Magnetic Equivalent Circuit Research Articles

Electromagnetic Design and Analysis of Inertial Mass Linear Actuator for Active Vibration Isolation System

Underwater radiated noise from anthropogenic structures must be reduced to protect the marine environment. Active vibration isolation that can reduce noise generated from vibration sources by providing counteracting forces can solve this issue. This paper presents a 120 N class electromagnetic inertial mass linear actuator for an active vibration control system in a large ship. The proposed actuator is operated based on the Lorentz force, also known as electromagnetic force. To achieve a high thrust force to weight ratio, a permanent magnet with outer radial magnetization is used. In order to design and analyze the proposed model, a simple magnetic equivalent circuit analysis was first conducted to achieve an appropriate force, and its value was compared and verified with the magnetostatic finite element method. The dynamic characteristics of the actuator were then evaluated, and the performance was analyzed at various operating frequency points. The bobbin housing supporting the coil causes an eddy current loss due to materials with electrical conductivity. As a result, the damping force is generated by the reduction in magnetic flux, and the control force tends to decrease.

Modeling of a Dual Air-Gap Liquid-Cooled Eddy Current Retarder Considering Transient Permeability

This paper proposes a model for the electromagnetic performance of the dual air-gap liquid-cooled eddy current retarder (DAL-ECR) considering the transient permeability. First, the structure and working principle of the DAL-ECR are introduced. Next, the analysis model of the static air-gap flux density considering the flux leakage and end effect is established based on the piecewise function method and the magnetic equivalent circuit (MEC). Then, based on the skin effect of the electromagnetic field in the retarder, an iterative method for solving the transient permeability of the stator is proposed. According to Faraday’s and Ampere’s laws, the analysis model of the static air-gap flux density, and the transient permeability, the analysis model of the transient air-gap flux density is established. The braking torque of the DAL-ECR is then calculated while taking the actual path of the eddy current and the skin effect on the permeability of the stator into consideration. Finally, the calculation accuracy of the model was verified by the finite element method (FEM) and the bench test.

An improved equivalent magnetic network model of IPM motor in electric vehicles for dynamic simulation of transient effects

The existing electric motor model for electric vehicles cannot address the simulation of transient conditions. Moreover, it is difficult to balance the computation time and simulation accuracy. To address these shortcomings, an improved internal permanent magnet motor model containing nonlinear magnetic field factors was proposed based on the equivalent magnetic circuit theory. The effects of the magnetic circuit saturation, cogging torque, and magnetic field harmonics on the electromagnetic torque could be reflected. Furthermore, the electromagnetic vibration and rotor eccentricity could be considered. To improve the computational efficiency of the equivalent magnetic network method, lumped parameter or mesh-based methods were used for flux paths with different complexities. Second, the single-layer mesh-based method with local variable permeability parameters improved the efficiency of the air-gap dynamic analysis and computational efficiency while simulating 2D flux paths. The radial and tangential electromagnetic forces were calculated using the Maxwell tensor method and the action on the rotor. The accuracy of the nonlinear magnetic field modeling was verified by finite element analysis and experimental. In addition, the motion modeling method and dynamic characteristics of the model were studied. A reference was provided for dynamic simulations of electric vehicles and other using permanent magnet motors.

Multi-Objective Optimization Design of a Radial-Tangential Built-In Combined Permanent Magnet Pole Generator for Electric Vehicles

In this paper, a multi-objective optimization method is proposed to address the problem in the optimization process of the generator that only a specific index of a generator can be optimized to the neglect of other performance indices. Based on the equivalent magnetic circuit method, a mathematical model of the magnetic circuit of a radial-tangential combined permanent magnet pole generator is established, and the expression of the cogging torque including the pole offset angle is derived. The pole offset angle is proposed as the design variable, and no-load induction potential, air-gap flux density, and cogging torque are used as optimization targets. The relative optimal designs of permanent magnet generators are based on Pareto front statistics and defined parameter matching coefficients. Finally, a prototype is made based on the optimal structural parameters. According to the experimental results of the prototype, the correctness of the theoretical analysis and the effectiveness of the optimal design are verified.

Claw‐pole magnetic levitation torque motor for 2D valve with automatic neutral adjustment

AbstractIn order to solve the problems of complex structure and the difficulty of neutral adjustment of the existing 2D valve electro‐mechanical converter, a kind of claw pole magnetic levitation torque motor (CPMLTM) was proposed, which automatically suspended the rotor in an axially and circumferentially neutral position by using the cogging torque and axial recovery forces between the stator claw pole and the rotor permanent magnet (PM). Compared with the conventional moving iron torque motor, it has positive magnetic stiffness, 1.54 times higher PM utilisation and 33.6% lower mass. A qualitative mathematical model of output torque is derived based on equivalent magnetic circuit model. Then, the response surface method was used to build the second‐order response surface model, and NSGA‐2 was used to optimise the design of five key structural parameters, and the non‐inferior solution sets satisfying the maximisation of the cogging torque, output torque and axial recovery force were obtained. The experimental prototype was developed, and static experiments were carried out on the experimental rigs. The results show that the relationship between the input current and the output angular displacement of the CPMLTM is linearly proportional when the magnetomotive force generated by the coil winding is from −50 to 50 A.

Research on a Novel High-Torque-Density Axial–Radial-Flux Permanent-Magnet Motor with Annular Winding for an Elevator-Traction Machine

The traditional radial flux PMSM and axial flux PMSM have an effective air gap on only one side, between the stator and rotor, and only the effective air gap generates electromagnetic torque. There are defects in the magnetic-field utilization, and it is difficult to improve the torque density. Therefore, this paper proposes an axial–radial-flux permanent-magnet synchronous motor (ARF-PMSM), which combines radial flux with axial flux, to be used in an elevator-traction machine-drive motor. The characteristics of the ARF-PMSM are that the stator core is made of a soft magnetic composite material and the winding is annular. The motor has three effective air gaps, which can achieve high torque density without increasing the overall dimensions. In this paper, the mechanical structure and operation mechanism of the ARF-PMSM are introduced, and the characteristics of its magnetic circuit structure are analyzed by using the equivalent magnetic circuit method. The torque characteristics and other electromagnetic characteristics of the ARF-PMSM, the traditional surface-mounted PMSM, and the spoke-type PMSM are compared and analyzed using the finite element method. The research results show that the proposed motor has high torque density, which provides a new design idea in the form of a high-torque-density PMSM for use in elevator-traction machines.

Variable-Reluctance Permanent Magnet Resolver Design Guidelines

This article presents the design considerations and geometrical optimization of a variable-reluctance permanent magnet resolver (VRPM resolver). The above-mentioned resolver utilizes permanent magnets (PMs) and magnetic flux measurement units (MFMUs) instead of excitation windings and signal windings. The operating principle of the VRPM resolver is presented, and the geometric and magnetic properties of its various components that influence the accuracy are identified. To study the performance of the resolver, the magnetic equivalent circuit (MEC) model is utilized to ensure both calculation speed and accuracy, while taking saturation and nonlinear <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${B}$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H}$ </tex-math></inline-formula> curve effects into account. The developed analytical model is coupled with a multiobjective optimization solver to conduct repetitive simulations and attain an optimal design for the studied VRPM resolver. The objective of the optimization process is to achieve the minimum position error, while simultaneously improving the computational time. Time-stepping finite-element analysis (TSFEA) is used to validate and measure the performance in detail. Finally, experimental tests on a prototyped VRPM resolver are employed to verify the simulation results.

Study of the Influence of the Reluctance of a High- Temperature Superconductor on an Eddy-Current Axial Flux Superconducting Coupling

This work presents the influence of the reluctance of a novel hybrid superconducting coupling (NHSC) with axial flux. The coupling is made of the PMs in the primary and the copper and split superconductor with variable reluctance in the secondary. The study is made when the superconducting is in the vortex zone. The distribution of torque and magnetic field properties are examined and computed using a magnetic equivalent circuit (MEC) model. Since the permeability and the conductivity vary according to the temperature and the magnetic field around the superconductor, the graph of the evolution of the eddy current density is derived. By employing the curve fitting technique, we obtained the polynomial equation of the eddy current density, then this equation allowed us to figure out the formula of the eddy current density. By knowing the density of the eddy current, we were able to deduce the expressions of the bulk conductivity, then the London penetration depth, and the relative permeability of the superconductor. These expressions allowed us to determine how the superconductor's reluctance varies depending on the temperature. The force and output torque are calculated using a combination of Kirchhoff's law and Ampere's loop law, respectively, and also by considering the variation of the reluctance according to the temperature. In order to expand the coupling's operating margin, the performance is examined by utilizing a high-temperature superconductor with a temperature range of 77 K to 130 K. The strong agreement between the torque simulation results and the outcomes of the proposed model's calculations demonstrates the accuracy of both results.

Fault Diagnosis/Separation of Surface Mounted Permanent Magnet Synchronous Machine by Current and its Homopolar Orders Analysis

Performance analysis of Surface Mounted Permanent Magnet Synchronous Machine (SM-PMSM) is investigated in this paper. The machine dynamic in both healthy and faulty cases is analyzed, where dynamic, static, and mixed eccentricities as well as inter-turn and demagnetization faults are considered by a unique model. Stator Current Signature Analysis (SCSA) is used for the fault detection, and a method is proposed for the faults diagnosis and identification. Also, a flexible Magnetic Equivalent Circuit (MEC) with adjustable accuracy is used to model saturation effect thanks to its more flexibility and shorter processing time compared to the Finite-Element Method (FEM). The Power Spectral Density (PSD) is used for the faults detection, where analysis of the homopolar orders is proposed to be able to differentiate various faults from each other. Performed validation by experimental and FEM-based results shows the effectiveness of the presented model and proposed fault detection method.

Analytical modeling and performance evaluation of an adjustable permanent magnet linear eddy current brake with mechanical magnetic adjuster

A novel mechanical flux-adjusting permanent magnet linear eddy current brake with high performance and its nonlinear analytical model are proposed. The innovative point lies in attaching an additional mechanical magnetic adjuster directly above the interior permanent magnet bar, which can achieve flexible adjustment of the air-gap flux and improve the generation capacity of the braking force and its regulation range. Considering the importance of the analytic model in practical design, the average air-gap flux density and eddy current density are estimated based on the equivalent magnetic circuit method and Ampere’s law, where the critical flux-weakening effect and leakage flux effect are calculated quantitatively. Then a practical theoretical model of braking force is derived based on the energy conversion and verified by the 3D finite-element method. Through analysis of the magnitude and regulation range of the braking force in a given range of speed, the advantages of the device and the electromagnetic force model are proved separately. Moreover, design suggestions for selecting the key geometrical parameters are further given, which offer useful information for pre-design and optimization.

Quantitive Harmonic Analysis and Force Ripple Suppression of a Parallel Complementary Modular Linear Reluctance Machine

Considering the fluctuating price of permanent magnet, magnetless machine is a new trend in development. Variable reluctance linear machines (VRLM) with simple structure, good robustness, and high dynamic performance, is one of the potential candidates for linear direct-drive wave energy conversion (WEC) application replacing PM-excited linear machine. To ameliorate the fault-tolerance performance of VRLM, the researchers have come up with modular or segmented design, denoted as modular variable reluctance linear machines (MVRLM) However, suffering from large thrust ripple, the design of MVRLM still needs to be improved. To relieve the force ripple of MVRLM, a novel H-shaped modular variable-flux linear reluctance machine (HMVF-LRM) is proposed in this paper. The principle of force ripple suppression by using parallel-complementary structure is analyzed deeply. In this paper, the analytical calculation of induced voltage is developed quantitively with equivalent magnetic circuit method (EMC) and harmonics analysis. Then the design mechanism of HMVF-LRM is illustrated. Further, the performance and fault-tolerant capability of the proposed machine are simulated and evaluated by finite element analysis (FEA), and the prototype is tested to verify the effectiveness of the machine design.

An Improved Magnetic Equivalent Circuit Method for Segmented-Halbach Axial-Flux Permanent Magnet Machines

Much attention is paid to axial-flux permanent magnet (AFPM) machines thanks to the compactness and high torque density. However, the finite element method (FEM) for AFPM machines will cause a large computational burden during simulation. Thus, this paper proposes an improved magnetic equivalent circuit method (MECM) to predict the performances of segmented-Halbach AFPM machines, which can consider the different magnetization directions of Halbach PMs. Magnetic circuit is built in the whole machine. Besides, the air gap is treated as a slide layer to avoid the additional models for position-dependent permeances. Then, the predicted performances are compared with those calculated by FEM and measured in an experiment. As a quasi 3D analytical method, it predicts the same air-gap flux density as the FEM. The only errors are due to the serious flux leakage caused by opening slots. The predicted back EMF is consistent with the measurement in the experiment. The electromagnetic torque is affected by the errors of air-gap flux density, which results in large ripples. However, the trend of torque with current coincides with the measurement. It means the proposed MECM is effective for the segmented-Halbach AFPM machine.

A review on analytical models of brushless permanent magnet machines

AbstractThis study provides an in‐depth investigation of the use of analytical and numerical methods in analyzing electrical machines. Although numerical models such as the finite‐element method (FEM) can handle complex geometries and saturation effects, they have significant computational burdens, are time‐consuming, and are inflexible when it comes to changing machine geometries or input values. Analytical models based on magnetic equivalent circuits (MEC) or solving Maxwell's equations can be faster and more flexible, but less accurate for complex machine structures. The paper focuses on the recent development of analytical models for brushless permanent‐magnet (PM) machines that have become increasingly popular in low and medium‐power applications. The literature review covers the recent developments in analytical models for PM machines with respect to various machine quantities such as magnetic flux density components, induced voltage, inductances, electromagnetic force/torque, efficiency, or unbalanced magnetic force (UMF). It outlines the advantages and disadvantages of different analytical models such as the zero‐dimensional (0‐D), one‐dimensional (1‐D), two‐dimensional (2‐D), and three‐dimensional (3‐D) analytical methods, as well as the Maxwell and basic mathematical analysis. Although the MEC models are faster than the numerical model, they are not as accurate for various structures of electrical machines including a great magnetic air gap. They also note that the analytical models based on the Maxwell equations are faster than the numerical ones and have the potential to obtain acceptable accuracy similar to the numerical models in electrical machines. Overall, this literature review provides valuable insights for researchers and engineers in selecting appropriate analytical models for PM machines. It highlights the trade‐offs between accuracy and computational efficiency when choosing between numerical and analytical models, and the flexibility of analytical models to address changes in machine geometries or input values. Additionally, this helps researchers save time in determining appropriate references regarding the analytical models of brushless PM machines.

Modeling of Vehicle-Mounted Flywheel Battery Considering Automobile Suspension and Pulse Road Excitation

The existing model of magnetic suspension force for flywheel batteries mainly focuses on the internal magnetic field and foundation motions. However, when applied to vehicle-mounted occasions, the accuracy of the model will inevitably be affected by the vehicle vibration system and road conditions. Therefore, in view of the shortcomings of the existing research, a typical road condition (pulse road excitation) is taken as an example in this study to establish a model of magnetic suspension force that comprehensively considers automobile suspension and pulse road excitation. First, on the basis of a static model for magnetic suspension force using the equivalent magnetic circuit method, a magnetic suspension force dynamic model that takes into account the influence of automobile suspension and pulse road excitation is established. The rules of dynamic response under the influence of automobile suspension and pulse road excitation are summarized, and the foundation offset is corrected in the form of main migration points. Therefore, a correction model of magnetic suspension force is established. Finally, performance tests are carried out. The better anti-interference capability of the correction model is proven by the experimental results.

Optimal force control of a permanent magnet linear synchronous motor with multiple shuttles

Using permanent magnet linear synchronous machines for transportation tasks offers a higher flexibility in production plants compared to conventional conveyor solutions. In this context, passive transportation devices (shuttles) with permanent magnets are commonly used. When multiple shuttles are operated in close vicinity, disturbances due to magnetic interaction can occur. To allow for high-speed operation of the motor with high position control accuracy, these coupling effects must be considered. This paper presents a model-based control strategy that is based on a magnetic equivalent circuit model which is able to describe the nonlinear magnetic behavior at low computational costs. A framework is derived for the model calibration based on measurements. An optimal control scheme for the multi-shuttle operation is derived that allows to accurately track the desired tractive forces of the shuttles while minimizing the ohmic losses at the same time. The control concept is experimentally validated on a test bench and compared to a state-of-the-art field-oriented control concept typically used in industry.

Parameter sensitivity analysis and efficiency optimization design of wireless charging system

Electric vehicle (EV) wireless charging technology has recently attracted a lot of attention and has a broad potential for commercial application development. A fundamental performance indicator of wireless charging systems is efficient transmission. Magnetic coupling mechanism design and circuit parameters have the greatest effects on the transmission efficiency of the system. In this study, the output power and efficiency of the wireless power transfer (WPT) circuit were theoretically computed based on the LCC-type resonant network. Simulation studies demonstrate that the transmission efficiency and output gain deviate significantly from the expected value when circuit parameters are changed. To improve transmission efficiency, the optimal impedance configuration was created using a semi-controlled rectifier circuit. Based on electromagnetic field theory and equivalent magnetic circuit model, a new contactless transformer structure was optimized and created, and the new contactless transformer had a higher coupling coefficient. The coil offset had a greater impact on the transmission efficiency. The results indicate that within a certain distance, the coupling coil offset had no impact on transmission efficiency, and beyond that distance, the transmission efficiency was almost non-existent. Both the feasibility of the practical verification and the accuracy of the theoretical study were tested using a low-power wireless charging experimental setup. This paper provides design guidelines for wireless charging systems using circuit parameter sensitivity analysis and contactless transformer optimization design.

Modeling and efficiency maximization of magnetostrictive energy harvester under free vibration

Vibration energy harvesting is becoming increasingly attractive in line with the development of wireless sensor technologies. Magnetostrictive materials inherently exhibit high mechanical strength and are thus suitable for various applications and mass manufacturing of energy harvesting devices. Many studies have been conducted to increase the output power of harvesters, and some utilized analytical methods. However, the optimization methods often take into account only the resonant frequency of the system under forced vibration. These models can produce correct predictions only when steady-state harmonic excitation inputs are considered.In this study, we propose the modeling and optimization method for a cantilever-type magnetostrictive harvester under free vibration. The cantilever has a double-beam structure composed of two parallel Fe-Ga beams with pickup coils. In the modeling, the shape function of the cantilever-type magnetostrictive energy harvester was derived based on the continuity of the internal force and magnetic flux. Hamilton’s principle for an electromagnetic-mechanically coupled system was derived from the virtual work principle. The equation of motion, magnetic circuit equation, and electric circuit equation of the system were respectively derived from the corresponding Euler–Lagrange equations. The harvestable energy of the magnetostrictive energy harvester was calculated by using the symmetric property of eigenvalues. In the efficiency maximization of the harvestable energy, we found that the optimal solution differs depending on the type of given energy. The optimal parameters to maximize the energy efficiency to potential energy and kinetic energy are respectively derived in the form of algebraic solutions. Experimental validation was conducted by measuring the energy harvesting efficiency at different loads.

An Electromagnetic Design of Slotless Variable Reluctance PM-Resolver

This paper proposes a novel design of the variable reluctance permanent magnet (VRPM) resolvers. It utilizes a slotless stator to reduce the resolver volume. The proposed design overcomes the complex structure of windings by replacing them with magnetic flux measurement units (MFMU). The new design eliminates the computationally-expensive demodulation process of output signals by relying on none-modulated signals. An analytical model based on the nonlinear magnetic equivalent circuit (MEC) method is used to extract the output signals of the proposed resolver design. The accuracy of applied analytical model is verified against the time-stepping finite-element method (TSFEM). An optimization is implemented to best improve the resolver performance by saturating the stator ribs targeting a minimum possible PM volume. The design aims high flux density of iron to make the resolver robust against external distortions, but at the same time, the flux density of core is kept within the linear region of the B-H curve to avoid saturation. TSFEM is used to further analyze the performance of the optimal slotless VRPM-Resolver in details. The simulation results are verified by experimental tests on a prototyped resolver design.

Analysis of magnetic field characteristics and no-load losses of three-dimensional wound core transformer

Three-dimensionally wound core transformers (TWCTs) are widely used because of their low iron loss. This paper investigates the triangularly arranged TWCT core structure and a conventional planar laminated core transformer’s flat “E” core structure (PLCT). First, the magnetic field structures of the two transformers are analyzed using the equivalent magnetic circuit method to study the symmetry of the three-phase reluctance. Then, using the finite element method, a three-dimensional simulation model was built to analyze the no-load performance of TWCT and PLCT with the same dimensional parameters and the same core material. The no-load flux of each coil, the induced voltage on the secondary side, and the no-load iron loss of the core are analyzed. The analysis results show that TWCT has a 7.48% lower no-load loss than PLCT, which verifies the superiority of TWCT in terms of no-load loss.

Electromagnetic Calculation of Tubular Permanent Magnet Linear Oscillation Actuator Considering Corrected Air Gap Permeance

Tubular permanent magnet linear oscillation actuator (TPMLOA), with the simple structure and convenient control, has been paid extensive attention in the field of compressors and industry applications. In this paper, an electromagnetic calculation method of the TPMLOA is proposed. Firstly, an improved topology of the TPMLOA is introduced. Then, based on the radially laminated stator and equivalent magnetic circuit method, the actual air gap length is derived, and the total corrected factor is given. Finally, the electromagnetic characteristic of the TPMLOA is analyzed by 2-D finite-element analysis (FEA) considering the corrected air gap permeance, and the results are compared with normal 2-D FEA and 3-D FEA results. Additionally, a prototype of the TPMLOA is manufactured and tested to verify the accuracy of the calculated results. The comparison results show that the proposed method can quickly and accurately calculate the electromagnetic performance.