannt werden muss. Weil kleine Fehlstellen jedoch hohe Testempfindlichkeit erfordern, wird die Prüfzuverlässigkeit durch Falschanzeigen vermindert. Diese Arbeit macht sich deshalb die Diversität unterschiedlicher zerstörungsfreier Oberflächenprüfmethoden zu Nutze, um mittels Datenfusion die Zuverlässigkeit der Fehlererkennung zu erhöhen. Der erste Beitrag dieser Arbeit in neuartigen Ansätzen zur Fusion von Prüfbildern. Diese werden durch Oberflächenabtastung mittels Wirbelstromprüfung, thermischer Prüfung und magnetischer Streuflussprüfung gewonnen. Die Ergebnisse zeigen, dass schon einfache algebraische Fusionsregeln gute Ergebnisse liefern, sofern die Daten adäquat vorverarbeitet wurden. So übertrifft Datenfusion den besten Einzelsensor in der pixelbasierten Falscherkennungsrate um den Faktor sechs bei einer Nutentiefe von 10 μm. Weiterhin wird die Fusion im Bildtransformationsbereich untersucht. Jedoch werden die theoretischen Vorteile solcher richtungsempfindlichen Transformationen in der Praxis mit den vorliegenden Daten nicht erreicht. Nichtsdestotrotz wird der Vorteil der Fusion gegenüber Einzelsensorprüfung auch hier bestätigt. Darüber hinaus liefert diese Arbeit neuartige Techniken zur Fusion auch auf höheren Ebenen der Signalabstraktion. Ein Ansatz, der auf Kerndichtefunktionen beruht, wird eingeführt, um örtlich verteilte Detektionshypothesen zu integrieren. Er ermöglicht, die praktisch unvermeidbaren Registrierungsfehler explizit zu modellieren. Oberflächenunstetigkeiten von 30 μm Tiefe können zuverlässig durch Fusion gefunden werden, wogegen das beste Einzelverfahren erst Tiefen ab 40–50 μm erfolgreich auffindet. Das Experiment wird auf einem zweiten Prüfkörper bestätigt. Am Ende der Arbeit werden Richtlinien für den Einsatz von Datenfusion gegeben, und die Notwendigkeit einer Initiative zum Teilen von Messdaten wird betont, um zukünftige Forschung zu fördern. / Fatigue cracking is a dangerous and cost-intensive phenomenon that requires early detection. But at high test sensitivity, the abundance of false indications limits the reliability of conventional materials testing. This thesis exploits the diversity of physical principles that different nondestructive surface inspection methods offer, by applying data fusion techniques to increase the reliability of defect detection. The first main contribution are novel approaches for the fusion of NDT images. These surface scans are obtained from state-of-the-art inspection procedures in Eddy Current Testing, Thermal Testing and Magnetic Flux Leakage Testing. The implemented image fusion strategy demonstrates that simple algebraic fusion rules are sufficient for high performance, given adequate signal normalization. Data fusion reduces the rate of false positives is reduced by a factor of six over the best individual sensor at a 10 μm deep groove. Moreover, the utility of state-of-the-art image representations, like the Shearlet domain, are explored. However, the theoretical advantages of such directional transforms are not attained in practice with the given data. Nevertheless, the benefit of fusion over single-sensor inspection is confirmed a second time. Furthermore, this work proposes novel techniques for fusion at a high level of signal abstraction. A kernel-based approach is introduced to integrate spatially scattered detection hypotheses. This method explicitly deals with registration errors that are unavoidable in practice. Surface discontinuities as shallow as 30 μm are reliably found by fusion, whereas the best individual sensor requires depths of 40–50 μm for successful detection. The experiment is replicated on a similar second test specimen. Practical guidelines are given at the end of the thesis, and the need for a data sharing initiative is stressed to promote future research on this topic.

There is currently a high demand for electric power from renewablesources. One source that remains relatively untapped is the motionof ocean waves. Anders Hagnestål has been developing a uniquelyefficient and simplified design for a point-absorb buoy generator byconverting its linear motion directly into alternating electric power usinga linear PM engine. To test this method, a smaller prototype isbuilt. Its characteristics present some unusual challenges in the designand construction of its winding.Devices of this type typically use relatively low voltage (690V typicallyfor a wind turbine, compared to the 10kV range of traditionalpower plants). To achieve high power, they need high current, whichin turn requires splitting the conductors in the winding into isolatedparallel strands to avoid losses due to eddy currents and current crowding.However, new losses from circulating currents can then arise. Inorder to reduce said losses, the parallel conductors should be transposedin such a way that the aggregate electromotive force the circuitsthat each pair of them forms is minimized.This research and prototyping was performed in absence of advancedindustrial means of construction, with limited space, budget,materials, manpower, know-how, and technology. Manual ingenuityand empirical experimentation were required to find a practical implementationfor: laying the cables, fixing them in place, transferringthem to the machine, stripping their coating at the ends and establishinga reliable connection to the current source.Using theoretical derivations and FEM simulation, a sufficientlygood transposition scheme is proposed for the specific machine thatthe winding is built for. A bobbin replicating the shape of the enginecore is built to lay down the strands.The parallel strands are then organized each into their respectivebobbin, with a bobbin rack and conductor funneling device being designedand constructed to gather them together into a strictly-organizedbundle. An adhesive is found to set the cables in place.Problems with maintaining the orientation and configuration of thecables in the face of repeated torsion are met and solved. A chemicalsolution is used to strip the ends of the conductors, and a reliableconnection is established by crimping the conductors into a bi-metalCu-Al lug.ivIn conclusion, the ideal transposition schemes required to cancelout circulating currents due to magnetic flux leakage are impossibleto put in practice without appropriate technological means. The feasibletransposition scheme turns out to be a simple mirroring of conductors’positions, implemented by building each half of the windingseparately around replicas of the core and then connecting them usingcrimping lugs. / Efterfrågan på el från förnybara källor är hög och inget tyder på att det kommer ändras den närmsta tiden. En källa till förnybar el som än idag står relativt orörd är den där man använder energin från havsvå- gor. Det är denna förnybara källa Anders Hagnestål haft i åtanke när han nu bygger en unikt effektiv generator med syftet att i ett senare skede utvinna el med hjälp av flytande punktabsorberande vågkraft- system. Generatorn är av den linjära typen och omvandlar det punk- tabsorberande systemet rörelse till el. För att testa denna generator- modell så påbörjades bygget av två fullskaliga prototyper 2017. Denna uppsats behandlar specifikt arbetet med generatorlindningen till pro- totyperna och innefattar processen från design till själva byggnatio- nen. Lindingen består av flertalet mindre och isolerade lindningsleda- re med uppgift att bland annat minska skinneffekt och virvelströms- förluster. När man använder denna metod så uppkommer dock ett nytt problem vilket härstammar från att lindningsledarna är samman- kopplade i vardera ända och bildar på så sätt n slutna strömkretsar. Konsekvensen kan vara stora förluster från cirkulerande strömmar på grund av det magnetiska ströflöde som finns runt järnkärnan som lindningen omsluter. Utgångspunkten för att minimera dessa cirkule- rande strömmar är att transponera alla lindningsledare på ett sätt så att den resulterande elektromotoriska spänningen för varje strömkrets blir så liten som möjligt. Med hjälp av förenklade modeller samt FEM simuleringar så bestämdes ett lämpligt sätt att transponera lindningstrådarna utifrån oli- ka kriterier. Lösningen blev att lindningstrådarna endast transponera- des en gång med en så kallad 180 grader transponering. Detta ger en tillräckligt god minimering av de cirkulerande ström- marna, men den stora fördelen med denna lösning är att det är möjligt att linda maskinen med de små resurser projektet hade tillgång till, dock var detta till en stor nackdel då väldigt mycket tid gick till att hitta egna tillvägagångsätt för att utföra byggandet av lindningen på ibland okonventionella sätt.