<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>

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 assessed. In this thesis a time-domain transformer model is presented. The model includes core phenomena as magnetic static hysteresis, eddy current and excess losses. Moreover, the model comprises winding phenomena as eddy currents, capacitive effects and leakage flux. The core and windings are first modelled separately and then connected together in a composite transformer model. This results in a detailed transformer model. One important result of the thesis is the feasibility to simulate dynamic magnetization including the inhomogeneous field distribution due to eddy currents in the magnetic core material. This is achieved by using a Cauer circuit combined with models for static and dynamic magnetization. Thereby, all magnetic loss components in the material can be simulated accurately. This composite dynamic magnetization model is verified through experiments showing very good correspondence with measurements. Furthermore, the composite transformer model is verified through measurements. The model is shown to yield good correspondence with measurements in normal operation and non-normal operations like no-load, inrush current and DC-magnetization. / QC20100708

<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>

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.

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. The focus of the presented work has been to develop and improve methods and tools supporting the development of magnetostrictive actuators. 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 modified generalised Fabry factor and the magnetisation inhomogeneity coefficient are two proposed new figures of merit. 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. 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. / QC 20101115

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. 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. 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. / QC 20101116

Lors de la réalimentation des auxiliaires d’une tranche nucléaire, l’étape la plus à risque est la remise sous tension brusque du transformateur à cause des surtensions. Dans un soucis perpétuel d’amélioration de la modélisation de ces transitoires, les modèles et techniques doivent évoluer. Le but de ces travaux de thèse est de proposer de nouvelles méthodologies permettant d’évaluer les paramètres mal connus de la modélisation. Lors des mises sous tension des lignes électriques, une méthodologie s’appuyant sur l’identification (optimisation ou techniques issues du traitement du signal) permet de déterminer les paramètres variables de la modélisation. Cependant, un des paramètres influents pour les surtensions est le flux rémanent. Face aux problèmes actuels rencontrés pour l’estimer (méthode non directe, dérive, …), une nouvelle méthode basée sur la mesure des flux de fuites du circuit magnétique est proposée. Des mesures réelles utilisant des capteurs de technologie « fluxgate » sont réalisées et permettent d’estimer le flux rémanent. / During the re-energization of the auxiliaries of a nuclear power plant, the more dangerous step is the re-energization of the power transformer, because of the temporary overvoltages. In order to improve the transient modeling, models and techniques may be improved. The purpose of this thesis is to suggest new methodologies to identify the uncertain parameters of the model. When the line re-energization occurs, an identification methodology (optimization or methods using signal processing) allows determining the model variable parameters. However, one of the most important parameters in the overvoltages is the residual flux. Given the actual problems found on estimation strategies (no direct method, derivation,…), a new method established for the leakage flux measurement of the magnetic circuit is proposed. Real measurements using « fluxgate » technology sensors were realized, permitting to estimate the residual flux.

In dieser Arbeit wird die Möglichkeit untersucht, durch die Messung magnetischer Streuflüsse und unter Berücksichtigung der durch die Steuerströme hervorgerufenen Durchflutung, auf die Position des Rotors im Magnetlager zu schließen. Die Streuflüsse werden in der Regel vernachlässigt, stehen aber im unmittelbaren Zusammenhang zur Luftspaltlänge, wie theoretische Betrachtungen zeigen. Anhand von analytischen und numerischen Modellen, welche durch Messungen verifiziert werden, ist eine Linearisierung und Kompensation des Einflusses der Durchflutung möglich. Auf dieser Basis wird ein Messsystem entwickelt, mit dem die streuflussbasierte Positionsregelung eines Testlagers realisiert wird. Hierfür kommen Hall-Sensoren zum Einsatz, die auf Leiterplatten sitzen, welche anstelle der konventionellen Nutverschlüsse in das Magnetlager eingebracht werden. Aufgrund der direkten Nähe der Sensoren zu den Lagerspulen und der gepulsten Steuerströme weisen die Messsignale jedoch ein erhebliches Rauschen auf. Um dem entgegenzuwirken, kommt ein Kalman-Filter zum Einsatz, mit dem eine deutliche Verbesserung der Signalqualität erreicht werden kann.:Verzeichnis der Formelzeichen, Indizes und Abkürzungen vii 1 Einleitung 1 1.1 Exkurs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Systematik magnetischer Lager . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Sensoren für Magnetlager . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Sensorlose Magnetlagerung . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.5 Motivation und Struktur der Arbeit . . . . . . . . . . . . . . . . . . . . . . 14 1.5.1 Motivation und Zielstellung . . . . . . . . . . . . . . . . . . . . . . . 14 1.5.2 Struktur der Arbeit . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.6 Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 Theoretische Betrachtungen zu magnetischen Streuflüssen 17 2.1 Magnetische Streuflüsse in Magnetlagern . . . . . . . . . . . . . . . . . . . . 17 2.1.1 Heteropolarlager . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.1.2 Homopolarlager . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.1.3 Dreischenkliges Magnetlager . . . . . . . . . . . . . . . . . . . . . . . 20 2.2 Verallgemeinertes Reluktanzmodell . . . . . . . . . . . . . . . . . . . . . . . 21 2.3 Zusammenhang zwischen Luftspaltlänge und Streuflussdichte . . . . . . . . 28 2.3.1 Intrapolarer Streufluss . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.2 Interpolarer Streufluss . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.4 Betrachtung der magnetischen Streuflüsse mit Hilfe numerischer Rechnungen 33 2.5 Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3 Magnetische Streuflüsse im realen Magnetlager 39 3.1 Auswahl eines geeigneten Lagertyps und möglicher Messpositionen . . . . . 39 3.1.1 Streuflüsse bei Rotorverschiebung entlang der x- und y-Achse . . . . 41 3.1.2 Streuflüsse bei Rotorverschiebung entlang der a- und b-Achse . . . . 43 3.1.3 Änderung der Streuflüsse bei Querverschiebung des Rotors . . . . . 45 3.2 Nutzbarkeit der intra- und interpolaren Streuflüsse als Lagemesssystem . . 48 3.3 Vergleich gemessener und berechneter Streuflusswerte . . . . . . . . . . . . 52 3.4 Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4 Realisierung des Messsystems 57 4.1 Erstellung von Kennfeldern . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2 Versuchsaufbau . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 v Inhaltsverzeichnis 4.3 Messsystem zur Messung der magnetischen Streuflussdichte . . . . . . . . . 60 4.3.1 Auswahl geeigneter Bauelemente . . . . . . . . . . . . . . . . . . . . 62 4.3.2 Sensordesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.3.3 Kalibrierung der Sensoren . . . . . . . . . . . . . . . . . . . . . . . . 66 4.4 Statische und dynamische Eigenschaften des streuflussbasierten Messsystems 69 4.5 Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5 Betrachtungen zur Verbesserung der Signalqualität 75 5.1 Modellbildung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.1.1 Übertragungsverhalten der Messsysteme . . . . . . . . . . . . . . . . 76 5.1.2 Elektromagnetisches Modell . . . . . . . . . . . . . . . . . . . . . . . 80 5.1.3 Mechanisches Modell . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.1.4 Modellierung variabler Induktivitäten . . . . . . . . . . . . . . . . . 93 5.1.5 Stromrichter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.2 Kalman-Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.3 Ergebnisse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.4 Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 6 Zusammenfassung und Ausblick 115 6.1 Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 6.2 Ausblick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6.2.1 Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6.2.2 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 A Mathematische Überlegungen zu Streuflussfunktionen 121 A.1 Grenzwerte für den intrapolaren Streufluss . . . . . . . . . . . . . . . . . . . 121 A.2 Anstieg intrapolare Streuflussfunktion . . . . . . . . . . . . . . . . . . . . . 122 A.3 Maximum des interpolaren Streuflusses . . . . . . . . . . . . . . . . . . . . . 123 B Tabellen 127 B.1 Gemessene Streuflüsse an verschiedenen Rotorpositionen und unterschiedlichen resultierenden Steuerströmen . . . . . . . . . . . . . . . . . . . . . . . 127 B.2 Ströme und Positionen nach Streuflussmesswerten sortiert . . . . . . . . . . 128 C Schaltpläne, technische Zeichnungen und Blockschaltbilder 129 C.1 Schaltplan Streuflusssensor . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 C.2 Kalibrierschaltung des Messkonverters . . . . . . . . . . . . . . . . . . . . . 130 C.3 Beispielgeometrie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 C.4 Magnetlagerrotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 C.5 Blockschaltbild des Modells eines Stromrichters . . . . . . . . . . . . . . . . 131 Literaturverzeichnis 133 Thesen 141 / In this work, the possibility of inferring the position of the rotor in magnetic bearings by measuring magnetic leakage fluxes is investigated. These are usually neglected, but are directly related to the air gap length, as theoretical considerations show. In addition, the magnetic flux caused by the control currents must be taken into account. By means of analytical and numerical models, which are verified by measurements, a linearization and compensation of the influence of the magnetic flux is possible. Based on this, a measurement system is developed to realize a flux leakage-based position control of a test bearing. For this purpose, Hall-sensors are used, which are located on printed circuit boards that are inserted into the magnetic bearing instead of the conventional slot locks. However, due to the direct proximity of the sensors to the bearing coils and the pulsed control currents, the measurement signals exhibit considerable noise. To counteract this, a Kalman-filter is used to achieve a significant improvement in signal quality.:Verzeichnis der Formelzeichen, Indizes und Abkürzungen vii 1 Einleitung 1 1.1 Exkurs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Systematik magnetischer Lager . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Sensoren für Magnetlager . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Sensorlose Magnetlagerung . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.5 Motivation und Struktur der Arbeit . . . . . . . . . . . . . . . . . . . . . . 14 1.5.1 Motivation und Zielstellung . . . . . . . . . . . . . . . . . . . . . . . 14 1.5.2 Struktur der Arbeit . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.6 Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 Theoretische Betrachtungen zu magnetischen Streuflüssen 17 2.1 Magnetische Streuflüsse in Magnetlagern . . . . . . . . . . . . . . . . . . . . 17 2.1.1 Heteropolarlager . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.1.2 Homopolarlager . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.1.3 Dreischenkliges Magnetlager . . . . . . . . . . . . . . . . . . . . . . . 20 2.2 Verallgemeinertes Reluktanzmodell . . . . . . . . . . . . . . . . . . . . . . . 21 2.3 Zusammenhang zwischen Luftspaltlänge und Streuflussdichte . . . . . . . . 28 2.3.1 Intrapolarer Streufluss . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.2 Interpolarer Streufluss . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.4 Betrachtung der magnetischen Streuflüsse mit Hilfe numerischer Rechnungen 33 2.5 Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3 Magnetische Streuflüsse im realen Magnetlager 39 3.1 Auswahl eines geeigneten Lagertyps und möglicher Messpositionen . . . . . 39 3.1.1 Streuflüsse bei Rotorverschiebung entlang der x- und y-Achse . . . . 41 3.1.2 Streuflüsse bei Rotorverschiebung entlang der a- und b-Achse . . . . 43 3.1.3 Änderung der Streuflüsse bei Querverschiebung des Rotors . . . . . 45 3.2 Nutzbarkeit der intra- und interpolaren Streuflüsse als Lagemesssystem . . 48 3.3 Vergleich gemessener und berechneter Streuflusswerte . . . . . . . . . . . . 52 3.4 Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4 Realisierung des Messsystems 57 4.1 Erstellung von Kennfeldern . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2 Versuchsaufbau . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 v Inhaltsverzeichnis 4.3 Messsystem zur Messung der magnetischen Streuflussdichte . . . . . . . . . 60 4.3.1 Auswahl geeigneter Bauelemente . . . . . . . . . . . . . . . . . . . . 62 4.3.2 Sensordesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.3.3 Kalibrierung der Sensoren . . . . . . . . . . . . . . . . . . . . . . . . 66 4.4 Statische und dynamische Eigenschaften des streuflussbasierten Messsystems 69 4.5 Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5 Betrachtungen zur Verbesserung der Signalqualität 75 5.1 Modellbildung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.1.1 Übertragungsverhalten der Messsysteme . . . . . . . . . . . . . . . . 76 5.1.2 Elektromagnetisches Modell . . . . . . . . . . . . . . . . . . . . . . . 80 5.1.3 Mechanisches Modell . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.1.4 Modellierung variabler Induktivitäten . . . . . . . . . . . . . . . . . 93 5.1.5 Stromrichter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.2 Kalman-Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.3 Ergebnisse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.4 Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 6 Zusammenfassung und Ausblick 115 6.1 Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 6.2 Ausblick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6.2.1 Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6.2.2 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 A Mathematische Überlegungen zu Streuflussfunktionen 121 A.1 Grenzwerte für den intrapolaren Streufluss . . . . . . . . . . . . . . . . . . . 121 A.2 Anstieg intrapolare Streuflussfunktion . . . . . . . . . . . . . . . . . . . . . 122 A.3 Maximum des interpolaren Streuflusses . . . . . . . . . . . . . . . . . . . . . 123 B Tabellen 127 B.1 Gemessene Streuflüsse an verschiedenen Rotorpositionen und unterschiedlichen resultierenden Steuerströmen . . . . . . . . . . . . . . . . . . . . . . . 127 B.2 Ströme und Positionen nach Streuflussmesswerten sortiert . . . . . . . . . . 128 C Schaltpläne, technische Zeichnungen und Blockschaltbilder 129 C.1 Schaltplan Streuflusssensor . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 C.2 Kalibrierschaltung des Messkonverters . . . . . . . . . . . . . . . . . . . . . 130 C.3 Beispielgeometrie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 C.4 Magnetlagerrotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 C.5 Blockschaltbild des Modells eines Stromrichters . . . . . . . . . . . . . . . . 131 Literaturverzeichnis 133 Thesen 141

The aim of this master´s thesis is to analyze core losses of a small induction motor. Analyzed values are obtained from laboratory measurements, software analysis and 2D finite element method simulation. The theoretical part of this thesis consists of two parts. The analysis of the higher spatial harmonics presents in the induction motor and the analysis of core losses of the motor. Practical part consists of laboratory measurements according to ČSN. Measured values are used to calculate individual losses. The next part consists of creating a model for software analysis (Maxwell RMxprt). The generated model is converted into a 2D simulation environment (Maxwell 2D), where it is adapted to obtain values from the examined parts (rotor and stator teeth and rotor cage). Results of simulations at different loads are compared and analyzed from the point of view of higher harmonics.