Inspection of aluminum alloys by a multi-frequency eddy current method

The paper proposes an experimental method of material inspection,which is based on digital processing of multi-frequency eddy current measurement data.The influences of various factors(conductivity,the gap between the sample surface and the sensor,the thickness of the sample) on the obtained hodographs are examined by taking the aluminum alloys for example,and the possibility of separation of various factors is analyzed.The results obtained are indicative of how much promise the proposed method offers for the inspection and testing of products made of aluminum alloys.

Eddy Current Analyses by Domain Decomposition Method Using Double-Double Precision

A matrix equation solved in an eddy current analysis,??-??method based on a domain decomposition method becomes a complex symmetric system.In general,iterative method is used as the solver.Convergence of iterative method in an interface problem is improved by increasing an accuracy of a solution of an iterative method of a subdomain problem.However,it is difficult to improve the convergence by using a small convergence criterion in the subdomain problem.Therefore,authors propose a method to introduce double-double precision into the interface problem and the subdomain problem.This proposed method improves the convergence of the interface problem.In this paper,first,we describe proposed method.Second,we confirm validity of the method by using Team Workshop Problem 7,standard model for eddy current analysis.Finally,we show effectiveness of the method from two numerical results.

NUMERICAL ANALYSIS AND EXPERI-MENT OF UNSTEADY THERMAL FIELD OF ROTOR PLATE FOR EDDY CURRENT RETARDER

The physical model based on heat transfer theory and virtual boundary method for analyzing unsteady thermal field of rotor plate for eddy current retarder used in automobile is established and boundary conditions are also defined. The finite element governing equation is derived by Galerkin method. The time differential item is discrete based on Galerkin format that is stable at any condition. And a new style of varying time step method is used in iteration process. The thermal field on the rotor plate at the radial and axle directions is analyzed and varying temperature at appointed points on two side-surfaces is measured. The testing and analytical data are uniform approximately. Finite element method can be used for estimating thermal field of the rotor plate at initial design stage of eddy current retarder.

New Method for 3D Transient Eddy Current Field Calculation and Its Application in Magneto-Acoustic Tomography

A new method of 3D transient eddy current field calculation is proposed. The Maxwell equations with time component elimination （METCE） are derived under the assumption of magnetic quasi static approximation, especially for the sample of low conductivity. Based on METCE, we deduce a more efficient reconstruction algorithm of a 3D transient eddy current field. The computational burden is greatly reduced through the new algorithm, and the computational efficiency is improved. This new algorithm decompounds the space-time variables into two individual variables. The idea is to solve the spatial vector component firstly, and then multiply it by the corresponded time component. The iterative methods based on METCE are introduced to recover the distribution of conductivity in magneto-acoustic tomography. The reconstructed images of conductivity are consistent with the original distribution, which validate the new method.

Validity and Accuracy of Eddy Current Field Analysis of Laminations by Introducing Equivalent Conductivities

对于分析叠片铁心中的涡流问题，利用各种等效电导率替代硅钢片实际电导率的匀质化方法是很有应用前景的。为了评估各种电导率模型，该文提出了铁心涡流场分析的二维解析验证方法，并分别基于引入各向异性或各向同性等效电导率的铁心连续体表述和实际叠片表述对涡流场进行了解析计算。通过比较连续体表述下所得到的平均磁通密度和涡流损耗值与相应由实际叠片表述所得到的精确解，对各种电导率模型的有效性和准确性在各种条件下进行了评估。为了进一步考察电导率模型对实际工程问题的适用性，利用有限元法进行了关于TEAM21面向工程基准问题的磁通和杂散场损耗计算。计算结果表明，由该文作者所提出的等效电导率模型优于其他模型。

A, ■-Ω METHOD FOR 3-D EDDY CURRENT ANALYSIS

After the field equations and the snonumuoo conditions between the interfaces for 3D eddy current problems Under various gauges were discussed, it was pointed cut in this paper that using the magnetic vector potential A. the electric scalar potential and Coulomb gauge △ .A = 0 in eddy current regions and using the magntetic scalar potential Ω in the non-conducting regions are more suitable. All field equations, the boundary conditions, the interface continuity conditions and the corresponding variational principle of this method are also given

Finite Element Method Based on Equivalent Magnetic Energy Method for Computation of 2D Nonlinear Eddy Current Field

In this paper, the finite element method using vector potential in applications to 2D nonlinear eddy current field is discussed. The authors use the equivalent magnetic energy method to deal with magnetization curve of ferromagnetic material,and present the formulation of 2D nonlinear eddy current field.With this method the authors analyze the eddy current field in an induction ladle furnace and the force distribution in the charge (molten metal),and plot the corresponding curves.

An Introductory Note on Finite Element Problems Based on the Eddy Current Testing Approach

The paper addresses the first eddy current benchmark problem proposed by the World Federation of Nondestructive Evaluation Centers (WFNDEC). The problem simulates the eddy current response to the presence of an axisymmetric circumferential defect in an Inconel-600 tube. All simulations employ the axisymmetric code of the electromagnetic field simulator Finite Element Method Magnetics. For three different frequencies of excitation, it is explained how the displacement of the detecting coil inside the tube leads to a variation in the impedance of the eddy current coil. Variations of the resistive and inductive components of the impedance with distance from the defect region are used to build the impedance trajectory for each frequency of analysis.

Design of Scenery Complementary Solar Water Heater Based cm Eddy Current Method

This paper uses scenery complementary heating method to discuss a new type of scenery complementary water heater design. This product can be divided into two parts. The first part is the eddy current method wind power heating part, which is driven by wind power and vertical axis wind turbines and the design of magnet array rotor disc rotation, namely, magnetic field rotating, induced eddy current in the stator, so as to generate heat. The second part is the solar heating part. This works has broad market prospect, which provides a new idea for large-scaled heating method.

Preconditioned BiCGSTAB algorithm and its applications to eddy current solutions

A new favorable iterative algorithm named as PBiCGSTAB （preconditioned bi-conjugate gradient stabilized） algorithm is presented for solving large sparse complex systems. Based on the orthogonal list, the special technique of only storing non-zero elements is carried out. The incomplete LU factorization without fill-ins is adopted to reduce the condition number of the coefficient matrix. The BiCGSTAB algorithm is extended from the real system to the complex system and it is used to solve the preconditioned complex linear equations. The locked-rotor state of a single-sided linear induction machine is simulated by the software programmed with the finite element method and the PBiCGSTAB algorithm. Then the results are compared with those from the commercial software ANSYS, showing the validation of the proposed software. The iterative steps required for the proposed algorithm are reduced to about one-third, when compared to the BiCG method, therefore the algorithm is fast.

3D Eddy Current and Temperature Field Analysis of Large Hydro-generators in Leading Phase Operations

As a common practice,a large hydro-generator will operate in leading phase conditions to absorb the reactive power of the power grid.However,the accurate and precise prediction of the leading phase operation capacity of a large hydro-generator has always been a formidable challenge to engineers and academicians because it is extremely hard to compute the eddy currents and losses as well as the local overheating in the pressure plate and finger.To address this problem,a full three dimensional(3D)finite element model and method of the coupled eddy current and temperature fields in the end region of a large hydro-generator are developed.The equivalent medium parameters used in the computations are comprehensively discussed.Moreover,some numerically based solution methodologies for accurate computation of the field and armature currents under different leading phase conditions are proposed.Numerical results on the coupled eddy current and temperature fields in the end regions of a 250 MW hydro-generator confirm positively the feasibility of the present work.

NEW ALGORITHM OF IDENTIFYING SHAPE OF FLAWS OR CRACKS IN EDDY CURRENT TESTING

Eddy-current inverse technique is a very important method to reconstruct the shape of flaws or cracks. Using the domain derivative of the far-field pattern for eddy- current inverse problem with Dirichlet boundary condition, a new algorithm to recover the shape of cracks was constructed and some numerical examples were given. The algorithm demonstrates that the algorithm is feasible and correct for obtaining a reasonable reconstruction of a shape of flaws or cracks from the far-field measurements even though using less data of directions of incidence and observations for fewer wave numbers are gived.

Calculation of Eddy Current Loss and Short-circuit Force in SSZ11-50000/110 Power Transformer

The ?method is used in this paper to calculate the leakage magnetic field of SSZ11-50000/110 Power transformer, and by which the structures’ influences to the main leakage flux are analyzed. Through the combination of the product and TEAM Problem 21B, the surface impedance method shows its great advantage in the calculation of eddy current loss.

Comparison of three formulations for eddy-current problems in a spiral coil electromagnetic acoustic transducer

Three differential equations based on different definitions of current density are compared. Formulation I is based on an incomplete equation for total current density （TCD）. Formulations II and {I1 are based on incomplete and complete equations for source current density （SCD）, respectively. Using the weak form of finite element method （FEM）, three formulations were applied in a spiral coil electromagnetic acoustic transducer （EMAT） example to solve magnetic vector potential （MVP）. The input impedances calculated by Formulation III are in excellent agreement with the experimental measurements. Results show that the errors for Formulations I ＆ II vary with coil diameter, coil spacing, lift-off distance and external excitation frequency, for the existence of eddy-current and skin ＆ proximity effects. And the current distribution across the coil conductor also follows the same trend. It is better to choose Formulation I instead of Formulation Ili to solve MVP when the coil diameter is less than twice the skin depth for Formulation I is a low cost and high efficiency calculation method.

Study on the Effect of Magnetic Pole Clipping Angle on the Eddy Current Loss of Permanent Magnets in the Rotor of Magnetically Levitated Permanent Magnet Synchronous High-Speed Electric Spindles

Aiming at the problem of high temperature and even demagnetization failure of permanent magnet (PM) due to PM eddy current loss in PM synchronous high-speed motors, this paper proposes a technique to lessen PM eddy current loss by cutting the angle of PM poles to change the shape of PM structure. Firstly, an analysis is conducted on the mechanism of PM synchronous high-speed motor eddy current loss production, the theoretical analytical model of PM eddy current loss is deduced, and it is theoretically proved that the magnetic pole shaving angle can reduce PM eddy current loss. Then, a 25 KW surface-type PM synchronous high-speed motor as an object, using two-dimensional time-step finite element method (FEM) to model and analyze PM eddy current loss. The results show that the smaller the PM pole shaving angle, the less its eddy current loss will be, it is possible to minimize the pole shaving angle of eddy current loss by 9.8% compared to the unshaved angle. Finally, the temperature field of the PM is calculated using a finite element method, and the outcomes demonstrate that the maximum temperature of the PM with a magnetic pole shaving angle can be reduced by about 5% compared with the unshaved angle.

A Moving Coordinate Numerical Method for Analyses of Electromagneto-Mechanical Coupled Behavior of Structures in a Strong Magnetic Field Aiming at Application to Tokamak Structures

Analysis of the electromagneto-mechanical coupling effect contributes greatly to the high accuracy estimation of the EM load of many EM devices, such as a tokamak structure during plasma disruption. This paper presents a method for the numerical analysis of the electromagnetomechanical coupling effect on the basis of Maxwell＇s equations in the Lagrangian description and staggered load transfer scheme, which can treat the coupled behaviors of magnetic damping and magnetic stiffness effects at the same time. Codes were developed based on the ANSYS development platform and were applied to solve two typical numerical examples： the TEAM Problem 16 and dynamic behavior analysis of a shallow arch under electromagnetic force. The good consistency of numerical results and experimental data demonstrates the validity and accuracy of the proposed method and the related numerical codes.

EFFECTIVE SHIELDING OF UNIDIRECTIONAL CURRENT GENERATED MAGNETIC FIELDS

This paper presented an effective shielding design of magnetic fields generated by unidirectional current. Theoretical formulas and numerical computation software based on boundary element method (BEM) are employed to evaluate the shielding effectiveness (SE) of cylindrical shell. It is shown that ungrounded or one end grounded metal shell is ineffective for such magnetic fields. SE can be obtained by connecting the two ends of the conducting shell with low impedance connector, or alternatively, grounding the two ends. The experimental results also support these conclusions.

轮缘推进永磁电机-护套-介质系统建模与仿真

为了降低轮缘推进器永磁电机的涡流损耗,研究护套材料与厚度对永磁电机涡流损耗的影响,基于有限元电磁分析软件ANSYS Electronics Desktop,建立电机-护套-介质系统模型,并通过仿真结果与数值计算结论的对比验证模型准确性;计算永磁电机定转子护套、永磁体涡流密度分布,分析护套材料与厚度对涡流损耗的影响规律。结果表明:护套材料电导率较高时护套中的涡流密度远大于永磁体中的,电导率较低时两者大小相近;采用电导率较低的护套材料时电机产生的涡流损耗远小于采用电导率较高的护套材料;护套材料对护套单位体积涡流损耗影响较大,对永磁体影响较小;定转子护套的厚度比与产生的涡流损耗呈正相关;随着护套厚度比增大,采用电导率较低的护套对永磁体及护套单位体积涡流损耗影响较小,而电导率较高的护套因为屏蔽作用能够通过降低永磁体的涡流密度来降低永磁体涡流损耗;气隙介质在空气、淡水、海水中的变化对电机的磁通密度分布没有显著影响。研究成果可为轮缘推进器永磁电机护套设计提供参考。

考虑精确磁通的电磁加载装置等效磁路建模

为提高电磁加载装置在控制应用时的模型预测快速性与精确性,考虑电磁加载装置硅钢片表面涡流磁场生成因素与不同轴偏心下有效气隙长度,采用非线性方程拟合硅钢片磁化曲线,建立包含磁极边缘效应、磁极铁心、转子硅钢片动态磁阻与涡流磁场的电磁加载装置非线性等效磁路模型。研究了硅钢片表面涡流磁场生成因素与气隙磁场分布,并与有限元仿真结果比较分析。应用该模型在水润滑轴承试验台上进行电磁加载力测试试验。研究结果表明:等效磁路法对磁场分布的表征与有限元法一致,且对气隙的计算更为精确;电磁加载力稳态误差小于4%,响应时间低于0.55 s。

双层复合护套高速永磁电机转子涡流损耗解析模型

在表贴式高速永磁电机中,双层复合护套可以有效抑制转子涡流损耗。目前,针对双层复合护套转子涡流损耗的研究主要采用有限元法,但该方法存在耗时、对薄护套网格剖分较困难等问题,因此该文基于精确子域法提出了一种考虑定子开槽、涡流反作用的双层复合护套高速永磁电机转子涡流损耗通用解析模型。该模型同时考虑了永磁磁场励磁和电枢磁场励磁,可以计算负载磁场作用下的双层复合护套转子涡流损耗。此外,该模型还可进一步拓展至多层复合护套转子涡流损耗计算。通过该解析模型研究了双层复合护套不同护套厚度配比、不同护套材料对转子涡流损耗的影响。最后,将解析计算结果与有限元及C型铁心实验结果进行对比,验证了该解析模型的有效性。