A Quantitative Comparative Analysis of a Novel Flux-Modulated Permanent Magnet Motor for Low-Speed Drive

Transcription

1 ANSYS 11 中国用户大会优秀论文 A Quantitative Comparative Analysis of a Novel Flux-Modulated Permanent Magnet Motor for Low-Speed Drive W. N. Fu, and S. L. Ho The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong A novel low-speed flux-modulated (FM) permanent magnet (PM) motor that breaks the traditional design rule, which stipulates that the number of stator pole pairs and the number of rotor pole pairs must be the same, is proposed. The FM motor has a special physical structure with iron segments in the airgap to modulate the magnetic field. In the design, the free space between adjacent stationary iron segments also acts as ventilating ducts to help improving the heat dissipation and ventilation of the motor. Its cogging torque is very small. In this paper a rule for comparing the power density of electric motors is proposed. The performance of the FM motor is compared with those of a magnetic-geared PM motor, a traditional PM motor and a fractional-slot PM motor by using magnetic field finite-element analysis. Index Terms Electric motor, finite-element analysis, flux modulation, low-speed drive, magnetic field, power density, ventilation. I I. INTRODUCTION N MANY industrial applications, low-speed drives are required. For an electric motor, its output torque is approximately proportional to its volume. As the output power of motor is proportional to the product of its output torque and speed, the motor will be very massive if it is designed to drive a low-speed mechanical load directly. A mechanical gear is usually needed to reduce the output speed of the motor before it is connected to the mechanical load. However, the mechanical gear reduces the energy transmission efficiency. Recently, magnetic gears are proposed to replace the mechanical ones [1-5]. Compared to their mechanical counterparts, magnetic gears have very competitive torque transmission capability and efficiency. The magnetic gear can also be directly combined with a conventional permanent magnet (PM) motor with the outer-rotor structure housed inside a low speed rotating frame [6-8]. The system torque density can be significantly improved. The disadvantage is that such a system has two rotating parts and its mechanical structure is complicated. A novel magnetic-geared motor with simple structure was presented recently [9]. Essentially it integrates a magnetic gear with a conventional outer-rotor PM motor. It has only one rotary part. The outer rotor is equipped with sintered NdFeB magnets. The stator has a 3-phase concentrated winding which produces a rotating magnetic field with 3 pole pairs. The outer rotor has pole pairs and its stationary iron segments are made of silicon steel laminations which can be exploited for modulating the airgap field space harmonics, and the rotor can rotate at low speed efficiently. The operating principle of the proposed magnetic field modulation is similar to that of the magnetic gear. However, the high-speed rotary field is created with an armature rather than with the magnets. As far as the authors are aware, there is no quantitative comparison between the proposed motor and traditional motors. In this paper this novel motor is referred as the fluxmodulated (FM) motor. A rule to compare the power density of various electric motors is presented. The performance of the FM motor is compared with those of a magnetic-geared motor, a traditional PM motor and a fractional-slot motor. Their advantages and disadvantages are discussed. II. BASIC COMPARISON RULES OF MOTORS BEING STUDIED The purpose of this paper is to compare the output power per unit volume of four different types of motors. All the motors being studied have three phases and are operated as synchronous motors. For the sake of simple performance comparison, the excitation currents in the motor windings are assumed to be sinusoidal at a frequency of Hz. The rated speed is 6 rpm. Rules to compare the power densities of different motors are: (1) All motors have the same outside radius and axial length; the same type and amount of PM materials; the same grade of iron and copper materials. () The temperature rises at full-load are the same for all four motors. Because the temperature-rise computation is beyond the scope of this paper, thus the power losses will be used as an indirect measure of the temperature rise of the four motors as a first order of approximation. Moreover, as the coreloss is only a small percentage of the total losses in these motors, one can take the copper loss as an indication of the temperature rise in all four motors. In other words, it is assumed that the same copper loss will have the same temperature rise approximately. In the analysis, the phase resistance of the winding in the effective region (excluding the end winding) is:

2 ANSYS 11 中国用户大会优秀论文 1 L 1 ρl 1 ρl R = NslotNconductor = NslotNconductor = NslotNconductor 3 σs S conductor 3 slot 3 Sslot Nconductor (1) where, N slot is the number of slots per phase, N conductor is the number of conductors per slot, S conductor is the cross-sectional area of one conductor, L is the axial length of iron core, σ is the conductivity and S slot is the cross-sectional area of one slot. The total copper loss is: 1 ρl ρl PCu = 3I R = 3I N slot Nconductor = I N slot Nconductor 3 S S / N = I L ρ Nslot Nconductor Stotal _ slot slot total _ slot where, I is the current, S total_slot is the cross-sectional area of all the slots and it will be the same in all the motors being studied for consistent comparison. N slot N conductor is the total number of conductors in all the slots of each motor. From () it can be seen that for all the motors, the ampere-conductors IN slot N conductor are the same if both S total_slot and the copper loss are the same. To allow for consistent performance comparison, threephase symmetrical currents are fed into the stator windings. The procedures to compare the performances of different motors are: (1) Perform a locked-rotor simulation. If the magnitude of the computed electromagnetic torque is high, it has high torque density. The initial rotor position for the full-load simulation can be determined according to the locked-rotor torque waveform [1]. () Perform full-load simulation to compute the full-load torque, back emf and coreloss using time-stepping FEM [11-13]. The corelosses of the four motors are computed by using the method presented in [1]. (3) Remove all windings, set all conductivities to zero, compute the cogging torque. III. MOTOR I - A MAGNETIC-GEARED MOTOR The magnetic-geared outer-rotor PM motor as shown in Fig. 1 is referred as Motor I in this paper. Its key design data are listed in Table I and its typical flux distribution is shown in Fig.. Assuming a current density limit of 9 A/mm in the stator conductors, the magnitude of the ampere-conductors in each stator slot is 86.7 A. Because the magnetic gear has a combination of 3 pole-pairs PM and pole-pairs PM, the output speed of the magnetic gear is 44 3/ = 6 rpm when the rotor rotates at 44 rpm. In other words, the output torque can be amplified /3 times. slot () Gear outer rotor Iron segment Gear inner rotor Motor outer rotor Stator Fig. 1. Overview of an intersection structure of a magnetic-geared outer-rotor PM motor (Motor I) Fig.. A flux plot on an intersection of the magnetic-geared motor (Motor I) TABLE I KEY DESIGN DATA OF MAGNETIC-GEARED MOTOR (MOTOR I) Frequency Hz 4 mm Outside radius of outer rotor 9 mm Outside radius of gear outer PM 88.6 mm Inside radius of outer rotor 86 mm Outside radius of stationary ring 85 mm Inside radius of stationary ring 7 mm Outside radius of gear inner PM 71.4 mm Inside radius of gear inner PM 68.8 mm Outside radius of motor iron 68. mm Outside radius of motor PM 63. mm Inside radius of motor inner rotor 6.6 mm Outside radius of stator 6 mm Inside radius of stator 17.5 mm Number of outer rotor pole pairs Number of stationary iron pieces 5 Number of stator pole pairs 3 Number of stator slots 36

3 ANSYS 11 中国用户大会优秀论文 Fig. 3. Simulation result showing the torque curve versus time when the rotor is locked (Motor I) Core loss (W) Fig. 5. Simulation result showing the coreloss curve versus time at full-load operation (Motor I) When the rotor is locked, the torque curve versus time is shown in Fig. 3. The maximum locked-rotor torque is 4 Nm. It is estimated that the torque after speed reduction via the magnetic gear is 4 /3 = 93.3 Nm. The induced emf curves versus time are shown in Fig. 4. It is worth noting that the induced emf in the stator winding contains two components. One is from the rotation of PM; the other is due to the alternating current flowing in the stator windings via self inductance and mutual inductances. Consequently, there is still induced emf in the stator windings even if the rotor is locked. Fig. 5 shows the coreloss curve versus time. Fig. 6 shows that the cogging torque on the PM of the motor is not very small. In essence, Motor I is a simple combination of a high-speed PM motor and a magnetic gear. It can output very large torque due to the speed conversion facility of the magnetic gear. However, it has two rotational parts and it is expensive to fabricate Fig. 4. Simulation result showing the induced emf curves versus time when the rotor is locked (Motor I) Fig. 6. Simulation result showing the cogging torque curve versus rotor position (Motor I) IV. MOTOR II - FM MOTOR Removing the two sets of PM (3 pole-pairs) between the stationary iron pieces and the stator in Motor I, a FM motor (referred as Motor II) as depicted in Fig. 7 is obtained. In the FM motor there are stationary iron pieces between the stator and the rotor. According to [1], the gear ratio of the stationary iron pieces is: G p N stator iron r = (3) pstator where, p stator is the number of stator pole pairs, N iron is the number of stationary iron pieces. The number of rotor pole pairs p rotor should be G r p stator. Therefore, the relationship among the number of stator pole pairs p stator, the number of rotor pole pairs p rotor and the number of stationary iron pieces N iron is: N p = p (4) iron stator In the example, G = =. The number of pole pairs r 3 3 in the stator is 3 but the number of pole pairs in the rotor is. Its key design data are listed in Table II. Between the rotor rotor

4 ANSYS 11 中国用户大会优秀论文 and the stationary iron pieces there is an airgap of.6 mm. Between the stationary iron pieces and the stator, there is another airgap of.6 mm. The rotor rotates at a low speed of 6 rpm. Its typical flux distribution on an intersection of the motor is shown in Fig. 8. Inside radius of stator 17.5 mm Number of outer rotor pole pairs Number of stationary iron pieces 5 Number of stator pole pairs 3 Number of stator slots 36 Iron segment Outer rotor Permanent magnet Stator Fig. 9. Simulation result showing the torque curve versus time when the rotor is locked (Motor II) 8 Fig. 7. Overview of an intersection structure of a flux-modulated PM motor (Motor II) Fig. 1. Simulation result showing the induced emf curves versus time when the rotor is locked (Motor II) Fig. 8. A flux plot on an intersection of the flux-modulated motor (Motor II) TABLE II KEY DESIGN DATA OF FM MOTOR (MOTOR II) Frequency Hz 4 mm Outside radius of outer rotor 9 mm Outside radius of gear PM 88.6 mm Inside radius of gear PM 8.8 mm Outside radius of stationary ring 8. mm Inside radius of stationary ring 67. mm Outside radius of stator 66.6 mm Fig. 11. Simulation result showing the torque curve versus time at full-load operation (Motor II)

5 ANSYS 11 中国用户大会优秀论文 Fig. 1. Simulation result showing the induced emf curves versus time at fullload operation (Motor II) Core loss (W) Fig. 13. Simulation result showing the coreloss curve versus time at full-load operation (Motor II) The number of stator slot can be much smaller than those of conventional low-speed motors, thus the space of the slots can be larger and can be used more efficiently. The free space between adjacent stationary iron segments can act as ventilating ducts to help improving the heat dissipation and ventilation of the motor. Its disadvantage is that because of the iron segments in the airgap, it is not easy to manufacture such motor. Nonetheless it is a good candidate for low-speed drives. V. MOTOR III CONVENTIONAL PM MOTOR To help assessing the performance of the FM motor, its performance is further compared with those of traditional motors. A conventional PM motor is shown in Fig. 15. Its key design data are listed in Table III. The stator has pole pairs. It is assumed that there are three slots per pole per phase. The total number of slots is 13. The phase distributions in the stator slots are: +A +A +A C C C +B +B +B. It has relatively long end windings. Its typical flux distribution is shown in Fig. 16. Fig. 15. Overview of an intersection structure of a conventional PM motor (Motor III) Fig. 14. Simulation result showing the cogging torque curve versus rotor position (Motor II) When the rotor is locked, the torque curve and induced emf curves versus time are as shown in Figs. 9 and 1, respectively. The maximum locked-rotor torque is 58 Nm. The torque curve and back emf curves versus time at full-load are shown in Figs. 11 and 1, respectively. Fig. 13 shows that the coreloss is small. Fig. 14 shows that the cogging torque is also very small. This is because that the combination of pole pair number and slot number is similar to that of a fractionalslot motor. Because the stator of the FM motor is designed as that of a high-speed motor, the number of stator pole pairs is small. TABLE III KEY DESIGN DATA OF CONVENTIONAL PM MOTOR (MOTOR III) Frequency Hz 4 mm Outside radius of outer rotor 9 mm Outside radius of gear PM 88.6 mm Inside radius of gear PM 8.8 mm Outside radius of stator 8. mm Inside radius of stator 17.5 mm 4 mm Number of outer rotor pole pairs Number of stator slots 13

6 ANSYS 11 中国用户大会优秀论文 Fig. 16. A flux plot on an intersection of the conventional PM motor (Motor III) When the rotor is locked, the torque curve and induced emf curves versus time are shown in Figs. 17 and 18, respectively. The maximum locked-rotor torque is 6 Nm. The torque curve and back emf curves versus time at full-load operation are shown in Figs. 19 and, respectively. Fig. 1 shows that the coreloss is large. Fig. shows that this motor has very large cogging torque. This is because that the cogging torques on each pole are directly added together. This design has too many stator slots and hence should be replaced by a fractional-slot motor which will be discussed in the following section Fig. 18. Simulation result showing the induced emf curves versus time when the rotor is locked (Motor III) Fig. 19. Simulation result showing the torque curve versus time at full-load operation (Motor III) Fig. 17. Simulation result showing the torque curve versus time when the rotor is locked (Motor III) -15 Fig.. Simulation result showing the induced emf curves versus time at fullload operation (Motor III)

7 ANSYS 11 中国用户大会优秀论文 Core loss (W) Fig. 1. Simulation result showing the coreloss curve versus time at full-load operation (Motor III) phase distributions in the stator slots are: +A A +A A C +C C +C +B B +B B. It has very relatively short end windings. Fig. 4. A flux plot on an intersection of the fractional-slot PM motor (Motor IV) Fig.. Simulation result showing the cogging torque curve versus rotor position (Motor III) TABLE IV KEY DESIGN DATA OF CONVENTIONAL FRACTIONAL-SLOT PM MOTOR (MOTOR IV) Frequency Hz 4 mm Outside radius of outer rotor 9 mm Outside radius of gear PM 88.6 mm Inside radius of gear PM 8.8 mm Outside radius of stator 8. mm Inside radius of stator 17.5 mm 4 mm Number of outer rotor pole pairs Number of stator slots Fig. 3. Overview of an intersection structure of a fractional-slot PM motor (Motor IV) VI. MOTOR IV FRACTIONAL-SLOT MOTOR Because the conventional PM motor (Motor III) has too many slots, a fractional-slot multi-pole PM motor is further studied (as shown in Fig. 3, referred as Motor IV). Its key design data are listed in Table IV. Its typical flux distribution is shown in Fig. 4. Its number of slots is reduced to 48. The Fig. 5. Simulation result showing the torque curve versus time when the rotor is locked (Motor IV)

8 ANSYS 11 中国用户大会优秀论文 Fig. 6. Simulation result showing the induced emf curves versus time when the rotor is locked (Motor IV) 6 6 is only reduced marginally. Fig. 3 shows that this motor s cogging torque is very small. The fractional-slot PM motor has the advantages of having relatively small number of stator slots, short end windings and small cogging torque Fig. 9. Simulation result showing the coreloss curve versus time at full-load operation (Motor IV) Core loss (W) Fig. 7. Simulation result showing the torque curve versus time at full-load operation (Motor IV) Fig. 8. Simulation result showing the induced emf curves versus time at fullload operation (Motor IV) When the rotor is locked, the torque curve and induced emf curves versus time are shown in Figs. 5 and 6, respectively. The maximum locked-rotor torque is 59.5 Nm. The torque curve, back emf curves and coreloss curve versus time at fullload operation are shown in Figs. 7, 8 and 9, respectively. From the simulation results it is observed that its output torque Fig. 3. Simulation result showing the cogging torque curve versus rotor position (Motor IV) The performance data of the four motors are summarized in Table V. TABLE V PERFORMANCE COMPARISON OF THE FOUR DIFFERENT MOTORS Motor type Motor I Motor II Motor III Motor IV Locked rotor maximum torque (Nm) Output torque (Nm) EMF of full-load (V) Cogging torque (Nm) Core loss (W) VII. CONCLUSION (1) The magnetic-geared motor produces very large torque at low speed. Its disadvantage is that it has two rotational parts. () Compared with conventional PM motors with the same ampere-conductors, the FM motor has similar torque density. However the proposed motor has a smaller number of slots and the ventilation is better than conventional PM motors,

9 ANSYS 11 中国用户大会优秀论文 hence its value of ampere-conductors is expected to be higher for the same temperature rise, which implies the torque density of the proposed motor is higher than that of conventional motors. (3) The conventional PM motor has too many slots; its slot area cannot be utilized efficiently; the end windings are too long; it also has very large cogging torque. Consequently, conventional PM motor is intrinsically not a good choice in low-speed drive. (4) The fractional-slot multi-pole motor has a small number of slots and short end windings. Its output torque is only a little smaller than that of the motor with conventional windings. It has small cogging torque. It can be used in lowspeed drive. finite element analysis, IEEE Trans. Magn., vol. 4, no., pp , March 4. [13] W. N. Fu and S. L. Ho, Enhanced nonlinear algorithm for the transient analysis of magnetic field and electric circuit coupled problems, IEEE Trans. Magn., vol. 45, no., pp , Feb. 9. ACKNOWLEDGMENT This work was supported in part by The Hong Kong Polytechnic University under Grants U489, 87RX and YH56. REFERENCES [1] K. Atallah, S. D. Calverley and D. Howe, Design, analysis and realisation of a high-performance magnetic gear, IEE Proceedings - Electric Power Applications, vol. 151, no., pp , Mar 4. [] K. Atallah and D. Howe, A novel high-performance magnetic gear, IEEE Trans. Magn., vol. 37, no. 4, Part 1, pp , July 1. [3] P. O. Rasmussen, T. O. Andersen, F. T. Jorgensen, O. Nielsen, Development of a high-performance magnetic gear, IEEE Trans. Industry Applications, vol. 41, no. 3, pp , May-June 5. [4] Cheng-Chi Huang, Mi-Ching Tsai, D. G. Dorrell and Bor-Jeng Lin, Development of a magnetic planetary gearbox, IEEE Trans. Magn., vol. 44, no. 3, pp , March 8. [5] M. Aubertin, A. Tounzi and Y. Le Menach, Study of an electromagnetic gearbox involving two permanent magnet synchronous machines using 3-D-FEM, IEEE Trans. Magn., vol. 44, no. 11, Part, pp , Nov. 8. [6] K. T. Chau, C. C. Chan, Chunhua Liu, Overview of permanent-magnet brushless drives for electric and hybrid electric vehicles, IEEE Trans. Industrial Electronics, vol. 55, no. 6, pp , June 8. [7] K. T. Chau, Dong Zhang, J. Z. Jiang, Chunhua Liu and Yuejin Zhang, Design of a magnetic-geared outer-rotor permanent-magnet brushless motor for electric vehicles, IEEE Trans. Magn., vol. 43, no. 6, pp , June 7. [8] L. Jian, K. T. Chau and J. Z. Jiang, A magnetic-geared outer-rotor permanent-magnet brushless machine for wind power generation, IEEE Trans. Industry Applications, vol. 45, no. 3, pp , May-June 9. [9] 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, -4 April 8, pp [1] W. N. Fu, Z. J. Liu and C. Bi, A dynamic model of the disk drive spindle motor and its applications, IEEE Trans. Magn., vol. 38, no., pp , March. [11] W. N. Fu, P. Zhou, D. Lin, S. Stanton and Z.J. Cendes, Modeling of solid conductors in two-dimensional transient finite-element analysis and its application to electric machines, IEEE Trans. Magn., vol. 4, no.,, pp , March 4. [1] D. Lin, P. Zhou, W.N. Fu, Z. Badics and Z.J. Cendes, A dynamic core loss model for soft ferromagnetic and power ferrite materials in transient