Download Influence of Number of Poles, Magnet Arrangement, and Current

IEEE PEDS 2011, Singapore, 5 - 8 December 2011
Influence of Number of Poles, Magnet Arrangement,
and Current Density on Characteristics of Inner and
Outer Rotor PMSMs
Yusuke Tani*, Shigeo Morimoto*, Masayuki Sanada*
* Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka, Japan
[email protected]
Abstract-Permanent magnet synchronous motors (PMSMs) have
been increasingly used in various applications for their small
size and high efficiency. There are two major classes of PMSMs.
One is the inner rotor type (IR type) PMSM, which has the rotor
on the inside and the stator on the outside. The other is the outer
rotor type (OR type) PMSM, which has the rotor on the outer
side of the stator. In this paper, the characteristics of seven kinds
of IR type and OR type motor structures are compared by
changing the magnet arrangement, number of poles, and
current density.
I.
(b) IR-V6
(c) OR-S6
Permanent Magnet
INTRODUCTION
Permanent magnet synchronous motors (PMSMs) have
been increasingly used in various applications for their small
size and high efficiency. PMSMs are classified into two types
according to their motor structure. One is the inner rotor type
(IR type) PMSM, which has the rotor on the inside and the
stator on the outside. The other is the outer rotor type (OR
type) PMSM, which has the rotor on the outer side of the
stator. An OR type has a larger moment of inertia than an IR
type of the same motor diameter. The OR type has been the
topic of much interest and research [1-3]. Additionally, it has
been reported that the characteristics of PMSMs can be varied
by changing the magnet arrangement and motor structure [47]. In this paper, to clarify the motor structure performance,
the characteristics of torque, output power, loss, efficiency,
etc. are examined based on 2-D finite element method (FEM)
analysis of several motor structure types.
II.
(a) IR-S6
Rotor
(d) IR-S24
(f) OR-S24
III.
(e) IR-V24
(g) OR-V24
Fig. 1. Analysis models.
CHARACTERISTICS AT THE RATED CURRENT
ANALYSIS MODELS
A. Torque Characteristics
Fig. 2 shows the magnet torque, reluctance torque, and total
The seven types of motor models evaluated in this study
torque of each model at the rated current of Ia = 11.8 A,
are illustrated in Fig. 1, and the motor specifications are
which corresponds to a current density of 5 A/mm2. The ORshown in Table 1. In Fig. 1, (a) through (c) are 6-pole
S24 model has the maximum average torque (31.65 Nm) of
machines, and (d) through (g) are 24-pole machines. The 6all models. This is because the OR-S24 model can use
pole machines have 9 slots, and the 24-pole machines have 36.
magnetic flux linkage effectively. In the IR type SPM
All of the stator models have concentrated windings.
structures, the average torque decreases because the magnetic
Regarding the rotor structures of the analysis models, the
flux leakage increases as the number of poles increases. The
models of (a), (c), (d), and (f) are surface-mounted PM (SPM)
SPM structures produce only magnet torque, while the Vmotors, and the models of (b), (e), and (g) are V-shaped
shaped IPM structures use both magnetic torque and
interior PM (IPM) motors. All of the models have nearly the
reluctance torque. This is because the V-shaped IPM
same amount of rare-earth PMs with a high coercivity.
structures have saliency. The total torques of IR-V6, IR-V24,
Additionally, the air gap lengths and stack lengths are the
and OR-V24 are almost identical, but their ratios of magnetic
same in each model.
torque to reluctance torque are different.
978-1-4577-0001-9/11/$26.00 ©2011 IEEE
711
Table 1. Specifications of the motors.
Model
IR-S6 IR-V6 OR-S6 IR-S24 IR-V24 OR-S24 OR-V24
Number of poles
6
24
Motor type
IR
OR
IR
OR
Rotor type
SPM
IPM
SPM
SPM
IPM
SPM
IPM
Number of slots
9
36
Motor outer diameter [mm]
250
Air gap length [mm]
0.5
Stack length [mm]
20
Rated current density [A/mm2]
5.0
Coercive force of PM [kA/m]
900
Torque (Nm)
40
30
Ia =11.8A
31.65
28.18
25.45
24.75
6.88
5000
Relactance torque
28.52
3.02
28.68
28.51
7.10
20
10
25.45
24.75
21.30
25.50
28.68
31.65
IR-V6
4000
Power (W)
M agnet torque
3000
IR-S6
2000
OR-S6
1000
21.41
Fig. 2. Torque characteristics.
0
OR-V24
OR-S24
OR-S6
IR-V6
IR-S24
IR-S6
IR-V24
0
0
1000
2000
3000
4000
5000
-1
Speed (min )
(a) 6-pole machines
5000
B. Speed-Power Characteristics
Fig. 3 shows the output power versus speed characteristics.
In this simulation, the voltage limit value Vam is 350 V, and
the current limit value Iam is 11.8 A. Maximum torque per
ampere control is applied below the base speed, where the
voltage reaches the voltage limit, and flux-weakening control
is used above the base speed. From Fig. 3, the constant-torque
regions of the 24-pole machines are wider than those of the 6pole machines. The OR type SPM model exhibits the largest
output power in the low-speed region because it produces the
highest torque, as shown in Fig. 2. This model also exhibits
the largest output power at the base speed. The 24-pole
machines have a lower limit speed than the 6-pole machines.
Of the 6-pole machines, the IR-V6 model has the widest
speed range. Of the 24-pole machines, the OR-V24 model has
the widest speed range. On the other hand, the OR type SPM
models cannot be used at the high-speed region, because the
effect of flux weakening is small. The OR-S24 model is
suitable for producing high torque and high power in the lowspeed region (below the base speed), and the IR-V6 model is
suitable for wide constant-power operation.
Power (W)
4000
3000
2000
OR-V24
1000
OR-S24
0
0
IR-S24
IR-V24
1000
2000
3000
4000
5000
-1
Speed (min )
(b) 24-pole machines
Fig. 3. Speed-power characteristics.
(Vam = 350 V, Iam = 11.8 A).
Table 2. Power and efficiency at the base speed.
Base speed [min-1]
Power [W]
Efficiency [%]
IR-S6
1282
3418
94.59
IR-V6
1187
3502
94.50
OR-S6
1208
3627
95.27
IR-S24
1405
3560
95.77
IR-V24
1283
3736
95.62
OR-S24
1201
3891
95.84
OR-V24
1367
3845
95.39
712
150
100
50
OR-V24
OR-S24
IR-V24
IR-S24
OR-S6
0
IR-V6
T: average torque (Nm) calculated by FEM,
Wiron: iron loss (W),
M: mechanical rotational speed (rad/s),
Wcopper: copper loss (W).
The copper loss is calculated as follows:
W copper  3R a I e 2 (W)
(2)
Iron loss
200
IR-S6
where
Cupper loss
250
Loss (W)
C. Efficiency and Losses
The power and efficiency at the base speed are shown in
Table 2, and Fig. 4 shows the losses at the base speed. The
efficiency is calculated as follows:
 T  Wiron
(%)
(1)
 M
M T＋Wcupper
Fig. 4. Losses at the base speed.
where
n 

  kf 
 kf 
2
2
Wedd i    
 Bk i  (W/kg)
 Brk i   

 100 
k 1 
  100 
(4)
2
Wiron   mi Whys i  Wedd i  (W)
2
N
IR-S6
IR-V6
OR-S6
80
60
Torque T (Nm)
Ra: armature winding resistance (),
Ie: phase current RMS value (A) (  I a 3 ).
The hysteresis and eddy-current losses are referred to
collectively as the iron loss, which is calculated as follows:
n
  kf 
 kf 
2
2
Whys i    
 Brk i   
 Bk i  (W/kg) (3)
 100 
k 1   100 

40
(5)
20
i 1
where
5
10
15
Current density (A/mm2)
(a) Torque
20
3.5
^
Normalized torque T
Whys-i: hysteresis loss of one element (W/kg),
k: harmonic order,
: constant of hysteresis loss,
f: fundamental frequency (Hz),
i: number of elements,
Brk-i: flux density amplitude in the radial direction at
harmonic order k and element number i (T),
Bk-i: flux density amplitude in the circumferential
direction at harmonic order k and element number i
(T),
Wedd-i: eddy-current loss of one element (W/kg),
: constant of eddy-current loss,
N: total number of elements,
mi: mass of the i-th element (kg).
The flux density of one electric cycle in each element is
calculated by analyzing the static magnetic field. The iron
loss is calculated from the data of each element. Moreover,
high harmonics of the flux density are also considered.
However, the eddy-current loss generated in the magnet is not
taken into account.
The copper losses of the 24-pole machines are small
because the end winding decreases as the number of poles
increases. On the other hand, the iron losses of the 24-pole
machines are large because the driving frequency is high
compared to the 6-pole machines. The 24-pole machines have
a higher efficiency than the 6-pole machines at the base speed.
3
2.5
2
1.5
1
5
10
15
Current density (A/mm2)
20
(b) Normalized torque
Fig. 5. Torque characteristics as a function of
current density (6-pole machines).
713
IR-S24
OR-S24
IR-V24
100
OR-V24
Normalized torque T
Torque T (Nm)
^
3.5
80
60
40
3
2.5
2
1.5
1
20
5
10
15
5
20
10
15
20
Current density (A/mm2)
Current density (A/mm2)
(a) Torque
(b) Normalized torque
Fig. 6. Torque characteristics as a function of current density (24-pole machines).
CHARACTERISTICS UNDER HIGH CURRENT DENSITY
A. Torque Characteristics
Figs. 5 and 6 show the torque and normalized torque for the
6-pole machines and the 24-pole machines, respectively. The
normalized torque is calculated with respect to the torque at a
current density of 5 A/mm2. In all of the models, the
normalized torque is not proportional to the current density
because of the magnetic saturation from the high current. For
the 6-pole machines, the IR type SPM model has the highest
normalized torque, and it has the highest torque at a high
current density (over 15 A/mm2). For the 24-pole machines,
the IR type SPM model has the highest normalized torque,
but the OR type SPM model has the highest torque.
In considering the influence of the magnet arrangement, the
V-shaped models, in which permanent magnets are embedded
in the rotor, are affected by magnetic saturation more than the
SPM models. Therefore, the normalized torques of the Vshaped models are low.
B. Magnetic Flux Linkage
Fig. 7 shows the normalized magnetic flux linkage ˆa ,
which is calculated by normalizing the magnetic flux linkage
a with respect to a at a current density of 5 A/mm2, where
a is calculated by
T
a  0
(6)
Pn I a
and where
T0: torque at the condition of id = 0,
Pn: number of pole pairs,
Ia : armature current (= iq).
IR-S6
OR-S6
IR-V6
1
Normalized a
The motors of electric and hybrid-electric vehicles are
driven by a large current in order to obtain a high torque [8].
In such situations, the motor parameters and characteristics
are changed due to magnetic saturation. Therefore, the
influence of current density is examined with respect to the
seven motor models shown in Fig. 1 by changing the current
density between 200%, 300%, and 400%.
0.8
0.6
0.4
5
10
15
20
Current density (A/mm2)
(a) 6-pole machines
IR-S24
IR-V24
OR-S24
OR-V24
1
Normalized a
IV.
0.8
0.6
0.4
5
10
15
20
Current density (A/mm2)
(b) 24-pole machines
Fig. 7 Normalized a.
The value of a decreases as the current increases because of
magnetic saturation. From Fig. 7, the values of a for the 6pole machines are more likely to decrease than for the 24pole machines, and the values of a for V-shaped models are
more likely to decrease than for SPM models.
714
8000
10000
OR-S24
IR-S24
8000
6000
OR-S6
4000
IR-V6
2000
Power (W)
Power (W)
IR-S6
6000
IR-V24
4000
OR-V24
2000
0
0
0
1000
2000
3000
4000
5000
0
1000
2000
3000
4000
5000
Speed (min-1)
Speed (min-1)
(a) 6-pole machines
(b) 24-pole machines
Fig. 8. Speed-power characteristics (Vam = 350 V, Iam = 23.6 A).
8000
12000
OR-S24
10000
6000
Power (W)
Power (W)
IR-S6
OR-S6
4000
IR-V6
2000
IR-S24
8000
6000
IR-V24
4000
OR-V24
2000
0
0
0
1000
2000
3000
4000
5000
0
8000
2000
3000
12000
IR-S6
4000
6000
OR-S6
4000
IR-V6
2000
5000
OR-S24
10000
Power (W)
Power (W)
1000
Speed (min-1)
Speed (min-1)
(a) 6-pole machines
(b) 24-pole machines
Fig. 9. Speed-power characteristics (Vam = 350 V, Iam = 35.3 A).
IR-S24
8000
6000
IR-V24
4000
OR-V24
2000
0
0
0
1000
2000
3000
4000
5000
Speed (min-1)
(a) 6-pole machines
0
1000
2000
3000
4000
Speed (min-1)
(b) 24-pole machines
5000
Fig. 10. Speed-power characteristics (Vam = 350 V, Iam = 47.2 A).
C. Speed-Output Characteristics
Fig. 8 shows the output power versus speed characteristics.
In this simulation, the voltage limit value Vam is 350 V, and
the current limit value Iam is 23.6 A, which corresponds to a
current density of 10 A/mm2. Figs. 9 and 10 depict the
situation where the current densities are 15 and 20 A/mm2,
respectively. Maximum torque per ampere control is applied
below the base speed, where the voltage reaches the voltage
limit, and flux-weakening control or maximum torque per
flux control is used above the base speed. In Fig. 8, the 6-pole
machines have a wide constant-power region because the
value of dmin in all of the 6-pole machines is less than zero.
The value of dmin represents the effect of flux weakening
(the operating limits become infinity when dmin < 0) and is
calculated by
dmin =a- LdIam
(7)
where
a: the magnetic flux linkage [Wb],
Ld : d-axis component of inductance [H],
Iam: current limit value [A].
The IR-S6 model has the highest power of the 6-pole
machines. Among the 24-pole machines, the IR-S24 model
has the widest speed range because its value of dmin is small.
715
IR-S6
OR-S6
IR-V6
IR-S24
OR-S24
OR-V24
10
15
20
0.2
0.5
0.1
0
dmin (Wb)
dmin (Wb)
IR-V24
-0.5
-1
0
-0.1
-0.2
-0.3
-1.5
5
10
15
20
5
2
2
Current density (A/mm )
(a) 6-pole machines
Current density (A/mm )
(b) 24-pole machines
Fig. 11. Minimum d-axis components of flux linkage.
The OR-S24 model has high power in the low-speed region
because it has the highest torque. Compared to Fig. 3, the
speed range and constant-power region widen when twice the
current is applied because the effect of flux weakening
increases.
In considering the influence of the current-density value on
the output power versus speed characteristics, the output
power in the constant-torque region increases because
maximum torque increases. In the 6-pole machines, there is
little change in the maximum output power when over twice
the rated current is applied. In the 24-pole machines, the
maximum output power increases under three-times the rated
current, but the output power at four-times the rated current is
almost equal to that at three-times the rated current. From Fig.
3, the maximum output power is 4000 W in all of the models.
However, at four-times the rated current, there are differences
among the models, and the OR-S24 model has the largest
output power.
D. Minimum d-Axis Components of Flux Linkage
The minimum d-axis components of flux linkage are shown
in Fig. 11. The value of dmin decreases as the current
increases because of the increase in armature reaction flux.
The values of dmin for all of the 6-pole machines, IR-V24,
and OR-V24 are negative when twice the rated current is
applied. The values of dmin for IR-S24 and OR-S24 are
positive when twice the rated current is applied. From Figs.
8-11, for the models with a small value of dmin, the limit of
the maximum output power is low. The OR-S24 model has
the largest value of dmin, and its maximum output power is
the highest.
V.
CONCLUSION
Seven kinds of motor structures, including IR type and OR
type, were compared by changing the magnet arrangement,
number of poles, and current density. At the rated current
density, the OR-S24 model (24-pole OR type SPM model)
had the highest power in the low-speed region.
At the high current density condition, the rate of torque to
current in the V-shaped IPM models decreased compared to
the SPM models because of the influence of magnetic
saturation. When twice the rated current was applied, the 6pole machines had wider constant-power and speed regions
than the 24-pole machines. When the rated current was
applied, the maximum output power was 4000 W in all of the
models, but under a high current density, there were
differences among the models. For the models with a small
value of dmin, the limit of maximum output power was low.
The OR-S24 model had the largest value of dmin, so its
maximum output power was the highest.
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