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Ruiwu Cao1, Ming Cheng1, Wei Hua1, Wenxiang Zhao2, Yi Du 1,2
1School of Electrical Engineering, Southeast University, Nanjing, China
2 School of Electrical and Information Engineering, Jiangsu University, Zhenjiang, China
Email: mcheng@seu.edu.cn
Abstract — In this paper, a new permanent magnet (PM)
linear motor is proposed, in which both the magnets and
armature windings are placed in the short mover, while the long
stator consists of iron core only. Hence, this new PM linear
motor can be called as primary permanent magnet linear motor,
which exhibits the advantages of robust and simple mover, low
cost, high efficiency, high power factor, and high thrust force
density, especially suitable for the long stator application such as
urban rail transit. Its topology structure and operation principle
are introduced firstly. Then, the static characteristics are
investigated, including field distributions, flux-linkage, back-
EMF, phase inductance and thrust force. In addition, the
technique of skewing stator teeth is adopted to improve the
electromagnetic performance. Finally, finite element method
(FEM) is used to verify the theoretical analysis results.
I. INTRODUCTION
Currently, the main types of traction motors used for urban
rail transit (URT) can be classed by rotate motor and linear
motor briefly. Obviously, direct linear drive motor has the
benefits of higher dynamic performance, improved reliability,
lower noise, and higher efficiency due to the avoidance of the
energy conversion from rotary to linear motion [1]-[3]. The
conventional permanent magnet (PM) linear motor exhibits
higher efficiency and power factor than those of the induction
linear motor [4]. However, in the long stator application such
as URT, this solution inevitably results in significant cost
increase due to a large amount of magnets or armature
windings set on the stator. In recent years, a new class of PM
brushless motors with PMs in the stator, namely the doubly-
salient PM (DSPM) motor [5]-[10], has received wide
attentions due to its merits of high power density, robust
mechanical integrity and free from thermal dissipation
problem.
Based on the rotary DSPM motor, a new primary PM
magnet linear (PPML) motor is proposed and investigated in
this paper. Firstly, the topology and principle of the proposed
PPML motor will be introduced in section . Then, the
additional teeth number will be discussed for reducing the
cogging force and balancing flux leakage resulted from end
effect in section . Thirdly, the electromagnetic
performances of the PPML motor will be investigated in
section . Finally, based on finite element method (FEM),
the influence of the skewed stator on the electromagnetic
characteristics of PPML motor will be discussed in section IV.
II. TOPOLOGY AND PRINCIPLE
A. Topology
Based on the rotary topology of a 12-stator-slot/8-rotor-
pole three phase DSPM motor [11], a new PPML motor is
proposed as shown in Fig. 1(a), in which both the PMs and
the armature windings are set on short primary mover while
the long secondary stator is only made of iron. For the URT
application, the primary should be set at the steering device
of the train and the iron stator be fixed between the two rails
along the whole line. Fig. 1(b) shows the cross-section and
configuration of the proposed PPML motor. In order to
balance the magnetic circuit of the end part for armature
winding, the additional teeth are set at each end part of the
primary mover. Also, five pieces of magnets are inserted in
the mover iron yoke, which are magnetized alternatively in
the motion directions. In addition, similar to the DSPM motor,
the concentrated armature windings are employed on the
mover teeth except for the additional teeth. The basic design
dimensions of the PPML motor are listed in Table I.
(a)
(b)
Fig. 1. The topology of PPML motor. (a) Configuration. (b) Cross-section.
TABLE I
DESIGN SPECIFICATIONS OF PPML MOTOR
Items PPML motor
Rated speed (m/s) 3
Mover and stator width (mm) 75
Mover yoke high (mm) 26
Mover slot high(mm) 19
Mover pole pitch m (mm) 33
Stator pole pitch s (mm) 49.5
Mover tooth width (mm) 16.5
Stator tooth width (mm) 22
Stator tooth high (mm) 15
Stator yoke high (mm) 17
Total magnet volume dimensions (mm3) 7*26*75*5
Magnet remanence (T) 1.2
Air gap length (mm) 0.6
Number of turns per coil (Turns) 74
Rated Peak current (A) 4.69
B. Operation principle
Assumption the fringing and end effect is negligible as
A New Primary Permanent Magnet Linear Motor for Urban Rail Transit
well as the permeability of the core is infinite, a linear
variation of PM flux linkage and thus a rectangular back-
EMF are resulted in each mover windings at open load as
shown in Fig. 2. Hence, a theoretical constant thrust force can
be achieved by applying a rectangular current in phase with
the back EMF waveform to the winding, i.e., a positive
current when the PM flux is increasing and a negative current
when the PM flux is decreasing.
PM
max
min
Em
-Em
Im
-Im
xps
xmt
x
x
x
e
i
0
0
0
Fig. 2. The operation principle of PPML motor.
III. INFLUENCE OF ADDITIONAL TEETH NUMBER
For the linear structure, the end effect on the cogging force
and back-EMF should be taken into account. In this section,
the performance of the proposed PPML motor with three
different additional mover teeth will be discussed. Based on
FEM, Fig. 3 shows the influence of the different additional
mover teeth (AMT) on the cogging force. Obviously, by
introducing three or two AMT, the cogging force can be
reduced significantly. Fig. 4 compares the back-EMF
waveforms with 1, 2, and 3 AMT at a speed of 3 m/s. It can
be seen that the waveform with 2 AMT are more symmetry
than the two others. Hence, two additional teeth are adopted
in this PPML motor and the following studies are based on
this structure.
-300
-200
-100
0
100
200
300
0 60 120 180 240 300 360
Mover position (Elec.degree)
Cogging force (N)
Cogging force-1 AMT
Cogging force-2 AMT
Cogging force-3 AMT
Fig. 3. Cogging force waveforms of the three topologies
20
45
70
95
120
0 60 120 180 240 300 360
Mover position (Elec.degree)
Back-EMF (V)
Fig. 4. Partial Back-EMF waveforms of three topologies.
IV. STATIC PERFORMANCE ANALYSIS
A. Field Distributions
Fig. 5(a) shows the open-circuit field distribution and Fig.
5(b) shows the air gap flux density from position “a” to
position “b”, respectively, where the flux-linkage of phase A
coils at the minimum value. It can be seen that the air-gap
flux density is non-sinusoidal and the peak air-gap flux
density is nearly 1.5T.
(a)
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 66 132 198 264 330 396
Displacement (mm)
Air-gap flux density (T)
(b)
Fig. 5. Flux distribution and air-gap flux density. (a) Flux distribution. (b)
Air-gap flux density.
B. Flux-linkage and back-EMF
The three phase flux-linkage waveforms of the proposed
PPML motor are shown in Fig. 6. Obviously, the three phase
flux-linkage waveforms are very symmetry and balanced as
well as nearly free from the end effect. The induced back-
EMF is given by:
v
x
d
d
t
dx
dx
d
d
t
d
emmm ⋅=⋅==
ψ
ψ
ψ
(1)
Where, x is the mover part displacement, v is the mover
speed, and m is the flux-linkage excited by PM only. Fig. 7
depicts the three phase back-EMF waveforms of the proposed
PPML motor by FEM. Since the additional teeth balance the
end part magnet circuit, the back-EMF waveforms are
perfectly symmetrical.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 60 120 180 240 300 360
Mover position (Elec.deg)
Flux-linkage(Wb)
Phase A (Wb) Phase B (Wb) Phase C (Wb)
Fig. 6. Flux-linkage waveforms of PPML motor.
-120
-90
-60
-30
0
30
60
90
120
0 60 120 180 240 300 360
Mover position (Elec. degree)
Back-EMF(V)
Phase A (V) Phase B (V) Phase C (V)
Fig. 7. Back-EMF waveforms of PPML motor.
C. Inductance
In order to calculate the inductance accurately, the method
considering the magnetic saturation [12] is adopted.
iL pm /)(
ψψ
−= (2)
Where, is the combined flux-linkage of phase-A
produced by both PM and phase current. pm is the PM flux-
linkage provided by PM only, L is the inductance of one
phase, i is the phase current. Hence, the self-inductance
waveforms of the proposed PPML motor with the positive
and negative currents are shown in Fig. 8, where
“Laa+4.69A” and “Laa-4.69A” denote the strengthening and
weakening action of the armature flux (with peak phase
current of 4.69A) to the PM flux of the complementary
structure, respectively.
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0 60 120 180 240 300 360
Mover position (Elec.degree)
Inductance (H)
Laa+4.6A Laa-4.6A
Fig. 8. Back-EMF waveforms of PPML motor.
D. Thrust Force
Fig. 9 shows the rated static thrust force of the proposed
PPML motor with 2 AMT excited by the traditional 120°
conduction method and cogging force waveforms.
Apparently, similar with that of rotary DSPM motor, the
thrust force ripple is relatively high due to the doubly-salient
structure. The detailed results are listed in TableĊ.
Fig. 10 shows the thrust force of the proposed motor with
different currents at BLDC operation mode.
-100
0
100
200
300
400
500
0 60 120 180 240 300 360
Mover position (Elec.degree)
Force (N)
Cogging force-2 AMT
Thrust force
Average thrust force
Fig. 9. Rated static thrust force waveforms of PPML motor.
TABLE II
CHARACTERISTICS OF THRUST FORCE AND COGGING FORCE
Items Cogging force Thrust force
Fmax(N) 62.3 315.2
Fmin(N) -62.5 177.1
Fave(N) -0.25 245.3
Fri
pp
le(N) 124.7 138.1
0
100
200
300
400
500
600
0246810
Phase current peak value (A)
Average thrust force (N)
Fig. 10. Static thrust force versus phase peak current.
V. EFFECT OF STATOR TOOTH SKEWING
Based on the above results, it can be seen that the cogging
force and thrust force ripple of proposed PPML motor are
relatively high. In order to minimization the DSPM motor
cogging torque, a skewing rotor teeth method was proposed
in [13]-[14]. Since the stator of proposed PPML motor are
also simple, hence the skewed stator teeth method is adopted
for PPML motor as shown in Fig. 11.
Fig. 11. The top view of the stator teeth skewed model.
Par
t
Hence, the skewed static characteristics, including the PM
flux-linkage, back-EMF, inductance, and cogging force can
be obtained from the un-skewed 2-D FEA results as follows:
() ()
¿
¾
½
¯
®
»
¼
º
«
¬
ª¸
¹
·
¨
©
§++
¸
¹
·
¨
©
§−+
+
=¦
=
N
k
ssss N
k
xf
N
k
xfxf
N
xf
1
'
2212
1
δδ
(3)
Where f (xs) and f ’(xs) denotes the static characteristics of
the proposed PPML motor with skewed and without skewed
stator teeth, respectively. 2N is the segments number of the
stator teeth along the teeth width axis, is the skewing
displacement and k is temporary variable iteration.
Fig.11 shows the top view of skewed stator teeth model.
Axis of x and y denote the direction of mover motion and
mover teeth width, relatively. Obviously, the static
characteristics of PPML motor with skewed teeth at position
xs can be modeled as the average of the sum values at a series
of mover position from xs-/2 to xs+/2 with un-skewed stator
teeth. So the influences of skewed stator teeth on the back-
EMF and cogging force waveforms are shown in Fig. 12.
In the process of computation, one period is divided into
90 steps, namely the stator pole pitch is divided into 90
segments. Hence, the “Skewed_10” denotes the skewing
displacement is s*10/90. Obviously, the skewed stator teeth
method can improve the back-EMF waveform to be more
sinusoidal and extremely reduce the cogging force.
It should be noted that by skewing stator teeth, the peak
value of the back-EMF is reduced to some extent, which is
unfavorable for the thrust force production. So, considering
the reduction and total harmonic distortion in back-EMF, the
“Skewed_34” is adopted in this proposed PPML motor.
Fig. 13 compares the back-EMF and cogging force
waveform without and with “Skewed_34” stator teeth.
Apparently, after skewing, the back-EMF waveform is close
to the sine waveform, indicating that the BLAC operation is
suitable for this motor. In addition, the cogging force is
reduced significantly, which is beneficial to the BLAC
operation with minimum force ripple.
Fig.14 compares the self-inductance under PM
strengthened “Laa+4.6A” and PM weakened “Laa-4.6A”
condition with and without stator teeth skewing. It can be
seen that in both cases the self-inductance waveforms with
skewed stator teeth are more sinusoidal than those of the un-
skewed stator teeth.
By skewing stator teeth, the back-EMF of the PPML motor
is sinusoidal and suitable for BLAC operation model. Hence,
if the sinusoidal phase current is applied into the winding in
phase with the back-EMF, the average static electromagnetic
thrust force can be express as
v
IE
F
v
eee
FFF mm
r
mamama
rpmem 2
3
≈+
++
=+= (4)
Where, ema, emb, emc, are the three phase back-EMF, v is the
motor speed, Em, Im are the peak value of the back-EMF and
phase current, respectively. Fpm is the PM thrust force. Fr is
the reluctance force, which is negligible comparison with the
PM thrust force.
Based on the above analysis, the thrust force (including the
cogging force) with “Skewed_34” stator teeth and without
skewed teeth under the same RMS phase current are shown in
Fig. 15. The detailed information is listed in Table ċ.
Obviously, the average thrust force value of the skewed teeth
motor is about 80% of the un-skewed structure, while the
force ripple is about 23.6% of the un-skewed motor.
-100
-80
-60
-40
-20
0
20
40
60
80
100
0 60 120 180 240 300 360
Mover position (Elec.degree)
Back-EMF (V)
Skewed_10
Skewed_16
Skewed_22
Skewed_28
Skewed_34
Skewed_40
Skewed
_
46
(a)
-60
-40
-20
0
20
40
60
0 60 120 180 240 300 360
Mover position (Elec.degree)
Cogging force (N)
Skewed_10 Skewed_16 Skewe d_22
Skewed_28 Skewed_34 Skewe d_40
Skewed_46
(b)
Fig. 12. The back-EMF and cogging fore waveforms of PPML motor with
different skewing teeth. (a) Back-EMF. (b) Cogging force.
-100
-75
-50
-25
0
25
50
75
100
0 60 120 180 240 300 360
Mover position (Elec.degree)
Back-EMF (V)
Unskewed
Skewed_34
(a)
-80
-60
-40
-20
0
20
40
60
80
0 60 120 180 240 300 360
Mover position (Elec.degree)
Cogging force (N)
Unsewed
Skewed_34
(b)
Fig. 13. The back-EMF and cogging fore waveforms of PPML motor with
and without skewing teeth. (a) Back-EMF. (b) Cogging force.
TABLE III
THRUST FORCE CAPABILITY COMPARISON.
Items Skewed stator teeth Straight stator teeth
Fmax(N) 217.6 315.2
Fmin(N) 184.9 177.1
Fave(N) 196.6 245.3
Fripple(N) 32.6 138.1
Par
t
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0 60 120 180 240 300 360
Mover position (Elec.degree)
Inductance (H)
Laa+4.6A
Laa-4.6A
Laa+4.6A_skewed
Laa-4.6A
_
skewed
Fig. 14. The phase inductance with different stator teeth.
0
50
100
150
200
250
300
350
0 60 120 180 240 300 360
Mover position (Elec.degree)
Thrust force (N)
Skewed thrust force
Unskewed thrust force
Fig. 15. Thrust force of PPML motor with different stator teeth.
VI. CONCLUSIONS
In this paper, a new primary permanent magnet linear
motor has been proposed and analyzed, in which the PM and
armature winding are all set on the short primary mover,
while the long stator is made force iron only. This motor
incorporates the merits of DSPM and linear motor, which is
perfectly suitable for the long stator applications, such as
urban rail transit, resulting in considerable reduction of
system cost. Then, different additional teeth added at each
end part of the primary mover have been studied, which make
the back-EMF waveforms are free from the end effect and
reduce the cogging force. Based on this structure, the
electromagnetic characteristics are studied by FEM. Finally,
the skewed stator teeth method has been adopted in this
motor to reduce the cogging force and eliminate the higher
harmonics in back-EMF, which make it is very suitable for
the BLAC operates with minimum thrust force ripple. The
proposed PPML motor offers a new scheme for the linear
motor drive system of urban rail transit.
VII. ACKNOWLEDGEMENT
This project was supported by National Natural Science
Foundation of China (Project No: 50907031), the Specialized
Research Fund for the Doctoral Program of Higher Education
of China (Project No: 20090092110034), the Fund Program
of Southeast University for Excellent Youth Teachers, a grant
from the Key Technology R&D Program of Jiangsu Province,
China (BE2009085) and 2010 foundation project of
technology innovation for graduate in Jiangsu Province.
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