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J Electr Eng Technol Vol. 8, No. ?: 742-?, 2013
http://dx.doi.org/10.5370/JEET.2013.8.5.742
742
Design Considerations and Validation of Permanent Magnet
Vernier Machine with Consequent Pole Rotor
for Low Speed Servo Applications
Shi-Uk Chung*, Yon-Do Chun
**, Byung-Chul Woo
**, Do-Kwan Hong
** and Ji-Young Lee
**
Abstract – This paper deals with design consideration and validation of a new pole-slot combination
for permanent magnet vernier machine (PMVM) with consequent pole (CP) rotor especially for
extremely low speed servo applications. A 136pole-24slot PMVM with CP rotor is introduced and
analyzed by 2D and 3D finite element analysis (FEA) and discussion on experimental validation is also
included.
Keywords: Consequent pole, Permanent magnet, Vernier machine, Low speed
1. Introduction
A lot of researches on different machine topologies have
been continually being reported with the rising need of low
speed direct drives in various industry areas. A Permanent
magnet vernier machine (PMVM) is widely acknowledged
as an attractive candidate for low speed applications due to
several distinctive features that belong uniquely to this
topology such as magnetic gear effect, and low number of
windings with high number of poles [1-5]. Even today, new
topologies are being studied and introduced based on
PMVM topology since PMVM topology still offers design
variants. A PMVM which utilize additional slot space for
DC field winding for flux control is introduced and
characterized for field weakening control [6]. A dual stator
structure was also introduced in PMVM topology to
increase torque density [7]. Another rotor design using
consequent pole (CP) concept was recently introduced and
yet to be further investigated [8].
This paper is a continuation of the previous research
work on PMVM with CP rotor with a different phase
winding arrangement. The most distinctive difference
between the former design and the one introduced in this
paper is that the proposed configuration in this paper
comprises multiple teeth at an equal pitch and each phase
is magnetically coupled.
The most important topic of this research is to introduce
another PMVM topology which can utilize CP rotor
structure since the CP rotor configuration needs a special
pole-slot combination which suppresses magnetic
unbalance caused by the CP rotor [8].
This paper introduces three major design considerations
for PMVM with CP rotor as follows:
To avoid magnetic unbalance, it needs special pole-slot
combinations which can be numerically expressed as (1)
where τp, Ns and Nt denote pole pitch, numbers of split-
poles/stator tooth, and numbers of stator teeth, respectively.
Flux leakage prevention needs to be carefully considered
since magnetic flux flows freely through the entire
magnetic circuit.
Motor symmetry is an important issue related to noise
and vibration.
γ � N� ∙ τ� 2τ�
3, τ� �
3 360°
Nt�3Ns 2�(1)
This paper analyzes the proposed PMVM with 2D and
3D finite element analysis (FEA) since no analytical design
tool for PMVM has been introduced. 2D and 3D FEA
results are also compared with the experimental results in
later section.
2. 2D and 3D FEA results
Fig. 1 shows the proposed topology which comprises CP
rotor of 136 poles and 24 slots at an equal slot pitch unlike
the previous design [8]. Detailed dimensions and geometric
symbols are listed in Table 1. Field distributions by 2D
FEA are shown in Fig. 2 which shows flux flow patterns
repeating every 45 mechanical degrees. This may be
understood that the proposed PMVM has 8 symmetries,
however, actual symmetry of the proposed PMVM is
considered to be 4 due to the CP rotor. The symmetry
issues will be discussed in this section.
Figs. 3(a) and (b) show cogging torque and rated torque
computed by 2D FEA, respectively. Considering the torque
† Corresponding Author: Electric Motor Research Center, Korea Electrotechnology Research Institute, Changwon, South Korea
** Electric Motor Research Center, Korea Electrotechnology Research Institute, Changwon, South Korea.
Received: November 30, 2011; Accepted: May 13, 2013
ISSN(Print) 1975-0102
ISSN(Online) 2093-7423
Shi-Uk Chung, Yon-Do Chun
Fig. 1. Analysis PMVM geometry
(a) No load state.
(b) Rated state.
Fig. 2. Field distribution by 2D FEA
U1
/V1
W1
/U2
V2
/W2
Split-pole
D1
D2
γ
LtLp
Do Chun, Byung-Chul Woo, Do-Kwan Hong and Ji-Young Lee
743
ripple period, the skew angle is 0.882 mechanical degrees
(≒1/3pole-pitch), which seems to be practically infea
So, 1.0 mechanical degree of skewing is chosen for
analysis and prototype. It is shown that
(peak value is 0.24Nm even before skewing, which is less
than 1.0% of rated torque) and low torque ripple even
before skewing (±1.6%). Based on typical FEA results
shown in Fig. 3, it can be stated that the proposed PMVM
can be applied for low speed servo applications due to low
torque ripple and extremely large number poles.
radial force density distribution at rated state
to check motor symmetry using Maxwell stress method by
2D FEA since CP structure induces high local force and
unbalance magnetic pull along with rotor eccentricity [9].
Fig. 3 (c) shows that the proposed topology
symmetry every 90 mech
structurally more stable compared to the previous design
in [8]. However, this is not easily predictable when
observing the flux lines even at rated state. As a result of
that, motor symmetry has to be carefully considered when
implementing CP rotor since this configuration halves
motor symmetry when compared to the
having alternating polarity of PMs.
The stack length of the proposed PMVM is considerably
short (stack length=35mm) and excessive flux leakage can
occur from the active parts to the inactive structural steel
parts. Therefore, 3D FEA is also performed to calculate no
load induced voltage and the overall field distribution
Comparison between 2D and 3D FEA is also performed
to compensate computational error which is possibly
caused by 2D FEA since 2D FEA cannot fully consider
Analysis PMVM geometry.
distribution by 2D FEA.
U1 2τp
Wm
C
Wp
D3
g
Hm
Table 1. Proposed PMVM design
specifications.
Item(Symbol)
Number of poles(Np)
Number of split-poles/stator tooth(N
Number of stator teeth (Nt)
Stack length(Ls)
PM width(Wm)
PM thickness(Hm)
Chamfer(C)
Airgap length(g)
Split-pole width(Wp)
Stator inner hollow diameter(D1)
Stator outer diameter(D2)
Rotor outer diameter(D3)
Tooth length(Lt)
Split-pole length(Lp)
Number of turns/coil(N)
PM material
Rotor/stator lamination material
Lamination stacking factor
Ph. Resistance(@20℃)
DC link voltage
Rated current/Ph.
Rated torque(2D analysis)
Rated speed
Rated output power
Young Lee
ripple period, the skew angle is 0.882 mechanical degrees
pitch), which seems to be practically infeasible.
So, 1.0 mechanical degree of skewing is chosen for the
analysis and prototype. It is shown that low cogging torque
0.24Nm even before skewing, which is less
% of rated torque) and low torque ripple even
Based on typical FEA results
shown in Fig. 3, it can be stated that the proposed PMVM
can be applied for low speed servo applications due to low
torque ripple and extremely large number poles. Airgap
radial force density distribution at rated state is examined
to check motor symmetry using Maxwell stress method by
2D FEA since CP structure induces high local force and
magnetic pull along with rotor eccentricity [9].
that the proposed topology has rotational
symmetry every 90 mechanical degrees which is
structurally more stable compared to the previous design as
However, this is not easily predictable when
observing the flux lines even at rated state. As a result of
that, motor symmetry has to be carefully considered when
mplementing CP rotor since this configuration halves
motor symmetry when compared to the conventional rotor
having alternating polarity of PMs.
The stack length of the proposed PMVM is considerably
short (stack length=35mm) and excessive flux leakage can
occur from the active parts to the inactive structural steel
parts. Therefore, 3D FEA is also performed to calculate no
the overall field distribution.
Comparison between 2D and 3D FEA is also performed
to compensate computational error which is possibly
caused by 2D FEA since 2D FEA cannot fully consider
design dimensions and major
Value Unit
136 -
s) 3 -
24 -
35.0 mm
4.0 mm
3.0 mm
0.7 mm
0.4 mm
2.7 mm
114 mm
174.2 mm
195 mm
22.5 mm
2.5 mm
80 mm
Br=1.3T, µr=1.05 -
S18 -
95 %
1.0 Ohm
300 Vdc
4.25 Arms
31.2 Nm
60 RPM
196 W
Design Considerations and Validation of Permanent Magnet Vernier Machine with Consequent Pole Rotor for Low Speed Servo~
744
leakage within the motor. Fig. 4 illustrates no load field
distribution considering all steel structure within the motor.
For the field computation, all the inactive steel parts are
conservatively considered as simple insaturable iron which
has a constant relative permeability of 4000. Considering
the overall field distribution, flux leakage seems to be
negligible. Fig. 5 compares no load induced voltage
obtained by 2D and 3D FEA. It should be noted that the
waveforms are well balanced due to the pole-slot
combination and the winding arrangement. However, there
is computational difference between 2D and 3D FEA
which is about 10.9%.
Therefore, it would be reasonable to apply a correction
factor of 0.891 to the 2D FEA results when comparing with
the experimental results based on this difference. This
correction will be discussed in the following section.
3. Experimental validation
3.1 Prototype and experimental setup
Rotor assembly and stator with windings are
respectively shown in Figs. 6(a) and (b). When the size of
the motor is taken into consideration, it is not difficult to
recognize excessively long end winding shown in Fig. 6(b).
This was nearly unavoidable due to easier winding
insertion in prototyping. This leads to copper loss increase
and efficiency decrease at the same time. Fig. 7(a) shows
static torque measurement setup where the prototype
PMVM is connected to a reduction gear box and excited by
external DC current source between Ph.U and Ph.V. A non-
contact torque sensor is located between the reduction gear
box and the prototype. The static torque was measured
every 0.22 mechanical degrees which corresponds to 15
electrical degrees. The rotation angle was measured with a
built in angular encoder of which resolution is 400,000
division/revolution. Fig. 7(b) shows dynamo test bench for
0 30 60 90 120 150 180-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Coggin
g torq
ue[
Nm
]
Before skewing
After skewing
Electrical angle[Deg.] (a) Cogging torque.
0 30 60 90 120 150 18030
31
32
33
34
35
Torq
ue[
Nm
]
Before skewing( Ripple 1.6%)
After skewing( Ripple 0.7%)
Electrical angle[Deg.]
_+_+
(b) Rated torque.
0.0
0.4
0.8
1.2
0
30
60
90
120
150
180
210
240
270
300
330
0.0
0.4
0.8
1.2
Rad
ial fo
rce
den
sity
[N/m
m2]
Mechanical angle[Deg.]
(c) Radial force distribution at rated state.
Fig. 3. 2D FEA results.
Fig. 4. No load field distribution by 3D FEA considering
inactive structural steel parts.
0 60 120 180 240 300 360-60
-40
-20
0
20
40
60
27.8Vrms
31.2Vrms
33.1Vrms
2D FEA(Before skewing)
2D FEA(After Skewing)
3D FEA
No load
induce
d v
oltage
at 120R
PM
[V]
Electrical angle[Deg.]
Fig. 5. No load induced voltage comparison.
Rotor structural parts
Simplified bearing
Shi-Uk Chung, Yon-Do Chun, Byung-Chul Woo, Do-Kwan Hong and Ji-Young Lee
745
dynamic torque and efficiency.
3.2 No load induced voltage and static torque
measurement
Fig. 8(a) shows linear variation of no load induced
voltage measured at several RPMs on the dynamo test
bench. Measured no load induced voltage and computed no
load induced voltage are compared in Figs. 8(b) and (c),
respectively. It can be seen that sinusoidal no load induced
voltage is obtainable and the measurement and the analysis
agree well each other within 3% differences.
Static torque measurement and 3D FEA are compared in
Fig. 9 which shows about 2% differences on average value.
It should be noted that the waveforms are quite sinusoidal.
Therefore, the prototype is expected to have smooth torque
characteristic which is required especially for low speed
servo applications. It is seen in Fig. 10 that the 2D FEA
results simulates much closer to the actual dynamic
situation when considering the computation error
correction factor which is mentioned in the preceding
section.
However, measured efficiency shown in Fig. 11 is not
much satisfactory and the maximum efficiency is measured
to be merely around 79%(at output power of 157W) since
the prototype has short stack and suffers appreciable flux
leakage within the motor as seen in the comparison of 2D
and 3D FEA. Moreover, due to the winding insertion issue
in prototyping, it suffers considerably higher copper loss
than expected. Therefore, a larger and better-made
(a) Rotor assembly (b) Stator winding
Fig. 6. Prototype PMVM.
(a) Static torque measurement setup
(b) Dynamo test bench
Fig. 7. Prototype and experimental setup.
PMVM
Reduction
gear
Torque sensor
PMVMLoad motor
Torque sensor
60 120 180 24010
20
30
40
50
60 3D_FEA
Measurement
Induce
d v
olt
age[
Vrm
s]
RPM (a) Linear variation of no load induced voltage.
(b) Measurement at 120RPM(27.0Vrms)
(c) 3D FEA at 120 RPM(27.8Vrms)
Fig. 8. No load induced voltage comparison between
analysis and measurement.
Fig. 9. Static torque under DC current excitation.
20V/div.
0 2 4 6 8 10 12 14 16 18 20-80
-60
-40
-20
0
20
40
60
80
Volt
age[
V]
Time[msec]
0 30 60 90 120 150 1800
5
10
15
20
25
100% of rated current
Symbol : Measurement
Line : 3D FEA
Sta
tic
torq
ue
by P
h.U
& P
h.V
[Nm
]
Electrical angle[Deg.]
50% of rated current
Design Considerations and Validation of Permanent Magnet
prototype is expected to display higher efficiency in such a
low speed region.
Table 2 compares loss components obtained by 2D FEA
after the correction with ones by the experiment. In the loss
computation, PM eddy loss is not considered and the
mechanical loss is considered using the value obtained by
the experiment. The mechanical loss coeffic
to be 0.01576W/RPM. It can be said that
efficiency after the correction is quite reasonable.
4. Conclusion This paper has presented another feasible pole
combination of PMVM with CP rotor and its geometric
relation has been also mathematically
0 1 2 3 40
15
30
45
Current[Arms
]
2D FEA
2D FEA after error correction
Dynamo test at 60RPM
Torq
ue[
Nm
]
Fig. 10. Torque vs. current characteristics
Fig. 11. Measured efficiency
Table 2. Loss components comparisons at 60RPM.
Item Unit
Ph. current Arms 0.95 2.55
Copper loss W 3.2 22.8
Core loss W 5.1 7.2
Mechanical loss W 0.9 0.9
Total loss W 9.2 31.0
Output torque Nm 6.1 16.7
Output power W 38.5 104.8
Efficiency(2D FEA) % 80.6 77.2
Efficiency(experiment) % 73 76
5 10 15 20 25
65
70
75
80 120RPM
60RPM(2D FEA)
60RPM
Torque[Nm]
Eff
icie
ncy
[%]
Permanent Magnet Vernier Machine with Consequent Pole Rotor
746
prototype is expected to display higher efficiency in such a
pares loss components obtained by 2D FEA
correction with ones by the experiment. In the loss
, PM eddy loss is not considered and the
mechanical loss is considered using the value obtained by
the experiment. The mechanical loss coefficient turned out
to be 0.01576W/RPM. It can be said that the estimated
efficiency after the correction is quite reasonable.
This paper has presented another feasible pole-slot
combination of PMVM with CP rotor and its geometric
mathematically introduced. An
exemplary PMVM has been analyzed by extensive 2D and
3D FEA and the validity of the analysis has been
experimentally examined for the prototype. Future research
on geometry optimization, performance improvement and
positioning control capability of the proposed PMVM
needs to be followed.
References
[1] A. Toba, and A. Lipo,
manent magnet vernier
Annual Meeting, Oct. 1999,
[2] A. Toba, and A. Lipo,
design methodology of
vernier machine,” IEEE Trans. Ind. Appl.
No. 6, pp. 1539-1546, Nov./Dec. 2000.
[3] E. Spooner, and L. Haydock,
chines,” in Proc. IEE Electr. Power Appl.
No. 6, pp. 655-662, Nov. 2003.
[4] J. Li, K.T. Chau, J.Z. Jiang, C. Liu, and W. Li,
new efficient permanent
Wind Power Generation
46, No. 6, pp. 1475-1478, June 2010.
[5] S. Niu, S.L. Ho, W.N. Fu, and L.L. Wang,
tative comparison of novel
machines,” in IEEE Trans. Magn.
2032-2035, June 2010.
[6] C. Liu, J. Zhong, and K. T. Chau,
controllable vernier permanent
IEEE Trans. Magn., Vol.
Oct. 2011.
[7] S. Niu, S. L. Ho, W. N. Fu,
dual-structure permanent
Trans. Magn., Vol. 46,
2010.
[8] S. U. Chung, J. W. Kim, B. C. Woo, D. K. Hong, J. Y
Lee, and D. H. Koo, “
three-phase permanent magnet vernier machi
consequent pole rotor,” IEEE Trans. Magn.
No. 10. pp. 4215-4218, Oct. 2011.
[9] D.G. Dorrell, M.F. Hsieh, and Y.G. Guo,
balanced magnet pull in large brushless rare
permanent magnet motors with rotor eccentricity,
IEEE Trans. Magn., Vol.
Oct. 2009.
Shi-Uk Chung
M.S. and Ph.D. degrees in mechanical
engineering from Pusan National Uni
versity, Busan, South Korea in 1997,
1999 and 2010, respectively.
2002 to 2005, he was with Samick
THK as a Researcher. Since 2005, He
has been with Electric Motor Research
5 6
orque vs. current characteristics.
Measured efficiency.
at 60RPM.
Value
2.55 4.25 5.2
22.8 63.3 94.7
7.2 11.2 13.9
0.9 0.9 0.9
31.0 75.4 109.5
16.7 27.6 33.3
104.8 173.4 209.1
77.2 69.7 65.6
69 66
30 35
120RPM
60RPM(2D FEA)
60RPM
Vernier Machine with Consequent Pole Rotor for Low Speed Servo~
exemplary PMVM has been analyzed by extensive 2D and
3D FEA and the validity of the analysis has been
experimentally examined for the prototype. Future research
on geometry optimization, performance improvement and
positioning control capability of the proposed PMVM
References
A. Toba, and A. Lipo, “Novel dual-excitation per-
ernier machine,” Proc. IEEE IAS
, Oct. 1999, Vol. 4, pp. 2539-2544.
“Generic torque-maximizing
ethodology of surface permanent-magnet
IEEE Trans. Ind. Appl., Vol. 36,
1546, Nov./Dec. 2000.
E. Spooner, and L. Haydock, “Vernier hybrid ma-
IEE Electr. Power Appl., Vol. 150,
662, Nov. 2003.
J. Li, K.T. Chau, J.Z. Jiang, C. Liu, and W. Li, “A
ermanent-magnet vernier machine for
Wind Power Generation,” IEEE Trans. Magn., Vol.
1478, June 2010.
S. Niu, S.L. Ho, W.N. Fu, and L.L. Wang, “Quanti-
ovel vernier permanent magnet
IEEE Trans. Magn., Vol. 46, No. 6, pp.
C. Liu, J. Zhong, and K. T. Chau, “A novel flux-
ermanent-magnet machine,”
Vol. 47, No. 10, pp. 4238-4241,
S. Niu, S. L. Ho, W. N. Fu, “A novel direct-drive
ermanent magnet machine,” IEEE
46, No. 6, pp. 2036-2039, June
S. U. Chung, J. W. Kim, B. C. Woo, D. K. Hong, J. Y
“A novel design of modular
phase permanent magnet vernier machine with
IEEE Trans. Magn., Vol. 47,
4218, Oct. 2011.
D.G. Dorrell, M.F. Hsieh, and Y.G. Guo, “Un-
balanced magnet pull in large brushless rare-earth
permanent magnet motors with rotor eccentricity,”
Vol. 45, No. 10, pp. 4586-4589,
Uk Chung He received the B.S.,
M.S. and Ph.D. degrees in mechanical
engineering from Pusan National Uni-
versity, Busan, South Korea in 1997,
1999 and 2010, respectively. From
2002 to 2005, he was with Samick
THK as a Researcher. Since 2005, He
has been with Electric Motor Research
Shi-Uk Chung, Yon-Do Chun
Center, Korea Electrotechnology Research Institute,
Changwon, South Korea, as a Senior Researcher. His
research interests include the design and
and rotary direct drive electric machines.
Yon-Do Chun He received
M.S. and Ph.D. degrees in electrical
engineering from Hanyang University
Seoul, Korea, in 1996
respectively. From 2001 to 2003, he
received a Japan Society for the
Promotion of Science (JSPS)
ship and he was with the Department
of Electrical Engineering at Waseda Univers
scholar. From 2004 to 2011, he was with M
Research Group, Korea Electrotechnology Research
Institute, Changwon, South Korea, as a Senior Researcher.
Since 2012, he has been with Electric Motors Research
Center as a Principal Researcher and Technical Leader
research interests include the design and analysis
industrial induction machines, permanent-
and high torque machines.
Byung-Chul Woo He received the B.S.
degree in mechanical engineering from
Youngnam University, Gyeongsan,
South Korea, in 1989, the M.S. and
Ph.D. degrees in mechanical design
engineering from Kyungpook National
University, Daegu, South Korea in
1991 and 2000, respective
currently with Electric Motor Research Center, Korea
Electrotechnology Research Institute, Changwon, South
Korea, as a Principal researcher and Technical Leader. His
research interests include the design and analysis of electric
machines and power plants.
Do Chun, Byung-Chul Woo, Do-Kwan Hong and Ji-Young Lee
747
Center, Korea Electrotechnology Research Institute,
won, South Korea, as a Senior Researcher. His
analysis of linear
He received the B.S.,
M.S. and Ph.D. degrees in electrical
ngineering from Hanyang University,
96, 1998 and 2001,
. From 2001 to 2003, he
received a Japan Society for the
Promotion of Science (JSPS) fellow-
with the Department
Waseda University as a visiting
was with Mechatronics
Korea Electrotechnology Research
as a Senior Researcher.
with Electric Motors Research
Principal Researcher and Technical Leader. His
design and analysis of
-magnet machines
He received the B.S.
degree in mechanical engineering from
Youngnam University, Gyeongsan,
South Korea, in 1989, the M.S. and
Ph.D. degrees in mechanical design
engineering from Kyungpook National
University, Daegu, South Korea in
1991 and 2000, respectively. He is
currently with Electric Motor Research Center, Korea
Electrotechnology Research Institute, Changwon, South
Korea, as a Principal researcher and Technical Leader. His
interests include the design and analysis of electric
Do-Kwan Hong
M.S. and Ph. D degree
engineering from Dong
Busan, South Korea, in 1998, 2000 and
2004, respectively. Since 2004, He has
been with Electric Motor Research
Center, Korea Electrotechno
search Institute
Korea, as a Senior Researcher. His research interests
include the design, analysis and performance
ultra-high speed machine, motor
turbine generator.
Ji-Young
M.S, and Ph.D degrees in electrical
engineering from Changwon National
University,
in 2000, 2002, and 2006 respectively.
She is currently
Research Center,
nology Research Insti
South Korea, as a Senior Researcher
include the design and analysis of various electromagnetic
devices, permanent-magnet machines and transverse flux
machines.
Young Lee
Kwan Hong He received the B.S,
M.S. and Ph. D degrees in mechanical
engineering from Dong-A University,
Busan, South Korea, in 1998, 2000 and
2004, respectively. Since 2004, He has
been with Electric Motor Research
Korea Electrotechnology Re-
search Institute, Changwon, South
esearcher. His research interests
design, analysis and performance evaluation of
high speed machine, motor-generator for micro gas
Lee She received the B.S.,
M.S, and Ph.D degrees in electrical
engineering from Changwon National
University, Changwon, South Korea,
in 2000, 2002, and 2006 respectively.
currently with Electric Motor
Research Center, Korea Electrotech-
nology Research Institute, Changwon,
South Korea, as a Senior Researcher. Her research interests
include the design and analysis of various electromagnetic
magnet machines and transverse flux