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It is difficult to calculate the magnetic force of an object of magnetic material in contact with other objects using the existing methods, such as Maxwell stress tensor method, magnetic charge method, or magnetizing current method. These methods are applicable for force computation only when the object is surrounded by air. The virtual air-gap concept has been proposed for calculating the contact force. However, its application is limited to magneto-static system. In this paper, we present the virtual air-gap concept for contact surface force in the eddy-current system. Its validity and usefulness are shown by comparison between numerical and experimental examples.

This paper presents a new analytical model for estimating the cogging torque in a multi flux-barrier interior permanent magnet machine (IPM). The model is based on a lumped circuit that considers the saturated bridge in the rotor's iron core. Finally, the cogging torque waveform of a multi flux-barriers IPM can be effectively predicted with the assistance of both the proposed virtual permanent magnet concept and the superposition principle. Utilizing the proposed concept, an IPM containing multi flux-barriers may be recognized as a multiple surface permanent magnet machine (SPM) having zero height and unit relative permeability. After decomposing the flux density of air-gap (Bg) in the IPM into multiple air-gap flux densities for a virtual SPM, the model is used for estimating the individual cogging torques which will be added or subtracted to the total cogging torque. For validation of our proposed concept, finite element analysis (FEA) was used. From the analysis results, it is shown that the proposed concept is practically effective in terms of finding optimal position, peak cogging torque, and waveform.

Purpose – The purpose of this paper is to present a new numerical technique, called adaptive level set method, for use with the finite element method. Design/methodology/approach – A conventional level set method using the smeared Heaviside function has been employed for shape and topology optimizations. The smeared Heaviside function yields an indistinct interface boundary, and so can increase computational time and cause numerical errors. The adaptive level set method does not use the smeared Heaviside function. To coincide with the material interface, it processes the zero level as the boundary data of element meshing. Findings – Usefulness and accuracy of shape optimization using the adaptive level set method are shown by comparison to the conventional level set method. A shape optimization procedure using the adaptive level set method is introduced. Numerical examples are employed to explain how the adaptive level set method is applied. Originality/value – The adaptive level set method is proposed to relieve the interface problem of the conventional level set method. Shape variation in the optimization is calculated from the continuum sensitivity analysis.

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.

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.

It is very important to calculate the forces at the distributed parts of electric machines for the prediction of performance. For this, calculation of distributed electromagnetic forces is certainly required. In this paper, the body force distributions of electric machines such as surface permanent magnet, interior permanent magnet and synchronous reluctance motors are presented and discussed for the first time using the recently developed body force calculation methods. It is shown that the total force of each part agrees well with its integrated body forces. Besides the interior permanent magnet motor, other types of machines are dealt with in the main paper

It is known that the magnetic attractive force generally occurs between the magnetic materials in the magnetic field. However, the recent study reports that the ferromagnetic bodies in the magnetic field can experience the repulsive force by changing the surface shape of them. In this paper, the repulsive electromagnet in the magnetic system is optimized to generate the maximum repulsive force. Continuum design sensitivity analysis and adaptive level set method are employed for the shape optimization. Continuum design sensitivity analysis is used to derive the sensitivity formula as a closed form and to calculate the sensitivity value on the boundary of the magnetic materials for using finite element method (FEM). Adaptive level set method is used to express complicated evolving geometry because it has an advantage to reduce numerical errors of sensitivity value compared with the results of the conventional method.

In this paper it is shown that Kelvin's 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

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.

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.

In this paper, a new design method using a 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.

In this paper, an adaptive mesh generator based on nodal errors is presented. The mesh generator is implemented using the nodal spacing values in order to concentrate elements on the area where estimated errors obtained from a finite element calculation is large. Especially, the sensitivity of energy of the nodal position is used to decide the nodal errors. The nodal spacing values for the initial mesh generation are given to the average values of distances from the node to the neighboring nodes. The next adaptive refinement stages are performed after updating the spacing values using the previous adaptive solution. The Delaunay algorithm is applied to the generation of both an initial mesh and a refined one. To show the practical behavior of the mesh generator, we investigate the energy and the maximum nodal error convergences with the results of magnetostatic finite element calculations on the refined meshes.

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

Cogging torque reduction methods are discussed and applied to the optimum design of a small brushless DC 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. Optimum design of the armature pole shape is then carried out using design sensitivity analysis and an evolution strategy whose design variables are based on the harmonic balance method, and the results are compared. With these 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.

For the electrowetting phenomenon, conventional studies on movement of micro fluids have been based on transition of contact angle. In this paper, an electrowetting-based suspended pipe system is presented and it is modeled and analyzed using a multi-physical approach of electromagnetics and fluidics. Its characteristics are numerically analyzed by finite element method. The experimental data of the manufactured setup are compared with the analysis data to validate the presented model and analysis methodology.

Vector control techniques are generally adopted to control conventional permanent magnet motors for high speed. These techniques have a limit on speed increase and risk of a demagnetization risk. To resolve this problem, some demerits such as nonlinearity absorber is presented. The flux absorber has advantages such as linear flux control and decrease of rebound forces. Three dimensional finite element analysis was performed to show the validity of the flux absorber

A permanent magnet linear synchronous motor (PMLSM) is shape optimized in Pareto sense to get a minimum detent force and maximum thrust force per mass. In the optimization, a surrogate objective function is constructed with the help of grid computing technique by using Multi-quadric radial basis function to reduce the computing time related with finite element analysis.

Up to this date, the conventional electromagnetic force calculation methods such as Maxwell stress, virtual work, Kelvin’s formula, equivalent magnetic charge, and equivalent magnetizing current produce results where the surface component takes up a major portion of the total force, with the portion of the body force being very small or even none. As the formulation of the above mentioned methods starts from the concept of body or volume force, there has been controversy over the true concept of electromagnetic force identity. In this paper, it is shown that electromagnetic body force, which is also called volume force, can be calculated using virtual air-gap scheme that is derived from the generalized equivalent source methods. For the body force calculation, the application of virtual air gap is extended to calculate the force of each finite element as if an element is an independent body surrounded by virtual air gap. The force calculation methods adopted in this paper include Maxwell stress, magnetic charge, and magnetizing current. The examination of the calculated force distribution shows that the force can be expressed only as body force distribution. The total force calculated by the volume integration of the body force on the magnetized body agrees well with the total force calculated by conventional approaches.

Mechanical deformation in incompressible linear and nonlinear magnetic materials was evaluated using various conventional electromagnetic volume and surface force density methods. These conventional force density methods are the Maxwell stress tensor method, Korteweg-Helmholtz force density method (KH), magnetic charge method, magnetizing current method, and Kelvin force density method (KV). The total force values obtained using these different force density methods were found to be the same and equal to the total force using the principle of virtual work, but the distribution of force density values calculated using the given force density methods was found to be different from each other. Using the given five force density methods, the mechanical deformations were evaluated and compared to one another. The KH and KV in incompressible material were shown to give the same mechanical deformation by employing the finite element method (FEM), verifying the theoretical equivalence. To implement the KV, the de...