ANSYS 2011中国用户大会优秀论文
A Novel Direct-Drive Dual-Structure Permanent Magnet Machine
Shuangxia Niu, S. L. Ho and W. N. Fu
The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong By incorporating the merits of fractional-slot concentrated windings and Vernier machine structure, a new multi-pole dual-structure permanent magnet (PM) machine is proposed for low speed, direct-drive applications in this paper. In the outer stator, a fractional-slot concentrated winding is adopted to reduce the slot number and stator yoke height, hence saving space and improving torque density. In the inner stator, a Vernier structure is used to reduce the winding slots, thereby enlarging the slot area to accommodate more conductors, thus the inner stator space is fully utilized. Consequently, the merits of these two structures can be ingeniously integrated into one compact PM machine and the torque density is improved, cogging torque is reduced and the control flexibility with two sets of independent stator windings is increased. By using time-stepping finite element method with curvilinear elements f
or moving between the stator and the rotor, the steady state and transient performances of the PM machine are simulated and the validity of proposed dual-structure PM machine is verified.
Index Terms—Curvilinear element, dual-structure, finite-element method, fractional-slot concentrated winding, permanent magnetic motor, Vernier structure.
I.I NTRODUCTION
IGH TORQUE, low speed permanent magnet (PM)
machines have a wide range of applications in direct-
drive systems, such as in wind power generation, electric
traction of electric vehicles and robots. In such low speed
direct-drive machines, the pole number of the machine is
usually large. For conventional PM machines with integer slot
windings, high pole number implies high slot number and for
machines with a limited outside diameter, large slot number
will result in low copper fill factor, long slots, narrow tooth
width, and high magnetic flux leakage. In order to avoid such
undesirable effects, fractional-slot concentrated windings are
used [1]. In fractional-slot concentrated windings, each coil is
wound on one tooth and the slot number per pole per phase is
generally less than one. Compared with integer slot windings,
the end winding is shortened and manufacture cost is reduced.
Another method to reduce the slot number and produce high
torque at low speed is to adopt a Vernier machine structure. A
Vernier PM machine with concentrated winding can produce
specific space harmonics in the airgap magnetic field with low
armature pole pairs and slot number [2].
In this paper, the fractional-slot concentrated windings and
Vernier PM machine structure are ingeniously incorporated
into a compact dual-structure PM machine. A time-stepping
finite-element method with curvilinear elements for the
modeling of the rotation movement is developed to simulate
the dynamic operation of the proposed machine.
II.P ROPOSED M ACHINE
A.Machine Structure
The proposed dual-structure PM machine has 11 pole pairs with 24 slots in the outer stator, 1 pole pa
ir with 3 slots in inner stator, 11 pole-pair surface mounted PMs on the inner and outer faces of the rotor, as shown in Fig. 1.
(b)
Fig. 1. Proposed machine. (a) Cross sectional view. (b) Structure.
1)Outer stator
For the outer stator, the fractional-slot concentrated windings are used, and the slot number
s
N and the pole number p
2 satisfies the following relationship
2
2±
=
s
N
p(1) In the outer stator, 24
=
s
N and 22
2=
p. This combination of slots and poles in the outer stator has the following merits [3]:
(1) The fractional-slot concentrated winding arrangement in the outer stator can shorten the end winding, thus improving the utilization of copper materials, and reducing the copper losses. The efficiency of the machine is increased.
H
ANSYS 2011中国用户大会优秀论文
(2) Since the outer stator has 24 slots and there are 22 poles in the rotor, the slot pitch is 11/12 pole pitch. As the cogging torque caused by the 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 fractional number of slots per pole per phase can significantly reduce the cogging torque that usually occurs in PM machines.
(3) The multi-pole structure results in minimum core yoke height and small iron mass. This structure can further save the material costs and increase the torque density of the machine.  (4) Since each coil is wound on alternate stator teeth, the phase windings are isolated magnetically and physically. The outer stator adopts modular structure in which only alternate stator teeth carry a wound coil, hence the stator may be assembled from pre-wound tooth/coil or stator segment sub-assemblies. Compared with conventional winding structures, the modular stator structure is more conducive to low-cost, high-volume manufacturing [4]. In addition, since the coil span of the stator windings is designed to have one slot pitch, the phase flux paths are independent of each other. Consequently, the mutual inductance of the phase windings is negligible, hence the controllability of the machine is improved.
2) Inner stator
For the inner stator, a Vernier structure is adopted. The fundamental rule is
p Z Z ±=12                      (2) where; 1Z is the flux-modulation poles on the stator surface, also named the stator teeth [2], [5];2Z is the PM pairs and p
is the winding pole pairs. For the inner stator in this proposed dual-structure PM machine, the parameters are 121=Z , 112=Z , and 1=p . Then, based on “magnetic gear effect”, the flux-modulation poles can modulate the low harmonic components of the airgap magnetic field to produce the specific high harmonic component and the armature fundamental field rotates at p Z /2 times of the rotor speed, but in an opposite direction. The advantages of this inner stator structure of PM machine are distinct [2], [5]:
(1) The Vernier machine structure can reduce the slot number and enlarge the slot area, hence more conductors can be accommodated into the inner stator and improved torque density is obtained.
(2) The concentrated winding structure in the inner stator can also simplify the stator structure, and ef
fectively save the inner stator space and further improve the torque density, accordingly.
(3) The modulation poles can modulate the low harmonic components, namely fundamental space harmonics, to produce the high harmonic components, namely the 11th  space harmonics, in the airgap magnetic field with low armature pole pairs and slot number. The open-slot structure is also
simpler, compared with multi-pole closed-slot structure. On the whole, the dual-structure machine is a complicated structure and manufacturing cost is higher than that of conventional PM machines.
B. TS-FEM Analysis
Due to its unique structure and operating principle of the proposed dual-structure PM machine, a time-stepping finite-element method (CFT-TS-FEM) is employed for the analysis.  Curvilinear elements are used to model the two sliding surfaces in the rotating PM machine. Maxwell’s equations applied to the airgap, iron core, stranded windings and PM regions give rise to the following diffusion equation [6,7]:
()c t
H J A
A ×∇+=∂∂+×∇×∇σ
ν                    (3) where, ν  is the reluctivity of material, A  is the magnetic vector potential and σ  is the conductivity. J  is the winding current density and it only exists in stranded windings; The second term on the right in (3) only exists in PM materials; H c  is the  coercivity of PM.
Simulating the rotation of the rotor between the two airgaps using matching boundary techniques is very important for the transient magnetic field analysis in the dual-structure machine. Each airgap of the machine is divided into two parts. One belongs to the stator mesh and another belongs to the rotor mesh. Three meshes, associated with one rotor and two stators, are generated separately. When the rotor rotates, the rotor mesh will rotate. The shape of the mesh is kept fixed; only the relations of the nodes on the moving interfaces are changed according to the positions of the rotor. Assuming the nodes on the sliding surface on the rotor mesh are the slave nodes, for example as shown in Fig. 2, the magnetic potentials on the slave nodes can be expressed as:
3322119A N A N A N A ++=                            55443310A N A N A N A ++= where N  is the shape function of the edge.
Sliding surface
Fig. 2.  A straight line sliding surface.
In general, the system equations can be expressed:
[]{}{}P A C =nodes all _                                  (4)
where; C  is the coefficient matrix; A all_nodes  is the magnetic potentials on all nodes including master nodes and slave nodes and P  is the column matrix associated with excitations. The relationship between the magnetic potentials on all nodes
ANSYS 2011中国用户大会优秀论文
A all_nodes  and the magnetic potentials A solve_nodes  required to be solved is:
{}[]{}nodes
solve nodes
all __A
M A
=                            (5)
where M  is the transformation matrix. Substituting the above relationship into the system equations gives:
[][]{}{}P A M C =nodes solve _                                (6)
Multiplying [M ]T  on the two sides of the equations:
[][][]{}[]{}P M A M C M T nodes solve T =_                      (7)
The new coefficient matrix [M ]T [C ] [M ] is still symmetrical. With rotation machines, the sliding surface is a circle. At the initial position, the meshes on the two sides of the sliding surface are consistent as illustrated in Fig. 3. However, after the rotor rotates, because the edge of the element is a straight line, the inner surface of the stator mesh and the outside surface of the rotor mesh on the two sides of the sliding surface become inconsistent as illustrated in Fig. 4. In some areas there may be a gap between meshes; in other areas the mesh may overlap. Here curvilinear elements, as shown in Fig. 5, are employed on the two sides of the sliding surface to model the rotation of the dual
structure PM machine.
Fig. 5.  Isoparametric second-order curvilinear element.
III. A NALYSIS R ESULTS
With curvilinear elements based TS-FEM, the steady and transient performance of the machine is analyzed. Fig. 6 shows a typical magnetic field distribution of the proposed machine on no-load and on full-load. Fig. 7 shows the flux
density waveforms in the inner and outer airgaps. It is shown that the armature field excited by the in
ner stator winding is effectively modulated by the split poles on the stator teeth. Fig. 8 shows the back emf waveforms induced in the inner and outer stator windings. It is shown that the magnitudes of the induced back emf in both sets of windings are almost the same. Due to the independent connection of the two sets of stator windings, they can be flexibly controlled by external circuits. Fig. 9 shows the transient load torque and the cogging torque waveforms at the rated speed of 270 rpm of the machine. It can be observed that the full load torque ripple is significantly larger than the cogging torque ripple. It is due to the fact that the harmonic torque, which is mainly caused by phase commutation during brushless DC operation and the high-order harmonic component in the full-load current, dominates the torque ripple. Meanwhile, the cogging torque is very small, namely only 1.3 % of the full load torque, which is actually governed by the inverse of the smallest common multiple of the numbers of slots and pole pairs. With this unique structure, the torque density can reach 50 kNm/m 3. The design data are shown in Table. I. Finally, the transient response of the eddy-current loss and phase current in the PMs during the commutation period are analyzed as shown in Fig. 10. It can be seen that the eddy-current loss increases drastically within the commutation time, which is actually due to a sudden large change in the armature current field during commutation.
(a)
(b)
Fig. 6. Magnetic field distribution. (a) No load. (b) Full load.
ANSYS 2011中国用户大会优秀论文
(a)
(b)
Fig. 7. Flux density in the airgap. (a) In the outer airgap. (b) In the inner
airgap.
(a)
modulate
(b)
Fig. 8. Back-EMF waveforms. (a) In the outer stator windings. (b) In the inner stator windings.
T o r q u e  (N m )
(a)
(b)
Fig. 9. Torque waveforms. (a) Transient load torque. (b) Cogging torque. (can you show the cogging torque after removing the harmonic torque in (b)?)    I believe Fig. 9 (b) shows cogging torque only. –WN Fu.
IV. C ONCLUSION
In this paper, a new multi-pole dual-structure PM machine is proposed for low speed, direct-drive applications. The merits of fractional-slot concentrated winding arrangements in the outer stator and the Vernier machine structure in the inner stator are incorporated in one compact PM machine. The torque density is improved, cogging torque is reduced, and the efficiency of the machine is increased. In this dual-structure machine, the inner and outer stator windings can either be used simultaneously or operated independently and fault tolerance capability is improved. By using time-stepping FEM with curvilinear elements for modeling the rotor rotation, the steady state and transient performance of the PM machine are simulated and the validity of proposed dual-structure PM
machine is verified.
(a)
0.160.20
0102030405060E d d y -c u r r e n t  l o s s  (W )
Time (s)
(b)
Fig. 10. Transient current and eddy-current loss response in PMs during commutation. (a)  Phase current. (b) Eddy-current losses.
TABLE  I
M ACHINE P ARAMETERS
Item
Proposed dual-structure
PM machine
Rated phase voltage  (V) 220 V Rated speed 270 rpm
ANSYS 2011中国用户大会优秀论文 Rated torque 115 Nm
Number of phase    3
Pole number 22
Inner stator slot number    3
Inner stator teeth 12
Outer stator slot number 24
Stack length 50 mm
Inner air-gap length 0.6 mm
Outer air-gap length 0.6 mm
Inner stator inner diameter 92 mm
Inner stator outer diameter 165 mm
Outer stator inner diameter 191 mm
Outer stator outer diameter 245 mm
Number of turns per coil in outer stator  10
Number of turns per coil in inner stator 30
PM material  Sintered NdFeB
R EFERENCES
[1]S. Niu, K.T. Chau, and C. Yu, “Quantitative comparison of double-stator
and traditional permanent magnet brushless machines,” Journal of
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[2]  A. Toba and T.A. Lipo, “Novel dual-excitation permanent magnet
vernier machine, ” IEEE Industry Application Conference, vol. 4, pp.
2539-2544, 1999.
[3]S. Niu, K.T. Chau and J.Z. Jiang, “Analysis of eddy-current loss in a
double-stator cup-rotor PM machine,” IEEE Trans. Magn., vol. 44, no.
11, pp. 4401-4404, Nov. 2008.
[4]J. D. Ede, K. Atallah, J. Wang, and D. Howe, “Modular fault-tolerant
permanent magnet brushless machines,” Internatinal Conference on
Power Electronics, Machines and Drives, Bath, U.K., pp. 415–420,
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[5]  A. Toba, and T.A. Lipo, “Generic torque-maximizing design
methodology of surface permanent-magnet vernier machine,” IEEE
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[6]W. N. Fu and S. L. Ho, “Enhanced nonlinear algorithm for the transient
analysis of magnetic field and electric circuit coupled problems,” IEEE
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[7]W.N. Fu and S.L. Ho, “Elimination of nonphysical solutions and
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IEEE Trans. Magn., to appear.

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