Publication: Fundamentos de ingeniería de mecanismos compuestos por imanes y superconductores en estado Meissner
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2011-12
Defense date
2012-03-09
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Abstract
A partir del desarrollo analítico para el cálculo de fuerzas entre superconductores e imanes basado en el modelo Pérez-Díaz/García-Prada (PDGP) hemos extendido su definición al cálculo de pares entre superconductores e imanes en estado Meissner completo. De las expresiones resultantes se han derivado varias pautas para la optimización y diseño de mecanismos levitantes. Hemos desarrollado un algoritmo para poder utilizar el modelo PDGP en programas de elementos finitos. Hemos estudiado además la sensibilidad a la caracterización del mallado. Hemos verificado experimentalmente la validez de estos algoritmos basados en el modelo PDGP mediante dos procedimientos. El primero basado en medidas de fuerza entre imán y superconductor y el segundo midiendo el ángulo de alineamiento entre imán y superconductor. En ambos casos obtenemos un buen acuerdo entre experimento y predicción teórica. Además, se ha demostrado que existe un fenómeno de alineamiento mecánico entre imanes y superficies superconductoras. Se ha estudiado este efecto analizando parámetros como el tamaño del imán y la altura sobre el superconductor. El acuerdo entre las medidas de fuerza y los valores calculados ha sido lo suficientemente bueno que nos ha permitido desarrollar un método mecánico para la determinación del campo de penetración inicial para superconductores de tipo II. Este método ha resultado ser más simple que los habituales hasta la fecha, además de proporcionar información adicional como la localización de la penetración inicial que otros métodos no pueden. Hemos utilizado las herramientas desarrolladas y verificadas para su cálculo en aplicaciones mecánicas concretas. Hemos calculado el comportamiento de un imán sobre una esfera superconductora comparando nuestros resultados con los obtenidos mediante otras expresiones para el cálculo de fuerzas basadas en el método de las imágenes. En una segunda aplicación, hemos aplicado el modelo para el cálculo de la interacción entre imán y superconductor toroidal demostrando que existe un efecto de volteo (o flip effect) entre un imán y un superconductor toroidal que puede ser utilizado en mecanismos levitantes. ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Pérez-Díaz/García-Prada have proposed a model for the calculation of forces between magnets and superconductors in the Meissner state (PDGP model). This model has been extended to include a calculation of torque. From this extended model we have derived some guidelines for the design and optimization of levitating mechanisms. A FEM algorithm was programmed in order to use the PDGP model in a practical and universal way. We also studied the model’s sensitivity to the refinement of the mesh. This algorithm, based on the PDGP model, has been experimentally verified by the following two procedures. The first was based on the force measured between a magnet and a superconductor. The second measured the alignment angle between a magnet and a superconductor. Both procedures supported the experimental and theoretical predictions. Furthermore, a mechanical alignment effect between magnet and superconductor surfaces has been shown. This agreement is strong enough that we can develop a mechanical method for determining the first penetration field for type II superconductors. This method turns out to be simpler and intrinsically more precise than other methods and additionally, it can provide not only the value of the first penetration, but also the point where that first penetration of the field takes place. Finally, we have used the tools that have been developed and verified to calculate some specific mechanical applications. We have calculated the mechanical behavior of a magnet over a superconducting sphere, comparing our results to those obtained by other expressions based on the method of the images. In a second application, we have used the tools based on the PDGP model in order to calculate the mechanical interaction of a magnet and a superconducting torus; a flip effect on the stable orientation between a magnet and a superconducting torus was demonstrated. This effect could be used to design different levitating mechanisms.
Pérez-Díaz/García-Prada have proposed a model for the calculation of forces between magnets and superconductors in the Meissner state (PDGP model). This model has been extended to include a calculation of torque. From this extended model we have derived some guidelines for the design and optimization of levitating mechanisms. A FEM algorithm was programmed in order to use the PDGP model in a practical and universal way. We also studied the model’s sensitivity to the refinement of the mesh. This algorithm, based on the PDGP model, has been experimentally verified by the following two procedures. The first was based on the force measured between a magnet and a superconductor. The second measured the alignment angle between a magnet and a superconductor. Both procedures supported the experimental and theoretical predictions. Furthermore, a mechanical alignment effect between magnet and superconductor surfaces has been shown. This agreement is strong enough that we can develop a mechanical method for determining the first penetration field for type II superconductors. This method turns out to be simpler and intrinsically more precise than other methods and additionally, it can provide not only the value of the first penetration, but also the point where that first penetration of the field takes place. Finally, we have used the tools that have been developed and verified to calculate some specific mechanical applications. We have calculated the mechanical behavior of a magnet over a superconducting sphere, comparing our results to those obtained by other expressions based on the method of the images. In a second application, we have used the tools based on the PDGP model in order to calculate the mechanical interaction of a magnet and a superconducting torus; a flip effect on the stable orientation between a magnet and a superconducting torus was demonstrated. This effect could be used to design different levitating mechanisms.
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Ingeniería de mecanismos, Imanes, Superconductores, Magnetismo, Efecto Meissner