基于磁链耦合分析的无轴承永磁同步电机通用数学模型

General model of BPMSM based on flux linkage interaction analysis

由于无轴承永磁同步电机内部有两套极对数不等的定子绕组(即转矩绕组与悬浮力绕组),所以电机气隙内存在着转矩绕组气隙磁场与悬浮力绕组气隙磁场两种极对数不等的磁场。对转矩绕组与悬浮力绕组之间的磁链耦合情况的分析,是建立精确数学模型的基础。通过应用机械/电气坐标系变换方法详细分析了不同极对数下转矩绕组与悬浮力绕组之间的磁链交链情况,并证明了当转矩绕组极对数PM=1,悬浮力绕组极对数PB=2(或PM=2,PB=1)时转矩绕组磁链ψM与悬浮力绕组磁链ψB之间相互耦合。当转矩绕组极对数PM与悬浮力绕组极对数PB均大于等于2且满足PB=PM±1时,转矩绕组磁链ψM与悬浮力绕组磁链ψB之间没有相互交链,该证明方法概念清晰、简单直观、便于理解。同时基于该证明结论建立了当转矩绕组极对数PM与悬浮力绕组极对数PB均大于等于2且满足PB=PM±1时的无轴承永磁同步电机的通用数学模型。所提出的通用数学模型为无轴承永磁同步电机仿真与实验研究提供了理论依据。

A bearingless permanent magnet synchronous motor（BPMSM）has two sets of stator windings with different pole-pairs,namely,torque winding and suspension force winding,so there are two types of air-gap magnetic fields,torque winding＆#39;s and suspension force winding＆#39;s with different pole-pairs in the motor.The analysis of the flux linkage interaction between the two sets of windings is the foundation of set up the precise mathematical model of the motor.Here,applying the mechanical /electrical transformation method,the flux linkage interaction between torque winding and suspension force winding was analyzed in datail.It was proved that when the pole-pairs of torque winding and suspension force winding are PM =1 and PB =2,respectively（or PB =1,PM =2）,the magnetic chains of the torque winding and suspension force winding are mutual coupled;when both the pole-pairs of torque winding and suspension force winding PM and PB are greater than or equal to 2 and satisfy the relationship PB =PM ＆#177;1,the phenomenon of the flux linkage interaction between torque winding and suspension force winding does not exist this proof method is simple, intuitive and easy to understand with a clear concept;furthermore,the general mathematical model of BPMSM is built based on the conclusion proved abrove.The general mathematical model proposed for BPMSMprovided a the oretical basis for simulation and experimental study of BPMSM.