France



—This paper proposes and compares two different 12 slots DC-biased dual-PM vernier machines. Both machines have tangentially magnetized magnets located in the slot openings, and an integrated winding is adopted to produce the armature field and excitation field at the same time. The slot-opening PMs not only improve the machine torque performance but also relieve the saturation caused by the DC-biased. The results show that both structures exhibit high torque density and slot-opening PMs in machine 1 contribute more to torque improvement while PMs in machine 2 are more for dc-saturation relief.&lt;br/&gt;&lt;i&gt;Index Terms&lt;/i&gt;—DC-bias, dual PM, finite-element method, vernier machine.&lt;br/&gt;Introduction&lt;br/&gt;With the emergence of the magnetic gear and the proposal of a unified theory of flux modulation, vernier machine has attracted people&#39;s attention. Due to its high torque density and wide operation range, vernier machine becomes the potential candidate for many applications such as electric vehicles and wind power generation. To further increase the torque density under the constrain dimension, dual-PM vernier machine is proposed, and several structures have been investigated. In order to achieve a more compact structure and wider flux weakening range, the integrated winding with DC-biased structures have also been studied.&lt;br/&gt;In this paper, two novel DC-biased dual-PM vernier machines with slot-opening PM are proposed and investigated. To showcase the effectiveness of the slot-opening PMs, the conventional DC-biased dual PM vernier machines will be presented first. Then the operation principle of proposed novel machines will be presented, and the comparison between different structures will be conducted.&lt;br/&gt;Structure, Operation Principle and Performance&lt;br/&gt;The structure of the proposed motors and their conventional structures are shown in Fig.1. To make a relatively fair comparison, the main dimensions of all the structures are the same. The outer diameter is 90mm, the air gap is 0.5mm, and the stack length is 80mm. As shown in Fig. 1, PMs are located on both the rotor and stator. The PMs in the rotor and stator tooth are both radially magnetized, while the slot-opening PMs are tangentially magnetized. The main difference between the two novel machines is the PMs in the stator teeth region, which is directly attached to the teeth surface in machine 1 while embedded in the teeth in machine 2.&lt;br/&gt;The phase windings are arranged as follows.&lt;br/&gt;I&lt;sub&gt;a1&lt;/sub&gt;=I&lt;sub&gt;ac&lt;/sub&gt;cos(2πft)+I&lt;sub&gt;dc&lt;/sub&gt;&lt;br/&gt;I&lt;sub&gt;b1&lt;/sub&gt;=I&lt;sub&gt;ac&lt;/sub&gt;cos(2πft-2π/3)+I&lt;sub&gt;dc&lt;/sub&gt;&lt;br/&gt;I&lt;sub&gt;c1&lt;/sub&gt;=I&lt;sub&gt;ac&lt;/sub&gt;cos(2πft+2π/3)+I&lt;sub&gt;dc&lt;/sub&gt;&lt;br/&gt;I&lt;sub&gt;a2&lt;/sub&gt;=I&lt;sub&gt;ac&lt;/sub&gt;cos(2πft)-I&lt;sub&gt;dc&lt;/sub&gt;&lt;br/&gt;I&lt;sub&gt;b2&lt;/sub&gt;=I&lt;sub&gt;ac&lt;/sub&gt;cos(2πft-2π/3)-I&lt;sub&gt;dc&lt;/sub&gt;&lt;br/&gt;I&lt;sub&gt;c2&lt;/sub&gt;=I&lt;sub&gt;ac&lt;/sub&gt;cos(2πft+2π/3)-I&lt;sub&gt;dc&lt;/sub&gt;&lt;br/&gt;The machines can achieve different operation mode by simply adjust the DC-bias. The magnetic field can be strengthened by applying the positive DC biased, while negative DC biased can weaken the magnetic field.&lt;br/&gt;The 2-D FE analysis is conducted to analyze the machine performances. Fig. 2 shows the torque comparison between the conventional and novel structures.&lt;br/&gt;It is obvious that both conventional and novel structures of machine 1 have better torque performances than machine 2. They have higher output torque and lower torque ripple. The output torque of conventional and novel machine 1 are11.44 Nm and 13.25Nm while machine 2 are 10.75Nm and 11.77Nm, respectively. The output torque of novel machine 1 improves 12.57% compares to novel machine 2. It also can be found that structures of machine 2 have better flux regulated capability. By injecting different direction of DC biased, the output torque can increase 6.68% and decrease 14.6% in conventional machine 1 while output increases 10.98% and decreases 22.98% in conventional machine 2.&lt;br/&gt;It also can be seen that the slot-opening PMs are more effectively in torque improvement in machine 1 and saturation relief in machine 2. The output torque increases by 15.82% after adopting the slot-opening PMs in machine 1, while machine 2 only increases by 9.49%. Furthermore, the torque improvement percentage with DC biased have a different degree of increase. After applying the slot-opening PMs, the percentage increases from 6.68% to 9.81% in machine 1 while 10.98% to 24.47% in machine 2.&lt;br/&gt;Conclusion&lt;br/&gt;Two novel DC-biased dual PM machine with slot-opening PM are proposed and compared in this paper. The structure, operation principle and performance are analyzed. The simulation result shows that the machine 1 has better torque performance while machine 2 has better flux regulation capability. More detailed characteristics will be reported in the full paper.

**References:**

[1] X. Zhao, S. Niu and W. Fu, IEEE Trans. Magn., vol. 55, p. 1-5 (2019)&lt;br/&gt;[2] Q. Wang, S. Niu and X. Luo, IEEE Trans. Ind. Electron., vol. 64, p. 6908-6919 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b81421f215e772db5c7a5ab9cfd6e63a.jpg)
Fig. 1. Structure of the proposed motors. (a) Conventional machine1. (b) Novel machine1. (c) Conventional machine2. (d) Novel machine2

![](https://assets.underline.io/uploads/markdown_image/1/image/cecc19a943460a3549e06acd090e80d2.jpg)
Fig. 2. Output torque comparison. (a) Machine 1 (b) Machine 2

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 Analysis of 12 Slots Novel DC-Biased Dual-PM Vernier Machines with Slot-Opening PMs

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—This paper proposes and compares two different 12 slots DC-biased dual-PM vernier machines. Both machines have tangentially magnetized magnets located in the slot openings, and an integrated winding is adopted to produce the armature field and excitation field at the same time. The slot-opening PMs not only improve the machine torque performance but also relieve the saturation caused by the DC-biased. The results show that both structures exhibit high torque density and slot-opening PMs in machine 1 contribute more to torque improvement while PMs in machine 2 are more for dc-saturation relief. Index Terms—DC-bias, dual PM, finite-element method, vernier machine. Introduction With the emergence of the magnetic gear and the proposal of a unified theory of flux modulation, vernier machine has attracted people's attention. Due to its high torque density and wide operation range, vernier machine becomes the potential candidate for many applications such as electric vehicles and wind power generation. To further increase the torque density under the constrain dimension, dual-PM vernier machine is proposed, and several structures have been investigated. In order to achieve a more compact structure and wider flux weakening range, the integrated winding with DC-biased structures have also been studied. In this paper, two novel DC-biased dual-PM vernier machines with slot-opening PM are proposed and investigated. To showcase the effectiveness of the slot-opening PMs, the conventional DC-biased dual PM vernier machines will be presented first. Then the operation principle of proposed novel machines will be presented, and the comparison between different structures will be conducted. Structure, Operation Principle and Performance The structure of the proposed motors and their conventional structures are shown in Fig.1. To make a relatively fair comparison, the main dimensions of all the structures are the same. The outer diameter is 90mm, the air gap is 0.5mm, and the stack length is 80mm. As shown in Fig. 1, PMs are located on both the rotor and stator. The PMs in the rotor and stator tooth are both radially magnetized, while the slot-opening PMs are tangentially magnetized. The main difference between the two novel machines is the PMs in the stator teeth region, which is directly attached to the teeth surface in machine 1 while embedded in the teeth in machine 2. The phase windings are arranged as follows. Ia1=Iaccos(2πft)+Idc Ib1=Iaccos(2πft-2π/3)+Idc Ic1=Iaccos(2πft+2π/3)+Idc Ia2=Iaccos(2πft)-Idc Ib2=Iaccos(2πft-2π/3)-Idc Ic2=Iaccos(2πft+2π/3)-Idc The machines can achieve different operation mode by simply adjust the DC-bias. The magnetic field can be strengthened by applying the positive DC biased, while negative DC biased can weaken the magnetic field. The 2-D FE analysis is conducted to analyze the machine performances. Fig. 2 shows the torque comparison between the conventional and novel structures. It is obvious that both conventional and novel structures of machine 1 have better torque performances than machine 2. They have higher output torque and lower torque ripple. The output torque of conventional and novel machine 1 are11.44 Nm and 13.25Nm while machine 2 are 10.75Nm and 11.77Nm, respectively. The output torque of novel machine 1 improves 12.57% compares to novel machine 2. It also can be found that structures of machine 2 have better flux regulated capability. By injecting different direction of DC biased, the output torque can increase 6.68% and decrease 14.6% in conventional machine 1 while output increases 10.98% and decreases 22.98% in conventional machine 2. It also can be seen that the slot-opening PMs are more effectively in torque improvement in machine 1 and saturation relief in machine 2. The output torque increases by 15.82% after adopting the slot-opening PMs in machine 1, while machine 2 only increases by 9.49%. Furthermore, the torque improvement percentage with DC biased have a different degree of increase. After applying the slot-opening PMs, the percentage increases from 6.68% to 9.81% in machine 1 while 10.98% to 24.47% in machine 2. Conclusion Two novel DC-biased dual PM machine with slot-opening PM are proposed and compared in this paper. The structure, operation principle and performance are analyzed. The simulation result shows that the machine 1 has better torque performance while machine 2 has better flux regulation capability. More detailed characteristics will be reported in the full paper.

**References:**

[1] X. Zhao, S. Niu and W. Fu, IEEE Trans. Magn., vol. 55, p. 1-5 (2019) [2] Q. Wang, S. Niu and X. Luo, IEEE Trans. Ind. Electron., vol. 64, p. 6908-6919 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b81421f215e772db5c7a5ab9cfd6e63a.jpg)
Fig. 1. Structure of the proposed motors. (a) Conventional machine1. (b) Novel machine1. (c) Conventional machine2. (d) Novel machine2

![](https://assets.underline.io/uploads/markdown_image/1/image/cecc19a943460a3549e06acd090e80d2.jpg)
Fig. 2. Output torque comparison. (a) Machine 1 (b) Machine 2

poster

Introduction In recent years, there has been an increase in requirements for motors, as well as its characteristics of high torque transmission, low vibration, low noise, maintenance free and overload protection. In particular, the coaxial magnetic gear (CMG) has become an attractive potential alternative to the traditional mechanical gear boxes [1][2]. Due to its complicated structure and multiple air gaps, however, the conventional radial type CMG is difficult to be manufactured and assembled, as a result its applications are restricted. The axial-radial magnetic gear (ARMG) could be a possible way to simplify such fabrication problems by putting the steel pole pieces around the outside of the two rotors instead of between them, but the longer flux paths between the two rotors lowers the torque and energy transmission. To overcome this drawback while retaining the advantages of the ARMG, this paper proposes a new axial-radial bevel magnetic gear (ARBMG), with new high-performance magnet additive manufacturing (or 3D printing) process to fabricate bevel shape structure. The design of the ARBMG not only shortens the total flux paths, but also increases the efficiency. These results are proved by the FEA simulation and measurement results of a prototype. Model Description and Simulation Fig. 1 shows the comparison between a traditional ARMG as well as an ARBMG with the same gear ratio. The pole pairs of the high-speed rotor (Rotor 1) are 4, while the low-speed rotor’s (Rotor 2) pole pairs are 13, and the number of steel pieces which surround the rotors on the outside are 15. It can be observed that the flux paths between the two rotors of ARBMG are shorter, as a result flux leakage is negligible therefore achieving higher efficiency. Fig. 2 (a) shows the assembly entity of ARBMG, and Fig. 2 (b) shows the ARBMG and ARMG efficiency at different input speeds with the same volume torque density, illustrating that the ARBMG has higher efficiency. Conclusion This paper proposes a new ARBMG with bevel type magnetic gear. With a bevel shaped magnet design, the new ARBMG has shorter flux paths, higher efficiency and much smaller structural volume when compared to the ARMG. Less flux leakage and higher efficiency are assumed, investigated and achieved via analytical as well as Finite Element Analysis (FEA) solutions. A prototype and experimental results based on magnetic 3D printing method are also provided to verify the proposed design.

**References:**

[1] W. Bomela, J. Z. Bird and V. M. Acharya, "The Performance of a Transverse Flux Magnetic Gear," in IEEE Transactions on Magnetics, vol. 50, no. 1, pp. 1-4, Jan. 2014, Art no. 4000104, doi: 10.1109/TMAG.2013.2277431. [2] Y. Li, J. Xing, Y. Lu and Z. Yin, "Torque Analysis of a Novel Non-Contact Permanent Variable Transmission," IEEE Transactions on Magnetics, vol. 47, no. 10, pp. 4465-4468, October 2011.

**Images:**
![](https://assets.underline.io/uploads/markdown_image/1/image/39d222abc7b53ad426a4427fb188b131.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/d15d2e3d122f7f10c5f61f31ebee4513.jpg)

 Design and Implementation of New Axial-Radial Bevel Magnetic Gear Based on Magnetic 3D Printing

I. Torque Density Limit of High Gear Ratio Coaxial Magnetic Gears Gearing system is a useful device used to get higher torque. Due to the advantages of non-contact power transmission and easy maintenance of magnetic gears, movement to apply them to gearing systems by replacing mechanical gears is becoming active. Early magnetic gears had a low torque density of 5 kNm/m3 and could not be considered as gearboxes [1]. However, after the coaxial magnetic gear (CMG) proposed by Atallah achieved a high torque density exceeding 100 kNm/m3, the total system torque density coupled with a motor has reached higher than the one motor, indicating the possibility of replacing the mechanical gears [1, 2]. Previous research has shown a high system torque density at a high gear ratio [2], and it is limited to the case where the magnetic gear shows the same torque density (about 100 kNm/m3) regardless of the gear ratio. However, it was observed that the higher the gear ratio, the lower the torque density [1-14]. Fig. 1 tendency shows that gear torque density is decreased when gear ratio is rising and the system torque density is increased up to specific gear ratio and decreased after that. In this paper, a series coupled magnetic gear is proposed to improve the torque density limit of high gear ratio CMGs. In addition, this structure shows reducing-loss effect, its superiority is demonstrated. II. Loss Issue and Series Coupled Coaxial Magnetic Gear In the high gear ratio model, the problem of not only torque density but also efficiency was confirmed. In this paper, a single CMG with a gear ratio of 63:1 was designed and the efficiency of 58.9% was confirmed with a torque density of 21.4kNm/m3. This is because it is accompanied by a rapid change in magnetic flux at once to show a high gear ratio. That is, each change must be magnetically separated while using the stepwise change of magnetic flux. Therefore, in this paper, a series coupled CMG is proposed. Fig. 2 shows a concept of the series coupled coaxial magnetic gear. The gear ratio of 63:1 was divided into 7:1 and 9:1, and each torque density is about 85kNm/m3 and 75 kNm/m3 according to Fig. 1. In addition, losses can theoretically be reduced by 3 and 2.6 times, respectively. In this paper, various series coupling methods were considered, and a model favorable for improving torque density and one for improving loss were finally selected. As a result of the study, the proposed series coupled CMG improves torque density of 3 times and reduces loss of 90% compare to the single high gear ratio CMG. The detailed design of the series coupled CMG will be presented in full paper. Acknowledgment: This research was supported by Korea Electric Power Corporation. (Grant number: R19XO01-34)

**References:**

[1] K. Atallah and D. Howe, “A novel high-performance magnetic gear,” IEEE Trans. Magn., vol. 37, no. 4, pp. 2844-2846, July. 2001. [2] 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. 2, pp. 135-143, 2004. [3] Y. Wu, c. Chan, “A novel bicycle rear hub transmission with a magnetic gear mechanism,” Advances in Mechanical Engineering, vol. 10, no. 7, pp. 1-9, 2018. [4] M. Desvaux, B. Traulle, R. Latimier, S. Sire, B. Multon, H. Ahmed, “Computation Time Analysis of the Magnetic Gear Analytical Model,” IEEE Trans. Magn., vol. 53, no. 5, pp. 7000409, 2017. [5] M. Kowol, J. Kolodziej, M. Jagiela, M. Lukaniszyn, “Impact of Modulator Designs and Materials on Efficiency and Losses in Radial Passive Magnetic Gear,” IEEE Trans. Energy Conversion, vol. 34, no. 1, pp. 147-154, 2019. [6] H. Shin, J. Chang, “Comparison of the Characteristics in the Surface Mounted Permanent Magnet and Flux Concentrating Coaxial Magnetic Gears Having the Solid Cores,” J. Electr. Eng. Technol., vol. 13, no. 3, pp. 1275-1284, 2018. [7] Y. Chen, W. Fu, S. Ho, H. Liu, “A Quantitative Comparison Analysis of Radial-Flux, Transverse-Flux, and Axial-Flux Magnetic Gears,” IEEE Trans. Magn., vol. 50, no. 11, pp. 8104604, 2014. [8] D. Jang, J. Chang, “Effect of Stationary Pole Pieces with Bridges on Electromagnetic and Mechanical Performance of a Coaxial Magnetic Gear,” Journal of Magnetics, vol. 18, no. 2, pp. 207-211, 2013. [9] X. Zhang, X. Liu, Z. Chen, “A Novel Coaxial Magnetic Gear and Its Integration With Permanent-Magnet Brushless Motor,” IEEE Trans. Magn., vol. 52, no. 7, pp. 8203304, 2016. [10] X. Liu, Y. Zhao, X. Zhang, J. Gao, S. Huang, “Investigation of the Dynamic Characteristics of a Coaxial Magnetic Gear under Loading Condition Based on Analytical Model,” International conference on electrical machines and systems, 2017. [11] M. Filippini, P, Alotto, “An optimization tool for coaxial magnetic gears,” The international journal for computation and mathematics in electrical and electronic engineering, vol. 36, no. 5, pp. 1526-1539, 2017. [12] O. Molokanov. P. Dergachev, V. Kiruhin, P. Kurbatov, “Analyses and Experimental Validation of Coaxial Magnetic Planetary Gear,” International symposium on electrical apparatus and technologies, 2014. [13] E. Gobl, G. Jungmayr, E. Marth, W. Amrhein, “Optimization and Comparison of Coaxial Magnetic Gears With and Without Back Iron,” IEEE Trans. Magn., vol. 54, no. 11, pp. 8001604, 2018. [14] G. Jungmayr, J. Loeffler, B. Winter, F. Jeske, W. Amrhein, “Magnetic Gear: Radial Force, Cogging Torque, Skewing, and Optimization,” IEEE Trans. Industry Applications, vol. 52, no. 5, pp. 3822-3830, 2016.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a3ca0046cbb1de078347b44c24d9f9ad.jpg)
Fig. 1. System torque density of preceding researches. (Using same torque density motors)

![](https://assets.underline.io/uploads/markdown_image/1/image/55229a7d699710e3bd380d3723a55ccd.jpg)
Fig. 2. Concept of the series coupled coaxial magnetic gear

 Series Coupled Coaxial Magnetic Gear Design for High Gear Ratio and High Torque Density

This paper shows that by using topology optimization, force density of a reluctance trans-rotary magnetic gear (TROMAG) can be improved significantly. TROMAG is a magnetic device that converts high-force, low-speed linear motion to low-torque, high-speed rotation, and vice versa [1]. The device is also referred to as magnetic screw [2] and magnetic lead screw [3]. As shown in Fig. 1a, a TROMAG consists of an inner and an outer component which are separated by an air gap. One component serves as a rotor and the other as a translator. The linear to rotary motion conversion is achieved via helically-shaped permanent magnet (PM) poles. TROMAG can offer large values of shear stress and gear ratio; resulting in light-weight and compact designs. In addition, similar to other types of magnetic gears, TROMAG offers low noise and high reliability. Advantages of TROMAG have made it a strong contender for a wide range of high force, low speed applications. Helical PM poles can assume different magnetization patterns. Radially-magnetized TROMAG (RMT), axially-magnetized TROMAG (AMT), and Halbach-magnetized TROMAG (HMT) have been proposed. Another configuration, shown in Fig. 1b, is reluctance TROMAG in which one component is furnished by helical PM poles while the other component has a variable reluctance structure. Reluctance TROMAG offers less shear stress compared to configurations having PMs on both components. However, lack of PMs on the variable reluctance component makes it potentially advantageous, for example, in applications with a long stroke. Reluctance TROMAG is investigated in multiple works; with radially-magnetized PMs (R-RMT) in [2], with Halbach-magnetized PMs (R-HMT) in [3], and with axially-magnetized PMs (R-AMT) in [4]. In all these works, teeth in the variable reluctance component are of rectangular shape. This paper aims to find the optimum tooth shape using topology optimization. Noting that 2D approximation of TROMAG introduces no more than a few percent error in force calculation compared to the 3D model, the former is used for topology optimization. Topology optimization has been applied to different electromagnetic devices [5]-[8]. The essence of topology optimization is to divide the design region into small elements and use an optimization algorithm to assign to each element a set of specific materials in order to achieve the optimum topology. In [5] and [6], a genetic algorithm (GA) is used along with the so-called on/off method in which each element can be either air or a pre-defined material. Since elements are triangular or quadrilateral, resultant topologies may have sharp corners. Hence, in [7], topology optimization is performed in two main stages. First, GA and on/off method are used to run a global search and obtain the optimum topology. Then, the level set approach which is gradient based is employed to smooth the corners and create a more practical design. Recently, a topology optimization method based on the normalized Gaussian network (NGnet) has been presented [8]. Here, the on/off method is applied to Gaussian circles mapped to the design region. The method is incorporated in JMAG-Designer software, which is employed in this paper for optimizing the reluctance TROMAG. First, the three reluctance TROMAG configurations, R-RMT, R-AMT, and R-HMT with rectangular teeth are optimized by sweeping teeth dimensions while keeping other design variables fixed. For all cases the results of which are presented here, the pole pitch is 10 mm, PM thickness along radial direction is 10 mm, and air gap length is 1 mm. Optimum values of shear stress for the three designs are 82, 95, and 119 kN/m2 respectively. Then, JMAG is used to apply topology optimization coupled with genetic algorithm to the three configurations. The design region has been divided into quadrilateral elements. Each element area is 0.25 mm2 and the number of circles in the design region is set to 21. The optimization objective is to maximize the shear stress. Fig. 2 shows two cases resulted from topology optimization of R-RMT, offering largest values of shear stress. It was revealed that 1) For R-RMT, trapezoidal tooth shape shown in Fig. 2a offers 10% higher, and elliptical tooth shape with non-magnetic material yoke, shown in Fig. 2b, offers 30% higher shear stress compared to R-RMT with optimized rectangular tooth. 2) Optimum shape for R-AMT is rectangular; i. e., topology optimization algorithm converges to a rectangular shape. 3) For R-HMT, trapezoidal tooth shape offers 5% higher shear stress, and elliptical tooth shape with non-magnetic material yoke offers almost the same shear stress compared to R-HMT with optimized rectangular teeth. Note that although the case of R-HMT with elliptical tooth shape and non-magnetic material yoke does not offer an appreciable increase in shear stress, it has the advantage of replacing iron yoke of the variable reluctance structure with non-magnetic material, resulting in significant weight reduction. The full paper will include detailed topology optimization results for the three configurations.

**References:**

[1] S. Pakdelian, N. W. Frank and H. A. Toliyat, IEEE Trans. Magn., vol. 49, no. 2, pp. 883-889, Feb. 2013. [2] H. M. Mohamed and K. Atallah, IEEE Trans. Magn., vol. 55, no. 7, pp. 1-4, July 2019, Art no. 8001504. [3] N. I. Berg, A. B. Christiansen, R. K. Holm and P. O. Rasmussen, in Proc. Int. Elect. Mach. Drives Conf., 2017, pp. 1–8. [4] M. Cirolini, A. F. Flores Filho, Y. C. Wu and D. G. Dorrell, IEEE Trans. Magn., vol. 55, no. 7, pp. 1-6, July 2019, Art no. 8001906. [5] Chang-Hwan Im, Hyun-Kyo Jung and Yong-Joo Kim, IEEE Trans. Magn., vol. 39, no. 5, pp. 2163-2169, Sep. 2003. [6] N. Takahashi, T. Yamada, S. Shimose and D. Miyagi, IEEE Trans. Magn., vol. 47, no. 5, pp. 1262-1265, May 2011. [7] Y. Hidaka, T. Sato and H. Igarashi, IEEE Trans. Magn., vol. 50, no. 2, pp. 617-620, Feb. 2014, Art no. 7015204. [8] T. Sato, K. Watanabe and H. Igarashi, IEEE Trans. Magn., vol. 51, no. 3, pp. 1-4, March 2015, Art no. 7202604.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3d37b9293d2c321253fe27683c82b738.jpg)
Fig. 1. 3D views of (a) RMT; and (b) Reluctance RMT.

![](https://assets.underline.io/uploads/markdown_image/1/image/b7f3a050a3b91a9f8e66932038ee6c7c.jpg)
Fig. 2. 2D views of promising R-RM topologies; (a) trapezoidal tooth; (b) elliptical tooth with non-magnetic yoke. Topologies are created by JMAG and reproduced in ANSYS Maxwell.

 Topology Optimization of the Reluctance Trans-Rotary Magnetic Gear

—This paper proposes a novel hybrid excitation alternate stator PM dual stator/rotor armature winding vernier machine with the DC-biased current. Due to the both armature windings and alternate stator PM interact with each other, this proposed machine contain six torque components. Compared with traditional stator permanent magnet machines and flux modulated machines, this machine makes full use of the space in rotor cavity, and giving full play to the flux modulation effect. This digest will introduce the coil-connection, current configuration, and the simulation results, such as flux density, back-EMF, and electromagnetic torque, which are predicted by finite element analysis (FEA). Index Terms—Hybrid excitation, DC-biased current, Vernier machine (VM), Dual stator/rotor armature winding. I. Introduction Recently, stator permanent magnet (PM) machines are gaining more and more research attention for their benefit of a robust rotor structure[1]. In the meantime, the flux modulated machines due to the natural high torque density characteristic are gaining more research interest, too [2]. Combining the advantages of both machines, the DC-biased hybrid excitation stator PM vernier machines (HEPMVMs) are proposed [3]. Compared with the stator PM machines, the DC-biased HEPMVMs improve the shortcomings of the inherent limited magnetic field adjustment ability, meanwhile, improve the torque density. However, these machines don't make full use of the space in the rotor cavity, and the reliability of torque output is poor, due to only contain stator armature winding. In this paper, the topology of DC-biased hybrid excitation alternate stator PM dual stator/rotor armature winding vernier machine (DAWVM) is proposed. As shown In Fig. 1, the stator has two phase DC-biased winding and the teeth located PMs alternately, the rotor has three phase winding. Therefore, high torque will be generated. The drive circuit, operation principle, and the electromagnetic characteristics will be illustrated in the full paper. II.Electromagnetic Performance Evaluation The simulation results of flux density, back-EMF, and electromagnetic torque are analyzed by the finite element analysis (FEA). The no-load flux distribution is shown in Fig. 2. The back-EMF and electromagnetic torque with various excitation modes are shown in Fig. 3. This machine exhibits larger torque due to contain six torque components, which will be illustrated in the full paper.

**References:**

[1] Z. Zhu, H. Hua, D. Wu, J. Shi, and Z. Wu, IEEE Trans. Ind. Appl., vol. 52, no. 1, pp. 199–208, Jan./Feb. 2016. [2] S. Jia, R. Qu, W. Kong, D. Li, and J. Li, IEEE Trans. Ind. App., vol. 54, no.2, Jul./Aug., pp:3187-3196, 2018. [3] S. Jia et al., IEEE Trans. Ind. Appl., vol. 54, no. 2, pp. 1339-1348, March-April 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/295cf1534770412071997534548c27db.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/0234029e49aa5b7b0a694f2c23a483d5.jpg)

 Hybrid Excitation Dual Stator/Rotor Armature Winding Vernier Machine with Alternate Stator PM

I. Introduction Permanent-magnet (PM) machines, which exhibit the merits of high torque/power density and high efficiency, have been widely employed in many industrial applications in recent decades, such as wind power generation and electric vehicles [1-5]. As these applications are safe-critical, the development of new machine structures with improved reliability is speeding up [6, 7]. To achieve the feature of fault tolerance, various design techniques of PM machines have been put forward, such as the redundant designs with multi-phase windings [8] or dual three-phase windings [9], and the modular designs with modular windings [10] or modular stator [11], etc. Recently, the stator-slot PM (SSPM) machine with inherent fault-tolerant ability is proposed to achieve high failure-safe capability during uncontrolled generator operation or winding short circuits [12]. However, relatively low torque density puts this structure at a disadvantage, particularly at light load condition. To improve the torque performances, the split-tooth (ST) structure is introduced in the machine [13], where the PMs are placed between the split tooth and tangentially magnetized with opposite polarities in the adjacent PMs, as shown in Fig. 1(a). In this paper, three new types of split-tooth stator-slot PM (ST-SSPM) machines are proposed as shown in Fig. 1(b)-(d), which are designated as Type-2, Type-3, and Type-4 machine, respectively. Four types of machines share the same structure with the split-tooth stator and salient-pole rotor but the PMs are arranged with different positions and polarities. The operation principles are introduced while the electromagnetic performances of four types of machines are comprehensively analyzed and compared by using finite-element analysis (FEA). Based on the analyzed results, the merits and demerits of four types of machines with different PM arrangements are concluded. II. Methodology Similar to the other stator-PM machine with salient rotor poles, the operation principle of four types of machines can be explained by the field modulation theory [14]. Then, the slot-pole combinations of Type-1 and Type-3 machines can be derived as Pa = min(|iNs/2±Nr|), (i=1, 3, 5…) while those of Type-2 and Type-4 machines can be derived as Pa = min(|iNs±Nr|), (i=1, 2, 3…), where Pa is the pole-pair number of armature winding, Ns is the stator slot number, Nr is the rotor pole number, and i is a positive integer. By performing FEA in JMAG-Designer, the torques and torque ripples of machines with various slot-pole combinations are optimized in Fig. 2. It can be seen that Type-1 to Type-4 machines can produce the largest torque with Nr=22, 16, 23 and 17 respectively, while the torque of Type-4 machine with Nr=17 is the largest among all the machines. However, Type-3 machine with Nr=23 and Type-4 machine with Nr=17 produce large unbalanced magnetic force due to the odd number of Nr, thus undesired electromagnetic vibration and noise will be incurred. To resolve this concern, it is desirable to achieve good torque performances with an even number of Nr. One can see that the torques of Type-3 and Type-4 machines with Nr=22 are the highest among all the machines with even numbers of Nr, despite slightly lower than those of Type-3 machine with Nr=23 and Type-4 machine with Nr=17, respectively. Therefore, the optimal Nr of Type-1 to Type-4 machines are preliminarily selected as 22, 16, 22, and 22, respectively. Furthermore, the torque ripples of these four machines are all lower than 10 %, and hence are acceptable. Finally, taking into consideration all the above factors, Type-1 to Type-4 machines are globally optimized with optimal Nr=22, 16, 22, and 22, respectively, which are further investigated, including the cogging torque, back-EMF, steady torque, PM utilization ratio, loss, efficiency, power factor and PM demagnetization. III. Conclusion Based on the analyzed results of four types of machines, some findings are listed as follows. a) Type-1 machine has the lowest cogging torque due to the circulation of PM flux in the stator at no load condition, whereas Type-2 machine shows the highest cogging torque due to the largest cogging torque factor. b) Type-1, Type-2 and Type-4 machines have the similar and largest average torque at rated condition. However, Type-4 and Type-2 machines offer the highest and lowest PMs utilization ratio, respectively. c) Type-4 machine exhibits the best torque performance at rated and light load conditions, while Type-1 machine has the best overload capability. Type-2 machine shows good torque performances both in light and overload conditions, despite not the best, d) Type-4 machine offers the highest power factor, despite the power factors of four types of machines tend to be low. However, their power factors can be improved by increasing the value of stator inner radius/airgap. e) Type-1 to Type-3 machines show irreversible PM demagnetization with different degrees at the inner corner of PMs under over load and high temperature condition, whereas this does not happen in Type-4 machine with the best PM demagnetization withstand. More detailed analysis and results will be given in the full paper. Acknowledgment This work was supported by a grant (Project No. 17205518) from the Hong Kong Research Grants Council, Hong Kong Special Administrative Region, China.

**References:**

 [1] K. T. Chau, C. C. Chan, and C. Liu, “Overview of permanent-magnet brushless drives for electric and hybrid electric vehicles,” IEEE Trans. Ind. Electron., vol. 55, no. 6, pp. 2246-2257, May 2008. [2] Z. Q. Zhu, and D. Howe, “Electrical machines and drives for electric, hybrid, and fuel cell vehicles,” Proc. IEEE, vol. 95, no. 4, pp. 746-765, Apr. 2007. [3] J. Li, K. T. Chau, J. Jiang, C. Liu, and W. Li, “A new efficient permanent-magnet vernier machine for wind power generation,” IEEE Trans. Magn., vol. 46, no. 6, pp. 1475-1478, May 2010. [4] C. Liu, K. T. Chau, J. Z. Jiang, and S. Niu, “Comparison of Stator-Permanent-Magnet Brushless Machines,” IEEE Trans. Magn., vol. 44, no. 11, pp. 4405-4408, Nov. 2008. [5] L. Cao, K. T. Chau, and C. H. T. Lee, “A new parallel-hybrid-excited permanent-magnet machine with harmonic-differential effect for electric vehicles,” IEEE Trans. Veh. Technol., vol. 69, no. 11, pp. 12734-12750, Sept. 2020. [6] A. M. E.-. Refaie, M. R. Shah, and K. Huh, “High-power-density fault-tolerant PM generator for safety-critical applications,” IEEE Trans. Ind. Appl., vol. 50, no. 3, pp. 1717-1728, Sept. 2014. [7] W. Zhao, L. Xu, and G. Liu, “Overview of permanent-magnet fault-tolerant machines: Topology and design,” CES Trans. Elect. Mach. and Syst., vol. 2, no. 1, pp. 51-64, Mar. 2018. [8] F. Barrero, and M. J. Duran, “Recent advances in the design, modeling, and control of multiphase machines—Part I,” IEEE Trans. Ind. Electron., vol. 63, no. 1, pp. 449-458, Jun. 2016. [9] X. Jiang, W. Huang, R. Cao, Z. Hao, and W. Jiang, “Electric drive system of dual-winding fault-tolerant permanent-magnet motor for aerospace applications,” IEEE Trans. Ind. Electron., vol. 62, no. 12, pp. 7322-7330, Dec. 2015. [10] P. Zheng, Y. Sui, J. Zhao, C. Tong, T. A. Lipo, and A. Wang, “Investigation of a novel five-phase modular permanent-magnet in-wheel motor,” IEEE Trans. Magn., vol. 47, no. 10, pp. 4084-4087, Oct. 2011. [11] G. J. Li, Z. Q. Zhu, M. Foster, and D. Stone, “Comparative studies of modular and unequal tooth PM machines either with or without tooth tips,” IEEE Trans. Magn., vol. 50, no. 7, pp. 1-10, Jul. 2014. [12] I. A. A. Afinowi, Z. Q. Zhu, Y. Guan, J. Mipo, and P. Farah, “A novel brushless AC doubly salient stator slot permanent magnet machine,” IEEE Trans. Energy Convers., vol. 31, no. 1, pp. 283-292, Mar. 2016. [13] H. Qu, and Z. Q. Zhu, “Analysis of split-tooth stator slot PM machine,” IEEE Trans. Ind. Electron., 2020, doi: 10.1109/TIE.2020.3031535 (Early Access). [14] M. Cheng, P. Han, and W. Hua, “General airgap field modulation theory for electrical machines,” IEEE Trans. Ind. Electron., vol. 64, no. 8, pp. 6063-6074, Mar. 2017.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3045adcb24c5b43ba666bbd3d248727b.jpg)
Fig. 1. ST-SSPM machines with different PM arrangements. (1) Type-1. (b) Type-2. (c) Type-3. (d) Type-4.

![](https://assets.underline.io/uploads/markdown_image/1/image/a177b936336d0e337ea63e54611f8851.jpg)
Fig. 2. Torques and torque ripples of four types of machines with different numbers of rotor poles. (a) Torques. (b) Torque ripples.

 Analysis of Split-Tooth Stator-Slot Permanent-Magnet Machines with Different PM Arrangements

1. Introduction The demand for low-speed and high-torque electrical machines is increasing in different industrial applications. Vernier permanent-magnet machines (VPM) and Pseudo-direct-drive machines (PDD) are especially suitable for this situation due to their magnetic gearing effect [1,2]. Generally, the power factor of the conventional VPM can be as low as 0.66 [3]. PDDs have the capability of high power factor as well as high torque density [2]. To output higher torque density compared with PDDs, a novel Vernier Pseudo-direct-drive machine (VPDD) is proposed in [4] as Fig. 1 (a) shows. In this paper, the subdomain analytical model is used to analyze and preoptimize a VPDD. After the preoptimization, a finite element model (FEM) is also used to optimize the slot opening and check the demagnetization. However, in this machine, the winding has not been optimized to reduce the size of end-winding, and as a result, the real torque density taking the end-winding into account is much lower. Our research focuses on further improving the torque density of the VPDD considering a structure that reduces the size of end-winding. A concentrated winding split-teeth VPDD topology (ST-VPDD), shown in Fig. 1 (b), is hence proposed. 2. Modeling and optimization The ST-VPDD can be regarded as a combination of a magnetic gear and a VPM. For the part that functions as a magnetic gear [4], the speed ratio can be expressed as Gtr=Ωt/Ωr=pr/pt=-Tr/Tt, where Ωt, Ωr are the rotational angular speed of the transmitter and of the low-speed (LS) rotor; pt, pr are the pole-pairs of permanent-magnets (PM) of the transmitter and of the LS rotor; Tt, Tr are the torque of the transmitter and of the LS rotor. The rotating magnetic field created by the armature winding drives the transmitter. The LS rotor will be driven by both the transmitter and by the field created by the armature winding. If the transmitter is removed, the ST-VPDD can be regarded as a VPM. According to [5], if Pf=nZ=pr±ps is satisfied, the rotating field of armature winding can drive the LS rotor. n is the number of split teeth per tooth, Z is the number of slots and ps is the pole-pairs of armature winding. The gear ratio can be expressed as Gsr=Ωs/Ωr=pr/(nZ-pr)=pr/ps, where Ωs is the rotational angular speed of the field created by the winding. We keep ps=pt so that Gsr=Gtr. Therefore, the part of the magnetic gear and the VPM will drive the low-speed rotor together at the same speed. The ST-VPDD is analyzed through a FEM. Its ferromagnetic material is made of M-45 steel. Fig. 2 (b) shows the proposed concentrated winding model. For comparison, the distributed winding model of the prototype VPDD is put in Fig. 2 (a). In the figure, lw is the length of the half-width of a slot, and ls depends on the winding material. According to the winding model, a mathematical model is built to calculate the torque density taking end-winding into account. The torque density of the ST-VPDD is optimized. The variable parameters are: 1. r1 is the radius of the transmitter iron; 2. hmt is the thickness of the transmitter PM; 3. hmr is the thickness of the rotor PM; 4. ls is the length of the split teeth; 5. c1=α1/α2; 6. c2=lt/ls; 7. c3=β1/β2. Once the optimization is done, we do the demagnetization check on the optimized ST-VPDD. 3. Results The following parameters of the ST-VPDD are assumed to be similar to the parameters of the VPDD [4]: Z=9, n=5, pt=ps=3 and pr=42, and its out radius ro is 90 mm and active length la is 75 mm. The optimized ST-VPDD can output 172.1 Nm of torque in theory. Without taking the end-winding into account, it provides 90.2 Nm/L of torque density, which is slightly lower than the torque density of 91.8 Nm/L of the VPDD in [4]. From the winding model of the VPDD and of the ST-VPDD, we get that the lengths of end-winding of VPDD and ST-VPDD are 96 mm and 49.6 mm, respectively. So, taking the end-winding into account, the torque density of VPDD and ST-VPDD are 40.3 Nm/L and 54.3 Nm/L. There is a 34.7% improvement in the torque density. The PM used for this design is VACODYM AP 776 [6]. When the temperature is 60 Celsius degree, its remanent flux density is 1.25 T and the demagnetization field is 1300 kA/m. No demagnetization occurs. 4. Conclusions With concentrated winding, the optimized ST-VPDD topology improves the torque density capability compared with the VPDD. And the concentrated winding is less complicated, which simplifies manufacture and hence decrease its cost. The split tooth allows more combinations of poles and slots, so the structure can be further optimized. 5. Acknowledgment This work was supported by the National Natural Science Foundation of China under Grant 51851110761. Corresponding author: P.-D. Pfister (e-mail: pierredaniel.pfister.public@gmail.com).

**References:**

 [1] A. Toba and T. A. Lipo, "Generic torque-maximizing design methodology of surface permanent-magnet vernier machine," in IEEE Transactions on Industry Applications, vol. 36, no. 6, pp. 1539-1546, Nov.-Dec. 2000, doi: 10.1109/28.887204. [2] K. Atallah, J. Rens, S. Mezani and D. Howe, "A Novel “Pseudo” Direct-Drive Brushless Permanent Magnet Machine," in IEEE Transactions on Magnetics, vol. 44, no. 11, pp. 4349-4352, Nov. 2008, doi: 10.1109/TMAG.2008.2001509. [3] D. Li, R. Qu and T. A. Lipo, "High-Power-Factor Vernier Permanent-Magnet Machines," in IEEE Transactions on Industry Applications, vol. 50, no. 6, pp. 3664-3674, Nov.-Dec. 2014, doi: 10.1109/TIA.2014.2315443. [4] X. Yin, Y. Fang, X. Huang and P. Pfister, "Analytical Modeling of a Novel Vernier Pseudo-Direct-Drive Permanent-Magnet Machine," in IEEE Transactions on Magnetics, vol. 53, no. 6, pp. 1-4, June 2017, Art no. 7207404, doi: 10.1109/TMAG.2017.2660241. [5] D. Li, T. Zou, R. Qu and D. Jiang, "Analysis of Fractional-Slot Concentrated Winding PM Vernier Machines With Regular Open-Slot Stators," in IEEE Transactions on Industry Applications, vol. 54, no. 2, pp. 1320-1330, March-April 2018, doi: 10.1109/TIA.2017.2778686. [6] VACUUMSCHMELZE. Rare Earth Permanent Magnets: VACODYM VACOMAX. Accessed: January 05, 2021. [Online]. Available: https://vacuumschmelze.de/Assets-Web/VACODYM-VACOMAX-PD002_2015_en.pdf.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bf5b96ee97deb34ae19d54612847229b.jpg)
Figure 1: (a) The structure of the VPDD [4]. (b) The structure of the proposed ST-VPDD.

![](https://assets.underline.io/uploads/markdown_image/1/image/14bd1a0ca6910cd527b238352b2c7e70.jpg)
Figure 2: (a) The distributed winding model of the prototype VPDD. (b) The concentrated winding model of the proposed ST-VPDD.

 A novel split-teeth Vernier pseudo-direct-drive permanent-magnet machine with concentrated winding

1. Introduction Direct drive machines are more and more used in several applications involving low speed operation at standard frequencies. This replaces conventional systems which use classical machines coupled to gearboxes thus improving the dynamic and the efficiency of the system while avoiding the maintenance drawbacks of classical solutions. The simplest way to obtain a direct drive machine consists in increasing the pole pair number of a classical machine and more specifically a PM synchronous machine. However, this leads to large diameters which are not well adapted for applications with limited volume. This is the case of traction applications as the mass and the volume of the machine are key points. PM Vernier machine is well known for its capacity to provide high torque density with reduced ripples. It requires smaller stator slot and pole pair numbers than classical PM machine with the same rotor pole pairs [1-2]. Therefore, it could constitute a good candidate to be used as a traction motor. In its common configuration, PM are mounted on the rotor surface with a radial magnetization and several studies have been dedicated to give the rules to well design a PM Vernier structure or to propose topologies to improve the torque density and power factor which is considered as the main drawback [3-4]. Recently some of them focused on another way to arrange the magnets on the rotor [5-6]. The present paper deals with the study of PM Vernier machine with a quasi-Halbach configuration of the magnets. The effects of the ratio between the tangential and the radial parts of the magnets on the machine performance (torque density, torque ripple) are evaluated using finite element analysis (FEA) method. Using an analytical approach with a pure radial magnetization of PM, a prototype is first designed and sized under the specifications of an urban traction application. Simulations are then carried out on the prototype with different stator slot openings and ratios of the tangential part of the magnet to quantify the effect of the two variables in term of average torque, ripples and harmonics of the no load emf. 2. Operation principle PM Vernier machine achieves the electromagnetic energy conversion on the basis of the interaction of the armature magnetic field with the one of the rotating magnets. As the pole pair numbers of both magnetic fields are different, the variation of the air gap permeance, which is due to the only stator slots, plays a key role by modulating the two fields so that they can interact. The analytical expression of the whole magnetic energy in a PM Vernier machine under the assumption of high permeability of the magnetic material shows that the latter is constituted of different terms. Only some of them are function of the rotor position and can then generate an electromagnetic torque. Therefore, to select one of these terms thus achieving an electromagnetic conversion in a continuous manner, a strong relationship should link the rotor PM pole pairs pr to the stator winding pole pairs ps and the number of stator slots Ns: Ns=│ps ± pr │ In the case of radial magnetization of the PM, previous studies have shown that the best arrangement is when the magnets are contiguous. Thus, for a given mechanical air gap thickness, only the opening of the stator slot influences the interaction and therefore the performance. In the case of a quasi-Halbach configuration, in addition to the opening of the stator slot, the tangential magnetization part of PM will also have a significant effect in terms of the average value of the electromagnetic torque but also in terms of torque ripples and harmonics of the no load emf. 3 Application A first prototype has been designed with PM magnetized in the only radial direction and its main geometries sized using analytical approach for the desired application with rated power 65 kW at 300 rpm and 55Hz. The rotor and stator pole pair numbers are 11 and 1 respectively. Thus, the slots number is equal to 12. The machine air gap radius is 0.177m and its active length is 0.532m. Figure 1a shows the magnetic flux density distribution in a cross section of the designed machine. It clearly looks like just 1 pole pair machine even if the rotor has 11 pole pairs. Figure 1b presents the two variables whose effects are evaluated, i.e. λH which represents the tangential angular part of a pole magnet and λss which is the angular opening of a stator slot. While keeping the same magnet and mechanical airgap thicknesses, different stator slot opening and tangential parts of the magnets have been investigated using FEA while taking into account the non-linear behavior of magnetic materials. Figure 2a shows the no load emfs for a ratio of the tangential part of the magnets equal to λH/λr =10% and λss/λs = 43, 50 and 57 %. Figure 2b presents the electromagnetic torque at load when the machine is supplied by three phase rated currents for λss/λs = 45% and 3 λH/λr =5, 10 and 15%. It can clearly be seen that both variables have non negligible effect on the no load emf in terms of magnitude and harmonic content and on the average value of the electromagnetic torque along with its ripples. In the final paper, more details about the design of the first prototype will be given and results leading to an optimal prototype with a quasi-Halbach configuration of the magnets will be presented and discussed.

**References:**

[1] D. Li, R. Qu, J. Li, L. Xiao, L. Wu and W. Xu, "Analysis of Torque Capability and Quality in Vernier Permanent-Magnet Machines," in IEEE Transactions on Industry Applications, vol. 52, no. 1, pp. 125-135, Jan.-Feb. 2016. [2] B. Kim and T. Lipo, “Operation and design principles of a PM vernier motor,” IEEE Trans. Ind. Appl., vol. 50, no. 6, pp. 3656-3663, Nov./Dec.2014. [3] L. Wu, R. Qu, D. Li and Y. Gao, "Influence of Pole Ratio and Winding Pole Numbers on Performance and Optimal Design Parameters of Surface Permanent-Magnet Vernier Machines," in IEEE Transactions on Industry Applications, vol. 51, no. 5, pp. 3707-3715, Sept.-Oct. 2015. [4] D. Li, R. Qu, and T .Lipo, “ High power factor vernier permanent magnet machines,” IEEE Trans. Ind. Appl., vol. 50, no. 6, pp. 3664- 3674, Nov./Dec. 2014 [5] L. Xu, G. Liu, W. Zhao, J. Ji and X. Fan, “High-Performance Fault Tolerant Halbach Permanent Magnet Vernier Machines for Safety-Critical Applications, ” IEEE Trans. Magn., vol. 52, no. 7, July 2016 [6] Y. Kataoka, Y. Anazawa, ‘Analysis of counter Electromotive force in a surface permanent magnet-type Vernier Motor using a Halbach array’, The 23d ICEMS, 2020, pp: 1257-1262

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/558f758ef55d9db0027a63989a28bde8.jpg)
Fig .1. a ) No load magnetic flux density in the cross section of the first prototype b) The two variables studied

![](https://assets.underline.io/uploads/markdown_image/1/image/40109d36ba8515bd38afe6b14076a09b.jpg)
Figure 2. No load emfs and rated electromagnetic torque for different configurations

 Design of a quasi-Halbach permanent magnet Vernier machine

I. Introduction Vernier permanent-magnet (VPM) machine takes advantage of high torque density and low rotational speed, which makes it a promising candidate in direct-drive applications. The industrial application prospect makes it a research interest in recent years. A fault-tolerant structure is proposed in [1], which can decouple the interaction between different phases and hence improve the fault-tolerant ability. However, as the fractional slot concentrated winding (FSCW) configuration is adopted, the torque capability is consequently reduced [2]. This paper proposes a split-pole fault-tolerant (SPFT) VPM machine as is shown in Fig. 1(a). The consequent-pole PM structure is adopted to improve the torque density with less magnet usage [3]. Meanwhile the stator affiliated PMs are employed to further enhance the torque capability. Last but not least, the inner stator is composed of alternately arranged modular teeth and fault-tolerant teeth. The modular tooth consists of root part and split-pole structure, and the split-pole structure plays the role of flux modulation poles (FMPs). The concentrated windings are wound around the modular teeth, so the fault-tolerant teeth can segregate the adjoining phases. The stator only has one modular tooth for each phase, and the winding pole pair is set to one. Thus, the coils can link nearly 120 mechanical degree of the flux linkage even if the FSCW configuration is adopted. In this way the torque capability can be maximized. In this paper the operation principle and working mechanism of proposed machine are described. The influences of the key parameters on electromagnetic performances are investigated by finite element analysis (FEA) method. A comparison between conventional FTVPM machine and proposed machine is discussed. Besides, the analytical model of proposed machine is illustrated and analyzed. The prototype is manufactured and tested which verifies the feasibility of calculation results. The analytical model and experiment results are not shown in the digest for space limitation, and will be added in the full paper. II. Parameter Optimization and Electromagnetic Performance Comparison The influences of the key parameters on electromagnetic performances are investigated to optimize the proposed structure. As can be seen in Fig. 1(b), the optimal stator modular tooth width is 18mm. It is because the proposed structure only has 3 stator teeth for windings. When the d-axis and the modular tooth coincide, all the flux linkage will pass through one of the modular teeth, so that the saturation problem is heavier. Therefore the modular teeth have to be wide enough. When the width is larger than 18mm the area for armature winding is reduced, thus the torque decreases instead. When the fault-tolerant tooth width increases, there is a small drop at first as is shown in Fig. 1(c). The reason is when fault-tolerant teeth is very thin, the split-pole occupies larger air-gap angle, so there will be more flux linkage passes through the coils. The stator and rotor PM thickness are also confined by the winding area since the outer diameter is fixed. The rotor yoke thickness has to be large enough to prevent the saturation problem, which is concluded in Fig. 1(e). It should be noted that when the rotor yoke thickness is large, the air-gap volume which stores the magnetic field energy is reduced as well as the winding area. The comparison between proposed machine and conventional FTVPM machine is discussed. The same main parameters are shown in Fig. 2(a). The proposed machine is 18/17-pole with one-pole-pair winding and the conventional topology is 18/13-pole with five-pole-pair winding. The no-load flux density at the air-gap is investigated to find out the harmonic characteristic of proposed machine. As can be seen in Fig. 2(c), the 5th and 13th harmonic of FTVPM are both larger that the fundamental and 17th harmonic of proposed machine. But as a VPM machine, the rotor with 17 pole-pair has larger pole ratio, which means the modulated magnetic field rotates faster. Meanwhile the proposed topology makes phase coil link more flux linkage, so the open circuit back-EMF is 2.45 times that of the conventional one. Moreover, according to Fig. 2(e), the proposed structure can provide larger average torque while maintain a low torque ripple. It is because the magnitude of torque ripple is inversely proportional to the lowest common multiple (LCM) of the number of stator and rotor pole pairs. III. Conclusion The split-pole fault-tolerant VPM machine is proposed in this paper. The topology and operation principle are presented. The FEA results show that the proposed structure takes advantage of large torque, low torque ripple, short end turn length and fault-tolerant capability. Compared with conventional FTVPM machine, the proposed machine can produce 145% higher output torque under the same copper loss. The analytical analysis and experiment results will be added in the full paper.

**References:**

[1] G. Liu, J. Yang and W. Zhao, IEEE Trans. on Magn., vol. 48, no. 11 (2012) [2] L. Xu, G. Liu and W. Zhao, IEEE Trans. on Energy Conversion, vol. 30, no. 4 (2015) [3] D. Li, R. Qu and J. Li, 2014 IEEE Energy Conversion Congr. and Expo., (2014)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e430a86c7bc6ac3985a6b6ff99d41d37.jpg)
Fig. 1. (a) Topologies of both machines. (b) Influence of modular tooth width on torque. (c) Influence of fault-tolerant tooth width on torque. (d) Influence of stator and rotor PM thickness on torque. (e) Influence of rotor yoke thickness on torque. (f) Influence of stator and rotor PM ratio on torque.

![](https://assets.underline.io/uploads/markdown_image/1/image/a159a16b049e0040224d3c011ce46c4a.jpg)
Fig. 2. (a) Main parameters of both topologies. (b) Flux density waveforms at the air-gap. (c) Flux density spectra at the air-gap. (d) Open-circuit back-EMF. (e) Torque performances

 Design and Analysis of Novel Split-Pole Fault-Tolerant Vernier Permanent Magneic Machine

—A novel dual permanent magnet (PM) dual three phase vernier machine is proposed for electric vehicles in this paper. Compared with conventional dual PM vernier machines, a dual three-phase winding connection is adopted to reduce sub-harmonics and improve working harmonics at the same time. The dual three-phase windings supplied by two separate converters can improve the reliability of the machine driving systems, which is an important issue in electric vehicles. Therefore, this proposed machine exhibits higher torque density, higher reliability, lower force ripple, and lower unbalanced force. The simulation result shows that with the proposed dual three phase winding, the torque is improved by 3.9% while the torque ripple and unbalanced force are reduced about 50% and 72.5%, respectively. Index Terms—Concentrate winding, permanent magnet, torque density, vernier machine. Introduction With the emergence and widespread use of automobiles, people's lives have been highly improved. However, while the cars bring convenience in our lives, they also cause excessive consumption of non-renewable energies and the emission of greenhouse gasses at the same time, which have aggravated environmental pollution. To solve these problems, electric vehicles are a potential solution. Therefore, the motors, which are the key components in the electric vehicles' driving system, have attracted a lot of attention in recent years. The induction motor and permanent magnet (PM) motor are the two main types of motors used in electric vehicles. Compared to the induction motor, the PM motor has higher power density, lower copper loss and smaller volume; hence it has become the mainstream in academia and commercial applications. However, there are only limited pole and slot combinations which have been investigated due to the high iron loss and unbalanced force under high-speed operation in electric vehicles. In this paper a novel dual three phase dual PM vernier machine with high torque density and low unbalanced force is proposed. Its structure will be presented first. Then the operation principle is illustrated, and the performance of the motor is shown. Structure, Operation Principle and Performance The structure of the proposed motor is shown in Fig. 1. The outer diameter is 220mm and the rated speed is 3980rpm. It has 12 slots and 10 poles; PMs are employed on both the rotor and stator. The windings on the stator are fractional slot concentrated windings (FSCWs). All the armature windings can be divided into two sets of 3 phases windings which are supplied by two separate converters. The two converters supply phase A1, B1 and C1, and phase A2, B2 and C2, which has π/6 shift. This arrangement can improve the fault tolerance capability since the motor can operate under one set of winding when a failure occurs in the other one. Referring to [1], the MMF of armature windings adopting dual three structure can be given as Ft(t,θ)=∑k=1,-5,7...∝(12NI/kπ)sin(kπ/12)sin((k-1)π/12)sin(kθ-ωt-(k-1)π/12) According to the equation, it is obvious that by adopting dual three structure, the subharmonic can be eliminated, and the 5th, 7th, 17th and 19th harmonics can be increased. Considering the modulation effect, the working harmonics of the proposed motor can be obtained which are 5th, 7th and 17th. Therefore, the output torque of the proposed motor is increased, and the torque ripple reduced. The analytical result is verified by 2-D FE analysis. Fig. 2 shows the torque comparison between the conventional dual PM vernier machine and the proposed one. It can be seen that the output torque increases 3.9% from 148Nm to 154Nm and the torque ripple reduces about 50% from 2.75% to 1.4%. The proposed machine not only improves the torque performances, but also the core loss and unbalanced force. After applying this structure, the unbalanced force is reduced a lot, which is from 1158.2N to 318.54N. The efficiency and torque density are also improved a little bit from 96.63% to 96.77% and 3.54*10-5 Nm/mm3 to 3.68*10-5 Nm/mm3. Conclusion A novel dual three phase dual PM machine is proposed in this paper. The structure, operation principle and the performance are analyzed. The simulation result shows that adopting this novel structure can reduce the subharmonics and improve the working harmonics. It increases the output torque, reduces the torque ripple and unbalanced force. It is a very effective way to improve the performance and more detailed characteristics will be reported in full paper.

**References:**

[1] A. S. Abdel-Khalik, S. Ahmed and A. M. Massoud, IEEE Trans. Magn., Vol. 51, p. 1-10 (2015). [2] Q. Wang, S. Niu and L. Yang, IEEE Trans. Ind. Electron., Vol. 64, p. 9924-9933 (2017).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bf5f772e696b4639e00ea3daa4addbc4.jpg)
Fig.1. Structure of the proposed motor.

![](https://assets.underline.io/uploads/markdown_image/1/image/85e8edc3a6931d4de9baf4ac75941535.jpg)
Fig. 2. Output torque comparison.

 Analysis of a Novel Dual-PM Vernier Machine with High Torque Density and Low Torque Ripple and Unbalanced Force

1. Introduction Vernier permanent magnet machines(VPMM) have a simple structure and high torque density due to the so-called magnetic-gear effect and are very suitable for direct drive applications, such as wind power turbines and electric vehicles [1]. In addition, the VPMM has low pulsing torque due to its more sinusoidal back-EMF, compared with traditional designs of PM machines [2]. However, the power factor of the VPMM is relatively low (sometimes even below 0.3), which requires a converter with a larger capacity for the fixed output power [1]. Many researchers have been carried out to address this problem and some improvements in structure have also been studied in recent decades. Vernier structure was proposed in the early 19th century and then applied to stepping motors [3]. The VPMM as a unique electromechanical device is firstly derived from the earlier Vernier reluctance machine [4-5]. Further, dual-excitation VPMM is invented with a dual stator and toroidal winding, which not only has high torque density at low speed but also improves space utilization [6]. In [7-8], dual-excitation VPMM is further investigated. A generic torque maximizing design methodology for the motor is proposed to improve the torque density in the machine in [6], and a new structure constructed with interior PM, spoke-array rotor, and dual-stator with a displacement of half slot is proposed to improve the power factor and the pole shoe was also investigated to further improve the torque performance [7-8]. In this paper, a novel effective, and convenient method aiming to improve the torque density and power factor of DS-VPMM is proposed. The key is to rotate the inset-type PMs in the rotor with a certain electrical angle as well as the excitation direction and it is found that the flux leakage is significantly reduced in the air-gaps and the flux distribution in the inner and outer stator windings can be compensated with each other. Hence not only the back-EMF and torque are boosted but also the power factor is greatly improved. The paper is organized as follows. The operation principles including the structure and magnetic field analyses are introduced first. In the third section, the electromagnetic characteristics of this machine are evaluated based on FEM analyses, including flux density in the two air gaps and their harmonic investigation to find the effective components of the flux density. Besides, back-EMF, cogging torque, and on-load torque, as well as torque density and power factor will be analyzed. Machines with different rotation angles are studied and compared. The power factor improving method proposed in this paper can also be extended to other machines to improve the torque density within a limited peripheral. 2. Machine Topology The original design of DS-VPMM is as shown in Fig.1 (a). A flux concentrating structure using spoke-array magnets rotor to increase the useful magnet flux and decrease the flux leakage between adjacent PMs is adopted. The stator has a tooth-pole structure, which functions as modulation pieces in a flux modulate machine. The windings with yellow, green, and red color refer to phase A, B, C respectively. Fig. 1 (b) shows the DS-VPMM that adopts the proposed method to rotate the inserted PMs as well as their excitation directions with a certain angle. The other parts of DS-VPMM are kept the same. Windings of inner and outer stators can be connected independently or series according to the applications. In order to investigate more explicitly, the windings of two stators are connected independently in this paper. This machine follows the following rule [7]: Z2 =Z1-p or Z1+p (1) where p, Z1, Z2 are the pole-pair number (PPN) of winding, stator teeth, and rotor, respectively. According to the modulation effect of magnet gear, the main effective harmonic order will be 1st and 11th order harmonics. 3. Initial Investigation Results Fig. 2 shows the variations of torque and power factor when changing the rotation angle of the inset-type PMs in the rotor iron core. It can be found that the highest torque density is 24.275 KN/m3, whereas the power factor is 0.726. Since a rotation angle of 15 degrees exhibits a more preferable power factor, the torque of the machine with a 15-degree rotation angle versus the current control angle is investigated and shown in Fig. 12. It is found that when the current control angle is 55 degrees, the power factor can reach nearly 0.8. The torque reaches the highest value when the current control angle is nearly 30 degrees and the power factor is around 0.7 at this control angle. In this abstract, only one machine topologies and its investigation results are shown. More machines applied with this method will be investigated in the full paper. 4. Conclusion A novel method to improve the power factor of VPMM machine is proposed in this paper and the analyses are strongly proved that this method is efficient and the power factor can be improved nearly to 0.8 which is significantly higher than the traditional VPMM. In addition, through the rotation of PMs, the machine can get more space for PMs, thus obtaining higher torque density within the limited volume.

**References:**

[1] G. Eason, B. Noble, and I. N. Sneddon, Phil. Trans. Roy. Soc. London, vol. A247, pp. 529-551(1955) [2] A. Ishizaki, T. Tanaka, K. Takasaki, Electrical Machines and Drives Seventh International Conference(2002) [3] C. H. Lee, IEEE Trans. Power App. And Syst., vol.82, no. 66, pp. 343-349(2007) [4] T. Toba, T. A. Lipo, Conference Record of the 1999 IEEE Industry App. Conference, vol.4, pp.2539-2544(2002) [5] A. Toba, T. A. Lipo, IEEE Trans. Indus. Appl., vol. 36, no. 6, pp. 1539-1546(2002) [6] Dawei Lin, Ronghai Qu, Thomas A. Lipo, IEEE Trans. Indus. Appl., vol.50, no.6, pp. 3664-3674(2014) [7] Dawei Li, Ronghai Qu, Jian Li, IEEE Energy Conversion Congress and Exposition, pp. 1885-1891(2015) [8] Ronghia Qu, Dawei Li, Jin Wang, 2011 International Conference on Electrical Machines and Systems, pp. 1-6(2011)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/afa91c099179c87a719ab4a8bb270ff7.jpg)
Fig. 1. The topology of the DS-VPMM. (a) Initial machine structure. (b) Machine with the rotated PMs.

![](https://assets.underline.io/uploads/markdown_image/1/image/293e2aaa11b0471adf5d1f87a9e9aff9.jpg)
Fig. 2. Power factor and torque versus rotor-PM rotation angle.

Analysis of 12 Slots Novel DC-Biased Dual-PM Vernier Machines with Slot-Opening PMs

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