France



I.INTRODUCTION&lt;br/&gt;The flux reversal permanent magnet (FRPM) machine, as a stator PM machine with a simple rotor configuration, is suitable for high speed electric propulsion applications However, the conventional 6-slot and 8-pole (6s/8p) FRPM machine has some disadvantages, such as low torque density and large torque ripple.&lt;br/&gt;An axial modular flux reversal permanent magnet (AM-FRPM) machine is proposed in this paper as shown in Fig. 1. It contains two modular parts including front modular part 1 and rear modular part 2, and the modular part topology evolves from the conventional 6s/8p FRPM machine. It is worth noting that the PMs of two modular parts have opposite magnetization directions at the same stator position. Meanwhile, the rotor poles in the rear part are shifted by 22.5° mechanically relative to those in the front part. In addition, the toroidal windings are wound around the yokes of the AM-FRPM machine, which are different from those of conventional FRPM machines. Besides, the winding factor is set as 1 to obtain a high torque density.&lt;br/&gt;&lt;br/&gt;II.PRINCIPLES AND PERFORMANCE&lt;br/&gt;Based on the magnetic field modulation theory, the operating principle of AM-FRPM machine is analyzed from three perspectives, including PM field modulation, armature reaction field modulation and torque production mechanism.&lt;br/&gt;For the PM field, the PM magneto-motive-force (MMF) of each modular part is modulated by the corresponding modular salient rotor teeth [1]. Then the air gap flux density expression &lt;i&gt;B&lt;/i&gt;&lt;i&gt;&lt;sub&gt;g&lt;/sub&gt;&lt;/i&gt; can be deduced, which contains the harmonics components (HCs) with |&lt;i&gt;n&lt;/i&gt;&lt;i&gt;P&lt;/i&gt;&lt;i&gt;&lt;sub&gt;s&lt;/sub&gt;&lt;/i&gt;±&lt;i&gt;kP&lt;/i&gt;&lt;i&gt;&lt;sub&gt;r&lt;/sub&gt;&lt;/i&gt;| order, where &lt;i&gt;P&lt;/i&gt;&lt;i&gt;&lt;sub&gt;s&lt;/sub&gt;&lt;/i&gt; is the number of stator slots, &lt;i&gt;P&lt;/i&gt;&lt;i&gt;&lt;sub&gt;r&lt;/sub&gt;&lt;/i&gt; is rotor poles number, &lt;i&gt;n&lt;/i&gt;=1, 2…, and &lt;i&gt;k&lt;/i&gt;=0, 1, 2…. The air-gap flux density harmonics distributions of the PM field are shown in Fig. 2(a). It can be found that harmonics distributions of two modular parts are similar, and the dominant harmonics components are 2nd, 4th, 6th, 12th, 14th and 24th orders, which verifies the HCs results by the field modulation theory. PMs of the two modular parts have opposite magnetization directions at the same stator position, so the phases differences of the flux density harmonics generated by the PM MMF, such as 6th, 12th and 24th, are 180&lt;sup&gt;o&lt;/sup&gt; between two parts. Besides, the PM-MMFs are modulated by two rotor parts with different initial angles, so the phases of modulated harmonics in two parts are also different. In addition, based on the flux density harmonics phases analysis, the PM flux linkages harmonics with even orders are cancelled as shown in Fig. 2(b).&lt;br/&gt;The armature reaction MMF mathematic model of the AM-FRPM machine cannot be obtained by three phases overlapping directly because its winding function is different from that of the conventional FRPM machine. The reason is that the armature coils of the AM-FRPM machine are with the same direction. Hence, the armature reaction MMF distributions need to consider three phases synchronously. In addition, the armature reaction MMF in two modular parts is modulated by the front and rear rotors in Fig. 1(a), respectively, then the armature reaction air gap flux density harmonics distributions can be obtained. It can be found from Fig. 2(c) that the number of HCs can be expressed as 2&lt;i&gt;k&lt;/i&gt; (&lt;i&gt;k&lt;/i&gt;=1, 2…), and the dominant harmonic orders are 2nd, 4th, 6th, 10th and 12th. It is worth noting that the rotors in two modular parts have different initial angle, and then the armature reaction flux density harmonic distributions of two parts obtain different harmonic performances, including amplitudes and phases. The harmonics characteristics analysis will be illustrated in detail in the full paper. Here it is clearly shown in Fig. 2(c) that the amplitudes of 4th harmonic in front and rear modular parts are 0.22T and 0.11T, respectively, which influence the harmonics contribution of electromagnetic torque.&lt;br/&gt;Based on the analysis of the PM field and the armature reaction field, it can be concluded that the electromagnetic torque is mainly contributed by the harmonics with 2nd, 4th, 6th and 12th orders. The 6th and 12th harmonics are generated by the PM MMF, while the 2nd and 4th harmonics are produced by the modulation of salient pole rotor on PM MMF. The electromagnetic torque waveforms are shown in the Fig. 2(d). It can be found that the torque ripples of front and rear modular parts are 8.4% and 8.3%, respectively, and the torque ripple of AM-FRPM machine is only 6.4%. Besides, the torque of front and rear modular are 5.23Nm and 5.24Nm, and the torque of AM-FRPM machine is 10.64Nm. The torque is generated by overlapping of two modular parts is 1.6% less than that of the whole machine, so the magnetic flux leakage between modular parts is small and the structure is compact.&lt;br/&gt;&lt;br/&gt;III.CONSLUSION&lt;br/&gt;The proposed AM-FRPM machine contains two modular parts and integrated toroidal windings. In this paper, the operating principle of the proposed machine was explained by the air gap field modulation theory. It can be found that the armature reaction flux density harmonic distributions of two parts obtain different harmonic performances. Besides, the AM-FRPM machine exhibits a high torque density and the torque ripple is suppressed effectively, which is suitable for electric vehicle applications.

**References:**

[1] X. Zhu and W. Hua, &quot;An Improved Configuration for Cogging Torque Reduction in Flux-Reversal Permanent Magnet Machines,&quot; in IEEE Transactions on Magnetics, vol. 53, no. 6, pp. 1-4, (2017).&lt;br/&gt;[2] X. Zhu, W. Hua and W. Wang, &quot;Analysis of Back-EMF in Flux-Reversal Permanent Magnet Machines by Air Gap Field Modulation Theory,&quot; in IEEE Transactions on Industrial Electronics, vol. 66, no. 5, pp. 3344-3355, (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/43d2798fc3d332c572d2e13b7e7dd580.jpg)
Fig.1  (a) The topology of AM-FRPM machine. (b) front modular part (c) rear modular part.

![](https://assets.underline.io/uploads/markdown_image/1/image/bd9cd746d7829d0311ec363aec69dd5e.jpg)
Fig.2  (a) The air-gap flux density harmonics distributions of PM field. (b) The harmonic spectrum of line flux linkage. (c)The air-gap flux density harmonics distributions of armature field. (d) Torque waveforms.

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 Analysis of Axial Modular Flux Reversal Permanent Magnet Machine

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I.INTRODUCTION The flux reversal permanent magnet (FRPM) machine, as a stator PM machine with a simple rotor configuration, is suitable for high speed electric propulsion applications However, the conventional 6-slot and 8-pole (6s/8p) FRPM machine has some disadvantages, such as low torque density and large torque ripple. An axial modular flux reversal permanent magnet (AM-FRPM) machine is proposed in this paper as shown in Fig. 1. It contains two modular parts including front modular part 1 and rear modular part 2, and the modular part topology evolves from the conventional 6s/8p FRPM machine. It is worth noting that the PMs of two modular parts have opposite magnetization directions at the same stator position. Meanwhile, the rotor poles in the rear part are shifted by 22.5° mechanically relative to those in the front part. In addition, the toroidal windings are wound around the yokes of the AM-FRPM machine, which are different from those of conventional FRPM machines. Besides, the winding factor is set as 1 to obtain a high torque density. II.PRINCIPLES AND PERFORMANCE Based on the magnetic field modulation theory, the operating principle of AM-FRPM machine is analyzed from three perspectives, including PM field modulation, armature reaction field modulation and torque production mechanism. For the PM field, the PM magneto-motive-force (MMF) of each modular part is modulated by the corresponding modular salient rotor teeth [1]. Then the air gap flux density expression Bg can be deduced, which contains the harmonics components (HCs) with |nPs±kPr| order, where Ps is the number of stator slots, Pr is rotor poles number, n=1, 2…, and k=0, 1, 2…. The air-gap flux density harmonics distributions of the PM field are shown in Fig. 2(a). It can be found that harmonics distributions of two modular parts are similar, and the dominant harmonics components are 2nd, 4th, 6th, 12th, 14th and 24th orders, which verifies the HCs results by the field modulation theory. PMs of the two modular parts have opposite magnetization directions at the same stator position, so the phases differences of the flux density harmonics generated by the PM MMF, such as 6th, 12th and 24th, are 180o between two parts. Besides, the PM-MMFs are modulated by two rotor parts with different initial angles, so the phases of modulated harmonics in two parts are also different. In addition, based on the flux density harmonics phases analysis, the PM flux linkages harmonics with even orders are cancelled as shown in Fig. 2(b). The armature reaction MMF mathematic model of the AM-FRPM machine cannot be obtained by three phases overlapping directly because its winding function is different from that of the conventional FRPM machine. The reason is that the armature coils of the AM-FRPM machine are with the same direction. Hence, the armature reaction MMF distributions need to consider three phases synchronously. In addition, the armature reaction MMF in two modular parts is modulated by the front and rear rotors in Fig. 1(a), respectively, then the armature reaction air gap flux density harmonics distributions can be obtained. It can be found from Fig. 2(c) that the number of HCs can be expressed as 2k (k=1, 2…), and the dominant harmonic orders are 2nd, 4th, 6th, 10th and 12th. It is worth noting that the rotors in two modular parts have different initial angle, and then the armature reaction flux density harmonic distributions of two parts obtain different harmonic performances, including amplitudes and phases. The harmonics characteristics analysis will be illustrated in detail in the full paper. Here it is clearly shown in Fig. 2(c) that the amplitudes of 4th harmonic in front and rear modular parts are 0.22T and 0.11T, respectively, which influence the harmonics contribution of electromagnetic torque. Based on the analysis of the PM field and the armature reaction field, it can be concluded that the electromagnetic torque is mainly contributed by the harmonics with 2nd, 4th, 6th and 12th orders. The 6th and 12th harmonics are generated by the PM MMF, while the 2nd and 4th harmonics are produced by the modulation of salient pole rotor on PM MMF. The electromagnetic torque waveforms are shown in the Fig. 2(d). It can be found that the torque ripples of front and rear modular parts are 8.4% and 8.3%, respectively, and the torque ripple of AM-FRPM machine is only 6.4%. Besides, the torque of front and rear modular are 5.23Nm and 5.24Nm, and the torque of AM-FRPM machine is 10.64Nm. The torque is generated by overlapping of two modular parts is 1.6% less than that of the whole machine, so the magnetic flux leakage between modular parts is small and the structure is compact. III.CONSLUSION The proposed AM-FRPM machine contains two modular parts and integrated toroidal windings. In this paper, the operating principle of the proposed machine was explained by the air gap field modulation theory. It can be found that the armature reaction flux density harmonic distributions of two parts obtain different harmonic performances. Besides, the AM-FRPM machine exhibits a high torque density and the torque ripple is suppressed effectively, which is suitable for electric vehicle applications.

**References:**

[1] X. Zhu and W. Hua, "An Improved Configuration for Cogging Torque Reduction in Flux-Reversal Permanent Magnet Machines," in IEEE Transactions on Magnetics, vol. 53, no. 6, pp. 1-4, (2017). [2] X. Zhu, W. Hua and W. Wang, "Analysis of Back-EMF in Flux-Reversal Permanent Magnet Machines by Air Gap Field Modulation Theory," in IEEE Transactions on Industrial Electronics, vol. 66, no. 5, pp. 3344-3355, (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/43d2798fc3d332c572d2e13b7e7dd580.jpg)
Fig.1 (a) The topology of AM-FRPM machine. (b) front modular part (c) rear modular part.

![](https://assets.underline.io/uploads/markdown_image/1/image/bd9cd746d7829d0311ec363aec69dd5e.jpg)
Fig.2 (a) The air-gap flux density harmonics distributions of PM field. (b) The harmonic spectrum of line flux linkage. (c)The air-gap flux density harmonics distributions of armature field. (d) Torque waveforms.

poster

-Introduction Smartphones are widely used in daily routines, and microspeakers are widely used in these devices for sound generation. The sound is important since they provide immersive experience when consuming multimedia contents. Therefore, acoustic performance of the microspeaker is an important feature for consumers when selecting smartphones. A round shape microspeaker was widely used in earlier version of cellular phones. The circular or elliptical microspeaker was designed and analyzed [1]. A rectangular microspeaker was developed to utilize the internal space in cellular phone more efficiently [2]. Lee et al. developed a rectangular microspeaker for acoustic performance improvement. Using a piezoelectric effect, engineers developed a piezoelectric speaker [4]. For smartphone featuring bezel-less display, indirect- and direct-vibration actuators were developed [5,6]. In the past, a few components inside the smartphone provided sufficient space for the microspeakers. However, recent design trend to bezel-less display and the slimmer design started to limit the allowable space for the microspeaker. In addition, many components such as sensors, stylus pen, etc., are mounted around the microspeaker that limit the allowable space. These trends reduce back volume of microspeaker that affect the acoustic performance which is SPL (Sound Pressure Level). The back volume is a sealed air volume under the diaphragm that affects acoustic performance. Reduced back volume adds an additional stiffness to the microspeaker system that increase the resonant frequency and decrease SPL at low frequencies. The smaller the back volume, the lower the SPL at low frequency. The prototype microspeaker termed as 1410_1VC consists of single coil with resistance of 6 Ω (DCR). The 1410_1VC can’t provide sufficient SPL at low frequency when placed in small back volume of 0.25 cc. To address this problem, a new microspeaker must be designed. In this paper, while remaining identical exterior size to the prototype, a novel dual-coil microspeaker termed as 1410_2VC is designed and analyzed for low frequency SPL enhancement. - Analysis methods and verifications by experiment (Prototype) The microspeaker is multiphysics system that consists of three domains which are electromagnetic, mechanical and acoustic domain, and they are coupled with certain parameters. The SPL can be obtained by solving theses multiphysics system with coupled analysis. Coupled analysis are conducted for obtaining SPL and displacement using 3D FEA (Finite Element Analysis). The SPL measurement of the prototype 1410_1VC was conducted in an anechoic chamber shown in Fig. 2 (a). The SPL and displacement are measured by B&K equipment and Klippel equipment, respectively. The analysis methods are verified comparing experimental and simulated data which show good agreement. The acoustic performance of the microspeaker at low frequency can be represented by arithmetic mean (average) of SPL at four frequencies which are 200 Hz, 300 Hz, 500 Hz and 700 Hz. The SPL at low frequency of the 1410_1VC is 80.98 dB. -New Microspeaker Design The moveable mass of the speaker consists of coil, center diaphragm, side diaphragm. Increasing moveable mass will decrease the resonant frequency leading to enhanced low frequency SPL. Among components consisting moveable mass, the coil is the heaviest component, and has the highest mechanical density. Maintaining same resistance, the coil mass can be increased by using large diameter coil. Changes in coil design cause magnetic circuit design modifications and affects electromagnetic force which is Lorentz force. The magnetic circuit includes top plates, coil, yoke and magnets. Thus, coil design is an important factor for the performance improvement. The 1410_1VC has a single coil with resistance, diameter, mass and total length as 6Ω, 0.077mm, 69.93mg, 1675.7mm, and 0.499N, respectively. Maintaining same DCR 6 Ω, dual coil can be connected in series with each coil of 3Ω, or parallel with each coil of 12Ω. The coil diameter is chosen to match height of the prototype 1410_1VC coil. The parallel connection shows the inferior force to the series because thicker coil resulted in lower flux density. Two 3Ω coils connected in series are designed with the diameter of 0.084 mm. Instead of two permanent magnets used in 1410_1VC, total seven magnets are used. The yoke is identical to the prototype. Put together, newly designed 1410_2VC has total mass, total length and Lorentz force as 93.4 mg, 1929.2 mm and 0.542 N, respectively. The structure and manufactured sample are shown in Fig. 1 (a) and (b). The SPL and displacement of 1410_2VC are measured through experiments. - Result The experimental data of the prototype and newly designed microspeaker are compared as shown in Fig. 2 (b). The results show that average SPL of 1410_2VC at low frequencies is 83.25 dB. It is 2.27 dB higher than 1410_1VC which is significant improvement. Remaining same exterior size, using dual coils and novel magnetic circuit, low frequency SPL is improved.

**References:**

 [1]. S.M. Hwang, G.Y. Hwag, J.H. Kwon, et al. “Performance comparison between circular and elliptical type micro-speakers for cellular phones.” IEEE Trans. Magn., Vol. 39, p. 3256–3258 (2003) [2] J.H. Kwon, S.M. Hwang, K.S. Kim, et al. “Development of slim rectangular microspeaker used for minimultimedia phones.” IEEE Trans. Magn., Vol.43, p. 2704–2706 (2016) [3] C.M. Lee, and S.M. Hwang, “Development of advanced rectangular microspeakers used for wide liquid-crystal display mobile phones.” J. Appl. Phys., Vol.109, p. 07E504 (2011) [4] S.H. Tseng, S.C. Lo, Y. J. Wang, et al. “Sound Pressure and Low Frequency Enhancement Using Novel PZT MEMS Microspeaker Design.” In Proceedings of the 2020 IEEE 33rd International Conference on Micro Electro Mechanical Systems (MEMS), p. 546–549 (2020) [5] J.H. Kim; Y.W. Jiang and S.M. Hwang, “Analysis and Design of New Actuator Used for Full-Wide Screen LCD.” Appl. Sci., Vol.9, p. 4599 (2019) [6] K. H. Park, Z.X. Jiang, Y. W. Jiang, et al. “Development of Direct-Vibration Actuator for Bezel-Less Display Panels on Mobile Phones.” Appl. Sci., Vol. 10, p. 4975 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bae3b24165b8c6a5be00fdedb2c851ad.jpg)
Fig. 1 Structure and manufacutrd componets of new microspeaker

![](https://assets.underline.io/uploads/markdown_image/1/image/a007f77e153a79dfd22ab5f5d7c235fc.jpg)
Fig.2 Experiment setup and result

 Novel dual coil microspeaker with reduced back volume

A biopsy is a medical test to examine the presence or extent of a disease using tools such as a scalpel, a needle, and forceps to extract sample tissues from a patient’s body. While excisional or needle aspiration biopsies take a tissue sample close to human skin, endoscopic or cardiac biopsies collect sample tissues located deep inside the human body by inserting a long tube or catheter along the tubular structure of the human body. Conventional wired biopsies have low steering ability and controllability, and mostly depend on the experience of physicians. Since a target region is sometimes located in a complicated and twisted tubular environment, conventional methods have limitations on reaching the narrow target region. Also, there is a possibility of causing bacteremia due to the penetration of external bacteria into the patient's body through the wires [1], [2]. This may cause sepsis in patients who have low levels of immunity and could lead to death [3], [4]. To overcome these problems, many researchers have studied wireless biopsy robots. Previous researchers have mainly explored biopsy robots for capsule endoscopes. However, such robots do not have their own propulsive force and are driven by the passive peristaltic motion of the intestine. In this paper, we propose a crawling biopsy robot (CBR) that can wirelessly crawl and perform biopsies in tubular environments. The proposed CBR performs various mechanical actions under the control of an external magnetic field, such as a crawling motion with the needle covered, an uncovering motion to expose the needle, the insertion of the needle into the target area, and a covering motion of the needle after the collection of sample tissues. Fig. 1 shows the structure of the proposed CBR, composed of a crawling part and a biopsy part. The crawling part is composed of three crawling bodies, and each crawling body contains an axially magnetized cylindrical magnet (CM) and two flexible legs. Each crawling body is freely rotatable with respect to the y-axis, and the motion of the crawling body is controlled using an external precessional magnetic field for stable navigation and needle insertion. When the CBR reaches a target area, the CBR is designed to open the cover to expose a needle to a target area by controlling the external magnetic field. Once the cover opens, the forward crawling motion of the CBR inserts the needle into the target area. Then, the backward crawling motion takes the needle out of the target area and automatically closes the cover to carry the needle and sampled tissues independently of the crawling motion; this is accomplished by controlling the external magnetic field. To verify the functions of CBR, we made a prototype of CBR using 3D printing technology except for the legs and magnets. The crawling legs are made of silicon rubber, and all magnets are NdFeB 45. The first experiment using the prototype of CBR was measuring the puncturing force of CBR. The proposed CBR should generate a puncturing force enough to insert a needle into the tissue to collect sample tissue. According to Yang et al. [5], a minimum force of 0.3 N is required to puncture the liver tissue of pigs. To verify the puncturing force of CBR, an experiment was done using load cell (Honeywell, Morris Plains, NJ, USA). The pseudo glass tube containing the CBR was fixed in a water container, and a jig connected to the load cell was placed in front of the pseudo glass tube. The experimental setup was then placed inside of the magnetic navigation system which generated external magnetic field [6]. The puncturing force was 0.46 N when the magnitude and the rotational frequency of the external precessional magnetic field were 14 mT and 25 Hz. The second experiment was to evaluate the crawling motion and biopsy performance of the CBR. We used a pseudo tissue made of agar filled at one end of a Y-shaped watery glass tube with a diameter of 14 mm, as shown in Fig. 2(a). In step 1, the CBR crawled to a target point, propelled by the external precessional magnetic field (B=8 mT, f=15 Hz, δ=30°), and the cover was closed during navigation as shown in Fig. 2(b). In the bifurcated branch, we controlled the joystick to change the unit vector of the rotating axis (N), which can be accomplished by controlling the applied currents of the developed MNS. In step 2, the cover was opened by a uniform magnetic field of 12 mT. In step 3, the uncovered biopsy needle punctured the tissue by the crawling motion generated by the external precessional magnetic field (B=14 mT, f=25 Hz, δ=30°). In step 4, the turning motions of the crawling bodies and flexible legs along the y-axis as well as the covering motion of the biopsy needle were performed by rotating the uniform magnetic field of 12 mT by 180° along the y-axis. Finally, in step 5, the CBR crawled back to the original point, propelled by the external precessional magnetic field (B=12 mT, f=15 Hz, δ =30°). Fig. 2 (c) shows the uncovered needle before the biopsy needle was inserted into the pseudo tissue. Fig. 2(d) shows a sampled tissue of 1-mm thickness extracted through this experiment. We confirmed from this experiment that the proposed CBR could crawl through a tubular structure and extract sample tissue successfully.

**References:**

[1] J. Rizzo, D. Bernstein, and F. Gress, Gastrointest. Endosc., vol. 51, no. 3, pp. 257–261, Mar. 2000. [2] K. A. Marr, Ann. Intern. Med., vol. 127, no. 4, p. 275, Aug. 1997. [3] C. Brun-Buisson, F. Doyon, and J. Carlet, Am. J. Respir. Crit. Care Med., vol. 154, no. 3, pp. 617–624, Sep. 1996. [4] M. H. Samore, M. A. Wessolossky, and A. W. Karchmer, Am. J. Cardiol., vol. 79, no. 7, pp. 873–877, Apr. 1997. [5] H. Yang, P. X. Liu, and J. Zhang, IEEE International Conference Mechatronics and Automation, 2005, 2005, vol. 2, p. 592–595 Vol. 2. [6] S. Jeon, G. Jang, H. Choi, and S. Park, IEEE Trans. Magn., vol. 46, no. 6, pp. 1943–1946, Jun. 2010

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d741c5f391854d56b44ea0b7884f5985.jpg)
Fig. 1. (a) Proposed CBR composed of a crawling part and a biopsy part. (b) Structure of a crawling body. (c) Structure of a biopsy part.

![](https://assets.underline.io/uploads/markdown_image/1/image/c2f464a6517e18db9ae42e258ef2f869.jpg)
Fig. 2. (a) Experiment testing the crawling and biopsy motions. (b) Covered needle. (c) Uncovered needle. (d) Collected sample tissue.

 Crawling Biopsy Robot Magnetically Actuated in Tubular Environments

Recently, Inertia Force Generators (IFGs) was reported to reduce undesirable vibrations in automobiles and precision devices, which consists linear oscillatory actuators (LOAs), sensors and a controller. In the IFG, inertia force for reducing vibrations that generated by the LOA is controlled by a controller and sensors [1]. Here, the LOA should effectively generate inertia force at wide frequency range because the frequency range of undesirable vibrations is wide. However, the conventional LOA can effectively generate inertia force at narrow frequency range because of one mechanical resonance. In this abstract, a LOA with two movers which can effectively drive using two mechanical resonance is developed and the pole configuration is discussed. The proposed LOA mainly consists a stator, an outer mover (0.485 kg) and an inner mover (0.545 kg), as shown in Fig. 1. The stator and outer mover are connected by two leaf springs (totally 139.4 N/mm), and the stator and inner mover are also connected by two leaf springs (totally 44.4 N/mm). The stator is mainly composed of 16 coils and yokes, and the outer and inner movers are mainly composed of magnets and a yoke. Magnets are magnetized at positive or negative radial-direction, and these are axial-directionally arranged with 4 magnetic poles in outer mover, and these are arranged with 8 magnetic poles in inner mover. Coil 1, 2, 5, 6, 9, 10, 13 and 14 are wound clockwise and others are wound counterclockwise. Then, Coil 1, 4, 5, 8, 9, 12, 13 and 16 are connected in series that are called as coil group 1, and others are connected in series that are called as coil group 2. Same-phase or reverse-phase current is applied to coil groups. Here, the former is sinusoidal current with same-amplitude and same-phase in coil groups, and the latter is sinusoidal current with same-amplitude and reverse-phase in coil groups. The 4 poles outer mover is reacted with magnetic fluxes generated by same-phase current, and the 8 poles inner mover is reacted with magnetic fluxes generated by reverse-phase current. In this way, two movers can be independently driven by controlling current. Also, the two movers simultaneously oscillate by superimposing with same- and reverse-phase current. By driving of movers, inertia force is effectively generated at two frequency range because of two mechanical resonance. Next, it is compared between a LOA with 2 and 3 poles movers [2] and the proposed LOA which has 4 and 8 poles movers. In the former, unintentional attractive force was generated between a 3 magnetic-poles and 2 magnetic-poles movers when no current was applied at initial condition because pole-combination of movers is odd and even numbers. So, it must be canceled out by mechanical springs that may have manufactured error or deterioration. In the latter, unintentional attractive force is made to theoretically be zero because that is different even and even numbers. By electromagnetic analysis using 2-D EFM [3], attractive force in the former LOA was calculated as 28.5 N and -9.5 N at each mover, and that in the latter LOA was calculated as 0 N at all movers. Thus, it was verified that the pole combination of the proposed LOA is effective to reduce the attractive force. The prototype of the proposed LOA is manufactured as shown in Fig. 1. The accelerations of outer and inner movers are measured when same-phase or reverse-phase currents with amplitude 0.5 A is applied at each frequency. Then, inertia force is calculated by multiplying measured accelerations and mover’s mass together. As shown in Fig. 2, an outer mover was mainly oscillated when applying same-phase current, and an inner mover was mainly oscillated when applying reverse-phase current. Then, large inertia force was obtained with two frequency at 37 and 84 Hz because of mechanical resonances of the outer and inner movers. For comparison, each mover positions are calculated using motion equations with current thrust and detent characteristics that derived from electromagnetic analysis, and analyzed inertia force is calculated. As shown in Fig. 2, measured results almost agreed with analyzed results.

**References:**

[1] M. Tagami, T. Yamashita and Y. Tagawa et al., Journal of System design and Dynamics., Vol. 2, No. 2, pp. 507-517 (2008) [2] F. Kitayama, K. Hirata and R. Kondo, Proceedings of XXIIIrd International Conference on Electrical Machines., pp. 1586-1592 (2018) [3] A. Yoshitake, K. Harada and T. Todata et al., IEEE transactions on Magnetics, Vol. 33, No.2, pp. 1662-1665 (1997)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/19613de9e4f5f03d0a2df58b863674f4.jpg)
Fig. 1 Proposed LOA.

![](https://assets.underline.io/uploads/markdown_image/1/image/509c3ff2c0a3b0ffbae213910d6fbae5.jpg)
Fig. 2 Measured and analyzed inertia force.

 Development of Linear Oscillatory Actuator with 4 poles and 8 poles Movers.

In recent years, electromagnetic propulsion technology has made many breakthroughs in the fields of aircraft launch and advanced artillery [1]. With the help of pulse strong current, electromagnetic propulsion technology can achieve a target speed of 2000 m/s or higher in a few milliseconds [2]. During the propulsion, the strong magnetic field generated by input pulse current interacts with the armature current to produce electromagnetic force, which propel the armature and the load. At the same time, the high-velocity of the armature will change the current distribution inside the rail and armature, and affect the magnetic field around the armature. However, the magneto-mechanical coupled simulation of moving armature cannot be solved by commercial software. Many scholars have overcome this problem by using various simplified, but it is not sure whether these methods will affect the accuracy of simulation results [3]. Therefore, the measurement is a relatively intuitive research method. In this work, we propose a multi parameter measurement method of magneto-mechanical coupled effect. The acceleration sensor, linear Hall sensor, Hall switch, signal processing module, memory module and control module are integrated into a 27*30 mm storage testing system. Fig.1a is a simulation model of electromagnetic propulsion system considering velocity skin effect. The influence of velocity skin effect on the current distribution in the rail and armature is simulated by reducing the thickness of the rail and the contact area between the rail and armature. Fig.1b is the storage testing system. Fig.2 is the comparison of dynamic storage test results, in which the velocity signal is obtained by integrating the acceleration signal. According to the test value, we can divide the electromagnetic propulsion process into three phases. In the first phase of 0 - 0.75 ms, the armature is stationary due to the influence of preload and static friction. The magnetic induction intensity is affected by the current in armature and rails, and continuously rises to 0.58 T; The second phase is 0.75 - 7.8 ms, when the armature is moving, the velocity increases continuously and reaches the maximum of 844 m/s in 7.8 ms. After that the armature flew out of the rails. At this phase, the maximum magnetic induction intensity is 2.2 T, and it is reduced to 0.54 T when the armature flew out. The third phase is 7.8 -10.75 ms, as the armature flew out of the rails. The circuit disconnected, and the magnetic induction intensity is reduced to 0. Among them, the change of Hall switch corresponds to the value of magnetic induction. The jumping time of Hall switch signal partly reflects the starting time and muzzle time of armature movement, which can be used as a simple method to judge muzzle time. However, the time error at the starting time and muzzle time is 0.75 ms and 2.45 ms, which needs to be corrected by introducing a correction coefficient.

**References:**

[1]. H. D. Fair. Advances in electromagnetic launch science and technology and its applications[J]. IEEE Transactions on Magnetics, vol. 45, no. 1, pp. 225–230, Jan. 2009. [2]. Li J, Li S, Liu P, et al. Design and Testing of a 10-MJ Electromagnetic Launch Facility[J]. IEEE Transactions on Plasma Science, vol. 39, no. 4, pp.1187-1191, Apr. 2011. [3]. Yin Q , Zhang H , Li H J , et al. Analysis of in-bore magnetic field in C-Shaped armature railguns[J]. Defence Technology, vol. 15, pp. 83–88, Feb. 2019.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a76f2ed704774749b74c4eeca0cc23e5.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/eb5c03e051f27581a78b6bf85c96ef2b.jpg)

 Analysis of magneto-mechanical coupled effect on electromagnetic propulsion

This paper investigates a design method of a Halbach magnet array which can produce multiple MMFs with desired amplitudes and phase position. The construction process and the operation principle of this new type of Halbach array is introduced in this digest. It reveals that through adjusting the proportion of two main working MMFs, higher back EMF and torque density can be achieved than the Halbach flux reversal machines with only one fundamental MMF. I. Introduction Flux modulation machines are attractive for their high torque density due to the magnetic gear effect. It has been validated that multiple airgap flux harmonics can both contribute to the back EMF and torque in flux modulation machines [1]. In stator PM flux modulation machines such as flux switching and flux reversal machines [2], multiple static MMF harmonics can be modulated by single rotor permeance and generate multiple airgap flux harmonics with same frequency, therefore can both contribute to the total back EMF. Different from regular stator PM machine with only fundamental MMF and its odd harmonics, recently a new kind of stator PM flux modulation machines with unequal magnet thickness has been proposed in [3]-[4]. By adjusting the pole arc of each magnet, several other stator MMFs can be generated, and more airgap working harmonics can be introduced to enhance 10% back EMF and torque capacity of machines. However, the oriented design of each working MMF has not been achieved yet in these papers. In [5], the analytical model of Halbach PM array with unequal pole arcs and arbitrary magnetizing directions has been proposed, which can be optimized with algorithm to get multiple main MMFs, but the processing and manufacturing is difficult. In this paper, a design method of Halbach PM array with only radial and tangential magnets has been proposed to produce multiple MMF harmonics with required amplitudes and phase angles. Then, the method is applied into the optimization of Halbach flux reversal machines. II. Forming Process of Multi-MMF Halbach PM Array The forming process of Halbach PM array with two main MMFs is illustrated in Fig. 1. At first, the amplitudes and phase angle of each required MMF harmonic are given, the ideal sine wave of these two MMFs can be presented, respectively. By the accumulation of these two sinusoidal MMFs, a composite MMF can be presented, which has irregular shape and is hard to process. Then, through setting positive and negative threshold values, the composite MMF can be simplified into 3-step PWM composite MMF form. According to this form, the arc length and the magnetization direction of each radial magnet can be determined. On the other hand, the tangential magnets are placed between the radial magnets with different polarities, and the magnetization directions of tangential magnets are determined by the mechanism of conventional Halbach PM array to achieve strong magnetic field on the airgap side. In addition, the gaps are left between two radial magnets with the same polarity. Based on these procedures, the magnet arrangement of Halbach PM array with two MMFs can then be derived. Similarly, the Halbach PM array with more than 2 MMFs can be built by adding the sine wave ideal MMFs at the first step. The simulation results, which will be given in the full paper, validate the accuracy of this method on the construction of required MMFs. III. Application of Multi-MMF Halbach Array in Flux Reversal Machines As one of its interesting applications, the proposed Halbach PM array can be used to increase the airgap working field harmonics in the stator PM flux modulation machines. As shown in Fig. 2 (a), a 6-slots-4-poles flux reversal machine (FRM) with 16-salient-pole rotor is selected as the research object. The proposed Halbach PM array with12th and 18th MMFs is mounted under the stator teeth of this machine. According to the flux modulation theory, the 12th and 18th MMFs are modulated by 16th rotor permeance and generate 4th and 2nd airgap flux harmonics separately, which both contribute to the back EMF but with different coefficients [3]. Fig. 2 (b) shows the back EMF and cogging torque of proposed machine varied with the proportion of 12th MMF. Since 2nd harmonic has two times pole ratio than the 4th harmonic, the FRM with only 18th MMF has higher back EMF than with only 12th MMF. Also, since the least common multiple between 18 and 16 is 144, which is much larger than the least common multiple between 12 and 16, 18th MMF can bring lower cogging torque than the 12th MMF in proposed FRM. However, it is interesting that when increasing the proportion of 12th MMF from 0 to 0.3, the back EMF of proposed machine can still get 10% increased on the basis of Halbach FRM with 18th MMF under the same magnet usage. The reason analysis and the theoretical upper limit of this growth under Halbach PM array with 2 and 3 MMFs will be studied in the full paper. IV. Conclusions A design method of multi-MMF Halbach PM array has been proposed, and its application in a 6-slots-16-poles flux reversal machine has been researched. Compared to regular flux reversal machines with single MMF, the proposed flux reversal machine with composite MMFs can achieve 10% higher back EMF and torque capacity under the same magnet usage. The influence of pole ratio and the selection of threshold values on the performance of machine will be given in the full paper.

**References:**

[1] Tianjie Zou, Dawei Li, Canruo Chen, etc., “A Multiple Working Harmonic PM Vernier Machine with Enhanced Flux-Modulation Effect,” IEEE Transactions on Magnetics, vol. 54, no. 11, June. 2018. [2] Dawei Li, Ronghai Qu, Jian Li, etc., “Synthesis of Flux Switching Permanent Magnet Machines,” Synthesis of Flux Switching Permanent Magnet Machines,” IEEE Transactions on Energy Conversion, vol. 31, no. 1, Mar. 2016. [3] Yuting Gao, Dawei Li, Ronghai Qu, etc., “A Double-Stator Flux Switching PM Machine with Multi-PM MMF Harmonics,” IEEE Transactions on Magnetics, vol. 55, no. 6, June. 2019. [4] You Zhou, Ronghai Qu, Yuting Gao, etc., “A Novel Flux Modulation Linear Machine with Dual-Sided Modular Primary and Multi Pole Pitches,” IEEE International Electric Machines & Drives Conference (IEMDC), May. 2019. [5] Hailin Huang, Libing Jing, Ronghai Qu, etc., "Analysis and Application of Discrete Halbach Magnet Array with Unequal Arc Lengths and Unequally Changed Magnetization Directions," in IEEE Transactions on Applied Superconductivity, vol. 28, no. 3, pp. 1-5, April 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9c73d18c76d2ea1125f18574efa58316.jpg)
Fig. 1. The Forming method of Halbach PM array with two main MMFs.

![](https://assets.underline.io/uploads/markdown_image/1/image/9ee687a19ed045776c6bf555c0e0b096.jpg)
Fig. 2. Sketch and performance of Halbach flux reversal machine with 12th and 18th MMF.

 A Design Method of Multi-MMF Halbach PM Array and its Application in Flux Reversal Machines

In this paper, dual-winding dual-flux-concentrated magnetic-field modulated brushless compound-structure machine (DDMFM-BCSM) is proposed, combing the magnetic-field modulated brushless dual-rotor machine (MFM-BDRM) and permanent magnet synchronous machine (PMSM) into one. Proposed machine has two sets of windings in stator slots and spoke type PMs on dual rotors. Besides, there are flux barrier on inner rotor to improve the performance of MFM-BDRM. First, the performance of proposed machine is analyzed, including MFM-BDRM part, PMSM part and the whole DDMFM-BCSM. Second, in order to analyze the influence of flux barrier on performance of DDMFM-BCSM, a DDMFM-BCSM without flux barrier is designed to compared their performance. I. Introduction Combination of planetary gear and permanent magnet synchronous machine (PMSM) is widely used in hybrid electric vehicles (HEVs). Considering its maintenance and reliability problem, scholars are searching for new structure to replace this combination. Due to high reliability and low maintenance cost, the magnetic-field modulated brushless dual-rotor machine (MFM-BDRM) has high potential in HEVs. But in HEVs, MFM-BDRM need work together with a PMSM, which raise the system cost and volume. MFM-BDRM with dual windings, which is combination of MFM-BDRM and PMSM, is an alternative solution. In this paper, dual-winding dual-flux-concentrated magnetic-field modulated brushless compound-structure machine (DDMFM-BCSM), which is combination of MFM-BDRM and PMSM, is proposed. Magnetic field modulation principle, working principle of DDMFM-BCSM, is introduced [1,2]. Electromagnetic performance of DDMFM-BCSM, such as back EMF, torque and efficiency, are analyzed and obtained. In order to verify the function of proposed machine, performance of MFM-BDRM and PMSM are also analyzed separately. II. Structure and Working Principle The structure of the proposed DDMFM-BCSM is shown in Fig.1. The stator iron core is similar to that of common PMSM. But there are two sets of windings in stator slots, regular winding and modulation winding. The outer and inner rotor are formed by the alternant placement of magnetic blocks and spoke type PMs whose flux-concentrating effect could improve the flux density efficiently. The difference of two rotors are the magnetic blocks of inner rotor connect together and flux barrier is added in the end of PMs of inner rotor. The MFM-BDRM part consists of modulation winding, magnetic blocks on outer rotor and PMs on inner rotor, while the PMSM part consists of regular winding and PMs on outer rotor. Working principle of DDMFM-BCSM is magnetic field modulation principle which is also the working principle of magnetic gears, magnet-geared machines and vernier machines. Based on analysis of magnetic field modulation principle, torque and speed characteristic of DDMFM-BCSM can be obtained. III. Performance Analysis By finite element method (FEM), the performance of DDMFM-BCSM is analyzed at the inner and outer rotor speed of 1000rpm. Spectrum analysis result of air gap flux density verifies the magnetic field modulation principle. From low mutual-inductance of two sets of windings, we can see the interaction between two sets of windings could be weakened efficiently with reasonable motor design. The power factor of MFM-BDRM is low (0.58), which is the disadvantage of all machines based on magnetic field modulation principle. Loss and efficiency of DDMFM-BCSM is also analyzed. To verify the function of MFM-BDRM part and PMSM part, torque performance of two parts is analyzed respectively and shown in Fig.2. It’s obvious that both of MFM-BDRM part and PMSM part could put out stable torque. The torque of outer rotor and inner rotor of MFM-BDBR satisfies the torque characteristic mentioned above. Dimension parameters of magnetic blocks and spoke array PMs of two rotors are changed to improve the amplitude of needed flux density harmonics. In DDMFM-BCSM model simulated by FEM, flux density harmonics of 4 and 11 PM pole-pairs could generate fundamental wave of back EMF in modulation winding and regular winding respectively. IV. Influence of flux barrier In order to prove the flux barrier effect on performance, DDMFM-BCSM without flux barrier is also simulated. Torque, efficiency and power factor of two topologies are compared. The result shows that flux barrier could improve the torque of MFM-BDRM while the power factor of MFM-BDRM and torque of PMSM is weakened. V. Conclusion A new DDMFM-BCSM topology is proposed, combining the MFM-BDRM and PMSM together. Magnetic field modulation principle, the working principle of DDMFM-BCSM, is introduced. FEM result shows that proposed machine could realize function of two machines. Flux barrier could improve the torque of MFM-BDRM while the power factor of MFM-BDRM and torque of PMSM is weakened.

**References:**

[1] J.G. Bai, P. Zheng, C.D. Tong, et al, “Characteristic Analysis and Verification of the Magnetic-Field-Modulated Brushless Double-Rotor Machine”, IEEE Trans. Ind. Electron., vol. 62, pp. 4023-4033, Jul. 2015. [2] G.P. Liu, Y. Sui, J.Q. Liu, et al, “Comparison of Vernier Machines with Different Rotor PM Configurations”, 2019 22nd Int. Conf. on Electrical Machines and Systems (ICEMS 2019), Harbin (China), Aug. 2019, pp. 1-4.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c54151c0a80bf0fd16783d5dca99f4e9.jpg)
Fig.1. Structure of proposed DDMFM-BCSM

![](https://assets.underline.io/uploads/markdown_image/1/image/f077aa7ed892dfe45b1510a0d56f7db4.jpg)
Fig.2. Torque waveform of DDMFM-BCSM, PMSM part and MFM-BDRM part

 Investigation of a Dual-Winding Dual-Flux-Concentrated Magnetic-Field Modulated Brushless Compound-Structure Machine

1. Introduction. Due to the merits of simple structure, mechanical robustness and high power density, flux reversal permanent-magnet machine (FRPMM) has been an appealing choice in many industrial applications [1]. However, similar to other solely PM-excited machines, the constant-power operation range of FRPMM is restricted by the uncontrollable PM flux [2]. To improve the flux regulation ability, the hybrid-excited design concept is introduced into flux reversal machine [3]. With the participation of direct current (dc) excitation, the air-gap flux density can be regulated flexibly. However, the dc-field winding and armature wingding placed in the same stator results in a serious space confliction, which deteriorates the torque production and flux regulation ability. To cope with the space problem, the partitioned stator hybrid excited flux reversal machine (PSHEFRM) is developed [4], in which the armature windings and field windings are placed separately in the inner and outer stators. Nevertheless, the solely stator-PM excitation limits the torque capability of PSHEFRPM. To further enhance the torque production and obtain the flexible flux regulation ability, this paper proposes a new partitioned stator hybrid-excited flux reversal machine with dual-PM (DP-PSHEFRM), in which the field windings are placed in the inner stator and the PMs are employed on both the rotor and outer stator. The topology and operation principle of the proposed DP-PSHEFRM are described. The electromagnetic performances of the machine are investigated by finite element analysis (FEA). 2. Machine topology and operation principle. Fig. 1 shows the topology of the proposed DP-PSHEFRM, which consists of two stators and one sandwiched rotor. It can be seen that the machine employs the outer stator to accommodate three-phase armature windings and PMs, and inner stator to place field winding. The PMs mounted on the top of outer stator teeth are separated by iron poles, which composes a consequent-pole PM arrangement. The non-overlapping armature windings and field windings are wound on the teeth of outer and inner stators, respectively, which offers the merits of short ending-length and low copper loss. In addition, the outer stator teeth are aligned with inner stator slots, which means the two stators have half teeth pitch displacement. Moreover, the alternate PMs and iron poles composes a consequent-pole PM rotor structure. The PMs on the rotor and outer stator are magnetized with the identical radially direction to enhance the flux densities in the air-gap and stator core. The operation principle of the proposed DP-PSHEFRM is based on the flux modulation effect, and the torque of machine is generated by taking advantage of the modulated air-gap field harmonics. In addition, the dc flux is mainly used to regulate the air-gap flux density to improve the flux weakening capability. 3. Electromagnetic performance evaluation. Fig. 2(a) shows the no-load back-electromotive forces (back-EMFs) of the proposed DP-PSHEFRM excited by stator-PM only, rotor-PM only and dual-PM at the field current density of 0 A/mm2. It can be seen that the back-EMFs excited by different PM excitations all have a symmetrical and sinusoidal waveform. In addition, compared with stator-PM, rotor-PM makes more contribution for the back-EMF production. Fig. 2(b) compares the torques of proposed machine under different PM excitation at the armature current of 6A. It can be seen that the torque with dual-PM excitation is 82% higher than that with stator-PM excitation only and 47% higher than that with rotor-PM excitation only, which illustrates a great enhancement of torque production by using dual-PM excitation. Then, in order to verify the flux regulation ability of DP-PSHEFRM, the dual-PM excited outer air-gap flux density and its harmonic spectra at different field current density are evaluated, as shown in Fig. 2(c) and (d). It can be observed that the amplitudes of working harmonics can be continuously regulated with the change of the field current density. Thus, the flux linkage at armature terminal can be effectively adjusted, as shown in Fig. 2(e). When the armature current is fixed as 6 A, the variation of average torque with field current density is investigated. As shown in Fig. 2(f), the average torque decreases by 9.2Nm from J=0A/mm2 to J=-15A/mm2, which illustrates the excellent flux weakening capability of the proposed DP-PSHEFRM. More detailed design considerations and electromagnetic performance analysis will be presented in the full paper.

**References:**

 [1] Y. Gao, R. Qu, D. Li, “Torque performance analysis of three-phase flux reversal machines,” IEEE Trans. Ind. Appl., vol. 53, no. 3, pp. 2110–2119 (2017). [2] X. Zhao, S. Niu, and W. Fu, “Design of a novel parallel-hybrid-excited dual-PM machine based on armature harmonics diversity for electric vehicle propulsion,” IEEE Trans. Ind. Electron., vol. 66, no. 6, pp. 4209–4219 (2019). [3] L. Xu et al., “Design and analysis of a new linear hybrid excited flux reversal motor with inset permanent magnets,” IEEE Trans. Magn., vol. 50, no. 11, Art. ID 8202204 (2014). [4] Z. Zeng, Q. Lu and X. Huang, "Analysis of a new partitioned-primary flux-reversal hybrid-excited linear motor," in Proc. IEEE Int. Elect. Mach. Drives Conf. (IEMDC), pp. 74-79 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bbde9754c49229479494cfe02b661303.jpg)
Fig. 1 Topology of the proposed DP-PSHEFRM

![](https://assets.underline.io/uploads/markdown_image/1/image/46d6a83d3bdaec0953d3139401617155.jpg)
Fig. 2 Electromagnetic performances analysis

 Design and Analysis of a New Partitioned Stator Hybrid-Excited Flux Reversal Machine With Dual-PM

This paper proposes a novel consequent-pole flux-switching permanent magnet (FSPM) machine with magnets in stator slot opening to improve the torque density, which is a critical concern of FSPM machines. The working principle of the proposed topology is investigated based on the magnetomotive force (MMF)-permeance model and numerical finite element analysis (FEA). The electromagnetic performance such as back EMF and electromagnetic torque is compared with the conventional consequent-pole FSPM machine. It is demonstrated that the proposed machine can achieve 27.8% larger back EMF and 20.2% higher torque density than the conventional counterpart. I. Introduction Recently, permanent magnet (PM) machines have been used in many industry applications, such as servo motors and electric vehicle. Flux-switching permanent magnet (FSPM) machine was first proposed in [1]. Due to simple rotor structure and excellent flux-weakening capability [2] [3], FSPM machines have received much attention in recent decades. To improve torque density of FSPM machines, many topologies have been proposed and investigated. Z. Q. Zhu et al. analyzed a novel multi-tooth FSPM machine [4] and the optimal slot/pole pair combination is determined by a simple analytical method in [5]. H. Yang et al. proposed a consequent-pole FSPM machine to increase the contents of low-order harmonics to enhance the torque capability in [6]. In this paper, a consequent-pole FSPM machine with magnets in the slot opening is proposed to increase the torque density. In Section II, the working principle of the proposed topology is analyzed based on magnetomotive force (MMF)-permeance model and numerical finite element analysis (FEA). The electromagnetic performance, such as back EMF and electromagnetic torque, is compared with the conventional consequent-pole FSPM machine in Section III. It is found that the proposed topology can achieve 27.8% larger back EMF and 20.2% higher torque capability than the conventional counterpart. In Section IV, some conclusions are drawn. II. Machine Topology and Working Principle The conventional consequent-pole and proposed FSPM machines are shown in Fig. 1(a) and Fig. 1(b) respectively. Different from the conventional consequent-pole FSPM machine, there are Halbach-type magnets in stator slot opening in the proposed topology. The magnetization directions of the magnets are represented by the yellow arrows. Owing to the unique structure of consequent-pole FSPM machine, there are relatively lower reluctance paths for low-order flux density harmonics. It can be demonstrated that the non-working 6-pole-pair flux density harmonic can be reduced by the magnets in the stator slot opening. Thus, the working flux density harmonics can be enhanced while comparable saturation degrees can be realized in the conventional and proposed FSPM machines. III. Electromagnetic Performance Fig. 2 shows the FEA-predicted phase back-EMF waveforms, FFT analysis results of back EMF and electromagnetic torque curves. It can be seen from the figure that the proposed machine can achieve 27.8% larger back EMF and 20.2% higher torque density than the conventional counterpart. It should be noted that the phase current of proposed machine is smaller than the conventional consequent-pole FSPM machine due to the smaller slot area when the cooper losses are kept constant. IV. Conclusion In this paper, a novel consequent-pole FSPM machine with magnets in stator slot opening is proposed to enhance the torque capability. It is demonstrated that the proposed topology can realize 27.8% larger back EMF and 20.2% higher torque density than the conventional counterpart.

**References:**

 [1] S. E. Rauth and L. J. Johnson, “Design principles of flux-switching alternators,” AIEE Trans., vol. 74, pt. III, no. 3, pp. 1261-1268, Jan. 1955. [2] D. Li, R. Qu, J. Li, W. Xu, and L. Wu, “Synthesis of flux switching permanent magnet machines,” IEEE Trans. Energy Convers., vol. 31, no. 1, pp. 106–117, Mar. 2016. [3] W. Hua, M. Cheng, and G. Zhang, “A novel hybrid excitation flux-switching motor for hybrid vehicles,” IEEE Trans. Magn., vol. 45, no. 10, pp. 4728-4731, Oct. 2009. [4] Z. Q. Zhu, J. T. Chen, Y. Pang, D. Howe, S. Iwasaki, and R. Deodhar, “Analysis of a novel multi-tooth flux-switching PM brushless AC machine for high torque direct-drive applications,” IEEE Trans. Magn., vol. 44, no. 11, pp. 4313-4316, Nov. 2008. [5] J. T. Chen, Z. Q. Zhu, and D. Howe, “Stator and rotor pole combinations for multi-tooth flux-switching permanent-magnet brushless AC machines,” IEEE Trans. Magn., vol. 44, no. 12, pp. 4659-4667, Dec. 2008. [6] H. Yang, Y. Li, H. Lin, Z. Q. Zhu and S. Lyu, "Principle investigation and performance comparison of consequent-pole switched flux PM machines," IEEE Trans. Transport. Electrifi., doi: 10.1109/TTE.2020.3022991.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/77be9b46bb5ba347cd39ca86a71b3594.jpg)
Fig. 1. Basic topologies. (a) Conventional consequent-pole FSPM. (b) Proposed FSPM.

![](https://assets.underline.io/uploads/markdown_image/1/image/fc2f6faeaa2b47661f704ce62af21ac5.jpg)
Fig. 2. Electromagnetic performance. (a) Back EMF. (b) FFT analysis results of back EMF. (c) Electromagnetic torque.

 Investigation of Consequent-Pole Flux-Switching Permanent Magnet Machines with Magnets in Stator Slot Opening

1. Background and Literature Review Since permanent-magnet vernier machines (PMVMs) can offer high torque directly without the aid of intermediate transmission devices such as mechanical gearbox, they are extremely suitable for low-speed large-toque direct-drive (LLDD) applications [1], such as industrial robots, wind power generation, ship propulsion, etc. Generally, PMVMs can be classified into three types according to the location of permanent magnets (PMs), i.e., stator type (ST), rotor type (RT) and stator and rotor type (SRT). The former two types mean that either PMs are only on stator or only on rotor, while the latter type signifies that PMs are on both stator and rotor. Since there are two PM excitation sources, the SRT type of PMVM is also called “dual-permanent-magnet-excited (DPME) machine”[2]. Clearly, DPME machine has one more PM excitation source than the other two types, so it can output higher torque compared with the other two types, which has been demonstrated in [2,3]. Thus, DPME machine has more advantages in the LLDD field, and much research on it is also growing increasingly. However, according to the literature review, research on DPME machine concentrates on the qualitative explanation of the bidirectional field modulated effect (BFME) [2], new structures [4], design and optimization [5], comparative study [6] and control strategies [7]. 2. Motivation Back-EMF is an important physical quantity in electrical machine (EM), which many designers often care about, as nonsinusoidal back-EMF may cause torque ripple, and increase inverter capacity [8]. For DPME machine (see Fig. 1), it has two PM excitation sources with different pole-pair numbers (PPNs), i.e. stator PMs and rotor PMs; it also has double-salient structure. Due to the double-salient structure, the magnetic field generated by stator PMs or rotor PMs can be modulated into abundant airgap field harmonics through rotor teeth or stator teeth. So, the airgap harmonics of DPME machine are more abundant and more complex than those of traditional PM machine. Regarding the back-EMF of DPME machine, two questions (Qs) arise naturally, i.e., Q1: do all airgap flux density harmonics make contribution to back-EMF? Q2: For these harmonics which contribute to the back EMF, do they all produce positive or negative back EMF? According to the previous literature review, only [4] answered Q1 by qualitative analysis, and pointed out that only specific harmonics can contribute to back-EMF. However, as far as we know, there is no literature to answer Q2. So, it is necessary to quantitatively identify the airgap flux density harmonics contributing to back-EMF, thus helping to suppress the harmonics which produce negative back EMF. 3. Method Magneto motive force (MMF) permeance analytical model (MPAM) is used to identify the airgap flux density harmonics contributing to back-EMF. Firstly, establish the MPAM of DPME machine. Next, derive the expressions of airgap flux density harmonics generated by stator and rotor PMs respectively based on the MPAM, and classify the harmonics into six types (see Table I). Then, deduce the expressions of PM flux-linkage by means of winding function and the derived airgap flux density harmonics. Afterwards, get back-EMF expressions by the derived PM flux-linkage. Finally, identify the airgap flux density harmonics contributing to back-EMF. 4. Results As shown in Fig. 1, a 12/10 DPME machine is selected as an example for analysis. Fig. 2(a) compares back-EMFs obtained by theoretical analysis and FEM. As can be seen from Fig. 2(a), the back-EMF obtained by the MPAM basically coincides with that obtained by FEM. The error between the analytical and FEM results is about 8.7%, which indicates that the MPAM is feasible. By means of the MPAM, one can also identify the airgap flux density harmonics contributing to back-EMF. Fig. 2(b) gives the identification results of the airgap flux density harmonics contributing to the fundamental back-EMF. Apparently, S-II and R-II types of harmonics generate negative back-EMFs, which weakens the total back-EMF; S-III, R-I and R-III types contribute to positive back-EMFs, and R-III type contributes nearly half the back-EMF; S-I type makes no contribution to back-EMF. 5. Note Limited by the length of the digest, 1) not all the references are given in the digest body, and the others will add in the full paper; 2) the derivation of the MPAM for DPME machine as well as the derived expressions will be elaborated in the full paper; 3) other results such as waveforms of flux density will be added in the full paper.

**References:**

[1] F. Wu and A. M. El-Refaie, IET Electr. Power Appl., Vol. 13, p. 127–137 (2019) [2] L. Jian, Y. Shi and C. Liu, IEEE Trans. Magn., Vol. 49, p. 2381–2384 (2013) [3] W. Zhao, X. Sun and J. Ji, IEEE Trans. Appl. Supercond., Vol. 26, p. 1-5 (2016) [4] L. Xu, W. Zhao and G. Liu, IEEE Trans. Veh. Technol., Vol. 69, p. 7104-7115 (2020) [5] Q. Lin, S. Niu and W. N. Fu, IEEE Trans. Magn., Vol. 56, p. 1-5 (2020) [6] Q. Wang, S. Niu and L. Yang, IEEE Trans. Ind. Electron., Vol. 64, p. 9924-9933 (2017) [7] S. Niu, S. L. Ho and W. N. Fu, IEEE Trans. Magn., Vol. 50, p. 805-808 (2014) [8] X. Ren, D. Li and R. Qu, IEEE Trans. Ind. Electron., Vol. 67, p. 6248-6258 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/33770a3501a2d61f1b501d622d324902.jpg)
Fig. 1 and Table I

![](https://assets.underline.io/uploads/markdown_image/1/image/b877c649b02d8cc9ff444a314279b6a8.jpg)
Fig. 2. (a) Back-EMFs. (b) Contribution of airgap flux density harmonics to the fundamental back-EMF.

 Quantitative Identification of Airgap Flux Density Harmonics Contributing to Back-EMF in Dual-Permanent-Magnet-Excited Machine

I.Introduction Recently, the flux-switching permanent magnet (FSPM) machines have been recognized as attractive candidates for electric vehicle (EV) and hybrid electric vehicle (HEV) propulsion on account of their high torque (power) density and robust rotor structure. The 6s/5p FSPM machine is considered for the high speed condition, since it reduces the fundamental frequency and exhibits improved torque performances. However, the topology utilization is restricted due to the unbalanced magnetic force in automotive applications. In order to address the above issues, this paper proposes a axial-modular flux switching permanent magnet (AM-FSPM) machine, as shown in Fig. 1. It contains two axial modular parts, namely front modular part and rear modular part, where the PMs of each part are sandwiched between the two U modular cores. It is worth noting that the PMs magnetization directions are opposite at the same stator position of two axial modular parts. The phase armature winding is composed of two toroidal coils, which are wound around the stator yokes. It can be found from Fig. 1(a) that the integrated toroidal windings are shared by the two axial modular parts, and then the winding function is different from that of the conventional FSPM machine. Meanwhile, the winding factor of the AM-FSPM machine is improved by the toroidal windings, which is helpful to increase the torque density. The rotor poles in the rear part are shifted relative to the front part by 180o mechanically. II.Electromagnetic performances of AM-FSPM machine For the AM-FSPM machine, the PM magneto-motive-forces (MMFs) of two axial modular parts are modulated by the corresponding salient rotor cores. Then the PM air gap flux density is produced, and the harmonic amplitudes in two modular parts are identical due to the same PM-MMF and rotor permeance model. However, the PMs magnetization directions of the two modular parts are opposite and the rotor positions are different, which leads to the flux density harmonic phase difference. Based on the PM flux density expression, the phase difference between two modular parts is obtained as |(2n-1)PPM±kPr|π, where PPM and Pr is the PM pole-pair number and rotor pole number, respectively. Meanwhile, the winding functions of two axial modular parts are the same due to the sharing of the integrated toroidal armature windings. Hence, the phases difference of the PM flux linkage between the front modular part and the rear modular part is |(2n-1)PPM±kPr|π. When k is an even number, the harmonics with even orders in flux linkages of two coils are cancelled, and then the sinusoidal flux linkage will be obtained as shown in Fig. 2(a). It can be found from Fig. 2(b) that the total harmonic distortion (THD%) of the single coil flux linkage is 31.57% in the modular part, where the harmonic with 2nd order is the highest (30.95%). Nevertheless, the THD% in the same coil of whole machine is 6.19% due to the cancelled harmonics with even orders. Moreover, the coil flux linkage harmonic distortion with 3rd orders is 6.18%, which is not contributed to the electromagnetic torque. In order to verify the merits and disadvantages of AM-FSPM machine, a comprehensive comparison between AM-FSPM and conventional 6s/5p FSPM machine is conducted. Two machines have the same outer diameter, axial stack length and air gap length. Meanwhile, the same PM and silicon steel materials are utilized and the rated current density of two machines are equal. Fig. 2(c) shows the electromagnetic torque waveforms of two machines. It can be found that the average torque of the AM-FSPM machine is 14.05Nm, which is 1.09 times of that of the FSPM machine. The reason is that the winding factor of AM-FSPM is 1, which is higher than 0.866 of traditional 6s/5p FSPM machine. In addition, the cogging torque in AM-FSPM (0.62Nm) is approximately identical to the FSPM machine. However, the torque ripple of AM-FSPM is 6.6%, which is 0.7% higher than that of FSPM machine. It is worth noting that the torque ripples without cogging torques are 3.6% and 4.1% in AM-FSPM and FSPM machines, respectively. Hence, the torque ripple is dominantly influenced by the cogging torque, which will be investigated and suppressed in the full paper. The electromagnetic torque with different current densities of two machines are shown in Fig. 2(d). It can be found that the average torque increases linearly as the current density rises, then the two machines exhibit the attractive overload capability. III.Conclusion This paper proposes a novel AM-FSPM machine and the flux density harmonics characteristics are deduced. Then the sinusoidal flux linkage of the toroidal coil can be obtained due to the flux density harmonics phases difference between two modular parts of the AM-FSPM machine. In addition, compared with the 6s/5p FSPM machine, the proposed machine with the same geometric parameters exhibits higher torque density, and lower torque ripple, which is suitable for the EV and HEV applications.

**References:**

[1] Y. Li, D. Bobba and B. Sarlioglu, "Design and Performance Characterization of a Novel Low-Pole Dual-Stator Flux-Switching Permanent Magnet Machine for Traction Application," in IEEE Transactions on Industry Applications, vol. 52, no. 5, pp. (2016) [2] C. Di, I. Petrov and J. J. Pyrhönen, "Unbalanced Magnetic Pull Compensation With Active Magnetic Bearings in a 2 MW High-Speed Induction Machine by FEM," in IEEE Transactions on Magnetics, vol. 54, no. 8, pp. (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3206b1e7f4867281e60da8fd9507796f.jpg)
Fig. 1. AM-FSPM machine and traditional 6s/5p FSPM. (a) front modular part of AM-FSPM, (b) rear modular part of AM-FSPM, (c) AM-FSPM. (d) 6s/5p FSPM.

![](https://assets.underline.io/uploads/markdown_image/1/image/f3bd9851267fe0221cdfb76a4c5e747c.jpg)
Fig. 2. 2D and 3D finite element analysis results of AM-FSPM and traditional 6s/5p FSPM parameters (a) flux linkage, (b) corresponding Fourier spectra, (c) electromagnetic torque, (d) current density.

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