三维瞬态涡流场—电路—运动系统耦合问题的研究
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摘要
含有运动导体的三维瞬态涡流场—电路—运动系统耦合问题是现代工业生产中经常遇到的一类复杂电磁场问题,目前对于该类问题的研究仍是国内外工程电磁场研究领域关心的难点问题。现有的理论分析方法计算精度较低而且求解时间冗长,因此需要加以改进;此外,以较高水平的理论分析为基础,研制并开发功能齐全、能够求解各种复杂电磁场问题的专业电磁场软件,对机电装置的优化设计和性能分析十分必要,具有重要的工程应用价值。为此,本文主要开展了如下几方面的研究工作。
首先,在理论分析方面本文对于以下问题作了较深入的研究。
1、非线性三维瞬态涡流场问题的计算精度是本文研究的一个重点。本课题应用罚函数的形式在电磁场控制方程中并入规范条件,改善了节点矢量位函数零散度规范条件在离散情况下满足的情况。针对不同结构问题寻找罚因子最佳值的大小和选取方法,实现了对非线性三维瞬态涡流场问题分析方法的改进。
2、提出一种以磁链为耦合因子的三维场—路直接耦合法,将节点矢量位函数与支路电流作为未知函数同时求解,并保持了代数方程组系数矩阵的对称性和稀疏性。
3、对三维运动电磁场问题求解方法的研究是本文的另一重点。首先,运动边界条件的处理是求解运动问题的关键,为提高前处理工作的效率并保持方程组系数矩阵的稀疏性和对称性,本文将插值运动边界法的理论分析由二维扩展到三维,并首次应用于三维瞬态场与运动系统耦合问题的求解;其次,推导了电磁场与机械运动两系统耦合问题的数学模型,为减少求解两系统方程时的耦合迭代次数,通过调整时步法中的时间步长实现了对迭代过程的简化。
4、基于上述研究,提出了一种求解非线性三维瞬态涡流场—电路—运动系统耦合问题的新方法。该方法在对材料非线性、外部电路以及运动等问题的求解过程中均考虑了如何保持方程组系数矩阵的对称性和稀疏性,以及求解效率等问题,提高了对含运动导体的瞬态电磁场问题的计算精度,缩短了计算时间。
其次,在理论分析的基础之上,应用Fortran语言完成了计算机软件编制与实际问题的分析。使得较难求解的三维瞬态涡流场与电路及运动系统耦合等复杂电磁场问题,应用本文的软件工具得到了很好的分析与计算。
最后,设计并制作了一个可用来验证非线性三维瞬态涡流场—电路—运动系统耦合问题分析方法的实验模型,并搭建了精度较高的测试系统。计算结果与实验结果基本相符,充分证明了本文所做理论研究工作的正确性以及软件的有效性。
The coupled transient electromagnetic problems containing moving conductors is a complicated issue in the production of modern industry. The study of such problems is a hot-spot topic and difficult point for the computation of electromagnetic field in electrical engineering nowadays. The existing theoretical analysis methods need to be improved because of their unsatisfactory computational precision and too long computation time. Besides, developing a special software which is multifunctional and can analyses complex electromagnetic field problems on the base of a high level of theoretical analysis is very important for the optimal design and performance analysis of some electromechanical devices. Therefore, in this paper the author focuses on the following studies.
Firstly, for theoretical analysis, the paper carried out the following work.
1. The analysis of 3D transient eddy current field problems including nonlinear material characteristics is one of the paper's emphasis. The author applied the penalty function method to incorporate the zero divergence condition to the electromagnetic field governing equation, and this improved the satisfaction of zero divergence of nodal potential function at the condition of discretization. Through searching the value of penalty factor and its choosing method, the improvement for the analysis of 3D transient eddy current field problem has been realized.
2. A 3D electromagnetic field-circuit directly coupled method which use flux linkage as the coupling unit is presented. The method can calculate the nodal magnetic potential functions and the branch current simultaneously. Besides, it can remain the symmetrical and sparse characteristics of equation coefficient matrix.
3. The solving of the 3D moving electromagnetic problem is another emphasis of this paper. Firstly, the treatment of the moving boundary condition is very important. In order to increase the efficiency of pre-processing and remain the symmetrical and sparse characteristics of the coefficient matrix of FE discretized equations, the interpolation movement interface method is extended to 3D theoretically and applied to analyze a 3D transient moving electromagnetic problem in this paper. Secondly, the electromagnetic field and moving system coupled mathematic model was derived, in which the adjusting time step method is applied to simplify the iteration of the two system equations.
4. A new method to analyze the 3D transient electromagnetic field-circuit -movement coupled problem is presented. With this method the following factors can be included, such as how to increase efficiency and remain the symmetrical and sparse characteristics of coefficient matrix of FE discretized equations in the process of solving nonlinear material characteristics, electric circuit and movement problems. Therefore it can increase the accuracy of analyzing the 3D transient moving electromagnetic field problems and decrease the calculating time obviously.
Secondly, based on the theoretical analysis, the Fortran program is created and applied to the analysis of a 3D moving electromagnetic field problem. The software can analyze the 3D transient eddy field and the electromagnetic field coupling with circuit and movement system problems commendably.
Lastly, designed and product a experimental model to verify the analytical method of 3D transient eddy field problem which effect by circuit and movement system factors. A test macro with good accuracy was developed also. The calculated and test results are equal approximately, which proved the correctness of the theory and the validity of the software this paper presented.
首先,在理论分析方面本文对于以下问题作了较深入的研究。
1、非线性三维瞬态涡流场问题的计算精度是本文研究的一个重点。本课题应用罚函数的形式在电磁场控制方程中并入规范条件,改善了节点矢量位函数零散度规范条件在离散情况下满足的情况。针对不同结构问题寻找罚因子最佳值的大小和选取方法,实现了对非线性三维瞬态涡流场问题分析方法的改进。
2、提出一种以磁链为耦合因子的三维场—路直接耦合法,将节点矢量位函数与支路电流作为未知函数同时求解,并保持了代数方程组系数矩阵的对称性和稀疏性。
3、对三维运动电磁场问题求解方法的研究是本文的另一重点。首先,运动边界条件的处理是求解运动问题的关键,为提高前处理工作的效率并保持方程组系数矩阵的稀疏性和对称性,本文将插值运动边界法的理论分析由二维扩展到三维,并首次应用于三维瞬态场与运动系统耦合问题的求解;其次,推导了电磁场与机械运动两系统耦合问题的数学模型,为减少求解两系统方程时的耦合迭代次数,通过调整时步法中的时间步长实现了对迭代过程的简化。
4、基于上述研究,提出了一种求解非线性三维瞬态涡流场—电路—运动系统耦合问题的新方法。该方法在对材料非线性、外部电路以及运动等问题的求解过程中均考虑了如何保持方程组系数矩阵的对称性和稀疏性,以及求解效率等问题,提高了对含运动导体的瞬态电磁场问题的计算精度,缩短了计算时间。
其次,在理论分析的基础之上,应用Fortran语言完成了计算机软件编制与实际问题的分析。使得较难求解的三维瞬态涡流场与电路及运动系统耦合等复杂电磁场问题,应用本文的软件工具得到了很好的分析与计算。
最后,设计并制作了一个可用来验证非线性三维瞬态涡流场—电路—运动系统耦合问题分析方法的实验模型,并搭建了精度较高的测试系统。计算结果与实验结果基本相符,充分证明了本文所做理论研究工作的正确性以及软件的有效性。
The coupled transient electromagnetic problems containing moving conductors is a complicated issue in the production of modern industry. The study of such problems is a hot-spot topic and difficult point for the computation of electromagnetic field in electrical engineering nowadays. The existing theoretical analysis methods need to be improved because of their unsatisfactory computational precision and too long computation time. Besides, developing a special software which is multifunctional and can analyses complex electromagnetic field problems on the base of a high level of theoretical analysis is very important for the optimal design and performance analysis of some electromechanical devices. Therefore, in this paper the author focuses on the following studies.
Firstly, for theoretical analysis, the paper carried out the following work.
1. The analysis of 3D transient eddy current field problems including nonlinear material characteristics is one of the paper's emphasis. The author applied the penalty function method to incorporate the zero divergence condition to the electromagnetic field governing equation, and this improved the satisfaction of zero divergence of nodal potential function at the condition of discretization. Through searching the value of penalty factor and its choosing method, the improvement for the analysis of 3D transient eddy current field problem has been realized.
2. A 3D electromagnetic field-circuit directly coupled method which use flux linkage as the coupling unit is presented. The method can calculate the nodal magnetic potential functions and the branch current simultaneously. Besides, it can remain the symmetrical and sparse characteristics of equation coefficient matrix.
3. The solving of the 3D moving electromagnetic problem is another emphasis of this paper. Firstly, the treatment of the moving boundary condition is very important. In order to increase the efficiency of pre-processing and remain the symmetrical and sparse characteristics of the coefficient matrix of FE discretized equations, the interpolation movement interface method is extended to 3D theoretically and applied to analyze a 3D transient moving electromagnetic problem in this paper. Secondly, the electromagnetic field and moving system coupled mathematic model was derived, in which the adjusting time step method is applied to simplify the iteration of the two system equations.
4. A new method to analyze the 3D transient electromagnetic field-circuit -movement coupled problem is presented. With this method the following factors can be included, such as how to increase efficiency and remain the symmetrical and sparse characteristics of coefficient matrix of FE discretized equations in the process of solving nonlinear material characteristics, electric circuit and movement problems. Therefore it can increase the accuracy of analyzing the 3D transient moving electromagnetic field problems and decrease the calculating time obviously.
Secondly, based on the theoretical analysis, the Fortran program is created and applied to the analysis of a 3D moving electromagnetic field problem. The software can analyze the 3D transient eddy field and the electromagnetic field coupling with circuit and movement system problems commendably.
Lastly, designed and product a experimental model to verify the analytical method of 3D transient eddy field problem which effect by circuit and movement system factors. A test macro with good accuracy was developed also. The calculated and test results are equal approximately, which proved the correctness of the theory and the validity of the software this paper presented.
引文
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