United States

Axial-flux magnetic-geared double-rotor machines (AMGDRMs) are verified a promising candidate for power splitting in hybrid electric vehicles (HEVs) [1]. However, in conventional AMGDRM, as can be seen in Fig. 1. (a), the modulating rotor is set in middle of stator and the permanent magnet (PM) rotor. Hence, the modulating rotor suffers from high axial magnetic force from the side of the PM rotor, resulting in low mechanical strength.&lt;br/&gt;In this paper, a new AMGDRM with interior-modulating-rotor is proposed to solve the problem of low mechanical strength. As shown in Fig. 1. (b)-(d), the PM rotor is set in middle of stator and the modulating rotor in proposed AMGDRM. Owing to that the PM rotor suffers from reverse axial magnetic forces from both sides simultaneously, the total axial magnetic force is dramatically reduced. The 3-D finite element analysis (FEA) simulation results shown in Fig. 1. (e) and (f) verify the low axial magnetic force property of proposed AMGDRM.&lt;br/&gt;Based on the magnetic-field modulating principle, the operating principle of proposed AMGDRM is investigated, and the speed and torque characteristics are also given. For the pole-pair configuration with &lt;i&gt;p&lt;sub&gt;s&lt;/sub&gt;&lt;/i&gt;=3, &lt;i&gt;p&lt;sub&gt;pm&lt;/sub&gt;&lt;/i&gt;=20,&lt;i&gt; p&lt;sub&gt;m&lt;/sub&gt;&lt;/i&gt;=23, the simulated magnetic field distribution and its spectrum verify the operating principle, as shown in Fig. 2. (a) and (b). As shown in Fig. 2. (c) and (d), the no load back electromagnetic force (EMF) verifies the speed characteristic. Fig. 2. (e) and (f) show that the torques of stator, the modulating rotor and the PM rotor are always in direct proportion, validating the torque characteristic.&lt;br/&gt;A simplified analytical model, as shown in Fig. 2. (g), is proposed to investigate the influence of geometry parameters. Based on it, the analytical description of the magnetic field is deduced by magnetomotive force (MMF) and permeability functions. The influences of ferromagnetic pole-piece and PM on torque output are investigated. Fig. 2. (h) shows that the optimal pole-arc coefficient is about 0.3 at any thickness of ferromagnetic pole-piece, which agrees well with the proposed analytical model. As shown in Fig. 2. (i), the optimal thickness of PM is about 3mm and torque output rises with the pole-arc coefficient of PM increasing.

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Investigation of an Axial-Flux Magnetic-Geared Double-Rotor Machine with Interior-Modulating-Rotor

2022 Joint MMM-INTERMAG

Electromagnetic Characteristic Analysis of an Axial-Flux Magnetic-Geared Double-Rotor Machine with Interior-Modulating-Rotor

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.

Axial-flux magnetic-geared double-rotor machines (AMGDRMs) are verified a promising candidate for power splitting in hybrid electric vehicles (HEVs) [1]. However, in conventional AMGDRM, as can be seen in Fig. 1. (a), the modulating rotor is set in middle of stator and the permanent magnet (PM) rotor. Hence, the modulating rotor suffers from high axial magnetic force from the side of the PM rotor, resulting in low mechanical strength. In this paper, a new AMGDRM with interior-modulating-rotor is proposed to solve the problem of low mechanical strength. As shown in Fig. 1. (b)-(d), the PM rotor is set in middle of stator and the modulating rotor in proposed AMGDRM. Owing to that the PM rotor suffers from reverse axial magnetic forces from both sides simultaneously, the total axial magnetic force is dramatically reduced. The 3-D finite element analysis (FEA) simulation results shown in Fig. 1. (e) and (f) verify the low axial magnetic force property of proposed AMGDRM. Based on the magnetic-field modulating principle, the operating principle of proposed AMGDRM is investigated, and the speed and torque characteristics are also given. 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. 2. (a) and (b). As shown in Fig. 2. (c) and (d), the no load back electromagnetic force (EMF) verifies the speed characteristic. Fig. 2. (e) and (f) show that the torques of stator, the modulating rotor and the PM rotor are always in direct proportion, validating the torque characteristic. A simplified analytical model, as shown in Fig. 2. (g), is proposed to investigate the influence of geometry parameters. Based on it, the analytical description of the magnetic field is deduced by magnetomotive force (MMF) and permeability functions. The influences of ferromagnetic pole-piece and PM on torque output are investigated. Fig. 2. (h) shows that the optimal pole-arc coefficient is about 0.3 at any thickness of ferromagnetic pole-piece, which agrees well with the proposed analytical model. As shown in Fig. 2. (i), the optimal thickness of PM is about 3mm and torque output rises with the pole-arc coefficient of PM increasing.

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![](https://assets.underline.io/uploads/markdown_image/1/image/9c410cd88934435eacfebcf8dee444bf.jpg)

Investigation of an Axial-Flux Magnetic-Geared Double-Rotor Machine with Interior-Modulating-Rotor

poster

Abstract — The magnetic lead screw (MLS) is a new linear actuator with a high force density that enables contactless energy transfer. Improving the force density and reducing the installation error of the approximate helical type permanent magnets (PM) are the key challenges to realize the MLS. In this paper, based on the study of several existing PMs shapes and magnetization methods for MLS, a new MLS based on a combination of PM structures and magnetization directions is proposed. it not only reduces the mounting error by approaching the helical pole in a simpler way, but also increases the force density of the MLS. The results show that in addition to the air gap and the sizes of the PM having a significant effect on the force density, the effect of backiron saturation on it also needs to be considered. Finally, the performance of the proposed structure is compared with several existing structures and it is concluded that the force density is increased by nearly 60% for the same MLS volume and amount of PMs. Index Terms — MLS, magnetization direction, structure, PM, force density. The three common structures of MLS are shown in Fig. 1. (a) is the traditional model of radial magnetization for PMs, (b) is the halbach model of PMs with halbach magnetization, (c) is the salient model of radial magnetization for PMs. (d) is the proposed model, which adopts halbach magnetization, the salient pole shape adopts the radial magnetization, and the rectangular shape adopts the axial magnetization, and the salient pole PM can fix the rectangular PM, which is easy to install. The operation principle and others will be detailed in the full text. The structure proposed in this paper is shown in Fig. 1(d), and the detailed design process will be described in the full text. At present, there are two kinds of processing and installation structures to simulate helical PM as shown in Fig. 2: half skew ring and discrete. This paper also makes a comparison of these two PM structures, so that a PM structure with simple processing and installation and high force density are given. Finally, the comparison of these structures is detailed in the full text.

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Proposed model

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Performance comparison of four models

Design optimization and Analysis of a Novel High Force Density Magnetic Lead Screw with Discretized PMs and Different Magnetized Directions

I. INTRODUCTION In recent years, novel primary-excited PMLMs (PE-PMLMs) attract more and more attention with the merits of high thrust force density and low cost in long stroke application [1]. Different from the conventional PMLMs, PE-PMLMs integrate both the armature winding and PMs in the short primary, while the long secondary only consists of salient iron core [2]-[4]. The total cost can be greatly reduced thanks to this simple structure. However, PE-PMLMs still suffers from several key issues: 1) Severe saturation problem in the primary core. 2) Low overload capability due to the saturation problem. 3) Low mechanical reliability due to the influence of normal force on the primary. To solve these drawbacks in PE-PMLMs, this paper proposes a double-sided flux concentrated permanent magnet linear machines (DS-FCPMLMs) with saturation relieving effect. The utilized dual PMs in the primary yoke and slot opening can significantly improve the force density while relieving the saturation. II. TOPOLOGY AND PERFORMANCES Fig. 1(a) shows the topology of DS-FCPMLMs. Cross-shaped modular primary segments can be used to reduce the cost and enhance the extendibility of primary. Each primary module consists of one cross-shaped primary tooth and two coils. Then, PMs are employed in both the primary yoke and slot opening between two modules. The basic operation principle of this machine is shown in Fig. 1(b). The PM flux switches among four coils of the same phase at different secondary position. Hence, sinusoidal bipolar phase flux linkage can be obtained. Fig. 2 shows the electromagnetic performances of DS-FCPMLMs compared with DS-BFPMLMs that only has yoke PMs. Due to the flux concentrated effect, the back-EMF of DS-FCPMLMs can be enhanced by 48% compared with DS-BFPMLMs. Besides, DS-FCPMLMs can provide the average force of 338 N, which is increased by 52% compared with DS-BFPMLMs. Moreover, the magnetic saturation can be relieved in DS-FCPMLMs with the effect of slot PMs. Therefore, the proposed DS-FCPMLMs have the potential to provide direct drive propulsion for long stroke application.

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Fig. 1. The topology and operation principle of DS-FCPMLMs.

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Fig. 2. The electromagnetic performances of DS-FCPMLMs.

Design and Analysis of Novel Double-sided Flux Concentrated Permanent Magnet Linear Machines with Saturation Relieving Effect

Introduction Transverse flux tubular linear machine (TF-TLM) has merits of high torque density and low side force and is suitable for wave energy conversion (WEC) application. However, excited by permanent magnets (PM), it is hard for TF-TLM to adjust the air gap magnetic field and keep the terminal voltage constant at different operation speed [1]. In this paper, a hybrid-excitation transverse-flux tubular linear machine (HE-TF-TLM) excited by consequent-pole permanent magnet (CP-PM) and DC windings in parallel is proposed. The 3D FEA results have proved that the voltage regulation ratio of HE-TF-LM reaches 87.36%, and thrust density of the machine is not compromised, which is calculated as 155kN/m3. Operation Principle Fig.1 (a1), (b1) (c1) illustrate the flux distribution of the generator of Phase A under condition of idc=0A, 6A and -6A respectively. Fig.1 (a2), (b2) and (c2) presents the magnetic field distribution via 3D FEA calculation. After applying DC current idc&gt;0A, due to the large reluctance of PM, φDCa travels through A2 and A6 to form the magnetic route. Therefore, flux linkages in A2 and A6 are enhanced by φDCa and φPMa together. After applying DC current idc&lt;0A, flux linkages in A2 and A6 are cancelled by φDCa and φPMa. However, as φDCa and φPMa join together in the field teeth, the saturation in the field teeth is inevitable under this condition. Results Analysis Fig.2 (a) presents the no-load back emf under different DC excitation (idc=0A, 6 A, -6A, Ndc=55). The 3D FEA results reveal that the back emf can be altered from 96mV/turn to 253mV/turn at unit speed. And the voltage regulation reaches 87.36%. Fig.2 (b) calculates the induced voltage under different working speed (0.5m/s, 1m/s and 2m/s). It is perceived that by altering the excitation current, the output voltage of the generator can keep constant. Fig.2 (c) presents the output thrust force of the machine under different DC excitations (idc=0A, 6 A, -6A). According to the FEA results, output thrust force reaches 279.14N, and the thrust density of the proposed machine can be effectively improved to 155 kN/m3 at rated excitation (idc=6A). Meanwhile, the output thrust force can be effectively changed by altering DC current.

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Design of a Novel Hybrid-Excited Transverse-Flux Tubular Linear Machine with Complementary Structure

I.Introduction Direct drive wave energy conversion (DDWEC) has attracted wide attention [1]. Various ways have been employed to further reduce the cost of wave energy conversion and promote the commercialization process, including the application of permanent magnets (PMs). PM generator has better electromagnetic performance for its high energy density [2,3]. The configuration of DDWEC proposed in this paper is combining the axial flux generator (AFG) and magnetic lead screw (MLS). However, the extensive use of PM will increase the manufacturing cost. For reducing the PM cost in DDWEC, a modified consequent-pole PM AFG (CPM-AFG) is proposed in this paper. By changing one side of PMs into iron-cores, which is called iron-pole, the volume of PM can be reduced. II.Generator Topology The whole configuration of the DDWEC system is that AFG located inside of the MLS is connected softly to the buoy when the screw and nut of MLS is connected directly to the buoy and rotor, respectively, as is shown in Fig. 1. Through MLS, the linear reciprocating motion of the wave can be transformed into the rotational motion of nut. When the buoy moves up and down, the rotor composed of modulation teeth in AFG rotate to generate energy. The rotor's angular velocity can be expressed as: ω=Gv=πv/τ where G is defined as gear ratio of MLS, v is screw's linear velocity and τ is the pole width of MLS. Similar to magnetic gear, the pole pairs of armature windings paw, the pole pairs of PM pPM and the iron pieces of rotor Ni should satisfy: Ni= paw + pPM Fig. 1 III.Results The simulation result shown in Fig. 2 indicates that although the volume of PM in the CPM-AFG is reduced by half, the flux linkage and torque are not reduced to half compared with the conventional surface-mounted PM axial flux generator (SPM-AFG). The amplitudes of SPM-AFG and CPM-AFG are 0.14Wb and 0.11Wb, respectively. The average electromagnetic torques of them are 23.2 Nm and 19.1 Nm, respectively. Fig. 2 IV.Conclusion Simulation results shown that the proposed CPM-AFG is suitable for DDWEC which can reduce the consumption of PM, reduce the cost of manufacture and improves the utilization ratio of PM.

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Axial Flux Generator with Consequent-Pole PM Stator for Direct Drive Wave Energy Conversion

Wireless power transfer (WPT) technology is being applied to many industrial applications [1]. It brings convenience and safety especially for undermine or underwater operation scenarios [1-2]. However, in those working scenarios, such as wireless charging for underwater robots or sensor networks, the system usually requires at least meter-range transmission distance, which is several times of the transmitter coil radius [2-3]. For traditional 2-coil-coupler system, the long-range operation will easily lead to unacceptable power loss and efficiency drop. Also, the traditional single-pad repeater is not suitable for underwater environment since the water flow will cause large and unstable angular misalignment. The variance of the mutual inductance between the coils can be very sensitive to the position relationships and the fluctuation may cause a system failure. To solve this problem, this paper presents an omnidirectional power extender for long-range underwater WPT systems. The proposed system configuration can be shown in Fig. 1. The power extender consists of two identical coils which are orthogonal and thus decoupled to each other [4]. The two coils are compensated separately for independent operation. Under the condition of the same internal resistances, the magnetic field generated by the two coils can be compensated by each other at arbitrary angles and the effect of the water flow can be effectively reduced. Thus, the system can have a relatively stable high output. Finite element analysis (FEA) has been conducted for a 100:1 scale-down system with the extender under the angular misalignment ranges from -90° to 90°. The simulated results of the output power are shown in Fig. 2. The system can reach over 70% efficiency for the transmission distance over 2 times the transmitter coil radius. The output power can be maintained over 35% even at the worst angular positions, which validates the effectiveness of the proposed system.

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Fig. 1. Proposed omnidirectional power extender. (a) Application for underwater WPT system (b) System configuration

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Fig. 2 Simulated output power versus angular misalignment

Design and Analysis of Omnidirectional Power Extender for Long-Range Underwater Wireless Power Transfer System

ABSTRACT Aiming at the problem of feature extraction and state identification of transformer DC bias vibration in HVDC transmission, the principle of transformer DC bias and the vibration mechanism of core and windings are studied and analyzed. Based on the dynamic simulation experiment platform, the vibration signals of transformer under different operating conditions are collected and carried out by the statistical calculation and Hilbert-Huang Transform (HHT). Then, the characteristic parameters and vibration law are obtained and explored. Taking the statistical parameters and HHT data of transformer as feature vectors, the DC bias state of transformer is identified by support vector machine (SVM) classification method, which provides a new idea and auxiliary decision-making means for DC bias fault diagnosis of transformer. The results showed that the ratio of windings vibration in 300 Hz frequency band increases under DC bias, while that of core vibration signal in 300 ~ 600 Hz frequency band increases. Through the SVM classification method, the mean identification rate of transformer DC bias state reaches 96.8%, which can accurately identify the problem of transformer DC bias. CONTENT This paper is organized as follows. In Section II, the mechanism of transformer vibration under HVDC bias magnetic state is described. In Section III, a identification method of HHT-SVM vibration signal is introduced. In Section IV, the vibration signal acquisition and result analysis based on HHT-SVM are presented and discussed in detail. CONCLUSION The vibration signals of transformer windings and core are affected by the distortion of excitation current and core saturation under the condition of DC bias magnetic field. Among them, the winding vibration signal changes little, but the amplitude of the 300 Hz frequency band increases, and the core vibration signal changes greatly, and the signal gradually shifts to the middle frequency band. By collecting vibration signals and combining with HHT-SVM identification method, the status of transformer DC magnetic bias can be effectively identified, which provides a new research idea and auxiliary decision-making means for transformer DC magnetic bias fault diagnosis.

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Feature Extraction and State Identification of Transformer DC Bias Vibration Based on HHT-SVM

ABSTRACT The surface vibration signals of 500 kV autotransformer with different structures are measured, and the frequency domain characteristics of which are analyzed in this paper. Firstly, the surface vibration signal measuring points are set according to the specific arrangement of the core and windings of the transformer. Secondly, the vibration signals at different transformer measuring points under the same load and different loads are measured respectively. Finally, the frequency characteristics of the measured vibration signals are compared and analyzed. Then, use adaptive blind source separation algorithm (ABSSA) for transformer surface vibration signal processing, the two signals obtained are close to the vibration characteristics of core and windings respectively, and the same is true of the separated signals. It is proved that the accurate vibration signals of core and windings can be obtained by blind source separation, and is helpful for further analysis of the operation state of the transformer core and windings. CONTENT This paper is organized as follows. In Section II, the vibration mechanism of transformer ontology is introduced and analyzed. In Section III, the selection of vibration measuring points on transformer surface is described. In Section IV, the measurement of vibration signals on transformer surface is presented, and the comparison and analysis of the results are discussed in detail. CONCLUSION Combined with the structure of the transformer, the vibration signals of different measuring points on the surface of the 500 kV autotransformer with two different structures in actual operation were measured, and the ABSSA based on the classical least mean square algorithm (LMSA) was used to process the vibration signals on the surface of the transformer, and the two source signals were obtained, which are close to the signals of the blind source separation of the transformer. It is necessary to take into account the correlation between the vibration of the core and the windings, as well as the non-linearity of the vibration signal transmission process. This will be more conducive to transformer fault signal extraction and fault diagnosis.

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Measurement and Frequency Characteristics Analysis of 500 kV Transformer Surface Vibration Signals

Wireless Sensor Network (WSN) node communication, which is used to gather information on a wide range of sensors, uses wireless communication that does not require wiring, but power is supplied via wired or battery[1]. In order to manufacture many small switches as battery-less, an economical self-powered generating application excluding additional elements such as piezoelectric elements are required. In addition, small electromagnetic induction studies are required because mechanical kinetic energy must be converted into electrical energy in a small spatial structure including pushbuttons[2]-[4]. This paper proposes a self-powered generating apparatus applicable to two-gang wireless switches. The electromagnetic induction phenomenon follows Faraday's law, which generates induced voltage when the magnetic field passing through the coil changes at time. Electromagnetic induction self-powered generating apparatus require magnets and conductors that generate electromotive force to create magnetic fields. Figure 1 shows the proposed new two-gang switch structure and magnetic flux flow. The right side of the Conventional one-gang switch magnetic material 2 was opened and magnet 2 and magnetic material 4 were added. The coil is in common use and is assumed to have the same winding resistance and inductance for comparison with the conventional one-gang switch. The no-load back Electromotive Force(EMF) waveforms of the convolutional one-gang switch and the proposed two-gang switch are shown in Figure 2. In the two-gang switch, when the switch lever 1 and 2 are operated, the no-load back EMF waveform is divided into a positive direction and a reverse direction. Therefore, the switch can be miniaturized because sensors are not required to distinguish each push operation. And the performance has been improved to the induced voltage ratio 84% of the one-gang switch. Later, the mechanism of the proposed two-gang switch will be described in full paper to compared with the existing one-gang switch mechanism, and optimum design according to the detailed shape will also be added.

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Design of Battery-less Wireless Switch that Share Coils in common using Electromagnetic induction Energy Harversting Mechanism

Design of Battery-less Wireless Switch that Share Coils in Common Using Electromagnetic Induction Energy Harversting Mechanism

Hydrogen is considered as a potential energy carrier, because there is no greenhouse polluting gas (such as carbon dioxide) generated during the energy releasing process. Water electrolysis is the best way to obtain pure hydrogen, but its low energy efficiency greatly limits its wide application. Hydrogen is a diamagnetic substance that can be manipulated by an external field. The various locomotion behaviors of the hydrogen bubbles under different magnetism are first shown in Fig.1. Fig. 1(a) shows that hydrogen bubbles move upward from the surface of the graphite electrode when the voltage of 150V is applied. Fig1. (b) shows that hydrogen bubbles evolving from graphite electrode slightly move towards the upper right when the magnet S-pole is faced with the cathode. This motion indicates that the magnetic field may help detach the bubbles from the surface of graphite electrode because of the micro-magnetohydrodynamic (MHD) effect. Fig.1 (c) shows that hydrogen bubbles move towards the right more significantly when the graphite electrode is changed to a platinum electrode, which is a paramagnetic material with a higher magnetic susceptibility than graphite. This result shows that the paramagnetic property will further enhance the locomotion of the bubbles and detach bubbles from the electrode more quickly. Figs. 2(a) and 2(b) respectively show a platinum electrode faced with a magnet generates a greater increase in the current density and conductivity of the water under the same applied voltage. In this paper, electrodes with different magnetism are adapted to hydrogen production in water electrolysis. The various moving behaviors of the bubbles under the different magnetism of electrode and the field conditions will be demonstrated in the full paper and the effects of working parameters related to magnetism and water electrolysis are discussed as well.

![](https://assets.underline.io/uploads/markdown_image/1/image/1c277bb1460ff3db5480660c4301df2b.jpg)

3-D view of Magnetic flux flow by conventional two-gang switch when the switch lever 1 is tilted down


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Fig.2 (a) Current density vs. Charging voltage (b) Conductivity vs. Charging voltage for the different electrodes with and without the effect of magnetic field.

The Effect of Magnetism and Magnetic field on Locomotion of Hydrogen and Hydrogen Production Efficiency

I. Introduction Arc permanent magnet (PM) machines (APMMs) can directly connect the load without auxiliary devices, which are promising in large telescope drives [1] [2]. However, the conventional APMM with rotor PM suffers from a low PM utilization. In this paper, two new dual-stator consequent pole flux reversal APMMs (DS-CPFRAPMMs) are proposed and studied. The topologies and operation principles of the proposed machines are described. The electromagnetic performances of machines are analyzed by finite element analysis. II. Machine Topology and Operation Principle Fig. 1 shows the topologies of the proposed DS-CPFRAPMMs, which are named as machines I and II, respectively. It can be seen that both machines consists of two stators and one rotor, and each stator is composed of three modules. The three-phase concentrated windings are wound on the teeth of stator, which can offer the merits of short end length and low copper loss. Besides, the alternatively PMs and iron poles are placed on the top of stator teeth, which forms a consequent pole PM arrangement. The polarities of PMs on the inner and outer stators are opposite for machine I, while those are the same for machine II. Moreover, the rotor structures of machines I and II are also different. For machine I, the iron-only rotor is designed with double-sided salient poles. However, for machine II, the rotor is made up of separated iron poles. For both machines, each stator module and rotor forms a 12 stator-slot/11 rotor-pole combination. The operation principles of DS-CPFRAPMMs are based on the flux modulation effect, and the torque of machines are generated by taking advantage of the modulated air-gap field harmonics. III. Electromagnetic Performance Evaluation As shown in Fig. 2 (a) and (b), machine II has higher no-load phase flux linkage and back-EMF than machine I. According to Fig.2 (c), the average torque of machine II is 20.7% higher than that of machine I. However, machine I has a relatively low cogging torque. In addition, compared with machine II, machine I has a better over-load torque capability. More detailed design considerations and electromagnetic performance comparison results will be presented in the full paper.

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Fig. 1

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Fig. 2

Next from 2022 Joint MMM-INTERMAG

Design optimization and Analysis of a Novel High Force Density Magnetic Lead Screw with Discretized PMs and Different Magnetized Directions

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