Download Design and Analysis of a New Dual-Stator Permanent

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Design and Analysis of a New Dual-Stator Permanent-Magnet Machine
for Direct-Drive Applications
S. L. Ho, Shuangxia Niu and W. N. Fu
The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
By virtue of their high torque density, double-stator permanent magnet (PM) electric machines can be effectively used for low-speed,
direct-drive applications. In this paper, a new magnetic gear based design of dual-stator PM machine is presented. The key is to use the
stationary ferrite poles to modulate the magnetic flux from the stator windings and integrate the magnetic flux modulating and
fractional-slot concentrated winding into both stators. The advantage is that it does not only maintain the compact structure with a
high torque density, it also renders the design more flexible when compared to the original Vernier structure. By using time-stepping
finite element method, the steady state and transient performances of the dual-stator PM machine are simulated and the validity of
proposed machine is verified.
Index Terms—Direct drive, dual-stator, electric machine, finite element method, permanent magnet, Vernier structure.
I. INTRODUCTION
A
LOW SPEED, direct-drive machine is more advantageous
than a high-speed drive machine with gear-box, because
the former one has low cooling requirement and simple
mechanical construction. Hence direct-drive machine is
becoming increasingly popular as the generator for wind
power generation or in propulsion systems for electric vehicles,
trains and vessels. Conventional low-speed machines are
usually bulky, heavy and have low efficiency. To reduce the
volume and improve the torque density, double-stator PM
machines have been studied recently [1, 2]. With the stator
windings carried by inner and outer stators, the space
utilization ratio of the machine is largely improved. To reduce
the slot number and hence improve the copper fill factor and
decrease the magnetic flux leakage, fractional-slot
concentrated-winding structure in the outer stator and Vernier
structure in the inner stator can be exploited [2]. Nevertheless,
the Vernier stator structure in [2] requires the auxiliary stator
slots to be a multiple of the stator slot number and this limits
the design choice.
As is well known that, Vernier stator structure is based on
the magnetic gear (MG) effect [3] to produce high torque at a
very low rotor speed. Based on similar operating principles,
another novel magnetic geared motor is investigated [4, 5].
The MG effect is incorporated into a conventional outer-rotor
PM brushless motor to improve the torque density and there is
only one rotary part. The airgap field space harmonics are
modulated by the stationary ferrite segments to transfer the
high-speed harmonic component to the low-speed one and the
high-speed harmonic is produced by the armature instead of by
the rotating PMs in MG. The rotor rotates at a low speed as
governed by the pole numbers in the rotor.
Although the operating principle of magnetic field
modulation of the magnetic geared motor is similar to that of
Vernier structure machine, the ferrite segments are isolated
from the stator by one layer of airgap. This airgap between the
ferrite segments and the stator surface increases the magnetic
resistance and makes it difficult to fix the stationary segments.
If there is no airgap, its related magnetic resistance can be
eliminated. However, a large leakage flux may appear.
In this paper, a novel design, with less flux leakage and yet
producing an effective magnetic flux modulation, is presented
and applied to the dual-stator PM machine. The key is to
divide the inner stator into two parts, one is fed with fractionalslot concentrated windings to provide the working flux and the
other is the flux modulating poles fixed on the surface of the
former part to serve changing the airgap permeance. The
fractional slot concentrated winding design is also used in the
outer stator. This proposed design not only inherits the dualstructure machine’s merits, such as compact structure, short
end windings, reduced copper loss, but also has a more flexible
choice of pole number when compared with the original
Vernier structure. The principle of operation of the machine is
introduced and the relationship between the pole numbers of
stator, rotor and flux modulating pole is illustrated. To deal
with the issue of large leakage flux in the inner stator, the
number of stator slots is intentionally reduced to alleviate flux
short circuits arising from the stationary iron segments.
Time-stepping finite element method (TS-FEM) has been
successfully used to analyze the transient performance of
electric machines. In TS-FEM the magnetic field equation is
coupled with external electric circuit equation and mechanical
balance equation and takes into account the effects of
saturation, eddy current and mechanical movement of the rotor
[6]. In this paper, TS-FEM is used to analyze the steady state
and transient performances of the machine so as to verify the
validity of the proposed dual-stator PM machine.
II. PROPOSED MACHINE
A. Machine Structure
As shown in Fig. 1, the proposed dual-stator PM machine
has 23 pole-pair PMs in rotor, 46-pole 48-slot windings in the
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outer stator, 10-pole 12-slot windings in inner stator, 28
stationary ferrite poles fixed with the inner stator.
(a)
maximized to increase the output torque and the torque density
of machine. Thirdly, with fractional-slot concentrated
windings, the coils are wounded on alternate stator teeth. The
phase windings are isolated magnetically, thermally and
physically. This modular machine structure can be
manufactured easily. Last but not the least, as the cogging
torque due to slotting is approximately related to the inverse of
the smallest common multiple of the number of slots and
number of pole pairs, this arrangement of 48-pole/46-slot can
significantly reduce the cogging torque ripples.
A typical magnetic field distribution of the PM machine
with outer stator only is shown in Fig. 2(a). The 46-pole 48slot winding distribution is shown in Fig. 3 and the coil is
wound on alternate teeth. The coil space harmonic MMF
distribution is shown in Fig. 3(b). It can be seen that the
amplitude of the 23rd MMF harmonic component is the
highest. At open circuit, the airgap flux density caused by the
PMs is shown in Fig. 4(a). Its corresponding space harmonic
MMF distribution is shown in Fig. 4 (b). It is the 23rd MMF
harmonic that interacts with the 23 pole-pair PM rotor to
produce continuous torque.
100
80
(b)
Fig. 1. Proposed machine. (a) Cross sectional view. (b) Structure.
1) Outer Stator
The fractional-slot concentrated windings are adopted in the
outer stator. The slot number N s and the pole number 2 p
satisfy the following relationship:
(1)
2p = Ns ± 2
The outer stator adopts 48-slot/46-pole winding distribution.
MMF
60
40
20
0
0
10
20
30
40
Harmonic order
50
60
(a)
(b)
Fig. 3. Outer stator coil. (a) 48-slot 46-pole winding distribution. (b) Space
harmonic MMF distribution.
(a)
(b)
Fig. 4. With outer stator only, the flux density waveform along the airgap. (a)
Flux density. (b) Space harmonic MMF distribution.
(a)
(b)
Fig. 2. Magnetic field distribution. (a) With outer stator only. (b) With inner
stator only.
This combination of slots and poles in the outer stator has
many merits [1], [2]. Firstly, the fractional-slot concentrated
winding arrangement in the outer stator can shorten the endwinding, thus improving the utilization of copper materials,
and reducing the copper losses. The efficiency of the machine
is thus increased. Secondly, with fractional-slot concentrated
windings, the stator yoke can be designed very thin. Under a
limited stator peripheral dimension, the airgap diameter can be
2) Inner Stator
For the inner stator, flux modulating structure is adopted and
the fundamental rule is expressed as:
Z 2 = Z1 ± p
(2)
where; Z1 is the stationary ferrite pole number; Z 2 is the PM
pole pair number and p is the winding pole pairs.
The inner phase winding is also designed with a fractional
slot concentrated winding to reduce slot number, and (2) can
be expressed as:
Z 2 = Z1 ± (N s 2 ± 1)
(3)
where, N s is the stator slot number. In this proposed machine,
the inner stator parameters are Z1 = 28 , Z 2 = 23 , p = 5 , and
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MMF
N s = 12 . The gear ratio is Z 2 / p .
A typical magnetic field distribution of the PM machine
with inner stator only is shown in Fig. 2(b). The 10-pole 12slot winding distribution is shown in Fig. 6 with alternate teeth
wound by coils. The coil space harmonic MMF distribution is
shown in Fig. 5(b). It can be seen that the amplitude of the 5th
MMF harmonic component is the highest.
At open circuit, the inner airgap flux density and space
harmonic MMF distribution caused by the PMs are shown in
Figs. 6(a) and 6(b), respectively. As similar to the outer stator,
its 23rd MMF harmonic is highest. After the flux modulation
by the stationary ferrite segments, the 5th MMF harmonic of
the flux distribution becomes the highest, as shown in Fig. 7.
The combination of the “MG effect” and the fluxmodulation poles can thus modulate the high-order harmonic
component (23rd space harmonic) of the airgap magnetic field
to produce the specific low-order harmonic component (5th
space harmonic). The field of the winding rotates at
Z 2 / p = 23 / 5 times of the rotor speed therefore synchronizes
the rotor to rotate and produces a positive torque.
Z 2′ = Z1′ ± p
(4)
Since the auxiliary stator slot is uniformly aligned on the stator
tooth surface, Z1′ = nN s′ . Also the stator windings have integer
slots, so N s′ = 2mpk . Eq. (4) can be expressed as:
Z 2′ = Z1′ ± p = N s′ (n ± 1 2mk )
(5)
′
′
where, Z1 is the auxiliary stator tooth number; Z 2 is the PM
pairs and; k , n are positive integers; m is the phase number.
The gear ratio is Z 2′ / p = 2mkZ 2′ / N s′ . It can be seen that
conventional Vernier structure auxiliary stator poles are
restricted by the stator slot number, while the flux modulating
ferrite segments have no such constraint. Consequently, it is
more flexible to find the relationship between stator winding
poles, PM poles, ferrite poles for the proposed structure when
compared to the conventional Vernier one.
3) Cup-shaped Rotor and Increased Width of Slot Open
In the proposed machine, the PMs are surface mounted on a
cup-shaped rotor and the inner and outer magnetic circuits are
connected in series, so the rotor iron core can be designed to
be very thin. The use of the maximum airgap diameter can
further improve the torque density. The pole-pair number of
the PMs is 46, which governs the rotor to rotate at a very low
speed and the stator iron core can be designed relatively thin.
III. TS-FEM ANALYSIS
(a)
(b)
Fig. 5. Inner stator coil. (a) 12-slot 10-pole winding distribution. (b) Space
harmonic MMF distribution.
A. TS-FEM
A two-dimensional (2-D) TS-FEM coupling with electric
circuit equations is used to simulate the operation of the
machine [6]. The basic equations of transient magnetic fieldcircuit coupled problem can be summarized as:
ld p N
∂A ld p N
iad +
iw = −lpJ m
+
Sa
Sa
∂t
ld p N
∂A
−
dΩ + Rdc iad = 0
Sa ∫∫Ω ∂t
ld p N
∂A
−
dΩ −Rdc i w = −u w
∫∫
Ω
Sa
∂t
Amplitude
lp∇ ⋅ (ν∇A) − lpσ
(a)
(b)
Fig. 6. With inner stator only, the flux density waveform along the airgap. (a)
Flux density. (b) Space harmonic distribution.
3
2
1
Amplitude
0
-1
-2
-3
0
180
360
540
Rotor position
(degree)
720
(a)
(b)
Fig. 7. With inner stator only, the flux density along the inner surface of the
stationary segments. (a) Flux density. (b) Space harmonic distribution.
Comparatively, for the conventional Vernier structure, the
fundamental rule is:
(6)
(7)
(8)
where; l is the depth of the model in the z-direction (axial
direction); p is the symmetry multiplier; ν is the reluctivity of
material ; σ is the conductivity; A is the z-component of the
magnetic vector potential; dp is the polarity (+1 or –1) to
represent, respectively, the forward paths or return paths; S is
the total cross-sectional area of the region occupied by the
winding in the solution domain; N is the total conductor
number of this winding; a is the number of parallel branches in
the winding; Rdc is the d.c. resistance of the winding; iw and uw
are the branch current and voltage of the winding, respectively;
iad is the additional current introduced to ensure the last
coefficient matrix of the system equations is symmetrical. The
second and the third terms in the left side of the field equation
(6) and the additional equation (7) exist only in the solid
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B. Analysis Results
With TS-FEM, the steady and transient performance of the
machine is analyzed. Fig. 8 shows a typical magnetic field
distribution of the proposed machine. It can be seen that a
majority of the flux lines traverse through the inner and outer
airgaps to react with the working windings. The flux density at
the stator teeth is below 2.2 T and it is reasonable at full load.
Fig. 9 depicts the back emf waveforms induced in the inner
and outer stator windings. It is shown that the magnitudes of
induced back emf in both sets of windings are almost the same.
The two sets of stator windings can be connected
independently or in series. When independently connected,
each can be flexibly controlled by external circuits. Fig. 10
shows the variation of maximum torque with different slot
widths of inner stator and with different distances between
ferrite segments and inner stator surface. So to maximize the
torque, the ferrite segment is fixed on the inner stator surface
and to alleviate flux short circuits arising from the ferrite
segments, the slot widths are intentionally designed large to
deal with the large leakage flux in inner stator. Fig. 11 shows
the transient load torque. A torque of almost 88 Nm is
produced at 240 rpm. The detailed design data are shown in
Table. I.
(a)
(b)
Fig. 8. Magnetic field distribution at full load. (a) Flux lines. (b) Flux density.
30
20
10
0
-10
-20
-30
0
100
200
300
400
Rotor Position (degree)
500
(a)
(b)
Fig. 9. Back emf waveforms. (a) The outer stator windings. (b) The inner
stator windings.
(a)
(b)
Fig.10. Variation of maximum torque. (a) With the slot open width of inner
stator. (b) With the distance between ferrite segments and inner stator surface.
IV. CONCLUSION
In this paper, a new dual-stator PM machine is proposed for
low speed, direct-drive applications. In inner stator, the
magnetic flux modulating is incorporated with a fractional-slot
concentrate winding. In the outer stator, a fractional slot
concentrated winding with high pole number is used. The
merit is that it does not just maintain the compact structure
with a high torque density, but it allows the design choice to be
more flexible when compared to the original Vernier structure.
By using TS-FEM, the steady state and transient performances
of the machine are simulated and the validity of proposed dualstructure PM machine is verified.
Torque (Nm)
conductor regions. The fourth term in the left of (6) and the
circuit equation (8) only exist in regions of stranded windings
and solid conductors.
Fig. 11. Full load torque waveform.
TABLE I
MACHINE PARAMETERS
Proposed dual-stator PM
Item
machine
Number of phases
3
Outer radius of outer stator
124.6 mm
Inner radius of outer stator
104.9 mm
Outer and inner airgap length
0.6 mm
Length of ferromagnetic segments
14.8 mm
Outer radius of inner stator
78.4 mm
Inner radius of outer stator
19.2 mm
Number of turns per coil in outer stator
12
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Number of turns per coil in inner stator
Rated speed
PM pole number
Inner stator slot number
Inner stator winding pole number
Outer stator slot number
Outer stator winding pole number
Stack length
Length of PMs
Magnetic remanence
28
240 rpm
46
12
10
48
46
65 mm
4.9 mm
1.2 T
ACKNOWLEDGMENT
This work was supported in part by The Hong Kong
Polytechnic University under Grants G-YX4B and B-Q18X.
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