Magnetic Equivalent Circuit Research Articles

A magnetic equivalent circuit model for segmental translator linear switched reluctance motor

Because of exclusive characteristics of Switched Reluctance Motor (SRM) particularly simple and robust structure and high reliability, it can be a good choice for many industrial applications. In terms of structure and performance principles, the Linear Switched Reluctance Motor (LSRM) is similar to rotary SRM (RSRM) and therefore their advantages are identical. The Segmental Translator Linear Switched Reluctance Motor (STLSRM) is a special type of LSRMs that can produce a higher thrust density in comparison to the simple type of LSRM. One of the most important models for predicting the characteristics of electric machines is the model based on the Magnetic Equivalent Circuit (MEC), which can be used to predict the performance characteristics of machines. Although the STLSRM has significant advantages, no MEC model has been introduced for it so far. With the aim of predicting the static and dynamic characteristics of this motor, a new analytical model based on MEC method is developed in the present paper. In addition to simplicity, the developed model has acceptable accuracy and speed. The proposed model is utilized for a three-phase STLSRM and different static and dynamic characteristics of the motor including static flux-linkage, static force, instantaneous current waveform and instantaneous thrust waveform are predicted. To validate these obtained simulation results, they are compared with those derived from the Finite Element Method (FEM).

Performance evaluation and optimization of flux-regulated axial-radial eddy current coupling

Abstract This paper proposes a novel axial-radial permanent magnet eddy-current coupling equipped with a mechanical magnetic adjuster. The innovative design integrates mechanical flux weakening technology with an enhanced magnetic method rooted in axial-radial hybrid flux topology. Concise analytical models for air-gap field and torque are developed, leveraging the magnetic equivalent circuit method and Faraday’s law. These models are subsequently validated using the 3D finite-element method. The results indicate that this device boasts an exceptionally broad torque adjustment range, reaching approximately 93% at a given slip. Furthermore, it exhibits a substantial optimal working area, spanning from 20% to 80% of the mechanical magnetic adjuster's movable distance. To comprehensively analyze the impact of structural parameters on overall performance, three novel metrics are defined. The analysis reveals that the pole pairs of the radial magnetic circuit (RMC) have the most significant influence on the device's comprehensive performance. In the end, a multi-objective optimization method to maximize the global torque regulation capabilities, local torque regulation abilities, and maximum torque potential is developed to enhance the overall performance of this innovative magnetic coupling design.

Impact of Air Gaps Between Microstrip Line and Magnetic Sheet on Near-Field Magnetic Shielding

This study experimentally analyzed the impact of air gaps between a magnetic sheet and a test board with a microstrip line, which is used to measure the near-field magnetic shielding effectiveness (NSE) of magnetic sheets made of metallic powder. To conduct the measurements, a material fixture equipped with a microstrip line to generate the near magnetic field, a rectangular loop probe, and an automatic probe positioning system capable of moving the loop probe along three axes were designed and fabricated. In addition, to systematically vary the thickness of the gaps, three paper spacers with a thickness of 0.11 mm per paper were used, and a 1.0 mm thick acrylic sheet, along with a specially designed material fixture, was used to press down the magnetic sheets during measurement. The magnetic shielding properties were measured and compared under various air gap conditions using a near-field magnetic loop probe. The effect of the gaps on the shielding performance of the magnetic sheets was quantitatively evaluated for three different magnetic sheets. The experimental results showed that as the gap thickness increased, NSE tended to improve up to a frequency around 1 GHz, while in the higher frequency range of a few GHz, NSE tended to decrease. The physical background of this phenomenon was explained using an equivalent magnetic circuit represented by reluctances for the structure, where the magnetic sheet is placed above the microstrip line with an air gap. This model helps to elucidate how the presence of the air gap affects the near-field magnetic shielding performance.

Optimization of Stator Structure for Improved Accuracy in Variable Reluctance Resolvers Using Advanced Machine Learning Techniques

This study presents an optimized design for a Segmented Sinusoidal Parameter Winding with Magnetic Wedge Variable Reluctance Resolver (SSPWMW-VRR), addressing challenges like winding asymmetry and harmonic distortion in conventional designs. By integrating particle swarm optimization (PSO) for winding design, magnetic equivalent circuit (MEC) analysis for leakage flux, and machine learning techniques (XGBoost and Multi-Layer Perceptron), the stator slot shape was fine-tuned for improved accuracy. XGBoost outperformed MLP in prediction accuracy with a mean absolute error (MAE) of 0.1172. Finite element analysis (FEA) simulations and experimental validation demonstrated a reduction in position errors from ±30′ in conventional VRRs to ±5′ in the optimized design, along with significant harmonic reduction.

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.

Decreasing the non-linearity of hybrid reluctance actuators by air gap design

This paper presents an air gap design approach to improve the linearity of rotational Hybrid Reluctance Actuators (HRAs) used in fast steering mirrors. The approach involves modeling a one-degree-of-freedom HRA with a magnetic equivalent circuit to identify and analyze sources of non-linearities. On the basis of the verified model, solutions for an improved linear system behavior are analytically searched. Two linearized HRA designs are proposed, one with linear cross-section dependency and the other with hyperbolic air gap length dependency. Finite element method simulations are employed to evaluate the performance with respect to the linearity and the motor constant of these designs, showing factor 50 improved system linearity.

Torque Performance Analysis of Asymmetric Magnetic Pole Permanent Magnet Synchronous Motor for New Energy Vehicles

In view of the problem of large torque ripple and poor output performance of permanent magnet synchronous motor, a new topology of asymmetric magnetic pole permanent magnet synchronous motor is proposed, and the torque ripple of this motor structure and the suppression method are analyzed. First, the equivalent magnetic circuit method and Lorentz force law are used to derive the analytical formula of torque ripple of the motor. Then, based on the analytical formula, the parameters of permanent magnet of the asymmetric magnetic pole permanent magnet synchronous motor are optimized and verified by finite element software simulation; on this basis, the method of rotor eccentricity is used to further weaken the torque ripple of the motor, and the optimal eccentricity distance is analyzed. The research shows that when the parameters of the magnetic pole of the asymmetric magnetic pole permanent magnet synchronous motor is appropriate, the harmonic content of the air gap magnetic density of the optimized motor is greatly reduced, and the motor has good output characteristics, and the torque ripple is reduced to 5.4%. Finally, the prototype is trial‐manufactured and tested. The results show that after optimization, the cogging torque of the motor is reduced, the torque output performance is improved, and the overall motor performance is improved. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

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.

Analytical modelling of the linear transverse flux permanent magnet motor using magnetic equivalent circuit method

AbstractThe authors propose an analytical modelling approach for the linear transverse flux permanent magnet motor using the magnetic equivalent circuit method. The main focus of this study is to predict the phase flux‐linkage characteristic of the motor. Essential equations required for implementation of the model and how to solve it are described clearly so that someone can use it easily. A typical motor is selected to apply the proposed model and simulation results, including static characteristics of flux‐linkage and thrust, are presented. To validate the developed analytical model, the discussed motor is also analysed with 3D finite element method using MAXWELL software and the obtained simulation results are compared to each other.

Analysis of a New Asymmetric Biased-Flux Operation for an Inter-Modular Permanent Magnet Motor

Net zero and electrification targets are continuing to enforce a need for the development of high-performance electrical machines, increasingly based on the use of rare earth permanent magnets. Biased flux motors have the potential to overcome some of the disadvantages associated with more conventional electrical machines. Since their introduction, there has been a consistent trend towards new and improved topologies, all relying on the same principles of operation. In this paper, a new alternative operation is proposed where the magnetic flux density offset of each module is different. The resulting asymmetric biased excitations of the magnets leads to a flux concentration in the air gap. Placement of magnets in the slot-opening area is shown to produce a higher average torque at a higher power factor. It is mathematically shown that the conventional methods used to investigate the effect of each group of magnets separately cannot be used for the explanation of this operation principle. Therefore, it is necessary to simultaneously consider both groups of magnets in the magnetic equivalent circuit. Due to the use of magnets in these motors, thermal conditions are also investigated. Finally, a comprehensive comparison between several stator-situated-magnet motors is presented. The performance of the proposed motor is improved in terms of average torque, torque density, PM torque density, power factor, and overload capability. The torque density specifically has increased by 9%. Moreover, both motors have suitable thermal behaviour which confirms the validity of the demagnetization analysis.

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.

Improved air gap permeance modelling for single-slice magnetic equivalent circuits of skewed induction motors

PurposeWhen rotor and stator teeth are close, the connecting air gap flux tube's cross-sectional area exceeds the tooth overlap area. This flux fringing effect is disregarded in the air gap permeance calculation of single-slice magnetic equivalent circuits (MECs) of electric motors with skewed rotors. This paper aims to extend an air gap permeance calculation method incorporating flux fringing for unskewed rotors to skewed and radially eccentric rotors.Design/methodology/approachAssuming axial independence, the unskewed air gap permeance is rotated according to the skew and integrated along the axial dimension, resulting in a first method. The integral is approximated analytically, resulting in a second method. Results are compared to a commonly used reference method and validated using a non-linear finite element method (FEM) simulation.FindingsThe proposed methods provide better alignment with the FEM validation compared to the reference method for skewed rotors and common rotor eccentricity, i.e. below 50% of the air gap length. The analytical method is shown to be competitive with the reference method regarding computational time cost.Originality/valueTwo novel air gap permeance methods are proposed for single-slice MECs with skewed rotors. Their characteristics are discussed and validated.

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.