A new dual stator linear permanent-magnet vernier machine with reduced copper loss Fangfang Bian, 1,2) and Wenxiang Zhao, 1,2) 1 School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China 2 Jiangsu Key Laboratory of Drive and Intelligent Control for Electric Vehicle, Zhenjiang 212013, China In this paper, a new dual stator linear permanent-magnet (PM) vernier (LPMV) machine with toroidal winding is proposed and analyzed. The proposed machine enjoys the advantages of less copper usage and copper loss without sacrificing the thrust force performance. For a fair comparison, the proposed machine is designed with the same geometrical parameters based on the conventional dual stator LPMV machine with concentrated winding. Finally, the electromagnetic performances of the proposed machine and the conventional one are compared and analyzed by using finite element method, verifying that the proposed machine with the low copper loss can obtain high force density. I. INTRODUCTION Due to the merits of high torque/force density, permanent magnet (PM) vernier (PMV) machines have been picked up as the most appropriate solution for the cost effective applications [1]-[3]. Recently, various PMV topologies have been proposed [4], [5]. Ref. [6] illustrated that the torque of the PMV machine with integral slot distributed windings was higher than that of the fractional slot concentrated windings one. However, the distributed winding suffered from the overlapping coils and bulky end-turn winding, which increased the difficulty of the processing and copper loss. To solve the contradictory problem, an outer rotor PMV machine with toroidal winding was proposed and verified to have the advantages in the end winding length and torque density compared to regular PMV machines [7]. The aim of this paper is to propose a dual stator linear PMV (LPMV) machine with the toroidal winding to reduce copper usage and loss without scarifying the force capability. The electromagnetic performances, such as the back electromotive force (back EMF), force density, copper loss and inductance, will be investigated by using finite element method between the proposed and the conventional machines. II. CONFIGURATION AND OPERATION PRINCIPLE To more directly compare the two dual stator LPMV machines, the conventional machine is called as C-machine for short in the following content while the proposed machine can be described as P-machine. As shown in Fig. 1, two machines consist of one short mover and two stators designed as the iron core with salient teeth. Their movers contain both PM arrays and windings. The PM array in the two machines has the same three magnets. The middle one is vertically magnetized while 1
the other two are horizontally magnetized. Each mover is separated into three elementary modules to achieve the independence of phases [8]. There are two main differences between the two machines. One is that the coils of three phases in the P-machine are wound onto the mover yoke core. The change of the coils connection types means that only a set of toroidal windings replaces the four sets of concentrated windings in one phase. And, the other is that the convex portions in the P-machine are removed. The dual stator LPMV machine is one of the PMV machines with magnetic gear effect, its operation principle can be illustrated by the magnetic gearing effect. The stator teeth of the dual stator LPMV machine modulate the PM magnetic field to produce the effective magnetic field which has the larger speed than that of the stator. So, the thrust force can be improved. The relationship can be expressed as p p p (1) w p G p w where p PM, p s and p w are the pole-pair number of the PM magnetic field, the number of stator teeth and the pole-pair number of the air-gap magnetic field, respectively. G is the magnetic gear ratio. PM s s (2) (a) FIG. 1. The dual stator LPMV machines. (a) The C-machine. (b) The P-machine. III. PERFORMANCE ANALISIS (b) The P-machine is designed based on the C-machine, except the mover yoke and the winding. The corresponding parameters are listed in Table I. The static characteristics of the two machines are analyzed and compared as shown in Fig. 2. It can be observed that the flux lines of the three modules in two machines are independent. Meanwhile, the field distributions in one module between the two stators also do not impact relatively, thus, the dual stator LPMV machines possess excellent fault tolerant capability. In the C-machine, the fluxes produced by the PM arrays travel across the air gap, stators, and then, back into the armature teeth as well as the mover yokes. The fluxes passed through these teeth are the same to that of the yokes. These features allow that the windings can be wound around the armature teeth as shown in the C-machine or the mover yokes as shown in the P- machine. Thus, the P-machine has the same magnetic path and quantity of the fluxes, except the convex portion in the mover and the type of the windings. 2
In the C-machine, the convex portions in Fig. 1(a) are just designed to fix the windings and easily assemble. Since the main fluxes do not cross the convex portion and the windings are wound around the yokes, it is unnecessary to have the convex portion in the P-machine. Due to the modular structures, the two machines have little end effect, so the detent force and average force in the P-machine will not be affected without the convex portions. TABLE I. Design specifications. Items C-machine P-machine Mover width (mm) 120 Mover high (mm) 100 95 Mover pole pitch (mm) 115 Mover yoke high (mm) 30 24 Armature tooth width (mm) 23 Area per slot (mm 2 ) 684.5 Number of turns per coil 100 200 Series coils per phase 4 1 Air gap length (mm) 2 PM volume (cm 3 ) 216 Rated current (A) 5 Speed (m/s) 1.5 Resistance (Ω) 6.56 3.36 (a) FIG. 2. Flux distributions at no load. (a) The C-machine. (b) The P-machine. (b) 3
Back EMF (V) 200 100 0-100 P-machine B B1+B2 C-machine B B3+B4 Amplitude (V) 150 100 50 P-machine B C-machine B -200 0 0 3 6 9 12 15 1 3 5 7 9 11 Position (mm) Harmonic order (a) (b) FIG. 3. Back EMF at no load. (a) Waveforms. (b) Spectra. In the C-machine with concentrated winding, each coil produces a quarter of the back EMF while in the P-machine with toroidal winding the total back EMF is created only by one coil, as shown in Fig. 3. Although the number of winding turns of per phase in the C-machine is twice that of the P-machine, the toroidal windings in the P-machine can achieve the same amplitude of the fundamental component. Meanwhile, the B1+B2 represents the waveform of the maximum back EMF of the two coils B1 and B2, and so do the B3+B4. Thus, the total back EMF of the C-machine can be obtained by the reverse connection of the B1, B2 and B3, B4. It is noted that the P-machine has higher utilizing ratio of the winding than the C- machine. Fig. 4 shows the cogging force and the fluctuating force. Both the fluctuating forces of the two machines have the opposite phase with their cogging forces. Meanwhile, the ratios of the fluctuating fore and cogging force to average force are less than 5%. Thus, they can obtain the thrust force with low ripple. Despite the administration of different winding types, the average thrust forces of the P-machine and C-machine are equal to 646 N and 649 N, respectively, while the ripples of the two machines are 3.8% and 3.4%, respectively. Even so, it should be mentioned that the thrust force density of the P-machine is improved because its volume is smaller than the conventional one. The thrust force densities of the P-machine and C- machines are 180 kn/m 3 and 161 kn/m 3 at the speed of 1.5 m/s, respectively, as shown in Fig. 5. Due to the application of the toroidal winding with less turns, the copper usage is significantly reduced, resulting in the lower copper loss. The copper loss P cu in the dual stator LPMV machines can be expressed as 2 I R (3) cu where I and R are the rated current and the total resistance of the armature windings, respectively. As can be seen, the copper loss in the C-machine with concentrated windings is 82 W while the one of the P-machine with toroidal winding is only 42 W. The copper loss of the P-machine is reduced by 49% as the force density of the P-machine is improved by 11.8%. It confirms that the P-machine contains the higher force density and lower copper loss. The self-inductance waveforms of the two machines are compared in Fig. 6, and the mutual inductance of the P-machine is shown in Fig. 7. As can be seen, the selfinductance of the C-machine is slightly higher than that of the P-machine. Although the turns of the windings per phase in the 4 P
P-machine decrease, the flux linkage in single-turn coil per phase of the P-machine is twice that of the C-machine. Thus, the windings per phase with 200 turns in the P-machine can achieve the same flux linkage comparing with the C-machine with 400 turns per phase. In an unsaturated solution, the self-inductances of the two machines are equal to each other with the same rated current. In addition, due to the modular structure, the three-phase mutual inductance of the P-machine almost equals zero. Force (N) 20 10 0-10 -20 P-fluctuating force C-fluctuating force P-cogging force C-cogging force 0 3 6 9 12 15 Position (mm) FIG. 4. Cogging force and fluctuating force. 200 Inductance (mh) 150 100 50 La_P-machine La_C-machine Lb_P-machine Lb_C-machine Lc_P-machine Lc_C-machine Force density (kn/m3) 200 Force density 150 100 50 0 P-machine Copper loss C-machine FIG. 5. Force density and copper loss. 10 Mab Mba Mca Inductance (mh) 7.5 Mac Mbc Mcb 5 2.5 100 80 60 40 20 0 Copper Loss (W) 0 0 3 6 9 12 15 Position (mm) FIG. 6. Comparison of self-inductance waveforms. IV. CONCLUSION 0 0 3 6 9 12 15 Position (mm) FIG. 7. Mutual inductance waveforms of the P-machine. In this paper, a new dual stator LPMV machine with toroidal winding has been proposed. The analysis results of the static magnetic field and back EMF confirm that the P-machine contains the merits of the high utilization ratio of the winding. Meanwhile, the cogging force and fluctuating force of the P-machine has the opposite phases, which is similar to the C- machine. Due to the relatively small volume, the force density of the P-machine is improved to 180 kn/m 3, which is higher than that of the C-machine. The P-machine with toroidal winding has decreased almost half of the copper consumption of the conventional one, thus, and the copper loss can be reduced by 49%. The P-machine contains so many merits that it can be an excellent solution in the linear direct drive applications. ACKNOWLEDGMENTS 5
This work was supported in part by the National Natural Science Foundation of China (51277194, 51422702), by the Qing Lan Project of Jiangsu Province, by the Priority Academic Program Development of Jiangsu Higher Education Institutions. REFERENCES 1 B. Kim and T. Lipo, IEEE Trans. Ind. Appl. 50, 3656 (2014). 2 M. A. Mueller and N. J. Baker, Proc. IEE Electr. Power Appl. 150, 647 (2003). 3 B. Kim and T. Lipo, IEEE Trans. Ind. Appl. 50, 3656 (2014). 4 W. Zhao, J. Zheng, J. Wang, G. Liu, J. Zhao, and Z. Fang, IEEE Trans. Ind. Electron. 63, 2072 (2016). 5 J. Li, K. Chau, J. Jiang, C. Liu, and W. Li, IEEE Trans. Magn. 46, 1475 (2010). 6 L. Xu, G. Liu, W. Zhao, J. Ji, H. Zhou, W. Zhao, and T. Jiang, IEEE Trans. Energy Convers. 30, 1483 (2015). 7 D. Li, R. Qu, J. Li and W. Xu, IEEE Trans. Ind. Appl. 51, 4470 (2015). 8 Y. Du, M. Cheng, K. T. Chau, X. Liu, F. Xiao, K. Shi, and L. Mo, IEEE Trans. Magn. 50, 4219 (2014). 6