Magnetic Equivalent Circuit Research Articles

Investigation of a Novel Consequent-Pole Flux-Intensifying Memory Machine

This paper mainly focuses on the investigation and analysis of a novel consequent-pole flux-intensifying memory machine (CP-FIMM). The proposed CP-FIMM exhibits the advantages of a satisfactory flux-regulation range, reduction of the required magnetizing current magnitude, as well as similar torque with much less PM utilization compared to its conventional counterpart. By designing the q-axis flux barriers, the flux-intensifying structure can be realized to enhance the demagnetization withstand capability of the CP-FIMM. The machine topology and operating principle are described. Moreover, the equivalent magnetic circuit model is developed to highlight the performance improvement of the proposed CP-FIMM. Finally, the electromagnetic performance of the proposed CP-FIMM is compared with that of a benchmark conventional FIMM by 2-D and 3-D finite element analysis.

Effect of Flux Barriers on Short-Circuit Current and Braking Torque in Dual Three-Phase PM Machine

This paper investigates the influence of stator flux barriers on the short-circuit current (SCC) and braking torque of a dual three-phase permanent magnet (PM) synchronous machine. By optimizing the position and width of stator flux barriers, the machine has a lower amplitude of short-circuit current and brake torque when the short-circuit fault occurs. First, the SCC and braking torque are analytically derived. The amplitude of SCC is proportional to the PM flux linkage and inversely proportional to the inductance. The braking torque is proportional to the square of the PM flux linkage and inversely proportional to inductance. Then, the equivalent magnetic circuit model of flux barriers is established. Its influence on flux linkage and inductance is analyzed, and the improvement mechanism of output torque and fault tolerance is revealed. Furthermore, the flux barriers’ width is optimized by finite element analysis and the theoretical analysis is verified. Finally, experiments on the prototype machine are carried out for the validation.

A Novel Hybrid Analytical Model of Active Magnetic Bearing Considering Rotor Eccentricity and Local Saturation Effect

To facilitate the active magnetic bearing (AMB) design and analysis, an accurate and fast model that considers both rotor eccentricity and the saturation effect is necessary. In this article, a novel hybrid analytical model (HAM) for effective calculation of the magnetic field of the AMB is proposed. Eccentricity and local saturation are considered in the proposed HAM. In the proposed HAM, the stator and rotor are modeled by elementary subdomains (ESDs) and the air-gap is modeled by magnetic equivalent circuit (MEC). Direct coupling between the solutions in the ESD regions with MEC completes the whole model matrices. Compared to the existing literature, the proposed model considers both the rotor eccentricity and material nonlinearity. The effectiveness and accuracy of the proposed HAM are validated by both the finite element model and experimental results. The results show that the proposed HAM can accurately predict the magnetic quantities of the AMB.

A novel methodology for accurate estimation of magnetic permeability of magnetorheological elastomers

Identifying a reliable nonlinear B-H curve for magneto-rheological elastomers (MREs) is a fundamental necessity for modeling and optimal design of MRE-based devices, particularly in the initial design stages. The main contribution of this study is to propose a novel methodology for the accurate estimation of magnetic permeability and nonlinear B-H curve for MREs. The proposed method involved three series of simple experiments employing an air gap electromagnet, which required only a Gauss meter to measure air gap magnetic flux density, together with formulation of an equivalent magnetic circuit (EMC). The data acquired from the first two series of experiments were used to characterize the relative magnetic permeability of MREs, while that obtained from the third series of experiments permitted an accurate estimation of the nonlinear B-H curve. For this purpose, isotropic MRE samples with 30% particle volume fraction were fabricated. Results showed that the relative magnetic permeability of MREs decreases with increasing magnetic field. The effectiveness of the proposed methodology for estimating magnetic permeability was demonstrated by comparing with that obtained from a VSM device, which revealed relatively low prediction error of 4.1%. The proposed method could thus be utilized for characterization of nonlinear magnetic permeability of MREs with minimal complexity and cost. The proposed methodology, unlike the VSM devices, could predict magnetic properties of MRE under tension/compression loadings.

Novel Axial Flux-Switching Permanent Magnet Machine for High-Speed Applications

Conventional high-speed flux-switching machines have either a high fundamental frequency or more even harmonics. This paper proposes a novel six-slot four-pole axial flux-switching permanent magnet machine for high-speed applications. The machine, consisting of two radially distributed stators and one rotor, can effectively eliminate even harmonics in the flux linkage. First, the structural parameters that affect the performance of the motor are determined by the equivalent magnetic circuit method, and the optimal structural parameters of the motor are obtained by simulation optimization. Then, through finite element analysis, the three-dimensional model of the proposed machine is built, and the static electromagnetic characteristics are analyzed, including magnetic field distribution, flux linkage, back-electromotive force, cogging torque, and efficiency. The simulation results show that the total harmonic distortion of the flux linkage and back-electromotive force waveforms of the proposed novel machine is 2.2% and 9.8% respectively. The cogging torque of the optimal model is only 9 N.

Analytical modelling of one cage rotor induction motor for electric submersible pumps

A new hybrid analytical model (HAM) based on conformal mapping (CM) method and magnetic equivalent circuit (MEC) model is presented in this paper for electromagnetic modelling of cage rotor induction motors (CRIMs) used in electric submersible pumps (ESPs). For every operating point, the iron parts are modelled with a non-linear MEC model to calculate the equivalent virtual currents, which represent the influence of magneto motive force (MMF) drops and MMF sources in stator and rotor cores. The effects of the equivalent virtual currents on the air-gap magnetic field are then considered using the CM method and Hague's solution. This approach for calculating the air-gap field is also used to prepare a 3-D lookup table (3-D LUT) for each element of inductance matrix and derivative of inductance matrix in terms of rotor position. These LUTs are then used for transient modelling and analysis of CRIM under no-load and loading conditions. The accuracy of proposed HAM is validated by comparing the results obtained through HAM with corresponding results obtained from finite element method and experiment set-up.

Magnetic Equivalent Circuit Modelling of Synchronous Reluctance Motors

This paper proposes a modelling technique for Synchronous Reluctance Motors (SynRMs) based on a generalized Magnetic Equivalent Circuit (MEC). The proposed model can be used in the design of any number of stator teeth, rotor poles, and rotor barrier combinations. This technique allows elimination of infeasible machine solutions during the initial machine sizing stage, resulting in a lower cohort of feasible machine solutions that can be further optimized using finite element methods. Therefore, saturation effects, however, are not considered in the modelling. This paper focuses on modelling a generic structure of the SynRM in modular form and is then extended to a full SynRM model. The proposed model can be iteratively used for any symmetrical rotor pole and stator teeth combination. The developed technique is applied to model a 4-pole, 36 slot SynRM as an example, and the implemented model is executed following a time stepping strategy. The motor characteristics such as flux distribution and torque of the developed SynRM model is compared with finite elemental analysis (FEA) simulation results.

Equivalent magnetic circuit method of estimating iron losses in induction motor spindles

The iron losses in the motor of motorized spindles have a significant effect on their heat generation, thermal deformation, and machining accuracy. The equivalent magnetic circuit (EMC) method for estimating iron losses in the spindle motor is proposed, where the magnetic flux density distribution of any cross section inside the spindle motor is assumed as a uniform one. A mechanical loss separation method of no load running combined with a sudden loss of power supply is also proposed. The EMC method is verified by prototype experiment and a different analysis method comparison. The EMC does not need to solve complex electromagnetic fields, and to do 2D or 3D eddy current analysis and the corresponding post-processing. There is only need to perform a simple magnetic circuit calculation. Therefore, it can realize a fast analysis and prediction. The proposed mechanical loss separation method requires only one prototype during a whole testing process. There is no need for any other same prototype and a coupling device. It is simpler, and can eliminate the braking torque and electromagnetic losses of the spindle motor.

A Displacement Sensing Method Based on Permanent Magnet and Magnetic Flux Measurement.

This paper proposes a displacement sensing method based on magnetic flux measurement. A bridge-structured magnetic circuit, formed by permanent magnets and two ferromagnetic cores, is designed and discussed. The analyses of the equivalent magnetic circuit and three-dimensional finite element simulations showed that the magnetic flux density changes linearly with the reciprocal of the sum of a constant and the displacement. A prototype sensor of the bridge structure is developed that consists of four permanent magnets as excitation, a Hall sensor as reception, and two ferromagnetic cores as the connection. Experiments have validated the feasibility of this method. The measured results show a good linearity between the sensor’s output and the reciprocal of the sum of a constant and the displacement, with a correlation coefficient greater than 0.9995 across different measurement ranges. Additionally, the measured results significantly indicate that the proposed sensor is compatible with different ferromagnetic materials with a worst-case error of less than 5%. The proposed sensor has the advantages of low cost and good linearity; however, the test object is limited to ferromagnetic materials.

Reluctance Mesh-Based Magnetic Equivalent Circuit Modeling of Switched Reluctance Motors for Static and Dynamic Analysis

Designing a switched reluctance machine (SRM) is an iterative process. Sizing of the motor is one of the fundamental steps where the main geometry parameters are determined to achieve the performance requirements. Usually, finite element method (FEM) is employed in all design stages, which might require extensive computational burden. The magnetic equivalent circuit (MEC) method is an alternative for typical FEM. There are two approaches for the MEC method: conventional MEC method and reluctance mesh-based MEC method. The conventional MEC method can be challenging when modifying the motor geometry while conducting dynamic analysis with current control. This article presents a reluctance mesh-based MEC model for SRMs that can overcome those challenges. Reluctance mesh-based MEC models are developed for three-phase 6/4, 6/16, 12/8 SRMs and four-phase 8/6, 8/10, and 16/12 SRMs. The models calculate the static and dynamic characteristics of the considered SRMs. The static and dynamic characteristics are compared with the results obtained from FEM and experimental tests.

Integrated-Induction-Based Hybrid Excitation Brushless DC Generator With Consequent-Pole Rotor

This article proposes a novel hybrid excitation brushless dc generator (HEBDCG), in which the main generator part and the induced excitation part share one set of the stator/rotor core (namely integrated-induction-based HEBDCG, i.e., II-HEBDCG). Hence the auxiliary magnetic path and additional airgap do not exist and then high space utilization are achieved. Moreover, the consequent-pole rotor featuring permanent magnet (PM) pole-iron pole-iron pole-iron pole (N-I-I-I) is adopted to utilize the high permeability of iron poles, which is favorable to the flux and voltage regulation. The selection rules of pole and slot combination are given by comprehensively considering the unbalance magnetic force and the relationship of the electrical coupling between the main generator part and the induction excitation part. Then, the principle of flux regulation is revealed by equivalent magnetic circuit, and validated by finite element (FE) analysis. In addition, the influences of key factors including the distribution of induction winding on the performance are discussed, and both the no-load regulation, load characteristics and armature reaction are investigated. Furthermore, the proposed II-HEBDCG is compared to the conventional three-stage brushless dc generator (TSBDCG). It is shown that the proposed II-HEBDCG achieves steady excitation current and flexible regulation of output voltage, and obtains both the higher output power and efficiency than the TSBDCG. Finally, a prototype is manufactured and measured to validate these analyses.

Analytical Model for No-Load Electromagnetic Performance Prediction of V-Shape IPM Motors Considering Nonlinearity of Magnetic Bridges

This paper proposes a novel analytical model which combines subdomain method and magnetic equivalent circuit (MEC) method to predict the no-load performance of V-shape interior permanent magnet (IPM) motors with any slot-pole combination considering the nonlinearity of magnetic bridges (MBs). The V-shape magnets are equivalent to the form of distribution along radial and tangential directions, and the motor is divided into two corresponding structures to facilitate the establishment of subdomains. To consider the saturation of MBs, the MEC method are employed to obtain the permeability of MBs to establish the boundary conditions. The no-load magnetic field of slotless motor can be obtained by solving the equations established by boundary conditions, and the conformal mapping is used to consider the effect of slotting. The proposed model can be used to calculate the no-load magnetic field, back electromotive force, and cogging torque of IPM motor. The results are verified by finite element analysis (FEA) and experiments, which confirms the validity of the model for facilitating the motor design and optimization. Compared with FEA, the proposed method has the advantages of faster modeling, shorter time consuming and meanwhile achieves the approximate accuracy. In addition, U-shape motors with MBs can also be analyzed by this model.

Calculation Model of Armature Reaction Magnetic Field of Interior Permanent Magnet Synchronous Motor With Segmented Skewed Poles

In an interior permanent magnet synchronous motor (IPMSM) with segmented skewed poles, the armature reaction magnetic field (AR-MF) changes nonlinearly due to the saturation of the rotor magnetic barrier. Meanwhile, this varies under different excitation currents. As a result, it is difficult to be calculated by means of analytical methods. In this paper, the calculation model of AR-MF of IPMSM is first established by vector superposition method, without considering the saturation effect of rotor and the slotting effect of stator. In the second step, the virtual magnetic field of the rotor is introduced to quantitatively calculate the influence of local inhomogeneous saturation on the AR-MF. The latter is derived by combining both the subdomain method and equivalent magnetic circuit method. The complex relative permeance is also introduced to establish the AR-MF accounting for the stator slotting effect. To validate the AR-MF calculation method proposed, an 8-pole 48-slot IPMSM with segmented skewed poles is considered as a case study, showing a comparison by both with finite element (FE) results and the electromagnetic torque measured on a test bench. The model proposed in this paper shows high accuracy and fast computation with respect to FE analysis.

Modeling and designing a hybrid reluctance actuator for fast-steering mirror

The actuator is a primary component of the fast-steering mirror (FSM), and its quality directly determines the performance of FSM. To achieve high compactness, high efficiency, large output torque, and effective linearity, a hybrid reluctance actuator (NHRA) for FSM was designed. To obtain a high-force density and small flux leakage, four permanent magnets (PMs) were designed on the side of the armature, which improves the linearity of the actuator by generating a bias flux. Meanwhile, to obtain the maximum output torque for a limited size, the structural model of the actuator was established in ANSYS Maxwell, and all structural parameters were optimized. In addition, an analytical model of the actuator was established via the equivalent magnetic circuit method. To improve the modeling accuracy, both PM and coil flux leakages were considered. The theoretical and simulation results were insignificant in agreement, and both showed the output torque of this actuator to be approximately twice that of a state-of-the-art actuator under the same volume, simultaneously improving the linearity.

Modeling, design and control of normal-stressed electromagnetic actuated fast tool servos

The normal-stressed electromagnetic actuated fast tool servo (FTS) plays an important role in modern ultra-precision manufacturing due to its high actuation force density and fast dynamics response. In order to promote the design and control of the normal-stressed electromagnetic actuated FTS, this paper proposes a comprehensive dynamics model based on the principles of magnetic equivalent circuits, which can be described as a Hammerstein-like structure. The electromagnetic phenomena, including hysteresis, magnetic saturation, and eddy currents, as well as the coupling between electromagnetic and mechanical dynamics are explicitly represented in the model. Based on a simplified version of this model, an integrated optimal design method for simultaneously determining actuator and mechanism parameters of the FTS is developed with full consideration of various practical physical limitations, which is then systematically verified through the finite element analysis (FEA). Afterwards, the comprehensive model of the assembled FTS prototype is identified and experimentally verified with a two-step identification strategy. Finally, a dual-loop control scheme is employed to improve tracking accuracy while suppressing the hysteresis and lightly damped resonance. Both open-loop and closed-loop performance of the FTS prototype validate the feasibility and effectiveness of the proposed model and methods.

Analytical modeling of permanent magnet linear eddy current brake using magnetic equivalent circuit method

In order to predict the performance of a permanent magnet linear braking (ECB) with cylindrical structure, an analytical model is established in this paper. The model is based on the magnetic equivalent circuit (MEC) method with the consideration of the often ignored magnetic saturation in pole shoe. The influence of induced eddy current is taken into account by introducing the magnetomotive force (MMF) in the model. To obtain braking force, a simple method for approximating the cross-section of the electric field with mean value method is proposed. The proposed model that can predict the braking force performance of ECB in a wide range of structural dimensions is obtained through referring to a small number of finite element models. A prototype test is carried out. The validity of the proposed method is verified through experiment and FEM. Results show that the braking force predicted by the presented method are in good agreement with experimental results and FEM results under different design parameters. The proposed model can accurately represent the variation trend of braking force and critical speed with design parameters.

A new hybrid analytical model for electromagnetic analysis of wound rotor induction motors

AbstractAccurate modeling of slotting and magnetic saturation effects has been two main challenges for analytical modeling of electric machines. In this article, first, different techniques such as sub‐domain (S‐D) model, winding function theory, magnetic equivalent circuit (MEC) model, and conformal mapping (CM) method are introduced to analytical model and analysis of electric machines. These techniques are also compared in terms of their accuracy, and computational complexity. Second, with respect to the comparison results, a new hybrid analytical model is presented for electromagnetic modeling of wound rotor induction motors, which consider the modeling accuracy of slotting and magnetic saturation effect, simultaneously. In this way, the air‐gap region is modeled by using S‐D model, and the iron parts are considered by using MEC model assisted by CMs. In final, the analytical results are verified by comparing with corresponding results obtained through finite element method and experiment set‐up.

Performance analysis of linear permanent magnet Vernier machine using mixed subdomain and magnetic equivalent circuit techniques including end‐effect

Performance analysis of a linear permanent magnet Vernier machine (LPMVM), which has a complex structure, is mostly based on the finite element methods, while for its optimisation or sensitivity analysis a quick mathematical technique is desirable. This paper introduces an LPMVM and its principles of operation. Then, a mixed subdomain and magnetic equivalent circuit are applied to extract magnetic field equations in various parts of the machine, in which the end-effect in included. Besides, the electromotive force, thrust force, normal force and electric equivalent circuit are determined. An LPMVM was prototyped and tested to verify the accuracy of the proposed method.

A Performance Prediction Model for Permanent Magnet Eddy-Current Couplings Based on the Air-Gap Magnetic Field Distribution

In this article, a clear analytical model for predicting the performance of permanent magnet (PM) eddy current couplers is proposed. The interaction of the reaction magnetic fields between adjacent eddy current rings was considered for the first time. Based on a magnetic equivalent circuit (MEC) and the Ampere circuital theorem, the accurate distribution of the air gap magnetic field under different slip velocities was deduced in a 2-D model, and the analytical expression of the transmission torque was obtained. 3-D effects were also taken into account to calibrate the model. The validity of the analytical model was verified by comparison with results from the 3-D finite element method (FEM). The comparison shows that the analytical model can accurately predict the magnetic field distribution and transmission torque over a wide range of slip velocity variations. This model can greatly reduce the number of calculations required and save time, and it is suitable for the preliminary design and optimization of PM eddy current couplers.

A Novel Asymmetric-PM Hybrid-Magnetic-Circuit Variable Flux Memory Machine for Traction Applications

In this paper, a novel asymmetric-permanent- magnet hybrid-magnetic-circuit variable flux memory machine (AH-VFMM) is proposed. The low coercive force (LCF) permanent magnets (PMs) are located on one biased side of the hybrid magnetic circuit branch, forming an AH configuration. Compared to its conventional symmetric-PM hybrid-magnetic-circuit (SH) counterpart, the proposed design benefits from the reduced usage of high coercive force (HCF) rare-earth magnet, alleviating the magnetic saturation to improve the flux regulation (FR) range, while the excellent load demagnetization withstand (LDW) capability can be still maintained. The topology evolution and operating principle of the proposed machine are introduced and described, respectively. Then, based on the combination of the magnetic equivalent circuit (MEC) method and Schwarz-Christoffel (SC) transformation, a hybrid analytical model is established to quantitatively reveal the mechanism of FR range extension, and facilitate the initial design of the machine. The electromagnetic characteristics of the proposed machine under different magnetization states (MSs) are investigated and compared with those of the conventional SH counterpart. Finally, an AH-VFMM prototype is manufactured, and the experimental measurements are carried out to verify the validity of the proposed design.