Magnetic Equivalent Circuit Research Articles

Calculation and Analysis of Eddy-Current Loss in Switched Reluctance Motor

The eddy-current loss of switched reluctance motor (SRM) is studied and analyzed in this paper. As a significant part of core loss, eddy-current loss has a great influence on motor performance. First, the average magnetic flux waveforms in every distributed region are derived from the magnetic equivalent circuit (MEC) model. Based on this, each harmonic of magnetic density is obtained by adopting the fast Fourier transform (FFT) method for further calculation. Then, each harmonic eddy-current loss is computed by sinusoidal magnetic density and the total eddy-current loss in different region of motor is derived by superposing of them. Therefore, the calculated results at different speed and conduction angles of each region are analyzed. Finally, the 3D finite element (FE) model is established in software FLUX and the experimental platform of the SRM prototype is built.

Comparative Analysis and Multi-Objective Optimization of Hybrid Permanent Magnet Motors Considering Different Saliency Characteristics

In this paper, a hybrid permanent magnet (HPM) motor with unique external q-axis flux barriers design is investigated. The equivalent magnetic circuit models of dq-axes are established. Based on this, the relationship between the design parameters of dq-axes and saliency characteristics is analyzed. By rational design of dq-axes parameters, the contrary saliency characteristics of HPM motors can be achieved. Then, two HPM motors with contrary saliency characteristics, namely positive saliency HPM (PS-HPM) motor and inverse saliency HPM (IS-HPM) motor are obtained by a multi-objective optimization method. To explore the impact of saliency characteristics on motor performance, the inductance, torque, anti-demagnetization characteristics of PS-HPM and IS-HPM motor are compared and discussed in detail. The comparison results indicate that the HPM motor with IS characteristic is a more competitive candidate for over-load operation due to better anti-demagnetization and overload capability.

Design Method Based On Asymmetry Factor of a Novel Three-Pole Magnetic Bearing

Asymmetric three-pole magnetic bearings (MBs) have higher power density and lower cost, compared to the symmetrical magnetic bearings with four poles or eight poles. This paper presents a new asymmetric three-pole structure with secondary air-gap for a radial magnetic bearing. Asymmetric permanent magnet (PM) biased MB can produce a static levitation force by bias magnetic flux. The secondary air-gap can ensure that the armature winding flux and PM flux are separated. The configures of the proposed MB are demonstrated. Analytical model with equivalent magnetic circuit method is deduced. The design method based on asymmetry factor is proposed for the three-pole MB (TPMB). The characteristics of the TPMB such as magnetic flux distribution and magnetic levitation force are analyzed by the finite-element method (FEM). The design values and FEM results are compared to validate the effectiveness of the presented design method.

Analytical calculation of leakage permeance of coreless axial flux permanent magnet generator

PurposeThis paper aims to study the relationship between leakage flux coefficient and the coreless axial magnetic field permanent magnet synchronous generator (AFPMSG) size and obtain the expressions of leakage flux coefficient.Design/methodology/approachIn this paper, a magnetic circuit model of coreless AFPMSG is proposed. Four kinds of leakage permeances of permanent magnet (PM) are considered, and the expression of no-load leakage flux coefficient is obtained. Solving the integral region of leakage permeances by generator size, which improves the accuracy of the solution.FindingsFinite element method and magnetic circuit method are used to obtain the no-load leakage flux coefficient and its variation trend charts with the change of pole arc coefficient, air gap length and PM thickness. The average errors of the two methods are 2.835%, 0.84% and 1.347%, respectively. At the same time, the results of single-phase electromotive force obtained by magnetic circuit method, three dimensional finite element method and prototype experiments are 19.36 V, 18.82 V and 19.09 V, respectively. The results show that the magnetic circuit method is correct in calculating the no-load leakage flux coefficient.Originality/valueThe special structure of the coreless AFPMSG is considered in the presented equivalent magnetic circuit and equations, and the equations in this paper can be applied for leakage flux evaluating purposes and initial parameter selection of the coreless AFPMSG.

Levitation Performances Analysis of a Novel Bearingless Switched Reluctance Motor

To deal with the coupling between the levitation force and torque, a new bearingless switched reluctance motor (BSRM) is presented in the paper, in which the torque flux is separated with the levitation flux. In addition, due to the low cost and power of the three-phase power converter, the radial levitation of the proposed BSRM is driven by a three-phase power converter. The structure of the proposed BSRM is first introduced. The mathematical models of radial levitation force are second established by employing equivalent magnetic circuit approach. Finally, the electromagnetic characteristics of the BSRM, such as flux field distribution, transient levitation force and force-current relationship are investigated through the MagNet 3D. The research results indicate that the novel structure has good performances.

Structural optimization and dynamic characteristics of the new type 3-degrees of freedom axial and radial hybrid magnetic bearing

A new type of three degrees of freedom axial-radial hybrid magnetic bearing (3-DOF ARHMB) with compact structure, shorter axial length and smaller volume is proposed for the flywheel energy storage system. The axial direction adopts the permanent magnet biased thrust bearing (PMB) made of soft magnetic composite materials (SMCs). In the radial direction, the laminated structure is used to reduce the eddy current, and the Halbach array is introduced to strengthen the magnetic density of the radial air gap. Firstly, the dynamic magnetic flux distribution of the 3-DOF ARHMB is analyzed by the finite element method (FEM). Based on the equivalent magnetic circuit method, the equivalent reluctance model with comprehensive consideration of eddy current effect and magnetic leakage effect is established, and then the frequency responses are analyzed. Secondly, a constraint model coupled with structural parameters, equivalent reluctance and magnetic leakage coefficient is established, and an adaptive particle swarm optimization algorithm (APSO) is used to optimize the bearing parameters. Finally, based on the equivalent reluctance model, the axial and radial force-current factor and force-displacement factor are derived, and the dynamic characteristics of bearings with different structures and materials are compared and analyzed. The results show that the new 3-DOF ARHMB made of SMCs can provide much larger and more stable magnetic force and larger bandwidth than that made of carbon steel materials, and has better dynamic characteristics under higher-frequency conditions, which can meet the industrial requirements of flywheel energy storage system.

Design and analysis of a novel AFPM with counter-rotation dual rotors based on non-linear magnetic circuit model

This paper presents a nonlinear iterative magnetic equivalent circuit (MEC) model for a novel counter-rotation dual-rotor axial flux permanent magnet synchronous machine (CRDR-AFPMSM). The proposed machine mainly consists of two rotors with opposite rotation directions, two sets of concentrated windings and a stator core sandwiched in between the two rotors. The model takes into account of the nonlinear characteristics of the saturable permeance in the stator core, and the permeance matrix is updated by an iterative procedure to accurately illustrate its nonlinear feature. The air gap flux density, back electromotive force (EMF) and torque are predicted by the model. Based on the nonlinear model, the thickness of the stator yoke is determined. All of the results obtained by the proposed model match with finite element analysis (FEA) results closely, thus the validity of the proposed MEC model is verified.

Magnetic Equivalent Circuit Model for Predicting Performance of 2DOF Wound Rotor Resolver

Expansion of Two Degrees of Freedom (2-DOF) electrical machines, for simultaneous linear-rotational motions, leads to employment of more than one sensor in closed-loop control systems. Such control systems can use two separate sensors for linear and rotational motions or employ a 2DOF sensor. The last, will result in lower volume and mass and also less complexity of the control system. Therefore, development and design optimization of 2DOF sensors can be an interesting research topic. However, 3-D geometry of such sensors needs 3-D finite element analysis. Due to high computational burden of 3-D time stepping finite element method (3-D TSFEM), it can hardly applicable in iterative design and optimization methods or performance evaluation of the sensor under fault conditions. Therefore, it is preferred to predict the accuracy of such linear-rotational sensors using an accurate, computationally fast method. Hence, in this paper, a comprehensive analytical model based on Magnetic Equivalent Circuit (MEC) is proposed for a helical motion resolver. The developed model can predict the performance of the sensor in health condition, as well as that under short circuit fault. Finally, the obtained results are verified using experimental measurements on the prototype helical motion resolver.

Structure principle and classification of Hybrid Excitation Motor

Hybrid excitation motor has two excitation sources: electric excitation and permanent magnet excitation. It has the advantages of convenient air gap magnetic field adjustment, high power density, wide voltage and speed adjustment range, etc. It has broad application prospects in industrial drive, new energy power generation and aerospace fields. Based on the magnetic adjustment principle of hybrid excitation motor, this paper summarizes the existing main classification methods and gives the equivalent magnetic circuit diagram. According to that coupling relationship between the permanent magnet magnetic circuit and the electric excitation magnetic circuit, the hybrid excitation motor is divided into series type, parallel type and parallel type, and further classified into stator main body type, rotor main body type and average type according to the placement position of the permanent magnet and the excitation winding. The typical motor structure and magnetic circuit characteristics are introduced.

Prediction of Power Generation Performance of Wound Rotor Synchronous Generator Using Nonlinear Magnetic Equivalent Circuit Method

This paper presents a nonlinear magnetic equivalent circuit method and an electromagnetic characteristic analysis and verification of a wound rotor synchronous generator (WRSG). The reluctance generated by the stator, rotor, and air gap is subdivided to form a reluctance construction. A nonlinear magnetic equivalent circuit (MEC) for the WRSG is constructed and solved by an iteration method. Moreover, to calculate the inductance of the generator, the reluctance circuit of the d−qaxis is constructed, and the inductance of the generator is obtained using the initial relative permeability of the material. Using the electromagnetic parameters obtained via the MEC method, the power generation characteristics of the generator are predicted. The results of this MEC method are also verified by comparing them with the finite element analysis (FEA) results and experimental results.

Multidomain modeling of nonlinear electromagnetic circuits using wave digital filters

SummaryAccurate models of electromagnetic systems can be derived by coupling electric and magnetic equivalent circuits together. The different nature of such physical domains constitutes a big challenge that puts a continuous strain on software simulators. To face this problem, a simulation approach based on Wave Digital Filters (WDFs) is proposed in this manuscript. The method is employed to solve nonlinear electromagnetic systems containing complex magnetic equivalent circuits while maintaining the modularity of the electric and magnetic subsystems. The nonlinearities can be locally handled, enabling the possibility to choose a dedicated model for each one of them. The proposed algorithm is a hierarchical generalization of the Scattering Iterative Method, which has shown, over the past few years, promising performance for the simulation of large nonlinear circuits. In addition, the method constitutes a further step towards the development of novel general‐purpose circuit simulators based on WDF principles. In a comparison with mainstream circuit simulation software, the proposed approach turns out to be considerably faster and thus particularly promising for parametric analyses of electromagnetic systems.

Performance Analysis of Variable Reluctance Linear Resolver by Parametric Magnetic Equivalent Circuit in Healthy and Faulty Cases

In this paper, the performance of Variable Reluctance Linear Resolver (VR-L-Resolver) with overlapping and non-overlapping windings is investigated by a novel parametric Magnetic Equivalent Circuit (MEC). The proposed MEC is capable of modeling various VR-L-Resolvers with arbitrary geometry and adjustable accuracy by changing the number of considered flux tubes. This technique is more suitable for modeling, analysis, and optimizing of the mentioned resolvers thanks to its flexibility and shorter processing time compared to the Finite Element Method (FEM). Moreover, it has the potential to model both healthy and faulty conditions by a unique model. Therefore, the resolver with two windings configurations under healthy and faulty cases are analyzed in this paper to study their performance. In faulty case, the inter-turn and asymmetrical air-gap faults are considered, and the position error is calculated for both cases. Finally, the MEC results are validated by 2D-FEM and experimental results to show the effectiveness of the proposed model. In general, applying a novel MEC-based modeling technique for the resolver sensitivity analysis, under mentioned faults and various windings configurations, is the main paper novelty.

Design optimization of tubular linear voice coil motors using swarm intelligence algorithms

This article presents design optimization based on swarm intelligence algorithms of a tubular linear voice coil motor (TLVCM). A magnetic equivalent circuit model is used, allowing a faster and more accurate evaluation of the initial design of the TLVCM. The design requirements are determined, and an initial design is formed based on the design requirements. The TLVCM design is considered a constrained optimization problem with complex linear and nonlinear constraints. The optimization process based on swarm intelligence algorithms is performed to find the optimal solution and improve the performance of the TLVCM. Finally, finite element analysis is used again to verify the optimized results, and different design outputs are compared. According to numerical experimental results, the average thrust is increased by 8.3% and the thrust ripple is reduced by 35.6%. Thus, a highly effective motor design meeting efficiency and performance requirements is achieved.

Simplified modeling of electromagnets for dynamic simulation of transient effects for a synchronous electric motor

AbstractThis study aims to show an approach for the dynamic simulation of a synchronous machine. The magnetic forces in the air gap are calculated efficiently using simplified approaches without neglecting important effects. For the modeling of the magnetic forces, an equivalent magnetic circuit is constructed in which the magnetic saturation and the leakage flux are taken into account and coupled with the electrical circuit at the end. The calculated magnetic forces are then passed to a mechanical model of the motor. Together with a predefinable load torque, the resulting motor rotation and the forces in the bearings are identified. The presented model is then investigated in a small example. This novel approach is intended to provide a method of calculating dynamically the forces transmitted from the shaft to the motor housing and to create the basis for evaluating electric motors for vibrations, noise, and harshness under varying loads and input voltages.

Modeling and analysis of variable reluctance resolver using magnetic equivalent circuit

Purpose The purpose of this paper is to propose a saturable model based on the magnetic equivalent circuit (MEC) for evaluating the electromagnetic performance of the variable area resolver. Design/methodology/approach The equivalent circuit is developed where three different reluctance types are used to calculate permeances based on geometrical approximations. The proposed model typically has two types of equations, including the magnetic and electrical equations. The magnetic and electrical equations are related to the resolver core and the windings, respectively. Applying the well-known trapezoidal method, the magnetic and electrical equations can be simultaneously solved. A nonlinearity of the magnetic equations, the algebraic equations system, which is obtained from Kirchhoff’s laws, should be solved by the Newton-Raphson technique in each step-time. Findings The flexible MEC model, in which the number of flux tubes in different parts of the resolver can be arbitrarily selected, is proposed to analyze the variable reluctance resolver. Besides, the design parameters such as geometrical dimensions, windings arrangement and a number of the rotor saliencies can be chosen as desired. To consider the effect of time harmonics, a new nonlinear function is used for the core magnetization. Furthermore, different winding layouts can be implemented in the model to take space harmonics into account. The model obtained results are compared with the finite element method in terms of accuracy and simulation time. Originality/value Generally, the accuracy of the predictions in the MEC method is dependent on the number of flux tubes; therefore, the flexibility of the proposed MEC model in its capability to choose the desired number of flux paths is the advantage of this work. Moreover, the proposed model can analyze both wound and saliency rotor resolvers by changing the design parameters.

Theoretical Computational Model for Cylindrical Permanent Magnet Coupling

Permanent magnet coupling is extensively studied owing to its economic efficiency and stability. In this study, a computational model for cylindrical permanent magnet coupling (CPMC) was designed using the magnetic field division method to divide an air gap magnetic field. An equivalent magnetic circuit model was also designed based on the equivalent magnetic circuit method. The novelty of this study is that both the skin effect and the working point of the permanent magnet are taken into consideration to obtain the magnetic circuit and induce eddy current characteristics of permanent magnet coupling. Furthermore, a computational model was obtained for the transmission torque of the CPMC based on the principles of Faraday’s and Ampere’s laws. Additionally, the accuracy of the model was verified using a finite element simulation model and a test bench.

Design and analysis of Lorentz magnetic bearing for magnetic suspended control and sensing gyroscope

To improve the control accuracy and output torque of magnetic suspend and control gyroscope, a Lorentz magnetic bearing with double second auxiliary air gap is proposed, and its mechanical structure is introduced. Frist, the structure and working principle of the Lorentz magnetic bearing with second air gap is introduced and the magnetic circuit model of the magnetic bearing is established by the equivalent magnetic circuit method. Second, on the basis of the circuit model, the maximum magnetic flux density of the winding area is analysed by finite element method. The fluctuation rate of magnetic flux density in winding area with double air gap scheme is 5.9%, and the maximum magnetic flux intensity at the winding coil can reach 0.462T. Finally, a bearing prototype is made, the theoretical calculation and finite element simulation results are verified by experiments.

Analysis of an IPMSM Hybrid Magnetic Equivalent Circuit

The most common type of electric vehicle traction motor is the interior permanent magnet synchronous motor (IPMSM). For IPMSM designs, engineers make use of the magnetic equivalent circuit method, which is a lumped constant circuit method, and the finite element method, which is a distributed constant circuit method. The magnetic equivalent circuit method is useful for simple design through fast and intuitive parameters, but it cannot derive the distribution of the magnetic field. The finite element method can derive an accurate magnetic field distribution, but it takes a long time and is difficult to use for analysis of intuitive design parameters. In this study, the magnetic equivalent circuit method and Carter’s coefficient were combined for rotor structure design and accurate identification and analysis of circuit constants. In this paper, this design method is called the hybrid magnetic equivalent circuit method. Intuitive design parameters are derived through this hybrid magnetic equivalent circuit method. The air gap flux density distribution according to rotor shape, no-load-induced voltage, and cogging torque was analyzed and compared to results of the finite element method. The proposed method was found to achieve a short solving time and acceptably accurate results.

Analytical magnetic field calculation for flat permanent-magnet linear machines with dual-rotor by using improved two-dimensional hybrid analytical method

PurposeThis paper aims to propose an improved two-dimensional hybrid analytical method (HAM) in Cartesian coordinates, based on the exact subdomain technique and the magnetic equivalent circuit (MEC).Design/methodology/approachThe magnetic field solution is obtained by coupling an exact analytical model (AM), calculated in all regions having relative permeability equal to unity, with a MEC, using a nodal-mesh formulation (i.e. Kirchhoff’s current law) in ferromagnetic regions. The AM and MEC are connected in both axes (x, y) of the (non-)periodicity direction (i.e. in the interface between the tooth regions and all its adjacent regions as slots and/or air-gap). To provide accuracy solutions, the current density distribution in slot regions is modeled by using Maxwell’s equations instead of the MEC characterized by an equivalent magnetomotive force (MMF) located in slots, teeth and yokes.FindingsIt is found that whatever the iron core relative permeability, the developed HAM gives accurate results for no- and on-load conditions. The finite-element analysis demonstrates excellent results of the developed technique.Originality/valueThe main objective of this paper is to make a direct coupling between the AM and MEC in both directions (i.e. x- and y-edges). The current density distribution is modeled by using Maxwell’s equations instead of the MEC and characterized by an MMF.

Load noise prediction of a power transformer

In this article, we propose a new regression equation to predict the noise of a power transformer based on the winding vibration under a loading condition. A regression between load noises and tank vibrations for multiple transformers with different rated powers was confirmed through measurements and regression analysis. A regression equation for load noise and winding vibration was derived considering the fact that the winding vibration level is proportional to the tank vibration level. The electromagnetic force, which is the excitation force of the winding, was obtained using the equivalent magnetic circuit network method to obtain the winding vibration required for the regression equation. Subsequently, the obtained force was applied to a finite element model for the winding to achieve the vibration response. The winding vibration obtained through these methods is closely correlated with the load noise, and the amount of winding vibration transferred to the tank could be changed according to the distance between the tank and the winding. Accordingly, an equation for predicting the load noise was established considering the winding vibration and the correlation factors according to the distance of the transmission path. The proposed prediction equation is considerably more accurate than the previous prediction equation.