In our previous papers, we investigated into fundamental natures of the discretization errors inherent to the boundary element method (BEM) in 3-D. We showed that the discretization error is smaller than usually expected even in the case where the lowest order of approximation is used for discretizing the unknown function to be solved. Our previous numerical experiments were conducted by arranging elements with an equal mesh size over the boundary surfaces. In practical applications to design problems of electron optical instruments, we have to treat boundary configurations with details of shape with different curvatures. In this paper, we describe another series of numerical experiments conducted to find out the effect of varying the mesh size upon the local accuracy of solution. From these results we can formulate a strategy to estimate the discretization error of a numerical solution in most of practical applications where no exact solution is available. Following this we found that in several practical applications the accuracy of the numerical solution of potential problems in general 3-D can be reduced sufficiently by adjusting the local mesh size.

View full abstract

In the field of oil well drilling, EM-MWD (Electromagnetic Measurement While Drilling) is taken note of. It can transmit measured data from the well bottom to the surface with high speed using electromagnetic waves. To develop the EM-MWD technology, it is necessary to analyze an electric field around a drillstring. In most of conventional works, the drillstring was usually assumed to be a perfect conductor and/or the earth was assumed to be a uniform medium. In this paper, we consider the drilistring as a rod with finite conductivity, and assume that the earth is composed of several formations. We take three steps for the electric field analysis. First, a quasistatic electric field near the drillstring is analyzed using Finite Element Method combined with Boundary Element Method. Secondly, results of the quasistatic electric field analysis are compensated to consider attenuation of electromagnetic waves propagated in the earth. Finally, the drillstring is divided into many small segments, and an electric field near the surface is calculated as a synthesized vector of electric fields generated by the segments. The verification of the method is shown by a field experimental system using a well of 500m depth.

View full abstract

We have developed the finite element simulation program for the vibration and stress analysis of three-dimensional electrostrictive materials such as ceramics. Mechanical forces are caused through the electro-mechanical coupling, which depends on the polarization in the materials. In the above program, the materials are assumed to be fully polarized in a certain direction. This is not the case in general. In order to polarize the materials, high electric field must in advance be applied through the electrodes suitably arranged and the residual polarization remains after the electric field is removed. In this paper, the polarization process in ferro-electric materials or ceramics is considered. The process of nonlinear electrical field is solved by the use of the finite element method coupled with the Newton-Raphson iteration algorithm for D-E (flux density-electric field strength) relation. The procedure is similar to that of the magnetization process in ferro-magnetic materials. The procedure has already been examined for the two-dimensional models. In the present paper, extension is made to the three-dimensional case, for which the formulation is made using eight-node isoparametric elements. The polarization is demonstrated for some simple model and the vibration problem is also considered making use of this result. Incomplete polarization affects the vibration characteristic so that it must be included for evaluation in advance.

View full abstract

This paper clarifies two matters, the source of equation of Ω and the nature of current vector T, of T-Ω method in magnetostatic field analysis. First, we derive a new formula including T₀ (T₀ obtained from exciting current density Js is expressed as T₀) from the Biot-Savart formula by dyadic operator. From this new formula, the source of equation of Ω is the surface density of magnetic charge (T₀•n) on the boundary of current area. Next, it is clarified that T₀ is the similar value of magnetizing vector M in the ferromagnetic material. Thus, in T-Ω method Js is converted the surface density of magnetic charge. So, this method is based on the new current model.

View full abstract

In the three dimensional electromagnetic field analysis using the magnetic vector potential, it is necessary to impose the gauge condition on the magnetic vector potential in order to obtain a unique solution. The usual method of imposing the gauge condition is, however, inconvenient since it is imposed everywhere in space as a constraint, not as a field equation.
In this paper, a new method is presented which imbeds the gauge term into the field equation and makes it appear only at the interface between different media and outermost boundary. This method is useful for the boundary integral equation method as well as the finite element method.
The new field equation involves an arbitrarily determined parameter and the optimum value of it has been seeked for the numerical computation. The functional corresponding to the field equation is also presented for the finite element method.

View full abstract

A finite element formulation of full Maxwell's equations in terms of a vector potential and a scalar potential is presented. The vector potential and the scalar potential are approximated by novel vector basis functions and usual scalar basis functions, respectively. The linear equation finally obtained in this formulation always becomes singular, and then it can be solved only when both the given electric current and the given electric charge satisfy the equation of continuity. It is found that a gauge fixing of the potentials is transformed into regularization of the indeterminate linear equation. Two convenient gauge conditions for solving electromagnetic problems, magnetostatic problems and eddy current problems are proposed. These are the gauge of φ=0 and the extended Coulomb gauge.

View full abstract

A finite element formulation of full Maxwell's equations in terms of a electromagnetic potential was presented in the previous paper. The magnetic vector potential and the electric scalar potential were approximated by novel vector basis functions and usual scalar basis functions, respectively. In this paper, three numerical examples are carried out. These are a cavity resonance problem, an eddy current problem and a magnetostatic field problem. To obtain unique solutions, the gauge of φ=0 is used in solving the cavity resonance problem and the eddy current problem and the extended Coulomb gauge is used in solving the rnagentostatic field problem. It is found that the eddy current problem can be solved by using only the magnetic vector potential.

View full abstract

For the radio frequency equipments, there were many analytical studies using the FEM (Finite Element Method). Various methods have been approached to avoid sprious solutions. But, they have problems in computing time, formulation technique, programing and so on. At this time, we studied about the sprious solutions and successfully eliminated them with the new finite element taking into account the vector divergence conditions.
In this paper, the new finite element formulation which can eliminate the sprious mode is discribed. As an application, the resonance frequency of the magnetron cavity resonator is successfully calculated.

View full abstract

Several papers for eddy current analysis of thin conducting plates have been presented. The eddy current analysis is performed by an integro-differential method using a current vector potential. The integro-differential method is formulated for differential equation by a finite element scheme where the impressed magnetic flux density and the induced magnetic flux density are evaluated by integral terms. In this paper, a method for eddy current analysis of thin conducting plates taking account of the source currents in the conductor is proposed. A scalar potential is introduced for the analysis of source current distribution and the distribution of the scalar potential is calculated by a 2-D finite element method which is expanded to 3-D arrangement of the thin plates. The formulations for the current vector potential and the scalar potential are shown and the applicability of the proposed method is verified by using three computation models and an experimental model.

View full abstract

In order to design optimal electrical machines, it is necessary to develop an optimal design method for determining the shapes, sizes, positions of the cores, permanent magnets and windings which produce the specified values, such as flux distributions and torques.
In this paper, a design method for determining the optimal sizes of core taking into account the nonlinearity of the core has been developed by using the nonlinear programming method and the magnetization integral equation method. The pole shape of an electromagnet which produces the uniform flux distribution is determined by using the design method for determining the optimal sizes of core. The effectiveness of the method is shown by designing the pole piece of the permanent magnet type MRI device.

View full abstract

Single phase AC electromagnets are used often in electromagnetic devices as a linear actuator. It is difficult to analyze the static attractive force characteristics of single phase AC electromagnet accurately because its model is a combination of the electrical, mechanical, and magnetic systems. In this paper, a new method to obtain the static attractive force characteristics of the AC electro- magnets by the numerical analysis taking into account the motion of the armature core attracted by the pulsating magnetic force is described. The usefulness of the new method is clarified by comparing calculated and measured static force characteristics and motion of the armature.

View full abstract

A DC electromagnetic flow coupler is one of the candidate driving methods of liquid sodium coolant in liquid metal fast breeder reactors (LMFBR). The fundamental structure of a flow coupler consists of two flow channels connected electrically in series under a transverse magnetic field. When the conducting fluid in one of the channels is driven by an external means like a mechanical pump, this channel (generator channel) works under the magnetic field as a DC power supply. With the transverse magnetic field, the induced current provides a pumping force to the conducting fluid in the adjacent channel (pump channel), realizing a high efficiency DC electromagnetic pump. An annular electromagnetic flow coupler, in which a number of rectangular channels are arranged in an annular under a radial magnetic field, is considered to have the possibility of reducing the FBR size. This report gives a description of the analysis methods of flow couplers, and describes the calculated results on the flow and electrical characteristics of the experimental (prototype) annular flow coupler.

View full abstract

On numerical calculation by Boundary Element Method (BEM), a preprocessing system is indispensable to users because it releases troublesome mesh generation. This paper describes a new automatic mesh generator for the BEM using the Constructive Solid Geometry (CSG). Geometrical objects in the engineering field can be frequently constructed by a few kinds of fundamentally primitives. Therefore, we define four primitives (a rectangular parallelepiped, an ellipsoid, a circular cone, and a cylinder) and construct the objective shape by logical operation of each primitive.
After generation of boundary elements on every primitive, the mesh generator applies adjustment rules to the parts where primitives intersect with each other. The proposed system operates, so that all nodes and elements are adjusted on the surface.
The process of this mesh generation is shown as follows.
(1) Input the shape construction by primitives.
(2) Generate triangular elements on every primitive.
(3) Adjust nodes near crossing lines by the adjustment rule.
(4) Adjust elements near crossing lines.
(5) Output the data (nodes, elements, and table of unknown variables).

View full abstract

Polarization of langmuir-Blodgett (LB) films of Z or X type is very large, because dipolar moment of molecules in all monolayers are in the same direction. Accordingly, it is possible that the very high electrical field is produced in the structure of Metal/Nonpolar film/Polar film (Z or X type LB film)/Metal by the charges induced in metals and nonpolar film. Production of such a electrical field mentioned above means generation of a potential well in the LB heterofilm formed by nonpolar and polar films.
In the present investigation, 2-Pentadecyl-7, 7'8, 8'-Tetracyanoquinodimethane (C₁₅•TCNQ) or 2-Dadecyl-7, 7', 8, 8'-Tetracyanoquinodimethane (C12•TCNQ) LB film was used as a polar film, and Al₂O₃ film naturally oxidized in air or arachic acid LB film (Y type, small polarization) was used as a nonpolar film. Al films were deposited on the both surfaces of the LB heterofilms by evaporation.
Tunneling current and absorption charge were investigated in the experiments. As a result, thickness of the tunnel barrier of the LB heterofilms of 100-500A in thickness were estimated to be 10-20A, and charge absorbed in such thin LB films came up to 3.3C/cm³ that is 10³ times as large as the charge of carriers in semiconductors. According to the experimental and the theoretrical results, it was considered that a potential well much lower than Fermi Level was generated in the LB heterofilms in the present investigation. Further it was possible that such a deep potential well was two dimentional conductive plane by a electron gas filled in the well.

View full abstract

LB heterofilms of double layer consisting of arachic acid and 2-Pentadecy 1-7, 7', 8, 8'-Tetracyanoquinodimethane (C₁₅•TCNQ) LB films were sandwiched between Al and Au thin evaporated films. Such layer structures of Al/LB hetero film/Au were deposited on the SiO₂ insulating film of silicon wafers.
Resistance in the surface direction of the above layer structure were measured by the four point probe technique. As a result, very low resistance of 10^-2-10^-3Ω was obtained by the electrode system of gap 3.3mm with width 10mm. It was clarified in the experiments that the current flowed through the LB heterofilms of about 200-300A in thickness, accordingly the resistivity of LB heterofilms were calculated to be 10^-8-10^-9Ωcm. Such a value of resistivity was much smaller than the metal resistivity of 10^-5Ωcm. Furthermore the current through the LB film was increased up to 1.3A that was equivalent to the very high current density of 4.1×10⁵A/cm². But the resistance was suddenly increased by 10⁶ times at that time and the current was decreased to 3×10^-4A. Such a switching phenomenon could be observed repeatedly in many times.
The ultralow resistance and the very high current density observed in the LB heterofilms will be explained by the model of the potential well filled with electron gas which was generated in the LB heterofilm by the polarization of C₁₅•TCNQ LB film.

View full abstract