The 50 most-cited articles in IEEE Transactions on Magnetics, 2023

Physics-informed neural networks (PINNs) have been successfully applied in electromagnetism (EM) for the solution of direct problems. However, since PINNs typically do not take system parameters (like geometry or material properties) as input, when embedded in inverse problems or adopted for parametrical studies, to output the solution of the governing equations, they require additional training for each new system parameter set. To overcome this issue, we propose a hypernetwork (HNN) that receives system parameters and outputs the network weights of a PINN, which in turn provides the solution of the direct problem. Therefore, once trained, the HNN acts as a parametrized real-time field solver that allows the fast solution of inverse problems, in which the objective(s) are defined a posteriori (i.e., after HNN’s training). This method is adopted for a coil optimal design task in magnetostatics.

Physics-informed neural network (PINN) has shown great potential in inverse and parametric designing problems in electrical engineering. Moreover, most existing works on PINN are dedicated to computational fluids, and very little attention has been paid to static and low-frequency electromagnetic near fields with multiple media in electrical engineering applications. In this work, a PINN for solving 2-D magnetostatic fields in electromagnetic devices and systems is proposed. The magnetic field intensity and the magnetic vector potential are solved by training a neural network (NN) which encodes partial differential equations (PDEs) and boundary conditions (BCs) as residuals. The computation of the spatial derivatives of media constitutive parameters, which negatively impacts the training of PINN, is eliminated. A mesh-assisted non-uniform sampling method for the selection of collocation points is proposed to further improve the performance of PINN. The proposed PINN is verified by comparing its results with those of the finite-element method (FEM) in two 2-D magnetostatic case…

Metasurfaces have received extensive attention for their unique electromagnetic properties. However, traditional metasurface design is hugely labor-intensive and computationally resource-intensive, especially when using complex structures to obtain suitable targets. In this article, a design method based on deep learning (DL) is proposed, which can efficiently reduce design time and resource consumption. The DL model is composed of two parts, an autoencoder (AE) and a DL network (DLN). It can quickly fit the relationship between the electromagnetic response and the metasurface structure. For demonstration, two different absorbers are designed based on the proposed DL method, and the target spectrum is in good agreement with the simulation results. The proposed DL method achieves an average accuracy of 95% and 85% on two different absorbers, respectively, verifying its powerful predictive ability. In addition, the high performance of DL on two different structures shows its transferability.

In this contribution, the authors investigate a modular structure of a wireless power transfer (WPT) system specifically dedicated to a quasistatic or dynamic operation mode in an urban environment. The proposed architecture has been simulated by using commercial software. Characteristics of the interoperability are analyzed when the modular transmitting and receiving coils are in proximity, and the architecture has proven to be characterized by excellent performances in terms of small interaction between each single module. Finally, an improved coil design has been introduced which is characterized by good uniformity of the coupling coefficient when the receiver travels between two adjacent transmitting sections.

In this article, a hybrid algorithm is proposed by combining the non-dominated sorting genetic algorithm (NSGA-II) with multi-objective particle swarm optimization (MOPSO) algorithm. The original NSGA-II is improved by using logistic mapping initialization and a dynamic selection mechanism of crossover and mutation operators is proposed. The performance of the proposed hybrid algorithm is verified using standard test functions and it is applied to the multi-objective optimization (MOO) benchmark problem TEAM 22. Numerical results demonstrate the effectiveness and superiority of the proposed hybrid algorithm.

This article proposed a monitoring method for inter-turn short-circuit (ITSC) fault for permanent magnet synchronous motor (PMSM). This article analyzes the electromagnetic performance of PMSM under single-phase ITSC fault working condition. On this basis, a new diagnosis method for ITSC fault based on second ripple of$d$-axis and$q$-axis current is proposed. The presence or absence of second current ripple indicates whether ITSC occurs, and the amplitude of the second current ripple can be used to identify the severity of ITSC fault. The correctness and effectiveness of the proposed method are verified by both finite element analysis (FEA) and prototype experiment.

To increase torque density, a combined-Halbach array for the axial flux permanent magnet machine (AFPMM) with a yokeless and segmented armature (YASA) is presented in this article. First, the YASA machine models with conventional axial magnets and combined-Halbach array magnets are established by using 3-D finite-element method (FEM). Then, the torque, torque per magnet-volume, and no-load back electromotive force (back EMF) are calculated, and the performance of the two machines is analyzed and compared. It is demonstrated that the combined-Halbach array can improve the torque density of the machine and the utilization rate of the magnets. Finally, the combined-Halbach array rotor is optimized, where the rotor with unequal-thickness magnets is established, and its torque density is calculated under different thickness. The results show that the combined-Halbach array with unequal-thickness magnets can decrease the amount of permanent magnet (PM) materials, thus improving the utilization of magnets and reducing the costs.

A cup winding permanent magnet synchronous machine (PMSM) is proposed in the application of large-capacity flywheel energy storage system (FESS), which can effectively improve the efficiency of the FESS and reduce the axial height of the flywheel. First, the structure of the whole flywheel system and the cup winding PMSM are given. Second, the preliminary design scheme of the machine is obtained, and the effect of changing each parameter on the machine performance is analyzed. On this basis, a new optimization strategy combining back-propagation artificial neural networks (BP-ANNs), genetic algorithm (GA), and multi-objective particle swarm optimization (PSO) algorithm is proposed to optimize the efficiency and volume characteristics of the machine, and the results of the optimization are compared with the preliminary scheme to verify the correctness of the optimization method.

In this article, a variation-aware ternary true random number generator (TTRNG) is proposed and simulated using stochastic switching of the magnetic tunnel junction (MTJ) in the current below critical current and carbon nanotube field-effect transistors (CNTFET). The proposed TTRNG does not need any converters and produces ternary random numbers directly. The stochastic behavior of the MTJ ensures the generation of a truly random sequence. At the same time, the CNTFET threshold voltage adjustability through flat band voltage allows the implementation of ternary logic circuits. A ternary post-processing block is also designed to ensure the equality of the ratio of the numbers generated by the proposed TTRNG, even with the process and voltage variations. Circuit-level simulations performed using the HSPICE tool indicate the correct operation of the proposed TTRNG circuit. Moreover, statistical simulations also authenticate that the ternary sequence generated by the proposed TTRNG is of excellent quality, even in the presence of significant process and voltage variations. The proposed…

Step-skew is a common technique for eliminating the cogging torque of a target harmonic order in permanent magnet synchronous motors (PMSMs). However, when step-skew is applied to the rotor, the cogging torque of the target harmonic order is not completely eliminated due to 3-D leakage flux. Therefore, the 3-D leakage flux should be considered in designing a PMSM with step-skew for cogging torque reduction. The most accurate way to consider the 3-D leakage flux is to perform 3-D finite element analysis (FEA), but it has the disadvantage of high computation time. To resolve this challenge, this article proposes a design method that utilizes transfer learning to reduce the time for 3-D FEA while maintaining accuracy. Through the proposed method, a large amount of 2-D FEA-based data and a small amount of 3-D FEA-based data are used instead of a large amount of 3-D FEA-based data, with similar accuracy as using a large amount of 3-D FEA-based data, and the computational time is highly reduced. Finally, a prototype is fabricated and tested to verify the validity of the proposed design…

This study proposes a novel topology optimization (TO) method for permanent magnet (PM) motors based on a variational autoencoder (VAE) and a neural network (NN). The VAE is trained to embed various shapes generated from the TO into the latent space. The NN is trained to predict the characteristics of the PM motor from its latent representation derived using the VAE. After training, TO is performed in the latent space based on the prediction using the NN. We adopt the Monte Carlo dropout to maintain prediction reliability using the NN during optimization, where prediction deviation is evaluated and used to eliminate unreliable solutions. The proposed method yields Pareto solutions within 80 s in a single-thread CPU machine, which is considerably faster than numerical analysis-based optimization, such as finite-element analysis.

A direct-drive permanent magnet (PM) motor and a magnetic-geared PM motor (MG-PMM) have the advantage of high torque density. Therefore, these motors are expected to be applied as in-wheel motors for electric vehicles (EVs). However, they have a problem that it is difficult to achieve the wide speed–torque characteristics required for EVs. This article presents a novel magnetic-geared motor that consists of a flux-modulated type magnetic gear (MG) and a switched reluctance (SR) motor. In this article, the SR motor part and the MG part are designed, and both parts are combined into a magnetic-geared motor. The proposed magnetic-geared motor has the wide speed–torque characteristic, which direct-drive PM motors or SR motors cannot achieve.

This article proposes a dynamic wireless charging scheme for electric vehicles (EVs) using autonomous frequency control. The key is to make the receiver circuit of an EV always operate in the splitting region by adopting proper transmitter coils and displacement between adjacent transmitter coils. Then, by sensing the primary current, the autonomous frequency control can achieve constant charging power in the splitting region even the EV is moving. The operating frequency of the system is monitored online. When the operating frequency indicates that the EV is leaving the current transmitter coil and approaching the next transmitter coil, the current transmitter circuit stops working and the next transmitter circuit starts to work, thus achieving continuous charging on the road. Both theoretical calculations and experimental results are given to validate the feasibility of the proposed scheme.

In this article, the electrical and mechanical characteristics of multilayer interior permanent magnet synchronous motors (ML-IPMSMs) using ferrite permanent magnets (PMs) are compared when driven at high speeds with respect to the type of electrical steel. In high-speed operation, the mechanical and electrical characteristics of ML-IPMSMs vary depending on the number of PM layers, PM shape, number of bridges, and bridge thickness. In addition, ferrite PMs have a lower coercive force than neodymium (Nd) PMs; therefore, irreversible demagnetization (ID) must be considered, and it is affected by the number of PM layers and PM shape of ML-IPMSMs. Thus, when designing a multilayer IPMSM using ferrite PMs for electric vehicle (EV) traction, all characteristics should be considered. Compared to conventional electrical steel (CES), high-strength electrical steel (HSES) offers advantages in mechanical properties, allowing for greater flexibility in ML shape. Consequently, it is possible to design a shape with improved electrical performance when compared to CES by adjusting the ML shape. In…

A compact and integrated wireless charging system is presented in this article for the purpose of charging a photovoltaic (PV) system attached to a building. In such an integrated system, cross-coupling interference presents a challenge, which is addressed by using DD coils and Q coils. Moreover, since cross-coupling has been eliminated, it is convenient and efficient to design corresponding compensation networks. The theoretical analysis shows that the well-designed inductor–capacitor–capacitor-series (LCC-S) compensation structures can provide load-independent constant voltage (CV) output. An experimental setup is successfully built to validate the characteristics of the presented system.

This study proposes a novel multi-objective topology optimization method for hybrid-type motors. In the proposed method, the optimization process is divided into two steps. First, combinatorial optimization is performed to obtain a solution with a geometry that combines, for example, the structure of a wound field motor (WF motor) and an interior permanent magnet motor. Thereafter, a local search is performed within the constrained design region for each Pareto solution obtained in the first step. The proposed method facilitated motor geometries with multiple advantages, for example, the flux adjustment capability of WF motors and high torque characteristics of interior permanent magnet motors (IPM motors). The proposed method was validated through its application to the optimization problem of a hybrid-field motor and a permanent magnet assisted synchronous reluctance motor (PMa-SyRM).

Magnetically controlled waveguide-based phase shifters are desirable for their high performance, but are bulky and heavy, thus cannot be easily integrated with printed circuit board (PCB) based circuits. To tackle this, substrate-integrated waveguide (SIW) technology has been utilized, which brings the waveguide to a standard PCB, but requires large numbers of vias as well as multiple cavities in the substrate for ferrite slab placement. This implementation technique involves complex fabrication and yields a relatively low figure of merit (FoM). To alleviate this, we present the first completely vialess ferrite substrate-based waveguide phase shifter realized through low-cost inkjet printing technique. All the four sides of a yttrium iron garnet (YIG) substrate have been metalized through inkjet printing, allowing the fabrication of a conventional rectangular waveguide on a standard magnetic substrate. The prototype has been tested in symmetric as well as antisymmetric modes of biasing and peak FoMs of 160°/dB at 7.22 GHz and 332°/dB at 7.46 GHz have been measured, which are higher…

Accurately modeling magnetic hysteresis plays a crucial role in developing precise digital twins for low-frequency electromagnetic systems. However, in large 3-D analysis systems, the evaluation of hysteresis performance at hundreds of thousands of points in components containing magnetic steels is challenging. It is of utmost importance that any modeling system can assess the hysteresis performance within the shortest possible timeframe. The utilization of neural networks (NNs) offers the potential to achieve this objective. This article provides a comprehensive review of various NN architectures that can be employed to address this requirement. Two types of learning approaches are explored: completely data-driven approaches and hybrid approaches that combine data and hysteresis laws. A comparative study is conducted to analyze the predictive power and computational cost of the different architectures under investigation.

The main requirements of magnetic components for power electronics applications are high power density and low power losses, driven by the need for more compact and more efficient power converters. Metal powder materials are a common choice for high-power and high-frequency inductors subject to a large magnetic field bias, since they feature high saturation flux density and low magnetic permeability (i.e., a “distributed” air gap), allowing for the adoption of un-gapped cores. Despite this, under high values of magnetomotive force (i.e., deep core magnetic saturation), the insertion of a concentrated air gap can lead to higher core inductance factor values with respect to an un-gapped configuration. In this context, this article proposes a straightforward procedure to maximize the inductance factor of metal powder magnetic cores by identifying the optimal air gap length for a specified design operating point. In particular, the procedure completely relies on information available in the core manufacturer’s datasheet and does not require experimental characterization of the core…

Local overheating and airgap magnetic leakage are severe due to the distribution of inter-tile airgap in wireless power transfer (WPT) ferrite pads. In this article, a thermal-magnetic multi-objective optimization function (MOF) is proposed to evaluate and mitigate the thermal-magnetic deterioration caused by the distributing airgap. The effects of the airgap on temperature and leakage distribution are analyzed based on the magnetic-thermal coupling finite element method (FEM) simulation. It is found that the trend of the local temperature is opposite to that of the magnetic leakage following the increase of the airgap width. An interesting range can also be found by using the proposed MOF strategy. When the airgap width is within the range, the gap thermal-magnetic problems can be mitigated effectively. Subsequently, a full-scale prototype with 11.1 kW at 85 kHz is fabricated to validate the effectiveness of the MOF strategy and the accuracy of evaluation. The pads with optimized airgap achieve greater comprehensive performance than that without the optimization.

Series-end winding motor drives double the dc-link voltage utilization compared with the conventional star-connected winding counterparts, which indicates that series-end winding motor drives are suitable for high-speed applications with limited dc-link voltage. To further improve the dc-link voltage utilization and extend the speed range of the dual three-phase series-end winding permanent magnet synchronous motor (DTSW-PMSM) drive system, this article proposes a novel winding connection sequence (WCS) for DTSW-PMSM drive, and the dc-link voltage utilization is further improved by 36.6% compared with the normal WCS. The dc-link voltage utilizations of different WCSs are analyzed through the phasor relationship between the phase and leg voltages. Besides, the corresponding carrier-based pulsewidth modulation (CBPWM) to drive the DTSW-PMSM with the proposed WCS is also developed. In the experimental tests, the speed range of the DTSW-PMSM drive with the proposed WCS is extended significantly. Therefore, adopting the proposed WCS can be an effective means for further speed range…

This article proposes a novel high-speed axial flux permanent magnet synchronous motor (AFPMSM) with hybrid permanent magnets (PMs) to reduce the magnet cost. Based on basic AFPMSM with sinusoidal NdFeB PMs, the proposed model is designed with an equal quantity of ferrite and NdFeB PMs, wherein the hybrid PMs are divided into parallel and vertical to the magnetization direction of the PM. Furthermore, three kinds of hybrid PM arrangements are adopted for the AFPMSM and the relative analysis of the magnetic circuits is carried out. Then the no-load, load electromagnetic performance, and torque cost of the AFPMSMs with three PM arrangements are simulated and compared by the finite element method (FEM). Finally, the demagnetization and stress analysis are performed to verify the stability of the AFPMSM with hybrid PM arrangements.

This article proposes a hybrid analytical model (HAM) for predicting ac copper losses in hairpin windings. The HAM combines the nonlinear semi-analytical model (SAM) and the 1-D ac copper loss computation model to solve the inaccurate boundary solutions of the 1-D ac copper loss computation model when magnetic saturation occurs in the stator teeth. The HAM is used to study the ac losses of the hairpin windings with four different conductor arrangements under different current excitation conditions, and the versatility of the HAM is verified. The HAM has high calculation accuracy, and the calculation speed is 66% faster than the finite element (FE) model. The primary contribution of this research is to present a quick and simple approach for accurately predicting ac copper losses in hairpin windings with arbitrary conductor arrangements.

This article investigates the effects of multiple flux barriers (FBs) and permanent magnet (PM) arrangements of flux intensifying (FI) interior PM (FI-IPM) motors at high-speed operation for spindle applications. Common FI-IPM motors possess a low constant power speed range (CPSR), thus limiting their applications. In this article, three multiple-flux-barrier FI-IPM (MFI-IPM) motors with different PM arrangements are studied. First, the air gap flux density, inductance characteristics, and torque component distribution are investigated with various rotor topologies. Then, the performance of the MFI-IPM motors in terms of CPSR and torque ripple is investigated and compared with an original V-shape FI-IPM motor. The analysis reveals that proper rotor designs can significantly improve the performance and CPRS of the MFI-IPM motor. Furthermore, considering the rotor mechanical strength of the MFI-IPM motor at high speeds, magnetic bridges and ribs are added, which thus increases flux leakage and slightly reduces motor performance. Finally, a rated power of 9 kW MFI-IPM motor prototype…

The high permanent magnet (PM) eddy-current loss will inevitably cause the risk of irreversible demagnetization, and the PM complete segmentation (CS) method is a common method to reduce the PM eddy-current loss. However, PM CS design will increase the cost and difficulty of assembly process, especially for axial flux PM (AFPM) machines. To address this issue, a new arc incompletion segmentation (AIS) method is proposed to reduce the PM eddy-current loss and cost, including double-side AIS and single-side AIS designs. Then, some of the key parameters are optimized. In addition, the PM eddy-current loss, cost, and torque performance are studied and compared with different segmentation methods under different conditions based on 3-D finite element method (FEM). Finally, two different 25 kW prototypes are manufactured and tested to validate the proposed method and analysis.

For the drone wireless in-flight charging system, the challenge is to keep a constant charging power under the large range of continuous fluctuation of mutual inductance ($M$), the variation of battery load ($R$), and the limited payload of drones, which has been rarely studied in the previous research. To address the issue, this article presents a primary-series and secondary-series-inductor-series–parallel-capacitor (SLSPC) high-order topology for the parity-time (PT) symmetric wireless power transfer (WPT) system, which can greatly expand the exact PT-symmetric region (constant power range) by the reduction of critical coupling coefficient in comparison with the traditional series–series topology. In addition, the constant power control scheme is proposed based on the series-SLSPC high-order topology to overcome the change of$M$and$R$. With the proposed control method, only the primary current needs to be detected, which enhances the real-time performance of the WPT system and reduces the payload of drones. Simulated and experimental results validate the expansion capability of…

Inverse hysteresis model with magnetic flux density and magnetic field intensity as input and output, respectively, is more preferred, compared with the forward one, for resolving the electromagnetic issues of electrical equipment in terms of magnetic vector potential or with voltage sources. And an inverse hysteresis model with high accuracy and high computation speed has a broader range of applications. However, the well-known classical Preisach hysteresis model is formulated with the forward form, and has the double integration of its distribution function, making it inconvenient and impractical in electrical engineering. In this article, an analytical inverse Preisach model is proposed for the first time. First, the analytical expressions of permeability of the initial magnetization curve, descending and ascending branches of the hysteresis loop are derived using one closed form of the Everett integral function. Subsequently, the analytical inverse Preisach model is derived by the difference method, considering the reversible magnetization component that the classical Preisach…

Dynamic magnetization curves of soft magnetic materials are often written in terms of magnetic flux density$b$and magnetic field strength$h$as$h = \mathcal {H}(b) + c {\text {d} b}/{\text {d} t}$, where$\mathcal {H}$is a static magnetization model and$c$is a real number describing eddy-current effects. In this article, an analytical derivation for$c$is presented for soft magnetic composite materials. The parameter$c$will depend explicitly on the conductivity of the material particles as well as the geometry of the particles, described by mean particle volume, variance of the particle volumes, volume fraction of the material and insulation thicknesses. No experimental or empirical parameters appear in$c$in our treatment.

In this article, we have worked on defect-assisted spin transport at the ferromagnetic (FM)/organic semiconductor (OSC) interfaces leading to modified TMR response in hybrid magnetic tunnel junction (MTJ) devices. The simulation considers non-equilibrium Green’s function (NEGF) assuming spin precession at the FM/OSC interface defect states. Both the carrier injection (band-to-band) and phonon-assisted tunneling through the organic spacer optical gap led to modified spin transfer torque (STT) across the MTJ devices. Higher compensation of spin damping due to out-of-plane STT led to higher TMR response for the MTJ devices.

The rotor eccentricity fault will cause the electric vehicle (EV) drive machine to generate unbalanced magnetic pull (UMP) and torque fluctuation. It may induce more complex rotor dynamics behavior and endanger the safe and reliable operation of the drive system. In this article, three spoke-type interior permanent magnet synchronous machines (IPMSMs) with different armature winding structures, which are integer-slot double-layer distributed winding, fractional-slot double-layer concentrated winding, and fractional-slot four-layer concentrated winding with star–delta (Y–$\Delta$) connection, are introduced. The armature magnetomotive force (MMF) analytical models of the three IPMSMs are built. Also, the air-gap permeability is analyzed when static eccentricity, dynamic eccentricity, and mixed eccentricity faults occur in IPMSMs. Furthermore, electromagnetic characteristics of the three IPMSMs under different rotor eccentricity faults are studied. Effects of static eccentricity and dynamic eccentricity faults on cogging torque, back electromotive force (EMF), radial electromagnetic…

This article proposes a novel optimization method to design the transmitting and receiving coils of a wireless power transfer (WPT) device considering its magnetic and circuit properties. In the proposed optimization, the coil shapes are determined by parameter optimization (PO) for manufacturability, whereas the magnetic core shapes introduced near them are determined by topology optimization (TO). The power transfer efficiencies of the optimized WPT device are evaluated using the SPICE simulation considering the coupling with an electronic circuit. The circuit parameters of the optimized coils are computed using the homogenization-based finite element method (FEM), which can effectively evaluate the eddy current loss in the coil windings. It is shown that the optimized WPT device has a power transfer efficiency higher than 90% even when there is a misalignment.

The authors developed the electrodeposition technique for CoPt thin films applicable to 3-D domain wall motion memory (3D-DWMM). CoPt films with perpendicular magnetic anisotropy (PMA) were obtained in a wide range of the Co composition which was controlled by adjusting the potential during electrodeposition. The magnetic properties of the CoPt films were controlled via the Co composition. The pulse electrodeposition method was conducted to obtain smooth morphology of the Co68Pt32 films. Ultra-thin Co68Pt32 films with smooth surface morphology and an excellent squareness ratio were obtained. This study promises the electrodeposition of the artificial ferromagnetic multilayers for the magnetic pillar of the 3-D-DWMM can be achieved.

This study investigates the accurate measurements of high-frequency core loss using a capacitive cancellation method for low-permeability magnetic material, which leads to high leakage flux during measurement. We observe that the core loss is underestimated with the lower coupling of the core-under-test (CUT). To solve the issue, we propose a new correction method, in which the effective permeability observed during the measurement is measured, and the core loss is corrected with that permeability. The core loss is corrected by the proposed method even when high leakage flux exists.

Automatic catering vehicles (ACVs) are increasingly adopted in restaurants to save expensive human resources. Especially in special situations such as a pandemic, ACV offers a wise choice to keep social distance. In this article, a wireless power transfer (WPT) system is proposed to charge four ACVs at the same time. With the help of ferrite cores, the flux can be guided through all four receivers while the leakage magnetic field can be reduced simultaneously. Two transmitters are utilized to confine the flux path further. Both areas #A and #B can charge ACVs with the consideration of the mechanical structure of the food preparation area and charging standby area (Areas #A and #B). The presented system can also realize zero phase angle (ZPA) to degrade the volt-ampere (VA) rating. Finally, an experimental setup is constructed, and the overall dc–dc efficiency is 87.6% when delivering 120 W to four loads.

This article presents a permanent magnet spherical motor (PMSM) with a soft magnetic composite (SMC) core. The analytical model of the no-load air-gap magnetic field of the PMSM with SMC core is obtained based on the Laplace equation with the boundary conditions. When the SMC core is added to the stator teeth, a cogging effect occurs, which makes the 3-D magnetic circuit of the entire spherical surface uneven. When the spherical motor completes a multi-degree-of-freedom motion, the air-gap magnetic field is severely distorted. In order to solve the above problems, this article proposes for the first time the method of adding spherical-shaped pole shoes to the stator teeth, which perfectly solves the problem of magnetic field distortion in this article. The air-gap magnetic field distribution is improved by optimizing the structure of the stator tooth pole shoes. Finally, the static torque measurement platform was built to test the rotation-energized output torque. The research results of this article lay a theoretical foundation for the structural optimization design of the PMSM…

In high-speed surface-mounted permanent magnet (SPM) brushless machines, time- and space-harmonic excitations can induce significant eddy currents flowing in the rotor conductive parts. An effective measure to suppress the eddy currents is to employ a copper shield between the magnets and the retaining sleeve. In this article, a Fourier-based analytical model is proposed to evaluate the rotor eddy current losses. The model is set up in the cylindrical coordinate system and is able to compute the eddy current fields and losses in all rotor domains, that is, the sleeve, shield, magnets, and shaft. Although it is generally believed that both ordinary Bessel functions (OBFs) and modified Bessel functions (MBFs) are workable for solving the magnetic vector potential, it is argued in this article that only the MBF-based models are numerically stable when the high-conductivity domain (e.g., the copper shield) exists, while the OBF-based models may result in irrational results. Both the OBF- and MBF-based analytical models for a prototype motor are established and comparatively studied,…

This article presents a new hybrid analytical model (HAM) based on sub-domain (S-D) model for surface-mounted permanent magnet (SMPM) synchronous motors, which helps from magnetic equivalent circuit (MEC) model to calculate the cogging torque (CT) under loading condition. For this purpose, the conformal mapping (CM) method and Hague solution are used to calculate the air-gap permeances, which are to be employed in MEC model for calculating the distribution of magnetomotive force (MMF) drops in iron parts of stator for every operating point. The distribution of MMF drops is then translated into the distribution of equivalent virtual currents in stator slots of SMPM motor for relevant operating point. While considering the permanent magnets (PMs) on the surface of rotor core and the virtual currents in the stator slots, S-D model is used to calculate the components of air-gap magnetic field under loaded condition. Maxwell stress tensor (MST) method is then used to calculate the CT under loaded condition. In final, the frozen permeability method (FPM) is used to verify the analytical…

In this article, a multi-objective topology optimization (MOTO) methodology using Non-dominated Sorting Genetic Algorithm II (NSGAII) and convolutional neural network (CNN) is proposed. The original NSGAII is improved to achieve better global search ability and uniform distribution of Pareto solutions. And CNN is applied as a surrogate model for finite element analysis (FEA). The framework of the proposed methodology is elaborated. To validate the proposed methodology, it is applied to the TO of an electromagnetic actuator. Numerical results validate the proposed methodology and demonstrate that computational cost of TO can be reduced.

The streamer discharge physical process can be described by the coupled Poisson’s equation and the convection–diffusion equation. It is a multi-physical field problem involving electromagnetism and hydrodynamics. We propose a streamer discharge model based on physics-informed neural networks (PINNs) to improve the computational efficiency regarding the classical approach. Poisson’s equation and the convection–diffusion equation are trained to generate sufficient data and construct a deep operator network (DeepONet). The performance of the PINN, in terms of accuracy, is analyzed by applying it to different datasets (electron density and potential distribution) and comparing to a reference solution (spatial evolution of electrons). The simulation results show that the neural network (NN) has high accuracy in learning two types of equations.

Vibration and acoustic noise caused by electromagnetic forces (EMFs) limit the application of switched reluctance machines (SRMs). In this article, the topology optimization (TO) is introduced to the rotor design of SRMs for reducing the stator vibration caused by resonance while retaining the output torque as possible. The TO freely forms the rotor to explore the potential best design. As the TO result, adopting the anchor-shaped rotor pole and opening a window inner the rotor pole are discovered as two tactics to mitigate stator resonance of the 12/8 SRM. With the aid of the two tactics, the resonance-induced displacement is reduced by 42% with a 5% average torque loss.

In the interior permanent magnet synchronous motor (IPMSM), an asymmetric rotor is used as a design method to reduce torque ripple or cogging torque by adjusting the saturation of the rotor core. The advantage of an asymmetric rotor is that it can reduce torque ripple or cogging torque in the forward direction while maintaining the average torque or output power. However, when driving in the reverse direction, the torque ripple or cogging torque can be increased. Therefore, the asymmetric rotor produces different characteristics in the forward and reverse directions. In this study, the asymmetric rotor shape is designed using an optimization technique taking into consideration the rotating direction. The optimum design is performed based on the symmetric rotor as the base model. When rotating in the forward direction, the asymmetric rotor has a lower torque ripple than the symmetric rotor, and when rotating in the reverse direction, the asymmetric and symmetric rotors are designed to be similar. The kriging surrogate model was used to determine the optimum design point that…

The ultrahigh-speed (UHS) electrical motor is an essential component for air compressors of hydrogen fuel cells and has been attracting more and more interest in the last decades. For UHS motor design, topology and material are two critical factors. This article presents the design and comparison of four 25 kW 100 000 r/min permanent magnet motors (PMMs) with two different topologies, namely six stator slots and two rotor poles (6S2P) and 12 stator slots and four rotor poles (12S4P), and two different stator core materials, namely high silicon sheet steel (10JNEX900) and amorphous magnetic alloy (ZOM-6). The magnetic material properties are measured at different frequencies using the ring sample and single sheet testers for accurate performance analysis. A comprehensive comparative study shows that the 12S4P UHS motor with an amorphous alloy stator core has the highest efficiency. The torque ripple of the 12S4P motor is much lower than that of the 6S2P motor. The radial electromagnetic force (REF), vibration, and noise analyses reveal that the motors with amorphous magnetic alloy…

Permanent magnet vernier motor (PMVM) possesses the advantage of high torque density. In split-tooth PMVMs, the modulation teeth can be evenly or unevenly distributed on each stator tooth, which leads to the corresponding evenly and unevenly distributed slot vector diagrams (SVDs). So, by selecting closer slot vectors into one phase, the winding factor can be improved, so the torque of PMVMs can be increased further by using the unevenly distributed modulation tooth (UDMT) structure. In this article, two split-tooth PMVMs with evenly and unevenly distributed modulation teeth are compared. The simulation and test results verify the correctness.

Eddy current testing (ECT) at different frequencies can identify surface and back-surface defects caused by the skin effect. Traditional ECT uses a pickup coil to measure the magnetic-field signal caused by eddy current. However, according to Faraday’s law of electromagnetic induction, the voltage signal detected at low frequencies is weak; thus, the signal is susceptible to interference from noise. By contrast, magnetoresistive (MR) sensors have high sensitivity at low frequencies. Therefore, we developed a rectangular wave ECT (RECT) system using an MR sensor. The system uses rectangular wave excitation, which can generate both low- and high-frequency signals, and the MR sensor detects the magnetic-field components. A 12 mm-thick aluminum plate with an artificial circular defect 10 mm in diameter and 4 mm in height was used as a specimen. The measurement results indicated that the developed system can accurately and quickly distinguish between surface and back-surface defects.

This study proposes a novel multi-objective design method based on Monte Carlo tree search (MCTS) for the design of permanent magnet (PM) motors. The global configurations that define the entire structure are represented by nodes in a tree structure. After MCTS is performed to select a route extending from the root to leaf node, multi-objective topology optimization (TO) is performed at the leaf node to determine the detailed shape, considering a trade-off relationship among objective functions. The novelty of this work lies in the integration of MCTS with multi-objective TO where the score of a node is provided by the number of Pareto solutions obtained by selecting that node. This enables the scoring of nodes and the determination of the node selection criterion. The proposed method is applied to the multi-objective optimization of a PM motor with respect to average torque, and either torque ripple or iron loss. The proposed method successfully obtained Pareto solutions, which comprise various global configurations and shapes.

A compact, reliable, and straightforward mathematical modeling of the eddy current (EC) braking torque is proposed in this article. First, the braking magnetic force, which curbs the movement of a rotating disk (RD), is evaluated using the basic laws of electromagnetism. Second, the braking torque is related to the braking force through a polynomial function model. The model parameters are evaluated by plugging in measurement samples in the equation of motion taking into account the nonlinear behavior of the aerodynamic drag forces. The proposed model neither has limitations on the braking system geometry nor the disk rotational speed as long as the measurement samples cover the whole speed range. Moreover, it is validated experimentally for constant and alternating magnetic flux profiles with best fit rates (BFRs) more than 85% and 93% for both rotational speed and braking torque, respectively. Furthermore, programmable braking application is demonstrated using the proposed approach and its applicability is verified experimentally.

The low-order high-amplitude component of the axial electromagnetic force is the leading cause of electromagnetic vibration and noise of axial flux permanent magnet (AFPM) motors. In this article, based on the analytical calculation of the axial electromagnetic force for a 20-pole 24-slot AFPM motor, the low-order axial electromagnetic force component is weakened by optimizing the motor’s electromagnetic structure. First, the three-dimensional (3-D) structural model of the motor is equated to a two-dimensional (2-D) analytical model, which is used to calculate the magnetic field generated by each armature winding and permanent magnet (PM). Then, combined with the Maxwell tensor method, the axial electromagnetic force waveform is further obtained, and the target low-order high-amplitude component is extracted by 2-D Fourier analysis. Finally, taking this axial electromagnetic force component minimization as the target function of optimization, considering the output torque and ripple as constraints, the genetic algorithm is used to search for the optimal point by varying the…

Sub-harmonic synchronous machines (SHSMs) are a relatively new breed of brushless wound field synchronous machines considered alternatives to many electric machines in transportation electrification applications. This article presents two dual inverter SHSMs (DI-SHSMs) having unique two-layer and three-layer stator winding topologies. The two inverters provide the stator windings with two sets of balanced three-phase currents. These two and three-layer windings are arranged in such a way that they can generate both fundamental and sub-harmonic magnetomotive force (MMF). Furthermore, the fundamental MMF component of this machine is four times the sub-harmonic MMF component used for the brushless operation. In contrast, the sub-harmonic MMF is used for field excitation, which leads to brushless operation. Two eight-pole, 48-slot, two-inverter, two-layer, and three-layer sub-harmonic machines are designed to validate the concept through a 2-D finite element analysis (FEA) of these new topologies, showing a better overall torque profile and performance as compared with the other…

Density-based topology optimization (TO) methodologies in magnetostatics interpolate either the magnetic permeability$\mu $or the magnetic reluctivity$\nu $to define intermediate materials and compute the problem sensitivities. These choices may lack physical interpretation and are not suited to model realistic permanent magnets. This work proposes the interpolation of the vector magnetic polarization$\boldsymbol {m}$as a more general alternative, which can model any magnetic material. It is then applied to the multimaterial TO of the rotor of a permanent magnet synchronous machine. The case of an ideal permanent magnet with a constant magnetic polarization is compared to that of AlNiCo. The results show that considering the nonlinearity of the permanent magnet can significantly impact the optimized geometry.

This study proposes a novel methodology for topology optimization, employing an explainable deep neural network (XDNN). This innovative approach utilizes Shapley additive explanations (SHAPs), a tool designed to elucidate the predictive reasoning of convolutional neural networks (CNNs). The contributing regions to the characteristics are revealed by SHAP and topology optimization is performed in restricted regions to reduce the computational cost during the search while ensuring an efficient search. As a practical demonstration of the efficacy of the proposed method, it is applied to an interior permanent magnet synchronous motor. The results comprehensively demonstrate the effectiveness and potential implications of the novel methodology.