Magnetic Equivalent Circuit Model Research Articles

Exploring torque characteristics of an integrated ultra conducting magnetic coupling incorporating axial magnetic field through magnetic equivalent circuit modelling

Ultra-conductors are a recent class of materials that display superconducting attributes at room temperature and even at higher temperatures. In this paper, we introduce a novel hybrid ultra-conducting coupling (NHUC) where the secondary component includes copper and an ultra-conductor (considered as a room temperature superconductor in much research). We suggest a model based on magnetic equivalent circuit (MEC) to evaluate the distribution of magnetic fields and characteristics related to torque. The 3D model accounts for boundary impacts during mating, and formulation for magnetic flux and torque are derived using Kirchhoff’s and Ampere’s loop laws, respectively. A 3D finite element (FEM) model is constructed, and simulations are performed using iodine-doped double-walled carbon nanotube (IDWCT) as the ultra-conductor for a wider operating range. At a high slip speed of 1200 rpm, a maximum torque of 309 Nm and stable torque of 113 Nm are observed. Adjusting air gap thickness or permanent magnet dimensions results in torque variations. Additionally, due to carbon nanotube (CNT) characteristics, a reduction in losses from the Joule effect is noted. The maximum error between torque results from simulation and the suggested model is 7.68%, confirming accordance. Comparison alongside the slotted eddy current coupling (SEC) reveals that the torque of the NHUC exceeds that of the SEC, diminishing as the air gap widens.

Armature Reaction Analysis and Suppression of Voice Coil Actuator Based on an Improved Magnetic Equivalent Circuit Model

The high thrust density voice coil actuator (VCA) is a key component for the deployers to determine the CubeSats' separation velocity in orbit directly. To improve the VCA's thrust density and power consumption, it is essential to analyze the armature reaction under heavy current work conditions. This paper proposes a dynamic splitting method of the magnetic equivalent circuit (MEC) model for analyzing the armature reaction of the VCA. This MEC model can effectively reveal the interaction mechanism between the dynamic winding field and the permanent magnet (PM) field, which provides an approach to readily and quickly analyze the armature reaction. Based on the understanding of the mechanism, we found an effective way to suppress the armature reaction and propose a new VCA with double PM flux circuits. The electromagnetic performances of the new configuration are evaluated by comparing it with the conventional one. Both the theoretical and experimental results show that the new structure achieves lower magnetic saturation, lower armature reaction, and higher thrust density. A research prototype was constructed and experimentally tested to verify the theoretical results of the armature reaction, magnetic field, thrust, separation velocity, and other performances. The new VCA realizes a wide and accurate modulation of separation velocity for the CubeSats.

Electromagnetic Design and Analysis of a Stator–Magnet Transverse Flux Linear Oscillatory Machine with Yokeless Mover Core

Conventional stator–magnet moving-iron transverse-flux linear oscillatory machines (CSMTLOMs) are widely applied in directly-drive reciprocating devices due to the merits of easy fabrication and robust mover. However, in order to keep the mover vibrating at a certain resonance frequency to save the energy and enlarge the output power, they still suffer from a higher requirement on spring stiffness due to their thick and heavy mover core, which would also narrow the frequency band with a high power factor due to the large inertial energy storage of the heavy mover. Hence, to reduce the mover core weight to reduce the demand of the spring and improve the operation performance, an improved linear oscillatory machine featured by a spoke-type interior permanent magnet inner stator (ISMTLOM) is proposed. Benefiting from its separated two stators, the tangential flux in the radial plane can return through the inner stator core, so that the yoke of the mover core can be eliminated directly. Then, to analytically investigate the influence of the special axial local saturation effect, the segmental equivalent magnetic circuit (EMC) model of the ISMTLOM is established, wherein a saturation coefficient is introduced to quantitatively consider the local saturation effect on the output force. Consequently, several important size parameters are optimally selected when keeping the same outer diameter and copper loss as that of the CSMTLOM. Afterward, the three-dimension finite element algorithm (3D FEA) is adopted for the electromagnetic performance validation and comparison. Finally, it is found that the nonlinear segmental EMC corrected by the saturation coefficient can quickly predict the output force more accurately within the wide load range, and benefiting from the topology improvement, the ISMTLOM has the merits over the CSMTLOM in its smoother output force, much lighter mover core, and less demand of mechanical spring stiffness, whilst preserving the similar output force density.

An optimal design method for magnetorheological fluid sealing structure for beam director using multi-objective optimizer

For beam directors, tight optical path sealing and low rotational friction torque are critical aspects for the tracking and positioning performance. To maximize sealing pressure and minimize rotational friction torque, a magnetorheological fluid sealing (MRFS) structure design method based on multi-objective COOT (MOCOOT) algorithm optimizer was proposed in this work. The MOCOOT integrates archive, grid strategy, chaotic mapping strategy and COOT optimization algorithm. Firstly, the magnetic field strength of the sealing clearance was derived based on the equivalent magnetic circuit model, the sealing pressure formula of MRFS with pole teeth structures was established, and the friction torque model of MRFS based on Bingham equation was also developed. Then, according to the actual requirements of optical path sealing of beam directors, the constraint conditions of structure parameters were determined, and the optimization target model of sealing pressure and friction torque was constructed. As follows, a multi-objective version of COOT optimization algorithm, named MOCOOT, was proposed to optimize the structural parameters of MRFS structure. Finally, the effectiveness of the proposed method was verified via pressure and rotating friction torque tests implemented on an established experimental platform.

Comparison of nonlinear solution methods for magnetic equivalent circuits of saturated induction motors

This work compares three nonlinear solution methods for the performance of an induction motor’s magnetic equivalent circuit model with magnetic saturation. The interrelation between magnetic flux density and permeability introduces nonlinearities in the differential system of equations. Three popular nonlinear solution methods are selected for comparison, namely (i) the Gauss–Seidel method, (ii) the Newton–Raphson method and (iii) the inverse Broyden’s method. While all three methods have been applied in this context before, no comparison study has been published to the authors’ best knowledge. The study finds that the inverse Broyden’s method is most performant in terms of the number of required iterations, the computation time per iteration and the resulting total computation time. However, for substantial saturation levels, the authors recommend a hybrid implementation of multiple solution methods to obtain robust and reliable convergence.

An approach to solving the effect of background in fluidized bed on electromagnetic tomography

As a non-invasive measurement technique, electromagnetic tomography (EMT) system based on tunneling magneto resistance (TMR) can detect the distribution of medium in the gas–liquid–solid fluidized bed by the difference of permeability. The distribution of medium in the three-phase fluidized bed is not uniform, and the solid clusters and bubble clusters are formed in the background of the gas–liquid–solid mixture. Since the effect of the background in the pipe of the fluidized bed on the boundary measurement data of the TMR-EMT system is much greater, it is difficult to detect solid clusters and bubble clusters when the image is reconstructed directly using the boundary measurement data. In order to improve the detection of clusters by the TMR-EMT system, a method to weaken the effect of the background is proposed. The equivalent magnetic circuit model is used to estimate the background permeability. Then the magnetic dipole theory and demagnetization effect theory are utilized to establish a simple background compensation model based on the estimated background permeability. Using the compensation model, the effect of the background is weakened from the boundary measurement data and the cluster distribution information is highlighted. Simulation and experimental results demonstrate the effectiveness of the proposed method.

Analysis of low saliency ratio and torque characteristics of the fractional slot concentrated winding surface mounted motors

In recent years, fractional slot concentrated winding permanent magnet synchronous motors (FSCW PMSMs) have become a hotspot in the research field. Due to the unique inductance characteristics of the FSCW PMSM, a fast and accurate calculation of the d/q-axis inductance and saliency ratio is necessary. In this paper, a method is proposed to calculate the d/q-axis reactance of the FSCW SPMSM, which constructs the equivalent magnetic circuit model of the d/q-axis armature reaction flux separately, and the saliency ratio characteristics of the FSCW SPMSM were demonstrated. In addition, to meet the high requirements of the modern industries, especially in servo systems, accurate consideration of the effect of stator resistance on torque and electromagnetic performance is important and more applicable. According to the relationship between the vector parameter, the explicit expression of the d/q-axis currents that consider the stator resistance is obtained, and the prediction of load angle at maximum electromagnetic torque is achieved. Then, combined with the finite element method, the influence mechanism of stator resistance on the motor steady-state performance is revealed. Finally, the experimental data are compared with the calculation data, and the correctness of the models and analysis was verified.

A novel stress concentration inspection method for marine oil and gas pipeline based on UNSM

Stress concentration of marine oil and gas pipelines can lead to deformation and cracks, laying out great hidden dangers for safe operation. This paper proposes a novel in-line inspection method for stress concentration based on UNSM (unsaturated magnetization) for oil and gas pipelines. Firstly, the stress concentration inspection mechanism with UNSM is analyzed, and the equivalent magnetic circuit model of the inspection probe is derived. Secondly, the response signal features of axial, radial and complex stresses were investigated parametrically by numerical simulation. Then, quantitative tensile stress inspection was carried out with the UNSM inspection probe. Finally, the pipeline stress state is continuously scanned by the self-developed defect dynamic scanning experimental system. The results show that the UNSM inspection probe can effectively detect the abnormal stress of the pipeline. Meanwhile, the axial tensile, radial compressive stress and complex stress increase the axial permeability of the pipeline, resulting in a negative correlation of characteristic signals. Besides, the signal feature shows the "basin" distribution and decreases gradually with the increase of the lift-off. The above research provides a reference for developing in-line inspection equipment for the abnormal stress of marine pipelines.

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

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

An accurate calculation method for inductor air gap length in high power DC–DC converters

High-power inductors are fundamental components in high-power DC–DC converters, with their performance being a crucial metric of converter efficiency. This paper presents an in-depth analysis of a novel calculation method for the air gap length in such inductors. Taking into account the effects of air gap diffusion and the winding magnetic field, an expression for the air gap diffusion radius is derived, focusing on a distributed air gap structure. Furthermore, models for calculating the air gap and winding reluctance are developed, grounded in electromagnetic field theory. An equivalent magnetic circuit model, formulated based on Kirchhoff's second law, facilitates the proposed method for air gap length calculation. This study also involves the development of 3D models for both discrete and decoupled integrated inductors. The comparison between simulation outcomes and calculated air gap lengths indicates a maximum error of less than 8%, with the minimum error being as low as − 0.79%. Compared with traditional methods, the calculation method proposed in this paper has significant advantages. Additionally, the discrepancy between calculated values and experimental measurements is found to be 1.11%. These results validate the accuracy and applicability of the theoretical analysis and calculation method, underscoring their significance in the design and optimization of high-power DC–DC converters.

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

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

Magnetic Equivalent Circuit Model for a Two Degree-of-Freedom Rotary-Linear Machine with Transverse Flux Structure

Magnetic Equivalent Circuit Model for a Two Degree-of-Freedom Rotary-Linear Machine with Transverse Flux Structure

A Novel Separated Hybrid-Magnetic-Circuit Variable Flux Memory Machine

Aiming at the problems of the existing hybrid-magnetic-circuit variable flux memory machine (HMC-VFMM), such as weak flux regulation (FR) capability and low efficiency in high-speed region, etc., this article proposes a novel separated HMC-VFMM (SHMC-VFMM), which innovatively arranges a series magnetic circuit on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -axis and a parallel magnetic circuit on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis. The SHMC design can simultaneously reduce the PMs fluxes through low-coercive-force PMs configured on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -axis and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis, which will improve the FR capability. The magnetic saturation is alleviated by reducing the usage of high-coercive-force PMs, which further broadens the FR range. The proposed design also simplifies the rotor mechanical structure, thereby improving the rotor design flexibility. Firstly, the topological evolution process and the working principle of the proposed machine are interpreted in in succession. Then, the mechanism of further expanding the FR range of the proposed machine is revealed by comparing its equivalent magnetic circuit model with that of the existing machine. Subsequently, the electromagnetic characteristics of the two compared machines are analyzed by using the finite element method, which validates the performance advantages of the proposed machine. Finally, an SHMC-VFMM prototype is manufactured and measured to verify the superiority of the proposed SHMC design.

A 2D hybrid analytical electromagnetic model of the dual‐stator axial‐field flux‐switching permanent magnet motor

AbstractThe two‐dimensional (2D) analytical model for the calculation of the components of the flux density distribution in the air gap in a dual‐stator axial‐field flux‐switching permanent magnet (PM) motor (DSAFFSPM) is presented. The novelties of this study are deriving a 2D hybrid analytical model and replacing the rotor teeth with some surface currents for the calculation of air‐gap magnetic flux density for the first time in the DSAFFSPM motor. The 2D analytical model for DSAFFSPMs is more challenging due to the doubly salient structure and inner PM of the stator. 1D analytical interior PMs are first transferred to the bore of the stator body using the magnetic equivalent circuit model (MEC). Next, the effects of the rotor teeth are taken into consideration by injecting virtual surface currents for 2D analytical model. Applying boundary conditions and solving the Laplace/Poisson equations, the vertical and tangential flux components of the flux density distribution in the air‐gap DSAFFSPM motor are computed. The verification of the proposed method and the obtained results are validated by the 3D finite element method.

A reluctance-based electromagnetic transient model for the Sen Transformer with inter-turn fault

In order to analyze the electromagnetic characteristics of the Sen Transformer (ST) in the event of an inter-turn fault (ITF), an electromagnetic transient model of the ST with ITF based on reluctance is proposed in this paper. Firstly, the magnetic equivalent circuit model of the ST with ITF is established based on the magnetic coupling relationship among the internal windings of the ST with ITF. Secondly, the electrical analytical model for the current in each winding of the ST with ITF is derived from the electrical connection established the ST with ITF and the external system. Finally, the electromagnetic transient model of the ST with ITF can be obtained by combining the magnetic equivalent circuit model with the electrical analytical model. The J-A hysteresis model is employed for representing the saturation characteristics of the iron core and the hysteresis effects. Meanwhile, an energy method is used to calculate the leakage reluctance between the windings. Three case studies have been conducted with the assistance of MATLAB and ANSYS/Maxwell. The results of the analytical calculations are compared with the time-domain simulation to verify the validity of the model. Furthermore, the growth of the current in the fault phase is significant after an ITF occurs in the ST, while the growths of the currents in the non-fault phases are very small. Moreover, the effects of the number of fault turns and the fault location on the current in the ST with ITF are further analyzed.

Modified magnetic equivalent circuit of double‐stator single‐rotor axial flux permanent magnet machine considering stator radial‐end flux‐leakage

AbstractA modified non‐linear magnetic equivalent circuit (MEC) model is presented for double‐stator single‐rotor axial flux permanent magnet (AFPM) (DSSR‐AFPM) machine considering stator radial‐end flux‐leakage, which is severer under a heavier load. Compared to the conventional MEC model for DSSR‐AFPM machine, the proposed model can predict the electromagnetic performance more accurately when the machine operates under a heavy load. The proposed MEC model is verified by the finite element analysis (FEA) on a 24‐slot/20‐pole DSSR‐AFPM machine. The comparison results show that the relative error between the proposed MEC model and FEA is &lt;4% for back electromotive force and &lt;5% for average electromagnetic torque, respectively. Specifically, the relative error of the average torque for the modified MEC model is 4.92% at 28.30 Arms/mm2 slot current density, which is lower than the conventional MEC model, that is, 7.75%.

Investigation of transmission characteristic for harmonic magnetic gears considering dynamic eccentricity using magnetic equivalent circuit

AbstractHarmonic magnetic gears (HMGs) have the advantage of lubrication‐free, high speed ratio and high torque density, which make it an attractive solution for safety critical applications. Due to eccentricity caused by machining and assembly, HMG suffers from dynamic eccentricity (DE) in operation, however, its effect on HMG performance is still unknown. Transmission characteristic of HMG under DE is studied. First, a magnetic equivalent circuit (MEC) model of HMG is proposed to build the magnetic coupling torque analytically, and the geometry of air gap is analysed parametrically to derive its equivalent reluctances. Flux density and coupling torque can be acquired by solving MEC equations. The accuracy of the MEC model is verified by finite element method. To study the transmission characteristic, an electromechanical coupling simulation framework for HMG is constructed, motion trajectories of rotors are investigated in case of DE, the output torque in locked‐rotor condition and speed response in continuous operation can be derived by simulation. It is found that torque ripples that have the same frequency with input rotor are induced by DE; the results are then verified in the experiment. This paper provides a theoretical guidance for the design and condition monitoring of HMG.

Optimal Design Method of Post-Assembly Magnetizing Device with Field–Circuit Coupling Analysis

Post-assembly magnetization can significantly simplify the manufacturing of the rotor of permanent magnet (PM) electrical machines. The optimization of the post-assembly magnetizing device using finite element analysis (FEA) is time-consuming; therefore, a globally optimal solution aiming at achieving an adequate magnetizing level and minimal energy consumption is difficult to achieve. In this paper, a field–circuit coupling analysis (FCCA) model is proposed to optimize the auxiliary stator-type magnetizing device for interior permanent magnet synchronous machines (IPMSMs). A reasonable simplification of the highly saturated magnetic circuit is made based on FEA results so that the magnetic equivalent circuit (MEC) model can be established. On the other hand, the eddy currents in the PMs are equivalent to an eddy current short-circuit; thus, by converting the field calculation into a circuit calculation, the time cost can be reduced significantly, which greatly improves the speed of multi-objective optimization of the magnetizing device with multiple degrees of freedom. A V-type IPMSM is taken as a study case, and its post-assembly magnetizing device is optimized with the proposed method. FEA and experimental results show that the PMs are fully magnetized, while the required energy consumption is greatly reduced when compared with an existing magnetizing device.

Typology and working mechanism of a hybrid power router based on power-frequency transformer electromagnetic coupling with converters

The power router (PR) is a promising piece of equipment for realizing multi-voltage level interconnection and flexible power control in the future distribution power grid. In this paper, a hybrid PR (HPR) topology based on power-frequency transformer electromagnetic coupling with converters is proposed for the medium distribution power grid. The power-frequency transformer is used to undertake power transmission, voltage conversion, and other main tasks, while the power electronic converters are combined to achieve active control. Equivalent magnetic and electrical circuit models are established to help discuss the operating principle of the proposed HPR. Additionally, the power flow and control principle of the HPR in different operating conditions are analyzed, with the control system design scheme presented. The theoretical analysis results are verified by MATLAB/Simulink + Plecs simulation and a controller hardware-in-the-loop study, as well as a down-scale experimental test, indicating that the proposed HPR is flexible in active voltage support and current control.

Analysis and Compensation of the Longitudinal End Effect in Variable Reluctance Linear Resolvers Using Magnetic Equivalent Circuit Model

This paper focused on the Longitudinal End Effect (LEE) in linear Variable Reluctance (VR) Resolvers. The LEE can significantly decrease the accuracy of the linear sensor. Therefore, a novel method based on Magnetic Equivalent Circuit (MEC) Model is proposed for accurate modeling of this phenomenon and used in an optimization routine to suppress that. The LEE is modeled by adding three extra permeances into the conventional MEC model without increasing the complexity and simulation time. Besides, the method of calculating these permeances is described. After that, some techniques are presented to decrease the computational burden of the MEC model. Then, the model is used to compensate the LEE by optimizing the turn number of coils. Comparing the results of the proposed model and the Finite Element Method (FEM) shows that the deviation of the model in the prediction of different inductances is less than 5%, while the simulation time is about 31 times less than that of FEM. Besides, the comparison between the initial design and optimal design shows the usefulness of the model in the optimization process which the accuracy of the sensor improved by 74.1%. Finally, Experimental tests on the prototype sensor verify the success of the analysis.