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Asymmetrical Conductor with a Hole (T.E.A.M. Problem 7)

Miscellaneous with MagNet for Solidworks

This problem consists of a thick aluminum plate with a square hole placed to the side. A current-driven coil is placed over the aluminum plate. A sinusoidal current is used to drive the coil at two different frequencies. Using MagNet for SOLIDWORKS, the flux density in the test rig was predicted with an AC (time harmonic) simulation.

The following problem is based on the Testing Electromagnetic Analysis Methods (T.E.A.M.) problem #7: Asymmetrical Conductor with a Hole. The benchmark can be found on the International Compumag Society's website.

Alumunium plate with coil

METHODS and RESULTS

MAGNETIC FIELD

The in-phase component of the magnetic field (shown at a cross-section) with a source frequency of 50 Hz.

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INDUCED CURRENT in the ALUMINUM PLATE

The accurate calculation of induced currents is important in a time-harmonic problem with a model including a large conducting body. The sinusoidal driving waveform creates a sinusoidally time-varying magnetic field, inducing eddy currents in the aluminum plate. At the phase instant θ = 0°, the coil creates a varying upward magnetic field which induces a clockwise current in the aluminum plate right under the coil.

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FLUX DENSITY in the AIR GAP

All the points of interest in this model are situated in the air gap between the coil and the aluminum plate. This is an image of the flux density in the air gap at the phase instant θ = 0° when a 50 Hz current waveform is driving the coil. The coil's outline can be distinguished with the strength of the magnetic field on this mesh slice. It can be observed from this that, when away from the current driven coil, the magnetic field strength drops to nearly zero.

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COMPARING MEASURED vs. SIMULATED FLUX DENSITY

On the left is plotted the flux density along the line A1-B1 (y=72, z=34 mm) at the two frequencies that were studied in this problem. The flux density values obtained with MagNet for SOLIDWORKS are compared to the experimental values included in the problem's definition.

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FLUX DENSITY ALONG SECOND LINE

Here is a graph of the flux density along the line A2-B2 (y=144, z=34 mm) at the frequencies studied in this problem. The graph's first dip corresponds to the hole in the aluminum plate. It is followed by a peak that happens at the edge of the hole. The flux density is then somewhat constant when under the inside of the coil. It then drops again when under the coil. The two frequencies have similar values of flux density on the entire line. The values obtained are also compared to experimental values.

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