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

(suchung@keri.re.kr)

** 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