Study on Systematic Numerical Analysis of Three Dimensional Magnetic Fields

三维磁场系统数值分析研究

基本信息

批准号：
63550215
负责人：
MORISUE Toshiya
金额：
$ 1.47万
依托单位：
Nagoya University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1988
资助国家：
日本
起止时间：
1988 至 1989
项目状态：
已结题

项目摘要

(1) The magnetic vector potential is very sensitive to the corner of a high-permeability material. This fact is demonstrated by a 2D magnetostatic field problem that has an exact solution. Then, the cause for this fact is theoretically clarified by using the theory of 2D incompressible and irrotational flow in fluid dynamics, and a method of decreasing the numerical error is developed.(2) 3D magnetostatic field calculations for gapless magnetic circuits are strongly affected by the discretization. The numerical error is considered to be generated by the imperfect cancelation of the permeability-free terms in the integral equation due to the improper size of the integration region containing a singular point. A method of reducing the numerical error is developed.(3) The usual method of imposing the gauge on the magnetic vector potential is inconvenient since it is imposed everywhere in space as a constraint. A new method is developed which imbeds the gauge term into the field equation a … More nd makes it appear only at the interfaces between different media and outermost boundary. The method satisfies the Coulomb gauge and yields a unique solution.(4) A method using the continuous magnetic vector potential and accompanying electric scalar potential is developed for 3D multiply-connected eddy current problems. This method has the advantage that it has no topological problem, while the method using the discontinuous magnetic vector potential accompanying no electric scalar potential is forced to introduce cutting to the multiply connected problem. From the computed results, this method is verified to be correct and effective.(5) A boundary integral-equation method using the magnetic vector potential is developed for the problems with unbounded free space, which satisfies the Coulomb gauge and yields unique solution.(6) Coupling between eddy currents and beam deflection is analyzed for a cantilevered beam problem, using the stream function, Biot-Savart's law and eigenfunction-expansion method. Computed results coincide well with experimental results.(7) A H-method using magnetic field intensity vector as variables is developed for a narrow air gap nonlinear magnetic circuit with a saturable iron core. It is obtained from the comparison of the computed results with the experimental results that the differential permeability should be used, instead of the normal permeability, for time-varying problems. Less

(1)磁矢量势对高磁导率材料的角点非常敏感，并通过具有精确解的二维静磁场问题证明了这一事实，并利用该理论从理论上阐明了这一事实的原因。提出了流体动力学中二维不可压缩无旋流的计算方法，并提出了一种大幅降低数值误差的方法。(2)无间隙磁路的3D静磁场计算受到离散化的影响。数值误差被认为是由于包含奇异点的积分区域大小不合适而导致积分方程中无渗透性项的不完全抵消而产生的。(3)将规范施加于磁矢量势的通常方法很不方便，因为它作为约束施加在空间的任何地方，因此开发了一种新方法，该方法将规范项嵌入到场方程中，并使其仅出现在两者之间的界面处。不同的介质和最外层的边界。该方法满足库仑规范并给出了唯一的解。(4)针对3D多重连接涡流问题，提出了一种使用连续磁矢量势和伴随电标量势的方法。该方法的优点是不存在拓扑问题。，而使用不伴随电标量势的不连续磁矢量势的方法则被迫在多重连通问题中引入切割。(5)边界。针对无界自由空间问题，提出了使用磁矢量势的积分方程方法，该方法满足库仑规范并产生唯一的解。（6）使用流分析了悬臂梁问题的涡流与梁偏转之间的耦合函数、毕奥-萨伐尔定律和本征函数展开法的计算结果与实验结果吻合良好。(7)提出了一种以磁场强度矢量为变量的H方法。含饱和铁芯的窄气隙非线性磁路通过计算结果与实验结果的比较得出，对于时变问题，应使用微分磁导率代替普通磁导率。