Magnetic Equivalent Circuit Model Research Articles

Design and Modeling of Coreless Magnetoelectric Transducers for Snake-like Wave Energy Converters

With the development of the economy, people’s demand for energy is increasing, which has led to a shortage of fossil fuels. Wave energy is a widely distributed renewable energy source, and the development of wave energy generation technology can greatly alleviate the energy shortage problem. This study takes the snake-like wave energy converter (WEC) as an example and designs a coreless magnetoelectric transducer for it. The structure of the coreless magnetoelectric transducer is relatively simple, eliminating the iron core in the transducer, which can eliminate its own damping. At the same time, this structure can minimize the gap between the magnet and the coil, improve energy conversion efficiency, and work continuously under complex working conditions. This study takes two types of coreless magnetoelectric transducers as examples to analyze. This study aims to establish equivalent magnetic circuit models for the coreless magnetoelectric transducers, explore the effects of different magnets on the performance of the transducers, and optimize the parameters in the transducers. We used simulation software to analyze the transducer and verify the accuracy of the models. Finally, prototypes of the coreless magnetoelectric transducers were made, and a testing system for the transducer was established to test its energy conversion capability. Our experiments show that coreless magnetoelectric transducers have good energy conversion capabilities and can be used as transducers for snake-like WECs. At the same time, this type of transducer can also be applied to other types of WECs, providing a new approach for the research of WECs.

Magnetic equivalent circuit modeling of a permanent magnet linear synchronous motor composed of curved segments

This paper advances magnetic equivalent circuit (MEC) modeling for permanent magnet linear synchronous motors (PMLSMs) with arbitrarily curved segments. As PMLSMs are increasingly utilized in industrial applications, accurate and computationally efficient modeling techniques are paramount. This research proposes a novel approach that meets these requirements and paves the way for real-time model-based control, observers, and estimation strategies. Existing MEC models for PMLSMs primarily consider straight stator segments, neglecting the impact of the curvature of curved segments commonly used in modern PMLSM designs. The approach proposed in this paper systematically incorporates these effects into the MEC model for PMLSMs to address this limitation. As demonstrated by several validation experiments, a calibration concept based on measurements further enhances the model’s accuracy. Finally, a method for efficiently implementing the proposed MEC model for a whole PMLSM setup significantly reduces the computation time compared to the standard implementation.

Research on Braking Characteristics of Hybrid Excitation Rotary Eddy Current Retarder

According to the different excitation methods, automotive eddy current retarders (ECRs) can be divided into electrically excited retarders (EERs) and permanent magnet excited retarders (PMERs), and EERs and PMERs have certain complementarity in control and braking characteristics. Therefore, based on literature research, this article proposes a hybrid excitation rotary electromagnetic retarder (HERER) and conducts numerical simulation analysis and experimental research on the braking performance of the HERER. Firstly, the structure and working principle of the HERER are introduced. Secondly, based on the principles of electromagnetics, an equivalent magnetic circuit analysis model of the HERER is established. Then, a finite element analysis model of the HERER is established using Jmag 14 electromagnetic simulation software, and the braking performance of the HERER under different current and speed conditions is studied. Finally, bench tests are conducted on the air loss torque and eddy current braking performance of the HERER. The effectiveness of the finite element analysis model and equivalent magnetic circuit model of the HERER is verified.

Torque and Eddy Current Behavior of a Magnet Rotating Axial Disk Type Magnetic Coupler: Analysis and Experimental Verification

This research explored the impact of air gap on torque and eddy current behavior of a magnet-north-pole rotating axial disk-type magnetic coupler using the magnetic equivalent circuit method. A magnetic equivalent circuit (MEC) model was developed to analyze the torque and induced eddy current behavior for the magnetic N-pole rotation angle 0° to 30° axial disk type magnetic coupler (MC). Torque equations were derived by combining Kirchhoff's law and the integral method, whereas induced eddy current equations were derived using Ampere's law. Flux leakage reluctance equations were obtained using an integral method. Furthermore, the study conducted 2D finite element simulations, and the results were validated against experimental data to ensure the accuracy and reliability of the proposed MEC model. Finally, the research findings suggested that an air gap length of 4 mm was an optimum length to obtain maximum torque and minimum magnetic saturation effects for a proposed MEC model of N-pole rotating axial disk type MC.

Analytical modeling of cylindrical eddy current brakes and multi-objective optimization based on game theory

With the research and development of eddy current brake (ECB), today ECBs have been applied in a variety of fields including vibration control and braking of strong impact loads.The application of a new cylindrical structure eddy current brake (ECB) for strong impact braking of large machinery has been discussed recently. Its high-speed and high-kinetic-energy braking conditions require different analytical and optimization design models and methods from what has been addressed in previous studies. For subsequent more engineering-oriented research and optimization, modeling methods are needed, as well as analysis and optimization studies for braking forces and critical speeds of interest. In this work, a magnetic equivalent circuit model is established, and the influence of eddy current induced during application is taken into account by considering it as a magnetomotive force in the model. The braking force is calculated with the MEC model and an approximate electric field cross-section method. A small prototype experiment is carried out and proves the correctness of the proposed model. Using the proposed and FEM model, parameters of the ECB are analyzed. Then, aiming at design objectives of the ECB that are somewhat competitive under this special braking condition, a multi-objective optimization model is established using the Stackelberg game strategy. An FEM model is built and assessed based on optimization results. The results indicate that the multi-objective optimization model based on the Stackelberg game is effective for the design of this ECB structure.

Exploring torque characteristics of an integrated ultra conducting magnetic coupling incorporating axial magnetic field through magnetic equivalent circuit modelling

Ultra-conductors are a recent class of materials that display superconducting attributes at room temperature and even at higher temperatures. In this paper, we introduce a novel hybrid ultra-conducting coupling (NHUC) where the secondary component includes copper and an ultra-conductor (considered as a room temperature superconductor in much research). We suggest a model based on magnetic equivalent circuit (MEC) to evaluate the distribution of magnetic fields and characteristics related to torque. The 3D model accounts for boundary impacts during mating, and formulation for magnetic flux and torque are derived using Kirchhoff’s and Ampere’s loop laws, respectively. A 3D finite element (FEM) model is constructed, and simulations are performed using iodine-doped double-walled carbon nanotube (IDWCT) as the ultra-conductor for a wider operating range. At a high slip speed of 1200 rpm, a maximum torque of 309 Nm and stable torque of 113 Nm are observed. Adjusting air gap thickness or permanent magnet dimensions results in torque variations. Additionally, due to carbon nanotube (CNT) characteristics, a reduction in losses from the Joule effect is noted. The maximum error between torque results from simulation and the suggested model is 7.68%, confirming accordance. Comparison alongside the slotted eddy current coupling (SEC) reveals that the torque of the NHUC exceeds that of the SEC, diminishing as the air gap widens.

Armature Reaction Analysis and Suppression of Voice Coil Actuator Based on an Improved Magnetic Equivalent Circuit Model

The high thrust density voice coil actuator (VCA) is a key component for the deployers to determine the CubeSats' separation velocity in orbit directly. To improve the VCA's thrust density and power consumption, it is essential to analyze the armature reaction under heavy current work conditions. This paper proposes a dynamic splitting method of the magnetic equivalent circuit (MEC) model for analyzing the armature reaction of the VCA. This MEC model can effectively reveal the interaction mechanism between the dynamic winding field and the permanent magnet (PM) field, which provides an approach to readily and quickly analyze the armature reaction. Based on the understanding of the mechanism, we found an effective way to suppress the armature reaction and propose a new VCA with double PM flux circuits. The electromagnetic performances of the new configuration are evaluated by comparing it with the conventional one. Both the theoretical and experimental results show that the new structure achieves lower magnetic saturation, lower armature reaction, and higher thrust density. A research prototype was constructed and experimentally tested to verify the theoretical results of the armature reaction, magnetic field, thrust, separation velocity, and other performances. The new VCA realizes a wide and accurate modulation of separation velocity for the CubeSats.

Investigation of a novel intensifying-flux hybrid excited permanent magnet machine for electric vehicles

PurposeTo address the issues of the insufficient output torque associated with the application of intensifying-flux permanent magnet (PM) machines in electric vehicles, this paper aims to propose an intensifying-flux hybrid excitation PM machine. It is possible to adjust the air gap magnetic field by adjusting the field current in the excitation winding, thereby increasing the torque output capability and speed range of the machine.Design/methodology/approachFirst, a novel intensifying-flux hybrid excited permanent magnet synchronous machine (IF-HEPMSM) is proposed on the basis of intensifying-flux permanent magnet synchronous machine (IF-PMSM) and an equivalent magnetic circuit model is established. Second, the tooth width and yoke thickness of the machine stator are optimized to ensure the overload capacity of the machine while effectively improving the wide flux regulation range. Furthermore, the electromagnetic characteristics of the IF-HEPMSM are investigated and compared with the IF-PMSM and conventional permanent magnet synchronous machine (PMSM) by using finite element simulations.FindingsThe id of IF-HEPMSM and IF-PMSM is greater than zero low-speed magnetizing current. And the flux-weakening current of the IF-HEPMSM is 18% and 3% smaller than of the conventional PMSM and IF-PMSM.Practical implicationsAiming at the problems of IF-PMSM applied to electric vehicles, this paper proposes an IF-HEPMSM. The air gap magnetic field is adjusted by controlling the current of the excitation winding to improve the reliability of the machine. Therefore, the IF-HEPMSM combines the advantages of high-power density and high efficiency of the PMSM and the controllable magnetic field of the electro-excitation machine, which is of great engineering value when applied in the field of electric vehicles.Originality/valueThe proposed IF-HEPMSM offers better flux regulation capability with electromagnetic characteristics analysis and maps of dq-axis current as compared to IF-PMSM and conventional PMSM. Moreover, the improvement of the torque can make up for the shortcomings of the insufficient torque output capability of the IF-PMSM.

Electromagnetic Design and Analysis of a Stator–Magnet Transverse Flux Linear Oscillatory Machine with Yokeless Mover Core

Conventional stator–magnet moving−iron transverse−flux linear oscillatory machines (CSMTLOMs) are widely applied in directly−drive reciprocating devices due to the merits of easy fabrication and robust mover. However, in order to keep the mover vibrating at a certain resonance frequency to save the energy and enlarge the output power, they still suffer from a higher requirement on spring stiffness due to their thick and heavy mover core, which would also narrow the frequency band with a high power factor due to the large inertial energy storage of the heavy mover. Hence, to reduce the mover core weight to reduce the demand of the spring and improve the operation performance, an improved linear oscillatory machine featured by a spoke−type interior permanent magnet inner stator (ISMTLOM) is proposed. Benefiting from its separated two stators, the tangential flux in the radial plane can return through the inner stator core, so that the yoke of the mover core can be eliminated directly. Then, to analytically investigate the influence of the special axial local saturation effect, the segmental equivalent magnetic circuit (EMC) model of the ISMTLOM is established, wherein a saturation coefficient is introduced to quantitatively consider the local saturation effect on the output force. Consequently, several important size parameters are optimally selected when keeping the same outer diameter and copper loss as that of the CSMTLOM. Afterward, the three−dimension finite element algorithm (3D FEA) is adopted for the electromagnetic performance validation and comparison. Finally, it is found that the nonlinear segmental EMC corrected by the saturation coefficient can quickly predict the output force more accurately within the wide load range, and benefiting from the topology improvement, the ISMTLOM has the merits over the CSMTLOM in its smoother output force, much lighter mover core, and less demand of mechanical spring stiffness, whilst preserving the similar output force density.

Method for Predicting Linear Eddy Current Braking Performance of the High-Speed Maglev Train Based on Magnetic Circuit Structure

On high-speed magnetic levitation (maglev) trains, the linear eddy current brake (LECB) is a key piece of equipment to ensure the safety of train operation. In the event of a sudden failure of the traction motor or the external power grid, braking by the LECB, which comes with the maglev train, is currently the only emergency braking method that can ensure the train can be safely stopped while operating at high speed. The braking performance of eddy current brakes is usually predicted based on symmetrical magnetic equivalent circuits, which usually ignore the interactions between the magnetic circuits. For LECB, such interactions should not be neglected. In this paper, to investigate an accurate and efficient method for predicting the braking performance of LECB for high-speed maglev trains, based on the structural characteristics of LECB and Kirchhoff’s law, a full structural magnetic equivalent circuit model considering the interactions between magnetic circuits is developed, and then combined with the subdomain method, a braking force model, to predict the braking performance of LECB. The performance prediction of LECB with different numbers of magnetic poles is compared with the traditional method using the results of the finite element method and the experimental method as references. The results show that the proposed method is more accurate in predicting the braking performance of LECB and better reflects the physical characteristics of the actual magnetic field.

An optimal design method for magnetorheological fluid sealing structure for beam director using multi-objective optimizer

For beam directors, tight optical path sealing and low rotational friction torque are critical aspects for the tracking and positioning performance. To maximize sealing pressure and minimize rotational friction torque, a magnetorheological fluid sealing (MRFS) structure design method based on multi-objective COOT (MOCOOT) algorithm optimizer was proposed in this work. The MOCOOT integrates archive, grid strategy, chaotic mapping strategy and COOT optimization algorithm. Firstly, the magnetic field strength of the sealing clearance was derived based on the equivalent magnetic circuit model, the sealing pressure formula of MRFS with pole teeth structures was established, and the friction torque model of MRFS based on Bingham equation was also developed. Then, according to the actual requirements of optical path sealing of beam directors, the constraint conditions of structure parameters were determined, and the optimization target model of sealing pressure and friction torque was constructed. As follows, a multi-objective version of COOT optimization algorithm, named MOCOOT, was proposed to optimize the structural parameters of MRFS structure. Finally, the effectiveness of the proposed method was verified via pressure and rotating friction torque tests implemented on an established experimental platform.

Comparison of nonlinear solution methods for magnetic equivalent circuits of saturated induction motors

This work compares three nonlinear solution methods for the performance of an induction motor’s magnetic equivalent circuit model with magnetic saturation. The interrelation between magnetic flux density and permeability introduces nonlinearities in the differential system of equations. Three popular nonlinear solution methods are selected for comparison, namely (i) the Gauss–Seidel method, (ii) the Newton–Raphson method and (iii) the inverse Broyden’s method. While all three methods have been applied in this context before, no comparison study has been published to the authors’ best knowledge. The study finds that the inverse Broyden’s method is most performant in terms of the number of required iterations, the computation time per iteration and the resulting total computation time. However, for substantial saturation levels, the authors recommend a hybrid implementation of multiple solution methods to obtain robust and reliable convergence.

An approach to solving the effect of background in fluidized bed on electromagnetic tomography

As a non-invasive measurement technique, electromagnetic tomography (EMT) system based on tunneling magneto resistance (TMR) can detect the distribution of medium in the gas–liquid–solid fluidized bed by the difference of permeability. The distribution of medium in the three-phase fluidized bed is not uniform, and the solid clusters and bubble clusters are formed in the background of the gas–liquid–solid mixture. Since the effect of the background in the pipe of the fluidized bed on the boundary measurement data of the TMR-EMT system is much greater, it is difficult to detect solid clusters and bubble clusters when the image is reconstructed directly using the boundary measurement data. In order to improve the detection of clusters by the TMR-EMT system, a method to weaken the effect of the background is proposed. The equivalent magnetic circuit model is used to estimate the background permeability. Then the magnetic dipole theory and demagnetization effect theory are utilized to establish a simple background compensation model based on the estimated background permeability. Using the compensation model, the effect of the background is weakened from the boundary measurement data and the cluster distribution information is highlighted. Simulation and experimental results demonstrate the effectiveness of the proposed method.

Analysis of low saliency ratio and torque characteristics of the fractional slot concentrated winding surface mounted motors

In recent years, fractional slot concentrated winding permanent magnet synchronous motors (FSCW PMSMs) have become a hotspot in the research field. Due to the unique inductance characteristics of the FSCW PMSM, a fast and accurate calculation of the d/q-axis inductance and saliency ratio is necessary. In this paper, a method is proposed to calculate the d/q-axis reactance of the FSCW SPMSM, which constructs the equivalent magnetic circuit model of the d/q-axis armature reaction flux separately, and the saliency ratio characteristics of the FSCW SPMSM were demonstrated. In addition, to meet the high requirements of the modern industries, especially in servo systems, accurate consideration of the effect of stator resistance on torque and electromagnetic performance is important and more applicable. According to the relationship between the vector parameter, the explicit expression of the d/q-axis currents that consider the stator resistance is obtained, and the prediction of load angle at maximum electromagnetic torque is achieved. Then, combined with the finite element method, the influence mechanism of stator resistance on the motor steady-state performance is revealed. Finally, the experimental data are compared with the calculation data, and the correctness of the models and analysis was verified.

A novel stress concentration inspection method for marine oil and gas pipeline based on UNSM

Stress concentration of marine oil and gas pipelines can lead to deformation and cracks, laying out great hidden dangers for safe operation. This paper proposes a novel in-line inspection method for stress concentration based on UNSM (unsaturated magnetization) for oil and gas pipelines. Firstly, the stress concentration inspection mechanism with UNSM is analyzed, and the equivalent magnetic circuit model of the inspection probe is derived. Secondly, the response signal features of axial, radial and complex stresses were investigated parametrically by numerical simulation. Then, quantitative tensile stress inspection was carried out with the UNSM inspection probe. Finally, the pipeline stress state is continuously scanned by the self-developed defect dynamic scanning experimental system. The results show that the UNSM inspection probe can effectively detect the abnormal stress of the pipeline. Meanwhile, the axial tensile, radial compressive stress and complex stress increase the axial permeability of the pipeline, resulting in a negative correlation of characteristic signals. Besides, the signal feature shows the "basin" distribution and decreases gradually with the increase of the lift-off. The above research provides a reference for developing in-line inspection equipment for the abnormal stress of marine pipelines.

Magnetic Field Analysis and Development of Disk Axial–Radial Hybrid Excitation Generator for Range Extenders in Extended-Range Electric Vehicles

Magnetic Field Analysis and Development of Disk Axial–Radial Hybrid Excitation Generator for Range Extenders in Extended-Range Electric Vehicles

An accurate calculation method for inductor air gap length in high power DC–DC converters

High-power inductors are fundamental components in high-power DC–DC converters, with their performance being a crucial metric of converter efficiency. This paper presents an in-depth analysis of a novel calculation method for the air gap length in such inductors. Taking into account the effects of air gap diffusion and the winding magnetic field, an expression for the air gap diffusion radius is derived, focusing on a distributed air gap structure. Furthermore, models for calculating the air gap and winding reluctance are developed, grounded in electromagnetic field theory. An equivalent magnetic circuit model, formulated based on Kirchhoff's second law, facilitates the proposed method for air gap length calculation. This study also involves the development of 3D models for both discrete and decoupled integrated inductors. The comparison between simulation outcomes and calculated air gap lengths indicates a maximum error of less than 8%, with the minimum error being as low as − 0.79%. Compared with traditional methods, the calculation method proposed in this paper has significant advantages. Additionally, the discrepancy between calculated values and experimental measurements is found to be 1.11%. These results validate the accuracy and applicability of the theoretical analysis and calculation method, underscoring their significance in the design and optimization of high-power DC–DC converters.

D-Q Axis Inductance Analytical Calculation for Fractional-Slot Distributed Winding IPM Motor Based on Big-Small Pole Space Method

The d-q axis inductance is the crucial parameter for the interior permanent magnet (IPM) motor. In order to facilitate the design, analysis, and optimization of IPM motors, it is of great significance to develop an accurate and simplified inductance analytical calculation method. Among the existing calculation methods, the magnetic equivalent circuit (MEC) has advantages in the inductance calculation of the IPM motor due to the simple modeling, the fine processing of the saturation region and the visualization of the magnetic field distribution. However, the traditional MEC method is only applicable to the IPM motor with integer-slot distributed winding (ISDW) or fractional-slot concentrated winding (FSCW), while lacking of in-depth research on fractional-slot distributed winding (FSDW). The magnetic circuit topology of FSDW IPM motors is not as single as that of FSCW/ISDW IPM motors. It leads to problems in the traditional MEC method when dividing the d/q axis flux path in FSDW motors. To solve this problem and expand the applications of MEC method, a big-small pole space (BSPS) method is proposed after fully considering the common characteristics of MMF distribution and reluctance distribution in FSDW motors, which fills the gap of MEC method applied to FSDW motors. The BSPS method divides the d-axis flux path according to the asymmetry of the d-axis magnetomotive force (MMF). Based on the divided flux paths, an improved nonlinear MEC model that considers the saturation of stator and rotor is established to calculate d- and q-axis inductances. The results of finite element analysis (FEA) verify the validity of the proposed MEC model with different geometry parameters. Experimental results of an 84-pole/360-slot FSDW I-type IPM wind generator further confirm the validity of the proposed MEC model

Magnetic Equivalent Circuit Model for a Two Degree-of-Freedom Rotary-Linear Machine with Transverse Flux Structure

Magnetic Equivalent Circuit Model for a Two Degree-of-Freedom Rotary-Linear Machine with Transverse Flux Structure

Distributed Magnetic Equivalent Circuit Modelling of Synchronous Machines

Distributed Magnetic Equivalent Circuit Modelling of Synchronous Machines