Overview
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Cogging torque is produced as a motor rotates. Problems such as a reduction
in efficiency, vibrations, and noise can be improved by reducing the amount
of cogging torque that occurs.
One factor that affects the cogging torque is the direction the magnets
are magnetized.
This example presents the use of a magnetic field analysis to obtain the
surface magnetic flux density for the radial pattern, parallel anisotropy
pattern, and the polar anisotropy pattern of magnets. Furthermore, the
flux linkage, induced voltage, and cogging torque are obtained for an SPM
motor that uses magnets with these magnetization patterns. |
Surface Magnetic Flux Density
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The surface magnetic flux density for magnets with a radial pattern, a
parallel anisotropy pattern, and a polar anisotropy pattern are indicated
in Fig. 1. Furthermore, the decay of the radial pattern and parallel anisotropic
pattern are compared at 10 degrees, 20 degrees, and 30 degrees. The polar
anisotropy is compared using the distance from the center pole.
When the magnetization direction of the magnets is compared, the radial
pattern is closest to a trapezoid, but the waveform of the parallel anisotropy
pattern and polar anisotropy pattern are the closest to a sinusoidal waveform.
The waveform of the induced voltage and the flux linkage can be calculated
as closer to sinusoidal waveform for the parallel anisotropy and polar
anisotropy patterns than the radial pattern.
Furthermore, the radial pattern and parallel anisotropy are closer to a
sinusoidal waveform the larger the angle of the decay.
The waveform of the polar anisotropy pattern is closer to a sinusoidal
waveform the further the distance is from the center pole. However, the
distance from the center pole is optimum at 15.35 mm because the waveform
when r=16.35 has a higher magnetic flux density around 45 degrees. |
Induced Voltage, Flux Linkage, and Cogging Torque
The induced voltage for the radial pattern, parallel anisotropy pattern,
and polar anisotropy pattern are indicated in Fig. 2, the flux linkage
in Fig. 3, and the cogging torque in Fig. 4.
When the induced voltage waveform is compared for each pattern, just as
the surface magnetic flux waveform, the waveform for the radial pattern
is closer to a trapezoid, while the waveforms for the parallel anisotropy
and polar anisotropy patterns are closer to a sinusoidal waveform. The
waveforms for the flux linkage are also the same.
Furthermore, when the angle of decay and the distance from the center pole
are compared, just as the surface magnetic flux density, the induced voltage
waveform and flux linkage waveform are closer to a sinusoidal waveform
the larger the angle of decay, or the longer the distance from the center
pole.
Therefore, after comparing the magnetization patterns, the parallel anisotropy
or polar anisotropy patterns have a smoother rotation that produces less
cogging torque than the radial pattern. Furthermore, when comparing the
angle of decay and the distance from the center pole, the torque is the
lowest with a radial pattern at 20 degrees, a parallel anisotropy pattern
at 30 degrees, or for the polar anisotropy pattern, a distance when r=
16.35 mm. |
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