EVS28
KINTEX, Korea, May 3-6, 2015
Cogging Torque Reduction in Surface-mounted Permanent
Magnet Synchronous Motor by Axial Pole Pairing
Soo-Gyung Lee1, Kyung-Tae Jung1, Seung-Hee Chai1, and Jung-Pyo Hong1*
1
Department of Automotive Engineering, Hanyang University, Seoul, South Korea
Corresponding Author Email: hongjp@hanyang.ac.kr
Abstract
In many machines, where permanent magnets are used, the effects due to cogging torque generated by PMs
aggravate the output characteristics of the machines. This paper presents the method for reducing cogging
torque in surface-mounted permanent magnet synchronous motor (SPMSM). A new cogging torque
suppression method called axial pole pairing is proposed. Compared to conventional pole pairing, axial
stack length is considered. Analytical formulas are used to estimate cogging torque and verify the validity
of axial pole pairing. Characteristics of cogging torque are investigated on various combinations of axial
pole pairing. From this result, improvement on space harmonic analysis has been researched about SPMSM
for reducing cogging torque.
Keywords: Axial Pole Pairing, Cogging Torque Reduction, Space Harmonic Analysis (SHA), Surface-mounted
Permanent Magnet Synchronous Motor (SPMSM)
1
Introduction
Surface-mounted
permanent
synchronous
motors (SPMSM) are widely used in industrial
applications with the high torque density and
high efficiency as well as the simple structure
they exist.
In many of these applications, the high strength
of permanent magnets not only leads to
generating remarkably high torque but also
causes the undesirable effects of high cogging
torque that can aggravate performance of motor.
Generally the cogging torque arises when the gap
of magnetic reluctances between the rotor
magnet and slotted stator exists. Design
parameters that affect to the magnitude of
cogging torque can be slot openings, the number
of slots per phase, thickness of teeth, width of
slot, pole ratio of PMs, and length of air gap, etc.
Minimization of cogging torque generation is
accordingly of great importance [1].
Analytical studies of cogging torque prediction in
surface mounted permanent magnet (PM)
machines are well documented [2]-[7], and various
methods of cogging torque reduction based on
different models have been analysed [8]-[11].
Suppression of cogging torque invariably leads to
some degree of compromise in the performance of
the machine, as well as cost penalties in
implementation. For example, by adjusting magnet
pole arc, not only the cogging torque but also the
back electromotive force (EMF) can be reduced
simultaneously. Thus, it is noteworthy that each
approach has its own limitations, and some are far
more difficult to implement than others.
In this paper a new cogging torque suppression
method called axial pole pairing is proposed. It is a
new technique to enable coils to be connected in
parallel, and can comprise different axial lengths
as well as different pole arc widths. In conclusion,
EVS28 International Electric Vehicle Symposium and Exhibition
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the axial pole pairing is referred to several
different-axial-length machines with the same
stator configuration axially adjoined [12].
Finally the estimated result by using the
presented method shows the trend map of model
parameters according to the variation of
combined axial pole pairing. The result maps can
effectively give designers the wide insights when
the desired parameters are selected.
2
Qs
2
b0  B
− Brib 2 2 
Tc = ∑ Lstk ∫  rib1
 rt drs
0
2 µ0
k =0


(2)
Where Lstk is axial stack length, b0 is width of slot
opening, B indicates flux density produced by PMs.
Coil
Core
Cogging Torque Analysis in
SPMSM
Air
The two torque components affect output
performance of SPMSM: Torque ripple and
Cogging torque. The former is produced from the
harmonic content of the input current and voltage
wave, and the latter is produced by the magnetic
attraction between the rotor mounted PM and the
stator teeth in the machine. In this paper, cogging
torque reduction is considered to improve the
output performance of SPMSM
Therefore cogging torque is first calculated by
using space harmonic analysis (SHA), and the
axial pole pairing is adopted to reduce the
cogging torque. Fig.1 shows a schematic of the
SPM motor used for analysis.
2.1
PM
Figure 1: Schematic of a SPM motor having
4-pole rotor and 6-slot stator
b0
b1 '
Core
rs
Brib1 b1
Air
b2 Brib 2
g
Figure 2: Air-gap representation for relative
Z-axis
permeance method in slot-opening region
Calculation of Cogging Torque
To reduce cogging torque, analytical estimation
of cogging torque should precede any process.
SHA is a reliable means of estimating the likely
level of cogging and its dependence on the motor
design parameters. Characteristic of cogging
torque are analysed by using the concept of
relative permeance in this paper, based on those
following assumptions:
Then cogging torque is derived by the varying
air-gap permeability due to slotting. By using the
concept of relative permeance p̂ , the flux density
of slot opening region expressed as:
Lstk B
N
Pole arc B
S
N
S
Lstk A
Pole arc A
Electric angle
(a)
A
Cogging Torque [mNm]
• The permeability of core is infinite;
• Slots are simplified to a rectangular shape;
• Magnetic field distribution is determined by
magnetic field and relative permeance;
• Stator surface is smooth for 2-D solution;
• Flux crosses the magnet and air-gap straight;
Bsi ( x1 ) = pˆ ( x ) Bair-gap
b2 '
0
(1)
As shown in Fig.2, the net cogging torque at any
magnet position is calculated from the flux
density in slot-opening region:
EVS28 International Electric Vehicle Symposium and Exhibition
B
A+B pole pairing
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
5
10
15
20
25
Mechanical Rotation Angle [°]
(b)
30
Figure 3: Side view of the axial pole-paired rotor
(a) Side view of rotor with axial pole pairing
(b) The principles of axial pole pairing
2
The phase of cogging torque can be reversed as
magnet pole arc changes, thus total cogging
torque can be reduced by conjoining magnets
having the same stack length but different pole
arc [12]. In addition to magnet pole arc, stack
length, proportional to magnitude of cogging
torque, can be considered as design variable
shown in Fig.3 (a). The principles of axial pole
pairing are illustrated in Fi.3 (b). Accordingly,
improved pole pairing considering axial stack
length is proposed in this paper.
Therefore cogging torque is examined by
altering the value of Lstk A , Lstk B and pole arc A,
B. Firstly stack length is fixed and only pole arc
is varied so that cogging torque using axial pole
arc pairing is examined as result. Then all the
variables change for cogging torque to be
compared with the precedence.
2.3
Cogging Torque Reduction Using
the Axial Pole Pairing
Cogging torque characteristics by conventional
pole pairing are illustrated in Fig.4. Tcog_pp
means the peak to peak value of cogging torque.
The contour map presents the peak to peak value
of cogging torque versus pole arc pairing of A
and B, when two of rotors having the same stack
length are aligned axially. From Fig.4 (a), a pair
of pole arc (A, B) = (0.97, 0.8) is selected to
verify the validity of axial pole arc pairing.
As shown in Fig.4 (b), cogging torque can be
reduced by 71.98% as a result of by pole arc
pairing.The same pole arc pair is adopted to see
how axial stack length pairing affects cogging
torque reduction. The optimal stack length pair of
5[mm], 11[mm] is obtained to reduce cogging
torque produced by axially pole arc paired
magnets.
The features of cogging torque with different
pole arc and stack lengths are illustrated in Fig.5.
In case of different stack length, given an
example of Lstk A=5[mm] and Lstk B=11[mm],
area for design is somehow different as shown in
Fig.5 (a). From this, the fact that pole arc of
magnet having shorter stack length wields
stronger influence on cogging torque than one
with longer stack length is derived. Also it is
concluded that some combinations of different
pole arc and stack length can be selected to yield
great effect on cogging torque reduction from
Fig.5 (b).
Table 1 indicates the representative models used
for analysis. Normal model X is one that the pole
pairing is not applied. It consists of 0.97 of magnet
pole arc ration and 16 [mm] of stack length. Model
Y represents the one axial pole arc pairing is
applied but two of conjoined magnets have the
same stack length. If a condition of different stack
length is added to model Y, then it becomes model
Z.
As illustrated in Fig. 6, proper pole arc and stack
length pairing can reduce cogging torque. Model Y
has 71.98 % of benefit compared to normal model,
and model Z has 86.02 % of advantage to the
normal one.
1.0
Pole arc / Pole pitch of A
Proposed Axial Pole Pairing
Tcog_pp [mNm]
1.395
1.231
1.066
0.9019
0.7375
0.5731
0.4088
0.2444
0.08000
0.9
0.8
0.7
0.6
0.5
0.5
0.6 0.7 0.8 0.9
Pole arc / Pole pitch of B
1.0
(a)
Normal
Conventional axial pole pairing
1.5
Cogging Torque [mNm]
2.2
1.0
0.5
0.0
-0.5
-1.0
-1.5
0
5
10
15
20
25
Mechanical Rotation Angle [°]
30
(b)
Figure 4: Effect of conventional axial pole pairing
(a) Cogging torque versus pole arc pairing
(b) Reduced cogging torque
Table 1: Combination of pole arc and stack length
Part A
Lstk A
Model 1
Model 2
Model 3
EVS28 International Electric Vehicle Symposium and Exhibition
pole arc
A
0.97
0.97
0.97
Part B
Lstk B
[mm]
pole arc
B
[mm]
8
8
5
0.97
0.8
0.8
8
8
11
3
Pole arc / Pole pitch of A
1.0
Tcog_pp [mNm]
0.9
1.395
1.231
1.066
0.9019
0.7375
0.5731
0.4088
0.2444
0.08000
0.8
0.7
0.6
0.5
0.5
0.6 0.7 0.8 0.9
Pole arc / Pole pitch of B
1.0
(a)
Conventional Axial Pole Pairing
Proposed Axial Pole Pairing
1.5
3
Conclusion
The axial pole pairing is investigated to reduce
cogging torque in a 3-phase SPM brushless
machine with 4-pole 6-slot configuration. By
adjusting the value of pole arc and stack length,
which aligned magnets consist of, cogging torque
can be reduced. Thus the output characteristics of
SPM motors can be improved. Reduced cogging
torque is demonstrated by using an analytical
method, based on space harmonic. Although the
investigation is undertaken based on analytical
approach, it is expected that the proposed method
can be validated by FEM and applied to other PM
machines with different configurations.
References
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[2]
Z. Q. Zhu and D. Howe, Analytical prediction of
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[3]
D. C. Hanselman, Effect of skew, pole count and
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EVS28 International Electric Vehicle Symposium and Exhibition
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Cogging Torque [mNm]
[1]
1.0
0.5
0.0
-0.5
-1.0
-1.5
0
5
10
15
20
25
Mechanical Rotation Angle [°]
(b)
Peak to Peak value of Cogging Torque [mNm]
Figure 5: Effect of proposed axial pole pairing
(a) Cogging torque versus pole arc pairing
(b) Reduced cogging torque
Model 1
Model 2
Model 3
2.0
30
1.5
1.0
0.5
0.0
Model 1
Model 2
Model 3
Figure 6: Reduced cogging torque using
the axial pole pairing
[10] T. Li and G. Slemon, Reduction of cogging
torque in permanent magnet motors, IEEE Trans.
Magn., ISSN, 2008, 2901-2903.
[11] M. Goto and K. Kobayashi, An analysis of the
cogging torque of a DC motor and a new
technique of reducing the cogging torque, Elec.
Eng. in Japan, Vol.5, 1983, 113-120.
[12] W. Fei and P. C. K. Luk, A new technique of
cogging torque suppression in direct-drive
permanent magnet brushless machines, IEEE
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Authors
Soo-Gyung received Bachelor’s
degree in Electrical engineering from
the Konkuk University, Korea in
2014. Currently she is pursuing
Master’s degree in Automotive
engineering from Hanyang
University, Korea. Her research
interests are designing and analysis of
electric motors
EVS28 International Electric Vehicle Symposium and Exhibition
Kyung-Tae received Bachelor’s
degree in Mechanical engineering
from the Hanyang University, Korea
in 2014. Currently he is pursuing
Master’s degree in automotive
engineering from Hanyang
University, Korea. His research
interests are designing and analysis of
electric motors.
Seung-Hee Chai received degree in
Mechanical engineering from the
Hanyang University, Korea, in 2009.
Currently he is pursuing the Ph.D.
degree in automotive engineering
from Hanyang University, Korea. His
main fields of interests are
optimization, analysis, design of
electric machine for Vehicle tractoion
and numerical analysis of
electromagnetic.
Jung-Pyo Hong received Ph.D. degree
in electrical engineering from the
Hanyang University, Korea, in 1995.
From 1996 to 2006, he was professor
of Changwon National Univ., Changwon, Korea. Since 2006 he has been
working as a professor in the Hanyang
University, Korea. His research
interests are the design of electric
machines, optimization and numerical
analysis of electro-mechanics.
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