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This article proposes a quantitative analysis model for the electromagnetic forces in rotor-permanent-magnet (rotor-PM) machines, decoupling the air-gap field modulation and the force modulation. First, a unified analytical model of the equivalent concentrated forces (ECFs) is deduced based on the air-gap flux density (AFD) harmonics. Second, the air-gap field modulation and the force modulation are decoupled by the ECF coefficient. Then, to determine the contributions of the modulated AFD harmonics, a quantitative analytical method is proposed. On this basis, the vibration performance of a 12-slot/10-pole (12s/10p) interior PM machine is investigated considering the modulation effect. The results reveal that the influences of rotation speed, PM-excited field, and armature field on the vibration can be clearly represented by the proposed method. Finally, the modal test and the acceleration measurement are conducted to validate the analysis. [ABSTRACT FROM AUTHOR]

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]

Permanent magnet Vernier motors (PMVMs) possess the advantage of high torque density for high-performance applications. However, the low power factor challenge makes it unacceptable for direct-drive applications. A lack of accurate modeling method based on the motor sizing law, i.e., air-gap flux density, linear current density, and motor geometry parameters, raises difficulties for machine designers to further conduct research on the performance metrics. This article presents a deep investigation into the analytical modeling technique for surface PMVMs (SPMVMs). It can identify an accurate approach to obtain the performance metrics, including electromagnetic torque and power factor. The modeling technique is developed based on the conformal mapping method. By using this, both radial and tangential permeability functions can be calculated to obtain the motor magnetic loading accurately, considering the leakage flux. The slotting effect on both air-gap flux density and armature-winding function is analyzed to achieve a precise formula for torque and power factor computations. The new modeling technique is applied to integral-slot SPMVMs with different slot/pole combinations, gear ratios, slot openings, and magnet thickness to evaluate the impacts of motor parameters on high-power-factor and high-torque-density designs. Finally, an SPMVM with the characteristics of high torque density and power factor is fabricated to verify the analytical model at the power rating of 0.8 kW and the speed of 500 r/min. The experimental results show that the prototype exhibits a high power factor of 0.9 and high torque density 22.5 Nm/L. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear analysis model for predicting the performance of eddy current recoil brakes (ECRB) is proposed by combining the magnetic equivalent circuit (MEC) model and the subdomain model. The subdomain model introduces the equivalent region to improve the inherent shortcomings of the equivalent current sheet (ECS) method. The outer tube is divided into a magnetic saturated region and an unsaturated region in the subdomain model to simulate the magnetic saturation of the outer tube during recoil. The MEC model is applied to calculate the air gap magnetic flux density and the relative permeability of the equivalent region. Leakage flux and magnetic saturation are considered in the MEC model. The eddy current resistance of ECRB is calculated by the subdomain model. The model is verified by the finite element model, and it is able to predict the performance of ECRB with different structural parameters. In addition, the prototype of the ECRB was manufactured. A test was carried out on a 155 mm artillery to verify the accuracy of the proposed nonlinear analysis model. [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]

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 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]

This paper proposed a hybrid subdomain model (HSM) for calculating the magnetic field distribution of interior permanent-magnet (IPM) machine accounting for slotting effect, rotor saliency, and iron nonlinearity. In the constant permeability region, i.e., slots, slot-opening, and air-gap, three subdomains are introduced to represent their magnetic field. By applying the subdomains interface conditions and nonlinear boundary conditions, the analytical air-gap field solution can be obtained based on the governing Laplace and Poisson equation. For the iron region, the magnetic reluctance network (MRN) is proposed to account for rotor saliency iron and nonlinearity. The magnetic voltage source is introduced to represent the permanent-magnet (PM) while the air-gap flux source is used to replace the air-gap reluctance network, which is the key to guarantee the computational efficiency and high accuracy. The electromagnetic performances of both flat-shaped and V-shaped IPM machines are investigated to show the advantages of different IPM machine topologies analytically. The HSM predictions for both IPM machines are validated by finite-element (FE) analysis and experimental results. [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]

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]

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]

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]

Accurate and computationally-efficient models of induction machines (IMs) are essential for many simulation programs and analysis of power systems transients. Conventionally, when modeling magnetic saturation in the classical qd0 models, only the fundamental component of magnetizing flux is considered. To represent the saturation air-gap flux harmonics, fairly complicated phase-domain and/or implicit models have been proposed in the prior literature. In this paper, a new explicit two-axis IM model is developed to include the air-gap harmonics caused by magnetic saturation. The new model is validated by experimental measurements and simulations in various steady state and transient scenarios and is shown to provide accurate results while being simple to implement. [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 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]

Large medium-voltage electric machine stators are usually equipped with form wound coils made of flat conductors (strands) and embedded in open (rectangular) slots. Air-gap magnetic flux lines can enter the slot and, sweeping the strands placed nearest the slot opening, induce eddy currents in them. Such eddy currents cause additional losses which can be much higher than usual skin-effect and proximity losses. In order to avoid dangerous overheating and hot spots, the additional losses in question need to be carefully predicted in the design stage. Time-stepping finite-element analysis (TSFEA) can be used for the purpose, which however implies a large computational burden and requires the machine geometry to be modeled in detail. This article proposes alternative methods based on time-harmonic finite-element analysis (THFEA) simulations performed on highly simplified machine models and with no need to take rotor motion into account. The proposed methods are shown to produce very accurate results, compared to TSFEA, but with very significant time and computational savings. [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]

Five-phase electric machines possess several distinct features and are sometimes considered in vehicular power systems and various special-purpose energy sources. Design and analysis of such machine-converter systems are highly dependent on simulation software programs, where accurate and numerically efficient dynamic models of five-phase synchronous machines are essential. Depending on levels of fidelity and interfacing compatibility, the traditional models for five-phase machines include the coupled-circuit-phase-domain (CCPD) and qd0 models. To achieve a computationally-efficient model suitable for many simulation programs, in this paper, a new constant-parameter voltage-behind-reactance (CPVBR) model is proposed for five-phase synchronous machines where a simple interfacing circuit is achieved with constant RL branches. The proposed model is validated by experimental measurements and simulation studies. The proposed CPVBR model is demonstrated to have superior numerical efficiency and simulation speed compared to the existing conventional models. [ABSTRACT FROM AUTHOR]

Braking torque is the most important performance parameter for a permanent magnet retarder used in heavy vehicles. This paper proposes a model of the permanent magnet retarder for braking torque at different speeds considering the skin effect, the magnetic leakage, and the actual path of the eddy currents. Based on the magnetic equivalent circuit and the piecewise function method, the static and the transient air-gap flux density models are established, and their accuracy is verified by comparison to the finite element method (FEM). The permeability distribution curve of the retarder stator is obtained by a simple permeability-measuring instrument, considering the skin effect on the permeability of the stator. Thus, the effective permeability function of the stator is obtained at different rotational speeds, and the transient air-gap flux density model is optimized using the effective permeability function. The simulation results showed that the optimized transient air-gap flux density of the calculation model was in good agreement with the FEM. Finally, the calculation model of the eddy current braking torque was verified by the bench test. [ABSTRACT FROM AUTHOR]

A passive compulsator is being designed and developed in this article to drive a railgun which has been built and tested earlier using a capacitor bank in the author’s laboratory. In this article, the analysis has been done for various machine parameters for a self-excited passive compulsator. A secondary armature on the stator has been used as a source for the self-excitation of the field winding as the primary armature is being optimized for the main discharge current pulse. The field excitation of the compulsator is assumed to be transient in nature. The main parameters to be analyzed in the compulsator design in this case are as follows: 1) the time required for the air gap flux density to reach the rated value; 2) the power loss in the compulsator during self-excitation; and 3) the maximum field current. During the self-excitation, currents induced in the compensation shield slow down the overall process of field excitation and also result in high field current affecting the design of the field circuit converter (FCC). A number of probable designs were modeled and simulated for different diameters of the rotor, the number of field winding turns, nominal field current density, and compensation shield thickness, and the above-mentioned parameters were compared. The same analysis has also been compared with the performance of the compulsator in the main operation, that is, driving the railgun, so as to decide the range for some of the design parameters. [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, by solving the Maxwell's equations, an analytical model is developed for the prediction of the air gap flux density in the eccentric permanent magnet (PM)-inset machines at no-load and on-load conditions. Since in this model neither Schwartz–Christoffel transformation nor perturbation analysis is used, it is fast and accurate. In the modeling process, the stator of the eccentric machine is replaced with an equivalent surface current (ESC), which is injected at the stator bore. Distribution of the ESC is unknown and must be selected, such that the resultant tangential field satisfies the boundary condition at the stator bore contour. To apply this condition, the flux density of the PMs, armature current, and the ESC are obtained by applying the subdomain analysis and using a conformal transformation. The armature current and ESC are considered as a surface current sheet at the stator bore. The back electromotive force and inductances of the eccentric machine are obtained in the proposed model. In addition, using the Maxwell stress tensor, the unbalanced magnetic force, and the electromagnetic torque are computed. Finally, the model is verified by means of finite element analysis. [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]

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]

DC arc evolution is a complicated and rapid time-dependent process. To better demonstrate the mechanism of the dc arc without external interference factors, a test circuit was built for the entire process of arc generation, maintenance, and extinction. Two different adjustment models were adopted. The macroscopic performance and characteristics of the arc were analyzed. The discharging and extinguishing conditions were measured and compared to the results of a burning candle located under a rod–rod air gap. This paper shows that the dc arc’s color changes from blue to purple and then yellow, finally forming a flame as the current increases. The macroscopic performance can be divided into eight periods in the first adjustment model, while only three periods are included in the second model. The arc discharging condition only depends on the applied high voltage, but the extinguishing condition may depend on either the limiting current or the drop-down voltage. Dynamic volt–ampere characteristics appear only if adjusted by the first model. The arc-root voltage is constant to 0.32 kV. The degradation of the ground electrode is far worse than that of the high-voltage electrode. This paper can be regarded as the first-step research for further studies on large-current dc arcs in arcing horns used in dc transmission grounding lines. [ABSTRACT FROM AUTHOR]

This paper presents a quasi-three-dimensional (3-D) nonlinear magnetic equivalent circuit (MEC) model for double-sided axial flux permanent magnet machines (AFPMMs) with fractional slot concentrated windings. The proposed model can take into account not only the local magnetic saturation effect but also the 3-D flux distribution. A coupled variable permeance element is proposed in airgap modeling that captures both axial and circumferential airgap flux densities. With the help of the coupled variable permeance element, the transient magnetic field is considered by the time varying connection of the airgap and the rotor. The proposed model can be used to predict the performance of AFPMMs, including the 3-D distribution of no-load and armature airgap flux densities, no-load back electromotive force, and electromagnetic torque. In order to verify the reliability of the MEC model, two AFPMM prototypes are taken as examples, and the accuracy is verified by comparing the calculated parameters of the MEC model with the finite element analysis and experimental results. Finally, the effect of local saturation on the performances of AFPMMs is investigated. [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]

Machine simulation models allow the use of embedded numerical computation techniques. The finite element model accuracy is usually gauged by comparing its performance with experimental measurements. In this paper, a large hydrogenerator is modeled and the sensitivity of various model parameters is investigated by comparing the simulated results with experimental measurements. Four hydrogenerator units with the same design drawings are considered in the analysis. The effect of the model parameters was studied by considering the response of the open-circuit voltage in comparison with the measured open-circuit voltage, of the different units. Parameters considered included the effective model depth for a two-dimensional simulation, effective air gap, and effective material permeability of the B–H curve. A 20% variation in operational air gap between two machines of the same design resulted in over 18% difference in open-circuit voltage, particularly beyond the knee point. Reduction in permeability of the soft magnetic materials resulted in agreement between the simulation and measured results at saturation. Consequently, for large machines, the B–H curves from the Epstein measurements are insufficient and should be adjusted accordingly. [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]

State-of-the-art design methods for electric machines use published correlations of either power or torque with electromagnetic and current loading, available for different cooling approaches. However, the applicability of these correlations for electric machines used within hybrid electric vehicles, with their different degrees of integration into the overall system, is limited. Using an integrated starter generator and an electric rear axle drive as example case applications, we study the influences of the thermal environment within the hybrid electric vehicle application, i.e., heat sinks and sources external to the machine on the thermal design of the machines. We quantify these influences by scaling factors for the air-gap shear stress of the machine. [ABSTRACT FROM PUBLISHER]

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, an integrated model for acoustic evaluation of electric vehicles is introduced. The paper focuses on the force excitation part of the model. The analysis is performed for permanent magnet synchronous machines. The excitation forces are placed on the stator teeth and calculated for a structure dynamic model of the power train. A model for the acoustic emission is adapted, and finally, the psychoacoustical behavior is characterized at the position of the driver of the e-car. An approach for the design of the rotor pole topology is introduced to ensure a beneficial acoustic behavior under consideration of air gap flux density and related force densities on the stator teeth. The calculation is performed using finite-element analysis simulation, but also analytical design methods are considered. Objective of this comparison is a very short computation time and, therefore, an efficient simulation process. The model is validated by measurements on test benches. [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]

Space harmonics of synchronous machines are investigated in this paper through a specially designed synchronous machine. A 2-D finite-element method is used to calculate the magnetic field of the machine. The space harmonic magnitude and phase angle can be computed based on the magnetic flux density. The machine is specially designed and can be excited from the direct axis, quadrature axis, and various intermediate axes. The overall finite-element calculation accuracy is validated by the measured open-circuit characteristic curves. The space harmonic investigation in this paper provides valuable insight of the space harmonic contents of synchronous machines, which can help to develop a more advanced harmonic prediction method for the synchronous machine's design and operation. [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]