Magnetic Equivalent Circuit Model Research Articles

Analytical Analysis of an Adjustable-Speed Permanent Magnet Eddy-Current Coupling With a Non-Rotary Mechanical Flux Adjuster

This paper proposes an adjustable-speed permanent magnet eddy-current coupling with a non-rotary mechanical flux adjuster (MFA) to regulate the speeds of large pump and fan for energy saving. The slip speed of the proposed coupling can be adjusted by shifting MFA along the axial direction. The structural feature and operation principle of the coupling are illustrated and addressed. A magnetic equivalent circuit model is established for analyzing the electromagnetic characteristics of the coupling efficiently. The air-gap magnetic fields, eddy-current densities, and torque–slip characteristics are investigated under different shifting distances of MFA, which reveals the fairly good torque regulation effects. The torque regulation range reaches to about 90% of the maximum torque, which indicates that the coupling can achieve a large speed regulation range by using the relatively simple approach.

Magnetic Equivalent Circuit Model Considering the Overhang Structure of an Interior Permanent-Magnet Machine

Overhang is a useful structure for increasing the torque and power densities of permanent-magnet (PM) machines without expansion of the machine space. A 3-D finite-element method (FEM) is needed to evaluate the performances of PM machines with an overhang structure because the overhang structure results in non-uniform magnetic flux distributions in the axial direction. However, it is computationally expensive, especially in the early design stage. In this paper, we propose a magnetic equivalent circuit (MEC) model considering the overhang effects of interior PM (IPM) machines. With the proposed MEC, the performances of IPM machines with an overhang structure were precisely calculated and the computational time was significantly reduced. The proposed MEC was verified by the 3-D FEM.

Flux Characteristics Analysis of a Single-Phase Tubular Switched Reluctance Linear Launcher Based on 3-D Magnetic Equivalent Circuit

This paper calculates the flux characteristic of a single-phase tubular switched reluctance linear launcher (TSRLL) with 3-D magnetic equivalent circuit (MEC) method. First, the 3-D finite element (FE) model of the single-phase TSRLL is established in FLUX, which is the foundation of the 3-D MEC model. The single-phase TSRLL is divided into different parts, including the teeth of the stator, the yoke of the stator, air gap, the teeth of the mover, and the yoke of the mover. The flux linkage at different mover positions and different currents is calculated with the proposed 3-D MEC model. Compared with the 3-D finite-element analysis (FEA) results, 3-D MEC model can obtain the flux characteristics of the single-phase TSRLL in a shorter time. The result of the 3-D MEC of the single-phase TSRLL is consistent with the 3-D FEM results and the experimental results, which validates the correctness of the proposed 3-D MEC model.

Flux Characteristics Analysis of a Single-Phase Tubular Permanent Magnet Linear Motor Based on 3-D Magnetic Equivalent Circuit

This paper gives a way to analyze the flux characteristic of a single-phase tubular permanent magnet linear motor (TPMLM) based on the 3-D magnetic equivalent circuit (MEC) method. By studying the flux tubes of this single-phase TPMLM with the finite-element analysis software—FLUX, a 3-D MEC model of this motor can be constructed, and the flux linkage of the single-phase TPMLM can also be calculated. The static and dynamic performances of the single-phase TPMLM calculated with the 3-D MEC model are compared with the 3-D finite-element model and experimental results, which verify the correctness of the proposed 3-D MEC model.

Design and Analysis of Dual-Electric-Excitation Hybrid Excitation Pulsed Alternator

Pulsed alternator (PA) is a kind of high-power pulsed supplies widely applied in the field of electromagnetic (EM) launch. Over the past decades, the self-excited air-core PA is widely studied, but it has the disadvantages of poor heat transfer and high electric field loss. The hybrid excitation PA combined with the advantages of electric excitation and permanent magnet excitation PA, and the output voltage of armature winding can be adjusted by the electric field current. This paper presents double-electric-excitation hybrid excitation compensated PA (DEE-HECPA). In order to improve the adjustable performance for the output voltage of HECPA, the rotor structure is changed and double excitation coils are used in PA. In this paper, the equivalent magnetic circuit model for hybrid excitation region is established and the air-gap flux density is calculated. The dimensional parameters are calculated by the special EM design method for PA, the characteristics of electric excitation are verified by finite-element analysis, and the characteristics of output current for DEE-HECPA are analyzed. The research results demonstrate that DEE-HECPA is a feasible topology for PA.

Direct Calculation Method of Fringing Field Reluctance in MEC Analysis for An Axisymmetric Solenoid Actuator

In this paper, a method is introduced to directly calculate the reluctances of fringing fields in analyzing a magnetic equivalent circuit model for an axisymmetric solenoid actuator including radial air gaps as well as axial air gaps. The introduced method was motivated by the possibility to calculate the cross section area depending on the radial position of an infinitesimal element when the infinitesimal element is defined to be integrated in the flux flow direction in a circular-arc straight-line model of an axisymmetric model. In this method, the reluctance of fringing field near an air gap can be calculated directly. For an objective model, the MEC analysis was performed using the introduced method and an iterative method. In the iterative method, the nonlinearity of the ferromagnetic material parts is resolved. In order to validate the introduced method, MEC analysis and FEA results are compared. And for validating the method in a view of computation also, an optimized design satisfying pre-defined constraints was searched using MEC analysis, and then the results of the MEC analysis using the introduced method and FEA results are compared for the searched design and the initial design.

Study of a Hybrid Excitation Synchronous Machine: Modeling and Experimental Validation

This paper deals with a parallel hybrid excitation synchronous machine (HESM). First, an expanded literature review of hybrid/double excitation machines is provided. Then, the structural topology and principles of operation of the hybrid excitation machine are examined. With the aim of validating the double excitation principle of the topology studied in this paper, the construction of a prototype is presented. In addition, both the 3D finite element method (FEM) and 3D magnetic equivalent circuit (MEC) model are used to model the machine. The flux control capability in the open-circuit condition and results of the developed models are validated by comparison with experimental measurements. The reluctance network model is created from a mesh of the studied domain. The meshing technique aims to combine advantages of finite element modeling, i.e., genericity and expert magnetic equivalent circuit models, i.e., reduced computation time. It also allows taking the non-linear characteristics of ferromagnetic materials into consideration. The machine prototype is tested to validate the predicted results. By confronting results from both modeling techniques and measurements, it is shown that the magnetic equivalent circuit model exhibits fairly accurate results when compared to the 3D finite element method with a gain in computation time.

Electromagnetic Characteristic of a Novel Linear Flux Switching Machine With Three-Dimensional Magnetic Circuit

The novel linear flux switching permanent magnet machine with a three-dimensional magnetic circuit is proposed in this paper, which is suitable for aerospace, missile launch, and other fields, benefiting from high thrust force and low cost. First, the basic structure and working principle of the machine are introduced. Second, the equivalent magnetic circuit model considering the variable reluctance is established and the equations are put forward for magnetic analysis. Third, the simplified finite element model is performed to calculate the field distribution, the air-gap flux density, the flux linkage of winding, and the back electromotive force. Finally, a prototype is constructed and experiments show a good agreement with analysis.

Modeling and Optimization of a Tubular Permanent Magnet Linear Motor Using Transverse-Flux Flux-Reversal Topology

In this paper, a novel tubular transverse-flux flux-reversal linear motor for long stroke applications is proposed. The proposed motor not only has the low-cost advantage of the existing flux-reversal permanent magnet (PM) linear motor (PMLM) by combining both PMs and armature winding in short primary, but also address the problem of complicated structure in conventional tubular PMLM by using the manufacturing process of the rotary motor. First, in order to reduce circumferential magnetic flux leakage and improve the utilization ratio of PM, the motor structure with the alternating distribution of double N poles and double S poles in the circumferential direction is designed, and the operating principle of the motor is presented. Then, the equivalent magnetic circuit model of the unit motor is established to derive the expressions of the back electromotive force (EMF) and the electromagnetic thrust. Third, the equivalent two-dimensional (2-D) finite-element method (FEM) is used to optimize the structural dimensions and analyze the static characteristics including the back EMF, the detent force, and the thrust. Meanwhile, the three-dimensional FEM verify the validity of the equivalent 2-D FEM. Finally, the experimental results verify the validity and the correctness of the topology structure and the design method of the motor.

Research on the Thrust Characteristics and Temperature Rise of Slot-less Tubular Linear Motor for Active Vehicle Suspension

This paper presents a Slot-less Tubular Permanent Magnet Linear Motor (ST-PMLM), which does not have the cogging structure in the stator. Meanwhile, its lateral stator core doesn’t split, so the motor only has longitudinal edge effect. Since the ST-PMLM is supposed to be used as the active damper for vehicle suspension system, this paper focus on two aspects: increasing the output thrust and restraining the thrust fluctuation of the motor. Firstly, the equivalent magnetic circuit model of the ST-PMLM is established. The influences of structural parameters, including the thickness of the magnetic pole, the length of the air gap, the thickness of primary iron core and the thickness of primary winding, on the air gap flux density and the output thrust are analyzed. Then, the distribution of the magnetic field at the end of the primary iron core is observed. Length compensation in the end of primary iron core is adopted in order to reduce the thrust fluctuation. Finally, the prototype of ST-PMLM is developed and the experiment test bench is built. Based on the no-load test of the prototype, the effectiveness of the primary core length compensation in suppressing end effects and inhibiting fluctuations are verified.

Analytical Model of Torque-Prediction for a Novel Hybrid Rotor Permanent Magnet Machines

This paper presents an analytical method for predicting the electromagnetic performance in permanent magnet (PM) machine with the spoke-type rotor (STR) and a proposed hybrid rotor structure (HRS), respectively. The key of this method is to combine magnetic field analysis model (MFAM) with the magnetic equivalent circuit model. The influence of the irregular PM shape is considered by the segmentation calculation. To obtain the boundary condition in the MFAM, respectively, two equivalent methods on the rotor side are proposed. In the STR, the average flux density of the rotor core outer-surface is calculated to solve the Laplace's equation with considering for the rotor core outer-surface eccentric. In the HRS, based on the Thevenin's theorem, the equivalent parameters of PM remanence BreB and thickness hpme are obtained as a given condition, which can be utilized to compute the air-gap flux density by conventional classic magnetic field analysis model of surface-mounted PMs with air-gap region. Finally, the proposed analytical models are verified by the finite element analysis (FEA) with comparisons of the air-gap flux density, flux linkage, back-EMF and electromagnetic torque, respectively. Furthermore, the performance that the machine with the proposed hybrid structure rotor can improve the torque density as explained.

Novel Analytical Method for Overhang Effects in Surface-Mounted Permanent-Magnet Machines

The torque and power densities of surface-mounted permanent-magnet (SPM) machines can be improved significantly using an overhang structure. However, it is difficult to analyze and design SPM machines with overhang because a 3D finite-element method (FEM) that uses high computation time is required to consider the overhang effects accurately. To reduce the computation time significantly, we propose an analytical method in which a magnetic equivalent circuit (MEC) model and an analytical solution (AS) of the Laplace and Poisson equations are combined. This method can accurately estimate the performances of SPM machines with overhang as well as significantly reduce the computation time compared with that required for the 3D FEM. The accuracy and generality of the proposed method were verified by comparison with the 3D FEM in different cases.

Comparison of three-pole AMB and HMB for magnetic suspended molecular pump

Molecular pumps have been widely used in the vacuum metallurgy, coating, semiconductor manufacturing and many other fields in which the high vacuum, ultra-clean environment is needed. The application of magnetic bearings can bring many advantages for molecular pump, such as eliminating the friction, decreasing the power loss, lowering the maintenance costs, and increasing the rotating speed and service life. Besides, the magnetic bearings can fundamentally solve the vacuum chamber pollution problem which is caused by the backflow of lubrication oil steam. The three-pole magnetic bearings are the simplest structure of radial magnetic bearings and can be driven by three-phase converter which has the advantages of low costs, small volume and low power loss. In this paper, the performance of the three-pole active magnetic bearing (AMB) and hybrid magnetic bearing (HMB) are compared based on radial force–current characteristics analysis. Firstly, the mathematical model of three-pole AMB and HMB is built by equivalent magnetic circuit model, and the radial force–current characteristics are analyzed. Then, simulation by the three-dimensional (3D) finite element method (FEM) is performed. Finally, the experiment is conducted. The FEM results are consistent with the analytical results, showing that the nonlinearity and coupling of three-pole HMB are lower than three-pole AMB. The reason of causing nonlinearity and coupling is also discussed.

Design of an Axial-Flux PM-Assisted Claw-Pole Generator Based on an Equivalent Magnetic Circuit Model

An axial-flux permanent-magnet (PM)-assisted claw-pole generator (APCG) is designed based on an equivalent magnetic circuit model (EMCM). It is designed for generating power in vehicle with the merits of high power density, no brush, and wide airgap flux density modulation range. This paper mainly focuses on establishing the EMCM of the APCG and designing a set of optimal structure parameters. First, the topology and operation principle of the APCG are introduced in detail, including material, fabrication, and magnetic flux distribution. Second, the magnetic circuits in claw poles are simplified and the relationships among the key parameters are discussed. Finally, based on the simplified model and the relationships among the key parameters, the EMCMs of current and PM excitation are established, respectively. According to the EMCM, a scheme of a 4 kW APCG is carried out. Comprehensive investigations demonstrate that the EMCM is time-saving and relatively accurate when compared with a finite element method.

A Quasi-Three-Dimensional Magnetic Equivalent Circuit Model of a Double-Sided Axial Flux Permanent Magnet Machine Considering Local Saturation

This paper presents a quasi-three-dimensional (3-D) nonlinear magnetic equivalent circuit (MEC) model for double-sided axial flux permanent magnet machines (AFPMMs) with fractional slot concentrated windings. The proposed model can take into account not only the local magnetic saturation effect but also the 3-D flux distribution. A coupled variable permeance element is proposed in airgap modeling that captures both axial and circumferential airgap flux densities. With the help of the coupled variable permeance element, the transient magnetic field is considered by the time varying connection of the airgap and the rotor. The proposed model can be used to predict the performance of AFPMMs, including the 3-D distribution of no-load and armature airgap flux densities, no-load back electromotive force, and electromagnetic torque. In order to verify the reliability of the MEC model, two AFPMM prototypes are taken as examples, and the accuracy is verified by comparing the calculated parameters of the MEC model with the finite element analysis and experimental results. Finally, the effect of local saturation on the performances of AFPMMs is investigated.

The characteristics analysis and cogging torque optimization of a surface-interior permanent magnet synchronous motor

This paper proposes optimal stator skewed slot analytical method for cogging torque reduction in surface-interior permanent magnet synchronous motor(SIPMSM) and analyzes the characteristics of SIPMSM. The series-parallel equivalent magnetic circuit models(EMCMs) of SIPMSM is built based on the characteristics of magnetic circuits, which is used to design the basic electromagnetic parameters of SIPMSM. Analytical expressions of cogging torque are derived from applying analytical techniques. Stator skewed slot for cogging torque minimum is adopted, and the stator skewed slot pitch is confirmed based on the analytical expressions of the resultant cogging torque. The cogging torque, torque ripple, back electromotive force(back-EMF), power-angle characteristics, efficiency and power factor of SIPMSM are analyzed by establishing 3-dimensional finite element model(3-D-FED) of SIPMSM with stator skewed slot and straight slot. It is shown that the comprehensive performance of optimized SIPMSM is improved as confirmed by finite element analysis and analytical calculation results.

Performance Analysis of Novel Single-Phase Parallel Hybrid-Excited Flux-Switching Machine

To obtain magnetic field regulation capacity and reduce copper loss in the field winding, a single-phase parallel hybrid-excited flux-switching machine (PHEFSM) is investigated in this paper. Because the permanent magnet with tangential magnetization is fixed at the slot opening of the field winding slot, the yoke width of the field winding slot determines the magnetic field regulation capacity, and the saturation condition varies significantly with the field current. To accurately calculate the performance of PHEFSM, a nonlinear magnetic equivalent circuit model that considers the iron saturation is derived, and it is verified by the finite-element method. A composite rotor with two kinds of rotor core laminations is adopted to obtain self-starting capability. Two prototype machines with a classical rotor and a composite rotor are produced and tested to verify the conclusions.

Design and Optimization of Traction IPMSM With Asymmetrical Damper Bars for Integrated Charging Capability Using Evolutionary Algorithm

The 3-phase windings of interior permanent magnet synchronous machines (IPMSMs) used in electric vehicles (EVs) for traction can also be utilized for charging a battery. This integrated charging technology eliminates the on-board charger, leading to a significant reduction in the overall weight and cost of the EV. However, during integrated charging, the induced magnetic fields across the IPMSM windings are unbalanced, which could lead to addition of harmonic current components at the battery side, demagnetization, noise, and vibrations. This paper provides a novel design solution by implementing asymmetrical damper bars in the IPMSM rotor to mitigate unbalanced magnetic fields during integrated charging, and, thus, overcome the aforementioned issues. However, the bars introduced could affect the useful torque production of the machine during traction. Therefore, a magnetic equivalent circuit model based differential evolutionary algorithm is proposed and implemented to optimize the IPMSM rotor structure with dampers to achieve balanced magnetic fields during integrated charging operation and satisfactory traction performance. A comprehensive performance analysis of the optimally designed traction IPMSM equipped with integrated charging capability under both operating conditions is presented in this paper using finite element analysis.

Flux Characteristics Analysis of a Double-Sided Switched Reluctance Linear Machine Under the Asymmetric Air Gap

This paper analyzes the flux characteristics and normal force of the double-sided switched reluctance linear machine (SRLM) under the asymmetric air gap. The magnetic equivalent circuit (MEC) of the machine and the details of the flux paths configuration at six distinct mover positions under the asymmetric air gap are included. Then, six special mover position magnetization curves are calculated by solving the MEC with the method of Gauss–Seidel. The magnetic flux-linkage model and thrust model based on six distinct mover positions are established by analytical polynomial. Three-dimensional (3-D) finite-element method (FEM) simulation and the experimental study with the prototype hardware are carried out to validate the accuracy of the MEC model calculated for the flux linkage and normal force. The six distinct mover positions flux linkage and normal force calculated by the MEC are consistent with the 3-D FEM calculated data and experimental data. It indicates that the proposed method to calculate the flux linkage and the normal force is feasible and effective. The dynamic analysis is also conducted. The simulated phase current waveforms are also consistent with the experimental results. It indicates that the presented method can be used to simulate the phase current under the asymmetry air gap effectively. The normal force under different asymmetry rates is analyzed, which provides the theoretical basis for reducing the unbalanced force of the double-sided SRLM.

Demagnetization and Permanent-Magnet Minimization Analyses of Less-Rare-Earth Interior Permanent-Magnet Synchronous Machines Used for Electric Vehicles

Rare-earth permanent magnet synchronous machines (RE-PMSMs) are widely used in electric vehicles (EVs) due to their characteristics of high efficiency, high torque density and high power factor. While the dramatic price fluctuations of the rare-earth permanent magnets (PMs) have been restricted the application of RE-PMSMs. Hence, the less-rareearth interior permanent magnet synchronous machines (LRE-IPMSMs), which combine the features of high electromagnetic performance as well as low cost, have attracted increasing attention in recent years [1]. The anti-demagnetization ability of the LRE-IPMSMs is crucial to the machine safety [2]. In [3], the tapered flux barriers are adopted to improve the anti-demagnetization ability of the LRE-IPMSMs. In [4], a practical analytical approach is proposed to express the direct link between the PM thickness and the demagnetization limit. In addition, the PM minimization is also a significant issue for the LRE-IPMSMs as it is crucial to decrease the machine cost. In [5], an analytical procedure is proposed to reduce the PM quantity in the LRE-IPMSMs without affecting the torque versus speed performance. In this paper, the demagnetization equivalent magnetic circuit (EMC) model of the investigated LRE-IPMSM is established and the effects of structure parameters on the PM flux density are investigated. The PM minimization design of the LRE-IPMSMs is obtained on the premise of no side effect on the machine output toque and anti-demagnetization ability.