Magnetic Equivalent Circuit Research Articles

Two Models for Time-Domain Simulation of Hybrid Magnetic Bearing's Characteristics.

A comparison of two developed simulation models for a hybrid magnetic bearing (HMB) transient states is presented. This applies to analyses using the flux-circuit directly coupled magnetic equivalent circuit and field-circuit indirectly coupled finite element analysis. The required control system was implemented for both models. The results obtained from the simulations were compared with those obtained from measurement tests.

Optimal force control of a permanent magnet linear synchronous motor based on a magnetic equivalent circuit model

This paper is concerned with the high dynamic and energy efficient operation of permanent magnet linear synchronous motors (PMLSM). In particular, a novel optimal force control strategy is developed and experimentally validated on a test bench. The proposed control concept is based on a detailed nonlinear magnetic equivalent circuit (MEC) model which, in contrast to classical dq-models, is able to systematically capture nonlinear magnetic saturation effects and non-harmonic motor quantities. The core of the control strategy is an optimization problem which calculates optimal currents and flux linkages such that the desired forces are accurately tracked and, at the same time, the ohmic losses in the coils are minimized. The control strategy comprises a flatness-based feedforward controller and a nonlinear PI-type feedback controller. Experimental results on a test bench confirm that the proposed control concept improves both the control accuracy and the energy efficiency and outperforms state-of-the-art field-oriented control concepts based on the dq-model.

An Efficient Modeling of Air Gap and Nonlinear Analysis of Magnetic Equivalent Circuit for Large Turbogenerators Under No-Load Condition

Fast and accurate modeling of large turbogenerators is of great importance for optimal design and commercial value. Therefore, a 2-D nonlinear magnetic equivalent circuit (MEC) model considering saturation and rotor motion is proposed in this article. When the node-based MEC adopts relaxation iteration for nonlinear calculation, it is not easy to converge by using traditional interpolation function and piecewise fitting of the core <i>B&#x2013;H</i> or <inline-formula> <tex-math notation="LaTeX">$u_{r} (B)$ </tex-math></inline-formula> curve. The main contribution of this article is to find that using continuous fitting function is of great significance for the convergence of nonlinear iteration. At the same time, a simple and effective MEC of air gap is also provided. The flux density of air gap and stator tooth obtained by the proposed method is in good agreement with results of the finite element. No-load characteristics were also verified by the finite element and experiment. The calculation time of a cycle takes about 700 s by the finite element, and however, MEC only takes about 2 s.

Optimization of a New Asymmetric-Hybrid-PM Machine With High Torque Density and Low Torque Ripple Considering the Difference of Magnetic Materials

In this article, a new asymmetric PM-placed rotor topology is applied to the conventional less-rare-Earth hybrid magnet machine, where such new placement of hybrid magnets can be designed to improve the torque performance effectively. Considering the difference between the two magnetic materials, the optimal placement scheme of NdFeB-PMs and ferrite-PMs in the rotor are determined by theoretical derivation of equivalent magnetic circuit and finite element analysis. Based on the torque component separation analysis using frozen permeability method, the sizes of the two magnets are preliminarily designed to improve the utilization of reluctance torque and to reduce the superposition coupling loss of PM torque. Then, based on the parameter sensitivity analysis, the proposed asymmetric-hybrid-PM machine (AHPM) is further optimized aiming at the multi-objective of torque performance and anti-demagnetization performance. Finally, a prototype motor is fabricated and tested. Both the theoretical analysis and experimental results verify the effectiveness and reasonability of the AHPM and the proposed design method.

ОПТИМІЗАЦІЙНИЙ ПІДХІД ДО ВИЗНАЧЕННЯ КОНСТРУКТИВНИХ ПАРАМЕТРІВ ЛІНІЙНОГО МАГНІТОЕЛЕКТРИЧНОГО ДВИГУНА ВІБРАЦІЙНОЇ ДІЇ

The constructional parameters of the linear permanent magnet vibratory motor in accordance with the set optimization criteria (minimum cost, force to volume ratio and efficiency) and mechanical load parameters are substantiated in the work. To do this, a computer model was developed, which is based on magnetic and electrical equivalent circuits with lumped parameters. The magnetic circuit of the model is built taking into account the saturation of the magnetic material, magnetic losses and leakage fluxes. The electromagnetic force amplitude of the motor is determined on the basis of the fundamental component of the Fourier series expansion of the air-gap flux density. The mechanical part of the model is constructed using the electromechanical analogy method, according to which, induced armature EMF is represented by a voltage drop on the equivalent mechanical resistance. The problem of choosing the constructional parameters for the given mechanical load characteristics is considered in conjunction with the nonlinear connections of the system and subject to thermal, magnetic and electrical constraints. Using the gradient descent method, the motor parameters were optimized and the most effective designs that meet the selected criteria were determined. References 8, figures 5, tables 2.

Improved magnetic equivalent circuit for dual stator consequent pole permanent magnet machine

This paper proposes a non-linear magnetic equivalent circuit (MEC) model for three different dual stator consequent pole permanent magnet (DSCP-PM) machines. It also includes both no-load and on-load electromagnetic performance criteria. The fundamental of the MEC model is that it takes into the influence of winding flux leakage and iron saturation consideration. Besides, winding magneto motive forces (MMF) of DSCP-PM machines are applied to model both distributed winding and concentrated winding. An iterative algorithm is applied to resolve the problem when magnetic steel is severely saturated. Furthermore, the modeling for DSCP-PM machine provides a standard for modeling this machine. Finally, the MEC model's accuracy and practicality for DSCP-PM machine are validated by the finite element (FE) method.

Two-Segment Magnet Transverse Flux Ferrite PM Generator for Direct-Drive Wind Turbine Applications: Nonlinear 3-D MEC Modeling and Experimental Validation

Transverse flux PM generator (TFPMG) is a capable option for direct-drive wind turbine (DDWT) applications due to its high-power characteristics at low speeds. NdFeB-based TFPMGs may suffer from a higher total cost and lower thermal capabilities compared to the ferrite-based TFPMGs. Not yet covered in the existing literature, in this paper a transverse flux ferrite PM generator (TFFPMG) is proposed, designed, and modeled, which can also resolve the unipolar flux generation and even-order harmonics in the flux linkage of the conventional TFPMGs that occurred in conventional TFPMGs through its innovative two-segment trapezoidal shape magnet structure. Due to the 3-D flux path nature in the proposed TFFPMG, either 3-D finite element analysis (FEA) or 3-D magnetic equivalent circuit (MEC) modeling should be used. As a computationally efficient modeling method, a nonlinear 3-D MEC is established to model the entire structure of the TFFPMG while the core saturation and nonlinear permeances are also fully considered to improve the modeling accuracy. The electromagnetic performance of the proposed TFFPMG modeled by 3-D MEC in various loading conditions is validated by both 3-D FEA and experimental results using a 2.5 kW TFFPMG. A close agreement between 3-D MEC modeling predictions, 3-D FEA, and test results confirms the reliability of the MEC modeling for the proposed TFFPMG.

Fast Design of Spoke-Type PM Motor With Auxiliary Notches Based on Lumped-Parameter Magnetic Equivalent Circuit Model and Hybrid Multiobjective Optimizer

The multi-objective design of PM motor is time-consuming. The accuracy complexity of the solver model and the efficiency of the optimizer affect the cycle of electromagnetic design. A fast design method of spoke-type PM motors with auxiliary notches based on lumped-parameter magnetic equivalent circuit (MEC) model and a hybrid multi-objective optimizer (HyMOO) are proposed in this article. The MEC model is established to quickly reflect the influence of design parameters on electromagnetic and torque performance in the account of auxiliary notch structure in the rotor lamination. Meanwhile, an HyMOO is proposed considering the Grey Wolves Optimization (GWO) model, to solve more complex multimode problems involving more parameters. The accuracy and high calculation speed of the proposed MEC are verified in comparison with the FE method. A benchmark test by general distance (GD) and inverted generational distance (IGD) proves the HyMOO with better converge speed and robustness. Based on the MEC model and HyMOO, a fast electromagnetic design is applied for the motor with requirements of 140Nm rated torque and 4.5% torque ripple. The optimal solutions are validated by FE analyses, and the best design are chosen, manufactured as prototype, and tested. Both the FE and experimental analyses verify the reliability of the fast design and the proposed motor.

3D Rotor Position-Dependant MEC Modeling of Different Claw Pole Machine Topologies

The paper is aimed at a 3D magnetic equivalent circuit (MEC)-based modelling of claw pole synchronous machine topologies. Beyond the magnetic saturation and the armature magnetic reaction, the proposed modelling approach takes into consideration the rotor position variation, yielding the so-called: rotor position-dependant MEC. Accounting for the complexity of the magnetic circuit of claw pole topologies, specific assumptions are adopted prior a general analytical derivation of their MEC models. The developed analytical approach focuses on the air gap reluctance under variable rotor position considering a simplified geometry of the claw. A dedicated numerical procedure based on the Newton-Raphson algorithm is proposed for the resolution of the designed rotor position-dependant MEC. The proposed approach is applied to three claw pole topologies. The two first ones are equipped with a single source of excitation achieved by a field. Their analytically-predicted features are validated by experiments. The third topology has a dual excitation achieved by a field and permanent magnets (PMs) in the rotor. Its analytically-predicted features are validated by 3D finite element analysis (FEA). It is found that both experimental and FEA results are in quite good agreement with the analytical predictions yielded by the proposed rotor position-dependant MEC.

Investigation of the Effects of the Pole Shoe Geometry on the IPM T-LSM Features: Application to Free Piston Engines

The paper is aimed at an analytical approach dedicated to the investigation of the effects of the pole shoe geometry on the no-load flux features of inner permanent magnet tubular-linear synchronous machines (IPM T-LSMs). It considers the most common geometries: (i) rectangular pole shoes, and (ii) trapezoidal pole shoes. The proposed approach combines two analytical models which are the magnetic equivalent circuit (MEC) and the permeance function. First, a basic MEC of an elementary part of the machine is considered to predict a preliminary air gap flux density trapezoidal waveform. Then, the accuracy of the proposed approach is enhanced by the incorporation of a mover permeance function that accounts for the PM spoke-type arrangement. The proposed approach is applied to the investigation of the impact of the mover pole shoe shape on the air gap flux density. The developed pole shoe sizing procedure makes it possible the selection of an IPM T-LSM with an appropriate mover geometry for which an investigation of the no- and on-load features is carried out by finite element analysis. The prototyping of the selected topology enables the experimental validation of the back-EMF and the load characteristic.

Understanding Switched-Flux Machines: A MMF-Permeance Model and Magnetic Equivalent Circuit Approach

Due to their particular structure, switched-flux permanent magnet machines have become a very interesting alternative for many applications. This is why some recent studies have been focused in the understanding of the operating mechanism of these machines via the MMF-permeance modelling. However, the models that can be found in the literature make some simplifications that reduce their accuracy when predicting the performance of switched-flux machines. For example, the models that can be found in the literature are commonly not precise enough for machines with a wide slot, because the influence of the modulator of the primary side of the machine is neglected. In this article, a precise analytical model is developed for a 6/13 C-Core switched-flux machine via a combination of a magnetic equivalent circuit and a MMF-permeance model. The model is based on the magnetic field modulation principle. The analytical model is used to explain the flux focusing effect and the force generation mechanism of switched-flux machines. A new concept of PM field harmonic efficiency ratio is used to identify the most efficient PM field harmonics of 2 switched-flux machines. The precision of the model is validated via 2D and 3D Finite Element Method simulations, and experimental measurements that were obtained with a linear machine prototype. The results show that the model can predict the performance of switched-flux machines with a high accuracy level.

Nonlinear Modeling of MGSPMs Based on Hybrid Subdomain and Magnetic Equivalent Circuitry

The need for combining two mechanical powers with electrical power is a vital part of many applications, such as hybrid electric vehicles. The magnetic geared surface permanent magnet (MGSPM) motor is a compact and efficient way of achieving this goal. However, their complex structure demands time-consuming optimizations, which requires a large number of simulations. In this context, a fast and accurate simulation method is required to reduce the design and optimization time. In addition to speed and accuracy in considering the complex structures of the machine, as the saturation effect has a major impact on the accuracy of the simulations in these machines, it must be included in the method. To tackle this problem, in this article, a hybrid subdomain (SD) and magnetic equivalent circuit (MEC) model is proposed, considering the saturation effect of the iron parts using current distributions in the SD model on the surfaces of modulators and rotor core, as well as in the stator slots. These currents are calculated using the MEC model of the respective parts and Ampere’s law. Furthermore, an example motor is simulated both using the proposed method and the FE method, and the accuracy of the method both for prediction of magnetic flux density inside iron parts and prediction of flux linkages of the machine for a variety of designs and excitations is verified.

Analysis of a Combined-Type Axial-Flux Permanent Magnet Machine

A combined-type axial-flux permanent magnet machine is proposed in this paper. The structure of the proposed machine is introduced. The torque density characteristics of the proposed combined-type axial-flux permanent magnet machine are studied, and the torque density advantages of this kind of machine are analyzed by comparing with radial-flux permanent magnet machines. The magnetic field analysis method of the machine is studied. In the process of magnetic field analysis, an air gap permeance element is proposed to improve the traditional magnetic equivalent circuit method, which can facilitate the establishment of magnetic equivalent circuit model at different times. The calculation results of the proposed method are verified by finite element method. The cogging torque optimization of this machine is investigated, which includes magnet skewing with different reference modes. The optimal magnet skewing angle is calculated and verified, and the characteristics of different cogging torque optimization methods are summarized.

Torque Characteristics Analysis of a Novel Hybrid Superconducting Magnetic Coupling With Axial-Flux Using a Magnetic Equivalent Circuit Model

A novel hybrid superconducting coupling (NHSC) is proposed in this paper, in which the secondary is composed of copper and a split superconductor. A magnetic equivalent circuit (MEC) model is presented to analyze and calculate the distribution of the magnetic field and torque characteristics. The 3D modeling considers the end effects encountered in mating. The expressions of the magnetic flux and torque are obtained by combining Kirchhoff&#x2019;s law and Ampere&#x2019;s loop law, respectively. A 3D finite element (FE) model is built, and the simulation is performed. Its performance is investigated using a 135K critical high-temperature superconductor to have a greater operating margin of the coupling. For a high slip speed of 1500 rpm, we observed a peak torque of 167 Nm and stability of 115 Nm. By varying the thickness of the air gap or the PMs, we observed the increasing or decreasing of the torque. Due to the cryogenics systems, we also observed the reduction of the losses by the joule effect. The maximum error between the results of the torque obtained by simulation and the results calculated using the proposed model is 6.74&#x0025;, which proves that both results are in good agreement.

Nonlinear Analytical Model for Performance Prediction of Eddy Current Recoil Brake

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

A Novel Linear Resolver Proposal and Its Performance Analysis Under Healthy and Asymmetry Air-Gap Fault

A novel linear resolver (L-Resolver) is proposed in this article. The excitation and signals windings are placed on the mover, and the stator structure is designed by a certain number of teeth/slots per the mover length. Therefore, the proposed structure is more simple compared to other resolver types and causes a low price structure. A flexible magnetic equivalent circuit (MEC) is used for analysis due to its capability, introducing various structures. The resolver performance under healthy and faulty cases is evaluated, where the position error under asymmetry air-gap fault is obtained. The performed analysis shows that the proposed resolver has less than 100- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathrm {\mu m}}$ </tex-math></inline-formula> position error. Hence, it can be a proper alternative as an accurate position sensor. The simple structure and high-accurate position estimation are the advantages of the proposed resolver compared to other types. Finally, the effectiveness of the proposed resolver is validated by experimental results.

Estimation of Solid Fraction Based on Equivalent Magnetic Circuit in TMR-Based Electromagnetic Tomography

For the gas-liquid-solid fluidized beds with magnetic catalyst, the solid fraction can be estimated through the reconstructed permeability distribution using the electromagnetic tomography (EMT) based on the tunneling magneto resistance (TMR) sensor. Considering that the existence of mixed phase and obscure phase interface leads to the inaccurate estimation of phase fraction, a new approach to estimating the solid fraction is proposed. Firstly, the equivalent magnetic circuit analysis method is introduced to abstract the magnetic field distribution, and the relationship between the boundary measurement data and the equivalent permeability of the cross-section is derived. Then, the effective medium model is employed to estimate the solid fraction of the cross-section based on the equivalent permeability. The solid fraction estimation method based on the above proposed method is more accurate than that based on the gray level of reconstructed images, especially when the permeability distribution is complex. When the true solid fraction is in the range of 0%-100%, the average of the absolute error of simulation and experiment is 2.5% and 4.8%, respectively.

Artificial Monitoring of Eccentric Synchronous Reluctance Motors Using Neural Networks

This paper proposes an artificial neural network for monitoring and detecting the eccentric error of synchronous reluctance motors. Firstly, a 15 kW synchronous reluctance motor is introduced and took as a case study to investigate the effects of eccentric rotor. Then, the equivalent magnetic circuits of the studied motor are analyzed and developed, in cases of dynamic eccentric rotor and static eccentric rotor condition, respectively. After that, the analytical equations of the studied motor are derived, in terms of its air-gap flux density, electromagnetic torque, and electromagnetic force, followed by the electromagnetic finite element analyses. Then, the modal analyses of the stator and the whole motor are performed, respectively, to explore the natural frequency and the modal shape of the motor, by which the further vibrational analysis is possible to be conducted. The vibration level of the housing is furtherly studied to investigate its relationship with the rotor eccentricity, which is validated by the prototype test. Furthermore, an artificial neural network, which has 3 layers, is proposed. By taking the air-gap flux density, the electromagnetic force, and the vibrational level as inputs, and taking the eccentric distance as output, the proposed neural network is trained till the error smaller than 5%. Therefore, this neural network is obtaining the input parameters of the tested motor, based on which it is automatically monitoring and reporting the eccentric error to the upper-level control center.

Vibration Mechanism and Compensation Strategy of Magnetic Suspension Rotor System Under Unbalanced Magnetic Pull

The existing imbalance compensation strategies for magnetic suspension motors mainly focus on the mass unbalance force, ignoring the effects of the unbalanced magnet pull (UMP). This paper studied the vibration mechanism and compensation strategy of magnetic suspended permanent magnet synchronous motor (PMSM) under the influence of UMP. Firstly, an analytical model of the flux density was established based on equivalent magnetic circuit method, then the analytical expressions of UMP was deduced by Maxwell stress tensor method. Furthermore, an unbalanced compensation method based on hypothetical reference frame (HRF) transformation was proposed. The stability of the closed-loop system with compensation was analyzed based on the complex-coefficients theory. The proposed model and compensation strategy were verified by the simulations and experiments. The results indicate that the proposed compensation strategy can achieve effective suppression of the magnetic rotor vibration.

Analysis of a Discrete Stator Hybrid Excited Flux Switching Linear Machine

A discrete stator hybrid excited flux switching linear machine (DSHEFSLM) is proposed in this paper. The proposed DSHEFSLM uses a discrete stator to reduce the iron loss and overall cost of the machine. Assistant teeth are used at both ends of the mover to overcome the unbalance in the three phases, which is a global issue in linear machines. Field excitation (FE) is used, which adds field regulation capability to the proposed machine and makes it suitable for a wide speed operation range. A magnetic equivalent circuit model is used to find the suitable coil combination and no-load flux linkage. The multiobjective genetic global optimization is used to optimize the design parameters of the whole machine while keeping the slot area, electric and magnetic loadings constant. A correlation table is drawn to show the impact of different design parameters on average thrust force. The optimization has increased the peak-to-peak flux linkage by 11%, average thrust force by 34.60%, thrust force density by 34.60%, decreased thrust force ripples, and detent force by 21.05% and 8.58% respectively. The proposed machine has reduced the volume of the permanent magnet by 39.18% and offers 28.09% higher average thrust force and thrust force density compared to the flux switching permanent magnet machine proposed in the literature.