• Title, Summary, Keyword: Maxwell stress tensor

### Dynamic analysis and control parameters deduction of Hybrid thrust magnetic bearing (하이브리드 스러스트 마그네틱 베어링의 제어변수 도출 및 동특성 해석)

• Jang, Seok-Myeong;Lee, Un-Ho;Sung, So-Young;Choi, Jang-Young;Kim, Soon-Yong
• Proceedings of the KIEE Conference
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• pp.724_725
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• 2009
• This paper deals with control parameters deduction and dynamic analysis of hybrid thrust magnetic bearing(HTMB). The flux density at air-gap is obtained from system modeling which considers permanent magnet and electro magnet. The vertical force is derived from flux density using maxwell's stress tensor. An accurate linear model is obtained by using linear approximations of the attraction force around the nominal equilibrium point. The dynamic simulation of the HTMB using the PD controller is conducted and control parameters are deducted.

### Electromagnetic Force Calculation using Magnetic Vector Potentials in 3-D Problems (자기벡터포텐셜을 이용한 3차원 전자력 계산)

• Yang, Jae-Jin;Lee, Bok-Yong;Lee, Byung-Hoan;Lee, Ki-Sik
• Proceedings of the KIEE Conference
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• pp.153-155
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• 1994
• Electric machines such as motors which have moving parts are desgined for producing mechanical force or torque. The accurate calculation of electromagnetic force and torque is important in the design these machines, Electromagnetic force calculation method using the results of Finite Element Method(FEM) has been presented variously in 2-D problems. Typically the Maxwell's Stress Tensor method and the method of virtual work are used. In the problems including current source, magnetic vector potentials(MVP) have mostly been used as an unknown variables for field analysis by numerical method; e, g. FEM. This paper, thus, introduces both methods using MVP in 3-D case. To verify the usefulness of presented methods, a solenoid model is chosen and analyzed by 3-D and axisymmetrical FEM. In each case, the calculated force are tabulated for several mesh schemes.

### Study on the Characteristic of Ld, LQ Parameter for Interior Permanent Magnet Synchronous Motor in different barrier width (배리어 길이에 따른 매입형 영구자석 동기전동기의 Ld, Lq 파라미터 특성에 관한 연구)

• Jang, Ik-Sang;Kim, Seung-Joo;Jin, Chang-Sung;Kim, Ki-Chan;Lee, Ju
• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.3
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• pp.496-501
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• 2009
• Interior Permanent Magnet Synchronous Motor (IPMSM) produces two kind of torque that Magnetic and Reluctance torque. The permanent magnet linkage flux ${\Psi}_a$ and d-axis and q-axis inductances have an important influence on the torque characteristic of IPMSM. Thus their accurate prediction is essential for predicting performance aspect such as the torque and flux-weakening capabilities. In this paper, the influence of barrier width on the ${\Psi}_a$ and $L_d$, $L_q$ is calculated by FEM analysis. Predictions are validated by comparison the average torques, using Maxwell Stress Tensor method.

### Maxwell Stress Tensor I. It's Meaning and Inherent Limits (맥스웰 응력텐서 I. 그 의미와 한계에 대하여)

• Choi, Hong-Soon;Park, Il-Han;Moon, Won-Kyu
• Proceedings of the KIEE Conference
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• pp.610-611
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• 2008
• 맥스웰 응력텐서는 전기기기의 전자기력을 해석함에 현재 가장 널리 사용되는 방법 중 하나이다. 본 논문에서는, 맥스웰 응력텐서 자체는 물리적인 의미가 없는 가상적인 응력텐서이며, 고체역학 또는 동역학적인 해석을 위해 이를 물리적인 기계력으로 취하면 안 된다는 것을 보이고자 한다. 물리적 의미를 부여할 수 있는 것은 응력텐서의 발산인 ${\nabla}{\cdot}T$ 이며 이는 전자기 체적력을 의미하고, 중력과 같은 원격 힘이다. 맥스웰 응력텐서의 유도과정을 에너지적인 접근에서 관찰하여 그 과정으로부터 본 결론을 유도 할 수 있음을 보인다. 본 논문은 두 개로 구성되는 데, 본 논문인 I에는 유효성의 한계에 대한 논의, 별도의 연작논문인 II에서는 대안으로서 가상공극을 사용한 체적력 계산법을 제시한다.

### Maxwell Stress Tensor II. It's Divergence Calculation based on Virtual Air-gap Scheme (맥스웰 응력텐서 II. 대안 : 가상공극법에 의한 응력텐서의 발산값 구하기)

• Choi, Hong-Soon;Park, Il-Han;Lee, Se-Hee
• Proceedings of the KIEE Conference
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• pp.612-613
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• 2008
• 맥스웰 응력텐서T와 맥스웰 응력 n.T는 물리적인 의미가 없는 가상적인 양이라는 것을 논문 I에서 논하였다. 본 논문 II 에서는 물리적 실체를 가지는 맥스웰 응력텐서의 발산양인 ${\nabla}{\cdot}T$의 계산을 위하여 가상공극을 도입하고, 그 것의 계산법에 대하여 제시한다. 가상공극법은 기존의 여러 전자기력 계산법의 상위개념으로 적용할 수 있는 접근법으로서 매체간에 접촉시에 전자기력 계산을 위하여 개발이 된 것이다. 이 방법을 각 유한요소에 적용함으로서 체적력밀도를 구할 수 있음을 보인다.

### Study on the Ld, Lq Characteristic Parameter of Interior Permanent Magnet Synchronous Motor in different barrier width (배리어 길이에 따른 매입형 영구자석 동기전동기의 Ld, Lq 특성 파라미터에 관한 연구)

• Jang, Ik-Sang;Jin, Chang-Sung;Jung, Dae-Sung;Kim, Seung-Joo;Park, Jae-Young;Lee, Ju
• Proceedings of the KIEE Conference
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• pp.709-710
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• 2008
• In this paper, we calculated permanent magnetic linkage flux ${\psi}_{\alpha}$ and Ld, Lq parameters of IPMSM and compared two model which has different barrier width. IPMSM has two kinds of torque that reluctance torque and magnetic torque. In constant torque region, using the Maxwell stress tensor method, we calculated the torque and current phase angle ${\beta}$ which has appeared maximum torque. In weakening flux region, we calculated the current phase angle ${\beta}$ which flux ${\psi}_o$ lower than limited flux ${\psi}_{omax}$. From the current phase angle ${\beta}$, we calculated torque by torque equation and compared two model characteristic.

### An Adaptive Finite Element Method for Magnetostatic Force Computations (정자력 계산을 위한 적응 유한 요소법)

• Park, Yong-Gyu;Jung, Hyun-Kyo;Lee, Ki-Sik;Hahn, Song-Yop
• Proceedings of the KIEE Conference
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• pp.24-27
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• 1988
• This paper presents an adaptive finite element method for magnetostatic force computation using Maxwell's stress tensor Mesh refinements are performed automatically by interelement flux density discontinuity errors and element force errors. In initial mesh, the computed forces for different Integration paths give great differences. but converge to a certain value as mesh division is performed by the adaptive scheme, We obtained good agreement between analytic solutions and numerical values In typical examples.

### Direct-Current Dielectrophoretic Motions of a Pair of Particles due to Interactions with a Nearby Nonconducting Wall (비전도성 벽과의 상호작용에 따른 한 쌍 입자의 직류 유전영동 운동)

• Kang, Sangmo
• Transactions of the Korean Society of Mechanical Engineers B
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• v.39 no.10
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• pp.805-815
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• 2015
• The present study numerically investigated two-dimensional dielectrophoretic motions of a pair of particles suspended freely in a viscous fluid, interacting with a nearby nonconducting planar wall, under an external uniform electric field. The results show that the motions depend strongly on the set of two electric conductivity signs and the particles-wall separation gap. When both particles have the same sign, they revolve and finally align parallel to the electric field. In contrast, with different signs, they revolve in the opposite direction and finally align perpendicular to the field. Simultaneously, they are repelled to move farther away from the wall regardless of their conductivity set. With further separation from the wall, the particles-wall interaction effect diminishes and tthe particle-particle effect dominates.

### Unbalanced Magnetic Forces in Rotational Unsymmetrical Transverse Flux Machine

• Baserrah, Salwa;Rixen, Keno;Orlik, Bernd
• Journal of Electrical Engineering and Technology
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• v.7 no.2
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• pp.184-192
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• 2012
• The torque and unbalanced magnetic forces in permanent magnet machines are resultants of the tangential, axial and normal magnetic forces, respectively. Those are in general influenced by pole-teeth-winding configuration. A study of the torque and unbalanced magnetic forces of a small flux concentrating permanent magnet transverse flux machine (FCPM-TFM) in segmented compact structure is presented in this paper. By using FLUX3D software from Cedrat, Maxwell stress tensor has been solved. Finite element (FE-) magneto static study followed by transient analysis has been conducted to investigate the influence of unsymmetrical winding pattern, in respect to the rotor, on the performance of the FCPM-TFM. Calculating the magnetic field components in the air gap has required an introduction of a 2D grid in the middle of the air gap, whereby good estimations of the forces are obtained. In this machine, the axial magnetic forces reveal relatively higher amplitudes compared to the normal forces. Practical results of a prototype motor are demonstrated through the analysis.

### A Study on Attractive Force Characteristics of Glass Substrate Using Alumina Electrostatic Chuck by Finite Element Analysis (유한요소해석을 이용한 알루미나 정전척의 글라스 기판 흡착 특성 연구)

• Lee, Jae Young;Jang, Kyung Min;Min, Dong Kyun;Kang, Jae Gyu;Sung, Gi Hyun;Kim, Hye Dong
• Journal of the Semiconductor & Display Technology
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• v.19 no.4
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• pp.46-50
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• 2020
• In this research, the attractive force of Coulomb type electrostatic chuck(ESC), which consisted of alumina dielectric, on glass substrate was studied by using the finite element analysis. The attractive force is caused by the high electrical resistance which occurs in contact region between glass substrate and dielectric layer. This research tries the simple geometrical modeling of ESC and glass substrate with air gap. The influences of the applied voltage, and air gap are investigated. When alumina dielectric with 1014 Ω·cm, 1.5 kV voltage, and 0.01 mm air gap were applied, electrostatic force in this work reached to 4 gf/㎠. This results show that the modeling of air gap is essential to derive the attractive force of the ESC.