Se-Hee Lee

General formulation of equivalent magnetic charge method for force density distribution on interface of different materials

The conventional force calculation methods can be applied only for the total force of the objects surrounded by air or vacuum. In this paper, a new general form of equivalent magnetic charge method is proposed for calculating force density and total forces of materials in contact including ferromagnetic and permanent magnet. It provides surface force density on the interface of different materials. The validity of this method is shown by direct observation of the formulas and numerical tests.

Concept of virtual air gap and its applications for force calculation

In this paper, the virtual air-gap formulae for electromagnetic forces are derived from the generalized forms of equivalent source methods, such as magnetic charge and magnetizing current. The virtual air-gap approach is based on the idea that insertion of infinitesimally thin air gap causes no real variation of electromagnetic field system. For total force calculation of a magnetic body in contact with other ones of ferromagnetic or permanent magnets, the virtual air-gap formulae can employ the conventional force methods, such as Maxwell stress, magnetic charge, and magnetizing current. The virtual air-gap approach is validated by numerical test results

Comparison of mechanical deformations due to different force distributions of two equivalent magnetization models

In magnetic systems, electromagnetic force density distribution may cause mechanical deformation, which results in the mechanical noise and vibration. The electromagnetic force density can be analyzed with several techniques such as stress tensors, equivalent magnetization models and energy approaches and etc. that may produce different force densities. From the view-point of mechanical deformation, they are theoretically analyzed and compared to explain the differences between the force fields using the property of scalar pressure. In uncompressible media the gradient of scalar pressure, which is a term of Korteweg-Helmholtz force density, does not cause any mechanical deformation. In this paper, two magnetization source models of magnetic charge and magnetization current, which produce quite different distributions of force density, are employed to see their mechanical deformations. Three numerical examples are tested to examine their validity and usefulness.

Derivation of a general sensitivity formula for shape optimization of 2-D magnetostatic systems by continuum approach

This paper presents a generalized sensitivity formula that is applicable to any objective function of the optimization problems in two-dimensional (2-D) linear magnetostatic systems. For the objective function defined on an interface boundary as well as in a region, the shape design sensitivity expression is derived in a closed form from the augmented Lagrangian method, the material derivative concept and the adjoint variable method. The resultant sensitivity formula is expressed as a line integral along the interface boundary undergoing shape modification. Three shape design problems, whose objective functions are defined on an interface boundary or in a region, are tested to validate the derived sensitivity formula.

Reduced modeling of eddy current-driven electromechanical system using conductor segmentation and circuit parameters extracted by FEA

To analyze the mechanical dynamic characteristics of electromechanical system, we present a new and fast method using the reduced modeling technique for the levitated conductor. As of now, to solve this electromechanical system, the finite element method (FEM) or the boundary element method (BEM) employing the finite difference time-stepping scheme is used. These approaches, however, need too much solving time because the system matrix equation should be solved at each time step. Additionally, when the operation condition is changed or it needs more incremental steps, the system should be solved from the beginning again. To reduce the solving time, we use the circuit parameters of self- and mutual inductances which are evaluated using the FEM and the conductor segmentation. The formulated ordinary differential equations are solved using the fourth-order Runge-Kutta method. To show validity and usefulness of this proposed method, the TEAM Workshop Problem 28 model is tested, and the results of the experiment and time-stepping FEM are compared to this new method.

Calculation of Temperature Rise in Gas Insulated Busbar by Coupled Magneto-Thermal-Fluid Analysis

This paper presents the coupled analysis method to calculate the temperature rise in a gas insulated busbar (GIB). Harmonic eddy current analysis is carried out and the power losses are calculated in the conductor and enclosure tank. Two methods are presented to analyze the temperature distribution in the conductor and tank. One is to solve the thermal conduction problem with the equivalent natural convection coefficient and is applied to a single phase GIB. The other is to employ the computational fluid dynamics (CFD) tool which directly solves the thermal-fluid equations and is applied to a three-phase GIB. The accuracy of both methods is verified by the comparison of the measured and calculated temperature in a single phase and three-phase GIB.

Force Calculation of Magnetized Bodies in Contact Using Kelvin's Formula and Virtual Air-Gap

In this paper it is shown that Kelvins formula can be implemented in a simple way using the external field, which is calculated from the virtual air-gap scheme recently proposed by the authors. External fields of all finite elements come from only one FEM solution. This implementation provides consistent numerical results of force calculation whether a magnetic body is in contact with another or not. The validity of this proposed method for magnetic force calculation is shown by numerical comparisons with other well-known methods

FE Analysis of Plasma Discharge and Sheath Characterization in Dry Etching Reactor

We present a full finite element analysis for plasma discharge in etching process of semiconductor circuit. The charge transport equations of hydrodynamic diffusion-drift model and the electric field equation were numerically solved in a fully coupled system by using a standard finite element procedure for transient analysis. The proposed method was applied to a real plasma reactor in order to characterize the plasma sheath that is closely related to the yield of the etching process. Throughout the plasma discharge analysis, the base electrode of reactor was tested and modified for improving the uniformity around the wafer edge. The experiment and numerical results were examined along with SEM data of etching quality. The feasibility and usefulness of the proposed method was shown by both numerical and experimental results.

Fast solving technique for mechanical dynamic characteristic in electromagnetic motional system by electro-mechanical state equation including extracted circuit parameter

This paper presents a method of the fast solving technique for electro-mechanical motional systems. Various numerical analysis methods such as finite element method (FEM), boundary element method (BEM) and others employ time-stepping method to analyze the dynamic characteristics of electromechanical systems. Since the system matrix must be solved at each incremental time, this time-stepping method proves to be time-consuming. To solve these problems, this paper presents a fast solving technique by using the extracted circuit parameters and electro-mechanical coupled state equations. To show validity and usefulness of proposed method, two electromagnetic motional systems were tested, and the time-stepping method using FEM was compared with the proposed method.

Generalized equivalent magnetizing current method for total force calculation of magnetized bodies in contact

In this paper, a new, general form of the equivalent magnetizing current method is proposed for calculating the total force of magnetized bodies in contact, including ferromagnetic and permanent magnet. This method is formulated in way similar to the generalized equivalent magnetic charge method. It provides consistent numerical results of force calculation, whether or not one magnetized body is in contact with the other one. The validity of this evaluation method for magnetic forces is shown by close observation of the formulae and numerical test results