Subdomain Method Research Articles

Vibro-acoustic behavior of a permanent magnet synchronous electrical machine: Influence of rotor displacement on Maxwell's pressures

Electric machines are often perceived as silent, yet the noise they produce has become a significant issue. This paper presents a focused approach to understanding the source of this noise, aiming to enhance machine design. Our study centers on the vibratory model of a permanent magnet synchronous electric machine. The stator and rotor components (shaft, laminations, magnets, and flexible bearings) are modeled using finite element analysis. We calculate the magnetic forces from Maxwell's pressures, which are analytically determined using the subdomain method. A key aspect of our study is the consideration of dynamic eccentricity. The paper explores how the vibratory responses of the rotor affect theses stress and how to address the complexity of magneto-mechanical coupling. Our findings reveal that the magneto-mechanical coupling of the rotor directly and significantly impacts Maxwell's pressures, and has to be taken into account to characterize the dynamics of rotor and stator.

Analytical prediction of the open‐circuit magnetic field for the V‐shaped interior PM machine by the improved subdomain method

AbstractThe open‐circuit magnetic field of the V‐shaped interior PM (IPM) machine is predicted by the analytical method. The method is implemented following the basic principle of the subdomain method. The machine model is divided into five different regions, including rotor slot, magnetic barrier, air gap, stator slot, and stator slot opening. To perform the analytical prediction process in the polar coordinate system, these regions should be transformed into the appropriate subdomains. The last four regions can be transformed into the subdomains with the required shape based on the existing method. The rotor slot cannot be treated as a single subdomain, for the shape of which is irregular. Herein, the PM and vacuum region in the rotor slot is divided into several fan‐shaped subdomains. The division method is described clearly. Then, the boundary conditions alongside the interface between adjacent subdomains are derived based on function transformation. On this basis, the open‐circuit magnetic field of the IPM machine can be predicted. The magnetic field of the 6p/36 s V‐shaped IPM machine is obtained by the proposed method, finite element method simulation, and experiment, respectively. Additionally, the comparison results verify the accuracy and efficiency of the proposed method.

Rapid Prediction of Magnetic and Temperature Field Based on Hybrid Subdomain Method and Finite-Difference Method for the Interior Permanent Magnet Synchronous Motor

Rapid Prediction of Magnetic and Temperature Field Based on Hybrid Subdomain Method and Finite-Difference Method for the Interior Permanent Magnet Synchronous Motor

A Combined Subdomain Method of Moments and Asymptotic Waveform Evaluation for Fast Wideband Bistatic Radar Cross Section Prediction

A Combined Subdomain Method of Moments and Asymptotic Waveform Evaluation for Fast Wideband Bistatic Radar Cross Section Prediction

Method for Predicting Linear Eddy Current Braking Performance of the High-Speed Maglev Train Based on Magnetic Circuit Structure

On high-speed magnetic levitation (maglev) trains, the linear eddy current brake (LECB) is a key piece of equipment to ensure the safety of train operation. In the event of a sudden failure of the traction motor or the external power grid, braking by the LECB, which comes with the maglev train, is currently the only emergency braking method that can ensure the train can be safely stopped while operating at high speed. The braking performance of eddy current brakes is usually predicted based on symmetrical magnetic equivalent circuits, which usually ignore the interactions between the magnetic circuits. For LECB, such interactions should not be neglected. In this paper, to investigate an accurate and efficient method for predicting the braking performance of LECB for high-speed maglev trains, based on the structural characteristics of LECB and Kirchhoff’s law, a full structural magnetic equivalent circuit model considering the interactions between magnetic circuits is developed, and then combined with the subdomain method, a braking force model, to predict the braking performance of LECB. The performance prediction of LECB with different numbers of magnetic poles is compared with the traditional method using the results of the finite element method and the experimental method as references. The results show that the proposed method is more accurate in predicting the braking performance of LECB and better reflects the physical characteristics of the actual magnetic field.

Magnetic Field Analysis and Thrust Verification of Solenoid Actuator Based on Subdomain Method

Magnetic Field Analysis and Thrust Verification of Solenoid Actuator Based on Subdomain Method

B-Spline Subdomain Method for static calculations of Double-Curved Arch structures

A static computational study of a new type of Doubly-Curved Arch (DCA) structure using the Spline Subdomain Method (SSM) has been conducted and a new subdomain and generalized model for the static analysis of compression DCA structures have been developed. The equations for the numerical calculations by SSM are derived. The model is based on the SSM for the subdomain division of DCA. For the discretization of the flat shell subdomain, two sets of uniformly distributed spline nodes are used along the neighboring edges of the rectangular projection of the shallow shell subdomain. The linear combination of the product of these two specially designed cubic B-spline interpolation functions is the displacement field. This model generates its overall structural stiffness matrix and load vector of the DCA by direct assembly following the discretization of the spline in the shallow shell subdomain. This method is characterized by high modeling efficiency, low computational cost, and a wide range of applications for the analysis of irregular shell structures. Abaqus software is used to verify the performance of the suggested method through numerical examples. The findings demonstrate that non-regular DCA structures subjected to static compression can have their mechanical properties analyzed using the suggested method.

Analytical and experimental study of electromagnetic loss and temperature rise in induction machines

This paper focuses on electromagnetic and loss analyses of an induction machine using the subdomain method. The proposed method derives an analytical solution for each subdomain using electromagnetic theory. On the basis of the derived analytical solution, electromagnetic performances are calculated and copper loss, iron loss, and rotor loss are derived. The validity of the proposed method was verified by comparing the analysis and loss analysis results with the finite element analysis results. In particular, the loss analysis results were input into an equivalent thermal analysis model, thermal analysis was performed, and the results were compared with those measured in the actual model. The reliability of the proposed method was verified through analysis and experimental results.

Improving force characteristics of linear oscillatory generator with spring permanent magnet for Stirling engines based on subdomain method

In this paper, an electromagnetic analysis method is proposed to improve force characteristics by using spring permanent magnets (PMs) along the axial and circumferential directions of a linear oscillatory generator (LOG). For accurate electromagnetic analysis, a detailed analysis model of the LOG is developed, and the governing equations of each subdomain are derived based on Maxwell’s equations and electromagnetic theory. Analytical solutions of the magnetic vector potential in each subdomain are derived using boundary conditions. The reliability of the proposed method is verified through a comparison with the results of a two-dimensional finite element analysis (FEA). In particular, the force characteristics depending on the spring PM is effectively derived by considering the three-dimensional (3D) circumferential and axial end effects. The proposed analysis method is used to determine the thickness of spring PM that transforms the detent force of the LOG with the spring PM into restoring force. The reliability of the proposed analysis method is verified through comparison with the results of a 3D FEA.

Prediction of Electromagnetic Performance for IPMSM Based on Improved Analytical Model Considering Saturation Effects

Unlike surface-mounted permanent magnet synchronous motors (SPMSM), the rotor structure of interior permanent magnet synchronous motors (IPMSM) is irregular and relatively complex. This makes the analytical calculation for IPMSM quite complicated. Except for the use of some equivalent methods to make irregular permanent magnets (PMs) regular, existing subdomain models often cannot effectively and directly account for the complex rotor structure and cannot be easily applied to IPMSM. For this reason, an improved analytical model applicable to IPMSM is presented, studied, and developed in this article. First, a novel subdomain model division method is innovatively introduced. Complex rotor structure can be well accounted for. This not only facilitates the expression of vector potential and satisfies the establishment of subdomain model, but also recovers the original rotor topology to the maximum extent and effectively avoids many uncertainties and unreliability caused by over-equivalence. Afterwards, the magnetic equivalent circuit and equivalent surface current method are combined to fully consider the saturation effects of magnetic isolation bridges, rotor ribs, and cores. Model analysis accuracy is well guaranteed. Further, the precise subdomain method is investigated to achieve fast prediction of key electromagnetic performance. Both finite element analysis (FEA) and prototype experiment strongly highlight the validity of the improved analytical model. In addition, compared to FEA, the improved analytical model does not require tens of thousands of computation cells, which saves a lot of time and storage while ensuring the same prediction accuracy. This opens up unlimited possibilities for the design and optimization of IPMSM.

Improved 2-D Analytical Model for Rotor Eddy Current Loss of HS PMSMs With Rotor Retaining Sleeve Based on Accurate Subdomain Method

Improved 2-D Analytical Model for Rotor Eddy Current Loss of HS PMSMs With Rotor Retaining Sleeve Based on Accurate Subdomain Method

Subdomain Analytical Modeling of a Double-Stator Spoke-Type Permanent Magnet Vernier Machine

This paper proposes an analytical model of the double-stator spoke-type permanent magnet vernier machine (DSSTVM) using the subdomain method (SDM), which can be used to calculate the magnetic field distribution and corresponding electromagnetic parameters of the DSSTVM. The whole field domain is divided into several subdomains according to the magnetic characteristics of each region, within which Laplace’s and Poisson’s equations are solved accordingly in terms of magnetic vector potential (MVP). Then, the corresponding magnetic flux density distribution, back electromotive force (EMF), and electromagnetic torque of the DSSTVM can be obtained. Ultimately, finite element analysis (FEA) is adopted to validate the proposed analytical model’s effectiveness for quickly predicting the no-load and on-load performances of the DSSTVM.

Volume optimization of high-speed surface-mounted permanent magnet synchronous motor based on sequential quadratic programming technique and analytical solution

This study proposes an innovative approach that integrates the subdomain method with sequential quadratic programming (SQP) to optimize the volume of a high-speed surface-mounted permanent magnet synchronous motor in an air compressor operating at 110 000 rpm. Unlike conventional optimization tools that often rely on finite element analysis (FEA) software, by leveraging the subdomain method for electromagnetic modeling, we obtain an analytical solution that rapidly represents the behaviors of the motor. Subsequently, the SQP technique is applied to optimize the volume of the model while satisfying design constraints. The proposed model is verified by FEA simulation.

Experimental verification and electromagnetic analysis of axial flux permanent magnet motor using the subdomain method

This study investigates a subdomain method for performing the characteristic analysis of an axial flux permanent magnet motor (AFPM). Initially, the AFPM was simplified for the analytical model and analysis regions were defined to apply the subdomain method. Subsequently, a general solution was derived for the governing equations of each analysis region using the variable separation method. Subsequently, the undetermined coefficients of the general solution were obtained from the matrix using appropriate boundary conditions, and the magnetic flux density in the air-gap region was derived based on the defined magnetic vector potential. Finally, the induced voltage and electromagnetic torque of the analytical model were calculated. The analytical results were verified using the finite element method and the experimental results.

Fast Calculation of Electromagnetic Vibration of Surface-Mounted PMSM Considering Teeth Saturation and Tangential Electromagnetic Force

In view of the shortcomings of the existing calculation methods of electromagnetic forces, this paper proposes an analytical method (AM) combining the magnetomotive force (MMF)-permeance method and the improved subdomain method. The amplitude of each force density component considering stator teeth saturation and current harmonics is calculated, and the specific order and frequency components in the radial and tangential electromagnetic force densities are analyzed and sorted out. In modal analysis, the stator core and the casing are regarded as cylindrical shells with axial ribs, the natural frequencies of the stator are obtained based on the energy method, and the accuracy is well verified by the modal test. Finally, the frequency response functions of low-order modes of the stator only related to the stator structure parameters are determined, and the vibration accelerations under different working conditions are obtained based on the linear superposition principle by only updating the electromagnetic forces. Compared with the multi-physical coupling finite element analysis, the total calculation time of the proposed AM is reduced by more than 92%, which facilitates the fast prediction and effective reduction of electromagnetic vibrations in the motor design stage.

Investigation of Effect of Wind-Induced Vibration on Typical Frame Structures on the Open Decks of Large Cruise Ships Based on the Subdomain Method

Due to the tall and large superstructures of cruise ships, the wind-induced vibration of frame structure on open decks cannot be neglected. This study investigated the wind-induced vibration of a typical frame structure on a cruise ship by using wind tunnel tests and numerical simulations. Wind tunnel tests were conducted to explore the simulation methods of the fluid–structure interaction (FSI). CFD simulations were performed to obtain the wind field data of the entire ship, which was utilized as an input for the open deck through the subdomain method. Subsequently, wind-induced vibration simulations of the guide rail frame structure on the open deck was carried out under various wind conditions. The results revealed that employing the turbulence model SST k-ω had a good agreement with the experimental data. The entire ship’s CFD results have a significant impact on the subdomain’s wind-induced vibration results. The vibration frequency of the guide rail frame structure was mainly concentrated between 0.8–10.1 Hz. The most unfavorable conditions appear at the wind attack angles of 0° and 120°. This study can provide some instructive insights for the prediction of wind-induced vibration and control of typical structures on the open decks of large cruise ships.

An Improved 2-D Subdomain Method Toward Electromagnetic-Performance Analysis of Line-Start Permanent Magnet Synchronous Motor

The 2-D subdomain method (SDM) has proven to be a time-efficient approach suited for determining the magnetic field of permanent magnet synchronous motor (PMSM). However, further application of this method into the field analysis for the line-start PMSM (LSPMSM) is limited by its natural defects including (a) inability to consider the saturation effect of iron material and (b) failure to deal with the rotor eddy currents allowing self-start. In this work, the step-by-step or iterative numerical calculation using the finite difference method (FDM) is embedded into the execution of conventional 2-D SDM, through which an enhanced version addressing all issues as stated above is obtained. The improved SDM avoids limitations of pure analytical method and possesses higher calculation efficiency than that of pure numerical method. Reliability of the presented method is validated by the finite element analysis (FEA) and tests.

Fast Magnetic Field Prediction Based on Hybrid Subdomain Method and Multiobjective Optimization Design for Interior Permanent Magnet Synchronous Machines

Benefiting from the prosperity of new energy industry, interior permanent magnet synchronous machines (IPMSM) have ushered in unprecedented development opportunities. To further suppress defects and enhance engineering practicality, fast magnetic field prediction based on hybrid subdomain method and multiobjective optimization design for IPMSM are studied. First, fast no-load magnetic field prediction model based on hybrid subdomain method for IPMSM is innovatively proposed. By combining master/slave subdomain division method and lumped parameter magnetic equivalent circuit, complex rotor structure and saturation effects of magnetic bridges and cores can be comprehensively considered. Prediction model has extremely high calculation accuracy and speed. After that, based on the proposed prediction model, a multiobjective optimization model combining Taguchi method and nondominated sorting genetic algorithm II (NSGA-II) is implemented. Model optimization efficiency has been greatly improved scientifically and effectively. Finally, the efficiency, advancement, innovation, and engineering practicability of studied prediction and optimization models are well verified through a series of finite element analysis (FEA) and prototype experiments. In addition, the generality and universality of this study are verified for other types of IPMSM.

Electromagnetic Performance Analysis of a Field-Modulated Permanent Magnet Motor Using Improved Hybrid Subdomain Method

The hybrid subdomain method (HSDM) combining conventional SDM with equivalent magnetic network has been proved to be a qualified approach to field prediction. However, this method still suffers two issues: first, the saturation effect of stator core is considered but that of rotor core is ignored, thus causing no-accuracy calculation; second, the mathematical complexity is inevitable due to adoption of virtual line-current density as extra interface conditions. This work is to develop an improved HSDM (IHSDM) for accurately and efficiently predicting the electromagnetic performance of a field-modulated permanent-magnet motor. The key of the proposed IHSDM is to fully consider magnetic saturation inside both stator and rotor cores. More importantly, the replacement of virtual-line current density by virtual-surface magnetization and current density makes interface conditions as simple as the SDM. The quantitative comparisons with conventional HSDM and FEA are conducted and the prototyping tests are also performed. It shows that the proposed IHSDM has lower time consumption and occupied memory, and electromagnetic quantities have about two times more accuracy than conventional HSDM. Additionally, a dynamic calculation is achieved by the IHSDM and verified by FEA.

An improved subdomain method for air gap flux density of interior permanent magnet machines based on rotor reconstruction and flux equivalence

AbstractThe aim of this article is to develop a rotor reconstruction method for the V‐shaped interior permanent magnet (IPM) machine so that the subdomain method to analytically calculate the air‐gap flux density can be applied. With the proposed method, the V‐shaped IPM rotor with rectangular magnets, magnetic barriers, and saturated iron bridges can be transformed into a U‐shaped equivalent analytical model. The geometry and material parameters of the magnets in the equivalent U‐shaped model can be determined according to the flux equivalence in the air‐gap of the motor. Then using the subdomain method on the U‐shaped equivalent rotor, the static magnetic field problem can be solved and the flux density distribution in the air‐gap be obtained. The validity of this method and accuracy of the solution is verified by the finite element method with case studies. Compared with existing methods, the improved subdomain method has higher accuracy in calculating flux density including radial and tangential components. The presented rotor reconstruction method is not only limited to single‐layer V‐shaped rotor, it can also be applied to other IPM rotors with more complex structures. It is valuable in the design, optimisation of IPM motors, and even development of new rotor topology.