Equivalent Magnetic Circuit Method Research Articles

Analytical modelling of the linear transverse flux permanent magnet motor using magnetic equivalent circuit method

AbstractThe authors propose an analytical modelling approach for the linear transverse flux permanent magnet motor using the magnetic equivalent circuit method. The main focus of this study is to predict the phase flux‐linkage characteristic of the motor. Essential equations required for implementation of the model and how to solve it are described clearly so that someone can use it easily. A typical motor is selected to apply the proposed model and simulation results, including static characteristics of flux‐linkage and thrust, are presented. To validate the developed analytical model, the discussed motor is also analysed with 3D finite element method using MAXWELL software and the obtained simulation results are compared to each other.

Research and Characteristic Analysis of A New Type of Dual Winding Electromagnetic Brake

Taking the electromagnetic brake as the research object, a new structure of double-winding electromagnetic brake is proposed in view of the serious temperature rise phenomenon of traditional single-winding electromagnetic brake, the high requirement of insulation level and the obvious decrease of electromagnetic force. The equivalent magnetic circuit method is used to analyze and calculate the magnetic field, and the simulation model of the new brake is constructed, and the influence of different parameters on the braking characteristics of the double-winding electromagnetic brake is analyzed by the single-variable method, and the influence curves of each parameter on the electromagnetic force and response time are obtained. At the same time, the magnetic-thermal coupling analysis of the double-winding electromagnetic brake is carried out, and the results show that the total ampere-turns and power of the double-winding electromagnetic brake decreases by 15.3% in the same proportion, the rated electromagnetic force decreases by 22.9%, the release time grows by 23.7%, and the closure time is shortened by 14.6%.

Analysis of Multi-Objective Optimization Design of Interior Double Radial and Tangential Combined Magnetic Pole Permanent Magnet Drive Motor for Electric Vehicles

A new type of interior combined pole permanent magnet drive motor is proposed in this paper, which aims to improve the power and comfort of electric vehicles. In view of the complex magnetic circuit structure and rich harmonic magnetic field of the motor, the initial magnetic pole parameters of the rotor are determined by the equivalent magnetic circuit method. Then, aiming at the complex magnetic circuit and rich harmonic magnetic field, a multi-objective optimization method based on the Taguchi method and response surface method is proposed to reduce the cogging torque, high harmonic content in air gap magnetic flux density and increase the output torque. Based on the finite element analysis of the electromagnetic performance of the new type interior combined magnetic pole permanent magnet drive motor before and after optimization, it can be seen that the improved rotor structure can effectively reduce the torque ripple and increase the torque density. Finally, a prototype was developed and experiments were conducted, and experimental results verified the correctness of the proposed multi-objective optimization algorithm.

Magnetic Field Analysis and Development of Disk Axial–Radial Hybrid Excitation Generator for Range Extenders in Extended-Range Electric Vehicles

Magnetic Field Analysis and Development of Disk Axial–Radial Hybrid Excitation Generator for Range Extenders in Extended-Range Electric Vehicles

Prediction of Electromagnetic Performance for IPMSM Based on Improved Analytical Model Considering Saturation Effects

Unlike surface-mounted permanent magnet synchronous motors (SPMSM), the rotor structure of interior permanent magnet synchronous motors (IPMSM) is irregular and relatively complex. This makes the analytical calculation for IPMSM quite complicated. Except for the use of some equivalent methods to make irregular permanent magnets (PMs) regular, existing subdomain models often cannot effectively and directly account for the complex rotor structure and cannot be easily applied to IPMSM. For this reason, an improved analytical model applicable to IPMSM is presented, studied, and developed in this article. First, a novel subdomain model division method is innovatively introduced. Complex rotor structure can be well accounted for. This not only facilitates the expression of vector potential and satisfies the establishment of subdomain model, but also recovers the original rotor topology to the maximum extent and effectively avoids many uncertainties and unreliability caused by over-equivalence. Afterwards, the magnetic equivalent circuit and equivalent surface current method are combined to fully consider the saturation effects of magnetic isolation bridges, rotor ribs, and cores. Model analysis accuracy is well guaranteed. Further, the precise subdomain method is investigated to achieve fast prediction of key electromagnetic performance. Both finite element analysis (FEA) and prototype experiment strongly highlight the validity of the improved analytical model. In addition, compared to FEA, the improved analytical model does not require tens of thousands of computation cells, which saves a lot of time and storage while ensuring the same prediction accuracy. This opens up unlimited possibilities for the design and optimization of IPMSM.

Research on transmission characteristics of sleeve type electromagnetic hybrid governor

Aiming at the shortcomings of the traditional permanent magnet governor air gap speed regulation, a sleeve-type electromagnetic hybrid governor is proposed by controlling the current instead of adjusting the air gap, the structural characteristics and working principle of the speed regulation model are introduced, and the electromagnetic torque mathematical expression is derived based on the equivalent magnetic circuit method, and the key parameters affecting the transmission performance of the governor are obtained, and the simulation model of the sleeve electromagnetic hybrid governor is established by using the finite element analysis method to analyze the electromagnetic field change law in the governor under the transient field. The change curve of air gap magnetic inductance intensity under different currents was obtained, and the influence of speed difference under different currents on the output torque was revealed, and finally, an experimental platform was built for testing, and the maximum error of torque simulation and the test was obtained by analyzing the results to verify the accuracy of the simulation method, on this basis, two structural schemes were proposed to improve the amplitude of the torque regulation of the governor by the current, under the structure of scheme 1, the adjustment amplitude of the torque increased from 35% of the original structure to 96%, and the improvement effect was ideal. Its laws and conclusions can provide a reference for the further design and optimization of sleeve electromagnetic hybrid governor.

D-Q Axis Inductance Analytical Calculation for Fractional-Slot Distributed Winding IPM Motor Based on Big-Small Pole Space Method

The d-q axis inductance is the crucial parameter for the interior permanent magnet (IPM) motor. In order to facilitate the design, analysis, and optimization of IPM motors, it is of great significance to develop an accurate and simplified inductance analytical calculation method. Among the existing calculation methods, the magnetic equivalent circuit (MEC) has advantages in the inductance calculation of the IPM motor due to the simple modeling, the fine processing of the saturation region and the visualization of the magnetic field distribution. However, the traditional MEC method is only applicable to the IPM motor with integer-slot distributed winding (ISDW) or fractional-slot concentrated winding (FSCW), while lacking of in-depth research on fractional-slot distributed winding (FSDW). The magnetic circuit topology of FSDW IPM motors is not as single as that of FSCW/ISDW IPM motors. It leads to problems in the traditional MEC method when dividing the d/q axis flux path in FSDW motors. To solve this problem and expand the applications of MEC method, a big-small pole space (BSPS) method is proposed after fully considering the common characteristics of MMF distribution and reluctance distribution in FSDW motors, which fills the gap of MEC method applied to FSDW motors. The BSPS method divides the d-axis flux path according to the asymmetry of the d-axis magnetomotive force (MMF). Based on the divided flux paths, an improved nonlinear MEC model that considers the saturation of stator and rotor is established to calculate d- and q-axis inductances. The results of finite element analysis (FEA) verify the validity of the proposed MEC model with different geometry parameters. Experimental results of an 84-pole/360-slot FSDW I-type IPM wind generator further confirm the validity of the proposed MEC model

Modelling and analysis of the intersecting axis permanent magnet eddy‐current coupler

AbstractThe permanent magnet eddy‐current coupler (PMEC) is a kind of non‐contact, stepless speed regulation device and has been widely used in transmissions. However, the current PMECs are coaxial and cannot achieve transmission and speed regulation in intersecting axes. An intersecting‐axis permanent magnet (PM) eddy current coupler (IPMEC), which consists of a disk‐type PM rotor and a barrel‐type conductive sheet (CS) rotor arranged with intersecting axes, is proposed. It generates eddy currents through the speed difference between the two rotors and uses the non‐contact electromagnetic force between the eddy currents and permanent magnets to transmit torque. During operation, the speed can be adjusted by altering the coupling area or air gap. A theoretical model of the IPMEC based on the equivalent magnetic circuit method is presented and verified by finite element simulation using ANSYS. Then, the effects of the pole number of the PMs, the radius of the CS rotor and the PM rotor on the performance were analysed, and the design method of the IPMEC was proposed. This study can be used to expand the application range of PMECs.

Full circumferential reluctance maglev coupling for 2D proportional flow rate valve: Design, modelling and experimental validation

A novel full circumferential reluctance maglev coupling (FCRMC) is proposed in this paper, which not only meets the requirements of force transmission and valve position feedback of two-dimensional (2D) valve but also has the advantages of closed-loop magnetic circuit and high magnetic energy utilization rate. To investigate the torque-displacement characteristic of FCRMC, a detailed analytical model based on the equivalent magnetic circuit method is formulated, which considers the leakage flux effect, edge effect, and magnetic permeability nonlinearity. The effects of the inclination angle, width, air gap, and number of teeth on the torque are explored by the analytical model, and appropriate structural parameters are selected to design and manufacture the prototype. A dedicated test bench is built and the static/dynamic characteristics of FCRMC are tested. The experimental results show that the FCRMC prototype has a step velocity of 20.8 × 10−3 mm/ms, a torque-volume ratio of 8.47 × 10−3 N m/cm3, a torque-permanent magnets(PMs) volume ratio of 0.050 N m/cm3, and a step velocity-PMs volume ratio of 2.63 × 10−3 mm/ms·cm3. Finally, to verify the feasibility of the FCRMC in real work situations, the FCRMC is applied to a 2D electro-hydraulic proportional flow valve. The experimental results show that, at 15 MPa, the no-load flow of the valve is 82.4L/min, with a hysteresis of 3.8 %, a step velocity of 17.5 × 10−3 mm/ms, and amplitude and phase frequency widths of 22.4 Hz and 26.5 Hz.

Structure and characteristic analysis of a novel magnetic bearing without thrust disk

Conventional thrust magnetic bearing (TMB) uses large thrust disk to generate axial levitation force. However, due to the existence of thrust disk, it will lead to many problems in assembling and dynamic balance. Moreover, it will even limit rotational speed. In order to solve these shortcomings, a novel TMB with uniform teeth on the stator and rotor is proposed. It replaces the conventional thrust disk with staggered teeth structure between the stator and rotor. This paper obtains analytical expressions of levitation force, current stiffness and displacement stiffness of the novel TMB by equivalent magnetic circuit method and method of air–gap ratio permeance. Considering slot effect between the teeth of stator and rotor, its influence is analyzed by finite-element analysis (FEA) and the expression of displacement stiffness has been modified. The simulation and experiment results show that the proposed TMB can ensure enough bearing capacity by reasonably designing the staggered distance between the teeth of stator and rotor. In addition, under the reasonable tooth structure, TMB can achieve self-recovery ability by utilizing the influence of slot effect on levitation force. Compared with conventional TMB, the proposed TMB has greater advantages in assembly, dynamic balance and high speed. It will be conducive to its application in medical, aerospace and other fields.

Analytical calculation method of a liquid-cooling eddy current brake considering magnetic saturation and skin effect

In this article, a clear and concise analytical method for predicting the performance of a Liquid-cooling eddy current brake (LC-ECB) is proposed. The LC-ECB has a coolant channel in the rotor to allow direct cooling of the inner surface of the stator. The static air-gap magnetic field distribution is obtained by the dynamic magnetic equivalent circuit (MEC) method, and the magnetic flux leakage and global magnetic saturation effects are fully considered. The magnetic field intensity distribution function of the eddy current reaction magnetic field is derived for the first time based on Ampere circuital theorem. Considering the local magnetic saturation and skin effect, a novel double-iteration algorithm based on the conservation principle of magnetic pressure drop is applied to obtain the transient air-gap flux density distribution, and then the brake torque expression is obtained. The finite element method (FEM) and experimental results show that the proposed method is feasible and effective. The new model is easy to program and can be easily used in the initial design and optimization of LC-ECB.

Enhanced robust diagnosis of multiple‐type demagnetisation fault for permanent magnet synchronous motor based on D‐axis magnetic network model using magnetic field reconstruction

AbstractDemagnetisation fault (DF) is a common rotor fault in the permanent magnet synchronous motor (PMSM). DF can cause obvious changes in the magnetic field of PMSMs. As a result, previous DF diagnosis methods mainly depends on magnetic field analysis. However, conventional analysis methods based on the magnetic potential‐permeability method, sub‐domain method and magnetic equivalent circuit method are not suitable for DF condition. In addition, DF diagnosis is further complicated by various operating conditions. To address these issues, a robust DF diagnosis method is proposed for PMSM based on d‐axis magnetic network model using magnetic field reconstruction. The proposed fault diagnosis method employs magnetic field reconstruction to obtain the radial air‐gap flux density under the open‐circuit condition. Subsequently, a d‐axis magnetic network is established to solve the demagnetisation coefficient matrix in the DF state. Finally, the effectiveness of the proposed method is validated through simulations and experiments. Both results demonstrate that the proposed method can accurately recognise uniform DF and partial DF with multiple demagnetised permanent magnets, exhibiting great robustness against different operating conditions.

Synergistic Optimization Design Method to Improve the Overload Capacity and Efficiency of Canned Permanent Magnet Synchronous Motor for Vacuum Pump

The efficiency and overload capacity are crucial performance factors during the design of the canned permanent magnet synchronous motors (CPMSMs) intended for driving vacuum pumps, due to their unique operational characteristics. The conventional multi-objective optimization design method is not suitable for the CPMSM due to the need to carefully consider additional influential factors, including the flat structure, eddy current losses in the cans, can thickness, and can material. To enhance the efficiency and overload capacity of the CPMSM, this paper introduces a synergistic optimization design approach that integrates the equivalent magnetic circuit method and the finite element method. A design example of a 1.5 kW CPMSM is presented, and experiments are performed to verify the effectiveness of the proposed method.

Multi‐Objective Optimization and Analysis of Asymmetric Hybrid‐Magnet Offset Motor for Electric Vehicles

Aiming at the high cost of permanent magnet synchronous motor and the reduction of motor output performance caused by high cogging torque and torque ripple, an asymmetric hybrid‐magnet offset motor is proposed. Based on the winding function theory and the equivalent magnetic circuit method, the expressions of stator and rotor magnetic potential are derived respectively, and the analytical model of torque ripple is established by combining with the Lorentz force law. By using the magnetic pole offset method, the phase offset model of the cogging torque is established, and the analytical expressions of the cogging torque and the magnetic pole offset angle are derived. The results of the simulation and experiments show that the asymmetric hybrid‐magnet offset motor has lower no‐load back‐EMF harmonic content and rare‐earth material ratio than the traditional permanent magnet motor, and its performance in terms of the cogging torque and the torque ripple is better than that of the traditional permanent magnet motor. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

A Planar Electromagnetic Actuator With Passive Adsorption for CubeSats Transport in a Weightless Environment

A planar electromagnetic actuator (PEA) with passive adsorption is proposed to transport multiple miniature satellites (CubeSats) in a weightless environment. It can realize reliable mover adsorption to the track and fast 2-Dof translational motion, even under the interference of external acceleration. Compared with the conventional layout of permanent magnets (PMs), the PEA with the structure of Halbach array can achieve higher force density. The magnetic equivalent circuits (MEC) method is applied to reveal the mechanism of electromagnetic performance improvement. An accurate electromagnetic force model is developed by combining the MEC and mirror magnetic charge methods to consider the positive effects of yokes on the PM operating point and airgap magnetic field distribution for PEAs with large airgaps. The influence of main structural parameters on adsorption and driving performances is analyzed. A kinetic model is derived to predict the mover velocity. A PEA prototype has been manufactured and tested to experimentally validate the improved models, electromagnetic performance, and motion characteristics.

The Influence of Speed Ratio on the Nonlinear Dynamics of a Magnetic Suspended Dual-Rotor System with a Fixed-Point Rubbing

Magnetic suspended dual-rotor systems (MSDS) provide the potential to significantly improve the performance of aero-engines by eliminating the wear and lubrication system, and solve vibration control issues effectively. However, the nonlinear dynamics of MSDS with rubbing is rarely investigated. In this work, the nonlinear support characteristics of active magnetic bearings (AMBs) are described by the equivalent magnetic circuit method, the impact force is characterized by the Lankarani–Nikravesh model, and the nonlinear dynamic model is established using the finite element method. On this basis, the influence of speed ratio on the nonlinear dynamics is investigated. Simulation results show that the fundamental sub-synchronous vibration of period n is the dominant motion of MSDS, where n is determined by the speed ratio. The frequency components of sub-synchronous vibrations of period k are integer multiples of the minimum dimensionless frequency component 1/k, where k is a positive integral multiple of n. Quasi-periodic and chaotic vibrations are more likely to occur near critical speeds, and their main frequency components can be expressed as a variety of combined frequency components of the rotating frequency difference and its fractional frequency. To reduce the severity of fluctuating stresses stemming from complicated non-synchronous vibrations, speed ratios, corresponding to smaller n and AMB control parameters attenuating vibration amplitude or avoiding critical speeds, are suggested.

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

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

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

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

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

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

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

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