Electromagnetic Problems Solving by Conformal Mapping: A Mathematical Operator for Optimization

Calixto, Wesley P.; Alvarenga, Bernardo Pinheiro de; Mota, J. C. da; Brito, Leonardo da Cunha; Wu, Marcel; Alves, Aylton J.; Neto, Luciano Martins; Antunes, Carlos Lemos

doi:10.1155/2010/742039

Cited by 12 publications

(9 citation statements)

References 5 publications

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“…, t k are the points in the canonical domain (in the T-plane) corresponding to the polygon corners. The analytical solution of Equation (20) is very difficult for geometries with more than three vertices [22], therefore, the SC Toolbox provides a numerical solution by a library of command-line functions which could be seen in [19]. In this paper, the rectangle domain (T-plane) is created by calling f = correctmap (p, alpha), p is the point and alpha is the corresponding angle as shown in Figure 5.…”

Section: Model Of Stator Slottingmentioning

confidence: 99%

Analytical Modeling of Static Eccentricities in Axial Flux Permanent-Magnet Machines with Concentrated Windings

et al. 2016

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Abstract:The aim of this paper is to calculate the static eccentricity (SE) of a double rotor axial flux permanent magnet (AFPM) machine by using a general analytical model. The flux density in the air gap under healthy conditions is calculated firstly, where the axial and circumferential magnetic flux densities are obtained using a coupled solution of Maxwell's equations and Schwarz-Christoffel (SC) mapping. The magnetic flux densities under SE conditions are calculated afterwards using a novel bilinear mapping. Some important electromagnetic parameters, e.g., back electromotive force (EMF), cogging torque and electromagnetic (EM) torque, are calculated for both SE and healthy conditions, and compared with the finite element (FE) model. As for the double rotor AFPM, SE does not contribute much effect on the back EMF and EM torque, while the cogging torque is increased. At each calculated section, FE models were built to validate the analytical model. The results show that the analytical predictions agree well with the FE results. Finally, the results of analytical model are verified via experimental results.

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Section: Model Of Stator Slottingmentioning

confidence: 99%

Analytical Modeling of Static Eccentricities in Axial Flux Permanent-Magnet Machines with Concentrated Windings

et al. 2016

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“…Equation (21) shows that in a three dimensional space, the integral of the dot product ⋅ B A d on a closed surface is only related to the magnetic charge contained inside the chosen surface.…”

Section: Gauss's Law On Magnetismmentioning

confidence: 99%

A discussion ofBlconservation on a two dimensional magnetic field plane in watt balances

Zhao

Huang

2016

Meas. Sci. Technol.

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The watt balance is an experiment being pursued in national metrology institutes for precision determination of the Planck constant h. In watt balances, the 1/r magnetic field, expected to generate a geometrical factor Bl independent to any coil horizontal displacement, can be created by a strict two dimensional, symmetric (horizontal r and vertical z) construction of the magnet system. In this paper, we present an analytical understanding of magnetic field distribution when the r symmetry of the magnet is broken and the establishment of the Bl conservation is shown. By using either Gauss's law on magnetism with monopoles or conformal transformations, we extend the Bl conservation to arbitrary two dimensional magnetic planes where the vertical magnetic field component equals zero. The generalized Bl conservation allows a relaxed physical alignment criteria for watt balance magnet systems. II. REVIEW OF AN IDEAL CASE WITH 1/r MAGNETIC FIELDThe analysis in this article is based on one of the most popular watt balance magnets employed 4,5,15,16 . Figure 1 shows the construction of the magnet with a symmetrical structure in both the r and z axes. The magnetic flux, generated by two permanent magnet disks oriented in repulsion, is guided by yokes of high permeability material through an air gap radi-

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“…As a matter of example, we should keep in mind that the BHF's given by Eqs. (34,35) for the concentric spheres are purely geometrical so far. If we want to solve a physical problem such as the electrostatic potential in the volume defined by b < r < a, when the two spherical surfaces are at potentials φ b and φ a , such a potential is given by Eq.…”

Section: Bhf's For Two Concentric Cylindersmentioning

confidence: 99%

“…Solutions of Laplace's equation, usually called Harmonic Functions (HF's) are very important in many branches of Physics and Engineering such as electrostatics, gravitation, hydrodynamics and thermodynamics [1,2]. Therefore, considerable effort has been done in solving Laplace's equation [28]- [35] in a variety of geometries and boundary conditions. On the other hand, the capacitance of electrostatic conductors is a very important quantity since capacitors are present in many electric and electronic devices [12]- [14].…”

Section: Introductionmentioning

confidence: 99%

Solutions of Laplace's equation with simple boundary conditions, and their applications for capacitors with multiple symmetries

Morales

Díaz

Herrera

2015

Journal of Electrostatics

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We find solutions of Laplace's equation with specific boundary conditions (in which such solutions take either the value zero or unity in each surface) using a generic curvilinear system of coordinates. Such purely geometrical solutions (that we shall call Basic Harmonic Functions BHF's) are utilized to obtain a more general class of solutions for Laplace's equation, in which the functions take arbitrary constant values on the boundaries. On the other hand, the BHF's are also used to obtain the capacitance of many electrostatic configurations of conductors. This method of finding solutions of Laplace's equation and capacitances with multiple symmetries is particularly simple, owing to the fact that the method of separation of variables becomes much simpler under the boundary conditions that lead to the BHF's. Examples of application in complex symmetries are given. Then, configurations of succesive embedding of conductors are also examined. In addition, expressions for electric fields between two conductors and charge densities on their surfaces are obtained in terms of generalized curvilinear coordinates. It worths remarking that it is plausible to extrapolate the present method to other linear homogeneous differential equations.

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Electromagnetic Problems Solving by Conformal Mapping: A Mathematical Operator for Optimization

Cited by 12 publications

References 5 publications

Analytical Modeling of Static Eccentricities in Axial Flux Permanent-Magnet Machines with Concentrated Windings

Analytical Modeling of Static Eccentricities in Axial Flux Permanent-Magnet Machines with Concentrated Windings

A discussion ofBlconservation on a two dimensional magnetic field plane in watt balances

Solutions of Laplace's equation with simple boundary conditions, and their applications for capacitors with multiple symmetries

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