Eddy Current Density Research Articles

Eddy current density asymmetric distribution of damper bars in bulb tubular turbine generator

AbstractThe major reasons that cause the damage of damper bars in the leeward side are found in this paper. It provides a route for the structure optimization design of a hydro generator. Firstly, capacity of a 24 MW bulb tubular turbine generator is taken as an example in this paper. The transient electromagnetic field model is established, and the correctness of the model is verified by the comparison of experimental results and simulation data. Secondly, when the generator is operated at rated condition, the eddy current density distributions of damper bars are studied. And the asymmetric phenomenon of the eddy current density on damper bars is discovered. The change laws of the eddy currents in damper bars are determined through further analysis. Thirdly, through the study of eddy current distributions under different conditions, it is confirmed that the stator slots and armature reaction are the main factors to affect the asymmetric distribution of the eddy current in damper bars. Finally, the studies of the magnetic density distribution and theoretical analysis revealed the asymmetric distribution mechanism of eddy current density.

Effect of circumferential segmentation of permanent magnets on rotor loss in fractional‐slot concentrated‐winding machines

Permanent-magnet (PM) segmentation is a plain and valid way for eddy current (EC) loss reduction in fractional-slot concentrated-winding (FSCW) machines and it has no passive effect on the machine itself. In this study, compared with PM asymmetrical segmentation, the authors prove that symmetrical segmentation adopted by most scholars, in general, is the optimal choice by using both analytical method (AM) and time-stepped transient finite-element method (FEM), when the skin effect is neglected. Furthermore, two surface-mounted PM machines with FSCW are proposed to investigate the effect of PM symmetrical segmentation on EC loss in rotor PMs. The actual effect of PM segmentation is to cut off the EC path and increase the resistance value in return circuit, thus decreasing EC density in PMs. In addition, some theoretical expressions evaluating the EC loss with consideration of magnet segmentation effect are derived step by step. Finally, Maxwell FEM software is used to verify the theoretical analysis, showing that the proposed AM is able to accurately predict the EC loss with different segmented numbers.

Electromagnetic properties of cylinder permanent magnet eddy current coupling

This paper focuses on the electromagnetic properties of new cylinder type twelve-pole permanent magnet eddy current coupling. By combining conventional equivalent magnetic charge method and superposition principle, the analytical calculation model of air gap magnetic field distribution for the cyli nder type permanent magnet eddy current coupling is established; by considering the skin effect, the analytical model of eddy current density is set; the analytical model of electromagnetic-transfer torque is given with the demagnetization effect taken into consideration. Based on the established analytical calculation model, the variation law of air-gap magnetic induction intensity, eddy current density distribution and magnetic torque characteristic curve are analyzed and plotted in detail. At the same time, finite element simulations of the air gap magnetic field, eddy current density and electromagnetic-transfer torque are carried out based on multi-physics, and the results are compared with analytical calculations. Moreover, the paper analyzed the thickness of magnet conductive plate impacts on eddy current and explored relations between torque and coupling distance under different pole pairs. Finally, in order to verify the simulations, the prototype test of torque transfer characteristics is carried out. This paper compares the experimental results with the theoretical analysis and simulation results, and finds out the error is within the allowable range.

On the Magneto-Heat Coupling Model for Large Power Transformers

AbstractThis paper studies the magneto-heat coupling model which describes iron loss of conductors and energy exchange between magnetic field and Ohmic heat. The temperature influences Maxwell's equations through the variation of electric conductivity, while electric eddy current density provides the heat equation with Ohmic heat source. It is in this way that Maxwell's equations and the heat equation are coupled together. The system also incorporates the heat exchange between conductors and cooling oil which is poured into and out of the transformer. We propose a weak formulation for the coupling model and establish the well-posedness of the problem. The model is more realistic than the traditional eddy current model in numerical simulations for large power transformers. The theoretical analysis of this paper paves a way for us to design efficient numerical computation of the transformer in the future.

Investigation of Gyroscopic Stabilization for Single-Stage Saddle Sextupole Field Electromagnetic Launcher

This paper presents a novel single-stage saddle multipole field electromagnetic launching mode for the realization of projectile linear acceleration with gyroscopic stabilization. The hollow cylindrical projectile with three symmetrical vertical slots can change the eddy current and magnetic field density distribution on the projectile surface. When twisted an angle relative to saddle multipole coils along the circumference, the projectile will be linear accelerated with spinning motion under the action of pulse current. In this paper, analytical calculations and simulation methods were used to analysis this mode, the simulation results indicated that the axial acceleration force and circumferential torque acting on the projectile were generated simultaneously, and an optimal initial twisted angle was existed to make the muzzle rotation speed reach peak. To verify the conceptual feasibility, a single-stage saddle sextupole field electromagnetic launcher was built and tested. The experiment demonstrate that the mode is indeed possible to realize the projectile linear acceleration moving with the gyroscopic stabilization, launching performance can be adjusted by changing the initial voltage or twisted angle, and the experimental results are accordant with the simulation results.

A Steel Ball Surface Quality Inspection Method Based on a Circumferential Eddy Current Array Sensor.

To efficiently inspect surface defects on steel ball bearings, a new method based on a circumferential eddy current array (CECA) sensor was proposed here. The best probe configuration, in terms of the coil quality factor (Q-factor), magnetic field intensity, and induced eddy current density on the surface of a sample steel ball, was determined using 3-, 4-, 5-, and 6-coil probes, for analysis and comparison. The optimal lift-off from the measured steel ball, the number of probe coils, and the frequency of excitation current suitable for steel ball inspection were obtained. Using the resulting CECA sensor to inspect 46,126 steel balls showed a miss rate of ~0.02%. The sensor was inspected for surface defects as small as 0.05 mm in width and 0.1 mm in depth.

CALCULATION OF LOSSES IN ELEMENTS OF CONSTRUCTION OF POWER TRANSFORMERS AND REACTORS BY FINITE ELEMENT METHOD WITH SURFACE IMPEDANCE BOUNDARY CONDITIONS

The purpose of the work. This paper offers the well founded mathematical model based on the applying of the finite element method, which allows more effective modeling of the eddy currents and losses in the tank of power transformers, reactors and elements of their constructions, caused by the dispersion fields.Research methods. Based on assumptions of equality to the zero of normal components of the magnetic and electric fields’ intensities in ferromagnetic half-space, this mathematical model enters the surface eddy current density in FEM equations.The obtained results. Conclusion that the offered mathematical model allows to calculate eddy currents and losses in the power transformers tank, reactors and elements of their constructions more effectively is done. Reduction in tens of times of the resulting system of equations is also arrived, that results to considerable decreasing of calculation time and computer resources without accuracy losses.Scientific novelty. The novelty of the offered mathematical model is the form that is comfortable for programmatic realization of the known surface impedance boundary condition describing the electromagnetic field distribution in a tank and construction elements and in addition these elements are represented as ferromagnetic conducting half-space.Practical importance. Examples of single-phase autotransformer 167MVA 345kV 161kV calculation in a program complex ELMAG - 3d software, created on the basis of the described method and in the program complex ANSYS software with the use of classic approach of solid modeling of transformer, demonstrate applicability and required accuracy of the described method in the context of problems of losses calculation in the tank and construction elements of power transformers.

Modeling of Eddy-Current Losses of Welded Laminated Electrical Steels

With the implementation of more stringent emissions standards, energy conversion efficiency in motor and transformer has drawn increasing attention. In this study, an analytical model to estimate the eddy-current losses of the welded electrical steel laminations has been developed. A numerical model has been developed to visualize the magnetic flux density, eddy-current density, and loss. The eddy-current losses obtained from the analytical model were in good agreement with those from the numerical model. Effects of weld bead size, sheet thickness, operating frequency, and magnetic flux density on the eddy-current losses have been quantitatively investigated. The results showed that the eddy-current losses of the welded laminations increased with the increase of the weld bead radius. Meanwhile, the eddy-current losses of the thinner laminations were much more sensitive to the welding process, especially at high operating frequency and high magnetic flux density. This work provided a quantitative model to calculate the eddy-current losses of the welded laminations.

Influence of parameters of cap‐lamination secondaries on performances in single‐sided linear induction motors

The secondary is an important design factor of single-sided linear induction motors (SLIMs), as well as has influence on the cost and performance of SLIMs. In this study, the cap-lamination secondary is designed and relations of the secondary parameter and performance of SLIMs are calculated. First, the aluminium (Al) cap and lamination back iron of the cap-lamination secondary are designed and discussed. Then, improvements in performance caused by two potentially significant effects of the cap-lamination secondary, i.e. the thick cap edge and lamination, are identified. Second, a flat-solid secondary is applied and two SLIMs, which are the same primary and two different secondaries, are calculated by three-dimensional finite-element method. Eddy current densities in the Al and back iron plate, which are two parts of the secondary, are analysed. Owing to different transverse edge effects, variations of the air-gap flux density are calculated with different secondaries. Finally, the numerical results of the thrust, power factor, and efficiency are experimentally validated by measurements on test rig of SLIMs. It shows that the SLIM with cap-lamination secondary, which has higher performance, is affected greatly by the conductor structure of the secondary and the lamination of the iron back plate.

Effects of Laser Cladding Layers Width on Total Indicated Runout Characteristics of Steam Turbine Rotor Surface

In order to solve the wear repair problem of large steam turbine rotor shaft journal, the material of steam turbine rotor shaft was used as a substrate and the self-made special laser cladding remanufacturing powder as the experimental material, and the experiments were carried out by a laser cladding remanufacturing method based on the laser cladding remanufacturing system with coaxial powder feeder. Focusing on effect of different widths of laser cladding layers on total indicated runout (TIR) of steam turbine rotor, the experiment research and mechanism simulation verification were performed, and the influence mechanism of different factors were analyzed. The total data indicates runout are closely related to probe diameter and laser cladding layer width. The width of cladding layer determines the turbine rotor surface magnetic, eddy current density and magnetic flux density distribution. Due to the interference of matrix magnetic field and eddy current density of the surface, the magnetic flux density suddenly changes in the laser cladding layer edge when the laser cladding layer width is less than 8 mm. The measurement results are too large caused by the comprehensive effect of the substrate and the laser cladding layer. According to the numerical simulation of magnetic flux density distribution of measured metal body surface, the critical value of laser cladding width is 9.82 mm.

Eddy current loss analysis of open-slot fault-tolerant permanent-magnet machines based on conformal mapping method

This paper proposed an analytical method, based on conformal mapping (CM) method, for the accurate evaluation of magnetic field and eddy current (EC) loss in fault-tolerant permanent-magnet (FTPM) machines. The aim of modulation function, applied in CM method, is to change the open-slot structure into fully closed-slot structure, whose air-gap flux density is easy to calculate analytically. Therefore, with the help of Matlab Schwarz-Christoffel (SC) Toolbox, both the magnetic flux density and EC density of FTPM machine are obtained accurately. Finally, time-stepped transient finite-element method (FEM) is used to verify the theoretical analysis, showing that the proposed method is able to predict the magnetic flux density and EC loss precisely.

Потери от вихревых токов в массиве постоянных магнитов магнитоэлектрических вентильных двигателей

Higher harmonic components of magnetic field in the air gap of permanent-magnet electrical machines cause eddy currents to occur in the bodies of permanent magnets, due to which the latter become heated and partially demagnetized. Expressions for the coordinate components of magnetic induction and eddy current density in the magnet body (given the known value of the n-th harmonic component of magnetic inductance on the magnet external surface) are obtained proceeding from analytical solution of the well-known Maxwell equations for the n-th harmonic component of magnetic field. It is shown that the electromagnetic wave energy enters into the magnet through the external cylindrical surface and lateral radial flat edges. It is also found that the power flux surface density in the first channel is constant, whereas that in the two other channels decreases exponentially in the radial direction. Therefore, it is not expedient to subdivide the pole magnet into elementary tiles in the transverse direction from the viewpoint of losses, because the losses in the first channel remain unchanged (i.e., they are invariant to decomposition), whereas the losses in the second channel increase (the total number of tile lateral edges increases in decomposing the magnet). The article presents a quantitative assessment of losses in samarium-cobalt magnets of a switched motor with a capacity of 15 kW due to a slotted stator surface outline, a non-sinusoidal waveform of the frequency converter voltage, and higher harmonic components of the stator winding MMF.

Nonlinear properties of multiphase high-temperature superconductors of the Bi–Sr–Ca–Cu–O system in the temperature range of the superconducting transition

The nonlinear characteristics of high-temperature superconductors of the Bi–Sr–Ca–Cu–O system have been experimentally investigated in the temperature range of the superconducting transition under the influence of a harmonic alternating magnetic field. The effect of the generation of odd harmonics in the signal of response to a harmonic alternating magnetic field for multiphase high-temperature superconductors containing regions with different values of the critical temperature in their bulk has been observed for the first time. The mechanism of harmonic generation in a superconductor in the resistive state, which is associated with the switch effect, i.e., with the redistribution of eddy current density between the local regions of the superconductor, has been considered.

Eddy current density by inversion of one measured component of the resulting magnetic field perturbation

In this paper we present a method to determine the current density inside an aluminum plate using eddy current testing procedure to determine the existence of surface cracks. The general idea consists in generating eddy currents in the plate, which in the case of flawless material, must be of unifo rm density pointing along a pre-defined direction inside a given area on the plate surface. These currents are produced using a planar coil. The eddy current density is determined by inversion of the data obtained from the measurement of a single component of the resultant magnetic field. Tikhonov regularization is applied to the inverted data.

Proposal of slack inspection method of high tension bolt of hexagon head using alternating magnetic field

The development of the inspection technique of detecting the slack of the high tension bolt is desired. The permeability inside the side of the bolt head is changed since the bolt head is compressed by bolting a plate. Therefore, the evaluation of the slack of the bolt is possible by detecting the difference of the magnetic characteristics. In this paper, the inspection method for measuring the slack of the steel high-tension bolt of hexagon head using a small electromagnetic non-contacting sensor is proposed. The distribution of stress, flux density and eddy current density near the bolt head is estimated by 3-D nonlinear electromagnetic finite element method (FEM) analysis taking account of the electromagnetic property under various compressive stresses. The results showed that the non-destructive inspection of the slack of the high-tension bolts is possible by detecting the change of flux density in the side of the bolt head.

Eddy current loss in double-sided cored slotless type permanent magnet linear synchronous generator using analytical method

This paper describes the eddy current loss analysis of a double-sided cored slotless-type permanent magnet linear synchronous generator using the space harmonic method. To calculate the eddy current, an analytical solution was derived by applying the Maxwell equation, magnetic vector potential, and Faraday’s law in a two-dimensional (2-D) Cartesian coordinate system. Based on the armature reaction field distribution produced by the armature winding current, we obtained an analytical solution for the eddy current density distribution. Then, an analytical solution for eddy current loss induced in a permanent magnet (PM) was derived using the equivalent electrical resistance calculated from the PM’s volume and eddy current density distribution solution. Finally, the resulting current was determined based on analysis of the eddy current loss. The analytical results produced using this application of the space harmonic method were validated extensively through comparison with finite element method results.

Optimal design of spiral coil electromagnetic acoustic transducers considering lift-off sensitivity operating on non-ferromagnetic media

The generation efficiency of electromagnetic acoustic transducers (EMATs) dramatically reduces with increasing lift-off, thus restricting their applications. This paper aims to provide methods to decrease lift-off sensitivity. The process of generating a shear wave in a spiral coil EMAT is established based on a 2-D axisymmetric model using the finite element method. An equivalent excitation circuit, including an impedance-matching network and a limited power source, is presented for calculating the excitation current. Such an equivalent circuit has not been given adequate attention in previous publications in this field, but it has proven to be of great importance in determining the efficiency of ultrasonic generation. The predictions of static magnetic field, eddy current density and excitation current are validated by experimental results. The conversion efficiency and lift-off sensitivity of the EMAT are analysed with respect to impedance matching parameters, magnet dimensions, the presence of a copper backplate between the magnet and the coil, and backplate-to-coil distance. The results indicate that impedance matching parameters, magnet diameter and plate-to-coil distance have obvious effects on lift-off sensitivity. The backplate can be used to decrease lift-off sensitivity, and it can rearrange the source current density across the cross-sectional area of the coil conductor. Furthermore, compared with the original EMAT, the lift-off sensitivity of the optimised EMAT can be decreased by 7.9 dB at 2 mm lift-off.

Shannon information entropy of eddy current density distribution

This paper presents a new method to evaluate the distribution of eddy current density excited by four different planar eddy current probe inducers. The proposed method uses the information entropy to analyse eddy current distribution in different directions in the whole, or in part, of surface. Four finite-element models show the eddy current distribution and allow the entropy calculation. Finally, the paper highlights strengths and weaknesses of the studied current probe inducers.

Modeling of disk-type permanent magnet eddy-current driver based on soft measurement method and performance analysis

In order to solve the problem of immeasurability of eddy current density on the conductor plate and magnetic field intensity in the air gap, this paper establishes the eddy current soft measurement model. Eddy current density of the PM eddy- current driver during run time can be calculated by measured data of slip speed and air gap in this model which is based on equivalent magnetic circuit. Then, the calculation formula of the torque can be deduced by applying this model. Transmit per- formance which provides an important basis for optimization calculation and preliminary design is also analyzed. All calculated soft measurement results are compared with results of finite element method using ANSYS software and experimental data. FEM results and experiment results confirm the validity of the soft measurement mechanism model.

Five‐phase travelling wave induction heater for continuous heating of flat material

This study proposed a novel travelling wave induction heating system with five-phase exciting current. The proposed system used special exciting current to obtain a homogeneous eddy current density, which affects the temperature pattern over the material surface. Five-phase system has been attracted from many industrial applications due to its inherent features compared to the three-phase system. An even number of phases is not preferred because the poles exchange with each other. A comparison investigation with other traditional methods is represented to realise the features of the proposed method. A finite-element method simulation is represented by using ANSYS 15®; the simulation results show that the proposed system gives superior performance of energy transferred, uniform heat distribution and higher power factor over that of the traditional three-phase system. Moreover, it performs identical eddy current, power densities, temperature and efficiency to that of the six-phase system with profits of reduction in size, weight, cost and winding copper losses.