Prediction of impedance components of eddy-current coils using a PC

The normalized components of impedance of eddy-current coils at the surface and in the encircling position can be predicted with a personal computer (PC), using short programs written in BASIC. The treatment for the first case is restricted to air-cored coils used with non-ferromagnetic metals.     

跑道型差动式涡流探头设计及其性能研究

针对传统差动式涡流探头几何尺寸大、缺陷检测灵敏度低的问题,在传统差动式涡流探头的基础上,设计了一种跑道型差动式涡流探头。它由激励线圈包裹2个尺寸相同、反向连接的感应线圈而构成。首先,利用COMSOL Multiphysics仿真软件建立了跑道型差动式涡流探头模型,比较了跑道型差动式涡流探头与传统差动式涡流探头涡流场分布的差异,并研究了在不同缺陷深度、不同扫查角度下2种差动式涡流探头的检测灵敏度。接着,制作了跑道型差动式涡流探头实物和碳钢板缺陷试件,利用试验测试的方法比较了跑道型和传统差动式涡流探头的检测灵敏度。试验结果表明,与传统差动式涡流探头相比,跑道型差动式涡流探头具有更紧凑的结构、更高的缺陷检测灵敏度。研究结果可为小尺寸、高精度差动式涡流探头的优化设计提供参考。     

A theoretical and computational model of eddy-current probesincorporating volume integral and conjugate gradient methods

A general three-dimensional computational model of ferrite-core eddy-current probes has been developed for research and design studies in nondestructive evaluation. The model is based on a volume integral approach for finding the magnetization of the ferrite core excited by an AC-current-carrying coil in the presence of a conducting workpiece. Using the moment method, the integral equation is approximated by a matrix equation and solved using conjugate gradient techniques. Illustrative results are presented showing the impedance characteristics and field distributions for practical eddy-current probe configurations     

Analytical model for tilted coils in eddy-current nondestructive inspection

The electromagnetic field and impedance of a cylindrical eddy-current probe coil are calculated analytically for arbitrary coil orientation above a conductive half-space. The remarkably simple closed-form expressions are provided as a function of coil tilt angle. The effect of tilt on the impedance change produced by a long crack is also investigated by combining the analytical model with an existing thin-skin theory for surface crack inspections. Results for both cracked and uncracked conductors are expected to be useful for evaluation of movement-generated noise in eddy-current inspections.     

Approximate model of eddy-current probe impedance for surface-breaking flaws

A theoretical model is derived for the prediction of eddy-current probe impedance changes caused by three-dimensional, surface-breaking flaws. Magnetic scalar potential theory and the surface impedance approximation are used to calculate fields on the flaw surface for arbitrary probe position and flaw geometry. Impedance changes are determined by a first-order perturbation calculation, with skin depth being the perturbation parameter. The end result is a relatively simple, three-dimensional model for simulating an eddy-current inspection. Numerical results for rectangular slots include maps of the impedance signals obtained in raster scan patterns and studies of skin-depth effects as a function of probe size, lift-off, and flaw dimensions.     

Analysis of eddy-current loss for design of small active magnetic bearings with solid core and rotor

As the size of rotors levitated by active magnetic bearings (AMBs) gets smaller, it becomes increasingly difficult to make laminated cores and rotors that have low eddy-current loss, and solid cores and rotors have to be substituted. Thus, accurate modeling of eddy-current loss is important for small-size AMB systems with solid cores and rotor. In this paper, we propose a new eddy-current loss model for AMB systems, based on the eddy-current brake concept. We show that the eddy-current loss in AMBs strongly depends on the arrangement and size of poles. We compare test results for hetero- and homopolar AMBs having nonlaminated cores and rotor to analytical findings based on the eddy-current loss model. The experimental results confirm that the eddy-current loss in small homopolar AMBs with nonlaminated cores and rotor can be greatly reduced by optimizing the arrangement and size of poles.     

Calculation of Skin Depths and Eddy-Current Power Losses for Magnetic Position Sensors

1. IntroductionIn a quasi-stationary magnetic field, eddy-currelltfrom an alternating-current excitation induces secondary currents and fields between magnetic material and position sensor. The skin depths and eddycurreat losses are also induced in a conductor whenan alternating external magnetic field is applied tothe conductor[1]. For a magnetic position sensort ifthe position of the moving sensor is given, the waveform of the output voltage induced by eddy-currentcan be used as an index to …     

Perfectly matched anisotropic layer for the numerical analysis ofunbounded eddy-current problems

An extension of the perfectly matched layer (PML) technique in quasi-static fields is developed. The new low frequency PML is based on a fictitious medium with diagonal tensor anisotropy. On the basis of a theoretical investigation, the material properties of the anisotropic layer are specified, so that it will be reflectionless for an arbitrary eddy-current field that may exist in free space. Furthermore, the PML is designed in such a way that outgoing eddy-current fields are sufficiently absorbed. The effectiveness of the low-frequency PML is validated by the implementation of the finite-element solution of a simple two-dimensional eddy-current problem as well as a more complicated three-dimensional one     

Vector potential integral formulation for eddy-current proberesponse to cracks

A boundary integral vector potential formulation has been developed to evaluate eddy-current interactions with three-dimensional finite cracks in conductors. The approach is compared with an electric field integral equation method also used for solving crack problems in eddy-current nondestructive evaluation. An important advantage of the vector potential integral formulation is that the kernel has a weak singularity, but a drawback is that two unknown functions must be found on the crack surface. One of these functions, the current dipole density, represents the effect of the crack in terms of an induced source, and the other function is a solution of the two-dimensional Laplace equation. By contrast, the source density alone is needed for a complete solution of the electric field integral equation. In order to determine the surface Laplacian for finite cracks of arbitrary shape, a general numerical solution utilizing the boundary element technique is introduced. Numerical predictions of the eddy-current probe response to a crack give good agreement with experimental measurements, supporting the validity of the formulation     

Eddy-current loss in the rotor magnets of permanent-magnet brushless machines having a fractional number of slots per pole

We develop an analytical model for predicting the eddy-current loss in the rotor magnets of permanent-magnet brushless machines that have a fractional number of slots per pole, when either all the teeth or only alternate teeth are wound, and in which the unwound teeth may be narrower than the wound teeth. The model enables the magnetic field distribution in the air gap and magnet regions to be determined, by neglecting the eddy-current redistribution effect and assuming that the eddy currents are resistance limited. It can account for space-harmonic magnetomotive forces (MMFs) resulting from the winding distribution and time-harmonic MMFs due to nonsinusoidal phase currents, as well as for the effect of curvature and circumferential segmentation of the magnets. We have validated the model by finite-element analysis, and used it to investigate the eddy-current loss in the magnets of three surface-mounted magnet brushless motors that have similar slot and pole numbers, and employ identical rotors but different stators, when they are operated in brushless ac (BLAC) and dc (BLDC) modes. We show that the stator winding configuration, as well as the operational mode, significantly influence the resultant eddy-current loss.     

Analytical and numerical solution of the eddy-current problem inspherical coordinates based on the second-order vector potentialformulation

The three-dimensional (3-D) eddy-current problem, described in spherical coordinates, is studied both analytically and numerically. Since the vector field equation is not separable in the spherical coordinate system, the second-order vector potential (SOVP) formulation is used to treat the problem by reducing it to the solution of the scalar field equation. While the analytical solution is expressed in terms of known orthogonal expansions, the numerical solution utilizes the finite difference method. Examples of engineering applications are provided, concerning computation of eddy-current distribution in a conducting sphere by a filamentary excitation of arbitrary shape     

Estimating the Eddy-Current Modeling Error

The eddy-current model is an approximation of the full Maxwell equations. We will give estimates for the modeling error and show how the constants in the estimates are influenced by the geometry of the problem. Additionally, we analyze the asymptotic behavior of the modeling error when the angular frequency tends to zero. The theoretical results are complemented by numerical examples using high order finite elements. These demonstrate that the estimates are sharp. Hence, this work delivers a mathematical basis for assessing the scope of the eddy-current model.     

Eddy-Current Coil Interaction With A Perfectly Conducting Wedge of Arbitrary Angle

In this article, a closed-form expression for the impedance of a tangential eddy-current coil in the presence of an infinite conducting wedge of arbitrary angle is derived. The truncated eigenfunction expansion (TREE) solution given here is valid in the quasi-static frequency regime. The theory was validated via comparison to an independent analytical expression for the impedance change of a horizontal coil over a conducting half-space due to Burke. We present results for three geometries: a conducting quarter-space, a conducting wedge of angle 225 degrees, and a semi-infinite conducting sheet. Our theory predicts a measurable change in the tangent coil reactance in the presence of all three geometries.     

Time-Harmonic Induction-Machine Model Including Hysteresis and Eddy Currents in Steel Laminations

We have studied electromagnetic losses of a frequency-converter-fed cage-induction motor by using a numerical machine model that includes eddy-current and hysteresis phenomena in electrical steel sheets. We used the model to solve the two-dimensional (2-D) time-harmonic field and winding equations of a cage-induction machine, utilizing a finite-element method and phasor variables. We used complex reluctivity to couple the hysteresis and eddy currents in the sheets with the 2-D analysis. The model modifies the absolute value of the reluctivity according to a one-dimensional (1-D) eddy-current solution developed in the lamination thickness. To define the argument of the reluctivity, we applied both the 1-D field solution and measured hysteresis data. We compared computations of additional electromagnetic losses in a 37-kW test machine due to the higher harmonics of a frequency-converter supply with experimental results. The agreement is found to be reasonable.      

Time-harmonic finite-element analysis of eddy currents in the form-wound stator winding of a cage induction motor

A finite-element model for calculation of eddy-current and circulating current losses in a multi-conductor stator winding of a cage induction motor is presented. In this model, the eddy current formulation of the series and parallel connected stator bars is solved together with the circuit and field equations using a two-dimensional time-harmonic approximation. The Newton-Raphson method is applied to solve the total system of nonlinear equations. The finite-element mesh is discretised finely enough in order to take the phenomena correctly into account. The eddy-current loss distribution of the stator bars and the quantitative results of eddy-current and circulating current losses have been studied with two different conductor arrangements inside the stator slots. The results show that the eddy-current loss in the stator winding is one of the most significant loss components. They also show that the radial position of the stator bars has a remarkable effect on the losses. The radial flux that passes through the stator bars can be guided to stator teeth by using magnetic slot wedge material to reduce the eddy-current loss.     

Experimental optimization of the probe for eddy-currentdisplacement transducer

The experimental optimization of the coil for an eddy-current displacement transducer probe is presented in the paper. The coil geometry is optimized for the special design of the transducer as a meter of the real part of the probe's impedance. Measurement of the transducer's transfer function has been performed with several samples of ring-shaped coils, as well as with the flat, pancake-shaped coil and with the single-layered cylindrical coil. For the sake of comparison, measurement with the ferrite-cored coil has been included too. The measurement results clearly indicate that the optimal coil geometry is a ring with a uniform and very small cross section of the winding     

Optimized radiofrequency coils for increased signal-to-noise ratio in magnetic resonance microscopy

The signal-to-noise ratio (SNR) is a major obstacle to achieving increased resolution in magnetic resonance microscopy (MRM). The SNR considerations for MRM are presented, with particular attention to the role of judicious receiver coil design in maximizing sensitivity and limiting noise contributions both from the sample and the coil. We present a number of different coil configurations that have been optimized for particular applications of MRM in the biological sciences. An overview of the literature regarding derivations of the SNR for birdcage-configuration volume coils, inductively coupled surface coils, and surgically implanted coils is presented in a unified fashion. Microscopy coils designed to reduce the total volume of excitation, thus coupling more closely to a given region of interest, are discussed. The volume coil is presented in terms of its application to lung imaging in small animals at 2 T and imaging of stroke at 7 T. The performance of traditional surface coils is demonstrated by application to spinal cord imaging in the rat. Finally, implanted coils are examined, as used in studies of the carotid arteries. © 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 277–284, 1997     

Stability of an electromagnetically levitated spherical sample in a set of coaxial circular loops

This paper presents a theoretical study of oscillatory and rotational instabilities of a solid spherical body, levitated electromagnetically in axisymmetric coils made of coaxial circular loops. We apply our previous theory to analyze the static and dynamic stability of the sample depending on the ac frequency and the position of the sample in the coils for several simple configurations. We introduce an original analytical approach employing a gauge transformation for the vector potential. First, we calculate the spring constants that define the frequency of small-amplitude oscillations. For static stability, the spring constants must be positive. Dynamic instabilities are characterized by critical ac frequencies that, when exceeded, may result either in a spin-up or oscillations with increasing amplitude. We found that the critical frequencies increase with the nonuniformity of the field. We show that for a spherically harmonic field, the critical frequency for the spin-up instability in a field of degree l coincides with the critical frequency for the oscillatory instability in a field of degree l+1.