Calculation Of Magnetic Field Research Articles

Accurate Analytical Method for Magnetic Field Calculation of Interior PM Motors

In this article, a rotor magnetic potential (RMP) model is proposed, which can accurately describe the rotor surface magnetic potential distribution under the interaction of multi-excitation sources. Furthermore, a new magnetic equivalent circuit (MEC) model is used to model the complex saturation in the bridge region, which employs an improved nonlinear reluctance modeling method. Then, the unknown parameters in the RMP model are obtained by solving the MEC model. In this article, the RMP model and MEC model are combined to consider the stator and rotor saturation effects, and the magnetic field is calculated accurately. Compared with the existing RMP model, the proposed one can take into account the effects of the stator saturation and PM magnetic field. Compared with the existing MEC and equivalent magnetic network (EMN), the area of the nonlinear reluctance in this paper varies with excitation conditions, which can accurately consider the saturation effects in the bridge region. This improvement can improve calculation accuracy on the basis of reducing the number of nonlinear reluctances. Moreover, the proposed method does not need to consider the change of the air-gap reluctances caused by rotor rotation. Finally, the proposed method is verified by both finite element analysis and experiments.

Regularization of an external boundary value problem for open axisymmetric magnetic systems

Important characteristic of magnetic-field with the high measure of intensity and heterogeneity in the swept volume of the electromagnetic systems is a size of tension of the field Н. Calculation of tension in the field H in these systems, characterized by relatively large air interval, given its three-dimensionalty, presents a very difficult task. Analytical decision of equalization of Laplace that describes distribution of magnetic-field in the interpolar volume of the axisymmetrical magnetic systems, difficultly from difficult geometry of bodies that is included in a calculation area, that is why for research of distribution of tension the expedient use of numeral methods of calculation - to the method of eventual differences, method of eventual elements, method of maximum integral equalizations. The calculation of distribution of scalar magnetic potential in open magnetic systems with the use of numeral methods of calculation causes the difficulties related to limitation of calculation  area in which the calculation is conducted. The static magnetic fields, analysed in this research, obey one of basic equalizations of mathematical physics, and namely, to equalization of Laplace in partial differential. In case of calculation of magnetic field of the axisymmetrical magnetic systems it is necessary to resolve the Cauchy problem for equalization of Laplace. It is known, that this task does not have characteristic of steadyness, and thus does not obey Hadamars third condition of correctness and, therefore, is considered incorrectly defined. For the number of unsteady tasks of mathematical physics of R.Lattes and ZH.Lions developed the quasi-random method, that can be applied both for evolutional tasks, as well as for constant. The basic idea of quasi-random method lays in proper update of differential operators that are part of the task. This change is done by introducing additional differential elements. Application of this method allows to use effectively the numeral methods of calculation of regional task for  open axisymmetrical systems.

CHARACTERISTICS OF A CYLINDRICAL INDUCTOR OF A ROTATING MAGNETIC FIELD FOR TECHNOLOGICAL PURPOSES WHEN IT IS POWERED FROM THE MAINS AT A GIVEN VOLTAGE

Introduction. A computational analysis of the characteristics of an inductor of a rotating magnetic field for technological purposes is presented. The design of its stator is borrowed from a three-phase induction motor. The cylindrical cavity inside the stator is occupied by a working chamber into which a granular or liquid processed substance is loaded. The processing is carried out with elongated ferromagnetic elements moving with a magnetic field. Problem. The purpose of the article is a study of the electromagnetic, phase, and energy characteristics of an inductor at its operation under load mode with a given voltage of the stator winding. Methodology. The study is performed on the basis of numerical calculations of the magnetic field, taking into account the anisotropy of the low-magnetic medium in the working chamber. Its discrete medium is represented homogeneous with different magnetic permeabilities on mutually perpendicular axes. The technique of transition from the results of the magnetic field calculation to the electric, magnetic, phase and energy parameters of the inductor is given. This is facilitated by the electrical equivalent circuit of the stator phase winding, the equilibrium equation of its electrical quantities, vector diagrams and an iterative method for determining the current at a given voltage. Results. Mutual dependencies of a number of inductor parameters are formed into a family of characteristics exhibiting its properties in an operating mode with a changing load. Characteristics include such quantities as magnetic flux linkage of the stator winding, its current and EMF, phase shifts between them, electromagnetic torque, expended and useful power and its losses, power factor and efficiency. In this article, a feature of this mode is the stability of the stator winding voltage in the inductor. This complements the earlier studies of the inductor in the mode with stabilization of the winding current, which allows to compare these options. On the example of a test sample of an inductor, a number of its characteristics are shown, vector diagrams of its electric and magnetic quantities illustrating their mutual phase shifts are given. Practical value. The presented technique for determining the electric and magnetic quantities of the inductor and their phase relationships, and also the shown family of characteristics can contribute to increasing the design efficiency and improving the inductors of the considered type. The developed technique has the universality property, as it is capable of displaying their various circuit and constructional design parameters.

Modeling of Dispersion Magnetic Fields Developed by the Main Electromagnetic Systems Used on Military Ships

Abstract In this paper, the authors present the modelling methods and numerical calculation of the dispersion magnetic field of electrical machines, as well as the results of their validation through practical measurements. An adequate analytic formula for magnetic induction calculation is proposed by the authors. The experimental results validate the proposed analytic model. Moreover, the proposed model is valid for both near and far field regions.

Studying Magnetic Field Variations Accompanying the 2011 June 7 Eruptive Event, by Using Nonlinear Force-Free Field Modeling

We study the features of the magnetic field variations within the 2011 June 7 eruptive event that includes a large filament eruption, a flare, and a CME formation. The magnetic field characteristics were obtained by using vector measurements of the magnetic field with the SDO/HMI and 3D magnetic field calculations based on nonlinear force-free field (NLFFF) modeling. Strong and relatively fast variations in the photospheric field characteristics after the flare onset are shown to be observed only within a small site ($20''\times 20''$) of the eruption region in the neighborhood of the polarity inversion line (PIL). We found that the magnetic field strength, the electric current density, current helicity density and free magnetic energy density above this region are growing with height reaching their maximums at the level of ∼15 Mm. After 2011 July 7 00:00 UT, this height started gradually reducing. The NLFFF extrapolation revealed the presence of a magnetic flux rope elongated approximately along the main PIL and an arcade of magnetic field lines over it. The flux-rope axis is located at height of ∼15 Mm. The flux-rope footpoints approximately coincide with the eruptive filament footpoints. Thus, we concluded that the detected flux rope is associated with the magnetic structure of the observed filament. The detected strong variation of the magnetic field within the eruption region are most probably associated with the magnetic field reconfiguration after the filament eruption. The $T_{n}$ parameter, which is the average magnetic field twist within the flux rope, was found to increase up to 2.5 rotations before the flare onset, and to dramatically decrease afterward. This may reflect the developing of kink instability that presumably triggered this eruption.

Fast evaluation of the Biot-Savart integral using FFT for electrical conductivity imaging

Magnetic resonance electrical impedance tomography (MREIT) and current density imaging (MRCDI) are emerging as new methods to non-invasively assess the electric conductivity of and current density distributions within biological tissue in vivo. The accurate and fast computation of magnetic fields caused by low frequency electrical currents is a central component of the development, evaluation and application of reconstruction methods that underlie the estimations of the conductivity and current density, respectively, from the measured MR data. However, methods for performing these computations have not been well established in the literature. In the current work, we describe a fast and efficient technique to evaluate the Biot-Savart integral based on the fast Fourier transform (FFT), and evaluate its convergence. We show that the method can calculate magnetic fields in realistic human head models in one minute on a standard computer, while keeping error below 2%.

Calculation of Magnetic Fields of Cables Laid in Tunnels with Insulation of Cross-Linked Polyethylene (XLPE)

The problem of ensuring the electromagnetic safety of service personnel manifests itself the most seriously in cable tunnels, where the distances between cables with high current loads and the human being is minimal. A computation technique by means of which the magnetic fields of a large number of single-phase cables may be calculated with one- and two-sided grounding of the screens with acceptable precision is proposed. Results of calculations of the magnetic fields produced by 42 cables with high current loads laid in a typical cable tunnel are presented. An analysis of the results is performed and ways of decreasing the strength of a magnetic fields are proposed.

The magnetic circuit analysis of the transverse magnetic flux generator in no-load mode

Purpose. The transversal flux generators are very perspective machine type. They can use low wind or water flow to transform their energy into the electricity with good efficiency value. Obtaining the dependence of the length of the permanent magnet on its magnetizing force on both radii of the rotor. This ratio allows us to correctly select the dimensions of the standardized permanent magnets to excite the generator. This dependence of permanent magnet length allows us to better analyze the electromagnetic processes in transverse magnetic field generator. Methodology. Analytic and computer calculation of magnetic field of the transversal magnetic flux generator in no-load mode. The analytical methodology must be proved by finiteelement method using the 3D simulation in the modern and powerful software such as Ansys Maxwell. It allows us to compare methodology of TFM design and find the most optimal method for TFM design in accordance with fast and accuracy design process. Results. An equivalent circuit is presented for the magnetic system of the transverse magnetic flux generator, which is characterized by a disk design of the rotor and excitation from permanent magnets in no-load mode. On the example of TFM-32-180, the principle of its solution using the working diagram of a permanent magnet is presented. Originality. The analytical calculation of the correct selection of the standardized permanent magnets dimensions to excite the transversal magnetic flux generator in no-load mode. Practical value. This generators work as a low speed machine and have a rather simple construction. It can be used as high effective machine in low speed rivers or wind turbines installations. Therefore, quality and accurate design process is a practically evaluated. Getting the possibility to analytically design the transversal magnetic flux generator more accurately is a good practical value of this perspective type of the machine.

Analytical calculation of magnetic field of bearingless flux‐switching permanent‐magnet machine based on doubly‐salient relative permeance method

A doubly-salient relative permeance method is presented herein to predict the magnetic field of bearingless flux-switching permanent-magnet machines (BFSPMMs). Firstly, the subdomain model method is used to compute the magnetic field of slotless BFSPMMs. Then, the slotting effect of the stator and rotor is obtained by the doubly-salient relative permeance method. By combining the two above, the air-gap magnetic field of slotted BFSPMMs can be obtained. The doubly-salient relative permeance method is based on the theory of the subdomain model method. The whole doubly-salient structure is divided into several subdomains, and the Laplace equations for subdomains are established. Then, according to the boundary conditions between subdomains and the core, and the continuity conditions between adjacent subdomains, the equations are solved to calculate the slotting effect. Based on the proposed analytical model, the flux density and electromagnetic performances including back-electromotive force (EMF), torque, and suspension force are predicted and compared with the finite element method results. Furthermore, the back-EMF of the prototype motor is measured and the suspension experiments are carried out based on the analytical method. The comparison results and experiment results verify the validity of the analytical method.

Alternative Approach for the Calculation of Magnetic Field due to Magnet for Magnetic Field Visualization and Evaluation

The magnetic field of different geometry of the permanent magnet is analytically calculated by using basic principles of the magnetism in very easier approach. Concept of origin shifting and geometrical shape transformation are used to formulate the formula for cuboidal, cubical and cylindrical permanent magnets. This concept can be used for the analysis of magnetic field distribution in space around for permanent magnet as well as electromagnet in a very easier approach. Handy and simplified software is made to calculate the magnetic field due to permanent magnet and electromagnet at any desired position on space. Magnetic field visualization is also done in both magnitude and direction by using MATLAB. 

Rapid 3-D Magnetic Integral Field Computation of Current-Carrying Finite Arc Segments With Rectangular Cross Section

The computation of 3-D magnetic fields is a demanding task in the analysis of electrical machines and other electromagnetic devices. In this context, integral field calculation provides a smooth solution, high precision and resolution, “on-demand”-calculation, and an origin-based formulation of the magnetic field and the magnetic vector potential. However, conventional elliptic methods lead to huge parallelizable computing efforts and significant errors. In this article, a 3-D generic current-carrying arc segment with rectangular cross section is studied. A new analytic formulation is proposed to speed up the computation of magnetic fields and reduce the error by more than three orders of magnitude. In addition, the proposed magnetic vector potential expression has a similar accuracy as numerical integration. In fact, a significant reduction of the error level has been showcased clearly with respect to the existing approaches. This article is promising for improving the design methodology and optimization of large superconducting dipole magnets or arched end-winding geometries of large electrical machines.

Improved Evaluation of Magnetic Loss Inside Silicon Steel Laminations Under 3-D Multi-Harmonic Magnetizations

An improved method is presented to study the efficient numerical modeling of stray-field loss in magnetic shielding excited by a 3-D harmonic magnetic field. The experimental platform is established to obtain the magnetic properties and loss model of the silicon steel lamination under harmonic magnetizations. Experimental determination is improved for more accurate stray-field loss based on the engineering-oriented model TEAM Problem 21c-M1. Prediction and evaluation of stray-field loss and additional iron loss due to harmonic excitations are achieved by special treatment of material properties in the numerical calculation of the harmonic magnetic field.

Research on the Influence of Vibrations on the Dynamic Characteristics of AC Contactors Based on Energy Analysis

Aimed at the influence of the vibration environment on the performance degradation of AC contactors, the purpose of this study is to investigate the failure mechanism of AC contactors under vibration conditions. During the closing process of AC contactors, the impact energy of the iron core may change due to the vibration stress, which may have an uncertain effect on the parameters of the dynamic response characteristics of the contact, and affect the working performance and service life of AC contactors. In this paper, a double-E AC contactor is selected as the research object. Based on the calculation of the transient magnetic field of the electromagnetic mechanism, an energy distribution model of the AC contactor is established. Based on this, considering the influence of vibrations and the input electrical energy under different closing phase angles, the energy model of the iron core collision under simple harmonic oscillation is investigated. The steady-state vibration energy at different frequencies and accelerations is calculated, and its influence on the dynamic response parameters of the AC contactor is analyzed. Finally, the simulation model is verified by experimental data. The results show that the energy analysis model can effectively reflect and explain the uncertainty of the dynamic characteristics of AC contactors under vibrations, from the perspective of the mechanism.

ANALISIS ANOMALI SINYAL ULTRA LOW FREQUENCY BERDASARKAN DATA PENGUKURAN GEOMAGNETIK SEBAGAI INDIKATOR PREKURSOR GEMPABUMI WILAYAH LAMPUNG TAHUN 2016

Regional research had been done to analysis anomalies signal of ultra low frequency based on measurement data as an indicator of the geomagnetic earthquake precursor of lampung in 2016. To achieve purpose of the study conducted by the following steps: (i) Calculation of the total magnetic field of data; (ii) Daily Trend Analysis; (iii) the Fourier transform of the data Geomagnetic Anomaly; (iv) Localization Frequency ULF; (v) Calculation of Ratio Vertical-Horizontal (Polarization Ratio Z / H); (vi) Correction magnetic storms or Disturbance Strom Time (DST); (vii) the identification of earthquake precursors; (viii) Determination of OnsetTime, leadtime,and the direction of precursors. The results of the analysis of ten earthquakes with a magnitude above 5 MW have precursors between 11 to 30 days before an earthquake. Nine out of ten earthquakes studied had an earthquake precursors and precursors that do not have, this is because the distance is too far from the station Magdas in Liwa, West Lampung. Thus it can be seen that the precursor using the magnetic data can be used to make short-term predictions.

Pitch Effect of Helical Coils of Electromagnetic Forming

At present, solenoid (helical) coils are widely used in various researches, especially electromagnetic forming (EMF), due to their advantages of simple manufacture and high magnetic field strength. However, in the study of EMF, there are still some defects in the high precision calculation of solenoid coils in the magnetic field the main reason is that the solenoid coil is of non-axisymmetric structure, which is generally equivalent to the 2-D or 3-D axisymmetric structure in practical research. Not only can it ignore the effect of the pitch effect of the solenoid coil, but also causes a certain deviation in the calculation of the magnetic field. Hence, this paper establishes 5 helical coils and 3-D axisymmetric finite element coils models with different layers for comparative analysis. The simulation results show that the magnetic flux density distribution deviation of helical coil and the 3-D axisymmetric coil is small and can be ignored when the coil layers are 1 or 2 layers. However, the number of linear circles increasing, the deviation between the two increases obviously. Therefore, in the study of EMF, the effect of solenoid coil pitch effect on magnetic field calculation can be ignored when the layers, radius and pitch of helical coils are used less whereas the effect of solenoid coil pitch effect on magnetic field calculation must be considered when the layers, radius and pitch of helical coils are used more.

Magnetic Field Calculation of a Novel Electromagnetic Clutch Based on an Interpolating Element-Free Galerkin Method

In this paper, the interpolating element-free Galerkin method (IEFGM) is introduced to calculate the magnetic field distribution of a novel permanent magnet bistable electromagnetic clutch (BPMEC), which is used in the in-wheel motor drive system to flexibly connecting the wheel and motor to release the mechanical shock and electromagnetic impulsion. Firstly, the fundamental of the IEFGM is introduced, and a new weight function for magnetic field calculation is proposed. Then the nodes distribution is discussed, and the magnetic field distribution of the clutch is analyzed. Simulation results show the IEFGM can impose the boundary conditions directly and fewer nodes are employed, make the calculation efficiency higher. Finally, some experiments are carried out, the experimental results verified the effectiveness of the IEFGM in magnetic field calculation. The study results provide references for the application of the interpolating element-free Galerkin method in the magnetic field calculation.

Measurement of magnetic field of capacitor-coil target using proton radiography

Proton radiography is a widely used method to diagnose the electromagnetic field of plasma. When protons pass through the electromagnetic field of plasma, they are deflected by Lorentz force and redistributed on the recorder. How to reconstruct electromagnetic field from the experimental result is an open problem. In this paper, we take the laser-driven capacitor-coil target for example to introduce and compare particle tracing and flux analysis, which are two widely used methods in proton radiography experiment to reconstruct the magnetic field. The capacitor-coil target is an important method to generate strong magnetic field in laser plasma experiment, where the strong current flows in the coil and its producing magnetic field may be larger than kilotesla. Firstly, the theoretical magnetic fields of capacitor-coil target are calculated with current being 10 kA and 50 kA. Secondly, the Geant4 is used to simulate the proton radiographs, where protons with 7.5 MeV pass through the target and the theoretical magnetic field is recorded. Thirdly, the theoretical proton radiographs are analyzed by the flux analysis method, and two magnetic fields are reconstructed. Finally, the theoretical magnetic fields are compared with the reconstructed ones, and the advantages and disadvantages of these two methods are analyzed. Particle tracing rebuilds the geometry distribution of proton source, plasma magnetic field and recorder in experiment, and it needs few assumptions. However, it strongly relies on accurate calculation of theoretical magnetic field and proton trajectory, and it requires to change the magnetic field over and over to achieve a closest result to the experimental proton radiograph. Meanwhile, particle tracing method consumes a lot of computation sources. The flux analysis directly reconstructs the magnetic field from experimental proton radiograph. However, it is only applicable to the case of weak magnetic field, and the error becomes larger for the case of stronger magnetic field. A dimensionless parameter <i>μ</i> is used to estimate the deflection of proton in the magnetic field, which measures the amount of deflection per unit length in the interaction region. The flux analysis method is applicable to the <inline-formula><tex-math id="M601">\begin{document}$\mu\ll 1$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20200215_M601.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20200215_M601.png"/></alternatives></inline-formula> regime. Additionally, the target may absorb the proton when the energy of proton is low and produces shadow on the proton radiograph, which leads to some difference between the original magnetic field and the reconstructed result.

Analysis of Devices to Detect Longitudinal Tear on Conveyor Belts

Currently mining enterprises more and more often use belt conveyors for mining operations. The length of transporting rock mass could be several kilometers, so in most cases conveyor are used. The transported rock mass is rather heterogeneous, as a rule, it has inclusions in a form of large pieces with sharp edges and, in some cases, metal objects, which might cause longitudinal tears of various lengths on conveyor belts. They lead to significant repair costs or replacement of expensive conveyor belt, loss of transported material, and downtime of the major enterprise equipment. In the world practice various devices and systems to detect longitudinal tears on conveyor belts have been developed for their successful operation. In this paper, there is analysis of existing devices to detect longitudinal tears on conveyor belts based on the use of mechanical (detection of the transported cargo on the lower the conveyor section and measuring the belt width), ultrasonic and electro-magnetic energy, evaluation of changes in the magnetic field configuration, computer vision, infrared laser and x-ray radiation, image recognition software and embedded transponder chips.

A novel analytical calculation of magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping

This paper presented a novel analytical method for calculating magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping. Firstly, flux density without slots and complex relative air-gap permeance of slotted air gap are derived from conformal transformation separately. Secondly, they are combined in order to obtain normalized flux density taking account into the slots effect. The finite element (FE) results confirmed the validity of the analytical method for predicting magnetic field and back electromotive force (BEMF) in the slotted air gap of spoke-type permanent-magnet machines. In comparison with FE result, the analytical solution yields higher peak value of cogging torque.

Analytical calculation and analysis of air gap magnetic field for electromechanical integrated toroidal drive

This article introduces the operating principle and structural characteristics of the electromechanical integrated toroidal drive system. For its inner and outer toroidal double-stator structure, the equivalent current method is applied to calculate its spatial magnetic field, which is produced by the sector cylindrical magnetic teeth and the helical variable cross-section magnetic beam. For the application of the equivalent current method in the modeling of the magnetic field, an effective correction method is proposed. The flux density calculation models for the main magnetic field in the inner and outer air gaps are established under the unified coordinate system, and the analytical expression of magnetic field distribution in spatial air gap is deduced. Finally, the feasibility of the mathematical analytical model is verified by comparing the analytical calculation results with the finite element simulation results. The influences of the main structural parameters on the distribution of the air gap magnetic field and the torque are analyzed, which lay a theoretical foundation for the optimal design of the electromechanical integrated toroidal drive system.