2014 17th International Conference on Electrical Machines and Systems (ICEMS),Oct. 22-25, 2014, Hangzhou, China
Torque Ripple Reduction in Permanent Magnet Synchronous Machines with
Concentrated Windings and Pre-Wound Coils
1
J. Richnow1, D. Gerling1, P. Stenzel2,
Universitaet der Bundeswehr Muenchen, D-85577 Neubiberg, Germany
2
AUDI AG, D-85045 Ingolstadt, Germany
Abstract — Ideally, improvements of the manufacturing
process do not cause deteriorations of the product characteristics.
Pre-wound coils for electrical machines with concentrated
windings are such an improvement. The easiest way to enable the
assembling of pre-wound coils is simply the absence of pole shoes.
This paper discusses the absence of pole shoes based on a sample
machine. The focus lies on changes of cogging, avg. nominal and
peak torque and the occurring torque ripple. Furthermore,
different technologies as a variation of the tooth thickness,
skewing, magnetic slot wedges and plug-in connections are
investigated to compensate deteriorations of torque behavior. In
addition, the effects of these technologies on the manufacturing
process of a stator are discussed.
I.
INTRODUCTION
Alongside high demands on power density, efficiency and
smooth torque, manufacturability is an important factor for
electrical machines used in automotive drive trains. Especially
in hybrid applications, permanent magnet synchronous
machines (PMSM) with concentrated windings are widely
used [1]–[3]. For this type of winding, the assembling of prewound coils makes sense from the manufacturing point of
view. The easiest way to enable the assembling of pre-wound
coils is to design the stator teeth without the thickening in the
area of tooth head and slot opening, also known as pole shoes.
In the context of this paper the impact of the absence of pole
shoes on the torque characteristics will be shown using a
sample machine.
Since the simplification of the manufacturing process
should not lead to a degradation of machine characteristics,
deteriorations have to be compensated. Especially the
reduction of torque ripple in PMSM has been topic of many
papers in recent years using various approaches e.g. presented
in [4], [5]. This paper will compare different methods to
reduce torque ripple relating to their impact on key machine
characteristics and their manufacturability. Finally, an
additional approach in which the stator sheet package consists
of multiple parts using plug-in connections is introduced in
order to assemble pre-wound coils to stator geometries
including pole shoes.
For the following investigations a sample machine has to be
chosen and its characteristics have to be measured on a test
bench. An equivalent FEA-model can be created and validated
based on the measurement results. With the validated model,
the impact of the discussed design changes can be simulated.
II.
windings. For the tooth geometry in Fig. 2 (b), b1 = 13 mm,
b2 = 11 mm and b3 = 13 mm applies.
III.
Torque ripple consist of load independent cogging torque
and an additional load depending component [6]. There are
several options discussed to reduce those torque ripple by
suitable control algorithms [7]–[9]. Below, some design
options will be discussed to reduce torque ripple based on the
requirement to assemble pre-wound coils.
A. Variation of Tooth Widths
In order to compensate the pole shoes the thickness of the
tooth in the area of the air gap can be increased. The easiest
design of such teeth without pole shoes would involve a
straight flank. However, such geometry does also create a
sudden permeability change in the air-gap from iron in the
tooth area to air in the area of the slot opening. This will lead
to higher harmonics in the air-gap flux and increased on-load
torque ripple. Therefore the tooth geometry should include
cavities at each flank close to the air gap.
The increase of tooth thickness is equivalent to a reduction
. This influences the thermal steady state
of the slot area
conditions and therefore the nominal torque.
SAMPLE MACHINE
The sample machine in Fig. 1 (a) is a 24teeth/32pole
interior permanent magnet (IPM) machine similar to
machines, used in the transmission-bell housing of today’s
parallel hybrid drive trains. The motor specifications are given
in Table I. The stator consists of single teeth with concentrated
2501
978-1-4799-5162-8/14/$31.00 2014 IEEE
TORQUE RIPPLE REDUCTION
(a)
(b)
Fig. 1. (a) Test bench machine. (b) Cross section of one single tooth with
relevant dimensions
TABLE I
MOTOR SPECIFICATIONS
Number of Poles
Number of Slots
Outer diameter (stator)
Inner diameter (rotor)
Active length
Air-gap length
Maximum power
Maximum torque
Nominal power
Nominal speed
32
24
269 mm
182 mm
55 mm
1 mm
37 kW
175 Nm
25 kW
4500 1/min
According to [10], [11] a body reaches its steady-state
temperature if the energy generated per unit volume is equal to
the heat flow,
0
where
is the thermal conductivity,
per unit volume
and
(1)
the thermal losses
the temperature
gradient in the direction of the heat flow.
For the joule losses in a conductor generated by a passing
dc-current
(2)
is the copper fill factor according to [12]
applies, where
and is a factor for all quantities in the general resistance
. Assumed that the
equation, which are independent from
change of the average coil length
can be neglected, the
relation between nominal current and slot area for a constant
maximum temperature and copper fill factor in a first
approximation becomes
(3)
Therefore, a reduction of the slot area is equivalent to a
reduction of nominal current.
However, the design change of the stator teeth has no
significant influence on the manufacturing costs.
B. Rotor Skewing
Skewing is commonly used to reduce torque ripple of
PMSM’s. The skewing angle has to be chosen according to the
periodicity of the torque ripple component to be eliminated.
The skewing angle can be calculated by
360°
,2
360°
2
(4)
(5)
according to [6], where is the number of pole pairs, is
the number of phases,
is the number of slots,
is the
load independent and
the load dependent component.
For PMSM’s a continuous skewing is not possible due to
manufacturing reasons. However, according to [4] a step
skewing by 3 segments achieves already results very close to a
continuous skewing. Since skewing also leads to a load angle
change in axial direction, only one rotor segment is operated at
the ideal load angle. This will lead to a decrease of average
nominal and maximum torque. As noted in [4], on-load
skewing cannot always reduce torque ripple completely.
This method increases the complexity of the rotor
manufacturing. For each segment, the lamination stack
geometry has to be adapted and the segments have to be
connected to a complete rotor in an additional manufacturing
step. This results in slightly higher production costs.
C. Magnetic Slot Wedges
Magnetic slot wedges (MW) are widely used for high
voltage machines with open slots. Although most of the
investigations are mainly conducted for induction motors [13][16] there are also some investigations for PMSM [17], [18].
However, the general influences of MWs on the magnetic
field are independent from the used machine type. The main
advantage is the reduction of harmonic components in the airgap flux distribution also known as slot harmonics. This leads
to reduced torque ripple. The drawbacks on the other hand are
an increased slot leakage flux, which leads to a decrease of the
average torque values, and a decreasing robustness with
increasing permeability [19].
In [20] several possible geometries for magnetic slot
wedges are described. According to [15] and [18] the
permeability of the magnetic material can vary from
1
20 for soft magnetic composites
(non-magnetic) to
(SMC). Common semi magnetic materials have a permeability
of 1
10. The variety of combinations decreases since
results indicate that the drawbacks of high permeability
outbalance the advantages [18]. A general conclusion on the
applicability of MWs is difficult to make. Most investigations
conclude that the right choice of material property and wedge
design is essential for the effect of the magnetic slot wedges
[13] – [19].
Since slot wedges are not used in the series production of
the sample machine, the assembly of MW means additional
material costs and an additional manufacturing process step.
Therefore it will increase the costs.
D. Plug-in Teeth
Various plug-in teeth are known from several patents and
patent applications made throughout the last years [21]-[23].
The dovetail connection (DT) shown in Fig. 2 a) has already
been known for more than 20 years [24]. For a dovetail
connection, a pre-wound coil is stuck on the tooth in the
direction of the air-gap. Afterwards, the tooth with the
mounted coil is inserted in axial direction into the respective
cavity in the the stator yoke. This manufacturing method does
not allow a cone-shaped tooth design. Therefore, high currents
could lead to saturation in the tooth area close to the yoke,
which could reduce the maximum torque. A further thickening
of the teeth would lead to a nominal torque reduction, as
already discussed.
A Snap-fit (SF) connection as described in [21] enables also
cone-shaped tooth design, because in the assembly process the
pre-wound coils are set onto the stator teeth radially in the
direction of the stator yoke. For applications which do not
allow big air-gaps inside the tooth, the invention in [21] is not
convenient. However, the design introduced in Fig. 2 b)
enables the reduction of the air-gaps between pairing
components to a minimum due to manufacturing tolerances
with simultaneously high mechanical stability.
The influence on the manufacturing depends on the design
of the plug-in connection. The dovetail connection can be
punched out of the same iron sheet and assembled to a
lamination stack by interlocking. This increases the
complexitiy of the stamping tool. The assembling of the teeth
to the yoke is an additional process step. On the other hand,
2502
the solid yoke simplifies the insertion of thhe stator into its
housing. Thus, the manufacturing costs will increase slightly
at the very most.
The introduced snap-fit connection requirees low tolerances.
This leads to high stamping tool costs. In adddition, the forces
which occur during the plug-in process aree high. Therefore
glueing instead of interlocking might be a reqquirement for the
assembly of the snap-fit lamination stack. The assembly of the
plug in connection is an additional process steep. All in all, this
connection will lead to higher manufacturingg costs compared
to the sample machine.
IV.
(a)
(b)
d (b) Snap-fit connection
Fig. 2. (a) Dovetail connection and
2D-FEA MODELS
The FEA-models are created and simulated using
MAXWELL 2D. The temperature of the maagnets is assumed
to be at 105 C. All 2D-FEA-models sharee the same rotor
geometry as shown in Fig. 3.
A. Sample Machine (SM)
The model of the machine in Fig. 3 is reduuced to 1/8 of the
machine due to electromagnetic symmetrry reasons. The
influence of the edge between single teeth segments is
neglected. This could be an important factor for rotor skewing
according to [25], but one of the advantagges of pre-wound
coils is a solid stator yoke. Therefore, it is assumed that the
negligence has no significant influence on thee investigation.
B. Variation of Tooth Width
The single tooth design is adjusted due tto the absence of
pole shoes. The new geometry is shown inn Fig. 4 a). The
variation consists of a three-step variation of the tooth width
b3 with b1 being kept constant, as depicted in Table II. The
decrease of the nominal current is calculateed using (3) and
based on the slot area calculated in MAX
XWELL 2D. The
results are presented in relation to the sample machine.
To reduce the on-load torque ripple as welll, a second design
according to Fig. 4 b) with b2new=b2old is also simulated
varying b3. After a comparison of the simullation results, the
most suitable version is used for rotor sskewing and the
assembly of a magnetic slot wedge.
C. Rotor Skewing
The common way to simulate skewingg with 2D-FEA
models is multi-slice modeling [4], [12] andd [26]. Using 2DFEA, the effect of flux density changes inn axial direction
between two rotor segments and other thhree dimensional
effects are neglected. Therefore, the simulaated results could
differ from the results of an equivalennt real machine.
However, for the sample machine (SM))
3.75°
60° is valid according to ((4) and (5). For
skewing, five segments are simulated baseed on [4] with a
length of 11 mm each.
D. Magnetic Slot Wedges
The Magnetic Slot wedge relates to the inntroduced designs
in [20] and can be seen in Fig 5. The heightt of the wedge is
dimensioned respectively to avoid a further reduction of the
copper cross section. Three different materiaals are simulated.
MW 1.5 has a relative permeability of
1.5, for MW 2
2 and for MW 2.5
2.5 applies.
2503
Fig. 3. 2D FEA-Model of th
he sample machine
(a)
(b)
Fig. 4. (a) FEA-model of the teeth without pole shoes and even flanks (b)
FEA-model of the teeth without pole shoess and cavities to reduce on-load
torque ripplee
TABLE III
COMPARISON OF TEST BENCH AND
D SIMULATION RESULTS OF
THE SAMPLE MA
ACHINE
Sample
machine
b1
13 mm
b2
11 mm
b3
13 mm
100 %
Geometry
Variation
V1
V2
V3
Vc1
Vc2
Vc3
b2
11 mm
11 mm
11 mm
b3
11 mm
12 mm
13 mm
11 mm
12 mm
13 mm
A
99.87 %
97.25 %
94.65 %
99.87 %
97.25 %
94.65 %
Even flank
Flank with cavity
,
Fig. 5. Magnetic slot wedge (lig
ght grey) inside a slot
E. Plug-in Teeth
For the dovetail connection a simple 2D-model based on the
technical drawings for the prototypes was used as shown in
Fig 6. a). In Fig 6. b) cavities are included to reduce the onload torque ripple. For the snap-fit connection it was not
possible to use the technical drawings since the smaller part
suffers a permanent deformation during the plug-in process.
Therefore, a model based on the actual plugged tooth sample
was created including the air gaps between the two
components, as shown in Fig. 6. c). Although this model
neglects negative influences on the material characteristic of
the lamination stack along the edges of the connection due to
the stacking and plug in process, it represents the small airgaps between the two parts very accurately.
For the dovetail connection 1 12
and 3 13
applies. With 1 12
the nominal current for this design
is identical to the SM. On the other hand, the chosen width
could lead already to a decrease of avg. maximum torque due
to saturation effects in the upper tooth area. For the cavities
2 11
applies. The values for the snap-fit connection
are equivalent to the tooth geometry of the sample machine.
F. Model Validation
The validation of the FEA-model is based on the measured
torque-speed-diagram with included IAC-curves in Fig. 7.
Table III shows the comparison between measurement and
simulated operating point. The operating points cover different
areas of the diagram. The results show only a small deviation
between measured and simulated average torque. In general
the simulated value seems to be slightly higher than the
measured value. However, the difference of around 2 percent
is sufficiently accurate, especially because there are several
factors, which could cause deviations, such as measurement
errors or the simplifications of the implemented FEA-model.
Another possibility are deviations of the material parameters
due to wrongly assumed material temperatures or
manufacturing influences. Even small deviations of the load
angle cannot be excluded. As already mentioned, the shown
simulation results match the measured results sufficiently.
Therefore, it can be assumed, that the design changes of the
FEA-models will also lead to accurate results.
V.
(a)
A. Absence of pole shoes
The basic absence of pole shoes already causes an avg.
torque reduction of about 4.5 % for nominal torque and 2.3 %
for maximum torque based on the results for sample machine
and design V1 in Table IV. At the same time, the torque ripple
(c)
Fig. 7. Torque-IAC-map and peak torque-speed characteristic of the sample
machine (measured) for UDC=295V
TABLE III
COMPARISON OF TEST BENCH AND SIMULATION RESULTS OF
THE SAMPLE MACHINE
Test Bench
Torque
Comparison
Simulation
Speed
IAC
No.
1/min
A
Nm
1
2
3
4
5
6
2004
2004
2004
4520
4520
5530
37.9
211
321.9
39.8
115
150.56
19
117.2
177.4
18.8
54.84
52.2
Torque Speed
1/min
IAC
Torque
Diff.
A
Nm
Nm
%
-0.14
2.38
0.82
0.36
0.41
1.07
0.74
2.03
0.46
1.91
0.75
2.05
2004 37.9
18.86
2004
211
119.58
2004 321.9 178.22
4520 39.8
19.16
4520
115
55.25
5530 150.56 53.27
Diff.
TABLE IV
TORQUE COMPARISON FOR VARIATION OF TOOTH WIDTHS
RESULTS
The presented results are simulated for 3 operation points.
At point no. 3 in Table III peak power is reached. For the
sample machine, the power electronics is the limiting factor
for the time range during which peak power is available.
Therefore, it is assumed, that the reduced copper cross section
has no negative influence on this time range. The cogging
torque is simulated at 2004 rpm, equal to the speed at point no.
3. The nominal torque is simulated at operation point 5 where
nominal power and nominal IAC current occur .
(b)
Fig. 6. (a) FEA-model of the dovetail connection (DT), the dovetail
connection with cavities (DTc) and (c) Snap-fit connection (SF)
Cogging torque
SM
V1
Ripple
(pk2pk)
Nm
1.99
8.84
Maximum torque
Nominal torque
Avg.
Ripple
(pk2pk)
Avg.
Ripple
(pk2pk)
Nm
178.21
174.21
Nm
21.4
29.63
Nm
55.25
52.75
Nm
3.91
10.01
increase by about 344% for cogging torque, 156% for nominal
torque and 38% for maximum torque.
B. Variation of Tooth Width
The simulation results in Fig. 8 show, that the tooth width at
the air-gap is the main determining factor for cogging torque.
The cavities at the flank have almost no influence on the
torque characteristics. With increasing tooth width the pk2pk2504
value of the cogging torque decreases. When the width of the
teeth reaches the level of the width of the sample teeth
including pole shoes the differences are negligible.
However, the cavities have an effect on the on-load torque
ripple as shown in Fig. 9. The effect increases with increasing
tooth width, which is reasonable, since the cavities increase to
the same extent. On the other hand, the cavities slightly
decrease the average torque because of higher flux densities in
the area of the cavities.
For variation Vc3 the same on-load and cogging torque
characteristic as for the sample machine is reached. However,
this is also the variation with the lowest nominal torque
because of the lowest copper cross section. This will also lead
to slightly higher copper losses. The thicker stator teeth on the
other hand have a positive effect on the iron losses. Therefore,
a closer look on the efficiency of the variations should follow
in future research.
Table V shows the calculated torque for the different tooth
widths. None of the shown option reaches the same results as
the sample machine. Therefore, this method is not able to
compensate pole shoes completely. However, this method is
comparatively cheap in production. If torque ripple or peak
torque are the most important characteristic of the machine,
Vc3 should be chosen. If nominal torque and copper cross
section are also important, Vc2 is a good compromise.
Therefore, the simulations of the magnetic slot wedge and the
rotor skewing are based on model Vc2.
The tooth designs with even flanks should only be chosen,
if torque ripple are no point of interest. The design V1, V2 and
V3 have an almost identical pk2pk-value of the on-load torque
ripple, as shown in Table V. This effect relates to the theory
that for on-load torque ripple the air-gap flux distribution is
the dominating factor. The same nominal torque values for the
different variations with different nominal currents are an
interesting fact. It seems that a deterioration of the air gap flux
distribution compensates the higher nominal current for
designs with smaller b3 values.
C. Rotor Skewing
As shown in Fig. 10, a skewing angle of 60°el with five
segments eliminates the cogging torque as expected. Every
segment has an almost identical avg. value. An angle of 45°el
and 30°el shown in Fig. 11 (top) only partly reduces the
cogging torque since the five segments are not evenly
distributed over a cogging cycle as for 60°el.
However, for on-load torque ripple as shown in Fig. 11
(middle and bottom) even an angle of 60°el does not eliminate
the ripple totally. The changing load angle leads also to a
changing avg. value of the torque characteristics of each
segment. With an increasing angle the average nominal and
maximum torque decreases.
Table VI shows the calculated torque for the different
skewing angles. Due to the significant decrease in nominal
and avg. torque the drawbacks of the theoretically ideal angle
of 60°el outbalance the advantages. A skewing angle of 30°el
shows the best results for the avg. torque and on-load torque
ripple. Depending on the most important characteristic of the
machine, the angle could be slightly reduced to increase the
average torque values.
Fig. 8. Cogging torque for different tooth widths for 2004 rpm
Fig.9. On-load torque for different tooth widths for peak current 177.4 A at
2004 rpm
TABLE V
TORQUE COMPARISON FOR VARIATION OF TOOTH WIDTHS
Cogging torque
SM
V1
Vc1
V2
Vc2
V3
Vc3
2505
Ripple
(pk2pk)
Nm
1.99
8.84
8.9
6.83
6.97
2.22
2.26
Maximum torque
Nominal torque
Avg.
Ripple
(pk2pk)
Avg.
Ripple
(pk2pk)
Nm
178.21
174.21
173.76
178.69
176.44
182.72
178.8
Nm
21.4
29.63
28.84
29.75
25.89
29.4
22.32
Nm
55.25
52.75
52.7
52.63
52.37
52.33
51.98
Nm
3.91
10.01
9.92
7.22
7.11
4.55
3.71
Fig.10. Resulting cogging torque due to the combination of 5 segments
skewed over 60°el
Fig.11. Cogging torque ripple (top), torque ripple at nominal torque (middle)
and maximum torque (bottom) for different skewing angles compared to the
same design without skewing and to the sample machine
TABLE VI
TORQUE COMPARISON FOR DIFFERENT SKEWING ANGLES
Cogging torque
SM
Vc2
Vc2 30°el
Vc2 45°el
Vc2 60°el
Ripple
(pk2pk)
Nm
1.99
6.97
4.17
2.14
0.17
Maximum torque
Fig.12. Cogging torque ripple (top), torque ripple at nominal torque (middle)
and maximum torque (bottom) for a magnetic slot wedge with different
permeabilities compared to the same design without slot wedges and to the
sample machine
TABLE VII
TORQUE COMPARISON FOR DIFFERENT MAGNETIC SLOT
WEDGES
Nominal torque
Avg.
Ripple
(pk2pk)
Avg.
Ripple
(pk2pk)
Cogging torque
Nm
178.21
176.44
173.97
170.98
166.91
Nm
21.4
25.89
18.47
13.33
9.61
Nm
55.25
52.37
51.76
51
49.94
Nm
3.91
7.11
3.95
1.69
1.99
Ripple
(pk2pk)
Nm
1.99
6.97
5.71
5.16
4.76
However, skewing to reduce torque ripple to the level of the
sample machine will bring a non negligible reduction of avg.
torque values. Therefore this method is not able to compensate
the absence of pole shoes. Still, it has its advantages, if
cogging torque reduction is most important.
D. Magnetic Slot Wedges
Magnetic slot wedges (MW) have a significant influence on
the maximum torque ripple even with a very small
permeability as shown in Fig. 12 (bottom). On the other hand,
they only slightly reduce cogging torque ripple as shown in
Fig. 12 (top and middle). Compared to the original design
Vc2, an assembled MW with a permeability of
1.5
reduces the maximum torque ripple by 15 %, but the avg.
torque by only 1 % according to Table VII. The nominal
torque ripple is reduced by about 25 % with almost no
reduction of the avg. torque.As for skewing, the permeability
of the MW effects avg. torque and torque ripple conflictively.
To prevent a significant decrease of avg. maximum torque, the
permeability has to be chosen in a range that only slightly
reduces cogging torque.
SM
Vc2
MW 1,5
MW 2
MW 2,5
Maximum torque
Nominal torque
Avg.
Ripple
(pk2pk)
Avg.
Ripple
(pk2pk)
Nm
178.21
176.44
174.69
172.81
170.88
Nm
21.4
25.89
21.54
18.08
15.09
Nm
55.25
52.37
52.18
51.95
51.68
Nm
3.91
7.11
5.33
4.56
3.93
Therefore, MW are not able to compensate the absence of pole
shoes completely. However, they are a suitable method to
reduce maximum torque ripple.
E. Plug-In Connections
The plug-in connections match the torque characteristics of
the sample machine (SM) completely for cogging torque and
maximum torque as shown in Fig. 13. Only the dovetail
connection without cavities shows a slightly increased torque
ripple for the because of the increased permeability gradient
between slot opening and tooth due to the very small pole
shoes. Since the shown results match almost perfectly with the
SM as the values in Table VIII show and the nominal current
of the plug-in connections is identical to the nominal current
of the sample machine, it is assumed that the characteristics
for nominal torque match as well.
Because there is no difference between the dovetail
connection with cavities and the snap-fit connection, the
dovetail connection is preferred due to its advantages in the
manufacturing process. However, it should be noted that the
2506
[2]
[3]
[4]
[5]
[6]
Fig.13. Cogging torque ripple (top) and and maximum torque (bottom) for
different plug-in connections and the sample machine
[7]
TABLE VIII
TORQUE COMPARISON FOR DIFFERENT PLUG-IN CONNECTIONS
[8]
Cogging torque
Ripple
(pk2pk)
Nm
1.99
2.37
2.41
2.31
SM
DT
DTc
SF
Maximum torque
Avg.
Ripple
(pk2pk)
Nm
178.21
179.53
177.88
177.79
Nm
21.4
24.61
21.41
20.99
[9]
[10]
[11]
[12]
[13]
reduction of 1 could have a significant influence due to
saturation on other machine designs.
VI.
[15]
CONCLUSION
In this paper, design changes based on a sample machine to
enable the assembly of pre-wound coils are investigated.
Initially the FEA-model of the sample machine is validated
by measurement results of an equivalent test bench machine.
Afterward, the impact of the absence of pole shoes is
simulated. The results show general deteriorations regarding
avg. torque as well as torque ripple.
Different options to compensate the absence of pole shoes
are introduced. The results indicate, that a variation of tooth
width as well as skewing and magnetic slot wedges are no
suitable alternative to pole shoes regarding avg. torque and
torque ripple. However, the results of the additional approach
of plug-in connections including pole shoes indicate that they
enable the assembly of pre-wound coils without a degradation
of any torque characteristic.
VII.
ACKNOWLEDGMENT
The authors gratefully acknowledge the business partners
whose work formed the foundation for the simulations and test
bench results presented in this paper.
VIII.
[1]
[14]
REFERENCES
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
P. B. Reddy. K.-K. Huh and A. El-Refaie, “Effect of Stator Shifting on
Harmonic Cancellation and Flux Weakening Performance of Interior
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