Contents
The paper deals with a practical method for the synthesis of two-dimensional magnetic fields. The proposed algorithm makes it possible to determine the optimal structure of areas and optimal source distribution which generate the required magnetic fields. The main idea of this algorithm is based on the application of a modified gradient method for solving the overdetermined, nonlinear system of algebraic equations obtained by the finite element method. Numerical calculations performed in 5 examples demonstrate possible applications of the proposed method.
Übersicht
Die Arbeit behandelt eine praktische Methode zur Synthese von zweidimensionalen Magnetfeldern. Das vorgeschlagene Verfahren ermöglicht die Berechnung der optimalen Form von Gebieten und optimalen Quellenverteilungen zur Erzeugung vorgegebener Magnetfelder. Die Grundidee des Berechnungsverfahrens basiert auf der Anwendung einer modifizierten Gradientenmethode zur Lösung von nichtlinearen, überbestimmten Gleichungssystemen, die mit der Methode der finiten Elemente entwickelt wurden. Numerische Berechnungen von 5 Beispielen illustrieren die Anwendungsbreite der vorgeschlagenen Methode.
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Abbreviations
- A,A :
-
vector potential
- J, J:
-
current density
- M,M x ,M y :
-
magnetic polarization
- ν x ,ν y :
-
reluctivity
- μ r :
-
permeability
- e x ,e y ,e z :
-
unit vectors
- B,B x ,B y :
-
flux density
- B o ,B ox ,B oy :
-
flux density in the synthesis region
- G :
-
region under investigation
- G 0 :
-
synthesis region
- F :
-
functional
- Q :
-
quality criterion
- r k :
-
direction vector
- r 0 :
-
minimal least squares solution
- e :
-
error vector
- z :
-
solution vector
- β min :
-
step-length factor
- D :
-
Jacobi matrix
- R :
-
Moore-Penrose pseudoinverse
- δ1, δ2, δ3 :
-
error criterion
- N :
-
number of points
- m :
-
number of equations
- n :
-
number of unknowns
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Palka, R. Synthesis of magnetic fields by optimization of the shape of areas and source distributions. Archiv f. Elektrotechnik 75, 1–7 (1991). https://doi.org/10.1007/BF01576118
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DOI: https://doi.org/10.1007/BF01576118