Low-Frequency Electromagnetic Fields and Finite Element Method

In traditional artificial-source electromagnetic exploration, the effects of the ionosphere and displacement current (DC) in the air were neglected, and only the geoelectrical structure of the earth's crust and upper mantle was considered, such as for controlled source audio-frequency magnetotelluric (CSAMT). By employing a transmitter (less than 30 kW) to generate source fields, the CSAMT method overcomes the problems associated with weak natural electromagnetic (EM) fields used in magnetotellurics. However, the transmitter is moved and the source–receiver offset is approximately less than 20 km, because of the limitation of emission energy. We put forward a new idea, that is, a fixed artificial source (greater than 200 kW) is used and the source location selected at a high resistivity region (to ensure a high emission efficiency), so there may be a possibility that as long as the source strength magnitude is strong enough, the artificial EM signal can be easily observed within a distance of several thousand kilometres. Previous studies have provided the evidence to support this idea; they used the ‘earth–ionosphere’ mode in modeling the EM fields with the offset up to a thousand kilometres. Such EM fields still have a signal/noise ratio over 10–20 dB; this means that a new EM method with fixed source is feasible. However, in their calculations, the DC which plays a very important role for large offsets was neglected. This paper pays much attention to derive the formulae of the ‘earth–ionosphere’ mode with a horizontal electric dipole source, and the DC is not neglected. We present some three layers modeling results to illustrate the basic EM field characteristics under the ‘earth–ionosphere’ mode. As the offset increases, the contribution of the conduction current decreases, DC and ionosphere were taken into account, and the EM field attenuation decreases. We also quantitatively compare the predicted and observed data. The comparison of these results with the data reveal the excellent agreement between the experimental and theoretical results. The DC and ionosphere affects the EM fields, however impedances (ratio of E to H) are unaffected, and this means we need to include ionosphere and DC effects to accurately model the EM field amplitudes for optimal setting of measurement parameters, but we do not need to include these complications for the interpretation of the data for the Earth conductivity.

Many devices contain parts that undergo motion due to electromagnetic forces. The motion causes the electromagnetic fields to change. Thus the electromagnetic fields must be computed along with the structural motion. In many cases the motion produced by electromagnetic forces is desired motion. However, in many devices, some undesired motion can occur due to electromagnetic forces. The motion creates motion-induced eddy currents which in turn affect the electromagnetic fields and forces. A finite element technique is described that fully couples structural and electromagnetic analysis in the time domain. The code is applied to a superconducting dipole model in order to study deformations and stresses during ramp and quench. The results of this coupled analysis enables the designer to visualize deformations, vibrations, displacements and all electromagnetic field quantities of the device and to try different solutions to enhance its performance.

Time-domain analysis of electromagnetic wave fields by boundary integral equation method

Two formulations of the BEM-FEM coupling method for 3D nonlinear magnetostatic problems are developed. Different ways of introducing the Coulomb gauge and handling of the respective boundary terms are discussed. Several iterative methods for the solution of the discretized equations are presented. An example of the TEAM workshop (Testing Electromagnetic Analysis Methods) has been used to examine the numerical behaviour.

Grain-oriented (GO) silicon steel laminations are widely used in iron cores and shielding structures of power equipments. When the leakage magnetic flux is very strong and enters the lamination plane perpendicularly, the eddy current loss induced there must be taken into account in electromagnetic design. It is preferable to accurately compute three-dimensional (3-D) eddy currents at least in a few outer sheets of the lamination stack. Since the coating film applied to each sheet is only 2-5 thick, finite element modeling of 3-D eddy currents is very difficult in GO silicon steel laminations of large electromagnetic devices. This paper proposes an inner-constrained separation technique (ICST) to compute the 3-D eddy currents. Instead of the coating film, the ICST introduces an inner constraint into the A-formulation to separate the laminations from each other. By the ICST, the 3-D eddy currents can be computed accurately without meshing the coating film. Numerical experiments are carried out on the TEAM (Testing Electromagnetic Analysis Methods) benchmark model P21c-M1 and the numerical results show good agreement with the measured data.

An analysis was made as to the usage of geological-geophysical methods for studying of low-amplitude tectonic dislocations in coal-enclosing massifs. As a result of geophysical researches conducted at coal fields, mine fields and mine workings of the Lviv-Volyn Coal Basin, the methods of field observations by means of natural electromagnetic and electric fields were worked and their results were processed for prediction and diagnostics of tectonic dislocations with a break of continuity and zones of unstressed state. To raise the efficiency of the methods of electromagnetic fields it is recommended to carry out measurements at wide frequency range (from 5 to 50 hz) with orientation of the antenna according to the world sides (azimuthal surveying) and at narrow frequency range (5; 12.5; 17 khz) with the southern orientation of the antenna (frequency sensing). According to azimuthal surveying one can calculate the vector of maximum intensity of electromagnetic radiation. It was ascertained that over distinctive dislocation one can observe the variation in the direction and absolute value of vectors. Displacement of the anomaly of electromagnetic radiation intensity at different frequency range by profile indicates the direction of dipping of the area of displacement of dislocations with a break of continuity. The method of natural electromagnetic impulse field of the Earth fixes both the dislocations, distinguishes by geological-geophysical methods before, and new low-amplitude dislocations and stressed zones.Tectonic dislocations, that are displayed only in Paleozoic deposits, are distinguished by contrast anomalies of electromagnetic radiation in electromagnetic field, but dislocations with a break of continuity that cut the Mesozoic thickness and in most cases are accompanied by zones of rock fracturing in the Cretaceous deposits: by wide destructive anomalies. Plots over worked-out lavas with stressed deformational state are characterized by strongly differential abnormal values of the intensity of natural impulse electromagnetic field of the Earth. The method of natural electric field allows us to detect zones with water-bearing fracturing rocks in the upper part of the geological section. Methods of natural impulse electromagnetic field of the Earth and natural electric field may be used both independently and in the complex with other geophysical methods for detection and tracing of tectonic dislocations and dynamically-unstressed zones. Thus, the optimum apparatus-methodical complex for detection and diagnostics of low-amplitude dislocations with a break of continuity of coal-enclosing series by electromagnetic methods (NIEMF, NEF) was formed and effective methods of field observations, processinf and interpretation of data were developed.

This paper describes an efficient method for both time- and frequency-domain solutions of electromagnetic (EM) field problems. In this method EM field problems are formulated using Laplace-domain finite element approach and are solved using complex frequency hopping (CFH) technique. CFH is a moment-matching technique which has been used successfully in the circuit simulation area for solution of large set of ordinary differential equations. Problems consisting of Dirichlet, Neumann and combined boundary conditions can be solved using the proposed algorithm to obtain both time and frequency responses. Several electromagnetic field problems have been studied using the new technique and the speed-up advantage (one to three orders of magnitude) compared to conventional finite element technique is demonstrated. A good agreement between numerical results obtained using the proposed method and the previously published results has been found.

In this study, we propose a two-step approach to evaluate electromagnetic interference (EMI) with a wearable electrocardiogram (ECG) sensor. The two-step approach combines a quasi-static electromagnetic (EM) field analysis and an electric circuit analysis, and is applied to the EMI analysis at frequencies below 1 MHz for our developed wearable ECG to demonstrate its usefulness. The quasi-static EM field analysis gives the common mode voltage coupled from the incident EM field at the ECG sensing electrodes, and the electric circuit analysis quantifies a differential mode voltage at the differential amplifier output of the ECG detection circuit. The differential mode voltage has been shown to come from a conversion from the common mode voltage due to an unbalance between the contact impedances of the two sensing electrodes. It may achieve nearly 0.6 V at the differential amplifier output under 10-V/m plane-wave incident electric field, and completely mask the ECG signal. It is essential to reduce the unbalance as much as possible to not cause a significant interference voltage in the amplified ECG signal.

Finite element analyses of electromagnetic fields are commonly used for designing various electronic devices. The scale of the analyses becomes larger and larger, therefore, a fast linear solver is needed to solve linear equations arising from the finite element method. Since a multigrid solver is the fastest linear solver for these problems, parallelization of a multigrid solver is quite a useful approach. From the viewpoint of industrial applications, an effective usage of a small‐scale PC cluster is important due to initial cost for introducing parallel computers. In this paper, a distributed parallel multigrid solver for a small‐scale PC cluster is developed. In high‐frequency electromagnetic analyses, a special block Gauss– Seidel smoother is used for the multigrid solver instead of general smoothers such as a Gauss– Seidel or Jacobi smoother in order to improve the convergence rate. The block multicolor ordering technique is applied to parallelize the smoother. A numerical example shows that a 3.7‐fold speed‐up in computational time and a 3.0‐fold increase in the scale of the analysis were attained when the number of CPUs was increased from one to five. © 2009 Wiley Periodicals, Inc. Electron Comm Jpn, 91(9): 28– 36, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecj.10160

Thermomechanical modeling of dissimilar-material interfaces in composite structures

PurposeThe purpose of this paper is to present the plan to develop the known algorithm for thermal and electromagnetic coupled problem calculation. This is used for three‐phase induction motor (IM) on nominal load. An additional purpose is verification empiric expressions of the heat transfer and equivalent thermal conductivity coefficients for external faces and air zones in analysed motor taken from literature.Design/methodology/approachThe numerical investigations proposed in this paper are based on 3D finite element models for thermal and electromagnetic fields analysis. Electromagnetic analysis includes iron core losses. It gives additional heat sources to thermal analysis. Heat transfer and equivalent thermal conductivity coefficients are assessed applying empiric expressions. Thermal model is experimentally validated.FindingsThe results of calculations and experimental test shows that heat transfer coefficient for external zones taken from literature does not guarantee the equal accuracy of the distribution of the temperature in all volume of the machine.Research limitations/implicationsTaken from literature, empirical equations do not give correct values of heat transfer coefficient. It states ways to go further in the evaluation of heat transfer coefficients.Originality/valueThis paper presents modelling methodology of 3D transient thermal field coupled with electromagnetic field applied in three‐phase IM at rated load conditions.

According to generating mechanism of electromagnetic noise from the permanent magnet synchronous motor on EV, this paper proposed how to use a multi-physics coupling analysis based on the electromagnetic, structural and acoustic fields of the motor to estimate the noise and vibration characteristics. Firstly, the two-dimensional transient electromagnetic field of the motor was calculated by using the step finite element method, and the electromagnetic excitation force on the surfaces of the stator in both frequency and time domain are obtained; Then, based on three-dimensional structure of the motor assembly, the simulation of the entire system natural frequencies and mode shapes was executed, and coupling the electromagnetic field analysis results of the motor, the vibration velocity level of the motor surface was achieved through the frequency response analysis. Finally, the coupled three-dimensional acoustic boundary element model was employed to calculate the motor acoustic radiation. The experimental results demonstrated that this multi-physics coupling numerical analysis method can effectively predict the electromagnetic noise in the motor design phase and help low-noise motor design and development.

In order to accurately analyze the temperature distribution of a high-speed magnetic suspension amorphous motor, a multi-physical coupling method, including flow field, electromagnetic field and temperature field, is proposed. The electromagnetic loss obtained by electromagnetic analysis is directly mapped to the temperature field and input to the boundary conditions of the flow field for several coupled iterations. This paper compares the thermal analysis results of two different temperature rise calculation methods, analyzes the temperature distribution of magnetic suspension amorphous motor under different working conditions, and discusses the simulation results and the measured results. The error between the multi-field coupling simulation results and the experimental results is less than 10 °C, and the error of the traditional temperature rise analysis method is 30 °C, which verifies the superiority of the proposed coupling analysis method in improving the calculation accuracy of motor temperature rise, and has important significance for the accurate prediction of motor temperature rise in the design stage.

Local heating of the pillbox‐type vacuum window employed in microwave heating of nuclear fusion apparatus TOKAMAK has been a problem when used under a high power, particularly under the ghost mode. This factor is used to determine the maximum power of the heating system. However, in the measurement in actual operation, only the electric field can be measured when the amplitude and reflection coefficient become small due to the loss. An analysis taking into consideration the dielectric loss is needed to determine the characteristics of the electromagnetic field distribution in the ghost mode. We have applied the spatial network method to the pillbox vacuum window excited by a rectangular waveguide. The method has a number of unique features as a time domain analysis method for three‐dimensional electromagnetic fields. After the basic treatment is described, the electromagnetic field of the ghost mode is simulated by the analysis taking into consideration the dielectric loss. The effectiveness of the three‐dimensional electromagnetic analysis for the entire system is presented.

Chapter 14 - Electromagnetic Methods in the Frequency and Time Domains