Approved for public release; distribution in unlimited. / In this thesis we develop a procedure for detecting erroneous payments in the Defense Finance Accounting Service, Internal Review's (DFAS IR) Knowledge Base Of Erroneous Payments (KBOEP), with the use of supervised (Logistic Regression) and unsupervised (Classification and Regression Trees (C & RT)) modeling algorithms. S-Plus software was used to construct a supervised model of vendor payment data using Logistic Regression, along with the Hosmer-Lemeshow Test, for testing the predictive ability of the model. The Clementine Data Mining software was used to construct both supervised and unsupervised model of vendor payment data using Logistic Regression and C & RT algorithms. The Logistic Regression algorithm, in Clementine, generated a model with predictive probabilities, which were compared against the C & RT algorithm. In addition to comparing the predictive probabilities, Receiver Operating Characteristic (ROC) curves were generated for both models to determine which model provided the best results for a Coincidence Matrix's True Positive, True Negative, False Positive and False Negative Fractions. The best modeling technique was C & RT and was given to DFAS IR to assist in reducing the manual record selection process currently being used. A recommended ruleset was provided, along with a detailed explanation of the algorithm selection process. / Lieutenant Commander, United States Navy

Orientador: Alcides Padilha / Banca: Ivan De Domenico Valarelli / Banca: Kamal Abdel Radi Ismail / Resumo: Neste trabalho apresenta-se uma análise teórica e experimental dos resultados comparativos entre as curvas características de um ventilador axial utilizado em um sistema de pulverização agrícola para um ângulo de ataque da pá em 32 graus nas rotações de 1500, 1750, 2600 e 3000 rpm e resultados numéricos da influência da variação do ângulo de ataque da pá em 28, 32 e 36 graus e da otimização do sistema de pulverização ambos para uma rotaç]ao de 2600 rpm. O campo médio turbulento foi obtido com a aplicação da média temporal sendo que o modelo de turbulência exigido para o fechamento do conjunto de equações foi o modelo k-ε de duas equações. A resolução de todos os fenômenos acoplados foi alcançada com o auxílio do código de fluidodinâmica computacional CFX que utiliza a técnica dos volumes finitos como método numérico. Para validação da análise teórica, realizaram-se experimentos em um túnel de vento horizontal de seção circular com diâmetro de 622 mm, usando um tubo de Pitot para as tomadas de pressão de acordo com a norma para ensaios em laboratório. Apresentam-se resultados qualitativos na forma de vetores e mapas de gradiente de velocidade e, quantitativos na forma de tabelas e gráficos para as curvas características. / Abstract: This paper presents a theoretical and experimental analysis of comparative results the characteristic curves of an axial fan used in an agricultural spraying system for a blade attack angle of 32 degrees at rotations of 1500, 1750, 2600 and 3000 rpm and numerical results for the influence of blade attack angle variation at 28, 32 and 36 degrees and optimization of the spraying system, both for a rotation of 2600 rpm. The average turbulent field was obtained from the application of time average where the turbulence model required for closing the set of equations was the k-ε model for two equations. Resolution of all connected phenomena was achieved with the help of the fluid dynamics computacional, CFX, which uses the finite volumes technique as a numerical method. In order to validate the theoretical analysis, an experiment was conducted in a circular section of a horizontal wind tunnel, 622 mm in diameter and 6220 mm in length, using a Pitot tube for pressure readings according to the norm for laboratory assays. Qualitative results are shown as vectors and gradient maps for speed and quantitative results are shown in tables and graphics for characteristic curves. / Mestre

A condutividade hidráulica de dois solos não saturados típicos da região de São Carlos, um arenoso e outro argiloso é estudada através de ensaios de campo empregando o permeâmetro Guelph. Duas alternativas de ensaio foram empregadas e os resultados experimentais foram analisados com os modelo teóricos de REYNOLDS e ELRICK (1985) e PHILIP (1985). Paralelamente, obtiveram-se em laboratório curvas de retenção de água dos solos o que possibilitou determinar a função condutividade hidráulica através das fórmulas empíricas de VAN GENUCHTEN, (1980) e de GARDNER (1958). As características e a variação dos valores da condutividade hidráulica não saturada de campo fornecidos pelo permeâmetro Guelph, são discutidos e confrontados com aqueles obtidos a partir dos métodos indiretos provenientes de laboratório. Observou-se que as condutividades hidráulicas saturadas nos solos foram praticamente iguais, quer se considerem os resultados de campo ou laboratório. Os resultados de campo mostraram-se mais consistentes para o solo argiloso qualquer que tenha sido a técnica de ensaio. O parâmetro &#945 da equação de GARDNER (1958) obtido no campo resultou maior que o valor sugerido na literatura ou obtido em laboratório para o solo arenoso. Para o solo argiloso, todas as opções de obtenção do parâmetro tenderam a fornecer valores praticamente iguais. / The unsaturated hydraulic conductivity of two typical soils from the region of São Carlos City, sandy and clayey soils, has been studied through field tests using the Guelph permeameter. Two different alternatives of tests have been performed and the experimental data have been analyzed following the theoretical models from REYNOLDS and ELRICK (1985) and PHILIP (1985). However, soil-water characteristic curves were obtained in such a way that the hydraulic conductivity function could be evaluated using the empirical expressions from VAN GENUCHTEN (1980), and GARDNER (1958). The characteristics and the variation of the field unsaturated hydraulic conductivity values from the Guelph permeameter are discussed and compared to those from laboratory indirect methods. The field results showed to be more consistent to the clayey soil independent on the test or calculation method. The &#945 value (GARDNER, 1958) parameter obtained in the fields was Iarger than the values suggested in the literature or obtained in laboratory for the sandy soil. To the clayey soil, all the obtaining options of the parameter tended to supply values quite the same.

Made available in DSpace on 2014-06-11T19:25:27Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-11-06Bitstream added on 2014-06-13T18:26:31Z : No. of bitstreams: 1 fogal_mlf_me_bauru.pdf: 1973940 bytes, checksum: 7fa4d89826d2cfb9214807f1ec353036 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho apresenta-se uma análise teórica e experimental dos resultados comparativos entre as curvas características de um ventilador axial utilizado em um sistema de pulverização agrícola para um ângulo de ataque da pá em 32 graus nas rotações de 1500, 1750, 2600 e 3000 rpm e resultados numéricos da influência da variação do ângulo de ataque da pá em 28, 32 e 36 graus e da otimização do sistema de pulverização ambos para uma rotaç]ao de 2600 rpm. O campo médio turbulento foi obtido com a aplicação da média temporal sendo que o modelo de turbulência exigido para o fechamento do conjunto de equações foi o modelo k-ε de duas equações. A resolução de todos os fenômenos acoplados foi alcançada com o auxílio do código de fluidodinâmica computacional CFX que utiliza a técnica dos volumes finitos como método numérico. Para validação da análise teórica, realizaram-se experimentos em um túnel de vento horizontal de seção circular com diâmetro de 622 mm, usando um tubo de Pitot para as tomadas de pressão de acordo com a norma para ensaios em laboratório. Apresentam-se resultados qualitativos na forma de vetores e mapas de gradiente de velocidade e, quantitativos na forma de tabelas e gráficos para as curvas características. / This paper presents a theoretical and experimental analysis of comparative results the characteristic curves of an axial fan used in an agricultural spraying system for a blade attack angle of 32 degrees at rotations of 1500, 1750, 2600 and 3000 rpm and numerical results for the influence of blade attack angle variation at 28, 32 and 36 degrees and optimization of the spraying system, both for a rotation of 2600 rpm. The average turbulent field was obtained from the application of time average where the turbulence model required for closing the set of equations was the k-ε model for two equations. Resolution of all connected phenomena was achieved with the help of the fluid dynamics computacional, CFX, which uses the finite volumes technique as a numerical method. In order to validate the theoretical analysis, an experiment was conducted in a circular section of a horizontal wind tunnel, 622 mm in diameter and 6220 mm in length, using a Pitot tube for pressure readings according to the norm for laboratory assays. Qualitative results are shown as vectors and gradient maps for speed and quantitative results are shown in tables and graphics for characteristic curves.

A condutividade hidráulica de dois solos não saturados típicos da região de São Carlos, um arenoso e outro argiloso é estudada através de ensaios de campo empregando o permeâmetro Guelph. Duas alternativas de ensaio foram empregadas e os resultados experimentais foram analisados com os modelo teóricos de REYNOLDS e ELRICK (1985) e PHILIP (1985). Paralelamente, obtiveram-se em laboratório curvas de retenção de água dos solos o que possibilitou determinar a função condutividade hidráulica através das fórmulas empíricas de VAN GENUCHTEN, (1980) e de GARDNER (1958). As características e a variação dos valores da condutividade hidráulica não saturada de campo fornecidos pelo permeâmetro Guelph, são discutidos e confrontados com aqueles obtidos a partir dos métodos indiretos provenientes de laboratório. Observou-se que as condutividades hidráulicas saturadas nos solos foram praticamente iguais, quer se considerem os resultados de campo ou laboratório. Os resultados de campo mostraram-se mais consistentes para o solo argiloso qualquer que tenha sido a técnica de ensaio. O parâmetro &#945 da equação de GARDNER (1958) obtido no campo resultou maior que o valor sugerido na literatura ou obtido em laboratório para o solo arenoso. Para o solo argiloso, todas as opções de obtenção do parâmetro tenderam a fornecer valores praticamente iguais. / The unsaturated hydraulic conductivity of two typical soils from the region of São Carlos City, sandy and clayey soils, has been studied through field tests using the Guelph permeameter. Two different alternatives of tests have been performed and the experimental data have been analyzed following the theoretical models from REYNOLDS and ELRICK (1985) and PHILIP (1985). However, soil-water characteristic curves were obtained in such a way that the hydraulic conductivity function could be evaluated using the empirical expressions from VAN GENUCHTEN (1980), and GARDNER (1958). The characteristics and the variation of the field unsaturated hydraulic conductivity values from the Guelph permeameter are discussed and compared to those from laboratory indirect methods. The field results showed to be more consistent to the clayey soil independent on the test or calculation method. The &#945 value (GARDNER, 1958) parameter obtained in the fields was Iarger than the values suggested in the literature or obtained in laboratory for the sandy soil. To the clayey soil, all the obtaining options of the parameter tended to supply values quite the same.

L'étude présentée dans cette thèse porte sur une analyse expérimentale des propriétés physiques (densités, porosité, granulométrie) et hydrodynamiques (isotherme de désorption, courbe caractéristique sol-eau, perméabilité à saturation) d'un sol type aride du Burkina Faso et une simulation numérique des transferts d'eau. La modélisation des transferts est abordée par une approche thermodynamique qui constitue un cadre général pour décrire à la fois l'état de l'eau dans le sol et les mécanismes de transferts mis en jeu : filtration de la phase liquide, diffusion de la vapeur d'eau, changement de phase liquide-vapeur. Des essais expérimentaux de transferts d'eau dans des colonnes de sol hermétiquement fermées et placées dans une enceinte régulée en température, ont permis d'établir l'évolution des profils de teneur en eau au cours du temps. La configuration expérimentale est choisie de sorte que seule la filtration de la phase liquide de l'eau dans le sol soit prépondérante. Les profils expérimentaux ont servi à l'estimation par approche inverse de la conductivité hydraulique dans les faibles teneurs en eau. La prise en compte des écoulements par films dans la modélisation du coefficient de perméabilité relative corrige les insuffisances des modèles capillaires. Les coefficients de changement de phase proche et loin de l'équilibre modélisés à partir de résultats expérimentaux permettent la mise en évidence du non-équilibre liquide/gaz dans les transferts aux faibles teneurs en eau. Il ressort que le non-équilibre dans les transferts aux faibles teneurs en eau est plus marqué avec le modèle capillaire avec un front de séchage plus franc à la surface. La prise en compte des écoulements par films prolonge la filtration de la phase liquide de l'eau jusqu'à l'état hygroscopique du sol avec un flux d'eau liquide maintenu à la surface du sol jusqu'à des temps plus longs. / The study presented in this thesis focuses on an experimental analysis of physical properties (densities, porosity, particle size distribution) and hydrodynamic properties (desorption isotherm, soil-water characteristic curve, saturated permeability) of an arid soil from Burkina Faso and numerical simulation of water transfers. The transfer modelling is addressed through thermodynamic approach which provides a general framework to describe both the water state in the soil and the transport mechanisms: filtration of liquid phase, water vapor diffusion, liquid/vapor phase change. Experimental attempts of water transfer in soil columns, sealed and placed into a controlled temperature chamber, have established the evolution of water content profiles over time. The experimental configuration is chosen so that only the filtration of water liquid phase is taken into account. These experimental profiles were used to estimate, by inverse approach, the unsaturated hydraulic conductivity at low water contents. Consideration of film flows in the relative permeability modelling corrects the shortcomings of capillary bundle models used to describe water flow from saturation to oven-dryness. The coefficients of phase change near and far from equilibrium modeled from experimental results prove non-equilibrium liquid/gas existence. It appears that the liquid/gas non-equilibrium at low water content is more pronounced with the capillary model with a frank drying front at the soil surface. Consideration of film flows extends liquid phase filtration into the soil until the hygroscopic state with a liquid water flux maintained at the soil surface for longer times.

En France, la recherche contre le cancer est un enjeu majeur de santé publique. On estime notamment que le nombre de nouveaux cas de cancer a plus que doublé entre 1980 et 2012. L’hétérogénéité des caractéristiques tumorales, pour un même cancer, impose des défis complexes dans la recherche de traitements efficaces. Dans ce contexte, des espoirs importants sont placés dans la recherche de biomarqueurs prédictifs reflétant les caractéristiques des patients ainsi que de leur tumeur afin d’orienter le choix de la stratégie thérapeutique. Par exemple, pour les cancers colorectaux métastatiques, il est maintenant reconnu que l’ajout de cetuximab (un anti-EGFR) à la chimiothérapie classique (ici le FOLFOX4), n’apporte un bénéfice qu’aux patients dont le gène KRAS est non muté. Le gène KRAS est ici un biomarqueur prédictif binaire, mais de nombreux biomarqueurs sont le résultat d’une quantification ou d’un dosage. L’objectif de cette thèse est dans un premier temps, de quantifier la capacité globale d’un biomarqueur quantitatif à guider le choix du traitement. Après une revue de la littérature, une nouvelle méthode basée sur une extension des courbes ROC est proposée, et comparée aux méthodes existantes. Son principal avantage est d’être non paramétrique, et d’être indépendante de l’efficacité moyenne des traitements. Dans un second temps, lorsqu’un biomarqueur prédictif quantitatif est étudié, la définition d’un seuil de marqueur au-delà duquel la première option de traitement sera préférée, et en-deçà duquel la deuxième option de traitement sera préférée se pose. Une approche reposant sur la définition d’une fonction d’utilité est proposée permettant alors de tenir compte de l’efficacité des traitements ainsi que de leur impact sur la qualité de vie des patients. Une méthode Bayésienne d’estimation de ce seuil optimal est proposée / In France, the cancer research is a major public health issue. The number of new cancer cases nearly doubled between 1980 and 2012. The heterogeneity of the tumor characteristics, for a given cancer, presents a great challenge in the research of new effective treatments. In this context, much hope is placed in the research of predictive (or treatment selection) biomarkers that reflect the patients’ characteristics in order to guide treatment choice. For example, in the metastatic colorectal cancer setting, it is admitted that the addition of cetuximab (an anti-EGFR) to classical chemotherapy (the FOLFOX4), only improve the outcome of patients with KRAS wild-type tumors. In that context, the KRAS gene is a binary treatment selection marker, but plenty of biomarkers result from some quantifications or dosage measurements. The first aim of this thesis is to quantify the global treatment selection ability of a biomarker. After a review of the existing litterature, a method based on an extension of ROC curves is proposed and compared to existing methods. Its main advantage is that it is non-parametric, and that it does not depend on the mean risk of event in each treatment arm. In a second time, when a quantitative treatment selection biomarker is assessed, there is a need to estimate a marker thereshold value above which one treatment is preferred, and below which the other treatment is recommended. An approach that relies on the definition of a utility function is proposed in order to take into account both efficacy and toxicity of treatments when estimating the optimal threshold. A Bayesian method for the estimation of the optimal threshold is proposed

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