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.

Inverse problem of pulsed eddy current field of ferromagnetic plates

To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy current testing on the plate. From time-domain analytical expressions of the partial derivatives of induced voltage with respect to parameters,it is deduced that the partial derivatives are approximately linearly dependent. Then the constraints of these parameters are obtained by solving a partial linear differential equation. It is indicated that only the product of conductivity and wall thickness, and the product of relative permeability and wall thickness can be determined accurately through the inverse problem with time-domain induced voltage. In the practical testing, supposing the conductivity of the ferromagnetic plate under test is a fixed value, and then the relative variation of wall thickness between two testing points can be calculated via the ratio of the corresponding inversion results of the product of conductivity and wall thickness. Finally, this method for wall thickness measurement is verified by the experiment results of a carbon steel plate.

Eddy current effects in a high field dipole

Eddy currents produced by a time-varying magnetic field will introduce time delay and thus affect field quality. This effect leads to drifting of the beam position over time, especially for a compact synchrotron.Simulations and measurements of different dipoles have been performed, to investigate the time delay and field quality. The simulations are conducted using OPERA software. The measurements are conducted using a long coil and Hall sensor. All results show that the magnetic field deviation is up to 0.4% for the dipole with stainless steel endplates. The simulations show that the main sources of eddy current are the field saturation effect and the field component Bz, introduced by the bedstead-type coil. Field correction using a power supply is adopted to reduce the deviation to less than 0.02%.

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.

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。

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.

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.

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.

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

An Investigation into the Influence of the Airflow Path on the Convective Heat Transfer for an Eddy Current Retarder Turntable

In order to improve the convective heat transfer relating to an eddy current retarder,the finite element model has been used to assess the performances of different possible designs.In particular,assuming the steady running state of retarder as the working condition,flow and temperature fields have been obtained for the rotor.The influence of airflow path on heat dissipation has been analysed,and the influence of the temperature field distribution on the performance of retarder has been discussed accordingly.The results show that when the steady running state of the turntable is considered,the maximum temperature is lower,the level of turbulence flow is mitigated,and the temperature distribution becomes more regular.These factors contribute to improve the heat dissipation ability of the retarder.

Speed Measurement Feasibility by Eddy Current Effect in the High-Speed MFL Testing

It is known that eddy current effect has a great influence on magnetic flux leakage testing(MFL).Usually,contacttype encoder wheels are used to measure MFL testing speed to evaluate the effect and further compensate testing signals.This speed measurement method is complicated,and inevitable abrasion and occasional slippage will reduce the measurement accuracy.In order to solve this problem,based on eddy current effect due to the relative movement,a speed measurement method is proposed,which is contactless and simple.In the high-speed MFL testing,eddy current induced in the specimen will cause an obvious modification to the applied field.This modified field,which is measured by Hall sensor,can be utilized to reflect the moving speed.Firstly,the measurement principle is illustrated based on Faraday’s law.Then,dynamic finite element simulations are conducted to investigate the modified magnetic field distribution.Finally,laboratory experiments are performed to validate the feasibility of the proposed method.The results show that Bmz(r1)and Bmx(r2)have a linear relation with moving speed,which could be used as an alternative measurement parameter.

高速列车关键部件涡流自动成像检测方法

涡流检测是一种非破坏性检测方法。以高速列车构架为检测对象,结合涡流与自动化设备检测技术,针对人工涡流检测效率低、结果一致性差等问题,提出涡流自动成像检测方法。通过建立构架焊缝的涡流探头仿真模型,分析激励电流方向对检测信号的影响,优化激励线圈相关参数并制作涡流探头;设计开发构架涡流自动成像检测系统,开展构架焊缝表面缺陷自动化检测试验。对比分析激励频率、激励电压等涡流检测工艺参数以及探头扫查速度、扫查轨迹间距等路径参数对缺陷涡流信号的影响,研究结果表明,利用涡流自动成像检测系统可以对构架整车进行自动探伤,能够将构架焊缝处缺陷以图像形式呈现,可以有效检出0.3、0.5 mm深的人工缺陷,对构架批量产线化检测具有参考价值。

基于磁网络法的正弦调磁环磁齿轮研究

提出的一种适合高速运行的磁齿轮,其调磁环具有正弦轮廓。为了研究这类磁齿轮性能,引入磁网络法,该方法将计算区域离散化,便于描述不规则边界条件,并建立等效磁网络模型。对比研究了矩形调磁块磁齿轮和正弦调磁环磁齿轮的气隙磁密、峰值转矩、稳态转矩和涡流损耗。结果表明,磁网络法和有限元结果整体吻合,局部存在偏差,正弦调磁环内、外转子峰值转矩的相对误差为12.95%和14.9%,相较于传统结构,正弦调磁环磁齿轮的峰值转矩减小了15%,涡流损耗降低了29%,验证了所提出结构在高速下的潜在应用前景。

基于A,Ф-A的变压器三维涡流场时域有限元POD降阶方法及其应用

为解决三维涡流场时域求解时间长和存储空间需求较多的问题,首先基于A,Ф-A的三维涡流场时域有限元法结合POD(Proper Orthogonal Decomposition,POD)降阶算法实现了三维涡流场的高效计算。其次,以国际TEAM第21基准问题的模型B为例,通过对比分析实测数据与自编程序和COMSOL的计算结果,验证了A,Ф-A的三维涡流场时域有限元求解方法的有效性。然后,通过POD不同阶数的降阶算例验证了POD降阶方法的有效性。最后,利用所提的基于A,Ф-A三维涡流场时域有限元法计算了一台三相变压器进行额定运行工况下的涡流场,并将计算结果与COMSOL仿真结果进行了对比。同时,还分析了三相变压器在负荷减少过程中的相电流和磁场变化,并分析了降阶模型阶数对计算时间和精度的影响,结果表明:15阶降阶模型耗时约为全阶耗时1/10,并且在方程降阶后各时间步的加速比最大,可达到70~165倍,在计算涡流损耗时相对误差不超过4.59%,计算精度相对较高。

Dynamical analysis of mesoscale eddy-induced ocean internal waves using linear theories

This study aims to explore generation mechanisms of the ocean internal wave using the dynamical analysis methods based on linear theories. Historical cruise measurements and recent synthetic aperture radar （SAR） observations of mesoscale eddies with diameter of several tens of kilometers to hundreds of kilometers show that the internal wave packets with wavelength of hundreds of meters to kilometer exist inside the mesoscale eddies. This coexistence phenomenon and inherent links between the two different scale processes are revealed in the solutions of governing equations and boundary conditions for the internal wave disturbance with a horizontally slowly variable amplitude in a cylindrical coordinate system. The theoretical solutions indicate that the instability of eddy current field provides the dynamical mechanism to internal wave generation. The derived dispersion relation indicates that the internal wave propagation is modified by the eddy current field structure. The energy equation of the internal waves clearly shows the internal wave energy increment comes from the eddy. The theoretical models are used to explain the observation of the mesoscale eddy-induced internal waves off the Norwegian coast. The two-dimensional waveform solution of the anticyclonic eddy-induced internal wave packet appears as ring-shaped curves, which contains the typical features of eddy stream lines. The comparison of theoretical solutions to the structure of the internal wave packets on SAR image shows a good agreement on the major features.

MULTI-FIELD COUPLING BEHAVIOR OF SIMPLY-SUPPORTED CONDUCTIVE PLATE UNDER THE CONDITION OF A TRANSVERSE STRONG IMPULSIVE MAGNETIC FIELD

In order to study the multi-field coupling mechanical behavior of the simply-supported conductive rectangular thin plate under the condition of an externally lateral strong impulsive magnetic field, that is the dynamic buckling phenomenon of the thin plates in the effect of the magnetic volume forces produced by the interaction between the eddy current and the magnetic fields, a FEM analysis program is developed to characterize the phenomena of magnetoelastic buckling and instability of the plates. The critical values of magnetic field for the three different initial vibrating modes are obtained, with a detailed discussion made on the effects of the lengththickness ratio a/h of the plate and the length-width ratio a/b as well as the impulse parameter on the critical value BOcr of the applied magnetic field.

TRANSIENT TEMPERATURE FIELD IN ACTIVE THRUST MAGNETIC BEARING

A transient temperature field model in a thrust magnetic bearing is built in which the heat resources come mainly from the eddy-current loss of solid cores and the copper loss of coils. The transient temperature field, system temperature rise and the thermo-equilibrium state during the rotor starting-up are calculated considering only the copper loss and the eddy-current loss. The numerical results indicate that the temperatures in coils and in magnets rise rapidly, their thermo-equilibrium states are formed within a short time. The temperatures in a thrust-disk and in a rotor rise slowly, their thermo-equilibrium states are formed aller a long period time. The temperatures of the thrust-disk and the rotor are far higher than the temperatures of coils and/or magnets aller the thermo-equilibrium state has come into being.

Design Optimization for Generating a High Static Magnetic Field

This paper details the creation of a device capable of generating a powerful and consistent static magnetic field. This apparatus serves the purpose of quantifying the magnetostrictive strain found in materials like annealed cobalt ferrite and Terfenol-D, specifically those shaped as cylindrical rods. In our investigation, the use of static magnetic fields proves most advantageous. This choice is made to mitigate the generation of eddy currents, which would inevitably occur if the magnetic field intensity were varied. The fundamental idea behind this design involves employing a C-shaped iron core constructed from low-carbon mild steel. On this core, three coils are mounted, each capable of producing one-third of the required 9000 Oersted (Oe) magnetic field strength. The test specimen is situated within the “jaws” of the C-shaped core, thus completing the magnetic circuit. To manage the heat generated by each coil, a cooling system consisting of copper tubes is employed. These tubes facilitate the flow of air to dissipate the heat. To model and predict the magnetic field strength produced by the coils, finite element analysis (FEMM) software is utilized, and the results align closely with the anticipated outcomes. This design effectively generates a robust and unchanging magnetic field measuring a stable 9000 Oe in total. Consequently, this equipment finds utility in characterizing the magnetic properties of specific materials.

核电半速汽轮发电机励磁绕组匝间短路时转子涡流损耗研究

为研究核电半速汽轮发电机励磁绕组匝间短路时转子涡流损耗特性,推导了核电半速汽轮发电机空载运行时励磁绕组匝间短路故障下,定子分数次谐波环流产生的合成磁动势表达式,分析合成磁动势相对于转子的转速,揭示了转子表面产生涡流的原因以及涡流的频率特性。结合涡流损耗计算方法,以一台核电半速汽轮发电机为例进行了仿真验证。在此基础上,对核电半速汽轮发电机励磁绕组不同位置发生相同程度匝间短路,以及励磁绕组发生不同程度匝间短路过程进行了仿真,计算了转子各阻尼条及槽楔中的涡流及涡流损耗,揭示了励磁绕组匝间短路时影响转子阻尼条及槽楔中涡流和涡流损耗的因素。为核电半速汽轮发电机励磁绕组匝间短路故障时,分析转子发热的影响因素提供了理论基础。

Aerospace Electromagnetic Thruster with Average Foucault Currents

The work is an attempt to find the force with which an electromagnetic system with Foucault currents acts on itself. It is taken into account that the average force with which the source of the alternating magnetic field and the inductive Foucault current is equal to zero, the self-force arises as a result of the interaction of unclosed Foucault conduction currents with the displacement current created by a conductor located in a non-uniform magnetic field. The average force acting on a symmetrical conductor located between the poles of an electromagnet turned out to be different from zero. The greatest value of this force is observed in the region of maximum inhomogeneity of the magnetic field.