Electromagnetic Field Computation Research Articles

The Analysis of Permanent Magnet Vernier Synchronous Machine Vibration and Noise

The permanent magnet vernier synchronous machine (PMVSM) has the characteristics of high torque density and high power density and has advantages in the field of low-speed and high-torque applications. The PMVSM utilizes rich harmonics for torque enhancement, but it can also cause an increase in radial electromagnetic force and vibration noise. In this paper, we take a 12-slot 10-pole PMVSM as an example to analyze the source of radial electromagnetic force, vibration and noise. The electromagnetic finite-element model and structural finite-element model of the PMVSM are established for calculation. Through the analysis and calculation of two-dimensional electromagnetic fields, the radial electromagnetic force distribution of the PMVSM is obtained. We derive the radial electromagnetic force formula of the PMVSM and verify the correctness of the formula through harmonic analysis of the radial electromagnetic force. The sources of radial electromagnetic forces at various orders and frequencies within the PMVSM are analyzed and summarized by coupling the radial electromagnetic force obtained from the electromagnetic finite-element model to the structural finite-element model and conducting electromagnetic vibration harmonic response analysis on the PMVSM. The measured acceleration spectrum of the prototype is compared with the finite-element method (FEM) results, verifying the correctness of the finite-element simulation results for electromagnetic vibration.

High-accuracy calculation of singular electromagnetic fields in regions with re-entrant peripheries

Accurate analysis of the electromagnetic fields inside waveguides and cavities with re-entrant boundaries is crucial for many multi-scale device applications. In earlier approaches, the singularities that exist in electromagnetic field gradients inside such waveguides and cavities significantly reduce the accuracy of the calculations. In our scheme, these singular behaviors are treated using Hermite finite elements combined with analytical regularization of the action integral. We show that this approach provides considerably higher accuracy as compared with other methods employed in the literature. Specific calculations are presented for three typical regions: (a) an L-shaped waveguide, (b) an L-cavity, and (c) a cubic cavity with an octant removed to form a triple-junction corner. The method can be adapted to evaluate very high electromagnetic fields in any complex structures displaying “hot points.”

The Complex Impedance of the Hemispherical Ground Electrode: An Open Analytical Problem

The hemispherical ground electrode is a basic electrode whose analysis appears in many textbooks on electromagnetics in chapters dedicated to steady currents. Considering a soil with a given resistivity and an electrode with a given perimeter, the electrode DC resistance is simply calculated from the ratio resistivity/perimeter. Strangely, the generalization of this result to AC regimes is missing. The issue of the frequency-domain impedance of the hemispherical ground electrode has been avoided in the literature despite its trivial geometry. But the problem is indeed not easy; electromagnetic field calculation involves Legendre and Bessel functions; the application of boundary conditions involves an infinite set of points, and some integrals involved need to be calculated recursively. We analyzed the math and physics of the problem but failed to find a closed-form solution. This article with “negative results” can, however, be useful; on one hand it may prevent researchers from wasting their time following the same steps, and, on the other hand, it may attract the interest of new researchers to the subject, ultimately, accelerating its analytical solution (if the solution exists).

Innovative technologies for strengthening of internal surfaces of suspension parts of heavy-loaded machines by laser and high-frequency induction methods

In the article innovative methods of surface hardening of internal surfaces of machine parts by laser and highfrequency induction heating are presented. The relevance of applying the methods of laser and induction hardening for the internal surfaces of heavily loaded parts of quarry equipment is proved. The results of modeling and calculation of thermal and electromagnetic fields under the influence of an external electromagnetic field and laser radiation beams are presented. The original design of a complex of equipment for processing the internal surfaces of suspension parts by external electromagnetic field is described. The optimal designs of inductors with magnetic circuits made of various materials are shown. The study of the structure and properties obtained on the internal surfaces of heavily loaded suspension parts of cars, line of the BelAZ company, treated according to the optimal modes of surface induction exposure is given. The developed original technology and equipment of laser surface hardening, which makes it possible to increase the wear resistance of heavily loaded parts, is described. Data on the implementation of research results at JSC “BELAZ” – the Management Company of the Holding “BELAZ-HOLDING” for processing a wide range of heavily loaded suspension parts are given.

Analytical solution of the field integrals of a cylindrical grid element

Many axisymmetric physical problems related to the calculation of gravitational or electro-magnetic fields can be favorably described by a Poisson potential problem – or the associated field problem – on a cylindrical grid. Numerical integration of the field integrals on such a grid can become expensive in terms of computing time or requires to compromise the accuracy, respectively. Here the analytical solution of the field integrals over a cylindrical volume element are presented and a very efficient implementation is discussed. The results are useful, e.g., for modeling space-charge effects in beams in cylindrical coordinates or gravitational effects in galaxies. The numerical implementation is based on modified relations originally derived by Carlson. A new limiting value and a new transformation relation of the complex elliptic integral of third kind are presented.

Simulation of Emission Processes in Strong Electromagnetic Fields

The problem of calculating the processes of electron emission from metal surfaces in strong electromagnetic fields is considered with allowance for relativistic effects. One of the methods of simulation in these processes is the particle method combined with grid calculation of fields on the basis of Maxwell’s equations. Similar techniques have been developed since the 1960s to the present. However, existing approaches have certain limitations. In this work, for an axisymmetric geometry of the generating system, a new numerical technique simulating the processes of electron emission from metal cathode surfaces is presented. The technique uses the representation of large smoothed Gaussian particles and implements the calculation of electromagnetic fields on Cartesian spatial grids. The software implementation is oriented to parallel computing. The aim of numerical experiments was to determine the parameters of electron emission. Diode and triode cylindrical systems were chosen as test problems. In numerical calculations, the spatiotemporal characteristics of relativistic electron beams generated by emission processes are obtained, including the reproduction of the Child–Langmuir current. The numerical technique developed has confirmed its correctness and efficiency.

Разработка конструкции индуктора для закалки детали сложной формы

Due to active process of import substitution, domestic industry starts producing the parts previously purchased abroad. These parts are necessary for stable and reliable operation of various technical objects and systems. Thus, the development of a technological installation for hardening a metal profile is topical. The task is complicated by the fact that the profile has very thin irregularly shaped walls, which should be hardened only from the inside, while the outer wall of the profile should be heated minimally to maintain strength. The studies have been carried out on simulation models of electromagnetic and thermal fields, which make it possible to reproduce the process of induction heating of the research object. Since the part has the same shape along the entire length, the simulation of the process of its induction heating is performed in two-dimensional space. The authors have developed a simulation model of the process of induction heating of a part of a non-standard shape, which includes calculations of thermal and electromagnetic fields. The design of the inductor is proposed, supplemented with ferrite inserts, which makes it possible to achieve the temperature regime necessary for the hardening process. The developed simulation model makes it possible to evaluate the distribution of the thermal and electromagnetic fields of the part, thereby predicting getting the temperatures required for its hardening when using various designs of inductors. The results of numerical experiments are consistent with the physical concepts of induction heating and prove the possibility to use induction hardening for thin-walled parts of complex shape instead of laser hardening used for this type of parts. The proposed model can be used in engineering practice to design inductors of non-standard parts.

A hybrid enrichment strategy for the efficient construction of reduced order models by the proper generalized decomposition

PurposeThe calculation of electromagnetic fields can involve many degrees of freedom (DOFs) to achieve accurate results. The DOFs are directly related to the computational effort of the simulation. The effort is decreased by using the proper generalized decomposition (PGD) and proper orthogonalized decomposition (POD). The purpose of this study is to combine the advantages of both methods. Therefore, a hybrid enrichment strategy is proposed and applied to different electromagnetic formulations.Design/methodology/approachThe POD is an a-priori method, which exploits the solution space by decomposing reference solutions of the field problem. The disadvantage of this method is given by the unknown number of solutions necessary to reconstruct an accurate field representation. The PGD is an a-priori approach, which does not rely on reference solutions, but require much more computational effort than the POD. A hybrid enrichment strategy is proposed, based on building a small POD model and using it as a starting point of the PGD enrichment process.FindingsThe hybrid enrichment process is able to accurately approximate the reference system with a smaller computational effort compared to POD and PGD models. The hybrid enrichment process can be combined with the magneto-dynamic T-Ω formulation and the magnetic vector potential formulation to solve eddy current or non-linear problems.Originality/valueThe PGD enrichment process is improved by exploiting a POD. A linear eddy current problem and a non-linear electrical machine simulation are analyzed in terms of accuracy and computational effort. Further the PGD-AV formulation is derived and compared to the PGD-T-Ω reduced order model.

A novel representation of electromagnetic field interaction with vertically stratified structures

PurposeThe purpose of this study is to develop an efficient model to solve the electromagnetic forward problem using a novel semi-analytical approach to compute the electromagnetic fields because of the presence of a scatterer.Design/methodology/approachThe proposed model involves a novel formulation of a complete orthonormal set of radiating/nonradiating polarization currents. Furthermore, an integral equation-based representation is derived, and the appropriate boundary conditions are imposed to get the scattered electromagnetic field. An error term is introduced to evaluate the obtained results.FindingsThe proposed model was tested using several examples at different frequencies. The results of this study show that the novel representation exhibits fast convergence behavior and achieves highly accurate results, when compared to the results provided by the transmission line method.Originality/valueThe derived formulations presented in this study are significant in the electromagnetic forward modelling field because of the meaningful physical representation they provide. This is an important aspect that leads to precise calculation of electromagnetic fields for various applications.

Electromagnetic field calculation and analysis of short primary linear induction motor for electromagnetic launch

AbstractThe aim of this study is to determine the electromagnetic field spatial distribution and longitudinal end effect characteristics of short primary linear induction motor (SPLIM) in the field of electromagnetic launch. First, in accordance to the electromagnetic model assumption of SPLIM and one‐dimensional electromagnetic field theory, the analytical expression of the whole‐region magnetic flux density of air‐gap is derived using electromagnetic field boundary conditions in line with the actual physical meaning. Second, the finite element method used in comparing the analytical calculation values of key physical quantities, such as air‐gap flux density and secondary eddy current in a multidimensional manner under various static and dynamic working conditions and verifying the correctness of the analytical calculation of the electromagnetic field. On this basis, the air‐gap flux density of SPLIM is decomposed according to the different generation mechanisms, and the spatial distribution of each part of the flux density is studied. Spatial Fourier analysis of flux density is conducted, the end effect coefficient is defined, and the change rule of the end effect coefficient with the design parameters of the motor is studied. Finally, a megawatt‐class high thrust prototype test platform was built, and the measured electromagnetic force was compared with the electromagnetic force calculated by air gap magnetic field and secondary eddy current. The steady‐state error of the two was less than 2%, which verified the accuracy of the analysis and calculation.

Lightning Electromagnetic Fields Computation: A Review of the Available Approaches

Lightning represents one of the most critical issues for electrical infrastructure. In dealing with overhead distribution line systems, indirect lightning strikes can lead to induced voltages overcoming the critical flashover value of the line, thus damaging the insulators. The computation of lightning-induced voltages requires the modeling of the lightning current, the evaluation of the lightning electromagnetic fields and the solution of the field-to-line coupling equations. The numerical calculation of the lightning electromagnetic fields is time-consuming and is strongly dependent on the lightning channel modeling and soil properties. This article presents a review of the most widely adopted methods to calculate the lightning electromagnetic fields, starting from the classical formulation, which requires numerical integration, and highlighting the most effective approaches that have been developed to reduce computational effort. This is done first for the case of a perfectly conducting ground, then the available formulations to account for the ground finite conductivity are presented together with their possible implementations in both the frequency and time domains.

Exact Expressions for Lightning Electromagnetic Fields: Application to the Rusck Field-to-Transmission Line Coupling Model

An exact analytical expression for the electric field of the return stroke as excited by a propagating step current source is derived in this paper. This expression could be advantageously used to evaluate the disturbances caused by lightning on overhead lines. There are three equivalent procedures to evaluate the voltages induced by lightning on power lines, namely, the Agrawal–Price–Gurbaxani model, the Taylor–Satterwhite–Harrison model, and the Rachidi model. In the case of a vertical return stroke channel, the coupling model developed by Rusck becomes identical to these three coupling models. Due to its simplicity, the Rusck model is frequently used by engineers to study the effects of lightning on power distribution and transmission lines. In order to reduce the time involved in the electromagnetic field calculation, the Rusck model is incorporated with an analytical expression for the electromagnetic fields of the return stroke excited by a propagating step current pulse. Our research work shows that the Rusck expression can be used to calculate the peak values of lightning induced voltages to an accuracy of about 10%. However, the use of this analytical expression to calculate the time derivatives of lightning induced voltages may result in errors as large as 50%. The derived expression in this paper can be used to correct for this inaccuracy. We also provide an exact expression for the electric field at any given point in space when the propagating current is an impulse function. This expression can be combined with the convolution integral to obtain the electric field corresponding to waveforms similar to measured return stroke currents.

Metasurface design with a complex residual neural network.

In recent years, researchers have made great progress in solving complex electromagnetic field computing problems by using deep learning methods. However, the approaches found in literature were devoted to solving the real-number problem of electromagnetic field calculations. For the complex number problem, there was no good solution. Here, we proposed an advanced computation method for metasurfaces based on a complex residual neural network (CRNN). We predicted the scattering (S)21 parameters of a cylindrical structure in the range of 1.2 to 1.7µm wavelengths. By providing a set of cylindrical structure parameters, we could quickly predict the S 21 parameters with CRNN and design a metalens, which proved the ability of the proposed method. In addition, our method can also be extended to the calculation of electromagnetic fields where the speed of the calculation of the complex number of metasurfaces should be accelerated.

Компьютерное моделирование процессов электронной эмиссии в сильных электромагнитных полях

The paper discusses the problem of computer simulation of electron emission processes in strong electromagnetic fields. In this work, a numerical method for calculating electron emission from the surface of a metal cathode for the axial symmetric geometry of a technical system is proposed. For modelling, the particle method and grid calculations of electromagnetic fields based on Maxwell's equations are applied. The approach uses the representation of large smoothed Gaussian particles and implements calculations of the electromagnetic fields on Cartesian spatial grids. The software realization is directed towards on parallel computing. The calculation of the emission process in a coaxial cylindrical diode with magnetic self-insulation with the use of developed technique was carried out. The process is considered for two situations: with and without the longitudinal plasma layer. The calculations show that the presence of plasma leads to an increase in the emission current. This result is consistent with the results of experiments.

A tube-like Pd@coordination polymer with enhanced solar light harvesting for boosting photocatalytic H2 production in a wide pH range and seawater.

Coordination polymers (CPs) have emerged as promising candidates for photocatalytic H2 production owing to their structural tailorability and functional diversity. However, the development of CPs with high energy transfer efficiency for highly efficient photocatalytic H2 production in a wide pH range still faces many challenges. Here we constructed a novel tube-like Pd(ii) coordination polymer with well-distributed Pd nanoparticles (denoted as Pd/Pd(ii)CPs) based on the coordination assembly of rhodamine 6G and Pd(ii) ions and further photo-reduction under visible light irradiation. Both the Br- ion and double solvent play a key role in forming the hollow superstructures. The resulting tube-like Pd/Pd(ii)CPs exhibit high stability in aqueous solution with the pH range from 3 to 14 due to the high Gibbs free energies of protonation and deprotonation, which provides the feasibility of photocatalytic hydrogen generation in a wide pH range. Electromagnetic field calculations showed that the tube-like Pd/Pd(ii)CPs have a good confinement effect on light. Therefore, the H2 evolution rate could reach 112.3 mmol h-1 g-1 at pH 13 under visible light irradiation, which is far superior to those of reported coordination polymer-based photocatalysts. Moreover, such Pd/Pd(ii)CPs could also reach a H2 production rate of 37.8 mmol h-1 g-1 in seawater under visible light with low optical density (40 mW cm-2) close to morning or cloudy sunlight. The above unique characteristics make the Pd/Pd(ii)CPs possess great potential for practical applications.

Уточненное моделирование и экспериментальное исследование энергоэффективной системы испытаний асинхронных машин

When testing asynchronous machines, it is important to use energy-efficient methods, for example, the method of mutual loading of two machines with articulated shafts. One machine operates in the mode of the motor – frequency converter, the second machine operates in the mode of the generator – industrial frequency network. Both machines are simultaneously tested under load and energy costs for testing are reduced due to its recuperation. The method requires a correct loading algorithm. The modeling of the method based on chain models does not consider the implementation feature. Thus, it is advisable to refine the simulation of the asynchronous machine testing system by the mutual load method. The method is based on strict models considering the coupling of machine torque on a common shaft, the operation of machines in the mode of frequency converter, non-sinusoidal supply voltage, saturation of steel, displacement of current in conductors, for example, based on the associated analysis of electromagnetic fields in both machines. The authors have applied the packages of electromechanical units with electrical and mechanical Ansys Simplorer ports and finite element analysis of electromagnetic fields Ansys Maxwell for refined simulation of the asynchronous machine testing system by the method of mutual loading. Experimental studies of the system have been carried out on laboratory equipment using certified devices. A refined simulation of an energy-efficient testing system of asynchronous machines by the method of mutual loading has been carried out. It is based on calculations of the electromagnetic field and allows us to read the transient and steady-state modes of operation of a two-machine unit with a common shaft. An automated stand has been created that allows testing asynchronous machines by the method of mutual loading. The developed refined simulation of electromechanical processes in asynchronous machines during tests by the method of mutual loading with associated calculations of electromagnetic fields in both machines provides calculated results with an error of no more than 5–7 % in comparison with 40 % error of calculations in the transient modes of operation using chain models.

COMPUTATION OF QUASISTATIC ELECTROMAGNETIC FIELDS OF COMPLEX ELECTRIC POWER FACILITIES

: Accurate computation of low-frequency quasistatic electromagnetic fields is important in the design of electricity transmission and conversion devices. This work presents the theoretical groundwork of a computation using integral equations. The procedures for solving these equations are defined by applying the method of moments and the point matching method. The unknown distribution of the source function density on the thin-wire elements is approximated by the third degree polynomials. On rectangular planes the approximation of an unknown source function is achieved by means of bilinear elements. A program has been developed for the parallel electromagnetic field computation based on the described method.

Electromagnetic field computation of multilayer vacuum chambers with physics-informed neural networks

The electromagnetic interaction of a charged particle beam with multilayer vacuum chambers is of particular interest in accelerator physics. This paper presents a deep learning-based approach for calculating electromagnetic fields generated by the beam in infinitely long multilayer vacuum chambers with arbitrary cross section. The presented approach is based on physics-informed neural networks and the surface impedance boundary condition of a multilayer structure derived from the transmission line theory. Deep neural networks (DNNs) are utilized to approximate the solution of partial differential equations (PDEs) describing the physics of electromagnetic fields self-generated by a charged particle beam traveling in a particle accelerator. A residual network is constructed from the output of DNNs, the PDEs and boundary conditions are embedded into the loss function and differential operators are calculated using the automatic differentiation. As a result, the presented approach is regarded to be mesh-free. The approach is applied to circular and elliptical vacuum chambers with a three-layer structure. It is verified in comparison with the recently proposed boundary element method. The effects of chamber geometries and multilayer structure on the beam coupling impedance are demonstrated.

An Efficient Method for the Computation of Electromagnetic Fields Associated With Tortuous Lightning Channels

Lightning electromagnetic (EM) fields are typically computed by assuming the current propagation within a straight vertical channel of negligible cross section. However, it is well known that the lightning path is tortuous and this can significantly affect the radiated fields and the lightning-induced voltages on power lines. Lupò <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (2000) proposed an analytical method evaluating the EM fields radiated by a tortuous channel assuming a step current source; to consider an arbitrary (realistic) current source, a slow-converging convolution integral was applied. The aim of this article is to reduce the computation time of such procedure by extending to the tortuous channel case the approach proposed by Brignone <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (2021) for the evaluation of the lightning EM fields with arbitrary current source, originally developed for a straight vertical channel. The performances of the present method are evaluated by means of comparison with the solution proposed by Lupò <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (2000), showing an excellent agreement with a significant reduction of the CPU effort. This in principle will allow the computation of lightning-induced overvoltages at both individual and statistical level without a prohibitive computational effort.

A deterministic numerical scheme for an electron heat transport model

In inertial confinement fusion plasma, the electron population may be strongly out-of-equilibrium on a duration and spatial domain comparable to those of the implosion process itself. At such a scale, full kinetic simulations are prohibitively demanding, which leads to persistent difficulties when trying to analyse effects of microscopic processes on the macroscopic evolution. For that purpose reduced kinetic transport models are developed. They aim at providing a kinetic closure to hydrodynamic equations through the computation of heat flux density, stress viscosity and electromagnetic fields from the electron distribution function. If sufficiently accurate, the latter would allow to analyse finer kinetic phenomena such as instabilities in plasma. The choice among existing models is thus dictated by a compromise between their precision and the efficiency of their numerical implementation. In this paper, a first order deterministic scheme is proposed for one such model that overcomes the difficulties appearing in previous implementations.