The topic of this thesis is a mathematically rigorous derivation of formulae for the magnetic force which is exerted on a part of a bounded magnetized body by its surrounding. Firstly, the magnetic force is considered within a continuous system based on macroscopic magnetostatics. The force formula in this setting is called Brown's force formula referring to W. F. Brown, who gave a mainly physically motivated discussion of it. This formula contains a surface integral which shows a nonlinear dependence on the normal. Brown assumes the existence of an additional term in the surface force which cancels the nonlinearity to allow an application of Cauchy's theorem in continuum mechanics to a magnetoelastic material. The proof of Brown's formula which is given in this work involves a suitable regularization of a hypersingular kernel and uses singular integral methods. Secondly, we consider a discrete, periodic setting of magnetic dipoles and formulate the force between a part of a bounded set and its surrounding. In order to pass to the continuum limit we start from the usual force formula for interacting magnetic dipoles. It turns out that the limit of the discrete force is different from Brown's force formula. One obtains an additional nonlinear surface term which allows one to regard Brown's assumption on the surface force as a consequence of the atomistic approach. Due to short range effects one obtains moreover an additional linear surface term in the continuum limit of the discrete force. This term contains a certain lattice sum which depends on a hypersingular kernel and the underlying lattice structure. / Das Thema dieser Arbeit ist eine mathematisch strenge Herleitung von Formeln für die magnetische Kraft, die auf einen Teil eines beschränkten, magnetischen Körpers durch seine Umgebung ausgeübt wird. Zunächst wird die magnetische Kraft in einem kontinuierlichen System auf Grundlage der makroskopischen Magnetostatik betrachtet. Mit Bezug auf W. F. Brown, der eine vor allem physikalisch motivierte Herleitung der Kraftformel gegeben hat, wird diese auch Brownsche Kraftformel genannt. Das Oberflächenintegral in dieser Formel zeigt eine nichtlineare Abhängigkeit von der Normalen. Um Cauchys Theorem aus der Kontinuumsmechanik in einem magnetoelastischen Material anwenden zu können, nimmt Brown an, dass die Oberflächenkraft einen zusäatzlichen Term enthält, der den nichtlinearen Ausdruck aufhebt. Der Beweis der Brownschen Kraftformel in dieser Arbeit beruht auf einer geeigneten Regularisierung eines hypersingulären Kerns und benutzt Methoden für singuläre Integrale. Danach gehen wir von einem diskreten, periodischen System von magnetischen Dipolen aus und betrachten die Kraft zwischen einem Teil einer beschränkten Menge und der Umgebung. Um zum Kontinuumslimes überzugehen, starten wir von der üblichen Kraftformel für wechselwirkende magnetische Dipole. Es zeigt sich, dass sich der Limes der diskreten Kraft von der Brownschen Kraftformel unterscheidet. Man erhält einen zusätzlichen nichtlinearen Oberflächenterm, der es ermöglicht, Browns Annahme als Konsequenz des atomistischen Zugangs zu sehen. Kurzreichweitige Effekte führen zudem zu einem linearen Oberflächenterm im Kontinuumlimes der diskreten Kraft. Dieser Zusatzterm enthält eine gewisse Gittersumme, die von einem hypersingulären Kern und der Struktur des zugrundeliegenden Gitters abhängt.

The topic of this thesis is a mathematically rigorous derivation of formulae for the magnetic force which is exerted on a part of a bounded magnetized body by its surrounding. Firstly, the magnetic force is considered within a continuous system based on macroscopic magnetostatics. The force formula in this setting is called Brown''s force formula referring to W. F. Brown, who gave a mainly physically motivated discussion of it. This formula contains a surface integral which shows a nonlinear dependence on the normal. Brown assumes the existence of an additional term in the surface force which cancels the nonlinearity to allow an application of Cauchy''s theorem in continuum mechanics to a magnetoelastic material. The proof of Brown''s formula which is given in this work involves a suitable regularization of a hypersingular kernel and uses singular integral methods. Secondly, we consider a discrete, periodic setting of magnetic dipoles and formulate the force between a part of a bounded set and its surrounding. In order to pass to the continuum limit we start from the usual force formula for interacting magnetic dipoles. It turns out that the limit of the discrete force is different from Brown''s force formula. One obtains an additional nonlinear surface term which allows one to regard Brown''s assumption on the surface force as a consequence of the atomistic approach. Due to short range effects one obtains moreover an additional linear surface term in the continuum limit of the discrete force. This term contains a certain lattice sum which depends on a hypersingular kernel and the underlying lattice structure. / Das Thema dieser Arbeit ist eine mathematisch strenge Herleitung von Formeln für die magnetische Kraft, die auf einen Teil eines beschränkten, magnetischen Körpers durch seine Umgebung ausgeübt wird. Zunächst wird die magnetische Kraft in einem kontinuierlichen System auf Grundlage der makroskopischen Magnetostatik betrachtet. Mit Bezug auf W. F. Brown, der eine vor allem physikalisch motivierte Herleitung der Kraftformel gegeben hat, wird diese auch Brownsche Kraftformel genannt. Das Oberflächenintegral in dieser Formel zeigt eine nichtlineare Abhängigkeit von der Normalen. Um Cauchys Theorem aus der Kontinuumsmechanik in einem magnetoelastischen Material anwenden zu können, nimmt Brown an, dass die Oberflächenkraft einen zusäatzlichen Term enthält, der den nichtlinearen Ausdruck aufhebt. Der Beweis der Brownschen Kraftformel in dieser Arbeit beruht auf einer geeigneten Regularisierung eines hypersingulären Kerns und benutzt Methoden für singuläre Integrale. Danach gehen wir von einem diskreten, periodischen System von magnetischen Dipolen aus und betrachten die Kraft zwischen einem Teil einer beschränkten Menge und der Umgebung. Um zum Kontinuumslimes überzugehen, starten wir von der üblichen Kraftformel für wechselwirkende magnetische Dipole. Es zeigt sich, dass sich der Limes der diskreten Kraft von der Brownschen Kraftformel unterscheidet. Man erhält einen zusätzlichen nichtlinearen Oberflächenterm, der es ermöglicht, Browns Annahme als Konsequenz des atomistischen Zugangs zu sehen. Kurzreichweitige Effekte führen zudem zu einem linearen Oberflächenterm im Kontinuumlimes der diskreten Kraft. Dieser Zusatzterm enthält eine gewisse Gittersumme, die von einem hypersingulären Kern und der Struktur des zugrundeliegenden Gitters abhängt.

<p>Induction machines convert more than 55% of electrical energy into various other forms in industrial and domestic environments. Improved performance, especially by reduction of losses in induction machines hence can significantly reduce consumption of electricity. Many design and control methods are adopted to make induction machines work more efficiently, however certain design compromises are inevitable, such as skewing the rotor to improve the magnetic noise and torque characteristics increase the cross current losses considerably in a cage rotor, degrading the efficiency of the motor. Crosscurrent losses are the dominating stray losses which are dependent on several factors among them are percentage skew and the contact resistance between the rotor bars and laminations. It is shown in this thesis that implementing a design change which has non-skewed asymmetrical distribution of rotor slots can serve the same purpose as skewing i.e., reduction of the magnetic noise, thereby avoiding the negative effects of skewing the rotor slots especially by reducing the cross-current losses.</p><p>Two design ethodologies to introduce asymmetry in rotor slots are proposed and the key performance characteristics like torque ripple, radial air gap forces are computed both numerically and analytically. Radial forces obtained from the finite element method are coupled to the analytical tool forcalculating the magnetic noise. A spectral method to calculate and separate the radial forces into vibration modes and their respective frequencies is proposed and validated for a standard 4-pole induction motor. The influence of rotor slot number, eccentricity and skew on radial forces and magnetic noise are studied using finite element method in order to understand the vibrational and acoustic behavior of the machine, especially for identifying their sources. The validated methods on standard motors are applied for investigating the asymmetrical rotor slot machines.</p><p>Radial air gap forces and magnetic noise spectra are computed for the novel dual and sinusoidal symmetrical rotors and compared with the standard symmetrical rotor. The results obtained showed reduced radial forces and magnetic noise in asymmetrical rotors, both for the eccentric and noneccentric cases. Based on the results obtained some guide lines for designing  asymmetrical rotor slots are established. Magnitudes of the harmful modes of vibration observed in the eccentric rotors, which usually occur in reality, are considerably reduced in asymmetrical rotors showing lower sound intensity levels produced by asymmetrical rotors. The noise level from mode-2 vibration in a 4-pole standard 15 kW motor running with 25% static eccentricity is decreased by about 6 dB, compared to the standard rotors. Hence improved performance can be achieved by removing skew which reduces cross current losses and by employing asymmetrical rotor slots same noise level can be maintained or can be even lowered.</p><p> </p><p> </p>

Vacuum bags in conjunction with autoclaves are currently employed to generate the consolidation pressures and temperatures required to manufacture aerospace level composites. As the scale of continuous fiber composite structures increases autoclaving becomes prohibitively expensive or impossible. The objective of this work is to develop flexible magnetic clamping structures to increase the consolidation pressure in conventional vacuum bagging of composite laminates, thereby obviating the need for an autoclave. A ferromagnetic rubber, which consists of rubber filled with iron, is being developed as a conformable and reusable vacuum bag that provides increased consolidation through attractive forces produced by electromagnets. Experiments and finite element modeling indicate that consolidation pressure in the range of 100 kPa can be generated by such a device with realistic power requirements. The effects of the magnetic clamping device process parameters on the consolidation pressure magnitude are modeled and characterized. In addition, a method for the efficient design of the magnetic clamping device is developed.

The continuously increasing demand for clean renewable energy has rekindled interest in multi-terminal high voltage direct current (HVDC) grids. Although such grids have several advantages and a great potential, their materialization has been thwarted due to the absence of HVDC breakers. In comparison with traditional alternating current (AC) breakers, they should operate and interrupt fault currents in a time frame of a few milliseconds. The aim of this thesis is focused on the design of ultra-fast electro-mechanical actuator systems suitable for such HVDC breakers.Initially, holistic multi-physics and hybrid models with different levels of complexity and computation time were developed to simulate the entire switch. These models were validated by laboratory experiments. Following a generalized analysis, in depth investigations involving simulations complemented with experiments were carried out on two of the sub-components of the switch: the ultra-fast actuator and the damper. The actuator efficiency, final speed, peak current, and maximum force were explored for different design data.The results show that models with different levels of complexity should be used to model the entire switch based on the magnitude of the impulsive forces. Deformations in the form of bending or elongation may deteriorate the efficiency of the actuator losing as much as 35%. If that cannot be avoided, then the developed first order hybrid model should be used since it can simulate the behavior of the mechanical switch with a very good accuracy. Otherwise, a model comprising of an electric circuit coupled to an electromagnetic FEM model with a simple mechanics model, is sufficient.It has been shown that using a housing made of magnetic material such as Permedyn, can boost the efficiency of an actuator by as much as 80%. In light of further optimizing the ultra-fast actuator, a robust optimization algorithm was developed and parallelized. In total, 20520 FEM models were computed successfully for a total simulation time of 7 weeks. One output from this optimization was that a capacitance of 2 mF, a charging voltage of 1100 V and 40 turns yields the highest efficiency (15%) if the desired velocity is between 10 m/s and 12 m/s.The performed studies on the passive magnetic damper showed that the Halbach arrangement gives a damping force that is two and a half times larger than oppositely oriented axially magnetized magnets. Furthermore, the 2D optimization model showed that a copper thickness of 1.5 mm and an iron tube that is 2 mm thick is the optimum damper configuration. / <p>QC 20150422</p>

In a synchronous machine, radial, tangential, and axial forces are generated. In this thesis, three different technologies to control them are proposed. The first one, involves the utilization of the radial forces that arise between the rotor and the stator. This is achieved by segmenting the rotor field winding into groups of poles and controlling their corresponding magnetization individually. This technology is particularly useful to achieve magnetic balance and to create controllable radial forces. The second technology, involves the control of the rotor field in order to influence the tangential forces that produce torque. This is achieved by inverting the rotor field winding polarity with respect to the stator field. With this technique, breaking and accelerating torques can be created. It is particularly useful to start a synchronous machine. Finally, the application of axial forces with a magnetic thrust bearing is discussed. The main benefits of this technology are higher efficiency and increased reliability. The work presented in this thesis was carried out within the Division of Electricity in the Department of Engineering Sciences at Uppsala University. It is based on original research supported by analytical calculations, computational simulations and extensive experimental work.

Induction machines convert more than 55% of electrical energy into various other forms in industrial and domestic environments. Improved performance, especially by reduction of losses in induction machines hence can significantly reduce consumption of electricity. Many design and control methods are adopted to make induction machines work more efficiently, however certain design compromises are inevitable, such as skewing the rotor to improve the magnetic noise and torque characteristics increase the cross current losses considerably in a cage rotor, degrading the efficiency of the motor. Crosscurrent losses are the dominating stray losses which are dependent on several factors among them are percentage skew and the contact resistance between the rotor bars and laminations. It is shown in this thesis that implementing a design change which has non-skewed asymmetrical distribution of rotor slots can serve the same purpose as skewing i.e., reduction of the magnetic noise, thereby avoiding the negative effects of skewing the rotor slots especially by reducing the cross-current losses. Two design ethodologies to introduce asymmetry in rotor slots are proposed and the key performance characteristics like torque ripple, radial air gap forces are computed both numerically and analytically. Radial forces obtained from the finite element method are coupled to the analytical tool forcalculating the magnetic noise. A spectral method to calculate and separate the radial forces into vibration modes and their respective frequencies is proposed and validated for a standard 4-pole induction motor. The influence of rotor slot number, eccentricity and skew on radial forces and magnetic noise are studied using finite element method in order to understand the vibrational and acoustic behavior of the machine, especially for identifying their sources. The validated methods on standard motors are applied for investigating the asymmetrical rotor slot machines. Radial air gap forces and magnetic noise spectra are computed for the novel dual and sinusoidal symmetrical rotors and compared with the standard symmetrical rotor. The results obtained showed reduced radial forces and magnetic noise in asymmetrical rotors, both for the eccentric and noneccentric cases. Based on the results obtained some guide lines for designing  asymmetrical rotor slots are established. Magnitudes of the harmful modes of vibration observed in the eccentric rotors, which usually occur in reality, are considerably reduced in asymmetrical rotors showing lower sound intensity levels produced by asymmetrical rotors. The noise level from mode-2 vibration in a 4-pole standard 15 kW motor running with 25% static eccentricity is decreased by about 6 dB, compared to the standard rotors. Hence improved performance can be achieved by removing skew which reduces cross current losses and by employing asymmetrical rotor slots same noise level can be maintained or can be even lowered. / QC 20110221

Nous étudions l'effet thermo-électrique et les phénomènes qui en résultent, forces et les courants thermoélectriques (TEC) sous l'action d'un champ magnétique externe imposé lors de la solidification d'alliages métalliques. Nous avons utilisé des simulations numériques, des observations directes et des examens de laboratoire. L'interaction entre les courants thermo-électriques et le champ magnétique externe lors de la solidification se produit des forces électromagnétiques et donc un écoulement du métal liquide. Le résultat est nommé effet magnétique thermoélectrique (TEME). Les formulations de TEC, les forces et les équations gouvernant les écoulements TEM sont donnés. Afin de mieux prouver l'existence de la TEME, des expériences par méthode d'imagerie à rayons X menées au synchrtron ont été utilisées pour observer in-situ et en temps réel l'action directe des forces et les mouvements TEM pendant la solidification directionnelle des alliages Al-Cu. Nous avons montré la cohérence raisonnable entre les calculs analytiques et des simulations numériques qui ont exécuté avec les mêmes conditions de traitement. En outre, la capacité des écoulements thermo-électriques à influer sur la microstructure lors de la solidification directionnelle sont expérimentalement évaluées dans les autres cas en réalité. La solidification directionnelle d'une seule phase de formation des alliages Al-Cu sous divers champs magnétiques montre que les écoulements TEM sont capables de modifier la forme de l'interface liquide-solide conduisant à des morphologies différentes. L'effet le plus intense se produit dans différents champs magnétiques pour différentes morphologies, en effet, le champ magnétique élevé est nécessaire pour la morphologie a une plus petite longueur typique. Ceci est en accord avec le comportement des vitesses de TEM qui varient avec les champs magnétiques imposés ainsi que les différentes échelles de longueur typique. Cette variation est confirmée par des simulations numériques 3D. Nous montrons que les dendrites primaires et à l'avant de la phase eutectique, peuvent être modifiés par les mouvements TEM et les forces de TEM dans le solide pour améliorer la croissance de la phase de Al2Cu facettes primaire pendant la solidification des Al-40wt%Cu hypereutectiques. Le mécanisme de renforcement de la croissance de la phase facettes Al2Cu est confirmé par la transmission électronique observation au microscope, et la raison de la formation de la structure de croissance de couple de Al-26wt% Cu alliages est vérifiée par le test de l'analyse thermique différentielle. Ainsi, nous pouvons affirmer que le champ magnétique élevé facilite la formation de la structure de la croissance de couple pour hypoeutectiques alliages Al-Cu, et favorise la croissance de la phase Al2Cu primaire pour hypereutectiques Al-Cu alliages. / We have investigated the thermoelectric magnetic (TEM) forces and flows resulting from the interaction between the internal thermoelectric currents (TEC) and the imposed external magnetic field during solidification. Numerical simulations, direct observations and experimental examinations were undertaken. As the natural phenomenon, TEC was discovered almost 200 years ago, therefore, our introduction begins from then on. It is shown that the interaction between TEC and external magnetic field during solidification in the cont put forth new interesting phenomena in the context of a rising field named Electromagnetic Processing of Materials. After that, it is discussed how the TEC appear and the TEM effect (TEME, referring to both TEM forces and flows) behaves at the liquid-solid interface in directional solidification under external magnetic field. Meanwhile, formulations of TEC, TEM forces and flows are given, and numerical simulations of TEME are performed to visually display the TEM forces and flows. In order to further prove the existence of TEME, in situ synchrotron X-ray imaging method was used to observe the direct resultant of TEM forces and flows during directionally solidifying the Al-Cu alloys. The observations show reasonable consistency with the analytical calculations and numerical simulations performed with the same process conditions. Except confirmation the existence of TEME, its abilities to affect the microstructure during directional solidification are experimentally investigated in the more realistic cases. The single phase forming Al-Cu alloys are directionally solidified under various magnetic fields, which shows that TEM flows are capable to modify the shape of liquid-solid interface, and the most intensive affect occurs under different magnetic fields for different interface morphologies. Indeed, the smaller the typical length of the morphology is the higher the magnetic field is needed. This agrees with the estimating regulation of the velocity of TEM flows changing with magnetic fields for different typical length scales, and is confirmed by 3D numerical simulations. Directional solidification of multiphase forming Al-Cu alloys under various magnetic fields shows that the mushy zone length (distance between the front of primary dendrites and eutectic phases) varies with the magnetic fields, which can be attributed to the redistribution of rejected solutes by TEM flows. In addition, apparent enhanced growth of the primary faceted Al2Cu phase is founded when Al-40wt%Cu alloys are solidified under sufficient high magnetic fields, this should be ascribed to the TEM forces acting on the solid because strains are able to lead the formation of defects and thus benefit to the growth of faceted phase. This is confirmed by comparison of the dislocations in samples solidified without and with a 10T magnetic field via transmission electron microscopy observation. In another aspect, an almost entire couple growth structure is achieved when Al-26wt%Cu alloys are directionally solidified under a 4T magnetic field, which can be explained by the effect of high magnetic field on changing the nucleation temperature and growth velocity of each phase. Moreover, the differential thermal analysis test on the nucleation temperature of both α-Al and eutectic phases verified this explanation. Therefore, we conclude that high magnetic field facilitates the formation of couple growth structure for hypoeutectic Al-Cu alloys, reversely, enhances the growth of primary dendrite for hypereutectic Al-Cu alloys.