Magnetic Circuit Method Research Articles

Magnetic-Inductance: Concept, Definition, and Applications

The magnetic circuit has been a popular and powerful tool to analyze the magnetic field in electromagnetic devices for a long history. However, in the conventional magnetic circuit there is only one kind of component namely reluctance, which cannot analyze the phase shift or the amplitude attenuation of the alternating flux in electromagnetic devices. In this article, a new physical concept of magnetic-inductance is proposed, based on which the alternating-flux magnetic circuit theory including two kinds of components namely reluctance and magnetic-inductance has been developed. Furthermore, the virtual magnetic power is defined as the analogue of electric power, and the magnetoelectric power law is derived for magnetic circuits. Using the proposed magnetic circuit theory with magnetic-inductance, the relationship between the electric power and the virtual magnetic power is revealed and the long-lasting confusions in previous magnetic circuit methods, i.e., power calculation and phase shifts of magnetic variables, are clarified. By experiments, the magnetic-inductance and the magnetoelectric power law are validated, and their applications in eddy current loss analysis and B-H curve estimation in magnetic materials are demonstrated.

Analysis of a novel flux adjustable axial flux permanent magnet eddy current coupler

Permanent magnet eddy current couplers have been widely used in large fan and pump loads to achieve the purpose of speed regulation and energy saving. In order to reduce the coupler axial volume and simplify the actuator, a novel flux adjustable axial flux permanent magnet eddy current coupler (FAAF-PMECC) is proposed in this paper. The permanent magnet rotor is divided into three parts: the inner, middle and outer parts, where the permanent magnets are embedded in the core and the adjacent poles are magnetised in opposite directions. The middle part is the adjusting permanent magnet ring (AR), which can rotate around the shaft. The inner part and outer part are fixed permanent magnet rings (FR) that are fixed with the shaft, and the output torque can be controlled by adjusting the relative angle of AR and FR. The structure and working principle of FAAF-PMECC are described in detail, and the output torque analytical model of the whole regulating process is established based on the magnetic equivalent circuit method. The AR regulation process is simulated by the variable reluctance model. The validation results show that the proposed structure can achieve a good speed regulation effect, and the output torque calculated by the analytical model in a certain slip speed range matches well with the output torque obtained using the 3D finite element method and experimental measurements. The sensitivity analysis of the structure parameters is also carried out. The analysis shows that the proposed coupler can achieve a wide speed range.

Magnetic Field Analysis and Performance Optimization of Dual-Rotor Hybrid Excitation Generator for Automobile

Aiming at the current problems of low excitation efficiency and poor reliability of single-rotor hybrid excitation generators, the large axial length of dual-rotor structure, and difficulty in magnetic field analysis, a new type of the dual-rotor hybrid excitation generator topology with high power density is proposed, with two rotors side-by-side coaxial, sharing a set of armature windings, and the magnetic fields do not interfere with each other, so the magnetic field analysis and optimization of the two rotors can be carried out separately. The magnetic density distribution of the new permanent magnet (PM) claw pole rotor is analyzed by the joint application of the equivalent magnetic circuit method and the equivalent magnetic network method, which ensures the simplicity of calculation and improves the calculation accuracy. The multi-objective optimization of the key structural parameters is carried out based on the Latin hypercube sampling–Pareto frontier solution method. The subdomain method is improved by segmented equivalence, the unique solution of the salient-pole rotor magnetic field is obtained, and the multi-objective optimization of the salient-pole rotor is used by the particle swarm algorithm. The trial prototype was experimental, and the results showed that the output characteristics of the optimized hybrid excitation generator were significantly improved, and the overall performance of the generator was improved.

Static Torque Analysis of Micro Claw-Pole Stepper Motor Based on Field-Circuit Combination.

Because of the complexity of the structure and magnetic circuit of the micro claw-pole stepper motor, it is difficult to analyze this kind of motor quickly and accurately. Therefore, it takes a lot of time to accurately model and use the three-dimensional finite element analysis method to accurately analyze the motor. Regarding the three-dimensional finite element method, the equivalent magnetic circuit method analysis is fast, but the accuracy is not high. In order to better study the performance of this kind of micro claw-pole motor and reduce the cost of optimization time, this paper adopts the method of combining the equivalent magnetic circuit method and three-dimensional finite element analysis to analyze the static torque characteristics of the micro permanent magnet claw-pole stepper motor. Firstly, the equivalent magnetic circuit method is used for theoretical analysis, the air-gap flux equation is deduced, and the relationship between the electromagnetic torque and the geometric parameters of the motor is deduced. Then, the three-dimensional finite element simulation results are substituted into the relevant formulas defined by the equivalent magnetic circuit method to obtain a more accurate electromagnetic torque. Finally, through the comparison and analysis of the experimental data, simulation data, and theoretical calculation values, the error rate of the derived motor torque is within 8.5%. The micromotor studied in this paper is optimized, and the holding torque is increased by 12.5% under the premise that the braking torque does not change much. The simulation calculation time is effectively shortened, the analysis difficulty is reduced, and the calculation accuracy is high. It is shown that the method combining the equivalent magnetic circuit method and the three-dimensional finite element analysis method is suitable for preliminary design research and optimization calculation of the micro claw-pole stepper motor.

Modeling and Design of a Novel 5-DOF AC–DC Hybrid Magnetic Bearing

This paper investigates a novel integrated AC–DC hybrid magnetic bearing (HMB) to reduce the volume, weight, manufacturing, and operation cost of magnetic suspension motors. Two radial MBs and an axial MB are integrated with the proposed HMB. The five-degree-of-freedom (5-DOF) suspension is realized in one unit. Two axially polarized permanent magnets provide the radial and axial bias fluxes. First, the HMB structure and the suspension mechanism are introduced. Second, based on the method of equivalent magnetic circuits, magnetic circuits are calculated. The mathematical models of suspension force are discussed. Third, the main parameters of the 5-DOF AC–DC HMB are given. The 3D finite element method (FEM) is adopted to analyze the proposed system’s electromagnetic characteristics, and the suspension mechanism of the 5-DOF is verified. The radial suspension forces versus the radial control current, the axial suspension forces versus the axial control current, the relationship between the axial suspension force and the axial control current with the X direction offset, and the relationship between the radial suspension force in the X direction and the axial control current with the Z direction offset are calculated. Based on the research results, it is shown that the HMB structure is compact and reasonable, and the mathematical models and suspension mechanism are correct.

Design and Analysis of a New Deployer for the in Orbit Release of Multiple Stacked CubeSats

More and more CubeSats cooperate to implement complex space exploration missions. In order to store and deploy more CubeSats in a rocket-launch mission, this paper presents a new CubeSat deployer with large-capacity storage. Different from the traditional one with the compression springs, the deployer with electromagnetic actuators is proposed to achieve the transportation and release. A new electromagnetic actuator with high thrust density was applied to adjust the release speeds of the CubeSats with different masses, and a new electromagnetic convey platform with attractive force was designed to transfer the stacked CubeSats to the release window. The equivalent magnetic circuit method was used to the establish electromagnetic force models. The simplified dynamic models of the transportation and release were built. The magnetic field, electromagnetic force, and motion characteristics were analyzed. The prototype was developed to verify the performance of the proposed configuration of the deployer with electromagnetic actuators. The experimental results show that stacked CubeSats can be transported smoothly even under constant external interference. The launcher achieved high thrust density and effectively adjusted the separation speed of the CubeSats.

Design and optimization of air‐cored double‐sided linear permanent magnet generators for wave energy conversion

AbstractRecently, linear generators have been widely employed to convert oceanic wave energy into electricity. Among various linear generators, linear permanent magnet generators (LPMGs) have gained attention due to their special characteristics such as high power density and simple control structure. In this paper, flat double‐sided LPMG is investigated and designed. Considering all effective design variables, a particle swarm optimization algorithm‐based optimization method is employed to maximize efficiency and minimize weight. The optimization results show an increase in efficiency and a reduction in the weight of the generator. Finally, the design results are evaluated and validated using magnetic equivalent circuit and finite element analysis methods.

Modeling and Analysis of New Power Devices Based on Linear Phase-Shifting Transformer

With the rapid development of new power systems, various new power devices have also been developed. It is very important to establish analytical models of new power devices to ensure or even improve the reliability and stability of the power system. A linear phase-shifting transformer (LPST) is a new type of power device that mainly relies on air gaps to transfer energy, so establishing an accurate air-gap magnetic field model is very important for improving the efficiency of this system. In this paper, an analytical model of an unequal-pitch linear phase-shifting transformer (UP-LPST) was established by combining the distributed magnetic circuit method (DMCM) and Schwartz–Christopher transformation (SCT). Taking the magnetic field strength as a variable, an accurate magnetic field analysis model for a UP-LPST considering saturation, cogging, and edge was established. Taking a 1 kw UP-LPST as a prototype, the accuracy of the model was verified by the finite element method and experiments. This modeling method could also be used to establish magnetic field models of other similar structures in new energy power systems, especially those with cogging structures.

Improvement calculation method of static magnetic field based on equivalent magnetic circuit method

Improvement calculation method of static magnetic field based on equivalent magnetic circuit method

A novel H-type linear permanent magnet eddy current brake

To improve the braking force of the Linear Permanent Magnet Eddy Current Brakes (LPMECB) under a large Air Gap (AG) length, this paper presents a novel structure of the LPMECB, named H-type Linear Permanent Magnet Eddy Current Brake (H-type LPMECB). To begin with, the analytical model of the LPMECB is established by using the equivalent magnetic circuit method, and it is found that the AG reluctance is greater than that of the other parts of the LPMECB. Based on this, a novel H-type LPMECB is proposed in order to compensate the influence of the AG. The H-type LPMECB adds Iron Foils (IFs) in the AG. These IFs are rectangular sheets made of pure iron. Furthermore, the finite element model of the H-type LPMECB is established to optimize the geometry parameter of the IFs, then the braking performance of the H-type LPMECB is measured. The simulations show that the optimal geometry parameter of the IFs of the H-type LPMECB is 0.25 ∗ L, and the braking performance of the H-type LPMECB is superior to that of the LPMECB, around three times. Finally, experiments were conducted, which validated the simulations.

Magnetic Field Prediction of the Saturated Surface-Mounted Permanent Magnet Synchronous Machine With Rotor Eccentricity

This article presents an analytical method to predict the magnetic field of eccentric surface-mounted permanent magnet synchronous machine (SPMSM) by applying the hybrid magnetic circuit and subdomain method. Taking stator saturation into account, the surface current is appended to the stator coil conductor, which can generate a magnetomotive force (MMF) to compensate the MMF drop across the stator core. The rotor yoke saturation effect is modeled by increasing the air-gap length. To solve the problem resulted from rotor eccentricity in analytical analysis, an equivalent transformation method is given. The transformation principle is that the eccentric machine can be equivalent to a concentric one with redistributed PM remanence and armature current density. On this basis, the subdomain method is adopted to predict the magnetic field of the reestablished machine. The proposed analytical method is implemented and evaluated on the 6p/36s and 8p/12s SPMSM and exhibits good agreement with the FEM and experiment results.

Influence of Low-Coercive-Force Magnet Property on Electromagnetic Performance of Variable Flux Memory Machine

The magnetization properties of low-coercive-force (LCF) permanent magnets (PMs), i.e., remanent flux density, coercivity, and hysteresis curve slopes, are closely related to the magnetization characteristics of variable flux memory machine (VFMM). Therefore, this article investigates the inherent relationship between the properties of LCF PMs and electromagnetic characteristics of VFMM using a combined solution integrated with magnetic equivalent circuit (MEC) and graphical methods. First, the hysteresis curve of the LCF PM is analytically modeled by a simplified piecewise linear hysteresis model to characterize the mathematical relationships among the key parameters of the hysteresis model. Then, a simplified MEC method is used to obtain the permeability curves of VFMM, thereby further determining the intrinsic relationship between the dimensional parameters of the LCF PM and the electromagnetic characteristics of VFMM. Afterward, the flux regulation characteristics and on-load magnetization state (MS) stabilization capability of VFMM are qualitatively analyzed using a newly developed coupled approach. Furthermore, the electromagnetic characteristics of three VFMMs equipped with different version LCF PM materials are comprehensively compared using the finite-element (FE) method. Finally, a VFMM prototype using the selected AlNiCo magnet is manufactured and tested to verify the correctness of the theoretical and FE analyses.

Multi-Objective Parameter Optimization-Based Design of Six-Pole Radial Hybrid Magnetic Bearing

To reduce the couplings between the radial suspension forces and control currents caused by the asymmetry structure of the three-pole hybrid magnetic bearing (HMB) which is driven by an inverter, a six-pole radial HMB is proposed. To improve the bearing capacity and reduce the eddy current loss and volume of the six-pole radial HMB, an improved multi-objective particle swarm optimization (MOPSO) algorithm is proposed to optimize the parameters. At first, the structure and working principle of the six-pole radial HMB are introduced based on the equivalent magnetic circuit method. Then, the optimization objectives and optimization variables are determined and the number of multi-objective optimization parameters is reduced by sensitivity analysis. Next, the fitting function of the suspension force is obtained by the response surface method (RSM). Based on the theoretical analysis of the MOPSO, the linear decreasing inertia weight and the concept of hybridization are introduced to improve the diversity and convergence of the MOPSO to get Pareto optimal sets. Finally, simulation analysis and prototype experiment are carried out on the optimized six-pole radial HMB. The feasibility of the optimization method is verified by the results of simulation and experiment.

Novel Axial Flux-Switching Permanent Magnet Machine for High-Speed Applications

Conventional high-speed flux-switching machines have either a high fundamental frequency or more even harmonics. This paper proposes a novel six-slot four-pole axial flux-switching permanent magnet machine for high-speed applications. The machine, consisting of two radially distributed stators and one rotor, can effectively eliminate even harmonics in the flux linkage. First, the structural parameters that affect the performance of the motor are determined by the equivalent magnetic circuit method, and the optimal structural parameters of the motor are obtained by simulation optimization. Then, through finite element analysis, the three-dimensional model of the proposed machine is built, and the static electromagnetic characteristics are analyzed, including magnetic field distribution, flux linkage, back-electromotive force, cogging torque, and efficiency. The simulation results show that the total harmonic distortion of the flux linkage and back-electromotive force waveforms of the proposed novel machine is 2.2% and 9.8% respectively. The cogging torque of the optimal model is only 9 N.

Equivalent magnetic circuit method of estimating iron losses in induction motor spindles

The iron losses in the motor of motorized spindles have a significant effect on their heat generation, thermal deformation, and machining accuracy. The equivalent magnetic circuit (EMC) method for estimating iron losses in the spindle motor is proposed, where the magnetic flux density distribution of any cross section inside the spindle motor is assumed as a uniform one. A mechanical loss separation method of no load running combined with a sudden loss of power supply is also proposed. The EMC method is verified by prototype experiment and a different analysis method comparison. The EMC does not need to solve complex electromagnetic fields, and to do 2D or 3D eddy current analysis and the corresponding post-processing. There is only need to perform a simple magnetic circuit calculation. Therefore, it can realize a fast analysis and prediction. The proposed mechanical loss separation method requires only one prototype during a whole testing process. There is no need for any other same prototype and a coupling device. It is simpler, and can eliminate the braking torque and electromagnetic losses of the spindle motor.

Analytical Model for No-Load Electromagnetic Performance Prediction of V-Shape IPM Motors Considering Nonlinearity of Magnetic Bridges

This paper proposes a novel analytical model which combines subdomain method and magnetic equivalent circuit (MEC) method to predict the no-load performance of V-shape interior permanent magnet (IPM) motors with any slot-pole combination considering the nonlinearity of magnetic bridges (MBs). The V-shape magnets are equivalent to the form of distribution along radial and tangential directions, and the motor is divided into two corresponding structures to facilitate the establishment of subdomains. To consider the saturation of MBs, the MEC method are employed to obtain the permeability of MBs to establish the boundary conditions. The no-load magnetic field of slotless motor can be obtained by solving the equations established by boundary conditions, and the conformal mapping is used to consider the effect of slotting. The proposed model can be used to calculate the no-load magnetic field, back electromotive force, and cogging torque of IPM motor. The results are verified by finite element analysis (FEA) and experiments, which confirms the validity of the model for facilitating the motor design and optimization. Compared with FEA, the proposed method has the advantages of faster modeling, shorter time consuming and meanwhile achieves the approximate accuracy. In addition, U-shape motors with MBs can also be analyzed by this model.

Reluctance Mesh-Based Magnetic Equivalent Circuit Modeling of Switched Reluctance Motors for Static and Dynamic Analysis

Designing a switched reluctance machine (SRM) is an iterative process. Sizing of the motor is one of the fundamental steps where the main geometry parameters are determined to achieve the performance requirements. Usually, finite element method (FEM) is employed in all design stages, which might require extensive computational burden. The magnetic equivalent circuit (MEC) method is an alternative for typical FEM. There are two approaches for the MEC method: conventional MEC method and reluctance mesh-based MEC method. The conventional MEC method can be challenging when modifying the motor geometry while conducting dynamic analysis with current control. This article presents a reluctance mesh-based MEC model for SRMs that can overcome those challenges. Reluctance mesh-based MEC models are developed for three-phase 6/4, 6/16, 12/8 SRMs and four-phase 8/6, 8/10, and 16/12 SRMs. The models calculate the static and dynamic characteristics of the considered SRMs. The static and dynamic characteristics are compared with the results obtained from FEM and experimental tests.

Calculation Model of Armature Reaction Magnetic Field of Interior Permanent Magnet Synchronous Motor With Segmented Skewed Poles

In an interior permanent magnet synchronous motor (IPMSM) with segmented skewed poles, the armature reaction magnetic field (AR-MF) changes nonlinearly due to the saturation of the rotor magnetic barrier. Meanwhile, this varies under different excitation currents. As a result, it is difficult to be calculated by means of analytical methods. In this paper, the calculation model of AR-MF of IPMSM is first established by vector superposition method, without considering the saturation effect of rotor and the slotting effect of stator. In the second step, the virtual magnetic field of the rotor is introduced to quantitatively calculate the influence of local inhomogeneous saturation on the AR-MF. The latter is derived by combining both the subdomain method and equivalent magnetic circuit method. The complex relative permeance is also introduced to establish the AR-MF accounting for the stator slotting effect. To validate the AR-MF calculation method proposed, an 8-pole 48-slot IPMSM with segmented skewed poles is considered as a case study, showing a comparison by both with finite element (FE) results and the electromagnetic torque measured on a test bench. The model proposed in this paper shows high accuracy and fast computation with respect to FE analysis.

Modeling and designing a hybrid reluctance actuator for fast-steering mirror

The actuator is a primary component of the fast-steering mirror (FSM), and its quality directly determines the performance of FSM. To achieve high compactness, high efficiency, large output torque, and effective linearity, a hybrid reluctance actuator (NHRA) for FSM was designed. To obtain a high-force density and small flux leakage, four permanent magnets (PMs) were designed on the side of the armature, which improves the linearity of the actuator by generating a bias flux. Meanwhile, to obtain the maximum output torque for a limited size, the structural model of the actuator was established in ANSYS Maxwell, and all structural parameters were optimized. In addition, an analytical model of the actuator was established via the equivalent magnetic circuit method. To improve the modeling accuracy, both PM and coil flux leakages were considered. The theoretical and simulation results were insignificant in agreement, and both showed the output torque of this actuator to be approximately twice that of a state-of-the-art actuator under the same volume, simultaneously improving the linearity.

Analytical modeling of permanent magnet linear eddy current brake using magnetic equivalent circuit method

In order to predict the performance of a permanent magnet linear braking (ECB) with cylindrical structure, an analytical model is established in this paper. The model is based on the magnetic equivalent circuit (MEC) method with the consideration of the often ignored magnetic saturation in pole shoe. The influence of induced eddy current is taken into account by introducing the magnetomotive force (MMF) in the model. To obtain braking force, a simple method for approximating the cross-section of the electric field with mean value method is proposed. The proposed model that can predict the braking force performance of ECB in a wide range of structural dimensions is obtained through referring to a small number of finite element models. A prototype test is carried out. The validity of the proposed method is verified through experiment and FEM. Results show that the braking force predicted by the presented method are in good agreement with experimental results and FEM results under different design parameters. The proposed model can accurately represent the variation trend of braking force and critical speed with design parameters.