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STUDY ON ROTOR STRUCTURE WITH DIFFERENT
MAGNET ASSEMBLY IN HIGH-SPEED SENSORLESS
BRUSHLESS DC MOTORS
K. Wang M.J. Jin J.X. Shen H. Hao
College of Electrical Engineering, Zhejiang University,
Hangzhou 310027, People’s Republic of China
241~248
老師:王明賢
學生:方偉晋
ABSTRACT
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High-speed permanent magnet (PM) brushless DC motors
have gained more and more interests for many applications.
The technique of detecting the electromotive force (EMF)
zero-crossings is a common method in sensorless operation
of PM brushless DC motors.
Based on these analyses, another method which can
improve both the third harmonic and fundamental
components in the airgap field, by segmenting the parallelmagnetised PMs, is employed and studied.
OUTLINE
Introduction
 High-speed motor configurations
 Enhancement of third-harmonic back-EMF
 Experimental verifications
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INTRODUCTION
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Sensorless operation is able to greatly strengthen the system
reliability and diminish the performance variations caused by
discrete rotor position sensors. Among various sensorless control
techniques, the most common one is based on the detection of
zero-crossings of the phase back-EMF.
The free-wheeling diode conduction has no influence on the
method of detecting the third-harmonic back-EMF zero-crossings.
Therefore, in this paper, the sensorless control using the thirdharmonic EMF instead of the phase EMF will be studied at the
motor design stage.
HIGH-SPEED MOTOR CONFIGURATIONS
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For the above-mentioned threephase PM brushless DC motor,
two configurations with the
same dimensions are studied, as
given in Fig. 1.
A two-pole six-tooth stator with
nonoverlapping windings is
directly used, since in such a
stator structure the thirdharmonic winding factor is 1,
which is beneficial to maximise
the third-harmonic EMF.
Figure 1 Motor configurations
a Using one magnet per pole
b Using two magnet segments per pole
ENHANCEMENT OF THIRD-HARMONIC
BACK-EMF
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Fig. 2 shows the open-circuit magnetic field distributions in a twopole six-slot motor, where the rotor has two magnets with the
magnet pole-arc to pole-pitch ratio (ap) being 1.0, 0.9, 0.7 and 0.5,
respectively.
Fig. 3 shows the airgap field distribution waveforms produced by
the parallel-magnetised magnets with different ap. As can be seen,
when the pole-arc to pole-pitch ratio (ap) decreases, the airgap
field distribution waveform becomes farther away from sinusoidal
waveform, containing more harmonics.
ENHANCEMENT OF THIRD-HARMONIC
BACK-EMF
Figure 2 Field distributions in two-pole
six-slot high-speed
motors with different pole-arc to polepitch ratio ap
a ap =1
b ap =0.9
c ap =0.7
d ap =0.5
ENHANCEMENT OF THIRD-HARMONIC
BACK-EMF
Figure 3 Comparison of FEM and analytical predictions of
airgap field distribution
ENHANCEMENT OF THIRD-HARMONIC
BACK-EMF
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Fig. 4 shows the typical
relationship between the
airgap field harmonics and
the magnet pole-arc to polepitch ratio (ap), which is
obtained from finite-element
analysis.
Figure 4 Airgap field harmonics with different magnet
pole-arc
ENHANCEMENT OF THIRD-HARMONIC
BACK-EMF
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Influence of the number of magnet segments on the airgap field
distribution is also investigated with FEM, as shown in Fig. 5,
where the number N in the curve legend denotes the number of
segments per pole.
It should be pointed out that the pole arc of each segment is p/N
rads, and the stator slot opening is neglected in the FEM analysis.
It is seen that the number of segments has a significant effect on
the airgap field waveform.
ENHANCEMENT OF THIRD-HARMONIC
BACK-EMF
Figure 5 FEM prediction of airgap field distribution with
different number of magnet segments per pole (N)
ENHANCEMENT OF THIRD-HARMONIC
BACK-EMF
 From Fig. 6, it can be seen that the structure with two magnet
segments per pole has the highest third harmonic in the airgap
field, and even the fundamental component is higher than that
with one segment per pole. This is beneficial to improve the motor
performance.
Figure 6 Variation of fundamental airgap field and thirdharmonic
airgap field with number of segments per pole (N)
EXPERIMENTAL VERIFICATIONS
 From the comparison shown in Fig. 7, it is seen that the
analytically calculated and FEM-predicted back- EMF waveforms
are very similar. The third-harmonic back-EMF component must
be high enough, usually over 20% of the fundamental, in order
that the sensorless control can be realised.
EXPERIMENTAL VERIFICATIONS
Figure 7 Comparison of FEM predicted and analytically
calculated phase back-EMFs at 120 krpm
a Structure of Fig. 2a with ap ?0.9
b Structure of Fig. 2b
EXPERIMENTAL VERIFICATIONS
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Ideally, it is preferable that a BLDC motor has a trapezoidal
phase back-EMF and a square-wave phase current, such that a
constant electromagnetic torque can be achieved.
However, in practical BLDC motors, especially in the high-speed
ones, the phase current is usually not regulated, hence, is
typically far away from the square-wave. This will certainly cause
torque ripples.