Exact analytical solutions for the quasistationary electromagnetic fields in the presence of conducting objects require the field solutions both internal and external to the conductors. Such solutions are limited for certain canonically shaped objects but are useful in testing the accuracy of various approximate models and numerical methods developed to solve complex problems related to real world conducting objects and in calibrating instruments designed to measure various field quantities. Theoretical investigations of quasistationary electromagnetic fields also aid in improving the understanding of the physical phenomena of electromagnetic induction. This thesis presents rigorous analytical expressions derived as benchmark solutions for the quasistationary field quantities both inside and outside, Joule losses and the electromagnetic forces acting upon a conducting spheroid placed in the proximity of a non-uniform field produced by current-carrying turns. These expressions are used to generate numerous numerical results of specified accuracy and selected results are presented in a normalized form for extended ranges of the spheroid axial ratio, the ratio of the depth of penetration to the semi-minor axis and the position of the inducing turns relative to the spheroids. They are intended to constitute reference data to be employed for comprehensive comparisons of results from approximate numerical methods or from boundary impedance models used for real world conductors. Approximate boundary conditions such as the simpler perfect electric conductor model or the Leontovich surface impedance boundary condition model can be used to obtain approximate solutions by only analyzing the field external to the conducting object. The range of validity of these impedance boundary condition models for the analysis of axisymmetric eddy-current problems is thoroughly investigated. While the simpler PEC model can be employed only when the electromagnetic depth of penetration is much smaller than the smallest local radius of curvature, the results obtained using the surface impedance boundary condition model for conducting prolate and oblate spheroids of various axial ratios are in good agreement with the exact results for skin depths of about 1/5 of the semi-minor axis when calculating electromagnetic forces and for skin depths less than 1/20 of the semi-minor axis when calculating Joule losses.

Exact analytical solutions for the quasistationary electromagnetic fields in the presence of conducting objects require the field solutions both internal and external to the conductors. Such solutions are limited for certain canonically shaped objects but are useful in testing the accuracy of various approximate models and numerical methods developed to solve complex problems related to real world conducting objects and in calibrating instruments designed to measure various field quantities. Theoretical investigations of quasistationary electromagnetic fields also aid in improving the understanding of the physical phenomena of electromagnetic induction. This thesis presents rigorous analytical expressions derived as benchmark solutions for the quasistationary field quantities both inside and outside, Joule losses and the electromagnetic forces acting upon a conducting spheroid placed in the proximity of a non-uniform field produced by current-carrying turns. These expressions are used to generate numerous numerical results of specified accuracy and selected results are presented in a normalized form for extended ranges of the spheroid axial ratio, the ratio of the depth of penetration to the semi-minor axis and the position of the inducing turns relative to the spheroids. They are intended to constitute reference data to be employed for comprehensive comparisons of results from approximate numerical methods or from boundary impedance models used for real world conductors. Approximate boundary conditions such as the simpler perfect electric conductor model or the Leontovich surface impedance boundary condition model can be used to obtain approximate solutions by only analyzing the field external to the conducting object. The range of validity of these impedance boundary condition models for the analysis of axisymmetric eddy-current problems is thoroughly investigated. While the simpler PEC model can be employed only when the electromagnetic depth of penetration is much smaller than the smallest local radius of curvature, the results obtained using the surface impedance boundary condition model for conducting prolate and oblate spheroids of various axial ratios are in good agreement with the exact results for skin depths of about 1/5 of the semi-minor axis when calculating electromagnetic forces and for skin depths less than 1/20 of the semi-minor axis when calculating Joule losses.

Στις ηλεκτρικές μηχανές ο υπολογισμός των απωλειών και οι μηχανισμοί που τις προκαλούν αποτελούν ένα πολύ απαιτητικό αντικείμενο μελέτης. Τα τελευταία χρόνια καθώς αυξάνεται η ανάγκη για ολοένα και πιο αποδοτικές μηχανές μεγάλο κομμάτι της έρευνας έχει επικεντρωθεί στον υπολογισμό των απωλειών τους και πιο συγκεκριμένα στον υπολογισμό των απωλειών σιδήρου. Οι απώλειες σιδήρου ή αλλιώς απώλειες πυρήνα αποτελούν σημαντικό μέρος των απωλειών μια μηχανής, ταυτόχρονα όμως ο υπολογισμός τους εμφανίζει ιδιαίτερη δυσκολία. Στην παρόυσα διπλωματική εργασία η προσπάθεια επικεντρωνεται στον υπολογισμό αυτών των απωλειών σε μια ασύγχρονη μηχανή με διάφορες μεθόδους. Πιο συγκεκριμένα, στο πρώτο κεφάλαιο γίνεται μια εισαγωγή στα σιδηρομαγνητικά υλικά και στις ιδιότητες τους. Αρχικά παρουσιάζεται το φαινόμενο της μαγνήτισης και του κορεσμού. Στη συνέχεια μελετάται το φαινόμενο της υστέρησης και οι ιδιότητες της που παίζουν καθοριστικό ρόλο στις απώλειες του πυρήνα της μηχανής, αλλά και το φαινόμενο των δινορευμάτων. Στο δεύτερο κεφάλαιο μελετώνται οι απώλειες της μηχανής. Με ποιό τρόπο δηλαδή το φαινόμενο της υστέρησης και των δινορευμάτων πρoκαλούν απώλειες στη μηχανή και με ποια μορφή εμφανίζονται. Παρουσιάζονται ακόμα οι μηχανισμοί που συνδέονται με τις απώλειες χαλκού, επιδερμικό φαινόμενο και φαινόμενο γειτνίασης και ο ρόλος τους. Παρουσιάζεται επίσης μια βιβλιογραφική έρευνα σχετικά με τις διάφορες μεθόδους που χρησιμοποιούνται για τον υπολογισμό των απωλειών σιδήρου. Το τρίτο κεφάλαιο αποτελεί ουσιαστικά μια εισαγωγή στα ηλεκτρονικά ισχύος και πιο συγκεκριμένα στον αντιστροφέα τάσης με τεχνική PWM. Σημαντικός θεωρείται ο τρόπος με τον οποίο διαμορφώνεται η τάση εισόδου στη μηχανή, αλλά και η μορφή της, καθώς επηρεάζει άμεσα τις απώλειες σιδήρου της μηχανής. Στο τέταρτο και τελευταίο κεφάλαιο βρίσκουν εφαρμογή όλα τα παραπάνω. Η εργασία γίνεται με τη βοήθεια ενός μοντέλου πεπερασμένων στοιχείων, δύο διαστάσεων, μιας ασύγχρονης μηχανής βραχυκυκλωμένου κλωβού. Αρχικά η μηχανή τροφοδοτείται από μια ημιτονοειδή τάση είσόδου. Υπολογίζονται οι απώλειες χαλκού και στη συνέχεια οι απώλειες σιδήρου με τη βοήθεια υπολογιστικών μεθόδων ανάλυσης του μαγνητικού πεδίου σε σειρές Fourier. Τέλος μελετάται η μορφή του μαγνητικού πεδίου σε διάφορα σημεία της μηχανής και οι απώλειες που εμφανίζεται σε κάθε στοιχείο του μοντέλου ανά περίπτωση. Τα βήματα αυτά επαναλαμβανονται τροφοδοτώντας αυτή τη φορά τη μηχανή μέσω αντιστροφέα τάσης με τεχνική PWM. Συγκρίνοντας τα αποτελέσματα από κάθε περίπτωση εξάγονται σημαντικά συμπεράσματα για τις απώλειες της μηχανής και τη συμπεριφορά των μηχανισμών που τις προκαλούν. / In electrical machines the calculation of loss and the mechanisms that cause them are a very demanding subject of study. Recently, the increasing need for ever more efficient machines has made the research focus on the calculation of their losses and more specifically the calculation of the iron losses. The iron losses or core losses, constitute an important part of the total machine losses, but also their calculation is particularly difficult. In this thesis we focus on the calculation of these losses in an asynchronous machine using various methods. More specifically, the first chapter is an introduction to the properties of ferromagnetic materials. First, we study the phenomenon of magnetization and saturation and then we examine the phenomenon of hysteresis and its properties which play a crucial role in the core losses of the machine. Finally we study eddy current phenomenon. In the second chapter we discuss the losses of the machine. In which way the phenomenon of hysteresis and eddy currents generate losses in the machine and the form in which they appear. Also presented are the mechanisms associated with the copper losses, skin effect and proximity effect. Also shown is a literature survey on various methods used to calculate the iron losses. The third chapter is essentially an introduction to power electronics, and more particularly to the PWM technique. Important in this chapter is the way in which the input voltage to the machine affects the iron losses. In the fourth and final chapter we produce results of the above theory using simulation methods. The work is done using a finite element model in two dimensions of a squirrel cage asynchronous machine. Initially the machine is fed by a sinusoidal input voltage. Firstly copper losses are calculated and then the iron losses with the help of computational methods which analyze the magnetic induction in Fourier series. Finally, we study the shape of the magnetic field in different parts of the machine and the losses occurring in each element of the model in each case. These additional losses are known as rotational core losses. These steps are repeated, this time powering the machine via inverter supply using the PWM technique.

La découverte de nombreuses planètes extrasolaires depuis 1995 est une source d’inspiration pour les modèles de formation et évolution des systèmes solaires. Une fraction de ces planètes ont un demi-grand axe inférieur à 0.1 UA; une planète qui migre à proximité de son étoile subit donc d’abord un fort vent solaire et, après son entrée dans la magnétosphère stellaire, un fort champ magnétique. Nous étudions séparemment l’interaction entre ces planètes et la composante périodique et indépendente du temps du champ magnétique dipolaire stellaire. L’interaction périodique est associée à des courants induits confinés dans la planète. Nous étudions deux effets qui pourraient augmenter le moment angulaire d’une planète gaseuse géante qui migre vers son étoile: un torque de Lorentz qui transferre du moment angulaire de la rotation de l’étoile vers l’orbite de la planète et une perte de masse induite par la dissipation ohmique dans la planète qui peut donner du moment angulaire à la planète lorsque cette masse est accrétée sur l’étoile. Nous modellisons l’interaction indépendente du temps comme un modèle d’inducteur unipolaire, dans lequel le courant induit circule dans une boucle fermée formée par la planète, le flux de tube, et le pied du flux de tube dans l’atmosphère stellaire. Nous calculons de fa con cohérente la dissipation ohmique dans la planète et le pied du flux de tube ainsi que le couple de Lorentz. Nous utilisons alors ce modèle pour expliquer l’aspect enflé de certaines planètes géantes. Finalement, nous suggérons que ce modèle permettrait également d’estimer la conductivité électrique des super-Terres qui interagissent magnétiquement avec leur étoile. / The numerous and diverse extrasolar planets detected since 1995 provide much inspiration for planetary astrophysics. A fraction of these extrasolar planets orbit their host stars at semi-major axes less than 0.1 AU; a planet which has migrated toward its host star would thus first encounter a strong magnetized wind and, as it enters the stellar magnetosphere, strong magnetic fields. We model the interaction of such a close-in extrasolar planet with the dipolar magnetic field of its host star and study separately the time-dependent and independent components. The time-dependent interaction gives rise to Eddy currents confined in the planet. We investigate two effects that may transfer angular momentum to a planet approaching its host TTauri star through type II migration: a Lorentz torque that transfers angular momentum from the stellar spin to the planetary orbit and a mass loss induced by the ohmic dissipation in the planet, which may transfer angular momentum to the planet as the gas is accreted onto the star. We model the time-independent interaction with the unipolar inductor model, which allows the current induced in the planet to flow along a closed loop constituted by the planet, the flux tube, and its footprint on the stellar atmosphere. We self-consistently calculate the ohmic dissipation in the planet and the star and the associated Lorentz torque. We then suggest that the ohmic dissipation may provide the extra energy needed to explain some planets with inflated radii. Finally, we propose that the model may also be used to remotely infer the electric conductivity of the outer layers of super-Earths interacting magnetically with their host stars.

The conversion of mechanical energy to electrical energy is done mainly with synchronous generators. They are used in hydropower generators and nuclear plants that presently account for about 80% of the electric energy production in Sweden. Because of the dominating role of the synchronous generators, it is important to minimize the power losses for efficient use of natural resources and for the economies of the electric power companies and their customers. For a synchronous machine, power loss means undesired heat production. In electric machines, there are power losses due to windage, friction in bearings, resistance in windings, remagnetization of ferromagnetic materials, and induced voltages in windings, shields and parts that are conductive but ideally should be non-conductive. The subject of this thesis is prediction of end region magnetic leakage fields in synchronous generators and the eddy current power losses they cause. The leakage fields also increase the hysteresis losses in the end regions. Magnetic flux that takes paths such that eddy current power losses increase in end regions of synchronous generators is considered to be leakage flux. Although only a small fraction of the total magnetic flux is end region leakage flux, it can cause hot spots, discoloration and reduce the service life of the insulation on the core laminations. If unattended, damaged insulation could lead to electric contact and eddy currents induced by the main flux between the outermost laminations. That gives further heating and deterioration of the insulation of laminations deeper into the core. In a severe case, the core can melt locally, cause a cavity, buckling and a short circuit of the main conductors. The whole stator may have to be replaced. However, the end region leakage flux primarily causes heating close to the main stator conductors which makes the damage possible to discover by visual inspection before it has become irrepairable.

Pour réduire les émissions de gaz polluants, les constructeurs automobiles cherchent à mieux contrôler le volume d'air introduit dans le moteur pour optimiser la combustion. Des dispositifs mécaniques ou hydrauliques couplés avec l'arbre à cames sont déjà en place dans certaines voitures et permettent des gains de 8 à 10% sur la consommation de carburant. L'utilisation d'un actionneur électromagnétique à la place de l'arbre à cames (application « camless ») pour commander les soupapes améliore nettement ce gain (15 à 20%). Les travaux de cette thèse consistent à modéliser une structure choisie, pour ensuite l'optimiser. Compte tenu des exigences de notre application et des contraintes d'environnement du moteur thermique, la modélisation doit être à la fois suffisamment précise et rapide pour estimer et améliorer les performances de l'actionneur. Pour la partie statique, nous avons opté pour un modèle réluctant 3D. Obtenu par extension de son homologue 2D, il reste rapide tout en donnant des résultats en accord avec les mesures. En régime transitoire, nous proposons une nouvelle approche analytique de la distribution des courants de Foucault, directement à partir de l'évolution du flux magnétique. L'équation de diffusion comporte alors des conditions aux limites de Neumann. Nous avons traité le cas d'un flux magnétique arbitraire grâce au théorème de Duhamel, ainsi que la saturation du matériau grâce à une approche semi-analytique. / Variable valve actuation is one of automotive constructors' strategies to fulfil environmental queries about emission of pollutant gases. It brings improvement to the thermal engine, and many constructors have their own devices associated to the camshaft, with a gain between 8 and 10% on fuel consumption. The use of camless actuator brings further more gain, from 15 to 20%. The established approach during this thesis consists in modelling a chosen topology of actuator, and next in optimization. However, camless specifications and constraints require fast models, but with correct accuracy. That's why we use 3D permeances network in steady state. That model is obtained from extension of its 2D version. It is still fast and gives results in good agreement with measurements. We proposed a new analytical approach of eddy currents distribution in transient state, directly from the evolution of magnetic flux. Thus we have Neumann's boundary conditions in the diffusion equation. Arbitrary magnetic flux excitation and saturated material (with semi-analytical approach) are considered.

This master thesis deals with the suppression of the skin and proximity effects in high-speed machines. The first part summarizes the general knowledge of high-speed machines. The second part is devoted to the principle and possible suppression of consequences caused by skin and proximity effects. The third part shows the simulation results of models of a synchronous machine with permanent magnets. The results of these simulations reveal the consequences of skin and proximity effects. In addition, design measures are proposed to limit these and other undesirable phenomena to achieve the highest possible efficiency.

High speed applications demands with a need for lower energy consumption lead to designing new types of bearings. In the last decades magnetic bearing, which would be able to obtain passive stable levitation using regular materials at room temperature, has been searched. This has lead to development of electrodynamic bearing based on eddy currents principle. Currently the electrodynamic bearings are still not fully explored and further research is needed. The aim of the work is to describe the theory about modern magnetic bearing, analysis and design of electrodynamic bearing according to given parameters. The finite element method is used for further analysis and evaluate behaviour of its properties.

The aim of this work is to analyze the methodology for executing examination heat transfer tubes of steam generator by method of eddy currents on EDU, to create the model for the estimate of standard combined uncertainty of efficiency value, quantify the individual components of standard uncertainties, analyse the influence of different components on the expressing of uncertainty, to make the final estimate of standard combined and enlarged uncertainty of efficiency value and as of minor objective to evaluate the suitability of the use of this method .

Die Dynamik von axialen Magnetlagern ist im besonderen Maße von den eingesetzten Materialien abhängig. Axiale Flussverläufe machen eine Blechung von Stator und Rotor unwirksam und hohe induzierte Spannungen rufen im Magnetkreis wirbelstrombedingte Gegenfelder hervor. Zusätzliche kompensierende Magnetisierungsströme lassen den messbaren Strom der Steuerspule dem kraftbildenden Hauptfluss vorauseilen. Durch Einsatz von Pulververbundwerkstoffen lässt sich dieser Effekt reduzieren. Aus mechanischen Gründen wird die rotierende Axiallager-Scheibe in konventionellen Anwendungen dennoch aus Stahl gefertigt. In dieser Diplomarbeit werden alternative Materialien und Ausführungsformen untersucht und die auftretenden Unterschiede im dynamischen Verhalten mit der Eisenkreiszeitkonstante quantifiziert. Neben dem zu Grunde liegenden analytischen Modell soll eine fortgeschrittene Systembeschreibung vorgestellt werden, die das atypische Übertragungsverhalten der Regelstrecke berücksichtigt. Dieses setzt sich aus Differenziergliedern gebrochen-rationaler Ordnung zusammen und bildet ein sogenanntes „Fractional-Order-System“. Die Modelle werden mittels FEM-Simulationen und Experimenten am eigens konstruierten Versuchslager verifiziert. / The dynamics of axial magnetic bearings are characterized by an above-average dependency on the used materials. Axially directed fields render laminated stators and rotors ineffective. High induced voltages inside the magnetic core evoke eddy currents and opposing fields, which are compensated by an additional magnetizing current. Therefore a significant delay between the measurable coil current and the force-related magnetic flux is observed. The use of soft magnetic composites can minimize this effect, though the bearing disk usually is manufactured from conventional steel for mechanical reasons in a wide range of applications. In this diploma thesis alternative materials and embodiments are considered and the occurring differences regarding the dynamic behavior will be quantified by means of the magnetic circuit time constant. Beside its underlying analytical model, an advanced system description is introduced to include the atypical transfer function of the closed loop control system, characterized by so-called Fractional-Order-Derivatives. All models will be verified by FE-analysis and experiments on a newly constructed magnetic bearing.