United States

Permanent magnet vernier machine (PMVM), as one novel embranchment of low speed large torque permanent magnet synchronous machine (PMSM) based on flux modulation principle, which has broad application prospects in wind power generation, electric vehicles and other fields [1]. The flux modulation pole (FMP) is introduced into the stator tooth of the magnetic gear motor as the magnetic modulation ring in the magnetic gear motor [2], which makes the motor structure more complex, as shown in Fig. 1(a). Although the finite element method (FEM) has the advantages of high calculation accuracy, the modeling of complex geometric structure of the motor is time-consuming, and the solution speed is slow [3]. Fast and accurate calculation of the magnetic field of the PMVM, which is conducive to the rapid initial design and optimization of the PMVM.&lt;br/&gt;This paper proposes a sub-domain model for accurate calculation of PMVM magnetic field, which based on Schwarz-Christoffel mapping technique. Schwarz-Christoffel mapping is the transformation of a continuous line segment on the real axis of the w plane to the boundary of a polygon in the z plane and the upper half plane of the w plane to the interior of the polygon [4]. Through twice Schwarz-Christoffel mapping to get regular magnetic field graphics. Firstly, the z plane is transformed into the w plane; then the w plane is transformed to the t plane by the logarithmic transformation. The z-w-t plane correspondence is shown in Fig.2. The detailed derivation process will be presented in the full paper.&lt;br/&gt;In order to verify the correctness of the proposed PMVM magnetic field accurate subdomain model, the magnetic field calculation results of the FEM and the analytical model are compared. Fig.3 shows the FEM results of the radial component of air gap flux density under no-load and load conditions. The complete calculation results of the accurate subdomain model will be given in the full paper.

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2022 Joint MMM-INTERMAG

Accurate Analytical Calculation of Magnetic Field of Permanent Magnet Vernier Motor

## Dr. Nishikant (Nish) Sonwalkar: Academician, Scientist, Musician

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Dr. Sonwalkar is regarded as a leading expert in the application of computers in education. He has extensive research and development experience in hypermedia authoring, mobile learning, adaptive learning, and brain-based synaptic learning, advanced scientific visualization, database management systems, and computer simulation.

After receiving doctoral degree from MIT in the area of Molecular Dynamics of Nano-interfaces, he joined MIT as faculty in Mechanical Engineering, but his passion for technology enabled education led him become the founding director of Hypermedia Teaching Facility (Hypermedia Lab) at MIT and later he was appointed as the Principal Educational Architect of MIT.

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NISH 2021

Permanent magnet vernier machine (PMVM), as one novel embranchment of low speed large torque permanent magnet synchronous machine (PMSM) based on flux modulation principle, which has broad application prospects in wind power generation, electric vehicles and other fields [1]. The flux modulation pole (FMP) is introduced into the stator tooth of the magnetic gear motor as the magnetic modulation ring in the magnetic gear motor [2], which makes the motor structure more complex, as shown in Fig. 1(a). Although the finite element method (FEM) has the advantages of high calculation accuracy, the modeling of complex geometric structure of the motor is time-consuming, and the solution speed is slow [3]. Fast and accurate calculation of the magnetic field of the PMVM, which is conducive to the rapid initial design and optimization of the PMVM. This paper proposes a sub-domain model for accurate calculation of PMVM magnetic field, which based on Schwarz-Christoffel mapping technique. Schwarz-Christoffel mapping is the transformation of a continuous line segment on the real axis of the w plane to the boundary of a polygon in the z plane and the upper half plane of the w plane to the interior of the polygon [4]. Through twice Schwarz-Christoffel mapping to get regular magnetic field graphics. Firstly, the z plane is transformed into the w plane; then the w plane is transformed to the t plane by the logarithmic transformation. The z-w-t plane correspondence is shown in Fig.2. The detailed derivation process will be presented in the full paper. In order to verify the correctness of the proposed PMVM magnetic field accurate subdomain model, the magnetic field calculation results of the FEM and the analytical model are compared. Fig.3 shows the FEM results of the radial component of air gap flux density under no-load and load conditions. The complete calculation results of the accurate subdomain model will be given in the full paper.

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poster

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Due to the magnetic field modulation of the modulating ring, a large number of harmonics can generate in the air gap. These harmonics act on the permanent magnet and magnetic ring, resulting in large eddy current losses and iron losses. In order to improve the harmonics in the air gap and reduce the losses, a novel magnetic gear with Halbach and copper bar is proposed in this paper. The permanent magnets (PMs) of the inner rotor adopted Halbach arrays. The iron yoke of outer rotor is slotted and add copper bar. The air gap flux density, output torque and loss of the magnetic are compared by finite element method. Compared with conventional magnetic gear, the results show that the proposed magnetic gear not only improves the air gap magnetic density and weakens the unworked harmonics, but also increases the output torque from 140.07Nm to 142.64Nm, reduces the eddy current loss by 32.24% and the iron loss by 16%. This model provides a new idea for loss analysis and optimization of coaxial modulated magnetic gear.

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Fig. 1 CMG topology

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Table I Torque ripple



Loss Analysis of Magnetic Gear with Halbach Arrays and Copper Bar

Magnetic-geared double-rotor machines (MGDRMs) are verified a promising candidate for power split application [1]. However, there remains undesired torque ripple in conventional MGDRM. A new MGDRM with ironless stator, as shown in Fig. 1. (a), is proposed. The ironless stator structure can eliminate stator slot effect and enable a more flexible winding configuration, resulting in low torque ripple. The simplified model of the proposed machine, as shown in Fig. 1. (b), is proposed. Thus, based on the magnetic-field modulating principle, the operating principle is investigated, and the speed and torque characteristics are also deduced. For the pole-pair configuration with ps=3, ppm=20, pm=23, the simulated magnetic field distribution and its spectrum verify the operating principle, as shown in Fig. 1. (c) and (d). As shown in Fig. 2. (a) and (b), the no load back electromagnetic force (EMF) with low distortion verifies the speed characteristic. Fig. 2. (c) shows that the torque ripple of the proposed machine is 0.18%, validating the low torque ripple property. Furthermore, the torque ratio equals the theoretical value (i.e. pole-pair ratio). Fig. 2. (d) shows that the torques of stator, the modulating rotor and the PM rotor are always in direct proportion, validating the torque characteristic. Based on the simplified model shown in Fig. 1. (b), the analytical model consisting of magnetomotive force (MMF) and permeability functions is deduced to investigate the influence of key geometry parameters. The influences of ferromagnetic pole-piece and PM on torque output are investigated. Fig. 2. (e) shows that the optimal pole-arc coefficient of the modulating rotor is about 0.2, which approximately agrees with the proposed analytical model. It can be seen in Fig. 2. (f) that the torque output rises with the increment of ferromagnetic pole-piece thickness in the beginning and remains approximately unchanged when thickness is larger than 7mm. As shown in Fig. 2. (g) and (h), torque output rises with the pole-arc coefficient of PM increasing and the optimal thickness of PM is about 3mm, respectively. The trends of all above simulated results can be explained by the analytical model, validating the proposed model.

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A Novel Ironless Stator Magnetic-Geared Double-Rotor Machine

1. Introduction A 12-slot-8-pole switched reluctance motor (SRM) has benefits in many applications due to no permanent magnet, low-cost, and simple and robust rotor structure [1]-[4]. However, noises and vibrations of the 12/8 SRM are large due to its large torque ripple. In order to solve this problem, a 12/10 SRM with a star connection has been proposed, which has less torque ripple [5], [6]. In this paper, we propose a 12/10 SRM with a hex connection. The hex connection does not need a neutral point, and the stator has a short coil end height. Therefore, the size of the motor with the hex connection becomes smaller. The characteristics of the hex connection was compared with the star connection through 2D finite element analysis. 2. Comparison Fig. 1 shows a 12/10 SRM, inverter, hex and star connections. The stator has a 6-phase concentrated winding from A-phase to F-phase, and the in-phase coils are connected in series. The torque ripple and efficiency of the 12/10 SRM with hex and star connections are compared, where the voltage application timing is adjusted to satisfy an output power of 1 kW. Figs. 2 (a), (b) and (d) show the torque and current waveforms, and efficiency, respectively. Fig. 2 (c) shows the ratio of each harmonic component against the fundamental component in the coil current. From Fig. 2 (a), the torque ripple ratio of the hex connection model is less than that of the star connection model. This is because, from Fig. 2 (c), the coil current of the hex connection model has the third harmonic components. From Fig. 2 (d), the efficiency of the hex connection model is larger than that of the star connection model. This is because, from Fig. 2 (c), the ratio of the DC and fundamental components in the coil current is different between the hex and star connection models. 3. Conclusion A 12/10 SRM with the proposed hex connection is superior to that with the conventional star connection in terms of a torque ripple and efficiency. In the final paper, the difference between hex and star connections is theoretically described using a mathematical model. Furthermore, their load characteristics are compared by carrying out measurements on a prototype.

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12/10 Switched Reluctance Motor with a Hex Connection

12/10 Switched Reluctance Motor with a Hex Connection

Switched reluctance motor (SRM) is a kind of doubly salient variable reluctance motor, which has the advantages of simple structure, reliable operation and large starting torque. The motor has the problem of large torque ripple, which causes vibration and noise during operation. In order to reduce torque ripple, a switched reluctance motor with hybrid excitation segmented rotor (HESSRM) is presented in this paper. Firstly, in HESSRM, aluminum block is used instead of silicon steel sheet rotor, the fan-shaped rotor core is embedded into the non-magnetic aluminum block, and stator has full pitch three phase windings. The permanent magnet is embedded in the stator tooth and its magnetization direction is consistent with the excitation direction of the winding. Secondly, in order to further reduce the torque ripple, the switch-on and switch-off angles of the power converter should be optimized. Finally, a three-phase 12/8 pole HESSRM model is established. Through parametric simulation, the optimal position and size of the permanent magnet are obtained, and the electromagnetic properties of the motor such as flux linkage, air gap magnetic field and torque are calculated. Compared with the conventional SRM, the average output torque of the proposed HESSRM is increased by 36.49% and the torque ripple is reduced by 36.41%.

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Topology of HESSRM

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Torque comparison

Torque Characteristic of Switched Reluctance Motor with Hybrid Excitation Segmented Rotor

The magnetic circuit of switched reluctance motor(SRM) has a non-sinusoidal structure, and the switching performance of the control circuit changes with the period, resulting in complex electromagnetic performance, therefore, it is difficult to accurately calculate the core loss of SRM. Considering that SRM is affected by both alternating magnetization and rotational magnetization, an improved vector Play model is proposed for finite element analysis. This model not only satisfies the rotational hysteresis loss property but also improves the calculation accuracy of the core loss in the alternating field[1]. The traditional loss separation model can get accurate results for core loss calculation of motor under sinusoidal excitation, but this method can not be fully applied to the SRM under non-sinusoidal excitation. To verify the accuracy of the finite element simulation results, the magnetic flux density of stator and rotor core of SRM is decomposed into radial component and tangential component, The finite element model of SRM and the flux density waveform of typical points are shown in fig.1 and fig.2 respectively. For eddy current loss and excess loss, Fourier decomposition method is used to decompose the radial component and tangential component flux density of the motor into a series of sinusoidal magnetic density waveform, which is calculated by accumulation. For hysteresis loss, the equivalent elliptic loop(EEL) method was used to model the hysteresis loop in time domain[2]. This model divides the magnetic field intensity into reversible component and irreversible component, therefore, the calculation accuracy of dynamic hysteresis loss is improved. The accuracy of the improved vector Play model can be verified by comparing the results of core loss calculation with the finite element simulation results.

![](https://assets.underline.io/uploads/markdown_image/1/image/b9d2a71a116dc1d4557a3660e4ff5173.jpg)

Fig.1 A two-dimensional model of a 12/8 structure switched reluctance motor

![](https://assets.underline.io/uploads/markdown_image/1/image/8270b60bfc73e0a089ae857b2c913cb1.jpg)

Fig.2 (a) Magnetic flux density waveform of stator pole (b) magnetic flux density waveform of rotor pole (c) magnetic flux density waveform of rotor yoke

Core Loss Analysis of Switched Reluctance Motor Considering Hysteresis Effect

Introduction Doubly-Salient machines (DSMs) have simple structure which provides high mechanical robustness and control flexibility, thus are suitable for wind power application [1-2]. However, due to the shortage of rare-earth resources, the rare-earth PM material becomes more and more expensive. In order to reduce the machine cost, decreasing the usage of rare-earth PMs without sacrificing steady torque becomes a hot topic. Consequent pole concept, which uses only half of the PMs with the same magnetization direction, is proposed to save the dosage of PMs [3-4]. Furthermore, rare-earth PMs are replaced with ferrite PMs to avoid the usage of rare earth resources. In this paper, slot-PM-assisted consequent-pole-PM doubly-salient machine (SPMA-CPM-DSM) is proposed. The key is that the consequent-pole ferrite PMs are employed in the stator yoke to reduce the cost and small amount of tangential magnetized rare-earth PMs is placed in the slot opening to improve the torque production. This proposed hybrid magnet design can greatly enhance the PM utilization ratio and reduce PM cost without sacrificing the steady torque. Machine configuration Fig. 1 shows the configuration of three machines. For the conventional DSM, the polarity of yoke ferrite PMs alternates around the circle. For CPM-DSM, the yoke ferrite PMs of one polarity remain while the yoke ferrite PMs of another polarity are replaced with iron core. For SPMA-CPM-DSM, based on the structure of CPM-DSM, tangential magnetized slot rare-earth PMs are added to further enhance the steady torque. Electromagnetic performance Fig. 2 shows the electromagnetic performance of three machines. It can be seen that the flux linkage amplitude, back-EMF amplitude, as well as average torque of CPM-DSM is almost the same as that of conventional DSM. Since the PM usage of CPM-DSM is half of that of conventional DSM, consequent pole structure can reduce the ferrite PM usage without sacrificing the electromagnetic performance of the machine. In addition, with the employment of slot rare-earth PMs, the flux linkage amplitude, back-EMF amplitude, as well as average torque of SPMA-CPM-DSM is 79% higher than that of CPM-DSM, denoting the torque enhancing ability of slot PMs.

![](https://assets.underline.io/uploads/markdown_image/1/image/964ca993a62a1567900765fc831a59cd.jpg)

Fig. 1

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Fig. 2

A Novel Slot-PM-assisted Consequent-pole-PM Doubly-salient Machine with Hybrid Magnets of Ferrite PMs and Rare-earth PMs

Abstract—This paper proposes a novel stator-PM consequent-pole dual stator/rotor armature winding flux modulated machine with the dc-biased current. Due to both armature windings and consequent-pole stator-PM interact with each other, this proposed machine contains six torque components. Compared with traditional stator permanent magnet machines and flux modulated machines, this machine makes full use of the space in the rotor cavity and giving full play to the flux modulation effect. Keywords—Hybrid excitation, DC-biased current, dual armature winding vernier machine. I. Introduction Recently, stator permanent magnet 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 consequent-pole 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 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 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 containing six torque components, which will be illustrated in the full paper.

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A Novel Stator-PM Consequent-pole Dual Stator/Rotor Armature Winding Flux Modulated Machine for Multi-Torque Components

Abstract—This paper proposes a novel dual armature winding vernier reluctance machine (DAWVRM) with stator five-phase DC-biased current. Due to the dual stator/rotor armature winding, this proposed machine can produce four different torque components which make the machine has a larger torque density and high fault-tolerant. Meanwhile, due to the five-phase DC-biased current of the stator winding, the fault-tolerant ability of the machine is further improved. Index Terms—Dual armature winding, Five-phase DC-biased current, Multi-torque components, Vernier reluctance machine. I. Introduction To improve the torque density and realize better rotor space utilization, flux reversal machines (FRM) with armature windings wound on both stator and rotor teeth were proposed in [1], [2]. Compared with conventional FRM, that machine can yield 60% higher torque density. Meanwhile, the three-phase DC-biased current vernier reluctance machine (DC-biased VRM) is proposed and studied due to the higher torque density compared with the conventional VRM [3]. To satisfy both the high torque density and high fault-tolerant, the method of multi-torque components output can be adopted. In this paper, the topology of DAWVRM with stator five-phase DC-biased current is proposed. As shown In Fig. 1, the stator has five-phase DC-biased winding and the rotor has three-phase winding. As a result, four different torque components will be generated. The operation principle and electromagnetic analysis will be illustrated in the full paper. II.Electromagnetic Performance Evaluation The electromagnetic performance of the machine is predicted by FEA. The no-load flux distribution is shown in Fig. 2, and the maximum magnetic density in the yoke is 1.4T. The back-EMF of stator and rotor windings are shown in Fig. 3, and the output torque is shown in Fig. 4. When the stator rotor windings are excited simultaneously, the output torque (torque ripple) is 5.42Nm (0.116). When the stator/rotor is excited separately, the output torque is 1.61Nm/1.55Nm. This machine exhibits a larger torque density and high fault-tolerant due to containing four torque components, which will be illustrated in the full paper.

A Dual Armature Winding Vernier Reluctance Machine with Stator Five-phase DC-biased Current

In field modulation machine (FMM), the high speed armature magnetic field is modulated to couple with a low speed magnetic field generated by rotor with multiple pole-pair number of permanent magnets (PMs) for high output torque [1]. In order to increase torque production furtherly, dual stator FMM (DSFMM) is proposed, which can fully utilize space and PMs [2]. Another approach to enhance torque production is to increase airgap flux density by using interior PM (IPM) or bilateral PM (BPM) arrangements in DSFMMs [3]. However, DSFMM excited by IPM or BPM alone can not achieve high sinusoidal airgap magnetic field. This paper proposes a new staggered DSFMM with O-shape PM arrangement (ODSFMM), which provides high sinusoidal airgap magnetic field for high quality torque production. Two radially magnetized PMs with opposite polarity are sandwiched between two tangentially magnetized PMs with opposite polarity, which forms the proposed O-shape PM arrangement for high sinusoidal airgap magnetic field with high flux density. The inner stator is rotated along shaft to form staggered DS structure for flux leakage reduction. The angle between the central axes of inner and outer stator teeth (α) is 15°. The open stator teeth play the role of modulation poles to modulate the magnetic field excited by O-shape PMs. The stator of the proposed machine employs three-phase 12-slot/2-pole single layer integral-slot distributed windings for high slot utilization and back electromotive force (EMF). To verify the merits of the proposed ODSFMM that is simply referred as Model I, the DSFMM with BPM excitation (simply referred as Model II) and with unrotated inner stator (simply referred as Model III) are designed, which share identical key design parameters, such as the volume of PM, outer radius, airgap length, and active stack length. The back-EMF, cogging torque, steady torque at rated state and steady torque at different current angles of the proposed designs are analyzed using finite element analysis (FEA). The FEA-predicted results show that the proposed ODSFMM can provide high sinusoidal back-EMF waveforms with high amplitude and high torque production with low torque ripple, which is desirable for accuracy operation applications.

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![](https://assets.underline.io/uploads/markdown_image/1/image/661dc67f894efd034b2b9f2e2da0db0d.jpg)

A New Staggered Dual Stator Field Modulation Machine with O-Shape Permanent Magnet Excitation

Field modulation machine (FMM) operates based on magnetic gear effect, which has the merit of high torque production at low operating speed [1]. Thus, FMM is suitable in direct-drive applications such as astronomical telescope and robot arms [2]. Hybrid magnet dual stator FMM (HMDSFMM) is developed for increasing output torque furtherly and obtaining high power factor [3]. Generally, the multiple-tooth stator is employed to increase split ratio for high torque density [4]. Nevertheless, the existing DSFMM with the same split ratio of inner and outer stators can not achieve the best electromagnetic performances. This paper proposes a new HMDSFMM with different split ratios of stators (DSR-HMDSFMM), which can achieve high quality torque production. The split tooth numbers of the outer and inner stators of the proposed DSR-HMDSFMM are designed as 2 and 3, respectively, which is expressed as K1=[2,3]. The inner and outer stators using different split ratios take the advantage of reducing flux leakage and increasing torque quality. The total tooth numbers of inner stator is equal to that of outer stator because the same armature windings and PM excitation are used. The consequent pole rotor with NdFeB magnets establishes the main magnetic circuit for high PM utilization. Ferrite magnets are embedded between split teeth, which aim to enhance the airgap flux density and suppress the harmonic distortion. In order to find out the optimal combination of split ratios of stators, the proposed DSR-HMDSFMMs with K2=[1,2], K3=[1,3] and K4=[2,2] are analyzed, which are simply referred as Model II, III, IV, respectively. Both of the inner and outer stators employ the three-phase 12-slot/2-pole integral-slot distributed double layer windings which can fully utilize slot space and high back electromagnetic force (EMF). The electromagnetic performances of proposed designs are analyzed by finite element analysis, including back-EMF, cogging torque, steady torque at rated condition and steady torque characteristics against current angle. The calculated results show that the proposed DSR-HMDSFMM with K1=[2,3] exhibits the highest back-EMF and high quality torque production, which is suitable for the accuracy operation applications.

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