表贴式永磁同步电机磁极优化建模与分析

Modeling and Analyzing of Surface-Mounted Permanent-Magnet Synchronous Machines With Optimized Magnetic Pole Shape Zhenfei Chen1,Changliang Xia1,2,Qiang Geng2,and Yan Yan1

1School of Electrical Engineering and Automation,Tianjin University,Tianjin300072,China

2Tianjin Key Laboratory of Advanced Technology of Electrical Engineering and Energy,Tianjin Polytechnic University,

Tianjin300387,China

Two types of eccentric magnetic pole shapes for optimizing conventional surface-mounted permanent-magnet(PM)synchronous machines with radial magnetization are presented in this paper.An analytical method based on an exact subdomain model and discrete idea is proposed for obtaining the air-gapflux density distribution in the improved motor.Cogging torque and back EMF analytical models are further built with thefield solution,which provide useful tools for investigating motor performances with unequal thickness magnetic poles.The accuracy and feasibility of the models have been validated by afinite element method.Based on the analytical models,the effects of pole shape parameters on motor performance are investigated.Results show that both pole shapes can perfect magneticfield distribution,decrease harmonic content of back EMF,reduce torque ripples,and improve the utilization of PMs.

Index Terms—Exact subdomain model,flux density distribution,magnetic pole shape optimization,surface-mounted permanent-magnet(PM)synchronous machine.

I.I NTRODUCTION

T HE surface-mounted permanent-magnet(PM) synchronous machine has been widely used in elevator,wind turbine,and hybrid electric vehicle applications due to its high efficiency,power factor,and torque density [1],[2].The PM pole,as a pivotal part of the PM motor, directly affects motor cost and behavior,such as magnetic field,back EMF,torques,and so on.As a result,magnetic pole design is particularly important in PM motor design and has attracted lots of attention.Studies in[3]–[6]point out that the contributions of different PM parts are not uniform and magnetic pole optimization can not only improve PM material utilization,reduce magnet material cost,but also achieve more sinusoidal magneticfield distribution and lower cogging torque performance.

The magneticfield calculation is an important prerequisite for the analysis of PM machines.Many methods have been proposed for magneticfield prediction in past few decades. In[7],the drawbacks and stability of numerical implementa-tion are discussed and a semianalytical framework is presented for solving2-D PM machine models in three different coordi-nates.Nevertheless,analytical modeling is usually much more complex for improved PM motors with optimized magnetic pole configurations,since the radial thickness of magnetic pole changes with the circumferential position,which makes its mathematical modeling more difficult than that of conven-tional magnetic poles.Several analytical methods are given in[8]–[10],which provide valuable theoretical references for magnetic pole design and analysis.Stator slotting is usually neglected or complicated pole boundary is simplified to reduce the difficulty of modeling,which also results in a low accuracy of the models.

Manuscript received March3,2014;revised May11,2014;accepted May24,2014.Date of current version November18,2014.Corresponding author:C.Xia(e-mail:motor@).

Color versions of one or more of thefigures in this paper are available online at .

Digital Object Identifier

10.1109/TMAG.2014.2327138Fig.1.PM pole shapes.(a)Conventional pole shape S0.(b)Outer arc eccentric pole shape SA.(c)Inner arc eccentric pole shape SB.

In this paper,two types of eccentric magnetic pole designs are chosen for pole shape optimization of surface-mounted

PM machines with radial magnetization.To solve the problem of unequal thickness magnetic pole modeling,a modified

subdomain model method based on discrete idea is proposed

to predict magneticfield distribution in the air-gap.With the field solution,cogging torque and back EMF models are built.

The effects of magnetic pole dimensions on motor behavior

are further investigated to draw some conclusions.

II.A NALYTICAL M ODELING

A.Eccentric Magnetic Pole Shapes

Compared with the conventional magnetic pole,two kinds of eccentric magnetic pole shapes for improving thefield

distribution of surface-mounted PM motors are shown in

Fig. 1.Fig.1(a)is the conventional magnetic pole shape designated as S0,Fig.1(b)is the outer arc eccentric magnetic

pole shape designated as SA,and Fig.1(c)is the inner surface

arc magnetic pole shape designated as SB.

As shown in Fig.1,O is the center of motor and h m is

the magnet thickness at the pole centerline.For conventional pole shape S0,its inner and outer arcs have the same centre

O and the radial thickness does not change with position. R r and R m are the radii of magnet inner and outer surfaces,and h m=R m−R r.For the shape SA,the center of its outer arc moves to O and the radius changes to be R o.For the shape

SB,the center of its inner arc moves to O ,and the radius

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