Conventional Magnetic Circuit Research Articles

Vector magnetic circuit analysis of silicon steel sheet parameters under different frequencies for electrical machines

AbstractSilicon steel sheets (SSSs), serving as the principal constituent of the magnetic circuit in electric machines, necessitates precise modelling and accurate computation using magnetic circuit theory as a prerequisite for analysing the characteristics of electric machines. Nevertheless, the conventional magnetic circuit theory, limited to a single reluctance component, fails to address the phase relationship between magnetomotive force and magnetic flux, and inadequately represents the magnetic flux distribution observed under high‐frequency conditions. Consequently, the existing magnetic circuit model for SSSs remains imperfect in its current state. Fortuitously, the advent of magductance has effectively addressed these challenges. Building upon magductance, this study deduces the fundamental laws and theorem within the vector magnetic circuit theory. Subsequently, a distributed parameter vector magnetic circuit model for the SSSs is constructed, accompanied by the derivation of expressions pertaining to its reluctance and magductance. The authors propose the transfer function composed of reluctance and magductance parameters, successfully resolving the phase between the magnetic circuit vectors, the magnetic flux distribution, and the magnetic circuit loss under different frequencies for SSSs. Finally, experimental findings affirm the efficacy and validity of the distributed parameter vector magnetic circuit model for SSSs. The proposal of vector magnetic circuit theory opens a whole new door for the analysis, computation, and optimisation of electric machines.

Electromagnetic design and performance analysis of coreless superconducting machine

With the development of offshore wind power generation, there is an urgent demand for high-power wind turbines. Superconducting machines with high power density and efficiency are one of the solutions for wind turbines of 10 MW and above. This paper summarizes the existing superconducting synchronous generators in several structural forms and features, and considers that the coreless machine can avoid the impact of core oversaturation on the power density increase of the machine, which is the development direction of the superconducting machine. In this paper, the structural topology of a coreless superconducting machine is established and the similarities and differences between its structure and that of a conventional one are analyzed. Since the conventional magnetic circuit method is no longer applicable, a designing model based on the analytical method is established for the designing of coreless machines, which considers the effects of slotless armature, the superconducting excitation winding thickness and the nonlinearity of the ferromagnetic material. Based on this method, the magnetic field distribution is solved and verified with the finite element method. Further, the effect of the superconducting excitation winding opening angle on the magnetic field in the air gap of the machine is investigated, and the machine structure is optimized based on this. The steady-state and transient performance analysis of the machine is carried out to illustrate the operating characteristics of the coreless superconducting machine. The design method and analysis results of this paper can provide a reference for building higher power density coreless superconducting wind turbines.

Equivalent Magnetic Circuit Model of IPMSM

This paper proposes a magnetic equivalent circuit model for an interior permanent magnet synchronous motor (IPMSM) for the optimal design of the entire system. The computational speed of the proposed model is greater than that of the finite element method (FEM), and the model is suitable for large scale optimization problems. Unlike conventional magnetic circuit models, the proposed model can reflect the dq-axis saliency, which enables analysis under operating conditions using the reluctance torque, which is essential in IPMSMs. In the proposed model, rotor rotation is represented by an AC magnetomotive source, and the saliency characteristics are represented by a multi-phase-q-axis transducer that simulates a q-axis magnetic path connected in parallel to the magnets. The effectiveness of the proposed method is verified by comparisons with the FEM, and the results reveal good agreement under several conditions. Furthermore, the computation of the N-T characteristics and efficiency maps is verified, and consequently, the proposed method is deemed capable of obtaining these maps with sufficient accuracy for the initial design, and the required computation time is four orders of magnitude lower.

An Enhanced Magnetic Equivalent Circuit Model for a Magnetorheological Clutch Including Nonlinear Permeability, Flux Fringing, and Leakage Effects

Magnetorheological (MR) clutches have significant potential in electromechanical interface and are a promising technology with high commercial value in the automotive industry. A quick and precise magnetic circuit modeling method is demanded to calculate performance or optimize design of the MR clutch. Conventional magnetic circuit models present poor accuracy because they often fail to accurately include nonlinearities such as magnetic saturation, magnetic fringing, and magnetic leakage. In this regard, an enhanced magnetic equivalent circuit (EMEC) model based on lumped parameter method is proposed. This model can not only cope with clutch geometry and material properties (nonlinear permeability) but can also consider flux fringing and leakage effects. Combined with the specific structure, formulae for the calculation of fringing permeances and leakage permeances in the magnetic circuit of the MR clutch are presented. Finite-element analysis (FEA) and experimental results show that the proposed EMEC model can provide better accuracy compared with magnetic equivalent circuit (MEC) model from available literature and provide less computational effort compared with FEA. Moreover, the influence of design parameters corresponding to device geometry and material properties on the output flux density is discussed based on the proposed EMEC model. All taken together, the proposed EMEC model provides a comprehensive knowledge in optimize design and performance prediction of MR device.

Magnetic-Inductance: Concept, Definition, and Applications

The magnetic circuit has been a popular and powerful tool to analyze the magnetic field in electromagnetic devices for a long history. However, in the conventional magnetic circuit there is only one kind of component namely reluctance, which cannot analyze the phase shift or the amplitude attenuation of the alternating flux in electromagnetic devices. In this article, a new physical concept of magnetic-inductance is proposed, based on which the alternating-flux magnetic circuit theory including two kinds of components namely reluctance and magnetic-inductance has been developed. Furthermore, the virtual magnetic power is defined as the analogue of electric power, and the magnetoelectric power law is derived for magnetic circuits. Using the proposed magnetic circuit theory with magnetic-inductance, the relationship between the electric power and the virtual magnetic power is revealed and the long-lasting confusions in previous magnetic circuit methods, i.e., power calculation and phase shifts of magnetic variables, are clarified. By experiments, the magnetic-inductance and the magnetoelectric power law are validated, and their applications in eddy current loss analysis and B-H curve estimation in magnetic materials are demonstrated.

Leakage Inductance Representation for a Magnetic Circuit Model of Three-Winding Transformers for Electromagnetic Transient Analysis

In order to study electromagnetic transient phenomena occurring in power systems such as inrush currents or ferroresonance, an accurate and practical three-winding transformer model is required because the power system to be studied includes three-winding transformers in many cases. Although a star-circuit representation (Steinmetz's equivalent circuit model) is often used for these kinds of studies, it sometimes causes numerical instability because its magnetizing circuit representation is inappropriate. A magnetic circuit model considering iron-core topology is capable of eliminating the problem. However, the conventional three-winding magnetic circuit model does not match the leakage inductance measurements (short circuit tests) of the transformer to be represented. In this paper, we develop the three-winding magnetic circuit model which can match the leakage inductance measurements by making use of mutually coupled magnetic resistances. As a result of verification using a 500 VA single-phase three-winding transformer, it is indicated that the leakage inductance calculated by the developed model are in good agreement with those obtained by the leakage inductance measurements of the test transformer.

Improved magnetic circuit analysis of a laminated magnetorheological elastomer device featuring both permanent magnets and electromagnets

As an essential and critical step, magnetic circuit modelling is usually implemented in the design of efficient and compact magnetorheological (MR) devices, such as MR dampers and MR elastomer isolators. Conventional magnetic circuit analysis simplifies the analysis by ignoring the magnetic flux leakage and magnetic fringing effect. These assumptions are sufficiently accurate in dealing with less complicated designs, featuring short magnetic path lengths such as in an MR damper. However, when dealing with MR elastomer devices, such simplification in magnetic circuit analysis results in inaccuracy of dimensioning and performance estimation of the devices due to their sophisticated design and complex magnetic paths. Modelling permanent magnets also imposes challenges in the magnetic circuit analysis. This work proposes an improved approach to include magnetic flux fringing effect in magnetic circuit analysis for MR elastomer devices. An MRE-based isolator containing multiple MRE layers and both a permanent magnet and an exciting coil was designed and built as a case study. The results of the proposed method are compared to those of conventional magnetic circuit modelling, finite element analysis and experimental measurements to demonstrate the effectiveness of the proposed approach.

An Improved Magnetic Circuit Model of a 3-DOF Magnetic Bearing Considering Leakage and Cross-Coupling Effects

This paper presents an improved magnetic circuit (MC) model considering the leakage, cross coupling, and saturation effects for the performance analysis of an integrated 3 degrees of freedom magnetic bearing (3-DOF MB). Compared with the conventional MC model, this paper analyzes the permanent-magnet bias field, radial and axial control current fields together. By using this improved MC model, it reveals the cross-coupling effect between radial and axial directions in such an integrated 3-DOF MB. The stiffnesses of radial force are significantly influenced by the axial control current, while the stiffnesses of the axial force are independent of the radial control current. Its accuracy is verified by the 3-D finite-element method.

Rotor/Stator Inter-Turn Short Circuit Fault Detection for Saturable Wound-Rotor Induction Machine by Modified Magnetic Equivalent Circuit Approach

This paper presents a new method to model healthy and faulty wound-rotor induction machines (WRIMs) with and without inter-turn short circuit fault by a single set of equations. The model is presented for a machine with arbitrary pole, and rotor and stator slot numbers. A single set of equations, including both electric and magnetic parts, is solved to obtain full dynamic behavior of the machine. Therefore, the modified magnetic equivalent circuit with non-linear elements is used for modeling and a numerical technique is employed to solve the non-linear equations. The proposed modified method has a simple calculation procedure in comparison with the conventional magnetic equivalent circuit method. Solving the electric and magnetic equations by a single set of equations is the main advantage of the presented method, which is proposed for a WRIM machine, for the first time. In addition, to increase the accuracy, the saturation phenomenon is also considered in the model. Due to the saturation effect, there are some non-linear algebraic magnetic equations, which should be simultaneously solved with differential equations. A trapezoidal technique is used to convert differential equations to algebraic ones. To solve the non-linear equations, non-linear equations, Newton Newton–Raphson method is employed. Current signature analysis is used for rotor and stator inter-turn short circuit fault detection. Finally, the finite-element method is used to verify the effectiveness of the proposed modeling method. It is worth noting that the proposed method can model a healthy and faulty machine with different faults by a single model.

Separation of surface, subsurface and volume fatigue damage effects in AISI 348 steel for power plant applications

Abstract A wide range of industries including energy, chemistry, pharmacy, textiles, food and drink, pulp and paper, etc. is using stainless steels. Metastable austenitic steels such as used in power plants and chemical industry are subjected to cyclic mechanical and thermal loading in air as well as under the influence of corrosive media. This paper provides an overview on different nondestructive and electrochemical measurement techniques, which allow differentiating fatigue damage effects in total strain controlled multiple and constant amplitude tests with respect to damage appearance on surface, in subsurface area as well as in volume of specimens or components microstructure. In addition to conventional mechanical stress-strain hysteresis curves, electrical resistance, magnetic and open circuit potential measurements have been applied to characterize the cyclic deformation behavior of the metastable austenitic steel AISI 348 (X10CrNiNb18-9) in laboratory air and in distilled water. Based on these results obtained, the paper provides an outlook on the possibility for an efficient (remaining) fatigue life evaluation approach, which is adapted to the needs of the application areas.

Double-Sided Iron-Core PMLSM Mover Teeth Arrangement Design for Reduction of Detent Force and Speed Ripple

This paper analytically and experimentally shows effectiveness and simplicity of mover teeth arrangement design, which dramatically reduces detent force and consequently speed ripple at low speed. For this purpose, this paper describes two design steps that include the conventional magnetic circuit optimization by response surface methodology (RSM) and a slight modification of the optimized model based on the proposed mover teeth arrangement. Two prototypes were fabricated, tested, and compared from various perspectives. It was experimentally confirmed that the proposed design is very effective in reduction of detent force and speed ripple with the least sacrifice of performance.

Design optimization of double-sided permanent-magnet radial-flux eddy-current couplers

It is essential for engineers to improve overall performance of electromagnetic devices. In this paper, single/multi-objective design optimization of double-sided permanent-magnet radial-flux eddy-current couplers is carried out. To this end, an analytical model of such devices is developed by combining conventional magnetic equivalent circuit techniques with Faraday's and Ampere's laws. The model is capable of easily dealing with complex geometries and material properties such as iron saturation and the PM characteristics as well as the associated design constraints so that the designs that are more realistic can be achieved. A genetic algorithm that enjoys a flexible objective function is finally adopted to find the optimal machine parameters. Finite-element method is also employed to verify the results.

Double‐sided permanent‐magnet radial‐flux eddy‐current couplers: three‐dimensional analytical modelling, static and transient study, and sensitivity analysis

Analytical models are widely utilised in the study and performance prediction of electric machines by providing fast, yet accurate solutions. By combining conventional magnetic equivalent circuit techniques with Faraday's and Ampere's laws, an analytical model for double-sided permanent-magnet radial-flux eddy-current couplers is presented that can easily handle complex geometries. The proposed approach is also capable of taking the three-dimensional (3D) impacts into account. The characteristics and design considerations are also studied for a surface-mounted permanent-magnet structure. Moreover, the 2D and 3D finite-element methods are employed to verify the results, as well as transient study of the device under two different scenarios. Finally, sensitivity analysis is carried out to investigate the influence of the design variables on the characteristics of the coupler, which provides valuable information in the current and future studies of such devices.

Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor

Abstract Due to flat structure of the axial flux permanent magnet disc motor (AFPMDM), the airgap magnetic field distribution is more complex. To study the static airgap magnetic field of AFPMDM, the conventional magnetic circuit method and the method of taking slice in finite element software Magnet are used respectively. Then axial airgap flux density distribution characteristics along circumferential direction and radial direction are analyzed. The accurate three-dimensional airgap magnetic field distribution can be gotten with the above methods. At last, analytical method, finite element method and average radius method are used to calculate the airgap magnetic flux of per pole respectively. Three results are approximate and can reflect per pole magnetic flux of AFPMDM generally. The research for airgap magnetic field of AFPMDM provides theoretical basis for its wide application.

Integral Design and Analysis of Passive Magnetic Bearing and Active Radial Magnetic Bearing for Agile Satellite Application

In this paper, the design and development of a magnetic bearing system which consists of passive magnetic axial/tilting bearing and active two-axial radial magnetic bearing (RMB) used in magnetically suspended wheel (MSW) or magnetically suspended control moment gyroscope (MSCMG) for agile satellite application is presented. The passive axial/tilting magnetic bearing supplies an axial position stiffness to stabilize the rotor in the axial direction and a tilting stiffness to restrain the rotor when subjected to gyroscopic torque. The active two-axis radial magnetic bearing with bias permanent magnet stabilizes the rotor on the axes perpendicular to the rotation axis. Considering the complex distribution of flux density the system performance cannot be accurately analyzed by the conventional magnetic circuit method because of the high coupling between force and moment produced by the axial magnetic axial/tilting bearing and RMB. To analyze the coupling problem of the force, moment, position stiffness, and tilting stiffness between the passive magnetic axial/tilting bearing and RMB, an integral design and analysis method based on three-dimensional finite-element method is presented. An example is given and analysis results prove that the high coupling occurs on the radial direction and the light occurs on the axial and tilting directions orthogonal to the spin axis. Then the linearized model is given in this paper.

Development of a nonlinear geometric transformer model based on an incremental circuit of its magnetic core

In this paper, the investigation is focused on the topology-based geometric models of power transformers. These models take into account any type of core design, the geometrical characteristics of the magnetic core, and the nonlinear characteristics of the core material. These models differ from each other in the way in which the magnetic part is described. The methods, which have been proposed for the description of the magnetic part of a power transformer, are based on the conventional magnetic circuit of the core and present disadvantages. In this paper, a new method for the derivation of the differential equations of the magnetic core of the transformer is proposed by introducing a new auxiliary incremental circuit, more easily handled mathematically in antithesis to the conventional magnetic circuit that is used in the literature until now. Specifically, using the proposed circuit one can directly write the differential equations of the magnetic part of the transformer, the coupling between the windings of the transformer is easily calculated, the equations of the electric and the magnetic part are decoupled as well as the state equations of the electrical part can be written in standard form. The proposed method can be combined with any methodology presented in the literature on the core losses modeling without any restriction. The simulation results show forth that the proposed method of transformer modeling is suitable for transients and power quality studies. Moreover, the proposed method can be a useful tool on sensitivity analysis during the design stage of small and large power transformers as well.

A Time-Saving Method for Analyzing Permanent Magnet Motors

This paper presents a unique method for simulating permanent magnet motors without time-consuming numerical methods used in the conventional magnetic circuit method. The conventional method gives us average values like torque and power over specified periods of time, but it is usually very difficult and time-consuming to obtain instantaneous characteristics like cogging torques and torque ripples. The convolution operations method we present, however, considers relative angle variations of stator magnetic circuits and rotor magnetic circuits. As a result, it makes uses of instantaneous values possible. The authors compare the new method with the coventional method and verify that calculating cogging torque values and back-emf values is possible with the proposed new convolution method.

Halbach Magnetic Circuit for Voice Coil Motor in Hard Disk Drives

Rotary-type voice coil motors are widely used as actuators in hard disk drives. The recent trend toward higher density and smaller form factors in data storage devices requires performance improvement of the voice coil motor. In this study, we introduce a Halbach magnet array to the voice coil motor in order to increase the force generation. The Halbach magnetic circuit outperforms the conventional magnetic circuit due to the confined magnetic flux. To investigate the performance of the Halbach magnetic circuit, we analyze air gap flux density with the various shapes and thickness of the magnets using 3-dimensional finite element analysis. Consequently the optimum shape of the Halbach magnetic circuit is proposed. Simulations and experimental results proved effectiveness of the proposed magnet array in the voice coil motor for a commercial hard disk drive.

A Study on the Analysis on the Direct-Driven High Power Permanent Magnet Generator for Wind Turbine

In the paper, the permanent magnet synchronous generator of 1.5[MW] output power which is driven directly without gear system is designed by conventional magnetic equivalent circuit method and analyzed by finite element method. We analyzed the characteristics of generator like no load, rated load, short circuit condition and demagnetization of permanent magnet in order to verify the design results by magnetic circuit method. The last, the analysis results of two kinds of rotor types are compared with each other. Especially the THD (total harmonic distortion) of output voltage is examined for the comparison.

Reducing computational effort in field optimisation problems

Design and optimisation of many practical electromechanical devices involve intensive field simulation studies and repetitive usage of time‐consuming software such as finite elements (FEs), finite differences of boundary elements. This is a costly, but unavoidable process and thus a lot of research is currently directed towards finding ways by which the number of necessary function calls could be reduced. New algorithms are being proposed based either on stochastic or deterministic techniques where a compromise is achieved between accuracy and speed of computation. Four different approaches appear to be particularly promising and are summarised in this review paper. The first uses a deterministic algorithm, known as minimal function calls approach, introduces online learning and dynamic weighting. The second technique introduced as ES/DE/MQ – as it combines evolution strategy, differential evolution and multiquadrics interpolation – offers all the advantages of a stochastic method, but with much reduced number of function calls. The third recent method uses neuro‐fuzzy modelling and leads to even further economy of computation, although with slightly reduced accuracy of computation. Finally, a combined FE/neural network approach offers a novel approach to optimisation if a conventional magnetic circuit model could also be used.