【摘要】 探讨如何建立描述正弦电磁场中铁磁材料振动的数学模型。首先,介绍电磁场理论中磁场力的一般数学表达式;然后基于电力设备中铁磁材料的物理和几何特点给出其力学模型,基于电力设备磁路的对称性给出其磁场力简化数学模型;随后介绍从不同角度描述铁磁质磁致伸缩现象的几种方法;在此基础上,引入弹性力学理论中的应变能密度概念,重点讨论如何从能量守恒和功能转换的角度描述表征磁致伸缩现象的磁场力;最后将上述两种模型相结合导出描述正弦交变电磁场诱发铁磁材料振动的数学模型。这些数学模型的建立为定性和定量分析大型电力变压器铁心及其它电力设备磁路的振动和噪声奠定了基础。更多还原

【Abstract】 This paper focuses on mathematical model of vibrations of ferromagnetic materials under magnetisation. First,general mathematical expression of magnetic forces are presented according to theory of electromagnetic field. Then,due to the symmetry of magnetic circuit of large power equipments, its simplified mathematical model of magnetic forces is discussed. After that, based on physical property (magnetostriction) of ferromagnetic materials of electric machines, the conception of density of strain energy, quoted from the theory of plastoelasticity, is introduced to describe magnetic forces of magnetostriction phenomenon. At the end of this paper, based on its geometrical and physical features, mechanical model of magnetic materials in electric machines is established, and combination of the above models is made to formulate the required models. The models, given in this paper, can be used to analyze vibration and noise of magnetic circuit of large power equipments.更多还原