Massive Conductors Research Articles

The mutual influence of exciting and induced currents in the circular solenoid – massive conductor system

Problem. The flow of currents in the conductive elements of electrical systems is accompanied by the excitation of electromagnetic fields and the occurrence of induced currents. The excitation of the induced signals, in turn, leads to a change in the parameters of the actual exciting currents. The purpose of the work is to obtain analytical expressions for the quantitative analysis of the results of the mutual influence of the exciting and induced currents and to calculate their ratio depending on the geometric characteristics of the inductor systems. Methodology. The analysis of the processes of mutual influence is carried out on the example of a widespread inductor system, where a flat circular solenoid is placed above the surface of a massive conductor. Analytical expressions for eddy currents excited in a massive conductor and numerical estimates of the effect of induced currents on exciting currents in a solenoid are obtained. Results. It is shown that the influence of the induced current on the current in the solenoid is very significant at small distances between the solenoid and the surface of the massive solenoid. It has been found that an increase in the width of the solenoid winding leads to a significant increase in the influence of the induced current on the excitation current in the solenoid. It is shown that the inductance of the «circular solenoid - massive conductor» system drops with a decrease in the distance between the solenoid and the massive conductor and an increase in the radial dimensions of the solenoid, which requires an increase in the amplitude of the exciting current to maintain a given value of the magnetic flux in the system. Originality. The scientific novelty of this work lies in the proposal of an analytical approach and obtaining numerical estimates of the mutual influence of conductors with exciting and induced currents. Practical value. Estimates of the mutual influence of conductors with currents are of interest for the practice of designing structures of electrical systems for various purposes. Very promising in the direction further research is seen as carrying out experiments with measurements of the quantitative characteristics of the mutual influence of exciting and induced currents in various designs of electrical systems.

Digital Induction Motor Model Based on the Finite Element Method

This article presents the design of a drive system for robots and manipulators, which is based on the finite element method of an induction motor. The design process involves constructing a computer-aided design (CAD) model of the induction motor, which enables the generation of design documentation and control programs for computer numerical control (CNC) tools for manufacturing motor parts or conducting further research. A CAD model is developed for performing a finite element analysis of the motor in the SolidWorks software based on the popular AIR63V2 motor. The design of the motor’s housing, rotor, and stator is developed. Additionally, the electrical parameters of the motor are calculated using Ansys Electronic Suite—Maxwell RMxprt, utilizing the classical analytical theory of electrical machines and the equivalent magnetic circuit method. This takes into account such effects as the non-linearity of electrical steel, the non-sinusoidality of the magnetic flux in the gap, and the displacement of electric current in massive conductors. A complete model of an induction motor for research has been created, enabling the study of dependencies of speed and electromagnetic torque of an induction motor. The natural frequency of the rotor is calculated, which ranges from 922 Hz to 1015 Hz. The obtained values of calculations of natural oscillations of the CAD model of the motor can be used for motor diagnostics. Furthermore, the created project in the Ansys software can be utilized to design an induction motor with its own characteristics, optimized for specific tasks.

Mutual influence of currents in plane inductor system with solenoid between two massive conductors

Introduction. Inductor systems, as tools for metal processing, widely used in industrial technologies using the energy of powerful pulsed electromagnetic fields. Problem. A common disadvantage of the known works on the creation of tools for magnetic-pulse impact on conductive objects has the use of physical and mathematical models, in which the exciting currents do not depend on the ongoing electromagnetic processes. Such the assumption, have distorts the picture of the real energy in the working area of the inductor system. Goal. To obtain design ratios and numerical estimates of the mutual influence of exciting and induced currents of a flat inductor system with a circular solenoid located between massive well-conducting objects, moreover to carry out a theoretical analysis of electromagnetic processes in this system. Methodology. Have applied integrating Maxwell’s equations using the Laplace and Fourier-Bessel integral transformations in the approximation of the ideal conductivity of the metal objects to be processed. Results. The calculated relations for the theoretical analysis of electromagnetic processes have obtained in the high-frequency approximation. It shown that the inductance of the studied system decreases as the objects being processed approach the solenoid and increases as they move away from it. It found that for the invariability of the power indicators, of the proposed tool, a corresponding correction of the amplitude (on average up to 20 times) of the exciting current has necessary in the solenoid winding. Originality. For the first time, the tool design with a circular solenoid located between the massive metal objects has proposed for flat magnetic-pulse stamping. As a result of the theoretical analysis, the influence of electromagnetic processes on the currents flowing in the system has confirmed. Practical significance. The use of the results obtained will allow to increase the efficiency of the tool of magnetic-pulse technologies, and to reduce the energy costs for performing the specified production operations.

Особенности распространения стоячих электромагнитных и электронных волн в металлическом проводнике с электрическим переменным током проводимости

The paper demonstrates the results of approximate calculations on the establishment of basic features of the propagation of standing transversal electromagnetic waves (EMWs) and standing longitudinal de Broglie electronic waves in a homogeneous not massive non-magnetic metallic conductor of finite dimensions (the radius r0 and the length l0 >>r0) with the alternating axial-flow current of conductivity of i0(t) of different peak-temporal parameters. The correlation for the rated estimation of the average velocity of propagation of the standing transversal EMWs and standing longitudinal de Broglie electronic waves in a metal (alloy) of the indicated conductor is presented. It is shown that quantized standing transversal EMWs arising in a metallic conductor of finite dimensions substantially differ from ordinary transversal EMWs, propagated in the conducting environments of unlimited dimensions. An important feature of the standing transversal EMWs in the examined conductor is the fact that their tension of an axial-flow electric-field advances by a phase their tension of an azimuthal magnetic-field on the corner of π/2. It was established that in the standing transversal EMWs of the used conductor the energy of their electric field only passes into the energy of their magnetic field and vice versa. Therefore the standing transversal EMWs do not transfer the flows of the electromagnetic energy on the surface of the studied conductor.

МОДЕЛЮВАННЯ РОЗПОДІЛУ ЕЛЕКТРИЧНОГО ПОЛЯ В МЕТАЛЕВОМУ РОЗПЛАВІ МЕТОДОМ РОЗБИТТЯ ПРОВІДНИКА НА ЕЛЕМЕНТАРНІ КОМІРКИ

Purpose. To show the functional possibilities of the method of dividing massive conductors into elementary cells and matrix 2D, 3D formalization of electric field characteristics in a metal melt during its electric current treatment. For foundry production technologies, the processes generated in the metal melt during its conductive electric current treatment (CECT) are studied. Methodology. Along with the material science aspects of the problem with the help of numerical simulation is the search for optimal parameters of the melt load. The finite element method (FEM) is used for this purpose. Originality. The tasks to be solved are not classic. This imposes problems on the choice of problem statement and methodological principles of calculations. Therefore, it is important to find another productive flexible numerical modeling method. This is especially important in the development of systems for the implementation of controlled conductive electric current treatment of liquid metals. The paper proposes to apply the known method of dividing massive conductors into elementary cells (M-C), which must be adapted to the CECT conditions in foundry production. At the same time, using this method in combination with FEM, it is possible to deepen the scientific achievements of CEСЕ and obtain validation and verification of the results of solutions. Results. A number of problems have been solved that show different possibilities of modeling with using of the M-C method. The results of using M-K method allows to relatively accurately reproduce the distribution of the base electric field in the metal melt during its treatment with electric current. The ensuring the validation and verification of obtained results, in combination with, for example, M-C and FEM methods can significantly influence the expansion of scientific work on the thermoforce influence of the melt. The obtained results, which be compatible with FEM data, describe the characteristics of basic electric field in the melt in 2D and 3D formats. It is shown that the 2D format enables to determine possible trends in the distribution of field characteristics for different types of currents and types of electrode systems. 3D format has greater functionality, but its productive application requires the improvement of computational algorithms in the matrix formalization of field characteristics in metal melts weighting several hundred kilograms. Figures 7, references 11.

Formation of dense plasma on the surface of a stainless steel conductor in superstrong magnetic fields

In experiments on the GIT-12 megaampere generator, the characteristics of conductors made of AISI 321 stainless steel were investigated in the microsecond regime of increasing superstrong magnetic fields. In this regime, a skin explosion of the conductor material takes place with the formation of a dense plasma and its expansion into the interelectrode gap of the vacuum transmission line. The values of the characteristic magnetic field B0 = 100 T are determined, above which there is the effect of nonlinear diffusion of the magnetic field into the conductor, and the critical magnetic field BCT ≅ 260 T, the excess of which leads to the formation of dense plasma on the surface of the massive conductor. A method is proposed for increasing the critical magnetic field on the surface of a conductor up to 1.5 times by choosing the optimal thickness of the conducting surface, and criteria for its determination are given. The effect of increasing the critical magnetic field on the surface of a two-layer sample and creating a pressure in the Mbar range until the moment of formation and expansion of explosion products of an inner conductor with high conductivity has been tested.

Efficiency Improvements of the Use of Electromagnetic Induction

The paper describes the results of the experiment about efficiency improvements of the use of high frequency current and сonfirmation that the devices are working better with this type of current. The results indicate the feasibility of further experiments using better installation,in comparison with the installation that was used in the described stages of the experiment below. This installation and method of using high-frequency current will help to use all devices (but not those with an electric circuit, since electronic devices are not adapted to high frequencies, through which they fail) at the power at which they should work, because in general, at a normal frequency of 50-60 Hz there are unnecessary and unprofitable losses.To achieve this goal, the following tasks were defined:Determine how the power changes depending on the frequency of the current in the receiving coil;Is it really possible to increase the efficiency of devices due to high-frequency current;Conduct experiments and draw conclusions based on them.Hypothesis: if you add two or more flat coils together, you will get a high level of frequency savings in electricity consumptionSo the experiment was conducted in the laboratory of cryogenic technology of NTUU "Igor Sikorsky KPI". Instead of an induction plate, we used a frequency generator and an ordinary flat coil (the results of the experiment are not affected by the type of flat coil: either bifilar or ordinary (from a single wire), the dependence has been established in any way). Based on the data taken from the oscilloscope and generator, a graph of the voltage dependence on the current frequency was constructed. Since the dependence of voltage and power is linear, and the current value does not change: with the increase in voltage, there is an increase in power.High-frequency current gives advantages in that it is possible to use conductors of a smaller cross-section and even then we do not get any losses.This kind of current is distributed in the layers of the conductor that are close to the surface, which is called skin effect. Eddy currents passing along the wire, directed so as to weaken the current as much as possible in the middle of the conductor and amplify it near the surface. As a result, the so called “quick-change” current is distributed unevenly-it seems like as if it is trying to be displaced to the surface of the conductor.In a conventional transformer with a core, which is designed to convert alternating current from one voltage to alternating current from another voltage at the same frequency, the resistance can be so small that eddy currents, or Fuko currents, occured. In such massive conductors, they are useless and ony interfere with the work through heating the transformer itself. But there are cases when people on the contrary use a heated property: an induction cooker.Examples of using electromagnetic induction are placing a conductor body in the middle of the coil, in which eddy currents will occur that can warm the body up to melting. In this way, metals are melted in a vacuum, which helps to obtain high-purity metals. Another example is an induction cooker, where you do not need to get rid of eddy currents, but on the contrary, use them as much as possible.

Enforcing Lumped Parameter Excitations in Edge-Element Formulations by Using a Fast Iterative Approach

In order to couple external circuits to edge-element discretized electromagnetic models, with full field equations, global constraints involving voltages or currents need to be enforced. There is no canonical way to impose a voltage or a current without additional modeling information on the distribution of field sources that rely on topological concepts. In this article, a fast solution of field sources within massive conductors in static and dynamic problems is proposed. Global basis functions, required to cope with non-trivial coil topologies, are directly generated by an iterative solver rather than pre-computing source fields, e.g., by tree-cotree decomposition.

PECULIARITIES OF THE MANIFESTATION AND INFLUENCE ON THE ELECTROMAGNETIC PROCESSES OF THE TRANSIENT SKIN EFFECT IN METAL CONDUCTORS WITH PULSED CURRENT

Purpose. Preparation of brief scientific review of basic results of the known theoretical researches of the electrophysics phenomenon of linear transient skin effect (TSE) in the non-magnetic homogeneous massive conductors of flat and cylindrical configurations on which in the discharge electric circuits of high-voltage electrophysical installations (EPHI) the pulsed currents ip(t) flow with given amplitude-temporal parameters (ATPs). Methodology. Theoretical bases of electrical engineering, bases of theoretical electrophysics, electrophysics bases of technique of high-voltage and high pulsed currents. Results. The brief scientific review of results of the known theoretical researches of the electrophysical phenomenon of linear TSE in non-magnetic homogeneous massive flat and cylindrical metal conductors with pulsed axial (azimuthal) current ip(t), formed in the discharge circuit of powerful high-voltage EPHI. In the generalized and systematized form the basic features of manifestation of linear TSE in the indicated conductors and influence of the considered skin effect on electromagnetic processes are presented at flow in conductors and discharge circuit of a high-voltage EPHI with the pulsed current ip(t) time-varying by law of attenuated sinewave. Influence of linear TSE is described in non-magnetic massive conductors during transient in a discharge circuit of EPHI with the pulsed current ip(t) of given ATP, depth of penetration of the electromagnetic field in materials of the indicated conductors, own integral electric parameters of the considered conductors and their good quality in the high-current discharge circuit of high-voltage EPHI. It is shown that at the analysis of electromagnetic transients in high-current discharge electric circuits of powerful high-voltage EPHI it is necessary to take into account flowing in materials of the examined massive conductors of such known electrophysical phenomenon as linear TSE. Originality. Generalization and systematization is first executed regarding domestic and foreign scientists-electrical engineers’ results of theoretical researches for long-term period of the electrophysics phenomenon of linear TSE in the flat and cylindrical metallic conductors of different thickness with the pulsed current ip(t)of given ATP. Practical value. The results presented in the generalized and systematized form will be useful for electrical engineers in deepening of understanding of basic features of manifestation in non-magnetic massive homogeneous conductors with the pulsed current ip(t) of given ATP of such widely widespread in area of high-voltage high-current pulsed technique electrophysics phenomenon as linear TSE and its influences on electromagnetic transients in similar metallic conductors and high-current discharge circuits of high-voltage EPHI.

PARAMETRIC ANALYSIS AND STRAY FIELDS OF TOROIDAL SUPERCONDUCTING MAGNETIC ENERGY STORAGE

Purpose. To carry out a parametric analysis of superconducting toroidal magnetic systems with a discrete winding, establishing the possibility of using an idealized model in the form of a toroidal current surface and an approximate method for determining the level of fields of scattering of a real magnetic system. Methodology. The calculation of the distribution of the magnetic flux density in the winding, the field of scattering and energy of the storage’s field was carried out using asymptotic methods for solution of the problems of electrodynamics in systems with massive curvilinear conductors with current. An iterative calculation procedure was used to determine the dimensionless characteristics. Results. The dimensionless characteristics of a toroidal magnetic system with a winding in the form of individual superconducting coils of circular shape are calculated. The results are obtained depending on the value of the storage's energy capacity for various values of the relative radial size of the torus. For a toroidal superconducting storage device with energy capacity of 450 MJ, enough to perform the function of damping irregular oscillations of power transmitted over the transmission line, magnetic fields of scattering are calculated for different numbers of coils and torus section sizes. Originality. Based on a comparison of the values of dimensionless characteristics calculated for a system with individual coils, and for an idealized mathematical model of a continuous current surface, it was established that the relative deviation of the dimensionless characteristics does not exceed 10 %. In contrast to the idealized model, the magnetic field of a toroidal system composed of individual coils spreads beyond the toroidal surface and decreases the faster, the smaller the relative radial sectional size of the torus, the greater the number of coils used and the closer they are to each other. Practical value. The results obtained for dimensionless characteristics allow to conclude that the idealized model can be used at the first stage of the development of a superconducting inductive storage. The estimation of the field of scattering can be made on the basis of a simple model of unidirectional current filaments.

Skin Parameter of Massive Conductors and Transients in Electrical Circuits of Pulsed Power Facilities

For massive conductors with the characteristic sizes exceeding the penetration depth of variable or pulse magnetic field, it is possible to define the skin parameter, which affects transients in electrical circuits with massive conductors and does not depend on time and frequency. This paper describes the peculiarities of transients in circuits with massive conductors, defines and justifies the skin parameter, presents the methods of its calculation and measurement, as well as the results of calculation of transients in electrical circuits with massive conductors.

ANALYSIS OF ELECTROMAGNETIC PROCESSES IN THE SYSTEM «CYLINDRICAL SOLENOID – MASSIVE CONDUCTOR»

Purpose. Defining the key parameters of the inductor geometry, as a long multi-turn solenoid, that influence on the current amplitude induced excited in a massive conductor with a flat boundary surface. Methodology. Performing a mathematical analysis of the electrodynamic problem solution for an area with variable structure by integrating Maxwell's equation within the given boundary and initial conditions and also physical assumptions simplifying the process of solving but not distorting the result and carrying out an experiment that confirms not only the correctly construction considered but also the acceptability of the chosen assumption the opacity applying of the metal blank for these operating fields frequencies. Results. Functional dependencies of the current induced parameters on the metal surface of the heating object have been obtained, along which numerical estimates of the electrodynamic process have been performed, and key parameters influencing the heating efficiency have been determined. The correctness of the solutions obtained was confirmed experimentally. The final form of the solution function of the physical-mathematical problem was shown to be acceptable for performing further engineering and research calculations. Originality. The functional connection of the measured values of the induced surface current and the parameters of the measuring system is determined, the experimental confirmation of which indicates the satisfactory calculation model of the induction heating system and the entire solution as a whole. Practical value. Based on the calculations performed, working samples of inductive systems for induction heating that meet the specified heating rate and area requirements can be constructed. The obtained analytical expressions were transformed and simplified for their further using for engineering calculations with a minimum error value.

Modeling of UHV and Double-Circuit EHV Transmission-Line Exposure to Direct Lightning Strikes

This paper comprises the first systematic investigation into the factors that render ultra-high voltage and double-circuit extremely high voltage transmission lines more vulnerable to direct lightning strikes by shielding failure. Such lines are typically characterized by one or more of the following features: massive conductor bundles, extreme conductor heights, and exceptionally high operating voltage. The model addresses the effects of the upward connecting leader onset of conductor proximity, ground field due to cloud charges prior to negative leader descent, positive space-charge generation at ground wires, as well as the operating voltage during the positive half cycle. It has been found that such factors have significant effects on the lateral attractive distance of both conductor bundles and ground wires. An agreement between model findings and field experience is found to be generally satisfactory.

Sensitivity of the diamagnetic sensor measurements of ITER to error sources and their compensation

The present paper is focused on the sensitivity analysis of the diamagnetic sensor measurements of ITER against several kinds of error sources, with the aim of compensating them for improving the accuracy in the evaluation of the energy confinement time and poloidal beta, via Shafranov formula.The virtual values of measurements at the diamagnetic sensors were simulated by the COMPFLUX code, a numerical code able to compute the field and flux values generated in a prescribed set of output points from massive conductors and generalized filamentary currents (with an arbitrary 3D shape and a negligible cross section) in the presence of magnetic materials. The major issue to face with has been to determine the possible deformations of sensors and electromagnetic sources. The analysis has been carried out considering the following cases:-deformed sensors and ideal EM (electromagnetic) sources;-ideal sensors and perturbed EM sources;-both sensors and EM sources perturbed.As regards the compensation, several formulas have been proposed, based on the measurements carried out by the compensation coils; they basically use the value of the flux density measured to compensate the effects of the poloidal eddy currents induced in the conducting structures surrounding the plasma.The static deviation due to sensor manufacturing and positioning errors has been evaluated, and most of the pollution of the diamagnetic flux has been compensated, meeting the prescribed specifications and tolerances.

Modeling and Circuit Analysis of an Electromagnetic Launcher System for a Transient Current

An electromagnetic launcher with a 4.8-MJ pulsed power supply has been fabricated, and experimental tests were started. Through the experiments and calculations, the factors influencing the electrical properties and the performance of the launcher have been investigated. The pulse-forming inductors of the power supply and the rails of the launcher are made of massive conductors showing a prominent skin effect for a transient current. The circuit analysis using constant impedance values has a difficulty in the calculation of the correct voltages between the terminals of the conductors. In addition, the frictional force between the rails and the armature should be considered for a better estimation of the armature motion. To obtain the calculated solutions close to the measured ones, the diffusion of the magnetic flux or current was considered, and the history of the armature motion was reflected in the electrical modeling of the rails. These effects were implemented as voltage correction terms in the circuit equations with the help of the electromagnetic responses to a step-function current. In the equation of the armature motion, a reasonable form of the frictional force was modeled considering the velocity skin effect and the structural analysis. In this paper, the application of the voltage correction method into the rails of an electromagnetic launcher was introduced in detail, and the comparison of the results between the experiments and modified calculations for the constructed launcher system was described.

Transient Analysis of Circuit Containing Massive Conductors

Inductive electrical components made of massive conductors are usually adopted in the high-power circuit. Since they are not the types of filaments, the diffusion of the electromagnetic fields inside the conductors plays an important role in the transient discharge. Though the behavior of the circuit can be described reasonably using constant electrical parameters, the voltage drop in the massive conductor is not expressed accurately when constant resistance and inductance are used in the analysis of the transient discharge. To obtain a more accurate waveform of the pulsed current, we have used a comprehensive method calculating the correction voltage in the voltage drop. Once the resistive voltage drop and the magnetic flux for a step-function current are obtained either analytically or numerically, the voltage drop in the massive component for any current waveform can be calculated using the Duhamel's integration. The equations of the circuit containing massive conductors can be solved through a few iterations using the method estimating the voltage drop. As an example, the method was applied to an analysis of an RLC circuit containing a massive pulse-forming inductor. Electromagnetic responses of the inductor for a step-function current were calculated numerically with the help of a finite element method. The current waveform calculated using the method of correction voltage showed a good agreement with the measured waveforms.

An Arbitrary Thick Shell Finite Element for Eddy-Current Dual Vector-Scalar Potential Formulations

In many eddy current problems, surface impedance conditions are currently used to avoid the modelling of the skin depth in volumes. In the finite element method context, such conditions lead to surfaces elements at boundaries of massive conductors, or to shell elements representing thin layers, which unfortunately require a complex specific implementation in the codes. We propose here a new shell finite element easy to implement in the standard $({\rm A}-\varphi)$ and $({\rm T}-{\mit\Omega})$ formulations. The advantage of this element is to be arbitrarily thick, so it takes into account some end-effects at its perimeter such as the connection between shell an 3D regions. The basic principles of the thick shell as well as a three-dimensional validation test dealing with a magnetic core-fault are presented.

A Three-Dimensional Electromagnetic Shell Finite Element for Coupled Vector-Scalar Potential Formulations

In many eddy current problems solved by FEM, meshing of the skin depth leads to CAD difficulties and large computing. In order to avoid such problems, one currently use surface impedance conditions: boundary conditions in the case of massive conductors or transmission conditions or shell elements in the case of thin conducting layers. In this paper, we propose a new shell finite element with arbitrary thickness that is compatible with the (A-φ) and (T-Ω) formulations. Both formulations exist in some general purpose finite element electromagnetic codes like Code_Carmel3D. To validate the approach, two elementary numerical tests are treated.

Time-Domain Surface Impedance Boundary Conditions Enhanced by Coarse Volume Finite-Element Discretisation

In computational magnetodynamics, surface impedance boundary conditions allow to accurately account for high-frequency flux components while removing the massive conducting regions from the computation domain. The time-domain approach previously proposed by the authors relies on the spatial discretisation of a 1-D eddy-current problem by means of dedicated basis functions derived from the analytical frequency-domain solution. In this paper, these time-domain impedance conditions are combined with a coarse volume finite-element discretisation of the massive conductors to capture slowly varying flux components. The accuracy of the hybrid approach can further be improved by introducing a fictitious frequency-dependent conductivity. The method is illustrated and validated by means of 1-D and 2-D test cases in the frequency and time domain.

A Low-Frequency Approximation to the Maxwell Equations Simultaneously Considering Inductive and Capacitive Phenomena

For many technical examples, low-frequency approximations to the full set of the Maxwell equations are applicable. Commonly, either the displacement current density or the induced current density are neglected depending on a priori knowledge about the dominating effects for a specific problem setup. This leads to different subsets of the Maxwell equations describing inductive-resistive or capacitive-resistive systems, respectively. In this paper, a formulation combining both scenarios while maintaining the quasistationary assumption, i.e., without modeling wave propagation and radiation, is presented. The formulation is applied to a simple test model consisting of a bounded massive conductor embedded in a dielectric insulation.