【作者】 杨光源；

【导师】 邵可然；

【作者基本信息】 华中科技大学 ， 电机与电器， 2011， 博士

【摘要】 现代电气工程领域应用的许多设备都包含运动的导体,如电机、电磁开关、电磁线圈炮、磁悬浮列车等,对这些设备进行参数分析和优化设计都离不开对其中的电磁场进行求解。运动导体涡流电磁问题一直是计算电磁学领域的研究热点和难点,传统的电磁场数值算法如有限元法需要对求解域进行网格剖分,在处理运动导体导致的模型形变问题时往往会遇到较大的困难。而新近发展起来的无单元算法则免除了网格的剖分,在处理耦合导体运动的电磁问题方面表现出了巨大的发展潜力。本文研究了一种纯无单元算法——径向基点配置法,并将其应用于二维运动导体涡流电磁问题的求解和分析,全文的工作主要包括以下几个方面：1、提出了一种新的叠加径向基点配置法。该方法基于场源叠加原理和径向基点配置法求解方程的线性特性,可以方便地对电磁场控制方程中包含的未知量进行解耦；通过引入运动坐标系来建立径向基节点模型,我们可以处理导体以任意形式运动的涡流磁场问题,磁场控制方程通过构造时域迭代来离散,便于考察任意时刻系统内的磁场以及涡流的分布情况。2、验证了本文提出的叠加径向基点配置法在分析稳态及瞬态电磁问题时与常规径向基点配置法的等价性；并通过工程问题算例验证了该算法在求解运动导体涡流问题时的有效性。此外还利用该算法构造了磁场—力—运动—电路综合分析模型对一个包含运动导体的实际工程装置的动态过程进行了模拟,并考察了装置的主要模型参数对其工作效率的影响。3、对径向基点配置法在更复杂电磁问题求解领域的应用进行了初步探索。针对非线性介质电磁问题,提出了基于牛顿迭代和拓延法初值优化的迭代型径向基点配置求解格式,并通过算例考察了其收敛性；针对多介质求解域电磁问题,将区域分解径向基点配置法从稳态扩展到瞬态问题求解领域,结合叠加径向基法推导了基于时域迭代格式的多介质运动导体涡流问题求解公式,并且指出该算法在求解涡流问题时可以有效地降低迭代过程中求解的矩阵方程的维数,从而极大地提高计算效率。更多还原

【Abstract】 Many devices in the modern electrical engineering field contain moving conductors, such as the electric machine, electromagnetic switch, coil gun, maglev train and so on. To analyze and optimize their parameters, the electromagnetic field in these devices must be calculated. The moving conductor eddy current problem has always been an attractive and difficult problem in the computational electromagnetics. The traditional numerical method, for example, the finite element method needs to mesh the solving domain to construct the shape function. This leads to a great difficulty when the model varies because of the movement of the conductor. The newly developed meshless method, which is free from domain meshing, shows a deep potential to deal with motion coupled electromagnetic problems. The radial basis function (RBF) collocation method, which is a kind of pure meshless method, is studied and applied to solve two dimensional moving conductor eddy current problem in this paper. The structure of the paper is as follows.1. A novel superposition RBF collocation method is presented. This method, which is based on the source superposition principle and the linear property of the governing equations of RBF collocation method, could conveniently decouple the unknowns in the electromagnetic field equations. The arbitrary movement of the conductor is expressed through introducing moving coordinate systems to build the node model. The governing equations of the field are discretized through time domain iteration, which enable us to analyze the magnetic field and eddy current in the system at any time.2. The equality of the proposed method and the normal RBF collocation method is examined in both static and transient electromagnetic problems. According to numerical examples, we also prove that the proposed method is effective to solve moving conductor eddy current problems. Furthermore, a global model combined the magnetic field, electromagnetic force, conductor movement and the circuit equations is presented to simulate the dynamic process of a practical engineering device containing moving conductors. The model parameters are also analyzed for optimization.3. The application of the RBF collocation method in complex media electromagnetic problems is presented. First, an iterative RBF collocation scheme on the basis of Newton iteration and continuation optimization of the initial value is presented to deal with nonlinear media electromagnetic problems. The convergence property of this method is analyzed with a numerical example. Moreover, the domain decomposition method (DDM) combined RBF collocation method, which has been used to solve electrostatic problems, is extended to compute transient electromagnetic field. Through combining the proposed superposition RBF collocation method and the DDM, a time domain iterative scheme for multi-media moving conductor eddy current problems is presented. One advantage of this method is that the dimensions of the matrix equations solved in each iteration step could be reduced and the efficiency of computation could be greatly improved.更多还原