以静代动有限元原理及其在凸极类电机中的应用  

Finite Element Method of Motion Replaced by Rest and Its Application in Salient Machines

作　　者：王世山[1] 虞振洋 谢仁和[1] 龚敏[1] 秦海鸿[1] 

机构地区：[1]南京航空航天大学江苏省新能源发电与电能变换重点实验室,南京210016

出　　处：《电工技术学报》2014年第1期68-76,84,共10页Transactions of China Electrotechnical Society

基　　金：国家自然科学基金(51177071);江苏省高校优势学科建设工程资助项目

摘　　要：凸极类电机磁场分布及其参数与位置角密切相关,若每一位置分别建立模型则计算量急剧增大。论文将电机转子、定子和邻近空气分为两个不同的子区域,以间隙中线为区域分界线,采用有限元法剖分,强使分界线上剖分节点均匀分布且分别单独存在于子区域中。若将分界线上单独节点的自由度对应地耦合,则转子处于某一位置并可求解;反之,将这些自由度"解耦",并进一步错位"耦合",则转子等效于另一位置并可以求解。由此,电机实现了"旋转",即以"静止"代替"运动"状态的求解,简称"以静代动法"(MRR)。以双凸极电机为样机:采用MRR有限元法求解样机电感变化规律,结合该类电机控制电路,得到电枢绕组电流波形,采用Fourier变换进一步得到电流谐波构成,由此可求解铁心涡流损耗。测试总体损耗构成,样机铁心磁滞损耗也可求解,由此可计算出样机对应硅钢片的磁滞损耗系数。在此基础上,对不同工况下电机进行计算和测量。对比表明,二者误差在15%之内,显示出MRR有限元法的方便性和快捷性。论文所提出的方法适合所有旋转、运动类设备,也适合于其他学科,具有广泛的普遍性。Magnetic field distribution and its parameters of salient machine are closely related to position angle. The calculation work will increase sharply if the model is established at every position. The rotor and the air surrounding it, stator and the air around it, are divided into two different sub-regions using gap midline as region boundary line. In order to distribute the nodes evenly and make the nodes exist in a separate sub-area respectively, the meshing of finite element method（FEM） is adopted for the air gap. If the degree of freedom（DOF） of nodes is coupled correspondingly, the field of the rotor at a certain position can be solved. On the contrary, decoupling these DOFs and further coupling it at another position, the rotor can be regarded as another location and finally it can be solved too. On basis of above analysis, the machine achieves the solution of ＂rotation＂, which is using the state of ＂rest＂ to replace of the ＂motion＂ state. This method is called ＂motion replaced by rest＂（MRR）. In this paper, doubly salient machine is selected as a prototype. The rules of inductance variation of prototype are solved using MRR FEM. After that, combing with the control circuit of this motor, the current of armature windings can be obtained. Eventually, Fourier transform is used to obtain the composition of the current harmonics, and the eddy current losses can be calculated. The internal demagnetization effect of the silicon steel sheet can be ignored because it is thin enough. Then, the total loss of eddy current can be solved. According to the constitution of the total losses from the testing, the hysteresis loss of the iron core about the prototype can also be solved. At the same time, the coefficient of hysteresis loss of the silicon steel sheet can be calculated. Based on above analysis, the losses under different speed and winding current are calculated and measured. According to the comparison of the calculated results and measured ones, the error is within 15%. It is shown that

关 键 词：以静止代替运动 有限元 凸极电机 涡流损耗 

分 类 号：TM153[电气工程—电工理论与新技术] TM352