Magnetic Circuit Method Research Articles

Non-linear analytical model for synchronous reluctance machine

This paper proposes an non-linear magnetic equivalent circuit (MEC) method for the synchronous reluctance machine (SynRM). The rotor geometry of the prototype machine is not simplified. In addition, the proposed MEC model can be used with different slot/pole combination or dimensions. While modeling SynRM, the non-linear effect and the leakage flux of the windings is taken into account. Due to the non-linear effect of the BH-curve, iterative algorithm process is used to find electromagnetic performances and magnetic permeability of non-linear reluctances. Finally, the proposed MEC is validated by both the finite element method (FEM) and experimental results to prove its accuracy and practicality.

Analytical Analysis of a Novel Flux Adjustable Permanent Magnet Eddy Current Coupling with Double-Sided Conductor

The permanent magnet eddy current coupling is widely used in fan and pump equipment as an energy-saving speed control device. The traditional coupling speed adjustment method occupies too much axial space, limiting its application in the process of upgrading old equipment. This paper proposes a novel flux adjustable permanent magnet eddy current coupling with a double-sided conductor to reduce the coupling axial distance while increasing the coupling output torque. The relative angle between the permanent magnet rings is controlled to adjust the output torque, and the double-sided conductor structure is used to improve the output torque. The working principle of the proposed design is illustrated. An analytical model for estimating the regulation performance of the proposed structure is proposed, which introduces the regulated reluctance into the equivalent magnetic circuit method. Based on this model, the expressions for magnetic flux density, eddy current density, and output torque are established. Finally, the accuracy of the analytical model was verified by the 3D finite element method, and the parameter sensitivity analysis was performed. The analysis results show that this device can achieve a relatively large range of output torque regulation under the condition of a fixed air gap, and the output torque is greatly improved by adopting a double-sided conductor structure.

Numerical Study on Unbalance Response of Dual-Rotor System Based on Nonlinear Bearing Characteristics of Active Magnetic Bearings

The magnetic suspended dual-rotor system (MSDS) has the advantage of a high power density. The system can be used in high-speed rotating machinery. The major purpose of this study is to predict the unbalance response of the MSDS considering the nonlinear bearing characteristics of active magnetic bearings (AMBs). Firstly, the nonlinear bearing model was established by a non-linear magnetic circuit method (NMCM). The model considers magnetic flux leakage, magnetic saturation, and working position flotation accurately. Then, the dynamic model of the system was established by using the finite element method and solved by the Newmark-β method. Finally, the effects of external load, rotational speeds, and control parameters were studied. Axial trajectory diagrams, stability zone diagrams, and waterfall diagrams were employed to analyze the dynamic behaviors of the MSDS. The results indicate that the external load, rotational speeds, and control parameters have a significant impact on the unbalance response of the system. Super harmonics of rotational frequencies and their combined frequencies may be excited by heavy load conditions. Appropriate control parameters can suppress the nonlinear phenomena. The obtained results of this research will contribute to the design and fault diagnosis of MSDSs.

Electromagnetic Torque Analysis and Structure Optimization of Interior Permanent Magnet Synchronous Machine with Air-Gap Eccentricity

Interior permanent magnet synchronous machine with air-gap eccentricity (AGE-IPMSM) has the advantages of low torque ripple and low noise. However, air-gap eccentricity will lower the power density of the machine to a certain extent. In this paper, an 18-slot/8-pole interior permanent magnet synchronous machine with air-gap eccentricity is taken as the research object. According to the magnetic circuit method, the no-load and load air-gap magnetic field analytical models are calculated, respectively. Then, by Maxwell’s tensor method, the variation law of radial and tangential air-gap magnetic density harmonic amplitudes and phase angle difference cosine values are analyzed, and it is concluded that the electromagnetic torque can be improved by increasing phase angle difference cosine values of the magnetic density harmonic, which produces the driving torque after eccentricity. On this basis, in order to improve the output characteristics of the machine, the eccentricity and the angle between the V-type permanent magnets are optimized with the total harmonic distortion (THD), electromagnetic torque, and torque ripple as the optimization goals, and then the optimal structure size parameters of the machine are finally determined. Finally, a prototype is manufactured on the basis of the optimal parameters, and the experimental results of the prototype verify the validity and correctness of the theoretical analysis and finite element analysis (FEA).

A quick electromagnetic performance analysis method for permanent magnet claw pole machine based on combined analytical and equivalent magnetic circuit method

A quick electromagnetic performance analysis method for permanent magnet claw pole machine based on combined analytical and equivalent magnetic circuit method

A Magnetically Controlled Current Transformer for Stable Energy Harvesting

The magnetically controlled current transformer (MCCT) is proposed to harvest stable energy from the magnetic field induced by the transmission-line fluctuating current. Compared with the conventional current transformer (CT), the advance of the proposed MCCT originates from the so-called constant magnetic flux control, which is achieved by connecting an electronic load on the secondary side of MCCT, and adjust the load impedance to make it equivalent to the corresponding resistive-capacitive impedance for magnetization or demagnetization. Furthermore, the working principle and the excitation characteristic of the MCCT system have been analyzed using the equivalent magnetic circuit and equivalent circuit methods. In addition, the details of the electronic load circuit and control system of the MCCT are presented in this paper, and the stability of the system is verified using logarithmic criterion and total harmonic current distortion (THDi) analysis. Finally, the co-simulation and experimental results show that MCCT can produce a stable output power of 13 W in the range of 50–500 A current fluctuations, demonstrating that the proposed magnetic energy harvester is capable of a high conversion efficiency and output stability.

Analysis of flux barrier effect of LCF PM in series hybrid magnet variable flux memory machine

Variable flux memory machines (VFMMs) with series hybrid magnets using both low coercive force (LCF) and high coercive force (HCF) permanent magnets (PMs) have been recognized as a viable candidate for wide-speed-range industrial applications due to the advantages of high torque density and wide speed range. Nevertheless, the adverse effects of LCF PM on the HCF PM in series-type VFMM under different magnetization states (MSs) are still unreported. In this paper, the flux barrier effect (FBE) of the LCF PM existing in series hybrid magnet VFMM is first revealed, and its causes are discussed as well as analyzed in depth on the basis of the equivalent magnetic circuit method and finite-element (FE) analyses. A topology of VFMM with dual-layer PMs is further developed to alleviate the FBE induced from LCF PMs. It can be found that the FBE can be effectively suppressed by employing the dual-layer (DL) PM arrangement and additional leakage flux paths. A prototype of the proposed design is built, and the theoretical and FE results are experimentally verified.

Evaluation and Analysis of Flux-Regulated Permanent Magnet Linear Eddy Current Brakes

In this study, a novel permanent magnet linear eddy current brake based on the field regulation theory is presented, and the corresponding analytical model is developed. By shifting transversely the field-regulated plate, the real-time and easy control of the braking force can be achieved, which is the intent of the proposed topology. The key structure and operation principle are addressed. In addition, to avoid the excessive computation time and cost when using the numerical method, a practical analytical model for calculating the electromagnetic and force performance is established based on the magnetic equivalent circuit method with variable reluctance. The validity of the model is verified using the 3-D finite element analysis and equivalent prototype experiments. Moreover, further analysis is carried out to investigate the effects of the key geometrical parameters on the braking force-speed characteristic.

Electromagnetic transient model and field-circuit coupling numerical calculation of Sen transformer based on finite-element method

• A finite-element (FE) model of electromagnetic transient of Sen transformer (ST) with field-circuit coupling is proposed, and the proposed model can characterize the effects of core and winding topology on the internal magnetic field distribution. • The proposed FE model can characterize the electromagnetic field changes of the ST device under different conditions, such as short-circuit fault, injected harmonics, and dynamic power flow control in the external power system. • The electromagnetic transient field-circuit co-simulation of the ST device and external power system is realized. The conventional electromagnetic transient model of Sen transformer (ST) is mainly established by the magnetic equivalent circuit method, which can be used for the fast calculation of transient characteristics for ST. Unfortunately, this approach may lead to oversimplification and missing significant information in the modeling process. To accurately calculate the transient electromagnetic field and reveal the internal magnetic field distribution of the ST under different operating conditions, an electromagnetic transient model and field-circuit coupling numerical calculation of ST based on finite-element (FE) method is proposed in this paper. The proposed model can characterize the effects of core and winding topology on the internal magnetic field distribution, as well as the complex nonlinear property of core materials, such as saturation, eddy current, and hysteresis. The field-circuit coupling method enables the FE model to establish a connection with external networks and realize the electromagnetic transient field-circuit co-simulation of the ST device and external power system. The case studies are performed on a FE model of the ST and a two-machine transmission system. The corresponding winding voltage and current variations of the ST in the presence of short-circuit fault, injected harmonics, and dynamic power flow control in the external networks are analyzed. The numerical calculation and co-simulation results of the proposed FE model of the ST and the external networks are compared with the commercial FE software, which demonstrates the effectiveness of the proposed FE model of the ST. Moreover, the co-simulation results of dynamic power flow control show that the ST can adjust the power flow distribution of two transmission lines through changing compensation voltage.

Design and Optimization Method with Independent Radial and Axial Capacity for 3-DOF Magnetic Bearings in Flywheel

The six-pole radial–axial hybrid magnetic bearing (RAHMB) has the advantages of small space and low power consumption, making it suitable for flywheel batteries. The bearing capacity and the volume are the main specifications of magnetic bearings that should be considered comprehensively. In this work, the six-pole RAHMB was used in a horizontal flywheel battery. As the axial bearing capacity is relatively smaller than the radial bearing capacity, a design method with independent radial and axial bearing capacity is proposed, and the parameters are optimized to minimize the volume. The mathematical model of six-pole RAHMB was derived from the equivalent magnetic circuit method. The relationships between bearing capacity, biased flux density, saturation flux density and the section area of magnetic poles were analyzed. The basic principle of the design method with independent radial and axial bearing capacity is to determine which five of the variables are preferred. According to the design method, one radial or axial biased flux density should be optimized to minimize the volume, and the genetic algorithm (GA) was adopted to search for the optimal value. The structural parameters were designed based on the optimized value of biased flux density. The total volume of the six-pole RAHMB was reduced by 24%. A 3D finite element (FE) model was built. The analysis results and experimental results show that the proposed design and the optimization method are feasible and valid.

Analysis of the Topology and Electromagnetic Characteristics of Novel Stator Partitioned Axial Flux Disk Generator for Vehicles

Internal combustion engines emit high-temperature, high-pressure, and high-speed exhaust gases, resulting in wasted energy and low thermal efficiency. In order to recover the available residual energy in the exhaust gas, this paper proposes a new topology of the disk-type axial flux stator-excited doubly salient generator (AFSDSG) with partitioned stator suitable for high-temperature and high-speed operation. Based on the analysis of the above generator inductance characteristics, the influence mechanism of three pole-slot structures on the induced electromotive force (IEMF) of the armature winding is clarified, the equivalent magnetic circuit method is used to analyze the influence of different winding arrangements on the no-load performance of the generator, and the principles of pole-slot structure optimization and winding arrangement are summarized. The finite element software is used to model and simulate different configuration. After focusing on the analysis of transient characteristics such as inductance, armature winding IEMF, and air-gap flux, it is concluded that different from the conventional pole-slot structure and winding connection method make that only the overlapping area of the stator and the rotor changes linearly can produce a constant voltage, the winding arrangement of Winding Partition Excitation Span 2 has a high IEMF amplitude value and low harmonic content. Finally, the prototype of a three-phase 12/8-pole was trial manufactured and tested. The consistency of the simulation results and experimental results is verified the innovation and feasibility of the new topology proposed in this paper.

Electromagnetic Field Analysis of Distributed Winding Permanent Magnet Synchronous Motor Considering Axial Leakage Flux using Two-Dimensional Finite-Element Analysis

This paper proposes a method for the electromagnetic field analysis of permanent magnet synchronous motors (PMSMs) considering the axial leakage flux. To the axial leakage flux while employing two-dimensional (2D) finite-element analysis (FEA), the permeance of the axial leakage path is added into a slot region by increasing the permeability of elements in that region. The increased permeability is calculated based on the permeance relationship of the main magnetic and axial leakage paths, which are calculated using the equivalent magnetic circuit method. The effect of the proposed method is verified by comparing it with the 3-dimensional FEA results. The proposed coupling method uses finite element analysis and is developed from the lumped method proposed in our previous research. The developed method enables the analysis of distributed winding machines, which is not possible with the existing method.

Self-Excited, Electromagnetic Braking and Heating System for Electric Buses

New energy vehicles usually recover the braking energy and store it back into the battery using the electric motor. Such a regenerative braking system improves the vehicle mileage. In the process of regenerative braking, all components of the system dissipate a great amount of energy, especially in winter. On the other hand, heating the vehicle's cabin consumes electric energy, further reducing its autonomy. Based on this, we propose a novel Self-excited, electromagnetic Braking and Heating System (SBHS), to solve problem of the driving range dramatic decline of electric bus when heating the bus cabin in winter. The system converts the kinetic energy of the electric bus into heat, via electromagnetic braking, and uses it to warm the vehicle's cabin in winter. Our system improves the conversion efficiency of regenerative braking. We present the structure of the system and calculate the air gap magnetic density using the magnetic circuit method. We develop the braking heat generation model and obtain the heat generation performance at different speeds using J-MAG. To improve the braking energy utilization efficiency, we design a braking force distribution strategy based on a fuzzy control system. We also characterize the braking and built-in generator performances in a test bench, and obtain the braking and heating characteristic at different speeds. We implemented our EBHS and installed on a test electric bus. The test records include SOC, temperature inside the vehicle and distance. The results show that the SBHS can provide both sufficient braking torque for the vehicle and heat energy for the cabin.

Comprehensive Analysis on a New Type VR-Resolver With Toroidal Windings Under Healthy and Eccentric Cases

A novel analysis for a new type of variable reluctance resolvers (VR-Resolvers) with toroidal windings based on the magnetic equivalent circuit (MEC) method is presented in this work. Different cases including various windings configurations as well as different rotor structures are considered in order to investigate the performance of the resolver precisely. The position error of both healthy and eccentric resolvers are studied by a flexible MEC model. The effect of the eccentricity fault on the resolvers with different specifications is also evaluated to analyze the manufacturing tolerance due to the eccentric rotor for several cases. It is notable that the presented MEC provides the opportunity to adjust accuracy and model several structures in both healthy and faulty conditions by just a single model. Finally, the MEC results are confirmed by finite element method and experimental results to show the effectiveness of the proposed model. In general, development of a new VR-Resolver and analyzing its performance under different windings configurations and rotor structures by proposing a modified MEC approach are the paper novelties.

Design and Analysis of a High Power Density Permanent Magnet Linear Generator for Direct-Drive Wave Power Generation

Wave energy is a new type of clean energy. Aiming at a low wave energy density and small wave height in China’s coastal areas, a tubular permanent magnet linear generator (PMLG) with a short stroke, small volume, and high power density is designed for wave power generation. Firstly, the generator’s electromagnetic parameters are analyzed by the analytical method, and the magnetic circuit topology and basic structure of the generator are analyzed by the equivalent magnetic circuit method (EMCM). Then, the finite element method (FEM) is used to analyze the influence law of the generator’s basic structural parameters on the output electromotive force (EMF) and its sinusoidal characteristics. The multi-factor and multi-level analysis is carried out based on the orthogonal test method to study the size parameters of the above analysis, and the optimal structure parameter combination for the generator is obtained. Finally, the prototype is trial-produced and tested for steady-state and transient performance to confirm the accuracy of the simulation calculations, and the output performance under no-load and load conditions is examined. The results show that both the optimized prototype’s power density and the output EMF’s sinusoidal properties have been improved under the proposed scheme.

An Improved Calculational Model for Inductance of CRDM Based on Equivalent Magnetic Circuit

In the magnetic lifting control rod drive mechanism (CRDM), it is essential to obtain the dynamic inductance of each coil for research of a mathematical model and state monitoring. It is demonstrated from the working principle and circuit model of the CRDM that the coil inductance has a significant effect on the current step response time. This article proposes an improved equivalent magnetic circuit (IEMC) model that takes into account flux leakage and coupling. The model focuses on calculating the dynamic inductance of the CRDM. First, the magnetic reluctance expression of each unit in the IEMC model is deduced. A flux area correction coefficient is introduced to consider the edge effect of working air gaps. Then, the dynamic inductance of the CRDM is analyzed and calculated based on the proposed model. Finally, the performance of the proposed method is compared with finite element analysis (FEA) and a simplified equivalent magnetic circuit (SEMC) method. Results show that the proposed method can approach the results of FEA better than the SEMC method.

Optimal Design of Permanent Magnet Synchronous Machine Based on Random Walk Method and Semi 3D Magnetic Equivalent Circuit Considering Overhang Effect

Permanent magnet synchronous machines (PMSMs) with an overhang structure can increase power density by compensating for the increased magnetic energy of permanent magnets. To analyze the overhang structure, a three-dimensional (3D) analysis of PMSMs is essential. However, 3D analysis takes a long time and the modeling process is complicated in the initial design stage. To overcome these problems, a magnetic equivalent circuit technique is applied to the 2D model. In this paper, an optimal design method for PMSMs with an overhang structure is proposed based on the semi 3D magnetic equivalent circuit (MEC) and random walk method. By using semi 3D MEC, it is possible to quickly analyze PMSM and obtain accurate electromagnetic analysis results considering the overhang effect. Moreover, the volume and weight of PMSM can be minimized by optimizing the rotor’s four design parameters using a random walk algorithm. To obtain high efficiency, the objective function is selected so that copper loss is minimized under the same constraints. The validity of the proposed design technique is verified by comparing the analysis results of semi 3D MEC and 3D finite element method for the derived optimal model.

Theoretical and Experimental Study on Claw-Pole Magnetic Levitation Torque Motor for 2D Valve Using Cogging Torque

In this paper, a claw-pole magnetic levitation torque motor (CPMLTM) utilizing cogging torque is proposed as an electromechanical converter (EMC) for two-dimensional valves (2D valve). Compared to the existing torque motor, CPMLTM utilizes the cogging torque between the stator and the rotor, and has the ability of automatic neutral adjustment, which greatly reduces the difficulty of neutral adjustment of two-dimensional valves and improves the accuracy of neutral adjustment. First, the structure and working principle of CPMLTM are introduced, followed by an analysis of the cogging torque of CPMLTM based on the energy method and Fourier expansion. The effects of the claw pole tooth (CPT) shape and slot opening coefficient on the cogging torque of CPMLTM are investigated. To analyze the sensitivity of the electromagnetic torque to each design parameter, a qualitative expression for the electromagnetic torque containing various design parameters was derived based on the equivalent magnetic circuit method, and a set of orthogonal tests were designed to calculate the electromagnetic torque using the finite element method (FEM). To demonstrate the feasibility of the proposed CPMLTM principle and to verify the correctness of the cogging torque analysis model and FEM, a prototype was fabricated and a test rig was constructed for experimental study. The experiments show that CPMLTM can indeed utilize cogging torque to achieve automatic neutral adjustment, and that the neutral adjustment is more accurate. Moreover, the CPMLTM has good static and dynamic characteristics: a neutral electromagnetic torque of 0.1 Nm at a coil magnetomotive force (MMF) of 100 A, step response time up to 4.575 ms, and amplitude frequency bandwidth and phase frequency bandwidth of 173.7 Hz and 86.5 Hz, respectively.

Electromagnetic and Mechanical Analysis and Measurements of Interior Permanent Magnet Motors Based on Equivalent Magnetic Circuit Method

This paper is about the magnetic field analysis of an interior permanent magnet motor (IPM motor) by using the equivalent magnetic circuit method (EMC method), which requires a small amount of computation time compared with the finite element method (FEM). IPM motors have a specific shape of rotor in which the permanent magnets are embedded. Therefore, in the bridge region, the magnetic saturation is generated due to the shape of the permanent magnet, which affects the magnetic flux density distribution in the air gap and the characteristics of the IPM motor. Thus, to design an IPM motor, the magnetic saturation effects should be considered along with the rotor shape. In addition, because the rotor of the IPM rotates at a high speed directly in connection with the load, the stress generated from the rotor must be stably distributed. Consequently, according to the rotor shape characteristics of the IPM, the stress is concentrated in the thin bridge region during high-speed rotation. When the stress generated in the bridge region exceeds the yield stress of the rotor iron core material, the bridge part is destroyed. Therefore, it is important to analyze the stress that occurs in the rotor during high-speed rotation in the rotor design stage of the IPM. In this study, we analyzed the magnetic field characteristics of an IPM motor using its equivalent magnetic circuit while considering the magnetic saturation in the bridge region. The stability of the rotor was determined by presenting a safety factor based on the maximum stress generated at the rotor for each speed. We derived the stator natural frequency to evaluate the resonance possibility between the electrical frequency and the stator natural frequency. Finally, the validity of the constructed equivalent magnetic circuit was verified by comparing the results with those obtained via the FEM analysis and experiments.

Online Detection and Location of Eccentricity Fault in PMSG With External Magnetic Sensing

The detection and location of eccentricity faults in a permanent magnet synchronous generator (PMSG) become increasingly essential, especially in safety-critical applications. However, the existing approaches for monitoring eccentricity subject to many limitations. In this article, a novel method for online detection and location of the eccentricity fault in a PMSG is proposed based on the external magnetic sensing. The noninvasiveness facilitates installation and maintenance work. In this article, the effect of different eccentricity faults on the external leakage flux density is analyzed theoretically with the magnetic equivalent circuit method first. Then, two indicators are proposed for detecting static eccentricity (SE) and dynamic eccentricity (DE), respectively. The amplitudes of the SE and DE indicators are proportional to the fault degree. The angle of the SE indicator proves to be the direction of SE. Meanwhile, two indicators show excellent robustness and are independent of loads and rotation speed. Moreover, these indicators can be applied in any surface-mounted PMSG with a three-multiple number of slots. Accordingly, an algorithm to diagnose the eccentricity fault is shown based on two indicators from three sensing points outside. The computation of the method is light, which leads to fast detection speed. Finally, the accurate results in multioperating conditions from simulations and experiments verify the feasibility of the proposed approach.