Calculation Of Magnetic Field Research Articles

Computationally Effective Modeling of Self-Demagnetization and Magnetic Field for Bodies of Arbitrary Shape Using Polyhedron Discretization

A performance-effective numerical method for magnetic field calculations is proposed. The method can accept either regular or irregular polyhedron discretization that enables us to construct magnetic object models of an arbitrary shape. A concise, closed-form expression for the magnetic field of a polyhedron is presented, which allows for the high accuracy of the method. As a case study, models of a solid sphere, an ellipsoid, a cuboid, and a well are considered. The models are approximated with a dense irregular grid, elements of which are polyhedrons. The approximation leads to the system of linear algebraic equations that we solve with a gradient method, which allows for finding the self-demagnetization of the body and then calculating the total magnetic field. For the presented example of a well in the medium of relatively strong magnetic susceptibility (0.2), the contribution of the self-demagnetization to the secondary magnetic field reaches an RMS of 24%.

Semi-Analytical Calculation of the Unsaturated Magnetic Field Distribution of a Slotted Spoke-Type Interior Permanent Magnet Machine With Conformal Mapping Method

The performances of an electric machine are closely related to magnetic field, and the magnetic field calculation is the basic work of machine design and optimization. In slotted spoke-type interior permanent magnet (IPM) machines, the analytical calculation of magnetic field is complicated because the boundary of machine is difficult to model. Therefore, this article introduces a conformal mapping (CM) method to calculate the magnetic field semi-analytically. First, the interior magnet is transformed into the surface-mounted magnet to reduce the complexity of boundary conditions. The air-gap magnetic field of the slotless spoke-type IPM machine is calculated by using the boundary conditions of the transformed surface-mounted permanent magnet machine. Then, based on the magnetic field of the slotless air gap, the magnetic fields of the slotted air gap and teeth are also calculated by the CM method. All the semi-analytically calculated magnetic fields are directly verified by the FEM simulation and indirectly verified by the comparison of torque and back EMF. In addition, the comparison of computation time between the semi-analytical method and the FEM shows that the semi-analytical method is time-saving.

A Novel 3-D Mathematical Modeling Method on the Magnetic Field in Nutation Magnetic Gear

Accurate prediction of the magnetic field is an essential guideline for permanent magnetic gear design and optimization. The existing magnetic field calculation methods are divided into 2-D and 3-D calculation methods. For coaxial magnetic gears, the calculation of a 2-D magnetic field can be employed to meet the design requirements. However, as a new spatial transmission mechanism, nutation magnetic gear relies on a 3-D magnetic field to transmit force and torque. Therefore, the 2-D magnetic field cannot meet the design requirements. Hence, it is necessary to accurately predict the 3-D magnetic field. In this article, an analytical mathematical model of the 3-D magnetic field of magnetic gears is established. To verify the accuracy of the model, the magnetic field generated by the same magnetic gear is predicted by the proposed model, finite element method, and equivalent current method. The results indicate that the 3-D magnetic field mathematical model proposed in this article can accurately predict a 3-D magnetic field, which is an essential guide for the research and optimization of magnetic gears.

Efficient calculations of magnetic fields of solenoids for simulations

This paper examines different models for calculating the magnetic field of solenoids. Accuracy and computation time are compared for a range of different simplified models: a current loop and a thin shell solenoid, and solenoids with finite length and thickness. There is no definitive answer to “what model is the best”, as it depends on the specific use case, but there are certain models that excel in speed or accuracy, and there are models that have very limited use. This paper serves as an overview and will help the reader make an informed choice of a model.

Numerical Analysis and Comparison of Magnetic Fields Caused by Constant and Time Varying Currents in Medium Voltage Underground Cables

The magnetic fields formed around the conductors carrying current alternating current in the power system adversely affect human health. Especially in medium voltage systems, where energy is mostly carried by underground cables for electrical safety, due to the high current levels and the installation of cables in areas where people live, studies in this field have gained importance. In literature, many studies have been carried out on the calculation of magnetic fields caused by underground cables using numerical methods and their comparison with limit values. In some of these studies, the boundary conditions for phase currents are defined as constant. However, alternating current, which is the source of the magnetic field, is a time-varying vector quantity. For this reason, it is important for the accuracy of the analysis to take into account the direction of the current, the time-dependent change of the current and the phase difference while calculating the magnetic flux density. In this study, the magnetic flux density values caused by a sample medium voltage underground cable system at the reference plane one meter above the ground surface are determined using Comsol Multiphysics. Analyzes are performed both in the stationary domain where the current is constant and in the time domain when it changes depending on time, and the results are discussed and compared. According to the results, it is determined that the maximum magnetic flux density exceeded the limit value of 0.2 mT, while the phase current values are constant. However, it is seen that the magnetic flux density obtained in time-dependent analyzes remains within the safe limit. In addition, it has been determined that the results obtained in the stationary domain are considerably higher than the results obtained in the time domain. As a result, it has been revealed that the time-dependent variation of the current must be taken into account in order to accurately determine the magnetic flux density in the magnetic field analyzes to be performed for underground cables or overhead lines carrying alternating current.

An Improved and Efficient Analytical Model for Magnetic Field Calculation in Linear Permanent Magnet Machines

A simple and improved analytical model (AM) for linear permanent magnet synchronous machine (LPMSM) based on the correction factor is presented in this paper. A slotless linear permanent magnet machine (PLPM) with AM developed in Cartesian coordinate is selected to investigate. Consequently, the fitting equations of curvature factors for the permanent magnet and armature are obtained. The subdomains for LPMSM are simplified from 6 down to 3 domains based on curvature equations. The magnetic flux density and force show that the proposed approach agrees with the finite element (FE) model. Moreover, the reduced calculation domains and harmonic orders make AM proposed in the paper much faster. The main contribution of the work is to present a simple strategy for coordinate transformation and calculation strategy for LPMSM, which provides guideline for designers to investigate the machines developed in Cartesian coordinate.

General relativistic calculation of magnetic field and power loss for a misaligned pulsar

In this study, we model a pulsar as a general relativistic oblique rotator, where the oblique rotator is a rotationally deformed neutron star whose rotation and magnetic axis is inclined at an angle. The oblique rotator spins down, losing rotational energy through the magnetic poles. The magnetic field is assumed to be dipolar; however, the star has a non-zero azimuthal component due to the misalignment. The magnetic field induces an electric field for a force-free condition. The magnetic field decreases as the misalignment increases and is minimum along the equatorial plane of the star. In contrast, the electric field remains almost constant initially but decreases rapidly at a high misalignment angle. The charge separation at the star surface is qualitatively similar to that of Newtonian calculation. We find that the power loss for a general relativistic rotator is minimum for either an aligned or an orthogonal rotator, which is in contrasts with Newtonian approach of calculation where the power loss increases with an increase in the misalignment angle.

Moment method based distributed multipoles for modeling magnetic materials in 2D and 3D magnetostatics

This paper aims to develop a new modeling method, referred to as a moment method based distributed multipoles (MMDMP), for precise and fast computation of magnetic field and force involving various magnetic materials such as a permanent magnet (PM), an electromagnet (EM) and a ferromagnetic material (FM). The method decomposes the magnetic materials into local sources, consisting of volume and surface elements. Then, the magnetic field from the local sources is computed with the magnetization and demagnetization tensors of the elements. The demagnetization tensors are derived as a closed-form according to the geometry of the elements, which can be further converted into multipoles based on the distance between an observation point and the elements for computational efficiency. Additionally, the MMDMP is applied to the FM and EM by analyzing the magnetization of both materials due to existing magnetic fields. Magnetic interactions among the materials are computed by the sum of the elemental forces, which are forces on the local sources. The computational accuracy and efficiency are verified by field distribution and the force and torque interaction between the PM and an iron-core EM in 3D space. The results are compared to numerical solutions from a finite element method (FEM) and fundamental integral form equations such as Biot–Savart law. Finally, the MMDMP is applied to analyze the magnetic field of a brushless direct current (BLDC) motor and validated by the FEM and experiments. The results show that the MMDMP can provide fast and accurate analysis of magnetic characteristics of electromechanical systems.

NMR Relaxation Modelling in Porous Media with Dual-Scale-Resolved Internal Magnetic Fields

A pore-scale forward modelling approach for NMR relaxation responses of sandstones incorporating their dual-scale nature is presented. The approach utilises X-ray micro-CT images to capture inter-granular porosity and scanning electron microscopy images to reconstruct clay regions via a resolved clay micro-structure model. A key to calculating the NMR response with resolved clay micro-structure is the development of a dual-scale internal magnetic field calculation. This is achieved by a separation of near- and far-field effects in a dipole approximation of the internal field with periodic clay micro-structures, the latter of which take local clay pocket porosity into account. Tri-linear interpolation of the micro-CT image before calculation of the internal magnetic field further reduces errors in the transition regions between coarse- and fine-scale structure, with final discretisation level matching the fine-scale clay micro-structure model across the whole domain. The method is validated against direct calculations of model media at full resolution and applied to Bentheimer sandstone. Measured and simulated NMR T_2 relaxation responses, including relaxation time distribution shape, are in excellent agreement and distributions of internal magnetic field gradients at the highest spatial resolution as well as diffusion-averaged effective gradients are reported.

Analysis of processes in magnetorheological sealer considering for magnetic fluid deformation

The small size of the working gap in the sealer makes many physical measurements difficult or impossible. The main way to study the processes inside the device is to use analytical and numerical mathematical modeling. Most researchers apply finite-element calculation of magnetic field and analytically find the difference in pressure. Currently, there are few studies devoted to multiphysics numerical calculations of the processes in magnetorheological seal. The use of numerical models allows considering the dependence of rheological properties of magnetic fluid on hydrodynamic, temperature and magnetic fields, the real geometry of the working zone. Compared to the analytical models, a numerical one includes a smaller number of assumptions and allows visualizing various flow parameters, which are especially important for the analysis. The purpose of this study is to analyze the effect of the deformation of the magnetorheological plug in case of pressure difference held by the sealer. The study is based on the developed numerical model with the related calculation of magnetic and hydrodynamic fields. The study is carried out based on the theories of ferrohydrodynamics, hydrodynamics and electromagnetic field. Integrated finite-element modeling of the magnetic and hydrodynamic fields of the magnetorheological sealer in Comsol Мultiphysics has been used. A numerical model of the magnetorheological sealer characterized by automatic rearrangement of the boundaries of the liquid plug based on the balance of pressures inside the liquid has been developed. The distribution results of magnetic induction and pressure in the working gap of the sealer, considering changes in the boundaries of the magnetic fluid, has been obtained. Comparison of the results of the obtained retained pressure drop and the results of other models has been carried out. A numerical mathematical model that considers the deformation of the magnetorheological plug has been developed. The model makes it possible to estimate the influence of centrifugal forces of the rotating shaft on the retained pressure drop. The results can be used to create high-speed seal components. The difference of the value of analytical calculation does not exceed 5 %. The assumption about full filling of the working gap with magnetic fluid 2,5 times underestimates the retained pressure difference at high shaft rotation speeds.

ЗНИЖЕННЯ РІВНЯ МАГНІТНОГО ПОЛЯ ПІДЗЕМНОЇ КАБЕЛЬНОЇ ЛІНІЇ НА ВІДПОВІДАЛЬНИХ ДІЛЯНКАХ ЗА ДОПОМОГОЮ КОМПОЗИЦІЙНИХ МАГНІТНИХ ЕКРАНІВ КІНЦЕВОЇ ДОВЖИНИ

In the article, the numerical calculation and analysis of three-dimensional magnetic field of underground power cable line with finite-length magnetic shields used to reduce the level of this field on the ground are carried out. Both fill-up soil and filling soil containing magnetic particles and then having effective magnetic properties (=1÷1000) are proposed to used as magnetic shields. The shielding efficiency is studied for underground 330 kV cable line depending on the dimensions and effective magnetic permeability () of the shields. As shown, the use of filling soil with magnetic properties gives a possibility to reduce the field on the ground five times. This type of shielding is more efficient as compared to magnetic fill-up soil. The computed results reveal the non-monotonic variation of magnetic field on the ground above the soil edge zones. The longitudinal size of these zones is in the order of the depth of the cables. References 16, figures 9.

An integrated fluid simulation platform on Hall thruster plasmas

In this work, a newly integrated fluid simulation platform, named DUT-HTFS, is developed for the multiple physical fields in Hall thrusters. The integrated simulation platform includes three inter-related parts: the geometry module, background magnetic field module, and plasma module. Using the geometry module, three sets of meshes for a Hall thruster are obtained. One set of the mesh is for the calculation of the background magnetic fields, the second is for the electric potentials, and the third is for the plasmas. Based on the meshes and using the background magnetic field module, a numerical result of the background magnetic field in the Hall thruster is obtained and discussed. Based on the meshes and the numerical result of the background magnetic field, using the plasma module, the numerical results of the plasmas in the Hall thruster are obtained. The results of the plasma density, the electric field, the electric potential, and the ionization rate are similar to those from HPHALL (Hybrid-PIC Hall thruster code) simulations and are qualitatively consistent with the experimental results from the literature. Furthermore, varying the neutral gas pressure from 0.02 to 0.03 Torr, the numerical results of the plasmas in the Hall thruster are obtained. These results reveal that neutral gas pressure effects contributed considerably to the shape, location, and magnitude of the peak plasma properties, including the ion density, axial electric field, and ionization rate. This fluid simulation platform could provide a new angle of view for better understanding of the physical mechanism in Hall thrusters.

MagTetris: A Simulator for Fast Magnetic Field and Force Calculation for Permanent Magnet Array Designs

MagTetris: A Simulator for Fast Magnetic Field and Force Calculation for Permanent Magnet Array Designs

Leakage Magnetic Field Calculation and Optimization of Double Inverse Series Coil Structure of Electric Vehicle Wireless Charging Systems

Leakage Magnetic Field Calculation and Optimization of Double Inverse Series Coil Structure of Electric Vehicle Wireless Charging Systems

Semi-Analytical Magnetic Field Calculation for Dual-Rotor Permanent-Magnet Synchronous Machines by Using Hybrid Model

Based exclusively on the exact subdomain (SD) technique and finite-difference method (FDM), this article proposes a 2-D hybrid model (HAM) for the semi-analytical magnetic field calculation in electrical machines at no-/on-load conditions. It is applied to dual-rotor permanent-magnet (PM) synchronous machines. The magnetic field is computed by solving Laplace’s and Poisson’s equations through exact SD technique in all regions at unitary relative permeability (i.e., PMs, air gap, and slots) with a numerical model based on FDM in ferromagnetic regions (i.e., teeth and rotor/stator yokes). These two models are specifically coupled in both directions (i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${r}$ </tex-math></inline-formula> - and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\theta }$ </tex-math></inline-formula> -edges) of the (non-)periodicity direction (i.e., in the interface between teeth regions and all its adjacent regions as slots and/or air gap). To provide accurate solutions, the current density distribution in slots regions is modeled by using Maxwell’s equations. The finite-element analysis (FEA) demonstrates highly accurate results of the developed technique. The 2-D HAM is ≈6 times faster than 2-D FEA.

Analytical Modeling for Magnetic Field Calculation of SPMSM Based on Equivalent Magnetic Network Method

In order to quickly calculate electromagnetic parameters and reduce total harmonics distortions (THD) of air-gap flux density for surface-mounted permanent magnet synchronous motor (SPMSM), the equivalent magnetic network method (EMNM) is used. Compared with traditional magnetic circuit method, the calculation result is more accurate and the calculation speed is faster than finite element method FEM). The EMNM considering the stator groove shape and core saturation is established by piecewide fitting of annular equivalence and magnetic ring curve formulas of the groove fan. The accuracy of EMNM is verified by FEM.

An Optimized Measurement Method for Magnetic Properties of Permalloy Sheet Under Demagnetization

Generally, a permalloy sheet is applied as the major shielding material for weakening the environmental magnetic field interference in a field of high-precision measurement. The demagnetization for a permalloy sheet determines its shielding performance; therefore, an enhanced method for measuring the magnetic properties under degaussing excitation is proposed in this paper. The excitation apparatus and a feedback control system are designed for regulating the B curve of a permalloy sheet as the desired amplitude and waveform. Furthermore, a method for applying degaussing excitation is proposed and the corresponding measurement approach under such magnetic conditions is investigated. Finally, the dynamic Jiles&#x2013;Atherton model is combined with a finite element method (FEM) algorithm for applying the tested data to the residual magnetic field calculation of a scaled-down model. The agreement between the calculated and tested remanence distribution indicates that the proposed measurement method is reliable and applicable.

Conceptual Fields and Magnetic Field: a theoretical model for epistemological classification of tasks in magnetostatics

This work presents a theoretical model for epistemological classification of tasks in magnetostatics aimed at High School and Higher Education. The approach is based on the theory of conceptual fields and includes classification in terms of thought operations necessary to solve the tasks and in these situations’ parameters. Four primary classes of situations are proposed, namely, description of magnetic interactions, analogic symbolization of magnetic fields, non-analogic symbolization of magnetic fields and calculation of magnetic fields. These classes cannot be reduced one to another, however they can occur simultaneously in the same task. Each one was subdivided in secondary classes of situations based on parameters they can assume and ordered by epistemological complexity. As contributions for physics teaching research this work offers a theoretical-methodological model for analyzing students’ progression in the conceptual field of magnetostatics, a conceptual structure for building situations based on predicative and operational competences for understanding the concept of magnetic field, and a practical example of epistemological classification of situations that can be adapted for other areas of Science like Quantum Mechanics, for example.

Procedure for selecting optimal geometric parameters of the rotor for a traction non-partitioned permanent magnet-assisted synchronous reluctance motor

This paper reports the construction of a mathematical model for determining the electromagnetic momentum of a synchronous reluctance motor with non-partitioned permanent magnets. Underlying it is the calculation of the engine magnetic field using the finite-element method in the flat-parallel problem statement. The model has been implemented in the FEMM finite-element analysis environment. The model makes it possible to determine the engine's electromagnetic momentum for various rotor geometries. The problem of conditional optimization of the synchronous reluctance motor rotor was stated on the basis of the rotor geometric criteria. As an analysis problem, it is proposed to use a mathematical model of the engine's magnetic field. Constraints for geometric and strength indicators have been defined. The Nelder-Mead method was chosen as the optimization technique. The synthesis of geometrical parameters of the synchronous reluctance motor rotor with non-partitioned permanent magnets has been proposed on the basis of solving the problem of conditional optimization. The restrictions that are imposed on optimization parameters have been defined. Based on the study results, the dependence of limiting the angle of rotation of the magnet was established on the basis of strength calculations. According to the calculation results based on the proposed procedure, it is determined that the optimal distance from the interpole axis and the angle of rotation of magnets is at a limit established by the strength of the rotor structure. Based on the calculations, the value of the objective function decreased by 24.4 % (from −847 Nm to −1054 Nm), which makes it possible to significantly increase the electromagnetic momentum only with the help of the optimal arrangement of magnets on the engine rotor. The results of solving the problem of synthesizing the rotor parameters for a trolleybus traction motor helped determine the optimal geometrical parameters for arranging permanent magnets.

Verification Methodology for Simulation Models of the Synchronous Generator on Transients Analysis

During transients that occur in an electric network, large currents can flow and large electromagnetic torques can be developed in electric generators. Accurate calculation of currents and magnetic fields during transients is an important element in the optimal design of generators and network parts, as well as mechanical parts of machines and other torque transmission parts. This paper describes the modeling of a sudden three-phase short-circuit on a synchronous generator using the finite element method (FEM) and the dynamic model. The model for simulations that use the FEM was built in the MagNet software package, and the dynamic model is embedded in the MATLAB/Simulink software package. The dynamic simulation model of a part of a network with two identical generators, represented by equivalent parameters, was developed. The results obtained after the simulation of a sudden three-phase fault in the generators by both methods are presented, including three-phase voltages, three-phase currents, machine speeds, excitation voltages, and mechanical power. In particular, the short-circuit current in the phase with the highest peak value was analyzed to determine the accuracy of the equivalent parameters used in the dynamic model. Finally, the results of these two calculation methods are compared, and recommendations are presented for the application of different modeling methods.