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ANSYS 2011 中国用户大会优秀论文 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 ANSYS 2011 中国用户大会优秀论文 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 ANSYS 2011 中国用户大会优秀论文 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 ANSYS 2011 中国用户大会优秀论文 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 ANSYS 2011 中国用户大会优秀论文 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. REFERENCES [1] [2] [3] [4] [5] [6] S. Niu, K.T. Chau, and C. Yu, “Quantitative comparison of double-stator and traditional permanent magnet brushless machines,” Journal of Applied Physics, vol. 105, no. 7, pp. 07F105-07F105-3, 2009. S. Niu; S.L. Ho, and W.N. Fu, “A novel direct-drive dual-structure permanent magnet machine,” IEEE Trans. Magn., vol. 46, no. 6, pp. 2036-2039, Jun. 2010. A. Toba, and T.A. Lipo, “Generic torque-maximizing design methodology of surface permanent-magnet vernier machine,” IEEE Trans Ind Appl, pp. 1539-1546, vol. 36, no. 6, Nov/Dec 2000. L.L. Wang, J.X. Shen, Y. Wang and K. Wang, “A novel magneticgeared outer-rotor permanent-magnet brushless motor,” 4th IET Conference on Power Electronics, Machines and Drives, pp. 33-36, 2-4 Apr. 2008. W.N. Fu and S.L. Ho, “A quantitative comparative analysis of a novel flux-modulated permanent magnet motor for low-speed drive,” IEEE Trans. Magn., vol. 46, no. 1, pp. 127-134, Jan. 2010. W.N. Fu and S.L. Ho, “Elimination of nonphysical solutions and implementation of adaptive step size algorithm in time-stepping finiteelement method for magnetic field–circuit–motion coupled problems,” IEEE Trans. Magn., vol. 46, no. 1, pp. 29-38, Jan. 2010.