• Title, Summary, Keyword: Magnetic vector potential

### Magnetic Field Computations of the Magnetic Circuits with Permanent Magnets using Finite Element Method (유한요소법을 이용한 영구자석 자기회로의 자석 해석)

• 박영건;정현규;한송엽
• The Transactions of the Korean Institute of Electrical Engineers
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• v.33 no.5
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• pp.167-172
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• 1984
• This paper describes the finite element analysis of magnetostatic field problems with permanent magnets. Two kinds of algorithms, one using the magnetic vector potential and the other using the magnetic scalar potential, are introduced. The magnetization of the pemanent magnet is used as the source instead of the magnetic equivalent current in both of the formulations using the magnetic vector potential and the magnetic scalar potential. A simple functional, which has only the region integral instead of the region integral and boundary integral, is derived in the formulation using the magnetic scalar potential. These make the formulation of the system equations simpler and more convenient than the conventional methods. The numerical results by the two proposed algorithms for a C-type permanent magnet model are compared with the analytic solutions respectively. The numerical results are in good agreement with the analytic solutions.

### Calculation of Magnetic Field for Cylindrical Stator Coils in Permanent Magnet Spherical Motor

• Li, Hongfeng;Ma, Zigang;Han, Bing;Li, Bin;Li, Guidan
• Journal of Electrical Engineering and Technology
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• v.13 no.6
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• pp.2158-2167
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• 2018
• This paper analyzed the magnetic field produced by the cylindrical stator coils of permanent magnet spherical motor (PMSM). The elliptic equations about the vector magnetic potential were given. Given that the eddy current effects are neglected, the magnet field of the PMSM is regarded as irrotational field, which can be calculated by scalar magnetic potential. The current density of cylindrical stator coil was proposed based on the definition of current density. The expression of current density of stator coil was obtained according to the double Fourier series decomposition and spherical harmonic functions. Then the magnetic flux density for scalar magnetic potential was derived. Further, the influence of different parameters on radial flux density was also analyzed. Finally, the results by the analytical method in this paper were validated by finite element analysis (FEA).

### Analytical Performance Modelling of Slotted Surface-Mounted Permanent Magnet Machines with Rotor Eccentricity

• Yan, Bo;Wang, Xiuhe;Yang, Yubo
• Journal of Electrical Engineering and Technology
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• v.12 no.2
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• pp.778-789
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• 2017
• This paper presents an improved subdomain method to predict the magnet field distributions and electromagnetic performance of the surface-mounted permanent magnet (SPM) machines with static or dynamic eccentricity. Conventional subdomain models are either based on the scalar magnet potential to predict the rotor eccentricity effect or dependent on the magnetic vector potential without considering the eccentric rotor. In this paper, both the magnetic vector potential and the perturbation theory are introduced in order to accurately calculate the effect of rotor eccentricity on the open-circuit and armature reaction performance. The calculation results are presented and validated by the corresponding finite-element method (FEM) results.

### Finite Element Analysis of 2-D Magnetostatic Problem using Magnetic flux density as an unknown variable (자속밀도를 미지변수로 한 2차원 정자장 유한요소 해석)

• Chang, Woo-Sok;Hahn, Song-Yop
• Proceedings of the KIEE Conference
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• pp.37-40
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• 1989
• When we analyze the magnetostatic problem by the FEM, it is a traditional method to use the magnetic vector potential as an unknown variable.(abbreviated to A Method) Therefore, we should differentiate this magnetic vector potential to get the magnetic flux density. In this procedure of differentiation, the accuracy of the calculation is reduced. In order to overcome this problem, this paper uses the magnetic flux density as an unknown variable.(abbreviated to B Method) The validity of this new method (B Method) to use the magnetic flux density directly as an unknown variable, is ensured as the result of the application example researches.

### A Computational Method to Consider the Saturation of Magnetic Field In a High Density Recording Head

• Park, Gwan-Soo
• Journal of Magnetics
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• v.8 no.4
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• pp.164-168
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• 2003
• In high density recording system, the recording head field on a medium should be focused in small bit area and should have a sufficient value to overcome the medium coercivity, which resulted in head saturation. In this paper, an efficient method to access the head field and field gradient considering head saturation is presented. The magnetic vector potential on the head surface is pre-calculated considering head saturation in several cases and accumulated into database. The head field on the recording media is easily produced solving Laplace equation using accessed magnetic vector potential boundaries. The computed head field is compared with a quantified magnetic force microscopy measurement.

### General Analytical Method for Magnetic Field Analysis of Halbach Magnet Arrays Based on Magnetic Scalar Potential

• Jin, Ping;Yuan, Yue;Lin, Heyun;Fang, Shuhua;Ho, S.L.
• Journal of Magnetics
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• v.18 no.2
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• pp.95-104
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• 2013
• This paper presents a general analytical method for predicting the magnetic fields of different Halbach magnet arrays with or without back iron mounted on slotless permanent magnet (PM) linear machines. By using Fourier decomposition, the magnetization components of four typical Halbach magnet arrays are determined. By applying special synthetic boundary conditions on the PM surfaces, the expressions of their magnetic field distributions are derived based on the magnetic scalar potential (MSP), which are simpler than those based on the magnetic vector potential (MVP). The correctness of the method is validated by finite element analysis. The harmonics of airgap flux density waveforms of these Halbach magnet arrays with or without back iron are also compared and optimized.

### Numerical Analysis on the Deformation of Free Surface of Magnetic Fluid (자성유체의 자유표면의 변형에 관한 수치해석)

• Nam S.W.;Kamlyama S.
• 한국전산유체공학회:학술대회논문집
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• pp.132-137
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• 1995
• Numerical analysis is conducted on the deformation of free surface of magnetic fluid. Steady magnetic fields are induced by a circular current loop. Governing equations of magnetic fields are solved by using the concept of vector potential. The free surface of magnetic fluid is formed by the balance of surface force, gravity, pressure difference, magnetic normal pressure and magnetic body force. The deformations of free surface of magnetic fluid are qualitatively clarified. And, the patterns of steady non-uniform magnetic fields induced by a circular current loop are quantitatively presented.

### Electromagnetic Field Analysis and Measurements of Cylindrical Linear Oscillatory Actuator using Transfer Relations Theorem (전자기 전달관계를 이용한 원통형 직선 왕복구동 액추에이터의 전자기 특성 해석 및 실험)

• Jang, Seok-Myeong;Kim, Hyun-Kyu;Choi, Jang-Young;Lee, Sung-Ho
• Proceedings of the KIEE Conference
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• pp.89-91
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• 2008
• This paper deals with the thrust calculations and the measurements of a cylindrical Linear Oscillatory Actuator (LOA) sing Transfer Relations Theorem (TRT), namely, Melcher's methodology. Using transfer relations derived in terms of a magnetic vector potential and a two-dimensional (2-d) cylindrical coordinate system, this paper derives analytical solutions for the magnetic vector potential, magnetic fields due to Permanent Magnets (PMs) and stator winding currents and the thrust. The analytical results are validated by non-linear Finite Element (FE) analyses. In particular, test results such as thrust and back-emf measurements are given to confirm the analysis.

### Analytical Prediction for Electromagnetic Characteristics of Tubular Linear Actuator with Halbach Array Using Transfer Relations

• Jang, Seok-Myeong;Choi, Jang-Young
• Journal of Electrical Engineering and Technology
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• v.2 no.2
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• pp.221-230
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• 2007
• This paper deals with analytical prediction for electromagnetic characteristics of a tubular linear actuator with Halbach array using transfer relations, namely, Melcher's methodology. Using transfer relations derived in terms of magnetic vector potential and a two-dimensional (2-d) cylindrical coordinate system, this paper derives analytical solutions for magnetic vector potential due to permanent magnets (PMs) and stator winding currents. On the basis of these analytical solutions, this paper also achieves analytical solutions for the magnetic fields distribution produced by PMs, stator windings current and axial thrust. The analytical results are validated extensively by finite element (FE) analyses. In particular, test results such as thrust measurements are given to confirm the analysis. Finally, this paper estimates control parameters using analytical solutions and test results such as thrust, back-emf, inductance and resistance measurements.

### Effects of Coulomb Gauge Condition and Current Continuity Condition on 3-Dimensional FE Analysis for Eddy Current Problems (3차원 와전류문제의 유한요소해석에서 쿨롱게이지조건과 전류연속조건의 영향)

• Lee, Hyang-Beom
• The Transactions of the Korean Institute of Electrical Engineers B
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• v.54 no.10
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• pp.483-491
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• 2005
• To solve the 3D eddy current problems by using FE(finite element) method with MVP(magnetic vector potential) and electric scalar potential, Coulomb gauge condition and current continuity condition have to be considered. Coulomb gauge condition enforced on existing FE formulations to insure the uniqueness of MVP looks unnatural and current continuity condition which can be driven from Ampere's law looks unnecessary. So in this paper the effect of two conditions on FE formulations are investigated in order to help to obtain accurate numerical simulation results.