用于平滑处理的卷积运算及其在有限元磁场分析后处理中的应用

Smoothing Convolutions and Applications in Postprocessing of Finite Element Analysis of Magnetic Field

在用一阶三角元计算磁场所得到的结果中,相邻单元磁通密度通常不等,所得到的是分片恒定的磁通密度及磁导率。为了计算电磁力在铁心中以及在不同介质交界面上的分布,需要对磁场能量或磁导率求导数,为此,本文采用卷积方法得到平滑分布的磁通密度及磁导率。首先推导进行平滑化处理的卷积运算基本公式,然后对比采用不同的核函数进行卷积运算所得到的结果,并给出求取平滑化处理核函数的一般方法;作为卷积方法的一个应用,得到考虑饱和时计算铁心内部电磁力密度的公式。

In magnetic field computations with linear triangular elements, piecewise constant magnetic flux densities are obtained, which are unequal over two adjacent elements. In order to compute magnetic force densities inside iron and along boundary of different media, derivatives of magnetic energy and permeability are needed. A convolution method is used to obtain smoothly distributed flux densities. Fundamental formulas for smoothing via convolutions are firstly derived, then a comparison between results of convolution by different kernel functions is made and a method to find kernel functions with required smoothness is given, lastly an application of the convolution method to compute magnetic force density inside iron is illustrated.