A Numerical Model for the Search of the Optimum Capacitance in Electromagnetic Metal Forming

Otín, Rubén; Mendez, Roger; Fruitos, Oscar

doi:10.1063/1.3623705

Cited by 5 publications

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“…For instance, the RM-Nodal formulation can converge in less than 5000 QMR iterations in problems with more than 2e6 second order elements (∼ 7e6 unknowns in the RMNodal formulation, ∼ 12e6 unknowns in the CC-Edge formulation) and element size differences of two orders of magnitude. The RM-Nodal formulation was also applied to the computing of eddy currents and Lorentz forces in the low frequency regime [3], retaining the same good behavior.…”

Section: Discussionmentioning

confidence: 99%

“…Therefore, although the regularized formulation had been applied successfully to a wide variety of problems (e.g., specific absorption rate computations [2,14,15], microwave engineering [1], electromagnetic compatibility [16], electromagnetic forming [3]) there is a question that remains unanswered: Is it worthy the investment of time and effort in the more complex implementation and modeling of the regularized formulation?. This is the question we try to answer in this work.…”

Section: Introductionmentioning

confidence: 99%

“…This formulation is described in [1]. There are several reasons to study this approach: It offers spurious-free solutions and well-conditioned matrices even at low frequencies [2,3]. Only the three components of E, or H, are the unknowns (there is no need of extra functions such as Lagrange multipliers or scalar potentials [4]).…”

Section: Introductionmentioning

confidence: 99%

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Computational Performance of a Weighted Regularized Maxwell Equation Finite Element Formulation

Otín¹,

Garcı́a-Castillo²,

Martínez-Fernández³

et al. 2013

PIER

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Abstract-The aim of this work is to asses the computational performance of a finite element formulation based on nodal elements and the regularized Maxwell equations. We analyze the memory requirements and the condition number of the matrix when the formulation is applied to electromagnetic engineering problems. As a reference, we solve the same problems with the best known finite element formulation based on edge elements and the double curl Maxwell equations. Finally, we compare and discuss the computational efficiency of both approaches.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Computational Performance of a Weighted Regularized Maxwell Equation Finite Element Formulation

Otín¹,

Garcı́a-Castillo²,

Martínez-Fernández³

et al. 2013

PIER

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“…Therefore, our frequency domain approach can be very useful for coil design and for testing modeling conditions on complex three-dimensional geometries. Also, it can be used to estimate the optimum frequency and capacitance at which the maximum work piece deformation is attained for a given initial energy and a given set of coil and work piece [26,29].…”

Section: Introductionmentioning

confidence: 99%

A frequency domain approach for computing the Lorentz force in electromagnetic metal forming

Otín

Mendez

Fruitos

2014

JAE

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In this paper we present a finite element model in frequency domain which computes the Lorentz force that drives an electromagnetic forming (EMF) process. The only input data required are the electrical parameters of the capacitor bank, the coil and the work piece. The main advantage of this approach is that it provides an explicit relation between the parameters of the EMF process and the frequency of the discharge, which is a key parameter in the design of an optimum EMF system. The method is computationally efficient because it only requires to solve time-harmonic Maxwell's equations for a few frequencies and it can be very useful for coil design and for testing modeling conditions on complex three-dimensional geometries.

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“…The model is applied to different forming processes and the results compared with theoretical predictions and measurements of other authors. The work described in this chapter has been presented in [79,80] and it is part of the project SICEM (SImulación multifísica para el diseño de Conformado ElectroMagnético), Spanish MEC National R+D Plan 2004-2007, ref. : DPI2006-15677-C02-01.…”

Section: Electromagnetic Metal Formingmentioning

confidence: 99%

Regularized Maxwell equations and nodal finite elements for electromagnetic field computations in frequency domain

Otín

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En esta tesis se presenta una alternativa a la formulación clásica de elementos finitos basada en elementos de arista (edge elements) y las ecuaciones de Maxwell curl-curl. Este enfoque alternativo se basa en elementos nodales y las ecuaciones de Maxwell regularizadas. Las ventajas son que, sin añadir incógnitas adicionales (tales como los multiplicadores de Lagrange), ofrece soluciones sin modos espurios y matrices bien acondicionadas. Además, su representación integral tiene en un orden de singularidad inferior (orden 1 en vez de 3), lo que la hace más adecuada para la hibridación con técnicas numéricas basadas en métodos integrales. Por otro lado, surgen nuevas dificultades que no estaban presentes en la formulación clásica. El principal inconveniente es que se obtiene una solución globalmente errónea si el campo electromagnético tiene una singularidad en el dominio del problema. Además, las condiciones de contorno y las discontinuidades de los campos al cambiar de medio son más laboriosas de implementar. Este trabajo explica la manera de superar estas dificultades y demuestra que se pueden obtener soluciones precisas con elementos nodales y la formulación regularizada. También se presenta ERMES, un código en C++ que es la implementación de la formulación de elementos finitos mencionada en el párrafo anterior. Calcularemos con ERMES los parámetros de scattering de filtros de microondas y la tasa de absorción específica inducida en un cuerpo cuando está expuesto a campos electromagnéticos. ERMES es también la herramienta de cálculo utilizado en dos nuevos modelos numéricos presentados por primera vez en esta tesis. El primer modelo sirve para caracterizar procesos de conformado electromagnético y el segundo para obtener la impedancia de transferencia del apantallamiento de cables coaxiales perforados. El modelo de conformado electromagnético calcula la fuerza de Lorentz impulsora del proceso y estima a su vez la frecuencia óptima a la que puede obtenerse la deformación máxima de la pieza. La principal ventaja del método es que proporciona una relación explícita entre la capacidad del banco de condensadores y la frecuencia de la descarga, que es un parámetro clave en el diseño de un sistema de conformado electromagnético. El uso de la formulación regularizada en esta aplicación pone de manifiesto su excelente comportamiento en problemas de baja frecuencia (cuasi-estáticos). El segundo modelo presentado en este trabajo calcula la impedancia de transferencia de los apantallamientos perforados de cables coaxiales. Este modelo reproduce el comportamiento en alta frecuencia de la impedancia de transferencia con mayor precisión que los métodos encontrados en la literatura y, además, es capaz de analizar una mayor variedad de geometrías y materiales. In this thesis, we present an alternative approach to the usual finite element formulation based on edge elements and double-curl Maxwell equations. This alternative approach is based on nodal elements and regularized Maxwell equations. The advantages are that, without adding extra unknowns (such as Lagrange multipliers), it provides spurious-free solutions and well-conditioned matrices. Besides, its integral representation involves a less singular kernel (order 1 instead of 3), which makes this approach best suited to hybridization with integral numerical techniques. On the other hand, new difficulties arise that were not present in the classical formulation. The main drawback is that a globally wrong solution is obtained when the electromagnetic field has a singularity in the problem domain. Also, boundary conditions and field discontinuities are more laborious to implement. This work explains how to overcome these difficulties and demonstrates that accurate solutions can be obtained with nodal elements and the regularized formulation. We also present ERMES, the C++ implementation of the finite element approach depicted above and the main deliverable of this work. We compute with ERMES the scattering parameters of microwave filters and the specific absorption rate induced in a body when exposed to electromagnetic fields. ERMES is also the computational tool used in two novel numerical models introduced in this thesis. The first one characterizes electromagnetic metal forming processes and the second one the transfer impedance of cable shields. The electromagnetic metal forming model calculates the driving Lorentz force and estimates the optimum frequency at which it is attained the maximum workpiece deformation. The main advantage of the approach is that it provides an explicit relation between the capacitance of the capacitor bank and the frequency of the discharge, which is a key parameter in the design of an electromagnetic forming system. The use of the regularized formulation in this application reveals its excellent behavior in the low-frequency (quasi-static) regime. The second numerical model introduced in this work computes the transfer impedance of cable shields. The model reproduces the high frequency behavior of the transfer impedance more accurately than the approaches found in the literature and, moreover, it is able to analyze a wider variety of geometries and materials.

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A Numerical Model for the Search of the Optimum Capacitance in Electromagnetic Metal Forming

Cited by 5 publications

References 0 publications

Computational Performance of a Weighted Regularized Maxwell Equation Finite Element Formulation

Computational Performance of a Weighted Regularized Maxwell Equation Finite Element Formulation

A frequency domain approach for computing the Lorentz force in electromagnetic metal forming

Regularized Maxwell equations and nodal finite elements for electromagnetic field computations in frequency domain

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