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Due to the enhanced air gap flux density and eddy currents in the favorable path, eddy current brakes with slotted conductors have attracted more attention in recent years. However, due to the increased difficulty in analytical modeling, there is currently no suitable analytical model available for the optimization design of eddy current brakes with slotted conductor. To solve this problem, an improved analytical model is provided based on the subdomain model and the least squares method in this article. The proposed analytical model considers slotted conductor disk, magnetic saturation of primary core and actual path of eddy currents in the conductor disk. The accuracy of the proposed analytical model is verified by finite-element method (FEM) and experimental measurement. The results show that the improved analytical model has good accuracy in the entire speed range. As the analytical model takes less computational time than three-dimensional FEM, it can be used as an effective tool for the optimization design. [ABSTRACT FROM AUTHOR]

Variable reluctance resolvers (VRRs) have been widely used for rotor position detection in harsh working conditions. However, conventional installation of VRRs inevitably occupies the axial space of machine systems, and may weaken the reliability of rotor position detection encountering shock and vibration. In this article, a novel VRR structure with inner stator is investigated, which is radially integrated inside a permanent magnet synchronous machine (PMSM) to construct compact machine topology. The hybrid machine topology is first discussed, and detailed electromagnetic design is carried out. Improved analytical analysis on air gap flux density distribution and inductance evaluation of the integrated VRR is derived based on modified winding function approach, and testified by finite element analysis. A prototype is manufactured from an existing 2.2 kW PMSM, and experiments are conducted to validate the effectiveness of proposed machine topology. [ABSTRACT FROM AUTHOR]

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]

This article proposes a hybrid evaluation method of electromagnetic force and vibration for electrical machines considering high-frequency current harmonics caused by the inverter. First, the permeance and armature magnetomotive force (MMF) is calculated based on the virtual MMF and the slot matrix. Then, the air-gap flux density and electromagnetic force construction process under arbitrary current is thoroughly studied. The vibration transfer function is obtained by utilizing the modal analysis and the modal test. Finally, the vibration can be calculated according to the modal superposition method. By applying this method to an interior permanent magnet machine, it can significantly reduce the computation efforts compared with the multiphysics procedure due to the extensive use of the finite-element method. In addition, the accuracy of this method is validated by conducting an experimental study. [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]

In this paper, the boundary discretization method is used to improve the traditional subdomain model. The improved model can be used to calculate the magnetic field distribution in the region containing non-orthogonal boundary, avoiding the influence of the simplified stator slot or permanent magnet shape on the results in calculating the motor magnetic field using the traditional subdomain model. In addition, the improved subdomain model can also be used to calculate the air-gap flux density when the rotor is eccentric, instead of segmenting the air-gap to an equivalent state without eccentricity. The calculation object of this paper is a surface-mount permanent magnet motor with a rectangular stator slot. The air-gap flux density under no-load and load conditions is calculated, respectively. Since the improved subdomain model does not need to simplify the stator slot shape, the magnetic potential in the stator slot is also calculated. Finally, the air-gap flux density under rotor eccentricity is calculated, and the influence of the calculating parameters on the results of the improved subdomain model is discussed. All the calculated results are compared with those obtained by the finite element method, which verifies the accuracy of the improved calculation model. [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 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 paper presents an analytical approach to determine the air-gap magnetic field and the winding inductance in the brushless doubly-fed reluctance machine (BDFRM) with flux barriers. By dividing one flux guide layer into several segments, a calculus method based on magnetic circuit analysis is developed and specific analytical expression of the air-gap flux density is rigorously derived. Then, the included angle between fundamental components with the same pole pairs is also discussed. Based on the air-gap flux density distribution, the inductance expressions between different windings are also presented. Three kinds of finite element analysis models are established and studied. As a result, the accuracy of the analytical model can be verified by simulations and experimental data from an existing BDFRM prototype. [ABSTRACT FROM AUTHOR]

Spoke structure can increase the torque density of coaxial magnetic gear (CMG). However, the outer rotor can produce a large number of magnetic leakages. To improve the utility of PMs, a novel magnetic gear was proposed in this paper. The structure of the auxiliary flux modulator is a slotted iron yoke, and the slot angle is same as the stationary ring. Among, the permanent magnets (PMs) of inner rotor are adopted uneven block structure to improve air gap flux density. At the same time, the stationary ring adopts high-temperature superconducting (HTS) bulks, replacing the epoxy resin. In addition, Genetic algorithm (GA) is applied to calculate the optimal parameters of the proposed CMG. Finally, the air gap flux density and output torque of the magnetic gear a compared by the finite element method. The results show that the output torque of the proposed magnetic gear is effectively improved. [ABSTRACT FROM AUTHOR]

Torque ripple reduction for permanent magnet assisted reluctance (PMAREL) machine has always been concerned by designers. In order to seek the internal factors of torque ripple for PMAREL, this article proposes an effective torque calculation model considering air-gap field time-space harmonics using finite element method (FEM) combined with two-dimensional fast Fourier transform (2D-FFT). It can be used to investigate the contribution of air-gap field time-space harmonics to average torque and torque ripple, and precisely extract the characteristic components of the air-gap field time-space harmonics that contribute to the torque. Besides, the details of time-space harmonic order, movement form, magnitude and initial phase will be obtained from the characteristic components. Hence, the time-space harmonics of air-gap field that mainly contribute to the torque ripple can be found through this model and suppressed by adjusting the angles of the flux-barrier ends for making torque smooth. According to the optimized design, a 36-slot 4-pole PMAREL is manufactured and tested. Both finite element analysis and experimental results confirm the effectiveness of the proposed model. [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]

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]

Performance prediction of induction machines (IMs) is highly dependent on the accuracy of the material characteristics and geometry of the machine during the modeling stage. To reduce the complexity of an IM model, normally the slotting effects are neglected. Likewise, the permeability of the stator and rotor cores are assumed to be infinite leading to an ideal set of partial differential equations (PDEs) for homogenous and isotropic materials. In this paper, the permeability of the stator and rotor cores are assumed not to be infinite and the slotting effects are taken into consideration to propose a more accurate and realistic model of an IM to reduce the discrepancies between the performance expectations and actual results. Fourier-based (FB) magnetic field approach is used to fulfill this aim via anisotropic layer theory (ALT) enabling the proposed model to include distortion of magnetic flux in the slotted regions. Air-gap flux density, core losses, efficiency and torque of an IM are predicted via the FB model and are validated through the finite element analysis (FEA) and experimental studies. [ABSTRACT FROM AUTHOR]

In this paper, superposition methods including the superposition of a single stator tooth and the superposition of a single rotor tooth, are proposed to predict the open-circuit performances of flux-reversal permanent magnet (FRPM) machines. By the proposed superposition methods, the electromagnetic performances, such as air-gap flux density, electromotive force, cogging torque, and unbalanced magnetic pull (UMP) are investigated and verified by 2D finite element analysis (FEA). Further, according to the superposition methods, cogging torque reduction techniques can be acquired from both stator side and rotor side. In addition, the influence of stator-slot/rotor-pole-pairs (slot/pole) combination on UMP is also studied, and consequently, a reasonable slot/pole combination rule is suggested to avoid UMP. Then, an improved configuration for UMP reduction is also investigated and verified by FEA. Finally, the prototype machines are manufactured and tested to further verify the theoretical analysis and FEA predictions. [ABSTRACT FROM AUTHOR]

In this article, three 6-slot/2-pole high-speed permanent magnet motors with 1, 2, and 3 coil-pitch windings are optimized by the finite element method taking into account stator copper loss and iron loss. Their electromagnetic performances are analyzed and compared, including air-gap flux density, back electromagnetic force, electromagnetic torque, winding inductances, and various loss components. For high-speed application, compared with 1 and 3 coil-pitch windings, the proposed 2 coil-pitch windings have a good tradeoff between winding factor and end-winding axial length which are attractive for improved torque density. Finally, the experimental results are given to validate some of the finite element predicted results. [ABSTRACT FROM AUTHOR]

In recent years, design studies of tubular linear voice coil motors for linear movement have been increasing. This is because the motor has performance criteria, such as high thrust force, high thrust density, and low thrust ripple. Therefore, different motor models and magnetic modeling have been studied. In these studies, especially the solutions that increase the air-gap magnetic flux density were emphasized. One of the most striking of these motor models is surely the end-iron-free structure. In this study, a single-layer (SL) (two-magnet) end-iron-free structure from a reference study was examined. A double-layer (DL) end-iron-free structure that has higher thrust force in the same motor volume, magnet volume, and parameters was proposed. An analytical approach is first developed, and then, a verification based on finite element analysis was performed. As a result of comparison with the reference study, the proposed motor provided a 10.5% increase in the thrust force and a 9.1% decrease in the thrust ripple. In addition, a design approach developed offers a practical and useful analogy between the DL and the SL. [ABSTRACT FROM AUTHOR]

In this paper, an improved magnetic equivalent circuit (MEC) model of a coreless axial-flux permanent-magnet synchronous machine (AFPMSM) with printed circuit board (PCB) winding is presented, which considers the curvature effect, fringing effect, leakage flux, and rotor yoke's magnetic saturation. The axial air-gap flux density distribution, no-load back electromotive force, winding inductances, and electromagnetic torque are predicted by the proposed MEC model. The steady-state performances of the machine under heavy load, as well as the dynamic response of the machine with a connected voltage source and mechanical load, are calculated. All the results obtained from the proposed model are in good agreement with those issued from the 3D finite element method (FEM). The computation time of the proposed model is greatly reduced compared to 3D FEM. Finally, a coreless AFPMSM prototype with a PCB stator is manufactured, and experiments are carried out to verify the predicted results. [ABSTRACT FROM AUTHOR]

In this article, a variable flux reluctance machine (VFRM) with dc field excitation and modular structure is proposed and it exhibits controllable flux, simplified manufacture, better fault tolerant capability, and potentially reduced material consumption. Its operational theory is illustrated by using flux modulation principles, and the working harmonics considering the modular structure are analyzed. Besides, the winding factors of modular VFRM are derived considering the flux gap width. The parameters are optimized by two-dimensional finite element method to maximize the back electromotive force (back-EMF) and the ratio of phase self-inductance to mutual inductance. Moreover, the electromagnetic performance including open circuit air-gap flux distributions, open circuit air-gap flux densities, flux linkage, back-EMF, inductance of armature windings, output characteristics, loss, power factor, and efficiency-map are compared for 12s10r and 12s14r nonmodular and modular VFRM. Additionally, the fault including short circuit and open circuit fault are analyzed. Finally, a modular 12s14r VFRM prototype is manufactured and tested to validate the theoretical and finite-element analyses. [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]

High-speed permanent magnet machine (HSPMM) design is considered with particular attention paid to machine electromagnetic, thermal, and mechanical analyses. In this article, a 140-kW, 15 000 r/min HSPMM is designed with its power losses evaluated at first. Afterward, the machine temperature distribution is obtained based on computational fluid dynamics modeling. HSPMM is prototyped with experimental tests conducted to verify the calculation results. Mechanical strength analysis is performed for the HSPMM rotor structure with pole filler by finite-element method for the rotor at three operational conditions, while the influences from sleeve parameters on rotor strength are comprehensively studied for the HSPMM rotor at the most challenging condition. In this article, stator auxiliary slotting is extensively researched to reduce the rotor eddy current loss with little effects on machine output torque. The air gap flux density for HSPMM with auxiliary slotting is analytically predicted, while the working mechanism is illustrated in-depth. The effects from auxiliary slot dimensions, numbers and positions, on machine performances are further proposed and investigated. The experimental tests also validate the reduction of HSPMM rotor eddy current loss by the application of auxiliary slotting. [ABSTRACT FROM AUTHOR]

In this article, a fast circuit-field coupling method is proposed for the analysis of the skewed induction motor. Based on the multislice model, the equivalent circuit of the skewed induction motor is established. The distributed magnetic field method is used to calculate air-gap flux density and deal with the core saturation at each axial slice. Based on the coupling analysis of the equivalent circuit and magnetic field, a two-layer iterative process is used to calculate the magnetic field distribution and performance indexes of the skewed induction motor. By comparing with finite element analysis and experiment results, the proposed method is proved to be correct and effective. The proposed method is characterized by fast computation speed and good accuracy, so it is an ideal approach to analyze the skewed induction motor. [ABSTRACT FROM AUTHOR]

This paper proposes a novel high-temperature superconducting stator-excited axial-flux magnetic gear (HTS-SEAFMG) for the high-torque transmitting system. The proposed magnetic gear combines the merits of both HTS-excitation and stator-excitation. By using the HTS-excitation, a high air-gap flux density can be easily obtained, thus achieving the high torque density. The HTS-excitation windings are placed on the stator with a static seal of cooling Dewar which greatly reduces the manufacturing difficulty and the cost of refrigeration system compared with the dynamic seal. Thanks to the stator-excitation pattern, both the high-speed rotor and the low-speed rotor comprise only iron, thus contributing to the high mechanical reliability. The axially sandwich structure can also simplify its assembly in the high torque transmission applications. The dimensional parameter optimization and the electromagnetic performance evaluation are conducted by using the finite element method, respectively. The results show that the torque density of the proposed HTS-SEAFMG can reach 123 kNm/m3. Theoretical analysis and results are both given to verify the feasibility of the proposed HTS magnetic gear design. [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 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]

This paper proposes an analytical model for analyzing the electromagnetic performance of axial flux permanent magnet machines (AFPMMs) with the coexistence of static rotor radial deviation and angular eccentricity. Firstly, a quasi-3-D analytical model for the healthy AFPMMs is established using the scalar potential. Then, the analytical model of AFPMMs with the mixed eccentricity is derived by the coordinate transformation and air gap length function. The end effect under the mixed eccentricity is considered by an end coefficient, which improves the accuracy of back EMF by 1.3%. Based on the analytical model, the air gap flux density distribution, back EMF and cogging torque of AFPMMs with different rotor radial distances and angular eccentricities are calculated and compared with the corresponding results obtained by finite element analysis (FEA). The proposed model has higher analysis speed and less computer performance requirement than FEA with the similar accuracy. According to the results, the back EMF reduces obviously as the rotor radial deviation distance increases, and the back EMF almost unchanged as the angular eccentricity becomes serious. [ABSTRACT FROM AUTHOR]

This article proposes a novel analytical model which combines subdomain method and magnet equivalent circuit (MEC) method to predict the cogging torque of surface-mounted permanent magnet (SPM) motors with rotor eccentricity and magnet defects in any slot-pole combination cases. Firstly, the general solution of open-circuit magnetic field distribution in a slotless SPM motor with magnet defects is derived. Then, the motor is divided into several subdomains along the air-gap circumferential direction to consider the non-uniform air-gap caused by rotor eccentricity, where the air-gap lengths of each subdomain are considered to be uniform. Finally, the methods of conformal mapping and MEC combined with equivalent current is used to consider the effect of slotting and saturation, which is beneficial to improve the calculation precision. The magnetic field distributions and cogging torque calculated by the proposed model are consistent with the results of finite element analysis (FEA). Compared with the FEA, the proposed model can perform fast calculations of air-gap flux density and cogging torque under rotor eccentricity and magnet defects for SPM motors, which can be utilized for optimizing the motor towards fault tolerance. [ABSTRACT FROM AUTHOR]

The fault-tolerant capability is a prerequisite for electrical safety-critical applications. In this regard, multi-phase induction motors are well-known actuators used to provide this feature. Compared to conventional three-phase machines with distributed windings, induction machines having concentrated windings could be more fault-tolerant because of increasing the number of phases. In addition, concentrated windings have shorter end-winding and less required copper weight which makes it a lower cost solution compared to distributed windings. However, concentrated windings adversely increase the distortion of the air gap flux density which affects motor performances. In this paper, a pseudo-concentrated winding layout has been proposed for six-phase squirrel-cage induction motors to improve performances compared to conventional concentrated windings. Winding function and equivalent circuit methods are used to analytically calculate performances. Finally, time-stepping finite element method and experimental measurements have been presented to confirm obtained analytical results. [ABSTRACT FROM AUTHOR]

In permanent magnet synchronous machine design, a limited number of stator and rotor slots distorts the air-gap flux distribution and its effective length. It causes machine parameters to vary with the rotor position. The rotor flux linkage harmonics introduce nonsinusoidal back-EMF, which causes current harmonics when conventional PI current controller is adopted. Those machines suffer from high-frequency torque ripple due to air-gap flux harmonics in low-speed region. However, in high-speed region, where the torque ripple is filtered out by the mechanical system, the torque ripple may be disregarded. In this case, torque-ripple suppression methods and the associated harmonic current components generate losses. Therefore, a sinusoidal current control is required to reduce the undesired harmonic losses. In this manner, this article focuses on the sinusoidal current control strategy based on harmonic voltage injection, which requires knowledge of rotor magnet flux linkage harmonics. This article also proposes both off- and on-line schemes for the identification of rotor magnet flux linkage harmonics. These methods do not require any proprietary machine design details such as the shape of stator or rotor for finite element analysis. Commonly used PI plus resonant controller is also designed and its disadvantages in terms of speed-dependent gain and stability, in comparison to the proposed scheme, are highlighted. Finally, experimental results are presented to compare the proposed scheme with the conventional method at different operating conditions. [ABSTRACT FROM AUTHOR]

This article investigates magnetic design aspects of the trans-rotary magnetic gear (TROMAG) that using a quasi-Halbach array. TROMAG is a magnetic gear that converts high-force, low-speed linear motion to low-torque, high-speed rotational motion and vice versa. It is shown that quasi-Halbach magnetization significantly improves the force capability of the device compared to that of radial magnetization. Finite element analysis is used to study several design aspects of the quasi-Halbach TROMAG, including optimization of magnet dimensions and core thickness, effect of air gap length, effect of magnet remanent flux density, and distribution of flux density in the air gap. Moreover, the possibility of demagnetization is studied, and it is shown that if the quasi-Halbach TROMAG becomes overloaded repeatedly, demagnetization of magnets can degrade its force performance down to that of a similar TROMAG with radial magnetization. A quasi-Halbach TROMAG is prototyped, and static force and flux measurements verify the theoretical results. [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, 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]

For the five-phase permanent magnet (PM) machines with conventional Halbach array rotor, although the third harmonic current is injected into the phase current, the torque density hardly increases due to the absence of the third harmonic air gap flux density. Hence, a Halbach array considering third harmonic air gap flux density is proposed in this paper, and the topology is described and compared with the conventional Halbach array. The magnetizing angle of the proposed Halbach array and the stator teeth width are optimized based on the nonlinear programing method. The electromagnetic performances of the five-phase PM machines with the proposed Halbach array, including open-circuit flux density, back electromotive force, flux density under the rated load, cogging torque, average torque, torque ripple, loss, and efficiency, are compared with the PM machine with conventional Halbach array by finite-element method. It is demonstrated that the torque density and efficiency of the PM machine with the proposed Halbach array are higher than that of the PM machine with conventional Halbach array. Finally, the five-phase 10-slot/8-pole PM machines with proposed Halbach array is manufactured and tested to verify the analysis. [ABSTRACT FROM AUTHOR]

This paper focuses on the electromagnetic vibration and its reduction in PM brush dc motors. First, the air gap flux density distribution and the radial force density distribution are derived in detail, and compared with the results of the finite element method. Next, two types of vibration sources, called pulsating force and bending moment, are analyzed. Then, two passive improvement methods, called varied PM pole width in axial direction and copper ring, are proposed to reduce the magnetic forces and their vibration, and their principles of the vibration reduction are described in detail. For further explanation, a rotor-skewed motor is used for comparison, and the radial force on the motor is discussed and the influence of four different thicknesses of copper ring on the motor vibration is analyzed. Finally, three 2p/24s sample motors are manufactured and the experimental vibration results confirm the analysis and the proposed improvement technique. [ABSTRACT FROM AUTHOR]

This paper proposes a novel mesh-based equivalent magnetic network (EMN) model for performance analysis and optimal design of permanent magnet (PM) machines. The key contribution of the EMN model is that a generalized air-gap model solution is proposed by considering the machine motion of PM machines. Meanwhile, a modular modeling method is presented, and then the optimal design of PM machines can be investigated without repetitive programming and modeling. Two kinds of mesh elements are comprehensively utilized in the EMN model, and a hybrid rotor PM (HRPM) machine with interior PM and surface PM configuration is selected as an example to illustrate the development processes of EMN model. Meanwhile, the electromagnetic characteristics of HRPM machine are calculated by the proposed EMN model, such as back electromotive force, air-gap flux density distribution, and average torque. Finally, the accuracy and effectiveness of the proposed EMN model are verified through comparisons with finite element analysis and experimental tests. [ABSTRACT FROM AUTHOR]

In this paper, the design of the concentrated flux-type synchronous motor (CFSM) using ferrite permanent magnets to improve torque is proposed for an automotive chassis actuator. The thin pancake type CFSM of this paper has considerable axial magnetic leakage flux due to structural reasons. It is, therefore, necessary to improve the torque. In order to meet the required specifications in a constrained installation space, this paper proposes two methods for torque improvement. The first method is the alternate-stacking core as this structure removes the magnetic leakage flux path. The second method is the rotor overhang that increases the air-gap flux density. Furthermore, the structures require a three-dimensional (3-D) finite element method (FEM) analysis for accuracy. However, to analyze the characteristics easily and quickly, the 3-D structure is made into the equivalent 2-D FEM through an analytical method using an equivalent magnetic circuit. Finally, in this paper, the validity of the design process and the effectiveness for torque improvement is verified through experiments. [ABSTRACT FROM AUTHOR]

Variable magnetization pattern permanent magnet synchronous machines (VMP-PMSMs) capable of dynamic changes in the magnetization spatial distribution are discussed in this paper. VMP-PMSMs are able to change the harmonic components in the air gap magnetic flux density due to the magnet by intentional demagnetization; hence, they can effectively manipulate the torque ripples and losses according to the required operating points. The objective of this paper is to provide a procedure to design VMP-PMSMs that can have both the sinusoidal and the trapezoidal back EMF waveforms by switching magnetization pattern. The performance of the designed VMP-PMSM following the reported procedure is confirmed through experiments as well as finite element analysis (FEA) simulations in terms of the back EMF shaping, torque ripple reduction, and loss reduction. Loss analysis of VMP-PMSMs is also given as contrasting with variable flux permanent magnet machines (VF-PMSMs), showing that VMP-PMSMs can reduce more losses than VF-PMSMs with the same torque density. [ABSTRACT FROM AUTHOR]

The compensated pulsed alternators (CPAs) have good applications in high-energy lasers, electromagnetic rail guns, and other electromagnetic launch devices. Among various electrical machine topologies, homopolar inductor alternators (HIAs) have attracted interest as CPAs due to their merits of simple and reliable structure, brushless excitation, and high-speed operation. However, the length of the conventional HIA is difficult to expand because it is limited by the rotor diameter, and the rotor diameter is restricted by the maximum speed of rotor tip, which results in low-energy storage capacity of a single machine. Besides, HIA suffers from the relatively low-power density due to its unipolar air-gap flux density (UAFD). To solve these problems, two novel HIAs with multistage stator cores (HIA-MSCs) are proposed in this paper. One is HIA with UAFD (HIA-UAFD) and the other is HIA with unipolar and bipolar air-gap flux density (HIA-UBAFD). First, the structure and operation principle of HIA-MSCs are illustrated. Then, the key parameters of HIA-MSCs are derived, and the corresponding models are built. Finally, the electromagnetic performances of HIA-MSCs are investigated by 3-D finite-element analysis method. Compared with HIA-UAFD, HIA-UBAFD has relatively higher discharge current and output power, which indicates that HIA-UBAFD is a better candidate for the pulsed alternator. [ABSTRACT FROM AUTHOR]

This paper presents a dual-stator permanent magnet synchronous machine (DS-PMSM) with diametrically magnetized cylindrical PMs (DMCPMs). The advantages of the proposed DS-PMSM are its small cogging torque and torque ripple, sinusoidal (low harmonic) air-gap flux density waveforms, and a high pole-pair number structure, which can be used to increase the torque density. To confirm the advantages of the proposed DS-PMSMs, first, the cogging torques produced with conventional arc PMs and cylindrical PMs are compared. Next, a DS-PMSM with DMCPMs is designed, and its cogging torque is calculated. Then, all the relevant machine characteristics, including the cogging torque, air-gap flux density, back electromotive force, and torque–angle characteristics, are predicted by the two- and three-dimensional finite-element method. Finally, the machine is prototyped, and the validity of its advantages is investigated with the experimental tests. [ABSTRACT FROM AUTHOR]

The length of the air gap in a negative corona discharge, which affects many corresponding parameters in the discharge process, is of vital importance for the physical investigations. A hydrodynamic drift–diffusion approximation model considering photoionization utilizing the finite-element method has been used in needle-to-plane air gaps. Trichel pulses, pulse frequency, electron, and electric field distribution, and surface current density distribution on the anode plate were presented to study the effect of the gap length. An approximate exponential relationship was found to exist between the corona current and the gap length, and also a linear function was found between the pulse frequency and the gap length. The analysis shows that the characteristics of the Trichel pulse are strongly dominated by the length of the air gap. [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 proposes a dual-stator consequent-pole permanent magnet vernier machine comprised of two stators and a sandwiched rotor. The proposed topology has high torque density owing to its special working principle and low cost due to the consequent-pole structure. To verify the superiority of the proposed machine, it is compared with an existing dual-stator vernier machine in terms of important electromagnetic characteristics. The finite-element analysis comparison of the two machines shows that the proposed machine achieves a higher average torque and a higher torque-per-magnet volume in comparison with the existing machine. Moreover, the proposed machine uses less magnet volume; therefore, the cost of the machine is significantly reduced. Furthermore, the proposed machine is more efficient compared with the existing machine. [ABSTRACT FROM AUTHOR]

In this paper, an improved flux-barrier geometry configuration of transversally laminated rotor synchronous reluctance machine (TLR-SynRM) is proposed to suppress the torque ripple. The flux-barrier geometry configuration has two remarkable features. First, its flux barriers are step shaped and their shapes could be described by the parameter X. Second, the widths of multi-flux barriers in the middle regions are changing in a gradient style. The conformal mapping method is introduced to calculate the reluctances of the improved flux-barrier geometry configuration, and the corresponding magnetic equivalent circuit is established to analyze how the parameter X influences air-gap flux density distribution in order to obtain the minimum torque ripple. Based on the above analysis, the results are used to improve the flux-barrier geometry configuration. Last, the effectiveness of the improved flux-barrier geometry configuration is verified by finite-element analysis. [ABSTRACT FROM AUTHOR]

In this paper, an analytical method for predicting the rotor overhang (OH) effect is presented using two types of conformal mappings (CMs), which are the ${r}$ – ${\theta }$ and zr plane CMs. First, the no-load air-gap flux density (AFD) of a slotted air gap without OH is determined using the ${r} {\theta }$ plane CM. Second, the complex relative air-gap permeance (CRAP) in the zr plane is obtained by the zr plane CM. This helps in taking the OH effect into account. Finally, the no-load AFD of the slotted and OH air gaps in cylindrical coordinates is derived from the no-load AFD in the ${r} {\theta }$ plane with CRAP along the ${z}$ -axis. The accuracy of the presented method is verified by comparing the results of no-load analysis with those of 3-D finite-element analysis. [ABSTRACT FROM AUTHOR]

This paper adopts simple analytical modeling to investigate the contribution of air-gap field harmonics to the torque production in some three-phase, 12-slot/8-pole doubly salient synchronous reluctance machines (DSRMs) with both conventional and mutually coupled winding configurations. The air-gap flux density has been calculated based on the analytically obtained magnetomotive force and doubly salient air-gap permeance for both the double-layer and single-layer DSRMs with different winding configurations. Then, the contribution of different air-gap field harmonics to average torque and torque ripple can be investigated and validated by direct finite-element analyses. It has been found that in the DSRMs, the 10th-order harmonic in the double-layer conventional winding (DLC), the 4th-order harmonic in the double-layer mutually coupled winding (DLMC), the 7th-order harmonic in the single-layer conventional winding (SLC), and the 10th-order harmonic in the single-layer mutually coupled winding (SLMC) have the highest contribution to positive average torque and with positive influence on torque ripple reduction. However, the 2nd-order harmonic in the DLC, the 8th-order harmonic in the DLMC, the 5th-order harmonic in the SLC, and the 2nd-order harmonic in the SLMC machines mainly reduce the average torque. [ABSTRACT FROM AUTHOR]

This paper presents the simple analytical modeling for switched flux memory machine to provide in-depth insight into its working mechanism. The analytical approach is based on the slotless open-circuit air-gap flux density and the slotted air-gap relative permeance calculations for a doubly salient structure. In addition, due to low coercivity and highly nonlinear hysteresis curve at the second quadrant, the piecewise and virtual-linear hysteresis models of AlNiCo permanent magnet (PM) are presented to determine the PM working point. This combined analytical solution allows rapid calculation of several electromagnetic characteristics, e.g., air-gap flux density and back electromotive force. The effectiveness of the analytical method is validated by both finite-element results and measurements. [ABSTRACT FROM AUTHOR]