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Surface-mounted permanent magnet (SPM) machines with skewed slots as vehicle drives are widely used. Due to skewed slots, electromagnetic characteristics are modulated by the skew effect. To analyze the skew effect, Maxwell’s equations-based 3-D analytical model is proposed. Based on differences in 3-D air-gap flux density distribution, the mechanism by which the skew effect modulates cogging torque, flux linkage, and back electromotive force (EMF) is investigated. The effectiveness of the theory about the skew effect is verified by both the finite element method (FEM) and the experimental result. [ABSTRACT FROM AUTHOR]

Due to the high power density, short axial size, and wide permanent magnet (PM) flux linkage regulation range, an axial-flux PM memory machine (AFPMMM) with hybrid Halbach array is investigated in this article. To solve the problem of magnetic density variation of Halbach array composed of different types of PMs in asymmetric bilateral air-gap structure, the analytical method for calculating the air-gap flux density of AFPMMM is presented through mathematical analysis, which uses cylindrical coordinate system instead of Cartesian coordinate system and is solved by equivalent method, separated variable method, and boundary conditions. The magnetic field generated by the Halbach array is divided into three directions: radial, circumferential, and axial. The analytical model is compared with the finite element method (FEM) simulation results to verify its effectiveness. In addition, an approximate piecewise linear hysteresis model with parallelogram return line is established based on the analytical expression of magnetic field. By applying different pulse currents to change the residual flux density of PM, the flux regulation characteristics of the motor are studied, and it is found that the air-gap flux density of the motor can be smoothly adjusted by continuously changing the pulse current, which plays a positive role in solving the problem of online magnetic regulation of the motor. [ABSTRACT FROM AUTHOR]

This article presents an accurate analytical model (AM) for synchronous reluctance machine (SynRM) that incorporates the effect of stator slots on the air gap flux density and torque waveforms. From the formulation of magnetic potential in the air gap for both the stator and rotor, the flux density is obtained, considering the first harmonic of the flux density and the electric loading, the average torque is calculated using the Lorentz’s force. The ripple torque is obtained from the energy stored in magnetic circuit. The method is developed for a rotor with one flux barrier per pole and then extended to a larger number of barriers. To validate the results obtained by the AM proposed finite element analysis have been carried out. Several comparisons have been derived considering different rotor positions as well as different harmonic orders, and the pros and cons of the method are highlighted. The model performs fast and can predict results with high accuracy, and can be adopted to speed up the preliminary design and optimizations of this type of motors, with respect to finite element. In addition, from the analytical expressions it is possible to obtain all the correlations between electrical, magnetic, and geometrical characteristics of the machine, with the advantage of enabling a faster machine design. [ABSTRACT FROM AUTHOR]

The peripheral magnetic field of the motor may cause magnetic field interference to the surrounding sensors, which would reduce the accuracy of sensors and affect the safety and concealment of vessel. This article explored the environmental magnetic field distribution law of a permanent magnet (PM) motor with two-pole parallel magnetization. A no-cogging magnetic field model was obtained by solving Maxwell equations, and the relationship between the air gap flux density and the environment flux density was built considering the motor cogging effect. In addition, a mathematical model of connections between the back electromotive force (EMF) and the environmental flux density was built, and the correctness of the model was verified by COMSOL. It is concluded that the circumferential and radial components of the environmental magnetic field are distributed sinusoidally, and the magnetic flux density modulus remains constant on the equidistant circumferential line, but attenuates squarely with the distance from the motor. It provides ideas for magnetic field analysis in the peripheral environment of other types of motors, sensors, and other anti-motor electromagnetic interference, magnetic field compensation for geomagnetic measurement, and motor fault diagnosis. [ABSTRACT FROM AUTHOR]

A new partitioned stator field modulation machine (PSFMM) with H-shape permanent magnet (HPM) excitation (HPM-PSFMM) is proposed, which is evolved from the conventional flux-switching machine (FSM) and flux-reversal machine (FRM). The proposed HPM-PSFMM combines the merits of high reliability and good heat dissipation characteristic. In addition, it exhibits high torque production with low torque ripple. Based on the theory of electrical machine operation, the FSM and FRM can be transformed into PSFMM with interior permanent magnet (IPM) and surface-mounted PM (SPM) excitation by changing the position of PM excitation, respectively. It benefits to improve space utilization and increase slot area for a large number of armature windings. For reducing the flux leakage and enhancing the flux density in air gaps, the IPM and SPM excitation are combined into HPM excitation. The iron-pole rotor between the inner and outer stators acts the role of modulator to modulate the magnetic field excited by HPM excitation to couple with the armature reaction for converting electromechanical energy. The evolution process, operating principle, and key design parameters of the proposed HPM-PSFMM are presented. Finally, using the finite element analysis (FEA), it can be proven that the proposed HPM-PSFMM has the merits of high torque production, low flux leakage, low total harmonic distortion (THD), and low torque ripple when compared to other stator-PM machines, which is a desirable choice for high stability applications. [ABSTRACT FROM AUTHOR]

The magnetic field distribution in the air gap is of great importance in the design of rotary machines. In this article, an efficient analytical method is presented, which is capable of plotting the air-gap flux density waveform of induction machines (IMs) less time-consuming than the finite element method (FEM) does. The proposed method, based on the product of the current linkage waveform and the permeance waveform, utilizes the calculations of the steady-state equivalent circuit to ensure the accuracy and an equivalent air-gap reluctance model to take into account both the slot opening effect and the rotor movement. The method is tested on a general IM with different load cases and different design parameters, and the results are compared to the FEM calculations. It can be concluded that the proposed analytical method is an efficient option in the motor design to investigate the influence of the parameters on the flux density distribution. [ABSTRACT FROM AUTHOR]

This article proposes a new hybrid-excited partitioned stator flux modulated machine with a dual-permanent magnet (HE-PSFMDPMM). The HE-PSFMDPMM employs consequent-pole (CP) permanent magnets (PMs) on the inner stator and Halbach array CP PMs on the rotor, which can yield abundant air-gap flux density working harmonics to increase the torque capability. Meanwhile, the field windings are housed in the inner stator to achieve flux weakening. The topology, working principle, and design optimization of HE-PSFMDPMM are investigated, respectively. The electromagnetic performances of HE-PSFMDPMM are analyzed and compared with that of a contrast model with conventional CP PMs on the rotor. The results indicate that by using dual-PM excitation, HE-PSFMDPMM can provide large flux linkage, high torque production with low torque ripple, and high efficiency. Meanwhile, a good flux weakening capability is obtained with the aid of direct current (dc) excitation. Moreover, compared with the contrast model, the proposed HE-PSFMDPMM with Halbach array CP PMs on the rotor can offer the merits of lower cogging torque and torque ripple, higher power factor, and better flux weakening capability. [ABSTRACT FROM AUTHOR]

This article proposes a novel axial field switched flux memory machine (AF-SFMM) which is analyzed by a combined analytical method. Compared with conventional axial field (AF) permanent magnet (PM) machines having magnets in the rotor side, the AF-SFMM benefits from good heat dissipation, high rotor robustness, and improved power density. Meanwhile, because of the utilization of low coercive force PM materials, the proposed machine can flexibly regulate air-gap flux. This analytical method is characterized by the combination of a quasi-3-D (quasi-3D) finite element method, a magnetomotive force–permeance-based method, and a virtual linear hysteresis model of low coercive force PM. In addition, compared with conventional time-consuming 3-D finite element analysis (FEA), the proposed method can improve the computational efficiency significantly with satisfactory accuracy. This makes the proposed combined analytical method suitable for preliminary sizing determination of AF-SFMM. Meanwhile, the effectiveness of the proposed analytical method is validated by FEA results. [ABSTRACT FROM AUTHOR]

This study investigated an efficient procedure for developing an accurate behavioral model of a cage induction motor (IM) based on the multiport Cauer ladder network (CLN). The CLN method was applied to a cage IM with semi-closed rotor slots as a model order reduction (MOR) technique, and a method for selecting the appropriate space harmonics (SHs) included in the air-gap flux density, which is necessary for a multiport CLN method for induction machines, was discussed. Then, the developed approach was applied to the transient analysis of the cage IM coupled with a control system, and its effectiveness in terms of computational accuracy and cost was investigated. [ABSTRACT FROM AUTHOR]

A new type of hybrid magnet dual stator field modulation machine with different split ratios of stators (DSR-HMDSFMM) is proposed in this article, which has the merit of high torque density. The split teeth of stator sever as modulators to modulate air gap flux density based on the magnetic gearing effect for high torque production. The total split tooth number of inner stator is equal to that of outer stator because the pole pair numbers of armature reaction and permanent magnet (PM) excitation on rotor are equal. Furtherly, the inner and outer stators with different split ratios and same split tooth number are employed to increase torque production because armature windings with high winding factor and high turn number can be used. In addition, the employment of hybrid magnet excitation can increase space utilization and enhance the air gap flux density with low harmonic distortion. Therefore, the proposed DSR-HMDSFMM can achieve high torque production with the same volume and PM usage. In order to find the optimal split ratio match of stators, several DSR-HMDSFMMs with different combinations of split ratios are proposed and calculated. The configuration and operating principle are illustrated, together with electromagnetic performances of the proposed machines analyzed using finite element analysis (FEA). The FEA-predicted results show that the proposed HMDSFMM exhibits high air-gap flux density with low harmonic distortion and high torque density, which is promising for the direct-drive applications. [ABSTRACT FROM AUTHOR]

This article presents a magnetic–pneumatic levitation system for gravity offload system of large deployable mechanisms, which combines the attractive force of magnetic stage and thrust force of air-bearing and is characterized by inner stability. The article focuses on the design of the hybrid magnetic stage. The equivalent magnetic circuit network method is used to analyze the electromagnetic (EM)-permanent hybrid magnetic field, the distribution of magnetic flux density of the air gap is solved, and then the magnetic force is obtained. To improve the design efficiency, the two-step design is adopted. First, the air gap is determined by sweeping the reluctance ratio to reduce the influence of parameter deviation of cast iron on the magnetic force. Then, the other parameters of the hybrid magnetic stage are optimized based on the multi-objective particle swarm optimization (MOPSO) algorithm. Through the comparison between the results of finite-element simulation and prototype experiments, the accuracy of the model is verified, and the expected design goal is achieved. [ABSTRACT FROM AUTHOR]

The consequent permanent magnet (CPM) pole rotor and harmonic utilization permanent magnet (HUPM) rotor are promising candidates for electric machines with less rare earth materials. Therefore, this article focuses on the analysis and comparison of these rotor types in terms of air-gap flux density characteristics, magnet utilization, and torque density. In the first part, an analytical approach is used to investigate the magneto motive force (MMF) distribution of the rotor and air-gap flux density characteristics. In the second part, finite-element methods (FEMs) are used to compare both rotor topologies with a conventional interior permanent magnet (PM) and spoke PM rotor. The results show that CPM and HUPM rotors can reduce the volume of PMs compared with the conventional configurations. However, with the HUPM rotor, a higher torque density and magnet utilization ratio can be achieved at the same time. [ABSTRACT FROM AUTHOR]

Fast and accurate modeling of large turbogenerators is of great importance for optimal design and commercial value. Therefore, a 2-D nonlinear magnetic equivalent circuit (MEC) model considering saturation and rotor motion is proposed in this article. When the node-based MEC adopts relaxation iteration for nonlinear calculation, it is not easy to converge by using traditional interpolation function and piecewise fitting of the core B–H or $u_{r} (B)$ curve. The main contribution of this article is to find that using continuous fitting function is of great significance for the convergence of nonlinear iteration. At the same time, a simple and effective MEC of air gap is also provided. The flux density of air gap and stator tooth obtained by the proposed method is in good agreement with results of the finite element. No-load characteristics were also verified by the finite element and experiment. The calculation time of a cycle takes about 700 s by the finite element, and however, MEC only takes about 2 s. [ABSTRACT FROM AUTHOR]

Offshore wind turbines are the key enabling technology to increase the green energy penetration in the electricity market. Increasing the power generation per tower and reducing the levelized cost of energy are the two significant problems faced by wind turbine manufacturers. Traditional turbine manufacturers use rare-earth permanent magnets (PMs) to increase the air-gap flux density and maximize the machine outer diameter (OD) to increase the torque output. Since the air-gap flux density achievable with available PM is limited, increasing the power output of a traditional generator invariably leads to a significant increase in the volume and mass on top of the turbine tower and associated manufacturing, transportation, and installation costs. Superconducting (SC) wind turbine generators offer 5 to 10 times the air-gap flux density of a PM generator, and a corresponding increase in specific power and power density. Previous MW scale SC wind turbines designs used heavy back iron in the design, iron saturation limits the achievable air-gap flux density in the designs and resulted in bulky generators and moderate efficiency. In this article, a hybrid design approach is proposed to reach an ultrahigh field (5 to 10 times of PM air-gap flux density) and high efficiency (>98%) SC wind turbine for offshore wind turbine. An additional stray field limitation is introduced for safety concerns and shielding techniques are explored. Electromagnetic, mechanical, and cooling designs are provided to support the feasibility of proposed SC wind turbines. A nacelle integration inside a commercially available 6 MW wind turbine is shown to demonstrate the size comparison of the proposed generator. [ABSTRACT FROM AUTHOR]

In this article, a novel spoke-type permanent magnet (PM) machine with two types of PM materials is proposed to reduce the cost. In order to improve torque density and reduce torque ripple, the multi-objective optimization combined finite element method (FEM) and genetic algorithm (GA) are used. In addition, the electromagnetic performances of the novel spoke-type PM machine, including no-load air-gap flux density, electromagnetic torque, torque ripple, efficiency, and cost are compared with the conventional spoke-type PM machine. It is demonstrated that the novel spoke-type PM machine obtains a 1.5% lower torque ripple and 36% lower cost, and the torque density is 4.3% lower than the conventional spoke-type PM machine. Meanwhile, the novel spoke-type PM machine has lower core loss and higher efficiency. Finally, a 40 kW spoke-type PM machine is manufactured to verify the analyzing method. Experimental results demonstrate that the proposed machine exhibits high torque density and low cost in the application of electric vehicles (EVs). [ABSTRACT FROM AUTHOR]

This article proposes a rotor design method suitable for double-layer interior permanent magnet synchronous motor (DIPMSM), which can reduce electromagnetic torque ripple and at the same time reduce the electromagnetic noise of the motor. In previous studies, the inverse cosine function (ICF) was used to modify the rotor shape for making the air-gap flux density distribution sinusoidal under no-load conditions, which can reduce the torque ripple. However, conventional ICF can only be used in a single-layer interior rotor structure. Consequently, this article proposes a piecewise inverse cosine function (PICF) based on ICF, which can be applied to DIPMSM. To verify the improvement of the proposed method in the electromagnetic and noise aspects of the motor, the electromagnetic model and a noise prediction model of the 36-slot/8-pole motor are established by the finite element method. The PICF model is compared with the prototype in the aspects of electromagnetic performance and noise. The torque ripple is reduced by 54.16%, from ±2.4 to ±1.1 N m, and the electromagnetic noise is reduced by about 4.9 dB. Finally, the accuracy of the noise prediction model is verified by the noise test of the prototype. [ABSTRACT FROM AUTHOR]

Electromagnetic performance of high-speed permanent magnet synchronous machines (PMSMs) is studied for electro-hydrostatic actuator (EHA) applications in this article. The electromotive force (EMF) of different magnet pole-arc to pole-pitch ratios is studied. The no-load air-gap density, cogging torque, average torque, torque ripple, core loss, and rotor eddy current losses are investigated by closed slots design. The rotor eddy current losses of different magnetic retaining sleeve materials such as stainless steel, titanium alloy, and carbon fiber are calculated by finite-element analysis (FEA). The results show that, compared with the opening slot structure, the torque ripple and the rotor eddy current losses of closed slot structure are extremely reduced due to the fact that the 11th and 13th harmonics of air-gap flux density are significantly reduced and the slotting effect are effectively weakened. Increase the closed slot height not only reduce the average torque and increase the core loss but also the torque ripple and the rotor eddy current losses reduction effect is slight. A high-speed PMSM with closed slots design is prototyped to verify the analysis. [ABSTRACT FROM AUTHOR]

In general, an air gap plays an important function in the magnetic core. It will enhance the stability of the inductance value of a reactor, increase the power density of the inductor, and optimize the properties of a high-frequency transformer. Hence, it is of great significance to study the influence of the air gap on the properties of magnetic cores. Based on a novel designed tester, the dynamic magnetic properties of the C-type amorphous (AMCC025) core and nanocrystalline (F3CC0125) core with different lengths of the air gaps are measured and analyzed when the cores are excited at different frequencies. In addition, the modified Steinmetz empirical formula which takes the fringing magnetic flux near the air gap into account is proposed. The calculated magnetic properties obtained from the modified formula show great agreement with the measured results. The average prediction error of the modified model is confined in 10%. Both the calculated and experimental results indicate that the influence of the fringing magnetic flux could be ignored when the length of the air gap is less than 5% length of the equivalent magnetic circuit. In particular, the frequency-dependent losses decrease to a minimum value and then increase with the increase in flux density accordingly. The modified loss model and results would be beneficial to the design of high-frequency inductors and transformer cores. [ABSTRACT FROM AUTHOR]

In this article, based on a 6-stator coil/17 rotor-tooth (6/17) conventional concentrated-winding multitooth flux-switching permanent magnet (C-MFSPM) machine, a novel full-pitch multitooth flux-switching permanent magnet (FP-MFSPM) machine is proposed by changing winding configurations. Then the electromagnetic performance of six FP-MFSPM topologies sharing the same 6-stator coil but with different rotor teeth combinations, namely, 6/13, 6/15, 6/17, 6/19, 6/21, and 6/23, is compared by using finite-element analysis (FEA). The results show that 6/17 and 6/19 are the optimal stator coil/rotor tooth combinations for FP-MFSPM machines, which exhibit better electromagnetic performance such as more enormous torque and smaller torque ripple. Thereafter, the existing C-MFSPM and the proposed FP-MFSPM machines with 6/17 and 6/19 structures are quantitatively compared in terms of no-load back electromotive force (back EMF), air-gap flux density, cogging torque, electromagnetic torque, torque ripple, and so on. The FEA-predicted results validate that the proposed FP-MFSPM machines have more sinusoidal back EMF, larger torque output, and smaller torque ripple, which are superior to the C-MFSPM topologies. [ABSTRACT FROM AUTHOR]

In order to solve the problems of poor capacity and unsatisfactory efficiency of flux-weakening control for the axial-flux permanent magnet (AFPM) machines with surface-mounted permanent magnet (PM) rotor structure, a new axial-flux hybrid-excitation machine (AFHEM) with double consequent-pole rotors is proposed, which combines the high torque density of the AFPM machine and the flexible flux regulation of the hybrid excitation machine. It meets the stringent requirements of the distributed in-wheel motor electric drive vehicle for high efficiency and high torque density. The topology, principle, and basic electromagnetic properties of the new axial-flux hybrid-excitation in-wheel motor are presented in this article. Based on the complex magnetic circuit of the AFHEM, a 3-D equivalent magnetic network (EMN) model is established. The air-gap flux density, flux linkage, back EMF, torque, and fault tolerance ability of the motor are solved through the EMN model and compared with the 3-D finite element analysis (FEA) to verify its validity and correctness. It is hoped to form a rapid design method for the new type of motor with the complex structure of 3-D magnetic flux path property. Finally, based on the EMN model, the influences of the magnetic saturation on the excitation regulation capability of the proposed AFHEM are analyzed, which provides a guideline for the optimization design of the new AFHE in-wheel motor. [ABSTRACT FROM AUTHOR]

This article presents a quasi-3-D analytical model for double-sided axial-flux permanent magnet machines (AFPMMs) with coreless structures. A simple, fast, and accurate technique is developed to calculate flux densities in different parts of the AFPMM combining the solution of Maxwell’s equations and the magnetic equivalent circuit (MEC). In this technique, Maxwell’s equations are used to generate flux sources that are used in the reluctance network of the MEC. After calculating all the reluctances and flux sources, the magnetic flux densities are obtained. This method takes into account the effects of permanent magnet (PM) reluctance, leakage flux between PM-to-PM, PM-to-rotor leakage flux at different PM edges, and the fringing flux effect. By considering these leakage fluxes as a factor called variation function in the design procedure of the machine, the analysis time is dramatically reduced compared to numerical methods while maintained high reliability. It should be noted that since considering saturation phenomenon effects in coreless AFPMM analysis does not give rise to significantly different performances, they are not included in the proposed model. Furthermore, the machine’s main features, such as the axial and tangential components of the no-load flux density in the air-gap and stator areas, as well as the back electromotive force (EMF), are derived by using magnetic field solutions and simple equivalent circuits. Finally, to validate the accuracy of the proposed method, the analytical results are compared to the case that no leakage fluxes are included in the analytical model and to the 3-D finite-element analysis (FEA) in terms of computation time and accuracy. [ABSTRACT FROM AUTHOR]

The shaping of the air gap of a V-typed fractional slot concentrated windings interior permanent magnet synchronous machines (IPMSMs) is investigated for compressed-air system (CAS) applications in this article. The harmonics of no-load air gap density, average torque, torque ripple, and iron losses are studied by the finite element analysis (FEA). The results show that the air gap shaping of the V-typed IPMSM can be effectively used to reduce the torque ripple and stator core loss. It is because the low-order harmonics of the air gap flux density can be reduced with a little decrease in the average torque. The proposed air gap shaping methods have the advantages of simple design and simple manufacture. A V-typed IPMSM with air gap shaping is prototyped to verify the correctness of the analysis results. [ABSTRACT FROM AUTHOR]

In this article, a process for reducing the electromagnetic vibration and noise by changing the shape of the stator is presented. Although the fundamental wave of the air gap magnetic flux density contributes to the average torque of the motor, other spatial harmonics which were except the fundamental wave of that cause vibration and enfeeble the output of the motor. Therefore, it is important to reduce the spatial harmonics for performance of the motor. Through the proposed process, it is possible to obtain an objective function to reduce the specific harmonics by assigning weights to each spatial harmonic. The reduction in the fundamental wave is minimized and it is possible to reduce the spatial harmonics that have an adverse impact on vibration. After the process, a model can be found that maintains the electromagnetic performance as much as possible while optimally reducing the vibration. To verify the process, the electromagnetic vibrations by a radial force of the proposed and conventional models were compared, and it was confirmed that the electromagnetic vibration of the proposed model was reduced. The validity of the analysis was proved through finite-element analysis. [ABSTRACT FROM AUTHOR]

In this article, a new method of enhancing the anti-demagnetization capability based on the modulation principle is proposed for a less-rare-earth permanent-magnet synchronous motor (PMSM). By means of analytical method, the relationship between the demagnetization effect and the air gap flux density, calculated by magnetic motive force (MMF) and magnetic permeance, is established. By implementing the design of the fundamental harmonic modulation, the anti-demagnetization capability of the less-rare-earth PMSM can be improved. Using the finite-element method, the electromagnetic performances of the initial and optimal motor are analyzed and compared in detail, including the demagnetization characteristics and torque characteristics. Finally, theoretical analysis and simulation results verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The interior permanent magnet synchronous motor uses a barrier structure to block the magnetic flux circulating inside the rotor and to send the magnetic flux into the air gap. Although the airgap magnetic flux density can be increased through the barrier, there is the disadvantage of increased torque ripple. Thus, this study is conducted to determine whether the torque ripple could be reduced by changing the barrier shape. The problem here is that the torque inevitably decreases when the torque ripple is decreased. Therefore, in this study, a novel shape of the bridge is proposed in a model in which the torque ripple is reduced but the torque is not. The notch structure is applied to the bridge and is analyzed through finite-element method analysis. To intuitively express the relationship between the torque and the torque ripple, a torque efficiency factor is devised, and as a result, the torque is maintained but the torque ripple is reduced. [ABSTRACT FROM AUTHOR]

In this article, to improve the adjustment ability of air gap flux, a new interior permanent magnet (IPM) synchronous machine with permeability modulation characteristics is proposed for electric vehicles’ (EVs) potential applications. The main trait of the machine structure is that a bridge between the rotor poles is intentionally established, which can produce a smooth magnetic path for the leakage flux. Thus, the flux leakage state can be adjusted by controlling the magnetic saturation of the bridge according to the machine load current. To clarify this feature, the machine performances are investigated by theoretical analysis and finite-element method. Finally, the designed machine is manufactured and its performances are verified by experiments. Both the simulation and experimental results prove that the torque of the proposed machine under loaded conditions can be flexibly adjusted by the magnetic permeability modulation without any complex control strategy. [ABSTRACT FROM AUTHOR]

An extremely fast magnetostatic magnetic field modeling method is developed that includes nonlinear relative permeabilities (or “magnetic saturation”) of soft magnetic materials with nonuniform magnetization. The model assumes regions of linearity within the material in order to apply analytic equations and superposition. This article presents the general theory and method for 3-D geometries, along with a 2-D axisymmetric example case study that is of interest for tubular linear actuator (or motor) design. The case study maximizes the average air-gap flux of an axially magnetized pole piece and shows a close correlation of the internal and external magnetic flux densities with a finite element analysis. This demonstrates the method as suitable for large parametric searches of topologies, toward the optimization of electrical machines, linear actuators, transformers, or more general 3-D electromagnetic problems. [ABSTRACT FROM AUTHOR]

In this article, a new low-cost small-scale three-phase brushless motor topology is proposed. This is a new topology for self-excitation of brushless wound rotor synchronous motor investigated initially for rated speed. For brushless excitation, the stator is designed to contain two windings, namely, three-phase armature winding and exciter winding. The rotor consists of two windings, that is, harmonic winding and field winding, and a diode rectifier. An inverter feeds the three-phase armature winding which is connected in series through an uncontrolled three-phase rectifier to a single exciter winding. When the current is supplied from the inverter, both the armature and exciter windings are energized eventually producing a flux in the air gap. Since the flux produced by the exciter winding is not synchronized with the field winding, it produces a harmonic to be intercepted by the harmonic winding on the rotor. Eventually, the voltage produced in the harmonic winding is used to feed dc current to the field winding for brushless operation. The results obtained by 2-D finite-element analysis (FEA) validate the brushless operation of the motor. The proposed motor is analyzed basically for topology verification with the FEA results. Since the topology can be verified, further effort can be put to investigate such low-cost topologies for brushless wound rotor synchronous motor. It can be an alternative to a costly permanent magnet synchronous motor for specific applications. [ABSTRACT FROM AUTHOR]

This article presents two novel double-layer permanent-magnet flux reversal (PMFR) machines to improve the torque capability, namely Machine A and Machine B. Both the Machine A and Machine B are designed as the consequent-pole PMFR machines. The rotors of two machines are identical, which adopt Halbach array permanent-magnet (PM) in the rotor slot to guide the flux into the rotor teeth to reduce the leakage flux. However, the PM relative positions of two PMFR machines on the adjacent stator teeth are different, which result in different pole numbers of air-gap flux density. The operation principles and performances of two machines are introduced and compared in this article. In addition, the air gap fields of two machines by PM magnetomotive force (MMF) are analyzed and the contribution of the dominant air-gap flux density harmonics to torque is revealed. [ABSTRACT FROM AUTHOR]

In this article, a new magnetic equivalent circuit (MEC) model was presented to predict torque characteristics and reaction flux in slotted-type eddy-current couplings (SECs). The magnetomotive force and reaction field caused by eddy current in the conductor were innovatively introduced into the model; particularly, the modulations of the magnetic field and eddy current by iron teeth in conductor disk were taken into account by dividing magnetic flux paths in air gap into several branches. The expressions of magnetic flux and torque were obtained by combining Kirchhoff’s law and Ampere’s loop law. The torque was calculated using the method proposed and was compared with those obtained by the 3-D finite element method (FEM) and experiment, respectively. The results indicated that the method proposed is accurate and effective under conditions of low slip speeds and short air gap lengths. [ABSTRACT FROM AUTHOR]

In this article, a novel hybrid analysis method for spoke-type permanent magnet (PM) machines (STPMMs) is presented, which considers axial flux leakage using the machine’s lumped magnetic circuit. The STPMM can increase its air-gap flux density due to its effective flux concentration, but high flux leakage occurs in the axial end of its PMs. This results in a discrepancy between conventional 2-D finite-element analysis results and experimental data. To correct the discrepancy resulting from the unwanted axial flux leakage, a virtual residual flux density of the PM is proposed through equivalent circuits and a finite analysis model. The modified residual flux density is applied to 2-D numerical analyses, and the accuracy and usefulness of the proposed method are confirmed through 3-D numerical analyses. [ABSTRACT FROM AUTHOR]

This article presents the open-circuit analytical magnetic field distribution model for a new permanent magnets (PMs) rotor configuration designed to improve the utilization of rare earth magnets for flux density production. The air-gap flux density is determined with the superposition method according to the magnetomotive force (MMF) and the air-gap permeance model. Since the new rotor consists of two different rotor topologies, e.g., lateral and spoke magnets, their MMF functions are determined separately. The rotor flux barrier (FB) effect on the rotor MMF harmonics is included and studied closely. The investigations carried out on different rotor topologies show high positive impact of FBs on the third or the operating wave. Compared to the conventional rotor, the utilization of PMs for air-gap flux density production significantly is improved. To verify the analytic model, finite elements (FEs) are used and several simulation results are presented. [ABSTRACT FROM AUTHOR]

Determining the stator slot design parameters of the alternator has a great importance to provide the desired magnetic flux distribution for a permanent magnet generator (PMG). The objective of this article was to investigate the optimum design parameters of PMG slot design for small-scale low-speed wind turbine generator by using the design of experiment techniques. The Maxwell simulations have been used for numerical experiments on geometric design variables of stator slots (Bs0, Bs1, Bs2, and Hs2) in order to evaluate the coefficients of second-order models for the responses. Efficiency, stator teeth flux density, stator yoke flux density, and air-gap flux density are determined as the responses that have to be optimized. A gradient search was used for optimization. The solution of this design problem shows how the experimental design method can be combined with the numerical simulation and how this approach is well adapted to the optimization process. As a result, the efficiency of the PMG is improved under the desired magnetic flux conditions. [ABSTRACT FROM AUTHOR]

In this article, two kinds of dual-layer segmented Halbach arrays have been proposed for permanent-magnet (PM) brushless machines. The analytical expressions of magnetic fields due to the inner-/outer-layer Halbach magnets have been separately obtained. For the maximal flux density in the air gap, the optimal magnet segment radian ratios or magnetization angles for each dual-layer Halbach array have been analytically determined separately. The induced back electromotive force and electromagnetic torque have been analytically obtained. The prediction results show that the optimized electromagnetic performances for each double-layer segmented Halbach array with different slot and pole combinations are better than those for the corresponding single-layer one. The proposed analytical model can also be applied for optimizing the multi-layer segmented Halbach array. The analytical prediction results of a PM machine with the double-layer segmented Halbach array have been compared with those obtained by a finite-element method. [ABSTRACT FROM AUTHOR]

This paper takes a Halbach permanent magnet linear motor (PMLM) without a core as the research subject; based on the traditional structure of a single-layer PM array, an improved PMLM with an optimized double-layer Halbach PM array is proposed to reduce the harmonic components of the air gap magnetic flux density (AGMFD) for direct-drive applications in the feeding system of the machine tool which need high force capability. The 3-D models of PMLMs with single-layer and double-layer Halbach PM arrays are established by using finite element (FE) software; the air gap magnetic field, the back electromotive force (EMF), and the electromagnetic thrust of the two types of motors are analyzed. The simulated results show that the PMLM with an optimized double-layer Halbach PM array can achieve better performances of the motor and reduce the cost of the PMLM. Finally, the experimental results verify that the proposed double-layer Halbach PMLM is effective and practical. [ABSTRACT FROM AUTHOR]

This paper presents the magnetic field analysis for the double layer Halbach array voice coil actuator (VCA). This VCA is composed of a stator and a mover supported by the flexure-based bearings. The mover gets three coils winded on the skeleton. The stator comprises the closed yoke and the double layer Halbach array permanent magnets (PMs). The boundary condition of the quadrangularly surrounded yoke and the aperiodic distribution of the Halbach array PMs complicate the magnetic analysis process. An equivalent VCA structure that has almost identical air-gap flux distribution to the original one is, therefore, proposed. For the equivalent structure, the boundary condition is simple and the Halbach array PMs is periodically distributed, thus the analysis process of air-gap flux density distribution via Fourier analysis is simplified. The equivalence between these two structures is validated by finite-element analysis (FEA). The analytical model is built by adopting Fourier analysis. The results of the FEA and experiments confirm the correctness of the developed model and prove the feasibility of the analytic method with the equivalent structure. [ABSTRACT FROM AUTHOR]

Electric vehicle (EV) is a promising technology for saving fossil energy and reducing pollution. Hybrid-permanent-magnet (PM) variable-flux machine is a competitive candidate for EV propulsion since it has wide speed range and high efficiency at high-speed region. A novel hybrid-PM variable-flux machine with magnetic barriers is proposed in this paper, and a new magnet material CeFeB is used. The structure and operating principle are introduced, and different magnetization states of the machine are analyzed. The equivalent magnetic circuit model of the machine is established considering the influence of magnetic barriers, and the model is proven with good precision for the calculation of air gap flux density and PM operating point. The electromagnetic performances are analyzed, and compared with a traditional variable-flux machine. It is verified that the added magnetic barriers improve the distribution of air gap flux and load magnetization performance of the machine. The no-load back electromotive force, electromagnetic torque, speed range, and load magnetization ratio of the proposed scheme are all improved. [ABSTRACT FROM AUTHOR]

In this paper, the influence of stator teeth number on permanent magnet (PM) field couplings of co-axial dual-mechanical-port flux-switching permanent magnet (CADMP-FSPM) machines for fuel-based extended-range electric vehicles is investigated. First, the relationships between the inner and outer stator teeth numbers are analytically evaluated. Second, four typical structures, including 5/6–12/22, 10/12–12/22, 5/6–18/42, and 10/12–18/42, of CADMP-FSPM machines are analyzed, and three key stator teeth types, namely, series, parallel, and independent teeth, are defined. Third, the PM field coupling levels of four structures, featured by PM field distributions and air-gap flux densities, are compared with stator teeth matchings. The results indicate that the 10/12–12/22 structure exhibits the lowest PM field coupling and the prior open-circuit performance. Furthermore, the PM field coupling effects on the inner and outer air-gap flux densities are analyzed. Finally, a prototyped 10/12–12/22 CADMP-FSPM machine is designed, optimized, and manufactured, and the experimental results verify that the PM field coupling level of the prototype is negligible, which agrees well with the finite-element predictions and the proposed matching criteria for the selection of the inner and outer stator teeth numbers of CADMP-FSPM machines. [ABSTRACT FROM AUTHOR]

This paper presents the design and analysis of a 4-poles-24-slots permanent magnet (PM) homopolar machine for the flywheel energy storage system (FESS), and the operating principle is investigated. Due to the unconventional flux distribution in this machine and the goal of the design is to minimize the torque ripple while maximizing the torque density, the parameter of this machine was obtained by the 3-D finite element global optimization genetic algorithm method. In addition, the air-gap flux density of double stator, open-circuit magnetic field distribution, flux linkage, back electromotive force stator, core loss, external characteristic were analysis, and the operating principle is verified by open-circuit magnetic field distribution. It was found that core loss can be reduced almost 34% by comparing with a heteropolar PM machine, which demonstrated that the homopolar machine is a promising candidate for the FESS. A prototype has been manufactured and tested to validate the finite-element and theoretical analyses. [ABSTRACT FROM AUTHOR]

This paper presents an electromagnetic (EM) analysis and feasibility design study of a 10 MW air-core fully superconducting (SC) generator for off-shore wind turbine applications. This machine topology uses MgB2 SC wires in both armature and field windings to reduce the generator cost. To reduce the weight of the machine, stator iron core in the traditional SC machine design is replaced with shield coils to contain the flux inside the machine. This air-core design allows the air-gap flux density to be increased without saturation to achieve an increased power density in machine design. Further, eliminating the iron core also eliminates the core losses. This is an attractive feature for off-shore wind turbine applications where machine weight can be reduced with increased efficiency. Preliminary EM studies are performed on a 10 MW, 10 r/min fully SC air-core machine design and its associated ac losses are evaluated. Design specification of the machine is provided with the armature, field, and shield winding parameter details. Finite element (FE) analysis is used to evaluate the flux density and torque profile of the machine. To reduce the ac losses in the armature coils, magnetic flux density at the armature winding is set to be 2 T. The preliminary results show this fully SC air-core generators show better performance in ac losses compared to the similar fully SC MW wind turbine designs. [ABSTRACT FROM AUTHOR]

This paper presents an analytical model of magnetic field of a permanent magnet synchronous motor (PMSM) with a trapezoidal Halbach permanent magnet array (THPMA). Compared with conventional Halbach array, the shape of each magnet in THPMA is transformed from rectangle to trapezium in polar coordinates. The THPMA is delaminated indefinitely radially and each layer is approximately considered to be a conventional Halbach array. The air-gap magnetic field of each layer is analyzed with the scalar magnetic potential. Then, the air-gap magnetic field of the THPMA is obtained by superposing magnetic fields of all layers. The validity of the analytical model is verified by a finite-element model (FEM). The air-gap flux density is optimized by adjusting the center angle coefficients of the THPMA, and a no-load phase back electromotive force (EMF) with the harmonic distortion rate (THD) of 0.75% is obtained by FEM. The back EMF is basically consistent with the measured result of a prototype motor. [ABSTRACT FROM AUTHOR]

The performance of a brushless permanent magnet machine topology equipped with axially and circumferentially magnetized ferrite permanent magnets is presented. Simulation studies show that for smaller ratios of axial length to active length, air-gap flux densities in excess of 1 T can be achieved, resulting in significant improvements in torque production and efficiency. A prototype machine is manufactured, and test results confirm the predictions of the EMF and the static torque. [ABSTRACT FROM AUTHOR]

In this paper, a novel switched reluctance motor with two magnetically dependent stator and rotor sets (TMDSRM) is proposed and tested. The novelty of the TMDSRM is that there is an assistant exciting winding (short for exciting winding), which is placed between the two-stator sets and can be energized by controllable dc current to boost the air-gap flux density and to improve the output torque and torque density. What deserves to be mentioned the most is that the air-gap flux density is compensated when armature winding is in commutation because of the exciting winding carrying dc current and being permanently energized, and thus, the torque ripple is reduced. This paper describes the magnetic structure and the principle of the proposed motor in detail. Moreover, finite-element analysis has been carried out to investigate the influence of exciting field on electromagnetic torque of the motor. A prototype TMDSRM is manufactured, and the experimental results are presented. [ABSTRACT FROM AUTHOR]

In this paper, the partitioned stator (PS) structure is extended to variable-flux memory machines, forming two newly emerged PS switched-flux memory machines (PS-SFMMs) with series and parallel hybrid magnet configurations. From the perspective of geometry, both two PS-SFMMs share identical outer stator and rotor segments, while two different types of permanent magnet (PM) arrangements are employed in the inner stationary part. Thus, the developed machines can inherent the geometric separation of the armature winding and PM excitations from the PS design, thus achieving acceptable torque capability, and excellent air-gap flux control. A comparative study between PS-SFMMs with series and parallel structures is established. First, the topologies and operating principle are introduced, respectively. In addition, the design tradeoffs and PM sizing of the two PS machines are revealed and optimized with a simplified magnetic circuit model. Then, the electromagnetic characteristics of PS-SFMMs with different magnetic circuits are investigated and compared with the finite-element (FE) method. The FE results are validated by the experiments on a parallel prototype. [ABSTRACT FROM AUTHOR]

By developing a simple permeance-magnetomotive force (MMF) model of switched-flux permanent magnet (SFPM) machines, the air-gap flux density produced by both PMs and armature current can be derived, in which harmonics with the same order and rotational speed are called an effective harmonic pair (EHP). By investigating the influences of armature current angle $\delta $ on both the phase and amplitude of each EHP, it is found that the amplitudes of both PM and armature reaction flux-density harmonics maintain fixed, whereas the space phase shift between them changes accordingly with armature current angle. Specifically, the PM and armature reaction flux-density harmonics are orthogonal in space if zero ${d}$ -axis current is fed. Therefore, the maximal torque is realized for each EHP. As the total torque of SFPM machines is the superposition of the contributions by each EHP, the zero ${d}$ -axis current control method turns out to be the optimum for maximal torque per ampere, thus verifying analytically that the ${d}$ - and ${q}$ -axes inductances are equal according to the general torque equation for the investigated machine topology. In addition, the torque adjustment mechanism of each EHP in SFPM machines has also been analytically demonstrated to be resemble that of the surface-mounted PM synchronous machine (PMSM). Finally, the finite-element analysis (FEA) has been performed to validate the previous analytical predictions. [ABSTRACT FROM AUTHOR]

This paper proposes a more convenient and more accurate air-gap permeance function for the calculation of the air-gap flux density of flux modulation machines with permanent magnets (PMs). First, we review the previous air-gap permeance obtained from the approximated linear model and explain the problem that the accuracy of calculation becomes worse as the magnet thickness becomes larger. To solve this problem, we introduce an equivalent model that reflects the actual cylindrical structure of the machine with slots and, then, derives the air-gap function that is easy to be converted into the Fourier series, and finally propose the new air-gap permeance function. Using the proposed permeance function, the working harmonic components in the air-gap flux density of the surface magnet vernier motor are easily predicted, and then additional characteristics as well as flux density are compared with the finite-element simulation results to check the validity of the proposed method. [ABSTRACT FROM AUTHOR]

An analytical output force model is proposed for noncontact Lorentz force actuators (NLFAs), which are used for positioning and vibration isolation control of space sensitive loads that require an extremely quiet environment. A biaxial NLFA is presented. The actuator mainly consists of a closed magnetic circuit and a novel biaxial exciting circuit board developed by printed circuit board technology. The closed magnetic circuit consists of a C-type yoke and two permanent magnets and is simplified by the magnetic image method. A model of the spatial magnetic flux density in the air gap of the simplified closed magnetic circuit model is derived by the Ampere molecular current hypothesis and the Biot–Savart law. Finally, an analytical output force model of the actuator is obtained by calculating the magnetic flux densities and forces at selected finite points by considering the winding of the coils. The influences of the key dimensional parameters of the actuator on the output forces and their variations are studied using the derived analytical model. To verify the derived analytical model, a measurement setup is established based on an electronic scale. The experimental results show that the forces calculated by the proposed analytical model agree with the experimental values very well, and the deviation between the results is less than 4% when a rated force of 3 N is produced. Moreover, the relation between the number of selected points and computing time and the relation between the number of selected points and the extra calculation deviation, which are important for real-time control, are discussed. The proposed analytical model can help to improve the design efficiency and output force control of this kind of actuator. [ABSTRACT FROM AUTHOR]

This paper compares the performance of inner-only and inner–outer type of magnetizing fixture designs to achieve the radial magnetization profile in an isotropic-bonded neo magnet. In inner-only fixture, the magnetization coils are located on only one side of the magnet circumference, and inner–outer fixture uses magnetization coils on either side of the magnet circumference. For both fixtures, the finite-element analysis (FEA)-based performance is presented and compared with the experimental validation. The effect of misalignment between the inner and outer coils in an inner–outer fixture is discussed using the FEA as well as experimental results, and a limit on the misalignment angle resulting in negligible reduction in mid-air-gap flux density integral per pole is arrived at. [ABSTRACT FROM AUTHOR]

This paper studies the output performance improvement of the spherical multi-degree-of-freedom (multi-DOF) motor. The multi-DOF motor is a motor that is designed to drive in multiple axes. Therefore, it is important that the shape of the motor should be fabricated to enable multi-axis driving when designing the multi-DOF motor. In addition, it is essential to consider the output density characteristics and stability characteristic analysis to reduce the volume of the multi-DOF motor and to operate of the motor in the stable range, respectively. In this paper, the structure and operating characteristics of the spherical multi-DOF motor with dual air gaps are described. In order to improve the output characteristics of the multi-DOF motor, characteristics analysis was performed according to the change of the number of the phases and pole pitch angles, and stability characteristic analysis for stable operation of the multi-DOF motor was performed. [ABSTRACT FROM AUTHOR]