Magnetic Equivalent Circuit Research Articles

Corrections to “Three-Dimensional Magnetic Equivalent Circuit Research of Double-Sided Switched Reluctance Linear Machine” [Jun 20 Art. no. 3603608

Corrections to “Three-Dimensional Magnetic Equivalent Circuit Research of Double-Sided Switched Reluctance Linear Machine” [Jun 20 Art. no. 3603608

Study on Process Derivation and Characteristic Analysis for BLDC Motor Design Using Dual Rotor Structure with High Torque Density

In this paper, the design process of brushless DC (BLDC) motor adopting the dual rotor structure that can reduce the overall size of the motor while generating the same torque as the conventional permanent magnet BLDC motor is analyzed. A simple size is selected by obtaining the torque per rotor volume (TRV), and a method of matching the counter electromotive force by selecting the pole-arc of the magnet through a magnetic equivalent circuit is analyzed. Since the efficiency is low because the 120-degree commutation method is selected, the middle stator is optimized through detailed design through the experimental design method. Afterwards, it has the advantage of being able to shift without stopping due to the characteristic of a dual rotor. For this, an analysis of the driving characteristics for each mode is performed.

A Novel Permanent Magnet Flux-Switching Linear Motor Performance Analysis by Flexible MEC Method

This paper presents a new structure of Permanent Magnet Flux-Switching Linear Motor (PM-FSLM) with a simple low weight modular primary and acceptable thrust ripple production. A flexible Magnetic Equivalent Circuit (MEC) is applied for modeling the proposed machine, which is capable to analyze the performance of different structures of PM-FSLMs. The saturation and end-effect phenomena are considered by a nonlinear permeability function and virtual zones at both ends of the machine, respectively. The machine operation under dynamic load is also investigated and its specifications are obtained. The proposed PM-FSLM has more power capability, lower current un-symmetry, and simpler mover structure compared to other ones, which can be mentioned as its benefits. Finally, the results of the proposed method are validated by the Finite Element Method (FEM) to show the effectiveness of the proposed MEC technique in terms of accuracy and processing time. The introduced linear machine and the proposed analysis method with adjustable accuracy are the paper novelties, which are presented in this work for the first time.

Multi‐objective comprehensive teaching algorithm for multi‐objective optimisation design of permanent magnet synchronous motor

The design of permanent magnet synchronous motor (PMSM) is a constrained multi-objective problem, and there are often conflicts between the goals. Aiming at the complexity of PMSM optimisation and a large number of variables, multi-objective optimisation design of PMSM using a multi-objective comprehensive teaching algorithm (MCTA) is proposed. This algorithm is improved based on the teaching–learning-based optimisation algorithm and can better adapt to large-scale sample space and multivariate optimisation. Also, based on a magnetic equivalent circuit, a static electromagnetic model of the radial magnetic field PMSM is derived, and the design requirements and goals of the PMSM are analysed. In the two PMSM multi-objective optimisation calculation processes, the optimal solution was calculated based on the composite fitness function and Pareto front, respectively. The results of the MCTA were compared with other natural optimisation algorithms. Finally, according to the optimisation results of two sets of experiments, the correctness of the optimal solution of the algorithm was verified by finite element analysis and actual measurement of the prototype. The analysis of results shows the effectiveness, simplicity, and inspiration of MCTA in the PMSM multi-objective structure optimisation design.

Performance Analysis of a Coreless Axial-Flux PMSM by an Improved Magnetic Equivalent Circuit Model

In this paper, an improved magnetic equivalent circuit (MEC) model of a coreless axial-flux permanent-magnet synchronous machine (AFPMSM) with printed circuit board (PCB) winding is presented, which considers the curvature effect, fringing effect, leakage flux, and rotor yoke's magnetic saturation. The axial air-gap flux density distribution, no-load back electromotive force, winding inductances, and electromagnetic torque are predicted by the proposed MEC model. The steady-state performances of the machine under heavy load, as well as the dynamic response of the machine with a connected voltage source and mechanical load, are calculated. All the results obtained from the proposed model are in good agreement with those issued from the 3D finite element method (FEM). The computation time of the proposed model is greatly reduced compared to 3D FEM. Finally, a coreless AFPMSM prototype with a PCB stator is manufactured, and experiments are carried out to verify the predicted results.

Static and Dynamic Modeling of the Electromagnets of the Maglev Vehicle Transrapid

This work provides a new approach for modeling the electromagnets of the magnetic levitation (Maglev) vehicle Transrapid intending to effectively and efficiently represent the statics and the dynamics in a frequency range relevant for Maglev control design and for the use in mechatronic simulation models. It includes the effects of magnetic reluctances, fringing and leakage flux, magnetic saturation, and eddy currents. The modeling follows a systematic approach by setting up the equivalent magnetic and electric circuits, and coupling the equations using Ampère's circuital law and Faraday's law of induction resulting in a system of differential algebraic equations. It allows to study effects occurring in the magnet design process or different operating points, resulting, e.g., from aerodynamic uplift, for which an extended validity range is needed. Since the computational effort of such models is significant, additionally, a numerical procedure for model reduction is presented yielding a simplified version, which possesses a nearly identical input-output behavior and is usable for control design or in large vehicle models. The proposed approach can be applied to any levitation or guidance magnet of the vehicle and is shown exemplarily for a Transrapid's levitation magnet. The model is validated for the parameters of the latest Transrapid vehicle, called TR09, showing good correspondence with the measured static force-current-gap characteristics and the inductance.

Semi-Analytical Model for Temperature Estimation of Permanent Magnet Couplers

Temperature estimation is highly significant in the design stages and analysis of permanent magnet (PM) machines. In this paper, for permanent magnet couplers (PMCs), a semi-analytical model to estimate the temperature is developed, which is able to give consideration to efficiency and applied in more complicated structure. Also, the magnetic flux path, as well as the eddy currents, are depicted through a simplified geometric topology. Moreover, the eddy current loss, taken as the heat source loss, is effectively and quickly calculated by employing magnetic equivalent circuit and Kirchhoff's law. Compared with the experimental results, this model has a good agreement with the experimental results where the deviation is within 6.67%. Finally, some constructive suggestions have been given for prediction, optimization and monitoring of PMCs.

Development and Investigation of Novel Axial-Field Dual-Rotor Segmented Switched Reluctance Machine

This article presents a new type of axial-field switched reluctance machine (AFSRM) and axial-field dual-rotor segmented switched reluctance machine (ADS-SRM), along with its design methodology. The proposed ADS-SRM is featured by the segmental stator and rotor poles, the auxiliary flux-conductive rings, and the concentrated windings. The yokeless topology reduces the active length of the motor. Besides, the adopted short-end winding layout increases the slot-fill factor and the motor's reliability. First, the basic topology of ADS-SRM is introduced along with its operating principle and various stator/rotor pole combinations. The three-phase 12/8 configuration of ADS-SRM is chosen for further analysis. Then, the design methodology considering the fringing and leakage field effects through the magnetic equivalent circuit (MEC) method is developed, and the flowchart detailing the design procedure is presented. Through the comparison with the conventional yokeless and segmented armature (YASA) topology, ADS-SRM exhibits excellent performance at overload conditions. The prototype is designed and fabricated, and the experimental results verify the motor performance.

Traction characteristics modeling of a linear motor for driving an electromagnetic press

The research relevance is connected with the need to improve the calculating methods of the linear press motor used in the drive of the press. As a research object, a cylindrical electromagnetic engine, powered by a pulse voltage source is examined in this paper. The results of the traction characteristics modeling of an electromagnetic motor, which determines the useful mechanical work and the efficiency of the electromagnetic press, are presented here. A simplified model is proposed in the form of an equivalent magnetic circuit of an electromagnetic motor. The calculation is based on the law of the total current for a closed magnetic circuit, depending on the core position coordinate. By solving differential equations of the second order, simple analytical expressions are obtained that allow calculating the electromagnetic traction force depending on the current and the position coordinates of the moving core of the electromagnetic press motor. An example of calculating the traction characteristics of calculating an electromagnetic motor is considered based on the created model. The results of comparing the calculated traction characteristics with the results of calculations obtained by other researchers are also presented.

Structural optimisation based on a snake‐like wave energy convertor with magnetoelectric transducer

Snake-like wave energy conversion (WEC) is a new type of WEC that combines raft WEC and magnetoelectric transducer. This type of WEC uses the magnetoelectric transducer, which is designed based on the permanent magnet linear generator and Halbach permanent magnet array, as its power take-off unit. The purpose of this study is to design a matching magnetoelectric transducer for WEC in common wave conditions and test its performance. The hydrodynamic model of the snake-like WEC is established to study the motion of WEC in regular waves. The equivalent magnetic circuit model of the magnetoelectric transducer is set up to optimise its ability to harvest wave energy in the ocean. Taking the maximum damping coefficient (cm ·max) as the optimisation goal of the magnetoelectric transducer, the induced voltage and output power of the magnetoelectric transducer in relatively uniform and sinusoidal motion can be calculated by simulation software. Finally, a prototype of the magnetoelectric transducer was made and its performance was tested. The experiment shows that the magnetoelectric transducer has a good ability to harvest wave energy, and snake-like WEC has wide applicability.

An Improved Subdomain Model for Magnetic Field Calculation of SPMSM Considering No-load Leakage Flux

Due to big leakage flux, the performance of permanent magnet (PM) motor will be much reduced. Especially for surface-mounted permanent magnet synchronous motor (SPMSM) with similar number of poles and slots, because the zigzag leakage flux is big and varies with the relative positions between stator and rotor, selecting no-load leakage flux coefficient with experience may cause a big calculation error to electromagnetic parameters by equivalent magnetic circuit model. Finite-element method (FEM) can directly calculate the coefficient, but entire process is time-consuming. Focusing on this problem, an analytical model of no-load leakage flux coefficient is proposed including air-gap leakage flux model and zigzag leakage flux model. Then, an improved subdomain model for magnetic field calculation of SPMSM is established, and the air-gap magnetic flux density, inducing flux linkage and line no-load back electromotive force (EMF) are calculated considering no-load leakage flux. To verify the improved model, an external rotor type SPMSM with 20-poles and 24-slots for bridge crane is designed and manufactured. Finally, the validity of improved model is verified by experimental test.

Torque Performance Enhancement in Consequent Pole PMSM Based on Magnet Pole Shape Optimization for Direct-Drive EV

Developing a permanent magnet synchronous machine (PMSM) for direct-drive electric vehicle (EV) has challenges such as obtaining high torque density and low torque ripple. The PMSM should have high pole numbers owing to low-speed operation, thereby increasing the use of rare earth magnets and cost. Therefore, in this article a consequent pole (CP) rotor topology is proposed in which the permanent magnet (PM) volume is reduced when compared with conventional surface PMSM (SPMSM). However, replacing south poles in an SPMSM with induced steel poles can increase torque ripple and reduce torque density. In order to improve torque density in a CP PMSM, structural modifications such as multilayer windings and non-ferromagnetic barriers have been proposed in the literature. These modifications increased the torque density while increasing the torque ripple. Therefore, this article proposes a novel two-level optimization method based on gradient descent algorithm, to address the challenges of improving torque density and reducing torque ripple simultaneously in a CP PMSM. Initially, an expression for the magnet pole arc angle is derived for CP PMSM based on magnetic equivalent circuit. A two-level optimization is performed on a baseline CP PMSM to determine the optimal magnet pole arc. The torque production and torque ripples of the optimized design are validated by simulation and experimental results.

Design, analysis and prototyping of a magnetic energy-harvesting suspension for vehicles

With the development of electric vehicles, the energy harvesters of vehicle’s suspensions have been widely investigated. However, most of the existing energy harvesters have replaced the original damper of the suspensions, which reduces vehicle safety. This paper proposes a magnetic energy-harvesting suspension (MEHS) for vehicles, with the advantages of high vehicle safety and a compact structure, which consists of a passive suspension and a harvester. In this paper, the working principle and the structure of the MEHS are introduced. To better analyze the magnetic field, the magnetic flux circuit model is established by combining the magnetic field division method with the magnetic equivalent circuit model. Furthermore, a dynamic model for a two-degree-of-freedom quarter-vehicle with the MEHS is built to analyze the energy-harvesting characteristics and the damping characteristics. A prototype of the quarter-vehicle that is considering the tire stiffness, is designed and manufactured, and the performances are investigated by simulations and experiments with different frequencies, external resistances and amplitudes. The experimental results indicate that the harvested peak power of the MEHS is 1.08 W with a sinusoidal input of 10 Hz and 2 mm. Moreover, the maximum energy-harvesting efficiency of the prototype reaches 67% at the sinusoidal input of 6 Hz and 2 mm. The harvested energy of the MEHS can power some electrical equipment of vehicles.

Halbach Array PM Machine Design for High Speed Dynamo Motor

For high speed motors, smaller rotor diameters are required to make the surface speed less than 250 m/s. At the same time, dynamo motors for propulsion systems often require high torque. In such an environment, permanent magnet (PM) synchronous motors are more suitable than induction motors. In this work, a 270 kW dynamo motor is designed with a Halbach array using samarium-cobalt PMs. It utilizes the rotor back iron and carbon fiber sleeve on the rotor surface. Two design goals are set when the rotor inner and outer radii are fixed preferentially: minimization of PM usage and maximization of air gap field. A magnetic equivalent circuit is utilized to identify the saturation level of the rotor back iron and air gap field density. The Levenberg–Marquardt algorithm is applied to find the optimal coverage of radial magnet in a pole pitch and the optimal PM height. It is also observed that the resulting Halbach array motor is superior to surface-mounted PM motor in torque performance when the same amount of PM is used. A prototype motor was built on a real scale, but with a reduced stack length.

Rectangular Closed Double Magnetic Circuit Offering Ultra-Long Stroke for Ultra-Low-Frequency Vibration Exciter

High-performance magnetic circuit offering uniform magnetic flux density (MFD) along ultra-long stroke is the key to develop a vibration exciter for ultra-low-frequency (ULF) vibration calibration. In this paper, a rectangular closed double magnetic circuit (RCDMC) offering ultra-long stroke up to 1.2 m is modeled and optimized. In order to overcome the modeling difficulty arising from the long stroke, a high-accuracy theoretical model is established taking advantage of the structural symmetry of the RCDMC through lumped parameter magnetic equivalent circuit method. Matrix equations are derived based on Kirchhoff’s law and solved by iteration calculation to deal with the strong nonlinear characteristics of the yoke material. The deviations between the model and finite element method (FEM) analysis results are less than 1% for non-saturated yokes and ~10% for saturated yokes. Theoretically, an MFD up to 122 mT and an acceleration waveform harmonic distortion (AWHD) as low as 0.45% are achieved through model-based optimization. Experiments are carried out using an RCDMC prototype assembled in a horizontal vibration exciter. The experimental results show that an MFD of 102 mT and an AWHD of 0.27% along 1.2 m stroke are achieved, making the proposed RCDMC a solution for ULF vibration exciter.

Analytical Model of Modular Spoke-Type Permanent Magnet Machines for In-Wheel Traction Applications

This article proposes an analytical model of modular spoke-type permanent magnet (MSTPM) machines based on air-gap field modulation (AFM) theory. Firstly, a fundamental AFM model of open-circuit MSTPM machines is introduced. The open-circuit air-gap field of MSTPM machines is determined by three fundamental elements including the primitive magnetizing magnetomotive force (MMF) produced by permanent magnet (PM), and two modulators which consist of stator and rotor permeance. The analytical MMF excited by PM (PM-MMF) can be calculated by using magnetic circuit method, while the stator and rotor permeance models are developed based on relative permeance (RP) method. Thereafter, a general model is proposed to calculate the open-circuit back electromotive force (EMF) of MSTPM machines. Further, the winding inductance model is established on the basis of equivalent magnetic circuit method and RP model. Finally, the machine performance is predicted by the analytical model, and verified by both finite element analysis (FEA) and experimental results.

Analytic Optimization of the Halbach Array Slotless Motor Considering Stator Yoke Saturation

Hybrid subdomain analysis is utilized to optimize the design of a high-speed compressor motor. Permanent magnets (PMs) are arranged in Halbach array and bounded by a carbon fiber sleeve. The stator core does not have a slot structure, so that it is advantageous in reducing the iron loss. Since the core saturation takes place, magnetic equivalent circuit (MEC) is used to find the permeability depending on the flux density of stator yoke. Furthermore, since the core is not infinitely permeable in the subdomain analysis, the solution is obtained in the whole subdomain regions: shaft, PM, air gap, coil, and stator yoke. The results of hybrid analysis are compared with those of finite-element analysis (FEA). Very close matching results are obtained in the flux density and torque even under yoke saturation. The stator yoke height is optimized against the rotor outer radius so that torque, power density, and efficiency are maximized, while stator outer radius, stack length, and coil area are fixed.

Nonlinear EMC Modeling and Analysis of Permanent-Magnet Slotted Limited-Angle Torque Motor

In this article, a high-precision equivalent magnetic circuit (EMC) model is first proposed for slotted permanent-magnet (PM) limited-angle torque motor (LATM) with nonuniform teeth, which leads to potential application in swing system substituting a lower torque density of the slotless structure. By the proposed relatively fine division method of magnetic reluctance in the stator tooth-tip segments, air-gap regions, and PM poles, the proposed EMC model can fully consider armature reaction and magnetic saturation problem. Subsequently, a multiobjective optimization method based on the EMC model is proposed to improve torque performance. Finite-element analysis is employed to validate the EMC model and optimization results. Following that, a curved nonwounded tooth shape is carried out and further optimized to decrease magnetic saturation of stator teeth and significantly improve symmetry of torque profile about stable equilibrium point, compared with the traditional straight tooth shape. Finally, the slotted LATM with curved teeth is prototyped, and its experimental results are presented and discussed. The simulation and experimental data show better accuracy of torque profile improvement.

A Novel 2-DOF Lorentz Force Actuator for the Modular Magnetic Suspension Platform.

The modular magnetic suspension platform depends on multi degree of freedom of Lorentz force actuators for large bearing capacity, high precision positioning and structure miniaturization. To achieve the integration of vertical driving force and horizontal driving force, a novel 2- (two degrees-of-freedom) DOF Lorentz force actuator is developed by designing the pose of the windings and permanent magnets (PMs). The structure and the working principle are introduced. The electromagnetic force mathematical model is established by the equivalent magnetic circuit method to analyze the coupling of magnetic flux. The distribution characteristics of magnetic flux density are analyzed by the finite-element method (FEM). It is found that the coupling of the magnetic flux and the large magnetic field gradient severely reduce the uniformity of the air-gap magnetic field. The electromagnetic force characteristic is investigated by FEM and measurement experiments. The difference between FEM and experiment results is within 10%. The reasons of driving force fluctuation are explained based on the distribution of air-gap magnetic field. The actuator performance are compared under the sliding mode control algorithm and PID control algorithm and the positioning accuracy is 20 μm and 15 μm respectively. Compared with the similar configuration, the motion range and force coefficient of the Lorentz force actuator in this paper are larger. It has a certain guiding significance on the structure design of the multi degree of freed Lorentz force actuator.

Analytical Study, Design and Optimization of Radial-Flux PM Limited-Angle Torque Motors

This paper presents an analytical study of the radial-flux slotless limited-angle torque motors. The modelling is based on the magnetic equivalent circuit of the actuators and uses the electromagnetic equations to calculate the air-gap flux as well as the produced torque. This model is then used for designing the actuators both in outer-rotor and inner-rotor structures, considering the design constraints and desired characteristics. As the objectives in design stage usually conflict with each other, an intelligent multi-objective optimization algorithm is required to design the best fit actuators. Analytical and simulation results are presented and compared to show the accuracy of the model and verify the design equations as well as the design approach. As this type of actuators is a key element in industrial control, the contributions of this paper are focused on new analytical field solution based on magnetic equivalent circuit, design and optimization approach for radial-flux structure and introducing a general procedure that could be extended to similar structures and actuators.