France



-In this paper, a novel yokeless magnetic gear (YMG) with trapezoidal Halbach PM array is presented for direct drive of electric vehicles. Compared to traditional structures, the proposed machine has huge performance improvement in the following two aspects: Firstly, by using the aluminum to replace the silicon steel as the rotor iron core, the iron loss and motor weight can be reduced and the torque density can be increased significantly; Secondly, the generated torque and ripple can be optimized by adopting a trapezoidal Halbach PM array, whose leakage flux is far more lower than YMG with Halbach PM array and YMG with conventional PMs. The performance of the proposed motor is compared and analyzed by using three-dimensional finite-element method and the best parameter combination of the proposed machine is found using optimization method.&lt;br/&gt;1. Introduction&lt;br/&gt;Magnetic gears provide solutions for replacing the mechanical gearbox in electric vehicle driving system since it inherently has the advantages of high transmission efficiency, overload protection, low working noise and physical isolation. In order to tap the potentials of industrial application, more researchers focus on the magnetic gears, including radial-flux, axial-flux magnetic gear and magnetic-geared machines, for finding high efficiency, high torque density and better performance solutions. Papers [1] proposed the types of a magnetic gear with Halbach PM array and discussed how the arrangement of Halbach PM affects the performance of the machine. However, due to the limit of machine structures, all of these magnetic gears have the rotor iron core, which is used to form the magnetic circuit of PM and reduce the magnetic resistance. However, the performance of the machine is weakened severely with adopting the yokeless structure since it introduces of great leakage flux. Hence, although the design and research in this topology have made some progress, in terms of its own design thought, the improvement level is very limited. In this paper, a novel yokeless magnetic gear (YMG) with trapezoidal Halbach PM array is proposed to solve the drawbacks mentioned above. Compared to the designs of the magnetic gears with Halbach PM array, the proposed machine has a better performance in the torque output capacity, torque density and efficiency.&lt;br/&gt;2. Working Principle and Motor Structure&lt;br/&gt;The overall structure of the proposed yokeless magnetic gear with trapezoidal Halbach PM array is shown in Fig. 1.&lt;br/&gt;As shown in Fig. 1, the proposed machine contains four kinds of magnetized PM and aluminum supporter for reducing the leakage flux and weight. The total axial length, outer radius of outer-rotor and inner radius of stator are 220 mm, 120 mm and 65.8 mm, respectively. All magnetic gears, including the proposed one, comply with the fundamental rule, which is expressed as:&lt;br/&gt;&lt;i&gt;P&lt;/i&gt;=&lt;i&gt;N&lt;sub&gt;L&lt;/sub&gt;&lt;/i&gt;±&lt;i&gt;N&lt;sub&gt;H&lt;/sub&gt; &lt;/i&gt; (1)&lt;br/&gt;where&lt;i&gt; N&lt;/i&gt;&lt;i&gt;&lt;sub&gt;L&lt;/sub&gt;&lt;/i&gt; , &lt;i&gt;N&lt;/i&gt;&lt;i&gt;&lt;sub&gt;H&lt;/sub&gt;&lt;/i&gt; and &lt;i&gt;P&lt;/i&gt; are the number of pole pairs of low speed rotor (LSR), high speed rotor (HSR) and modulator, respectively. For getting a better performance, &lt;i&gt;P &lt;/i&gt;should be equal to &lt;i&gt;N&lt;/i&gt;&lt;sub&gt;H&lt;/sub&gt;+&lt;i&gt;N&lt;/i&gt;&lt;i&gt;&lt;sub&gt;L&lt;/sub&gt;&lt;/i&gt;. Besides, similar to the above equation, the operation speed of MG should also follow the following relationship:&lt;br/&gt;&lt;i&gt;ω&lt;/i&gt;&lt;i&gt;&lt;sub&gt;H&lt;/sub&gt;&lt;/i&gt; /&lt;i&gt;ω&lt;/i&gt;&lt;i&gt;&lt;sub&gt;L&lt;/sub&gt;&lt;/i&gt;= -&lt;i&gt;N&lt;/i&gt;&lt;i&gt;&lt;sub&gt;L&lt;/sub&gt;&lt;/i&gt;/&lt;i&gt;N&lt;/i&gt;&lt;i&gt;&lt;sub&gt;H&lt;/sub&gt;&lt;/i&gt; =- &lt;i&gt;G&lt;/i&gt;&lt;i&gt;&lt;sub&gt;r&lt;/sub&gt;&lt;/i&gt; (2)&lt;br/&gt;where &lt;i&gt;ω&lt;/i&gt;&lt;i&gt;&lt;sub&gt;L&lt;/sub&gt;&lt;/i&gt; and &lt;i&gt;ω&lt;/i&gt;&lt;i&gt;&lt;sub&gt;H&lt;/sub&gt;&lt;/i&gt; are the mechanical speed of LSR and HSR. The proportion of the two speed &lt;i&gt;G&lt;/i&gt;&lt;i&gt;&lt;sub&gt;r&lt;/sub&gt;&lt;/i&gt; is the gear ratio, which is used to indicate that the speed ratio of MG equals the inverse ratio of the PM pole-pair numbers in two rotors. In this paper, the rated operation speed for the HSR and LSR are 2400 r/min and 300r/min, respectively, which is close to the rated operation speed of direct-drive electric vehicle system.&lt;br/&gt;3. Performance Comparisons and Analysis&lt;br/&gt;The output torque comparison between the proposed machine, conventional magnetic gear (MG), yokeless magnetic gear (YMG) and YMG with conventional Halbach PM array are shown in Fig. 2 (a). Simulation results show that the output torque of the proposed machine increases by 169.1%, 97.2% and 21.0% compared to YMG, YMG with conventional Halbach PM array and conventional MG, reaching 1840.5 Nm with the ripple of 1.28%. Besides, the proposed machine has a minimum iron loss and the highest efficiency compared to the other types of MG, reaching 110 W and 99.38%, respectively. Furthermore, the torque density of proposed machine reaches 51.18 Nm per kilogram and 88.1 Nm per PM weight (Kg), which increased by 96.8% and reduced by 7.3% compared to conventional MG.&lt;br/&gt;Fig. 2(b) shows the distributions of radial flux density &lt;i&gt;B&lt;/i&gt;&lt;i&gt;&lt;sub&gt;r&lt;/sub&gt;&lt;/i&gt;&lt;i&gt;&lt;sub&gt;δ&lt;/sub&gt;&lt;/i&gt; in the air gap under no load condition. The comparison of leakage flux between YMG with conventional Halbach PM array and proposed machine, YMG and proposed machine are indicated in Fig.4 (c) and (d), respectively. Compared to those two types of YMG, the proposed machine has the lowest density of magnetic flux line in both the outer region of outer PMs and inner region of inner PMs, which means the leakage flux of the proposed machine is the lowest and that is the reason for the high torque density of the proposed machine.&lt;br/&gt;4. Conclusion&lt;br/&gt;This paper proposes a yokeless magnetic gear with trapezoidal Halbach PM array for electric vehicle driving. First, the structure, PM arrangement and working principle are introduced. Then, the performance comparison among the proposed machine, conventional MG, YMG and YMG with Halbach array are conducted. Finally, the simulation results verify the efficiency of the novel structure.

**References:**

[1] Yiduan Chen; W. N. Fu; Wei Li. &quot;Performance analysis of a novel triple-permanent-magnet-excited magnetic gear and its design method&quot;.&lt;i&gt; IEEE Trans. Magnetics&lt;/i&gt;, vol. 52, no.7, pp. 1-4, 2016.

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 Design and Comparison Study of a Yokeless Magnetic Gear with Trapezoidal Halbach PM Array for Electric Vehicle Driving

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-In this paper, a novel yokeless magnetic gear (YMG) with trapezoidal Halbach PM array is presented for direct drive of electric vehicles. Compared to traditional structures, the proposed machine has huge performance improvement in the following two aspects: Firstly, by using the aluminum to replace the silicon steel as the rotor iron core, the iron loss and motor weight can be reduced and the torque density can be increased significantly; Secondly, the generated torque and ripple can be optimized by adopting a trapezoidal Halbach PM array, whose leakage flux is far more lower than YMG with Halbach PM array and YMG with conventional PMs. The performance of the proposed motor is compared and analyzed by using three-dimensional finite-element method and the best parameter combination of the proposed machine is found using optimization method. 1. Introduction Magnetic gears provide solutions for replacing the mechanical gearbox in electric vehicle driving system since it inherently has the advantages of high transmission efficiency, overload protection, low working noise and physical isolation. In order to tap the potentials of industrial application, more researchers focus on the magnetic gears, including radial-flux, axial-flux magnetic gear and magnetic-geared machines, for finding high efficiency, high torque density and better performance solutions. Papers [1] proposed the types of a magnetic gear with Halbach PM array and discussed how the arrangement of Halbach PM affects the performance of the machine. However, due to the limit of machine structures, all of these magnetic gears have the rotor iron core, which is used to form the magnetic circuit of PM and reduce the magnetic resistance. However, the performance of the machine is weakened severely with adopting the yokeless structure since it introduces of great leakage flux. Hence, although the design and research in this topology have made some progress, in terms of its own design thought, the improvement level is very limited. In this paper, a novel yokeless magnetic gear (YMG) with trapezoidal Halbach PM array is proposed to solve the drawbacks mentioned above. Compared to the designs of the magnetic gears with Halbach PM array, the proposed machine has a better performance in the torque output capacity, torque density and efficiency. 2. Working Principle and Motor Structure The overall structure of the proposed yokeless magnetic gear with trapezoidal Halbach PM array is shown in Fig. 1. As shown in Fig. 1, the proposed machine contains four kinds of magnetized PM and aluminum supporter for reducing the leakage flux and weight. The total axial length, outer radius of outer-rotor and inner radius of stator are 220 mm, 120 mm and 65.8 mm, respectively. All magnetic gears, including the proposed one, comply with the fundamental rule, which is expressed as: P=NL±NH (1) where NL , NH and P are the number of pole pairs of low speed rotor (LSR), high speed rotor (HSR) and modulator, respectively. For getting a better performance, P should be equal to NH+NL. Besides, similar to the above equation, the operation speed of MG should also follow the following relationship: ωH /ωL= -NL/NH =- Gr (2) where ωL and ωH are the mechanical speed of LSR and HSR. The proportion of the two speed Gr is the gear ratio, which is used to indicate that the speed ratio of MG equals the inverse ratio of the PM pole-pair numbers in two rotors. In this paper, the rated operation speed for the HSR and LSR are 2400 r/min and 300r/min, respectively, which is close to the rated operation speed of direct-drive electric vehicle system. 3. Performance Comparisons and Analysis The output torque comparison between the proposed machine, conventional magnetic gear (MG), yokeless magnetic gear (YMG) and YMG with conventional Halbach PM array are shown in Fig. 2 (a). Simulation results show that the output torque of the proposed machine increases by 169.1%, 97.2% and 21.0% compared to YMG, YMG with conventional Halbach PM array and conventional MG, reaching 1840.5 Nm with the ripple of 1.28%. Besides, the proposed machine has a minimum iron loss and the highest efficiency compared to the other types of MG, reaching 110 W and 99.38%, respectively. Furthermore, the torque density of proposed machine reaches 51.18 Nm per kilogram and 88.1 Nm per PM weight (Kg), which increased by 96.8% and reduced by 7.3% compared to conventional MG. Fig. 2(b) shows the distributions of radial flux density Brδ in the air gap under no load condition. The comparison of leakage flux between YMG with conventional Halbach PM array and proposed machine, YMG and proposed machine are indicated in Fig.4 (c) and (d), respectively. Compared to those two types of YMG, the proposed machine has the lowest density of magnetic flux line in both the outer region of outer PMs and inner region of inner PMs, which means the leakage flux of the proposed machine is the lowest and that is the reason for the high torque density of the proposed machine. 4. Conclusion This paper proposes a yokeless magnetic gear with trapezoidal Halbach PM array for electric vehicle driving. First, the structure, PM arrangement and working principle are introduced. Then, the performance comparison among the proposed machine, conventional MG, YMG and YMG with Halbach array are conducted. Finally, the simulation results verify the efficiency of the novel structure.

**References:**

[1] Yiduan Chen; W. N. Fu; Wei Li. "Performance analysis of a novel triple-permanent-magnet-excited magnetic gear and its design method". IEEE Trans. Magnetics, vol. 52, no.7, pp. 1-4, 2016.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a8ff0c0c0dfc22ea052cc3b30fcf7880.jpg)
Figure1

![](https://assets.underline.io/uploads/markdown_image/1/image/d940fdd58db79b3a85e7c86d5842a5d9.jpg)
Figure2

poster

A novel brushless dual-electrical-port dual-mechanical-port machine with opening stator slot is proposed to improve the torque density. Compared to the regular BLDD machine, which can be regarded as the combination of the magnetic gear machine (MGM) and permanent magnet synchronous machine (PMSM), the proposed BLDD is formed by MGM and vernier PM machine (VPM). The stator teeth are not only used to go through the main flux, but also worked as a modulator to change the pole pairs and construct the VPM part. Due to the flux modulation effect and reduced effective air-gap, the torque density is significant improved. The operation principle is introduced and electromagnetic performances of the regular and proposed BLDD machine are compared by 2-D finite element analysis (FEA). I. Introduction Continuously variable transmission (CVT) is the key component of the hybrid power system, which has the advantages between the electric drive system and engine [1]-[3]. With the development of the flux modulation principle [4], a new type of CVT called brushless dual-electrical-port dual-mechanical-port (BLDD) machine, which can realize the function of a generator, a motor and the planetary gear in the hybrid power system, has been proposed in [5]. This paper proposes a higher torque density BLDD machine with opening stator slot, as shown in Fig. 1. II. Structure and operation principle The proposed BLDD machine has the same outer and inner rotors structure with the regular BLDD machine [6]. The major difference is the stator configuration. A split-teeth stator structure is used and two sets of windings are placed in the auxiliary teeth and main teeth respectively. In the regular BLDD machine, the auxiliary teeth are closed slot structure, and only used to provide flux path. In the proposed BLDD machine, the auxiliary teeth are opening slot structure, and not only used to go through the magnetic path, but also worked as a modulator to change the PM pole-pair to vernier winding pole-pair. As shown in Fig.1 (a2) and (b2), the MGM part is composed of the modulation winding, teeth in the inner rotor and spoke-array PMs in the outer rotor, which is the same for both regular and proposed BLDD machines. The operation principle of the MGM portion is based on the magnetic gear effect, and the modulation winding pole-pair is equal to the difference between the PM pole-pair and inner rotor teeth number. The other portions of regular and proposed BLDD machines are completely different, one is PMSM portion, and the other is VPM portion. The PMSM portion of the regular BLDD machine in Fig.1 (a3) is formed by regular winding, stator with closed slot and spoke-array PM outer rotor. PMSM works on the same operation principle as a conventional PM machine, and the regular winding pole-pair is equal to PM pole-pair. Nevertheless, the VPM portion of the proposed BLDD machine in Fig.1 (b3) consists of vernier winding, stator with opening slot and spoke-array PM outer rotor. The operation of VPM is based on the flux modulation principle, in which stator auxiliary teeth work as a pole pair transformer and the vernier winding pole-pair is equal to the difference between the stator auxiliary teeth number to PM pole-pair. III. Comparison of the Regular and Proposed BLDD Machines The two BLDD machines with the same machine volume and current density are used to compare the electromagnetic performance. The two BLDD machines have been optimized respectively. Compared to the regular BLDD machine, the proposed BLDD machine has 53.3% higher MGM torque due to increased pole ratio (ratio of PM pole-pair to winding pole-pair) and 77.8% higher VPM torque because of flux modulation effect. IV. Conclusion This paper proposes a novel BLDD machine with opening stator slot. The proposed BLDD machine can significantly improve the back EMF and torque density. Because the composite structure of the proposed BLDD machine is changed and the operation principle is different. More details about machine operation principle, operation features and some design considerations of the proposed BLDD will be given in the full paper.

**References:**

[1] Z. Q. Zhu and S. Cai, "Hybrid excited permanent magnet machines for electric and hybrid electric vehicles," CES Trans. on Electrical Machines and Systems, vol. 3, no. 3, pp. 233-247, Sept. 2019. [2] A. Emadi, Y. J. Lee and K. Rajashekara, "Power Electronics and Motor Drives in Electric, Hybrid Electric, and Plug-In Hybrid Electric Vehicles," IEEE Trans. Ind. Electron., vol. 55, no. 6, pp. 2237-2245, June 2008. [3] X. Zhang, C. T. Li, D. Kum etc., "Prius+ and volt- : configuration analysis of power-split hybrid vehicles with a single planetary gear," IEEE Trans. Veh. Technol., vol. 61, no. 8, pp. 3544-3552, Oct. 2012. [4] D. Li, R. Qu and T. A. Lipo, "High-Power-Factor Vernier Permanent-Magnet Machines," IEEE Trans. Ind. Appl., vol. 50, no. 6, pp. 3664-3674, Nov.-Dec. 2014. [5] D. Li, R. Qu, X. Ren etc., “Brushless dual-electrical-port, dual mechanical port machines based on the flux modulation principle,” in Proc. IEEE Energy Convers. Congr. Expo,2016. [6] Z. Liang, X. Ren, D. Li, etc., "Analysis of a Spoke-Array Brushless Dual-Electrical-Port Dual-Mechanical-Port Machine With Reluctance Rotor," IEEE Trans. Ind. Electron. vol. 68, no. 4, pp. 2999-3011, April 2021.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2227f1374d906f15e29edd7415114e42.jpg)
Fig.1 Configurations. (a1) Regular BLDD machine. (a2) MGM portion of regular BLDD machine. (a3) PMSM portion of regular BLDD machine. (b1) Proposed BLDD machine. (b2) MGM portion of proposed BLDD machine. (b3) VPM portion of proposed BLDD machine.

![](https://assets.underline.io/uploads/markdown_image/1/image/534945c16b478183b1896e4b123720b8.jpg)
Fig.2 Comparison of regular and proposed BLDD machines. (a1) Back EMFs of modulation winding. (a2) Back EMFs of regular or vernier windings. (b1) MGM torque component. (b2) PMSM or VPM torque component.

 A Novel Brushless Dual-Electrical-Port Dual-Mechanical-Port Machine with Opening Stator Slot

This paper proposes a novel hybrid reluctance machine with dual-layer slot PMs and zero-sequence excitation. Dual-layer slot PMs are utilized to evoke DC-saturation-relieving and flux modulation effect respectively. By introducing zero-sequence current excitation which functions as virtual DC field source, extra dc field winding can be removed. Moreover, flux can be flexibly controlled through regulating zero-sequence current, thus speed range can be greatly extended. In this paper, the machine configuration, DC-saturation-relieving principle, flux modulation effect, and zero-sequence current control are introduced. Electromagnetic performance of the proposed machine is evaluated by finite element analysis (FEA), including variation of flux-linkage, back-EMF, as well as torque density with different zero-sequence currents. Furthermore, a prototype is manufactured and relevant experiments are performed to verified the correctness of FEA. 1. Introduction Nowadays, electric vehicles have attracted more and more attention due to fossil fuel depletion and severe environment pollution [1]. It is required that the motor operates at wide speed range [2]. Reluctance machine has come to be a good solution for electric vehicle application, which includes switched reluctance machine (SRM) [3], doubly salient machine (DSM), flux switching machine (FSM) [4], flux reversal machine (FRM), as well as variable flux reluctance machine (VFRM) [5]. In this paper, a novel DC-saturation-relieving flux-modulated hybrid reluctance machine with zero-sequence current excitation is proposed. Zero-sequence current, which acts as dc field excitation, is injected into ac and dc integrated winding, thus dc field winding is removed. 2. Machine configuration and operation principle The structure of flux-modulated DC-saturation-relieving hybrid reluctance machine with integrated ac and dc winding is presented in Fig. 1. Inner rotor consists of only iron core which provides mechanical robustness. Outer stator comprises only one set of winding, namely ac and dc integrated winding. Zero-sequence current, which acts as dc field excitation, is injected into ac and dc integrated winding. There are two layers of PMs on the slot opening. Inner layer slot PMs are radial magnetized to generate effective torque with flux modulation effect. Meantime, outer layer slot PMs are tangential magnetized to enhance torque density through relieving DC saturation. A dual inverter drive circuit is also showed in Fig. 1. Each phase winding is split into two sub-phase windings. Two sub-phase winding groups are driven by two inverters respectively and the neutral points of which are connected. The advantages of proposed machine are listed as following. (1) Since all excitation sources are mounted in the stator side and the rotor consists of only iron, no brush and slip rings are needed, which enhances mechanical robustness. (2) Radial magnetized PMs are mounted in the slot opening, which provides valid torque with flux modulation effect. Tangential magnetized PMs are placed in the slot opening, which improve torque density through relieving DC saturation. (3) Independent dc field winding is eliminated, which will leave more space for ac and dc integrated winding, thus more load current can be reached. (4) Through regulating zero-sequence current, flux can be flexibly regulated, thus extensive speed range can be realized. 3. Electromagnetic performance Fig. 2 shows on-load steady torque and no-load back-EMF with different zero-sequence currents. It can be seen that the on-load average torque is 3.4 Nm without zero-sequence current, 0.8 Nm with -10 A zero-sequence current, and 5.4 Nm with 10 A zero-sequence current. Also, the peak-to-peak value of no-load back-EMF is 12.8 V without zero-sequence current, 2.1 V with -10 A zero-sequence current, 28 V with 10 A zero-sequence current. By regulating zero-sequence current, on-load steady torque and no-load back EMF can be controlled, thus speed range of the proposed machine can be greatly extended. 4. Conclusion In this paper, the flux-modulated DC-saturation-relieving hybrid reluctance machine with zero-sequence current excitation is proposed. Zero-sequence current, acting as dc field excitation source, is injected into ac and dc integrated winding, thus dc field winding can be eliminated. Initial finite element analysis shows that the on-load steady torque and no-load back-EMF can be controlled by regulating zero sequence current, thus speed range of the proposed machine can be greatly extended. Later, DC-saturation-relieving principle and flux regulation principle will be illustrated in detail. In addition, more electromagnetic analysis will be performed and more conclusions will be drawn from the FEA results. Furthermore, a prototype of the proposed machine will be manufactured and relative tests will be performed. This work was supported in part by grants from the Hong Kong Research Grants Council, Hong Kong, China, under Project PolyU 152058/17E and PolyU 152143/18E.

**References:**

[1] X. Zhao, S. Niu, and X. Zhang, "Design of a New Relieving-DC-Saturation Hybrid Reluctance Machine for Fault-Tolerant In-Wheel Direct Drive," IEEE Trans. Ind. Electron., vol. 67, no. 11, pp. 9571-9581, Nov. 2020. [2] S. Hemmati and T. A. Lipo, "Field weakening of a surface mounted permanent magnet motor by winding switching," International Symposium on Power Electronics Power Electronics, Electrical Drives, Automation and Motion, Sorrento, 2012, pp. 736-740. [3] X. D. Xue, K. W. E. Cheng, and T. W. Ng, “Multi-objective optimization design of in-wheel switched reluctance motors in electric vehicles,” IEEE Trans. Ind. Electron., vol. 57, no. 9, pp. 29–29, Sep. 2010. [4] C. Yu and S. Niu, “Development of a magnetless flux switching machine for rooftop wind power generation,” IEEE Trans. Energy Convers., vol. 30, no. 4, pp. 1703–1711, Dec. 2015. [5] J. T. Shi, X. Liu, and D. Wu, “Influence of stator and rotor pole arcs on electromagnetic torque of variable flux reluctance machines,” IEEE Trans. Magn., vol. 50, no. 11, pp. 1–4, Nov. 2014

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4d0f859ab7e3b8556f78ec13bbbba70b.jpg)
Fig. 1. Structure of flux-modulated DC-saturation-relieving hybrid reluctance machine and dual inverter drive control system.

![](https://assets.underline.io/uploads/markdown_image/1/image/8b10fb9e70ef75e14f27745d5fa53162.jpg)
Fig. 2. On-load steady torque and no-load back-EMF with different zero-sequence currents.

 Flux-Modulated DC-Saturation-Relieving Hybrid Reluctance Machine using Zero-sequence Current Excitation for Electric Vehicle Application

I. Introduction The multi-tooth flux-switching permanent magnet (PM) (FSPM) machines have attracted wide attention due to the advantages of fewer permanent magnet materials and higher torque density, compared with the conventional FSPM machines[1]. Recently, a 6-stator-coil/17-rotor-pole (6/17) multi-tooth FSPM machine with concentrated windings, namely, the C-multi-tooth FSPM machine, was proposed in paper [2], as shown in Fig 1(a). In this paper, in order to evaluate the electromagnetic performance of the multi-tooth FSPM machines with different winding configurations, the full-pitch windings are adopted as is shown in Figure 1 (b), called the FP-multi-tooth machine. II. Performance comparisons In this paper, the electromagnetic performance of the 6/17 multi-tooth machine with different winding configurations is evaluated by finite element analysis (FEA), which is mainly in terms of no-load back EMF, harmonic components, air-gap flux density, cogging torque, electromagnetic torque, etc. Figure 2(a) shows the no-load phase back-EMF per turn waveforms of the two multi-tooth machines at 1500N/min. It can be seen that the winding configuration has an impact on the amplitude of the back-EMF for the multi-tooth machine. The amplitude of the FP-multi-tooth machine is much larger than the C-multi-tooth one with concentrated windings. Figure 2(b) presents the FFT results of the no-load phase back-EMF waveform of the 6/17 multi-tooth machine shown in Figure 2(a), where it is adopted different winding configurations. The fundamental wave amplitudes are respectively 2.45 V (C-multi-tooth machine) and 4.47V(FP-multi-tooth machine), moreover, the total harmonic distortion (THD) is 2.21%, 1.38%, and that the harmonic components are the same, mainly odd-numbered harmonics. Hence, in terms of the 6/17 multi-tooth FSPM machine, the motor with the full-pitch winding exhibits larger amplitude of the fundamental component than the concentrated winding one, and the THD is slightly smaller. Figure 2 (c) shows the two multi-tooth machines air-gap flux density distribution in the air-gap region of coil A1and A2. Furthermore, for the C-multi-tooth and the FP-multi-tooth machine, the average values of Brδ are -0.391T and -0.603T respectively, which means the no-load PM fluxes flowing through the coil A1 and A2 of the FP-multi-tooth machine are larger. Correspondingly, its back EMF should be larger than the C-multi-tooth one, since part of the magnetic flux of the C-multi-tooth machine will flow through other phases to form a closed-loop magnetic circuit. Figure 2(d) presents the cogging torque waveforms of the two multi-tooth machines. The result indicates that the cogging torque waveforms phase of two multi-tooth machines is not the same, since their rotor position is different when the peak value of the maximum back EMF is obtained. To compare the torque performance of the 6/17 multi-tooth machines with different winding configurations, the study is conducted by 2-D-FEA with Flux software under id=0 control, where the slot package factor is kpf =0.45, as shown in Fig. 2(e) and (f). When the current density is changed from 1A/mm2 to 10A/mm2, the FP-multi-tooth machine with full-pitch windings exhibits greater average torque and smaller torque ripples than the C-multi-tooth one. Figure 2(g) shows the electromagnetic torque waveform at the rated current density Jsa=5A/mm2, where the load is 1.0. It can be seen that the average torque of the FP-multi-tooth machine with full-pitch windings (16.8Nm, 4.96%) are greater than that of the C-multi-tooth one (12.7Nm, 11.1%), and that the torque ripple of the FP-multi-tooth machine is smaller than the C-multi-tooth one. III. Conclusion In this paper, the study on the electromagnetic performance of the multi-tooth machine with different winding configuration is conducted by FEA. The results indicate that for the 6/17 multi-tooth FSPM machine, the FP-multi-tooth machine with full-pitch windings exhibits higher no-load phase back EMF, torque density, and smaller harmonic distortion and torque ripple, hence, the FP-multi-tooth machine with full-pitch windings is superior to the multi-tooth one with concentrated windings. A comparative study of other types of multi-tooth machines, such as the 6/10 multi-tooth FSPM machine, will be shown in the full paper.

**References:**

[1]Y. Du, C. Zou,andX. Zhu, "A Full-Pitched Flux-Switching Permanent-Magnet Motor," in IEEE Transactions on Applied Superconductivity, vol. 26, no. 4, pp. 1-5, June 2016, Art no. 0604505, doi: 10.1109/TASC.2016.2541308. [2]G. Zhao and W. Hua, "Comparative Study Between a Novel Multi-Tooth and a V-Shaped Flux-Switching Permanent Magnet Machines," in IEEE Transactions on Magnetics, vol. 55, no. 7, pp. 1-8, July 2019, Art no. 8104908, doi: 10.1109/TMAG.2019.2900749.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/49124426790a017123757c7bd3f86a52.jpg)
Fig. 1 Topologies of 6/17 multi-tooth FSPM machines. (a) C-multi-tooth machine. (b) FP-multi-tooth machine.

![](https://assets.underline.io/uploads/markdown_image/1/image/1bb200063963f8258738af158c0e488b.jpg)
Fig. 2 Performance comparisons. (a) Phase back-EMF per turn waveforms at 1500r/min. (b) Harmonics of back-EMF. (c)Radial air-gap flux density Brδ in the air-gap region of coil A1and A2(d) cogging torque. (e) Electromagnetic torque waveforms versus current densities. (f) Torque ripple waveforms versus current densities. (g) Electromagnetic torque waveforms under Jsa=5A/mm2.

 Comparative Study of Winding Configuration on a Multi-tooth Flux Switching Permanent Magnet Machine

This paper proposed a new slot-PM-assisted reluctance generator with self-excited DC source for stand-alone wind power generation. The key is that several ac armature coils are used to provide electrical power to dc field winding through a rectifier. Compared with separately excited dc source, self-excited dc source is more suitable for stand-alone wind power generation and greatly reduces device costs since no independent dc source is needed. In this paper, the machine configuration and operation principle are introduced. Some leading dimension parameters are optimized to obtain maximum torque and minimum torque ripple. the feasibility of the optimal design with this novel structure is verified by finite element analysis and prototype testing. 1. Introduction: When it comes to provide energy to remote area, stand-alone wind power system with battery appeals to an excellent solution with relatively maintenance simplicity and low system cost [1-2]. The most important part of wind power generation system is the generator. Permanent magnet (PM) machine has been widely used as wind power generator due to simple structure, high efficiency, as well as high power density [3-4]. However, PM machines have no flux regulation ability. In this case hybrid excited machine, which excited by both PMs and dc field source, has been applied. The problem is that they all need independent dc excitation sources, which are not suitable for stand-alone wind power system. To solve abovementioned problem, several ac armature coils are used to supply electrical power to dc field winding through a rectifier, which are called ac rectifier winding. In this way, a novel slot-PM-assisted reluctance generator (SPMA-RG) with self-excited DC source (SEDC) is proposed. 2. Machine configuration and operation principle As shown in Fig. 1, a novel slot-PM-assisted reluctance generator (SPMA-RG) with self-excited DC source (SEDC) has three sets of stator windings, namely dc field winding, ac armature winding as well as ac rectifier winding. Radial magnetized PMs are placed in the slot opening of stator to enhance the torque density compared with traditional variable flux reluctance machine. Reluctance rotor consists of only iron core which provides mechanical robustness. The current produced by ac rectifier winding passes through controlled rectifier to provide excitation current to dc field winding. The advantages of the proposed generator are listed as following. (a) Since all excitation sources are placed in the stator side and the rotor comprises only iron, there are no brush and slip rings, which provides mechanical robustness. (b) Radial magnetized PMs are mounted in the slot openings which enhances the torque density compared with traditional variable flux reluctance machines. (c) Flux produced by dc field winding does not pass through the slot PMs, which will not lead to demagnetization of slot PMs. (d) Output voltage of ac armature winding can be controlled through regulating the dc field excitation, thus variable speed constant voltage can be realized in wind power generation system. (e) Several ac armature coils, namely ac rectifier winding, are used to provide excitation current to dc field winding through a controllable rectifier. In this way, no extra dc source is needed, which not only improves independent characteristic of wind power generation system, but also realizes energy feedback utilization. 3. Electromagnetic performance Fig. 2 shows rectified voltage and current generated from ac rectifier winding and rectified by the controllable rectifier. Furthermore, output voltage of the ac armature winding appears to be stable and achieves three-phase symmetric when rectified voltage and current arrive a stable value. It verified the feasibility of proposed wind power generation system. The ac rectifier winding can be used to provide dc excitation current to dc field winding through the controllable rectifier. 4. Conclusion In this paper, a novel slot-PM-assisted reluctance generator with self-excited DC source is proposed for wind power generation. Several ac armature coils, namely ac rectifier winding, provide electricity to dc field winding through a rectifier. This self-excited dc source greatly reduces device cost and improves the independent characteristic of the wind power system. In the full paper, the electromagnetic performance of proposed SPMA-RG is analyzed in detail. The prototype of proposed generator is manufactured and relative testing is conducted. This work was supported in part by grants from the Hong Kong Research Grants Council, Hong Kong, China, under Project PolyU 152058/17E and PolyU 152143/18E.

**References:**

[1] Ming-Shun Lu, Chung-Liang Chang, Wei-Jen Lee and Li Wang, “Combining the Wind Power Generation System with Energy Storage Equipment”, IEEE Trans. Ind. Appl., Vol.45, No.6, pp.2109-2115. November / Dec. 2009. [2] Ronan Doherty, Ronan Doherty and Mark O’Malley, “Establishing the Role That Wind Generation May Have in Future Generation Portfolios”, IEEE Trans. Power Sys., Vol.21, No.3, pp.1415-1422. Aug. 2006. [3] Y. Fan, K. T. Chau, and M. Cheng, “A new three-phase doubly salient permanent magnet machine for wind power generation,” IEEE Trans. Ind. Appl., vol. 42, no. 1, pp. 53–60, 2006. [4] Y. Chen, P. Pillay, and A. Khan, “PM wind generator topologies,” IEEE Trans. Ind. Appl., vol. 41, no. 6, pp. 1619–1626, 2005.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a6eb1bf5fe4031c1e8acfed478176d03.jpg)
Fig. 1. Wind power generation system based on the proposed SPMA-RG.

![](https://assets.underline.io/uploads/markdown_image/1/image/b824cd8942dc7188e35ae3accd9e65e0.jpg)
Fig. 2. Rectified voltage/current and Back-EMF.

 Development of Slot-PM-assisted Reluctance Generator with Self-excited DC Source for Stand-alone Wind Power Generation

This paper proposes a novel hybrid-excited outer-rotor machine with skewed permanent magnets (PM) placed at the stator slot opening. The key novelty is that the skew-magnetized PMs can achieve both torque production promotion and stator core saturation relieving. Compared with DC-excited reluctance machine, the proposed machine with skewed PMs has higher torque production and efficiency. Compared with synthetic slot PM excited machine, it is easier for machine assembly and manufacture, and the manufacture cost is reduced. In this paper, the machine structure of the prosed machine is presented. Then, the working principle are introduced briefly, including the relieving-DC-saturation effect and the flux modulation effect. The derivation will be presented in more detail in the full-page paper. Finally, the machine performance under different DC field current is presented. I. Introduction The DC-excited reluctance machine is a promising solution for electric vehicle because of its inherent reliable and simple rotor structure, good thermal dissipation ability and wide speed range [1]. However, the torque production and efficiency are not satisfying, because the excitation ability of DC winding is usually lower than PM [2]. Besides, the saturation in stator core limits the DC current due to the biased field [3]. To address the two problems, this paper proposes a novel skewed PM structure. The radical component of the PMs can provide an effective flux to the armature winding, so that the torque production can be promoted directly. The tangential component of the PMs can relieve the saturation in the stator core, so that higher DC field current can be applied, and hence the torque production can be raised accordingly. II. Machine structure The structure of the proposed machine is presented in Fig. 1(a). The rotor consists of iron core only, so, it is reliable and easy for manufacture. In the stator side, there are two groups of windings, one is the DC field winding and another one is the 3-phase armature winding. The skewed PMs are placed at the slot-openings. The radical component of magnetization of every PM is outwards direction, but the tangential component of magnetization has alternate polarity in every tooth. The purpose of radical component is to provide an additional field linked to armature windings, so that the torque production can be raised directly. The purpose of tangential component is to provide a constant flux in the stator core, of which the direction is opposite with the flux from DC current, so that higher DC current can be applied. The armature winding configuration is presented in Fig. 1(b). The concentrated single-layer winding configuration is used. II. Working principle In this part, to introduce the working principle of skew-magnetized PM clearly, the tangential magnetization component and the radical magnetization component are introduced respectively. For the radical magnetization component of PMs, the following relationship should be satisfied. NPM-Nr+Nw=0 NPM, Nr and Nw represent the pole pair number of PM, rotor teeth number and the order of working harmonic. In this case, the values of NPM, Nr and Nw are 12, 22 and 10, respectively. The pole pair number of armature winding is the same with the order of working harmonic. Hence, 10-pole-pair armature winding is used. The flux path of the tangential magnetization component is presented in Fig. 2(a) together with the flux from DC current. The tangential component contributes little torque production directly if the current is kept unchanged, because the flux from the tangential component of PM is a constant biased flux. But the stator saturation is largely relieved because the directions of flux of DC current and the tangential component of PM are opposite. Hence, higher DC current can be applied when the PMs are used, and hence the torque production can be raised accordingly. III. Machine performance To show the effectiveness of the skew-magnetized PMs, an FEA model is built. The maximum diameter is 150 mm, stack length is 80 mm, and air gap length is 0.5 mm. DC windings have the same number of turns and rated current as armature windings, the values are 52 turns and 6 A respectively. The torque production under different field excitation is presented in Fig. 2(b). Either the DC field current or skew-magnetized PMs can be used for excitation individually. The torque production from skewed PMs is higher, but the torque production from DC field current is easier to regulate. IV. Conclusion In this paper, a novel hybrid-excited machine with skew-magnetized PM is proposed. The radical magnetization component of PM is used to promote the torque directly, and the tangential magnetization component of PM is used to relieve the saturation. The flexible DC excitation current provide a wide speed range, and the additional skewed PM raises the torque production. An FEA model is built and the torque production is presented to verify the effectiveness of the proposed machine. The other features of the proposed machine will be presented and analyzed in the full-page paper. Acknowledgement This work was supported in part by grants from the Hong Kong Research Grants Council, Hong Kong, China, under Project PolyU 152058/17E and PolyU 152143/18E.

**References:**

[1] C. H. T. Lee, K. T. Chau and C. Liu, IEEE Trans. Magn., Vol. 49, p.3969-3972 (2013) [2] Q. Wang and S. Niu, Renew. Sust. Energ. Rev., Vol. 68, p.475-491 (2017) [3] X. Zhao, S. Niu and W. Fu, IEEE Trans. Magn., Vol. 55, p.1-5 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ba1c165a7e100b914ff4f9e684f65ffa.jpg)
Fig. 1. The proposed machine. (a) Machine structure. (b) Armature winding configuration.

![](https://assets.underline.io/uploads/markdown_image/1/image/ccc85cbb6967248ee6a295b8876e1d75.jpg)
Fig. 2. Main flux path and torque production. (a) Flux path of DC current and tangential component of PM. (b) Torque production under rated armature winding.

 A Novel Relieving-DC-Saturation Hybrid-Excited Machine with Skewed Permanent Magnets for Electric Vehicle Application

This paper investigates the influence of DC/AC winding split ratio on electromagnetic performance of hybrid reluctance machine with synthetic slot PM excitation. The machine structure and working principle are introduced briefly at first. Then, the machine performance, including power factor, torque production, loss, efficiency, and voltage regulation rate, are investigated with different DC/AC winding ratio. It is found that the machine has higher torque production and efficiency when the AC windings take up more space. But higher voltage regulation rate can be achieved when the space used for DC windings is close to AC winding. More detailed investigation will be presented in the further version. I. Introduction Recently, the DC-excited reluctance machine has attracted lots of research interests and it is a very promising solution for electric vehicles because of its reliable rotor structure and wide speed range [1]. However, the torque production and efficiency are not satisfying. To address this issue, a novel hybrid reluctance machine with synthetic slot PM is proposed in [2]. But the influence of DC/AC winding split ratio, which is one of key design parameters on machine performance, has yet to be comprehensively studied. To give a design guideline for this hybrid reluctance machine, this paper will fully investigate the power factor, torque production, loss, efficiency and voltage regulation rate with different DC/AC winding ratio. II. Machine structure and working principle The machine structure is presented in Fig. 1(a). The rotor consists of iron core only, so it is reliable and easy to manufacture. There are two groups of winding, one is the 3-phase armature winding and another one is the DC field winding. There are two groups of PMs located at slot openings. One group is radically magnetized PMs with the same magnetization direction. Another group is tangentially magnetized PMs with alternate polarity in every tooth. In the proposed machine, the flux excited by DC current varies as rotor permeance to provide an effective flux. However, the biased flux can cause saturation in stator core. To address this issue, the tangentially magnetized PMs are used to relieve saturation. They produce a constant biased flux with opposite direction with DC current field in the stator core, so that the flux density can be reduced. As for the radically magnetized PMs, they are used to provide an effective flux linked to armature winding to enhance the torque production directly. III. Machine performance In this part, the machine performance under different DC/AC winding split ratio is presented based on FEA result. The maximum diameter is 150 mm, the stack length is 80 mm, the air gap length is 0.5 mm, the slot filling factor is 0.7 and the rated current density is 6A/mm2. The DC/AC winding split ratio is defined as follow. kdc=Ndc/(Nac+Ndc) kac=Nac/(Nac+Ndc) kdc and kac are the winding split ratios of DC and AC winding, respectively. And Ndc and Nac are the number of conductors of DC field winding and armature winding in one slot, respectively. The rated torque, loss, efficiency and voltage regulation rate are presented in Fig. 2. The higher rated torque and can be achieved when less space is used for DC field winding, because the excitation ability of DC field current is poorer than PMs. The higher torque production brings with higher efficiency when armature winding takes up more space in slot, in spite of higher core loss. High power factor can be obtained when DC field winding takes up more space because it brings stronger excitation ability. As for voltage regulation rate (kVRR), it is defined as follows. kVRR=(V2r-V0)/Vr V0, Vr and V2r are the open-circuit back EMF when the DC field current is at zero, rated value and twice of rated value. It reflects the voltage regulation ability of the DC field winding and it is directly related to the speed range. When DC field winding split ratio is very small, the excitation ability of DC current is also very small. When DC field winding ratio is very large, the saturation effect becomes very severe. Hence, the voltage regulation rate is not high when DC field winding ratio is either too high or too low. From Fig. 2(d), it can be found that the highest voltage regulation rate can be achieved when the AC winding ratio is at around 40%. IV. Conclusion This paper presents the machine performance of the hybrid-excited reluctance machine with synthetic slot PM excitation under various DC/AC winding split ratio. It is concluded that when the more slot space is used for armature winding, the higher rated torque, core loss and efficiency can be achieved, but the power factor is lower. The highest voltage regulation rate can be obtained when the armature winding ratio is at around 40%. Acknowledgement This work was supported in part by grants from the Hong Kong Research Grants Council, Hong Kong, China, under Project PolyU 152058/17E and PolyU 152143/18E.

**References:**

[1] E. Trancho, E. Ibarra and A. Arias, IEEE Trans. Ind. Electron. Vol. 65, p.2986-2995 (2018) [2] X. Zhao, S. Niu and X. Zhang, IEEE Trans. Ind. Electron. doi: 10.1109/TIE.2020.2996140 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4591486958f5f351e30729cab9a67925.jpg)
Fig. 1. Machine structure.

![](https://assets.underline.io/uploads/markdown_image/1/image/6df4037a5e04493e5bc01b1b09a49803.jpg)
Fig. 2. Machine performance under different armature winding ratio. (a) Rated torque. (b) Power factor. (c) Core loss and efficiency. (d) Voltage regulation rate.

 Influence of DC/AC Winding Split Ratio on Electromagnetic Performance of Hybrid Reluctance Machine with Synthetic Slot PM Excitation

I. INTRODUCTION Axial flux permanent magnet (AFPM) machines with tooth-wound concentrated windings (TCWs) and segmented stator were founded a growing interest for high-performance drive applications such as electric vehicles, aircrafts, ships, etc. [1] Four dual-rotor single-stator (DRSS) axial flux permanent magnet vernier (AFPMV) machines with segmented stator and consequent-pole (CP) embedded rotors are proposed and compared in this paper. The configuration and operating principle of AFPMV machines are introduced first. Then, the critical design parameters and electromagnetic performances of proposed AFPMV machines are analyzed and compared both in no-load and load conditions. Finite element analysis (FEA) results demonstrate that the machine with Halbach arrays employed on the stator split teeth features higher torque capability and lower rotor eddy current loss compared to its counterparts with conventional PMs or stator magnet less machines. In addition, for better flux-weakening capability, the AFPMV machine with hybrid field excitation from both rotor PM and stator DC coils is also discussed. II. MACHINE CONFIGURATIONS AND OPERATION PRICIPLE The proposed AFPMV machine A is shown in Fig.1(a) as the benchmark. The machine has a single stator sandwiched between two-disc rotors which embedded CPs. The stator consists of 12 segments, each with three split teeth on the major tooth. TCWs are employed to shorten the end length and suppress copper loss. With the absent of the stator yoke, such machines take the advantageous performance of lower stator core loss. Furthermore, as shown in the Fig.1(b) and Fig.1(c), the radially magnetized PMs and the Halbach arrays are equipped in the split slots to form machine B and C, respectively. Finally, each stator segment of machine D is wounded with a DC field winding on the middle split tooth, which is illustrated in the Fig.1(d). The flux modulation effect has enhanced the torque producing capability according to the pole ratio of rotor and AC windings [2]. In the vernier machine with modulation poles fixed on the stator, the angular speed of the working flux harmonic component is ωp = -NPMωPM /(Nm-NPM) where NPM and Nm are the pole-pair number of the magnetic fields excited with PM and the number of modulation teeth, respectively, ωp and ωPM are the speed of the working rotation magnetic field produced by the stator windings and the speed of the PMs, respectively. III. PERFORMANCE ANALYSES AND COMPARISONS A. No-Load Flux Linkage and No-Load Back-EMFs The flux distributions of four investigated machines were conducted by the FEA, the simulation results show that the machine C tend has lower flux leakage in the stator split teeth and higher magnetic density compared with the machine B because of the PM with circumferentially magnetization. Lower magnetic density is distributed in machine D when the DC winding produces the reverse flux, that is, the flux adjustment can be realized through the DC winding in the split teeth. The waveforms of no-load back-EMFs of the models are illustrated in Fig.2, in which the DC winding of the machine D operates in the flux-weakening condition. It can be seen that the amplitude of the no-load back-EMFs increase with the introduction of the PM in the split teeth. For the machine C, with the increase of circumferential PM volume, the amplitude of the back-EMF first increases and then decreases, that is, it is necessary to balance the flux leakage and the main flux. B. Output Torque and Losses Fig. 3 shows the output torque of the machines, the average output torque of the machines with PMs in the stators generate an average output torque at least 37% higher than those of the machines without PMs in the stators. The results of comprehensive comparison are shown in table I, which verify that the machine with Halbach arrays employed in the split slots tend to have higher output torque and lower stator core loss and rotor PM loss. And the parametric sensitivity studies and design optimizations will be presented in the final paper. III. CONCLUSION This paper extends the theory of magnetic field modulation into AFPM machines with DRSS and TCWs, making it particularly suitable for low-speed, high-torque, and axial length limited applications. The comparative analyses of four topologies of AFPVM machines are conducted by FEA. The results verify that it is a feasible method to modulate the magnetic field in the air gap with the split teeth in the segmented stator modules of the AFPM machine. By comparing the relative merits and disadvantages of the performances of the proposed machines, it is concluded that the machine with Halbach PMs embedded in the stator split slots shows the characteristics of higher torque density and lower loss compared with other topologies, and machine with DC field winding in the stator split slots shows the adequate flux-weakening performance.

**References:**

 [1] F. Giulii Capponi, G. De Donato and F. Caricchi, "Recent Advances in Axial-Flux Permanent-Magnet Machine Technology," IEEE Trans. Ind. Appl., vol. 48, no. 6, pp. 2190-2205, (2012). [2] R. Qu, D. Li and J. Wang, "Relationship between magnetic gears and vernier machines," 2011 International Conference on Electrical Machines and Systems, Beijing, pp. 1-6, (2011).

**Images:**

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 Electromagnetic Performance Analysis and Comparison of Fractional-Slot Non-Overlapping Winding Dual-rotor Axial Flux Permanent Magnet Vernier Machines with Segmented Stators

I. Introduction Flux-switching permanent magnet (FSPM) motor, possessing the potential merits of high torque and power density, has aroused considerable attention and extensive research in recent years [1]. Electromagnetic torque, which is the most important evaluation index of the FSPM motor, is researched in majority of the existed papers. For the FSPM motor, the magnetic density of the motor has a decisive influence on the electromagnetic torque. As the excitation source, PMs serve to generate the magnetic power, which goes through stator, airgap and rotor to form the effective magnetic path. In other words, the electromagnetic torque relies heavily on the magnetic flux density of the stator, airgap and rotor. Actually, the improvement of the magnetic flux density of the stator, airgap and rotor may contribute to the increasing of electromagnetic torque. In [2], from the perspective of the magnetic flux density of the stator, different types of PM arrangement are investigated, which indicates that the arrangement of V-shaped PMs is superior to that of the I-shaped and Arc-shaped PMs in the stator in terms of torque output capability. On the other hand, from the perspective of the magnetic flux density of airgap, various parameters close to the airgap are selected during the multi-layer design of the FSPM motor for improved torque in [3]. Based on the above research, many attempts are made to study the magnetic flux density of stator and airgap related to airgap for the torque improvement. Yet, few efforts are made to analyzing the effective magnetic flux density of the rotor which contributes to the magnetic energy transmission and torque production. Hence, the concept of flux density harmonic deterioration rate is introduced to analyze the rotor effective magnetic flux in this paper, which eventually reflects the loss of magnetic energy transmission from the airgap. By analyzing the influence of harmonic flux density variation from airgap to rotor yoke on electromagnetic torque, the relevant between electromagnetic torque and flux density harmonic deterioration rate is explored, and the resulting torque represents to be increased, which provides a new perspective for motor performance analysis. II. Motor topology and analysis of the performance The topology of the studied I-shaped FSPM motor is shown in Fig. 1 (a), with the related structure parameters marked in Fig. 1 (b). In order to select the harmonic for research use, the torque contribution of different harmonic is obtained as depicted in Fig. 2, and contributions of the 4th-, 18th-, 28th-, 30th- and 40th-order harmonic are chosen as the basis of the comprehensive deterioration rate. The flux density and harmonic amplitude of airgap and rotor yoke are illustrated in Fig. 3 (a) and (b). It is obvious that the 4th- and 18th-order harmonic remain high amplitude at both airgap and rotor yoke, while the 28th-, 30th- and 40th-order harmonic present a sharp decline. The single harmonic deterioration rate is also calculated in Fig. 3 (b), where the positive value denotes an actual downward trend while the negative one indicates the opposite. To further investigate the relationship between torque capability and harmonic deterioration rate, the parameters are selected from both stator and rotor side, and the partial results are shown in Fig. 4 (a) and (b). With the PM cost keeping constant and the PM width bpm and the rotor tooth width brt increasing, the total torque decreases while the comprehensive deterioration rate mainly represents uptrend as expected. Considering the lowest comprehensive deterioration rate, the final value of bpm and brt are chosen to be 2deg and 3.4deg for comparison. Moreover, the magnetic field and flux distribution of the initial and final motor are shown in Fig. 5, which indicates that the final motor possesses less flux leakage. Meanwhile, the back-EMF and torque of the motors are presented in Fig. 6 and Fig. 7. The rationality of analysis perspective of flux density harmonic deterioration rate is confirmed by the higher back-EMF and torque with lower comprehensive deterioration rate of the final motor. III. Conclusion In conclusion, the above results reveal that during the process of magnetic energy transmission, the proposed flux density harmonic deterioration rate has the certain relevant with the electromagnetic torque. The decrease of the comprehensive deterioration rate contributes to the improvement of the flux modulation effect and electromagnetic torque to some degree, which verifies the effectiveness of deterioration rate concept. Finally, more theoretical analysis, performance simulations and experimental results will be presented in the full paper.

**References:**

[1] X. Zhu, M. Jiang, Z. Xiang, L. Quan, W. Hua and M. Cheng, "Design and Optimization of a Flux-Modulated Permanent Magnet Motor Based on an Airgap-Harmonic-Orientated Design Methodology," IEEE Trans. Ind. Electron., vol. 67, no. 7, pp. 5337-5348, July 2020. [2] T. Fukami, Y. Ueno and K. Shima, "Magnet Arrangement in Novel Flux-Modulating Synchronous Machines with Permanent Magnet Excitation," IEEE Trans. Magn., vol. 51, no. 11, pp. 1-4, Nov. 2015, Art no. 8206104. [3] L. Mo, T. Zhang and Q. Lu, "Design and Analysis of an Outer-Rotor-Permanent-Magnet Flux-Switching Machine for Electric Vehicle Applications," IEEE Trans. Appl. Super., vol. 29, no. 2, pp. 1-5, March 2019, Art no. 3601305.

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 Investigation on electromagnetic torque of a flux-switching permanent magnet motor from perspective of flux density harmonic deterioration rate

-This paper has proposed a 3-airgap magnetic geared vernier machine for low-speed direct-drive applications. By combining dual PM split-tooth vernier machine with magnetic gear, an impressive 150 Nm/L output torque density under 140 mm outer diameter can be achieved. The Halbach consequent pole structure is applied to the dual-layer-magnet rotor, which can largely reduce the thickness of rotor back iron compared to regular magnet arrangement, while increasing the airgap flux density. The performances of magnetic gear machines with different topologies are compared in this paper, it shows that proposed MG-DPSTVM has at least 40% higher torque density than all the previous MGM topologies. I.Introduction The magnetic geared machine (MGM) is attractive in continuous low speed direct-drive applications since it has remarkable torque density under relatively low electrical load. The contactless feature of magnet gear makes it more suitable for occasions when maintenance is difficult, such as wind/tide power generation, marine propulsion, oil pumping. In recent years, many MGM topologies were proposed for high torque density between 60-110 Nm/L[1]-[5]. To further enhance the torque density of MGM to a new level, a magnetic-geared dual PM vernier machine is proposed in this paper, which can exceed 150 Nm/L active torque density under low heat load, which also remains 0.8 power factor under rated load. II.Topologies of MG-DPVM The topology of proposed MG-DPVM is shown in Fig. 1, which can be divided into magnetic gear (MG) part and vernier machine (VM) part radially. The structure of proposed machine has been carefully designed for higher torque density. One of the distinct structures is PM rotor, which has two layers of Halbach consequent pole (HCP) magnets with different pole pairs. Compared to surface mounted magnets in [6], this topology can minimize the magnetic circuits and the thickness of back iron between two layers of magnets, while maximum the airgap flux density in both airgaps. For the VM part, there are consequent pole magnets on the stator. Through dual flux modulation effect [7], it can increase the torque density by introducing additional airgap working flux, and the power factor is also higher than regular vernier machines. III.Performance Comparison of MGM Topologies As shown in Table I, under the same outer radius and gap thickness, several MGM topologies are compared in this paper, including pseudo direct drive machine in [2], vernier pseudo direct drive machine in [5], 3-airgap outer rotor magnetic geared machine in [3], and magnetic geared vernier machine newly proposed in this paper. Considering slip risk and operating point of machine, the output torque is selected as 80% of the MG stall torque, and the heat load as well as copper loss (considering the winding) of each model can then be derived. It is obvious that proposed MG-DPVM has the highest MG stall torque density and output torque density, and the DC copper loss is also the lowest. IV.Conclusions A novel 3-airgaps magnetic geared split-tooth vernier machine is proposed in this paper. Through dual stage of magnet gear effect, high output torque density can be achieved under low current density and copper loss. It is impressive that proposed machine has achieved 150 Nm/L active torque volume density and 23 Nm/kg active mass density. According to the comparison, this value is much higher than the existing topologies of MGM, which makes it competitive in long-term low-speed high-torque industrial fields such as wind generation and marine propulsion. The power factor of proposed machine is lower than other MGMs due to the application of vernier machine, however the copper loss and heat load are largely reduced, therefore higher efficiency can be expected.

**References:**

 [1] K. T. Chau, D. Zhang, J. Z. Jiang, C. Liu, and Y. Zhang, “Design of a Magnetic-Geared Outer-Rotor Permanent-Magnet Brushless Motor for Electric Vehicles,” IEEE Transactions on Magnetics, vol. 43, no. 6, pp. 2504-2506, Jun. 2007. [2] K. Atallah, J. Rens, S. Mezani, and D. Howe, “A Novel ‘Pseudo’ Direct-Drive Brushless Permanent Magnet Machine,” IEEE Transactions on Magnetics, vol. 44, no. 11, pp. 4349-4352, Nov. 2008. [3] S. Gerber and R.-J. Wang, “Design and Evaluation of a Magnetically Geared PM Machine,” IEEE Transactions on Magnetics, vol. 51, no. 8, pp. 1-10, Aug. 2015. [4] L. Jian, W. Gong, G. Xu, J. Liang, and W. Zhao, “Integrated Magnetic-Geared Machine with Sandwiched Armature Stator for Low-Speed Large-Torque Applications,” IEEE Transactions on Magnetics, vol. 48, no. 11, pp. 4184-4187. [5] X. Yin, Y. Fang, X. Huang, and P.-D. Pfister, “Analytical Modeling of a Novel Vernier Pseudo-Direct-Drive Permanent-Magnet Machine,” IEEE Transactions on Magnetics, vol. 53, no. 6, pp. 1-4, Jun. 2017. [6] M. Johnson, M. C. Gardner, H. A. Toliyat, S. Englebretson, W. Ouyang, and C. Tschida, “Design, Construction, and Analysis of a Large-Scale Inner Stator Radial Flux Magnetically Geared Generator for Wave Energy Conversion,” IEEE Transactions on Industry Applications, vol. 54, no. 4, pp. 3305–3314, Jul. 2018. [7] S. Niu, S. L. Ho, and W. N. Fu, “A Novel Stator and Rotor Dual PM Vernier Motor with Space Vector Pulse Width Modulation,” IEEE Transactions on Magnetics, vol. 50, no. 2, pp. 805–808, Feb. 2014.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9d773001e780f823a2203c7317816374.jpg)
Fig. 1 The topology of proposed MG-DPVM

![](https://assets.underline.io/uploads/markdown_image/1/image/b3332c72ac4fe162128c794872159d3a.jpg)

 A High Torque Density Magnetic-geared Dual-PM Split-tooth Vernier Machine with Halbach Consequent Poles

I. Introduction: Magnetic gears are good candidates to replace mechanical gearboxes, since it has higher efficiency, lower noise and self-protection characteristic [1], [2]. Radial-type magnetic gears (RMGs) are sometimes not suitable for special application scenarios where there is strict requirement for space. Axial-type magnetic gears (AMGs) have an even higher torque density than RMGs and a shorter axial length, [3]. Therefore, AMGs can be applied in scenarios where the weight is a crucial concern. However, one drawback of AMGs is the large amount usage of permanent magnets (PMs), which significantly increases manufacture cost. In this paper, an iron-made flux-enhancing plate is added to the outside of AMGs to increase the output torque. Then, the flux-enhancing principle is elaborated by analyzing the flux path variation before and after the installation of the auxiliary flux-enhancing slice. Finally, the performances of three AMGs are compared, and it is proved that the proposed structure has the highest torque density. II. Machine Configuration The proposed auxiliary flux-enhancing structural axial-type magnetic gear (AFS-AMG) contains four slices, and its structure together with the magnetic flux density distribution are depicted in Fig. 1 (a), (b). Two rotors are those with surface-mounted PMs on them, and the one with less PM pieces is the high-speed rotor, while the one with more PM pieces is the low-speed rotor. The first and third slices from the left to the right are steady slices, and they formed as one stator component. The PMs on the high-speed rotor are magnetized on the axial direction, while the PMs on the low-speed rotor are magnetized on the circumferential direction. To produce a steady electromagnetic torque, the pole-pair number of high-speed and low-speed rotor PMs Phigh and Plow and the number of modulator pieces Qmodulator must satisfy Eq. (1) [4]. Additionally, since the auxiliary flux-enhancing slice serves as a complementary structure for the magnetic flux to form a shorter loop, its tooth number Qteeth should be equal to the number of modulator pieces, as given in Eq. (2). Then, based on the operating principle of magnetic gear, the rotating speed and output torque relations between the high-speed and low-speed rotor satisfy Eq.(3) and (4), where Thigh and Tlow are the electromagnetic torques on the high-speed and low-speed rotor, respectively. Ωhigh and Ωlow are the rotating speeds of the high-speed and low-speed rotor, respectively. III. Flux Enhancing and AMG Evolution The flux-enhancing effect of the auxiliary slice can be illustrated by the flux line path, as shown in Fig. 1 (c). It can be observed that without the auxiliary slice, the magnetic flux path passes through the air region several times to form a close loop. Since the permeability of air is much lower than that of the iron, the magnetic reluctance of the whole loop is very large, leading to a small magnetic flux density and a low torque. When the auxiliary slice is added to the outside of the spoke-type PMs, the corresponding flux line changes to pass through a path with smaller reluctance. Hence, the magnetic flux density on the air gap increases, leading to a larger electromagnetic torque. In fact, the structures of AMGs can be derived from its RMG counterparts, as illustrated in Fig. 2 (a)-(c) [5]. The operating principle of AMGs and RMGs are similar, and their differences lie in two aspects. First, the magnetic flux density direction of the two types of magnetic gears are different: the main flux paths in AMGs are in axial direction, and in radial direction for RMGs. Second, the different rotors are distributed on axial direction for AMGs, making it more suitable to have multi-slice structure. However, adding an auxiliary structure in RMG will lead to a very large size. Therefore, the flux-enhancing slice can maximize its effect for AMGs. IV. Validation and Comparison: To obtain a better electromagnetic performance, three AMGs with the same inner and outer radii are constructed in JMAG to compare their performances, whose parameters are provided in TABLE I. The corresponding simulation results are provided in TABLE II and Fig. 2 (d). It can be observed that AMG (c), namely the proposed AMG, has the highest efficiency and the highest torque density per PM usage. The axial component magnetic flux density distributions and the corresponding Fast Fourier Transform of the AMG (b) and (c) outside the low-speed rotor with the same radius are depicted in Fig. 3 (e), (f). It can be observed that for AMG (c), the amplitude of working harmonic (14th) is much larger than AMG (b), leading to a torque increase. IV: Conclusion In this paper, a novel AFS-AMG is proposed. By introducing an auxiliary flux-enhancing slide to shorten the flux path, the proposed AFS-AMG has a higher torque density per PM usage and a higher efficiency compared to conventional AMG structure. This work was supported by a grant (Project No. 52077186 and 51677159) from NSFC of China; a grant (Project No. JCYJ20180307123918658) from STIC of Shenzhen Municipality, China; a grant (Project No. SGDX2019081623101559) from Shenzhen – Hong Kong Innovation Circle Category D Project from the Science Technology and Innovation Committee of Shenzhen Municipality, China.

**References:**

 [1] H. Zhao, C. Liu, Z. Song and J. Yu, "A Fast Optimization Scheme of Coaxial Magnetic Gears Based on Exact Analytical Model Considering Magnetic Saturation," in IEEE Transactions on Industry Applications (Early Access). [2] P. O. Rasmussen, T. O. Andersen, F. T. Jorgensen and O. Nielsen, "Development of a high-performance magnetic gear," in IEEE Transactions on Industry Applications, vol. 41, no. 3, pp. 764-770, May-June 2005. [3] Y. Chen, W. N. Fu, S. L. Ho and H. Liu, "A Quantitative Comparison Analysis of Radial-Flux, Transverse-Flux, and Axial-Flux Magnetic Gears," IEEE Trans. Magnetics, vol. 50, no. 11, pp. 1-4, Nov. 2014. [4] K. Atallah and D. Howe, "A novel high-performance magnetic gear," IEEE Trans. Magnetics, vol. 37, no. 4, pp. 2844-2846, July 2001. [5] X. Zhang, X. Liu and Z. Chen, "A Novel Dual-Flux-Modulator Coaxial Magnetic Gear for High Torque Capability," in IEEE Transactions on Energy Conversion, vol. 33, no. 2, pp. 682-691, June 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/aadd04789f60af98e91ba09d679eaa4f.jpg)
 
Fig.1 The proposed AFS-AMG: (a) Explosive view; (b) magnetic flux density distribution, (c) illustration of flux path.

![](https://assets.underline.io/uploads/markdown_image/1/image/7f7c1e534454863de5d4c72c331811b5.jpg)
 
Fig.2 (a) Conventional AMG, (b) Circumferentionally magnetized AMG, (c) AFS-AMG, (d) torque waveform comparisons, (e) magnetic flux density distribution, (f) the corresponding FFT.

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