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In this paper, we present an efficient modeling scheme based on a level set approach for electromagnetic systems including moving parts. The combination of finite elements and the level-set technique allows us to trace the interface variation on a fixed mesh of finite element. It does not require remeshing for the evolving geometry. The material data of moving objects is easily set using the Heaviside function obtained from the level set equation. For the driving force of dynamics equation, the total force on dielectric object is obtained by integrating the body force density of electric charge method. The numerical results of the test model show usefulness of the proposed scheme. Index Terms--Dynamics, finite element modeling, level set method, moving object.

In this paper, an implementation of virtual work principle in virtual air gap is proposed for the calculation of contact and body forces. To calculate the proper values of the magnetic field at virtual air-gap, we exploit the generalized magnetic source methods. It is shown that appropriately sized virtual elements can be allocated in the virtual air-gap by one-dimensionally extending the virtual gap while keeping the previously calculated field intensity. Both an element's and total forces can be obtained by virtual distortion of the concerned virtual elements. The proposed method provides a good accuracy even when the two contacting objects have the different permeability. As a validation, numerical examples are presented for the force distribution and total force. Index Terms--Body force distribution, force calculation, virtual air gap, virtual element, virtual work principle.

This paper proposes a coupling method involving the finite element (FE) equation of a discretized region and an analytical equation along with the field singularity of line currents in two-dimensional space. The singular field in the interior region is represented by Green's function of the line source, and the exterior region of air, conductor, or ferromagnetic material is represented by using the finite element method (FEM). An analytical expression for a magnetic field that contains unknown coefficients is coupled with the FE formulation for a coupled system equation with a matrix form. A numerical experiment relating to a line current near a ferromagnetic material shows the validity of this coupling method. Index Terms--Analytical solution, coupling schemes finite element method (FEM), Fourier series expansion, singular line current.

In this paper, a numerical scheme for obtaining ferrofluid shape formation is presented using the revisited Kelvin's force formula. The formula adopts the newly appreciated field intensity from the original Kelvin's concept and the virtual air gap scheme. For the hydrostatic equilibrium subject to magneto-static field, both electromagnetic and gravitational body forces should be considered. The free surface profile of ferrofluid can be obtained through numerical iterations based on the fact that the pressures on the free surface should be the same. Test models are presented as validations of the proposed scheme. Index Terms--Ferrofluid, hydrostatics, Kelvin's formula, magnetic body force, virtual air gap.

It is required to calculate the electromagnetic forces at the distributed parts of electric machines for the prediction of performance. In this paper, the body force distribution of electric machines such as surface permanent magnet and interior permanent magnet is presented and discussed for the first time using the recently developed body force calculation methods which are based on the virtual air gap scheme. The torque contribution of the body force is investigated according to radial and circumferential directions. Index Terms--Electromagnetic body force, interior permanent-magnet motor, surface permanent-magnet motor, virtual air gap.

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. Index Terms--Force calculation, generalized magnetic charge method, generalized magnetizing current method, virtual air gap.

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. Index Terms--Magnetic force, magnetized material, magnetizing current method.

For the mechanical structure design of electric machines, each force component on parts of an electric machine need to be separated. In this paper, a separation scheme of each torque component is presented. It is based on the magnetic force density analysis of the general formulation of equivalent magnetic charge method and Lorentz force density. The force density analysis can be applied to all parts of the system region including the inside of material and the interface of different materials. An interior permanent magnet motor and a surface permanent magnet motor are adopted for numerical test in this paper. Their numerical results show validity and usefulness of the presented method. Index Terms--Force density, general equivalent magnetic charge method, permanent magnet motor, torque component.

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. Index Terms--Eddy current levitation, electromagnetic motional system, extracted circuit parameter, finite element method (FEM), Runge--Kutta method.

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. Index Terms--Force density, magnetic charge method, total force.

Cogging torque reduction methods are discussed and applied to the optimum design of a small Brushless D.C. motor. Because the cogging torque has a close relation with the distribution of the magnetization, the magnetizing system for permanent magnets is analyzed numerically by using the time-stepping finite element method. Based on the remnant magnetic flux densities, the cogging torque is computed by using finite element analysis. After that, optimum design of the armature pole shape is carried out using design sensitivity analysis and evolution strategy whose design variables are based on the harmonic balance method, and then the results are compared. With the design results, sample motors are constructed and cogging torques are measured. By comparing the computational and experimental results, the problems in the usage of the numerical design method are discussed.

The magnetoelastic deformations of soft and hard magnetic materials are evaluated by employing the body force calculating methods incorporating the virtual air-gap concept along with the finite-element method. By introducing the virtual air-gap scheme, we have recently developed generalized methods for calculating body force field such as the generalized magnetic charge force density method, the generalized magnetizing current force density method, and the generalized Kelvin force density method. Unlike the conventional methods resulting in a surface force density, these generalized methods are novel methods of evaluating body force density. These generalized methods yield the actual total force, but their distributions have an irregularity, which seems to be random distributions of body force density. Here, we tested the magnetoelastic deformation in soft and hard magnetic materials by adopting the irregular force density itself. To verify the proposed method, a circular soft magnetic material subjected to an externally applied magnetic field and two squared permanent magnets facing each other were tested. Index Terms--Hard magnetic material, magnetic body force, magnetoelastic deformation, soft magnetic material, virtual air-gap scheme.

In this paper, a new design method using space mapping algorithm is presented for the design of magnetic systems. The method mathematically combines the magnetic equivalent circuit method and the finite element method and the optimal design is achieved by employing a quasi-Newton iteration in conjunction with first-order derivative approximations updated by the classic Broyden formula. Therefore, this method can preserve the computational efficiency of the magnetic equivalent circuit method and the accuracy of finite element method. Two numerical examples are tested to prove feasibility and numerical efficiency of the implementation of the proposed design method. Index Terms--Finite element method, magnetic circuit method, parameter extraction, space mapping.

Deals with a study which presented an adaptive mesh generator based on nodal errors. Details on the implementation of the mesh generator with nodal spacing values; Analysis through mesh generation; Methods to estimate computational errors.