Magnetic Circuit Model Research Articles

A Novel Three-Stage Optimization Design Method of Asymmetric-PM Variable Flux Memory Machine Considering Magnet-Axis-Shifting Effect

Asymmetric-permanent-magnet variable flux memory machine (APM-VFMM) commonly suffers from the optimization issues, i.e., variable magnet-axis-shifting (MAS) effects result in distinctly differentiated electromagnetic characteristics under multiple magnetization states (MSs). Thus, this article proposes a novel three-stage optimization method for APM-VFMM considering the MAS effects to achieve efficient optimization. In the first stage, an analytical model based on the magnetic equivalent circuit (MEC) and torque models considering the MAS effects is developed to determine the key optimization objectives of the investigated machine while theoretically revealing the internal mechanisms for the improvement of the flux regulation range and torque capability. In the second stage, the comprehensive sensitivity analyses of the main geometric parameters are implemented based on a self-organizing map (SOM) method. Subsequently, the geometric parameters with higher sensitivity are selected for the multiobjective optimization process, thus effectively reducing the computational burden. In the third stage, a multimode circuit control model is developed and utilized in a single finite element analysis (FEA) case to consider multiple MSs and different MAS effects simultaneously for multiobjective optimization. The FEA predictions and experimental tests carried out on an APM-VFMM prototype confirm the effectiveness of the proposed three-stage optimization method.

Investigation of Six-Phase Surface Permanent Magnet Machine With Typical Slot/Pole Combinations for Integrated Onboard Chargers Through Methodical Design Optimization

This article presents an analytical magnetic equivalent circuit (MEC) modeling approach for a six-phase surface-mounted permanent magnet (SPM) machine equipped with fractional slot concentrated winding (FSCW) for integrated onboard chargers. For the sake of comparison, the selected asymmetrical six-phase slot/pole combinations with the same design specifications and constraints are first designed based on the parametric MEC model and then optimized using a multiobjective genetic algorithm (MOGA). The commercial BMW i3 design specifications are adopted in this article. The main focus of this study is to achieve optimal design of the SPM machine considering both the propulsion and charging performances. Thus, a comparative study of the optimization cost functions, including the peak-to-peak torque ripple and core losses under both motoring and charging modes and electromagnetic forces (EMFs) under charging, is conducted. In addition, the demagnetization capability in the charging mode and the overall cost of the employed machines are optimized. Since the average propulsion torque is crucial in electric vehicle (EV) applications, it is maintained through the design optimization process. Furthermore, finite element (FE) simulations have been carried out to verify the results obtained from the analytical MEC model. Eventually, the effectiveness of the proposed design optimization process is corroborated by experimental tests on a 2-kW prototype system.

A Novel Modeling Technique via Coupled Magnetic Equivalent Circuit With Vector Hysteresis Characteristics of Laminated Steels

This paper proposes a method to include the anisotropic hysteresis characteristics of soft-magnetic laminated steels in the magnetic equivalent circuit (MEC) modeling. The loop-based MEC formulation is improved to handle the nonlinearity of the anisotropic magnetic hysteresis, including the dynamic classical eddy-current and excess fields. The developed MEC model is coupled with both the single-valued <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 (SVC) in magnetostatic and the dynamic vector hysteresis model (VHM) in transient analysis. Results with a single elementary MEC element show that an alternating magnetic field in a single direction with a peak value smaller than 300 A/m causes a discrepancy of more than 10% between the magnetic flux densities calculated by the VHM and SVC at 50 and 200 Hz excitation frequencies. Moreover, the proposed modeling technique is verified experimentally using the laminated transformer core of TEAM problem 32. The induced voltage calculated by the MEC model with the VHM demonstrates a good agreement with the measurements, while the MEC model with the SVC calculates inaccurate voltage waveforms. Lastly, the total iron loss dissipated in the transformer's iron core is investigated to verify the proposed technique under different excitation levels and frequencies up to 500 Hz. It is observed that the proposed MEC model with the vector hysteresis characteristics of laminated steels is able to calculate the iron loss accurately, while the conventional single-valued curve method fails to estimate the iron loss.

Design Tradeoff Between Saliency Ratio and PM Flux Linkage in Variable Flux Memory Machines

To achieve flexible flux regulation, variable flux memory machines (VFMMs) are normally characterized by a high permanent magnet (PM) flux linkage design, which generally reduces the saliency ratio of the machine. In order to further reveal the internal performance tradeoffs, this paper investigates the relationship between the saliency ratio and PM flux linkages of VFMMs by combining the equivalent magnetic circuit models and the finite element (FE) method. Three hybrid-magnetic-circuit (HMC) VFMMs having different PM grades and saliency ratios are chosen as the case studies to analyze and reveal the influence of flux linkages and saliency ratios on the major electromagnetic characteristics. First, the no-load and dq-axes equivalent magnetic circuit models of the investigated machines are established successively to obtain the PM flux linkages and dq-axes inductances of the machines. Then, the relationships between the electromagnetic torque and the key design parameters are obtained based on the space vector model. Next, the maximum torque per ampere (MTPA) trajectory is portrayed to determine the flux-weakening characteristics of the VFMMs. Afterwards, the electromagnetic characteristics of the three machines are compared and analyzed to confirm the previous theoretical analyses. Finally, an HMC-VFMM prototype is fabricated and tested to verify the effectiveness of the analysis.

Reduction of Unipolar Leakage Flux and Torque Ripple in Consequent-pole PM Vernier Machine

This paper proposes a new consequent-pole permanent magnet vernier machine (CPMVM), which can be regarded as a combination of two conventional CPMVM with opposite polarities. Based on the simplified axial magnetic circuit model, it is verified that the proposed CPMVM can reduce the unipolar leakage flux. In order to reduce the torque ripple of machine and improve the output torque of machine, the flux barrier is placed on the rotor of the proposed machine. Then, the parameters of the proposed CPMVM are optimized and determined. Moreover, the electromagnetic performance, including no-load air-gap flux density, average torque and torque ripple, flux linkage, back-electromotive force, cogging torque, average torque, torque ripple, power factor and loss, is compared with conventional surface-mounted permanent magnet vernier machine (SPMVM) and CPMVM. Finally, it is demonstrated that proposed CPMVM with flux barrier can effectively reduce the unipolar leakage flux and greatly reduce the torque ripple of machine. Also, compared with the SPMVM, the proposed CPMVM with flux barrier saves more than 45% of the permanent magnet material without reducing output torque.

Transmission Performance of Halbach Array Cylindrical Permanent Magnet Governor

A novel cylinder permanent magnet governor (CPMG) with Halbach segmentation is proposed in this paper. In order to improve the transmission performance of the CPMG, different permanent magnet (PM) arrangement methods are adopted. To achieve a fair comparison result, all the PMs are of the same size. The main magnetic fluxes are considered to obtain a comprehensive equivalent magnetic circuit model of the CPMG with Halbach array and analytical output torque that is calculated. The analytical method of transmitted torque for CPMG is then presented. Additionally, the effect of the average output torque of CPMG under parameters of the thickness of the copper rings, the slip rate and the effective coupling of the copper rings are investigated. Finally, the prototype platform is ready for testing on the field. The results were consistent with the results of the simulation, and the error was kept within the range of 5%. This research can provide a theoretical and practical reference for the optimal design of the transmission characteristic of CPMG.

An Accurate Magnetic Equivalent Circuit Model for Modeling and Analysis of Variable Reluctance Energy Harvesters

An Accurate Magnetic Equivalent Circuit Model for Modeling and Analysis of Variable Reluctance Energy Harvesters

Design Optimization of an Axial Flux Magnetic Gear by Using Reluctance Network Modeling and Genetic Algorithm

The use of a suitable modeling technique for the optimized design of a magnetic gear is essential to simulate its electromagnetic behavior and to predict its satisfactory performance. This paper presents the design optimization of an axial flux magnetic gear (AFMG) using a two-dimensional (2D) magnetic equivalent circuit model (MEC) and a Multi-objective Genetic Algorithm (MOGA). The proposed MEC model is configured as a meshed reluctance network (RN) with permanent magnet magnetomotive force sources. The non-linearity in the ferromagnetic materials is accounted for by the MEC. The MEC model based on reluctance networks (RN) is considered to be a good compromise between accuracy and computational effort. This new model will allow a faster analysis and design for the AFMG. A multi-objective optimization is carried out to achieve an optimal volume-focused design of the AFMG for future practical applications. The performance of the optimized model is then verified by establishing flux density comparisons with finite element simulations. This study shows that with the combination of an MEC-RN model and a GA for its optimization, a satisfactory accuracy can be achieved compared to that of the finite element analysis (FEA), but with only a fraction of the computational time.

Magnetic equivalent circuit and finite element modelling of anisotropic rotor axial flux permanent magnet synchronous motors with fractional slot distributed winding

AbstractAxial flux motors have been in the focus of many research work due to their promising properties when compared to conventional radial flux machines. Axial flux permanent magnet synchronous motors (AFPMSM) studied in the literature were mostly limited to surface‐mounted permanent magnet machines (SPMSM), excluding only a few studies about axial flux internal permanent magnet (AFIPM) or permanent magnet‐assisted synchronous reluctance (AFPMaSynRM) machines. Since numerous rotor topologies have been proposed and investigated in case of radial flux motors, analogous design methodologies can be developed in case of axial flux motors with rotor saliency. The parametrisation and modelling of a magnetically anisotropic rotor axial flux motor are presented. This approach is described generally and the method is applied to an example motor geometry. The results were validated by FEA (Finite Element Analysis), using the 2D multi‐slice and 3D modelling approaches. The modelling error was calculated and the analytical and numerical methods were compared. It was found that the proposed model was suitable for calculating important parameters of the anisotropic rotor axial flux permanent magnet synchronous motor (AnR‐AFPMSM) during the design process.

Analysis of linear permanent magnet switched reluctance motors with modular and segmental movers

AbstractHere, the authors propose two new Permanent Magnet (PM) embedded linear switched reluctance motors; one is a modular linear hybrid reluctance motor (MLHRM), and the other one is a segmental linear hybrid reluctance motor (SLHRM). Both structures employ PMs between the side teeth of the modules/segments. The main contribution of the PMs is to increase the air‐gap flux density, which results in an enhanced thrust, and decrease the magnetic saturation in iron parts. The magnetic equivalent circuit model is used to demonstrate the positive effect of inserting PMs in the MLHRM and SLHRM compared to their PMless counterparts. The optimal pole number and design procedure are illustrated. The simulation results are obtained in terms of static thrust, flux linkage, flux density distributions, and steady‐state current and thrust. The results show that the proposed MLHRM and SLHRM offer a higher thrust and lower current compared to their PMless form. Also, the PMs decrease the root mean square (RMS) current under the steady‐state performance of the motors, in which a higher thrust is produced with a lower RMS current. Finally, the MLHRM and SLHRM are fabricated and the test results are obtained and compared with the simulations, which illustrate a satisfactory agreement.

Dynamic characteristics of large permanent magnet direct‐drive generators considering electromagnetic–structural coupling effects

AbstractDynamic characteristics of large permanent magnet direct‐drive generators (PMDGs) considering electromagnetic–structural coupling effects are analyzed in this study. Using the conformal mapping method, the scalar magnetic potential of the air gap magnetic field considering the slot effect is calculated. On the basis of the discrete current element and magnetic equivalent circuit model, the local magnetic saturation effect of the stator and rotor is quantitatively simulated and the air gap magnetic field intensity distribution is obtained via numerical simulation. A series of uniformly distributed equivalent electromagnetic springs are introduced to develop an electromagnetic–structural coupling finite element PMDG model. The proposed air gap field analysis method is verified by the finite element analysis results. On the basis of the test platform for the Goldwind 1.5 MW PMDG, both modal and dynamic response tests for the stator/rotor coupling system are conducted, and the results are compared with the natural frequencies, mode shapes, and vibration responses obtained using the numerical model. The effects of the air gap length and rotor speed on the natural frequencies of the coupling system are analyzed. The proposed model has the potential to accurately evaluate the PMDG vibration energy, avoiding resonance points, and maintaining stable operations of the unit.

Analysis and Design of a Novel Doubly SalientPMMotor Based on Parallel Path Magnetic Technology

AbstractIn this paper, a novel doubly salient PM motor based on parallel path magnetic technology (PPMT) is presented. PPMT is an advanced magnetic control technology, which can be applied to linear and rotary actuators. First, the fundamental principle of the PPMT prototype is elaborated, and then a comprehensive research and analysis of PPMT motor is carried out, with particular emphasis on machine topology, operation principle and electromagnetic performance. The equivalent no‐load PM magnetic circuit model is established and equations for calculating the main PM flux are derived. Besides, a dual‐stator 6‐pole PPMT motor prototype has been developed to valid the analysis. According to the similarity of topology and operation principle, comparison between the FSPM machine and PPMT machine is conducted, which leads to the conclusion that the PPMT motor has lower cogging torque, lower torque ripple and better sine back EMF waveform, the PPMT motor is more suitable for servo applications compared to FSPM motor. Finally, to improve the power density of PPMT motor, FE parametric modeling method for designing the three coupled stator parameters, which are the PM width, the stator yoke width and the second airgap length is given out. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Optimal torque control with radial force compensation for multiphase PMSMs under an open-circuit fault

Open-circuit (OC) faults of permanent magnet synchronous machines (PMSM) yield deviations from the desired torque and result in undesired radial forces, which cause vibrations and noise. Multiphase PMSMs give additional degrees of freedom for the control of the machine, which allow to (partially) mitigate the impacts of an OC fault. Therefore, a fault-tolerant control strategy with radial force compensation under single open-circuit (OC) faults is developed in this paper for multiphase PMSMs. It is based on a magnetic equivalent circuit (MEC) model, which ensures a high model accuracy even for motors with non-fundamental wave behavior and magnetic saturation, and which is applicable to arbitrary multiphase PMSM designs both for the healthy-circuit (HC) and the OC fault case. The proposed method allows to minimize the torque tracking error, the power losses and the radial forces. The results of the proposed fault-tolerant control strategy, which are presented for an experimentally validated model, prove that almost complete mitigation of an OC fault is possible.

Magnetic Equivalent Circuit Model for Performance Prediction of Two-DOF Planar Resolver

Magnetic Equivalent Circuit Model for Performance Prediction of Two-DOF Planar Resolver

Design Optimization of a New Hybrid Excitation Drive Motor for New Energy Vehicles

In this paper, a new hybrid excitation drive motor (HEDM) was proposed to solve the problem of an uncontrollable magnetic field of a permanent magnet motor. The rotor part of the motor was composed of a combined magnetic pole permanent magnet rotor and a brushless electric claw rotor, in which the combined magnetic pole permanent magnet rotor has a parallel magnetic circuit structure. According to the characteristics of the parallel rotor structure, the equivalent magnetic circuit model was established, and the no-load leakage flux coefficient of the claw pole rotor was calculated. The Taguchi method was used for objective optimization of the permanent magnet rotor structure. The distortion rate of no-load back electromotive force (EMF) was taken as the first optimization goal; the cogging torque and the average torque were taken as the second optimization goal; and the torque fluctuation coefficient was a constraint condition. The optimal parameter matching under the mixed horizontal matrix was obtained. The parameters of the claw pole were optimized by using the method of uniform variables, and the dimension parameters of the motor were obtained. Finite element analysis and prototype tests were carried out for the optimized motor structure. The rationality and feasibility of the new HEDM as a vehicle motor were verified, which provided a possibility for the application of the new energy vehicle drive motor field.

Stress-Dependent Magnetic Equivalent Circuit for Modeling Welding Effects in Electrical Steel Laminations

Welding has a severe impact on the efficiency of electrical machines. The heat added during the welding process affects the microstructure of the material and causes residual stress. This results in local degradation of the magnetic permeability and facilitates additional iron losses in the machine core. With the purpose of modeling and simulating welding effects in electric machines, this paper proposes a stress-dependent magnetic equivalent circuit (MEC) model for welded non-grain-oriented electrical steel laminations. A modified iron loss model is proposed to accommodate these welding effects. Furthermore, the proposed MEC model is applied to a M270-35A stator core as a case study. It was demonstrated that the core losses increase by 25% when four welding joints are applied. With a limited number of magnetic measurements on a welded and unwelded core, the model can be fully parametrized. Finally, the model was successfully validated on a core with eight welding seams at 100 Hz. The proposed model can be integrated into the design of electric machines to consider the welding effects.

Determination of Design Parameters Considering Working Harmonic and Irreversible Demagnetization for Flux-Modulated Linear Actuator

This article proposes a design process for a flux modulated (FM) permanent-magnet linear actuator for a five-axis gantry robot system by investigating the parameters affecting working harmonics. A detailed design process using the magnetic gearing effect was developed by considering the magnetic equivalent circuit and finite element analysis models of the FM-linear actuator. Considering natural cooling, the design process includes the effect of irreversible demagnetization when selecting the design parameters. Using the design parameters, a final simulation model was created to check the electromagnetic performance under both no-load and full-load conditions. A prototype was built to validate the results obtained using the proposed analytical model.

Presentation of a Novel Variable Reluctance Tubular Resolver

Encoders and resolvers are the most common position sensors in controlling electrical machines. However, due to their ability to work under harsh conditions, resolvers are more preferred. In linear position detection, the transversal edge effects and the longitudinal end-effects adversely affect the accuracy of conventional linear resolvers. On the contrary, due to the cylindrical symmetry of tubular machines, they are not subject to the edge effects. With this idea, this article presents a novel linear VR resolver with a tubular structure to achieve higher accuracy than the existing linear resolvers. A magnetic equivalent circuit model is then developed to prove the correct performance of the proposed resolver. It is discussed that the proposed resolver is tolerant of mechanical eccentricities. Different configurations are studied, and finite-element analysis is conducted to analyze the resolver's outputs considering longitudinal end-effects and under mechanical eccentricities. The results show the proposed configuration has a robust performance under eccentricities while its accuracy sharply deteriorates due to the longitudinal end effect. Therefore, an effective method is proposed for compensating the longitudinal end effect. Finally, the compensated resolver is experimentally built and tested to verify the success of the developed sensor.

Optimal Pole Ratio of Spoke-type Permanent Magnet Vernier Machines for Direct-drive Applications

Due to magnetic gearing effects, spoke-type permanent magnet vernier machines (ST-PMVMs) have the merit of high torque density, where an extra torque amplification coefficient, i.e., pole ratio (the pole-pair ratio of PMs to armature windings) is introduced. However, different from surface-mounted PMVM, the variation of torque against pole ratio in ST-PMVMs is non-linear, which is increased at first and then decreased. This article is devoted to identify the optimal pole ratio of ST-PMVMs by equivalent magnetic circuit model. It is found that except the P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> air-gap magnetomotive force (MMF) harmonic having the same pole-pair of PM, the Pa <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> air-gap MMF harmonic having the same pole-pair of armature winding is also induced due to the modulation of doubly salient air-gap structure. The P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> MMF harmonic produces positive torque, while Pa <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> MMF harmonic produces negative torque. With the increase of pole ratio, the proportion of Pa <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> MMF harmonic as well as negative torque is increased, which reduces the advantages of high pole ratio coefficient. Further, the influence of dimension parameters on the performance of ST-PMVMs under different pole ratio are investigated. Results show that ST-PMVMs with pole ratio 2.6 have high torque density, low cogging torque and high power factor simultaneously. Finally, a prototype is manufactured to validate the analysis.

Numerical simulation of an electromechanical brake concerning associated difficulties

The biggest challenge in developing any type of brake (or any other actuator) is overcoming its inherent disadvantages. Brakes that use materials whose rheological properties change under the influence of an external magnetic field are called magnetorheological brakes. In addition to the mechanical issues, magnetorheological brakes are troubled with cooling, sealing, settling, fluids' gap size, etc. Furthermore, there are issues with brake’s magnetic field density distribution and propagation. The poor distribution of the magnetic field density through the body of the magnetorheological brake is one of these inherent disadvantages. Magnetorheological’s brake magnetic circuit modeling forms the basis for further development. This paper is part of ongoing research into the feasibility of using magnetorheological brakes in automotive applications. Certain points of the numerical simulation process are addressed. The research uses part of the results from previous numerical simulations, carried out using commercial finite element method software - COMSOL Multiphysics, AC/DC module, and results from the previous experiments.