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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 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]

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]

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]

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 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 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]

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]

This paper presents an optimal design for a surface-mounted permanent magnet (SPM) motor to suppress torque pulsations and save the magnet cost, by using multi-grade permanent magnets. Based on a conventional SPM motor with single-grade bonded NdFeB magnets, the proposed SPM motor is designed with two-grade bonded NdFeB and one-grade ferrite magnets, and then optimized by combining the Kriging method with a genetic algorithm, for further minimizing torque pulsations and saving the magnet cost by maintaining the high average torque. As a result, the cogging torque, torque ripple, and magnet cost of the optimized SPM motor are highly reduced compared to those of the conventional SPM motor. Furthermore, the optimized SPM motor is verified to have superior endurance against the magnet’s irreversible demagnetization within three times of the rated current excitation. All motor characteristics, including airgap flux density, cogging torque, electromagnetic torque, and demagnetization ratio are first predicted with the aid of a finite-element method. Finally, the optimal design and analysis results are validated by the experimental results. [ABSTRACT FROM AUTHOR]

Electromagnetic performance of three multi-layered interior permanent magnet (IPM) machines are investigated and compared for electric vehicle applications in this paper. The rotor structure, air-gap field distribution, torque density, torque ripple, core loss, magnet eddy-current loss, and output power are studied with finite-element analysis. It is demonstrated that the two-layered rotor structure with magnets buried deeply has the lower torque density and magnet eddy-current loss due to the utilization of magnets and the block effects of the armature-reaction flux is lower. The three-layered IPM machine has the lower torque ripple and core loss than two-layered IPM machines because the harmonics of air-gap density are reduce by the increase of magnet layers. Finally, an IPM machine with three-layered magnets rotor is prototyped to verify the 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]

A nonlinear equivalent magnetic network (EMN) model is proposed for a linear permanent magnet vernier (LPMV) machine. The meshing method is employed to solve the problem of the modeling of complex flux paths in stator teeth tips. Especially, an end-region model based on the electromagnetic principle is developed to consider the longitudinal end effect of the LPMV machine. The key contribution of this paper is to present a faster and simpler approach to separate the detent force (end force component and cogging force component) than finite-element analysis (FEA). Besides, taking the iron saturation and air-gap flux leakage into account, the proposed model is used to predict the electromagnetic performances of the LPMV machine, such as air-gap flux density, back-electromotive force, cogging force, and thrust force. Finally, through comparisons among the FEA simulations, experimental measurements and EMN analyses, the accuracy and effectiveness of the proposed model are verified. [ABSTRACT FROM PUBLISHER]

In this paper, the air-gap flux density components in the eccentric surface-mounted phase modulation (SPM) machines are predicted analytically. In the provided model, the slotting effects of the armature are taken into account. In the modeling process, conformal transformations (CTs) are employed to obtain an equivalent concentric slotless machine for the eccentric slotted PM machine. To satisfy the condition of using CTs, i.e., having a Laplace equation, the PMs are replaced with an equivalent current sheet at the surface of the rotor. The approach of finding this current sheet is approved by the basis of the electromagnetic theory. One of the contributions of this paper is that the provided model is capable of modeling the eccentric SPM machines with any PM magnetization pattern by means of CTs. Substituting the predicted air-gap flux density components in the Maxwell stress tensor, the machine unbalanced magnetic force and its cogging torque are computed. Finally, the accuracy of the obtained results is evaluated by means of finite-element analysis. [ABSTRACT FROM PUBLISHER]

This paper develops a novel magnetomotive forces (mmfs) distribution model along the transverse direction for the 3-D analysis of linear induction motor, and it investigates the influence of a laterally asymmetric cap-secondary on the thrust, vertical force, lateral force, and efficiency in a prototype single-sided linear induction motor for linear metro. First, the mmf distribution model and its working conditions are defined, and the model is transferred into a mathematical model. Second, the air-gap flux and secondary eddy current in a prototype linear motor with a cap-secondary are obtained by a 3-D space harmonic analytical method. Third, the thrust, vertical force, lateral force, and efficiency of the test motor are analyzed with various lateral deflection, and the power factor in secondary is also presented. Finally, these results are experimentally verified by measurements on the test rig of the linear motor, and the comprehensive effect on the operating performance can be accurately calculated by the mmf model. [ABSTRACT FROM PUBLISHER]

This paper compares the performance of three different topologies of spoke-type permanent-magnet vernier machines (PMVM): 1) dual airgap dual stator winding (DSW); 2) dual airgap single stator winding (SSW); and 3) single airgap (SA). These topologies were compared in terms of torque/machine volume, cogging torque, and torque ripples. The 2-D finite element method was utilized to compare the performance of the three models. The dual airgap PMVM with a SSW showed similar performance with the same machine outer diameter and similar power in terms of torque/machine volume and torque ripples compared with the DSW model. The performance of the SSW model was better than that of the SA model for the same outer diameter and rotor. Furthermore, stator slot optimization was performed to improve torque/machine volume and reduce torque ripples in the SSW model. [ABSTRACT FROM AUTHOR]

This paper investigates the characteristics of the radial force density according to the shapes of the flux modulation poles (FMP) in a surface-mounted vernier machine (SPMVM). The air-gap flux density harmonics obtained from the finite-element analysis method are analyzed using the analytical equations derived from the magnetomotive force and the air-gap permeance distributions. Then, in order to find the radial force density harmonics that generate the exciting force on the stator, the spatial orders and the angular frequencies of the radial force density harmonics are calculated by using the Maxwell stress tensor method. The analysis results show that the permeance harmonics generate the radial force density harmonics, but the resulting harmonics of the radial force density are time-invariant in the spatial domain. Consequently, the variation of the FMP shape can improve the torque characteristics of the SPMVM without the increase of the exciting force on the stator core. [ABSTRACT FROM AUTHOR]

This paper deals with accuracy improvement of a traditional magnetic model for saliency switched reluctance machines. The machine is with high power density for traction application. The calculation is featured by taking conductor layout and slotting effect. Fundamental characteristics, such as flux linkage and air-gap flux density, are analyzed, based on magneto-motive force (MMF) as well as magnetic permeance. Specifically in the MMF model, the winding function is featured by conductor distribution of coils in stator slots, and relation between air-gap flux harmonics and conductor layout is discussed, which helps to reduce harmonics. In the magnetic permeance model, emphases are made on the air-gap permeance fitting using a fourth-order polynomial, followed by a fitting method of magnetic saturation especially with high excitation. A finite-element method is used as a reference. [ABSTRACT FROM PUBLISHER]

In this paper, a novel magnetic equivalent circuit (MEC) is proposed to calculate magnetic flux of saturated electrical machines. The machine features double salient poles with high saturation. Emphases are made on modeling of air-gap permeance and magnetic saturation using a fitting method. The analyses are applied based on a 4-phase 8/6 switched reluctance machine (SRM) with high power density, which was designed for traction application. The air-gap reluctance in MEC that connects a tooth pair is studied, followed by distribution of magnetic saturation on teeth. The magnetic reluctance of circuit loop can be fitted as well as saturation quantity if the electrical steel is known. The proposed network offers a fast and accurate way of estimating flux characteristics of especially highly saturated machines with double slotting effect. [ABSTRACT FROM AUTHOR]

This paper proposes an analytical method that combines the superposition and the subdomain methods to predict the air-gap field distribution in permanent magnet (PM) machines with rotor eccentricity. The original machine with rotor eccentricity is divided into a number of air-gap sections along the circumferential direction. For each air-gap section, a concentric model is employed by adopting an equivalent air-gap length to predict the air-gap field using the subdomain method. The air-gap field distribution of the original model can then be synthesized from these concentric models. Consequently, the electromagnetic performance can be predicted accordingly, such as flux-linkage, back EMF, and so on. Finally, the direct finite element analysis is used to validate the efficacy of the proposed method. The proposed analytical method can be extended to other machines with different slot/pole number combinations and is particularly useful for analyzing the machines with large slot and pole numbers. [ABSTRACT FROM AUTHOR]

This paper presents a simple analytical model for two types of three-phase surface-mounted permanent magnet machines: modular and unequal tooth (UNET) width machines with different slot/pole number combinations. It is based on the slotless open-circuit air-gap flux density and the slotted air-gap relative permeance calculations. This model allows calculating the opencircuit air-gap flux density, phase flux linkage, back electromotive force, and average torque of both the modular and UNET machines. Its accuracy has been validated by the 2-D finite-element (FE) method. A flux focusing/defocusing factor has also been introduced to analyze the influence of flux gaps in alternate stator teeth of modular machines on the machine electromagnetic performances. It has been found that by properly choosing the slot/pole number combination and flux gap width, the open-circuit air-gap flux density, the winding factor, and the flux focusing effect can all be improved. As a result, the performance of the modular machine can be significantly boosted. The analytical and FE models have been validated by experiments. [ABSTRACT FROM AUTHOR]

The clamping of the power transformer magnetic circuit allows maintaining the sheet stack and provides an additional mechanical rigidity. It has consequences on the acoustic noise of transformers as the magnetic cores of power transformers vibrate because of the magnetostriction and, if the corners are considered, Maxwell’s forces. The indirect impact of a lack of clamping on the core losses is studied, especially on the interlaminar air gaps in the corners. In this paper, it is shown numerically with finite element modeling and experimentally with a specific testbench that induced vibrations can change the flux distribution and thus the losses. [ABSTRACT FROM AUTHOR]

An overhang structure is used to enhance the air-gap flux density and increase the torque density of a motor. In the preliminary design stage, consideration of the overhang effect is important for a precise prediction of the performance of a motor with overhang and for the selection of the proper overhang length. The 3-D finite-element method (FEM) is essential when analyzing a motor with an overhang structure due to the asymmetry in the axial direction caused by overhang. However, it is computationally expensive and time-consuming, especially during the initial design stage. In this paper, we propose a magnetic equivalent circuit model, which considers the overhang structure of a surface-mounted permanent-magnet motor. With the proposed analytical method, the computational time is significantly reduced in the preliminary design stage. The proposed analytical model is verified with a 3-D FEM analysis. [ABSTRACT FROM PUBLISHER]

This paper proposes to determine the radial forces in bearingless permanent magnet motor topology. We consider normal and tangential components of the magnetic field in the air gap. Their harmonic components and their evolution versus current and rotor position are considered. This allows establishing the semianalytical expressions of the radial forces considering different field sources. Their precision has been verified using a full finite element model and statistic analysis. The advantage of this semianalytical model lies in the swiftness of the different force components evaluation and consequently the reduction of CPU time. [ABSTRACT FROM PUBLISHER]

This paper analyzed thrust characteristics by considering the step-skew method and permanent magnet (PM) overhang in a linear synchronous motor. Although the PM overhang increases the thrust, it also influences the air-gap flux density distribution in the stacking direction, and thus, each step length should be adjusted according to the existence and length of the PM overhang. 3-D finite element analysis is used to calculate the magnetic field and the thrust characteristics are compared each other. The analysis results show that the stacking length of both ends of the step should be reduced to get lower detent force and thrust ripples, and higher generated thrust as the PM overhang is increased. [ABSTRACT FROM PUBLISHER]

This work deals with the modeling of the magnetohydrodynamic (MHD) phenomena in the air-gaps of low speed radial flux AC electrical machines filled with incompressible and electrically conductive fluids. The proposed model concerns laminar flows and it is based on a weak MHD coupling at the steady state regimes. The MHD power losses are evaluated and discussed. The model is easy to implement and could be a useful tool for the design and the optimization. An application to marine current turbine is considered. [ABSTRACT FROM PUBLISHER]

A simple magnetic circuit method (MCM) is developed for analytical calculation of the air-gap magnetic flux density waveform of a permanent magnet embedded salient pole wind generator (PMESPWG), which can consider the saturation in the side frame and the upper core of its pole shoe. In the MCM, the magnetic circuit is divided into a series of sub-circuits according to the flux paths to cope with different lengths of air-gap and different saturation levels of the pole shoe upper core. In order to evaluate the validity of the proposed method, air-gap flux densities of a 3.3 MW machine prototype are calculated and validated by the finite-element method (FEM) results. By utilizing the developed MCM, the air-gap flux distribution of the PMESPWG is optimized to obtain the maximum fundamental and minimum total harmonic distortion. [ABSTRACT FROM PUBLISHER]