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Figure 7.27: Displacement Plot as a Function of Excitation Frequency

7.8. Example Magnetic Cyclic Symmetry Analysis

This magnetic cyclic symmetry analysis uses a model of a simplified electrical machine where the model size can be reduced via cyclic boundary conditions.

7.8.1.Problem Description

7.8.2.Problem Specifications

7.8.3.Input file for the Analysis

7.8.1. Problem Description

Figure 7.28: Two-Phase Electric Machine – Full Model (p. 217) shows a typical example, the full model of a 2-phase electrical machine.

In the full model, flux parallel boundary conditions can be formulated at the outer surface of the stator frame. If only phase A were excited, the magnetic flux would point in the y direction at x=0 plane; flux parallel condition could be formulated at the x=0 plane, allowing an analysis on a half model in the x>=0 space. Similarly, if only phase B were excited, the magnetic flux would have only x component

on the y=0 plane; again, flux parallel could be applied to a half model in the y>=0 plane.

Typically, however, both coils are excited, and no flux parallel conditions could be formulated over the x=0 or y=0 planes. However, due to the cyclic nature of the field, the field pattern repeats itself after 180 degrees. In particular, on the y=0 plane:

By(x) = By(-x)

A similar pattern can be observed in Figure 7.29: Two-Phase Electric Machine – Half Model (p. 217), where the flux lines (equi vector potential lines) are plotted:

Az(x) = - Az(-x)

In this example, the field has a two pole pattern. In general, there are 2p poles; the repetition would take place after 180/p degrees.

Figure 7.28: Two-Phase Electric Machine – Full Model

Figure 7.29: Two-Phase Electric Machine – Half Model

7.8.2. Problem Specifications

The material properties for this analysis are as follows:

Iron relative permeability: 1000

Iron electrical resistivity: 9.579E-8

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Aluminum relative permeability: 1.0

Aluminum electrical resistivity: 2.65E-8

Copper relative permeability: 1.0

Copper electrical resistivity: 1.74E-8

7.8.3. Input file for the Analysis

Use this input file to perform the example magnetic cyclic symmetry analysis. This file contains the complete geometry, material properties, and solution options for the finite element model. Magnetic cyclic symmetry commands of particular interest are preceded by the comment:

!!!Apply Cylic

/title,Cyclic Symmetry Model for EMAG Analysis (Dual Coils with Iron Yoke) /com

/com ***** Quarter Symmetry Model Expanded to Half Then to Full *****

/com

/com

/com

/nopr

/out,scratch

!!! Setup Model Parameters

r1=3

r2=4.5

r3=5

r4=7

r5=11

ncoil=(4*p)

i1=1

i2=2

*dim,alpha1,,ncoil

*dim,alpha2,,ncoil

*dim,current,,ncoil

*dim,coilname,string,ncoil

coilname(1) = 'coil1' coilname(2) = 'coil2' coilname(3) = 'coil3' coilname(4) = 'coil4'

*do,i,1,ncoil

alpha1(i) = -alpha + (i-1)*(90/p) alpha2(i) = alpha + (i-1)*(90/p)

*enddo

ii=0

*do,i,1,p

ii = ii + 1 current(ii) = i2 ii = ii + 1 current(ii) = i1

ii = ii + 1 current(ii) = -i2 ii = ii + 1 current(ii) = -i1

*enddo

/prep7

!!! Setup Model using Parameters

PCIRC,r1, ,0,alpha,

PCIRC,r1, ,0,beta

PCIRC,r1, ,0,gamma

PCIRC,r2, ,0,alpha

PCIRC,r2, ,0,beta

PCIRC,r2, ,0,gamma

PCIRC,r3, ,0,alpha

PCIRC,r3, ,0,beta

PCIRC,r3, ,0,gamma

PCIRC,r4, ,0,alpha

PCIRC,r4, ,0,beta

PCIRC,r4, ,0,gamma

PCIRC,r5, ,0,alpha

PCIRC,r5, ,0,beta

PCIRC,r5, ,0,gamma

AOVLAP,ALL

!!! Setup Material Properties

!IRON MP,MURX,1,1000 MP,RSVX,1,9.579E-8

!AL

MP,MURX,2,1

MP,RSVX,2,2.65E-8

!Copper MP,MURX,3,1 MP,RSVX,3,1.74E-8

!Air MP,MURX,4,1 MP,RSVX,4,0

!!! Setup Components and Atributes

! Iron Core

CSYS,1 ! Enter Cylindrical Mode

ASEL,S,LOC,X,0,r1

CM,Inner_Iron,AREA

AATT,1,,1,

!Al Core ASEL,S,LOC,X,r1,r2 CM,Outer_AL,AREA AATT,2,,1,

!Air Gap ASEL,S,LOC,X,r2,r3 CM,AIR,AREA AATT,4,,1

!Coil 1 ASEL,S,LOC,X,r3,r4 ASEL,R,LOC,Y,0,alpha CM,COIL1,AREA

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AATT,3,,1

!Coil 2 ASEL,S,LOC,X,r3,r4 ASEL,R,LOC,Y,beta,gamma CM,COIL2,AREA AATT,3,,1

!Iron Yoke ASEL,S,LOC,X,r3,r4 ASEL,R,LOC,Y,alpha,beta ASEL,A,LOC,X,r4,r5 CM,YOKE,AREA

AATT,1,,1 ALLSEL

!!! Setup and Mesh Model

MSHKEY,1

CSYS,1

LSEL,S,LOC,Y,0

LSEL,A,LOC,Y,gamma

LESIZE,ALL,,,6,,1,,,1,

CMSEL,S,Inner_Iron

AMESH,ALL

CMSEL,S,Outer_AL

AMESH,ALL

CMSEL,S,Air

AMESH,ALL

CMSEL,S,Coil1

AMESH,ALL

CMSEL,S,Coil2

AMESH,ALL

CMSEL,S,Yoke

AMESH,ALL

ALLSEL

CSYS,0

!!! Reflect Model across X-axis

!! Create HALF model from QUARTER model

arsym,x,all

! Apply BFE Current loads to each coil

*do,i,1,ncoil

asel,s,loc,x,r3,r4

asel,r,loc,y,alpha1(i),alpha2(i)

esla,s

cm,coilname(i),element

bfe,all,js,,,,current(i)

*enddo

csys,0

allsel cmsel,s,extnode d,all,az,0

d,all,temp,25 allsel FINISH

/solu

/out,scratch

antype,static allsel

solve

FINISH

/post1

!!! Plot Out Result Plots plvect,b,,,,VECT,ELEM,ON,0

FINISH parsav,all /clear,nostart

resume,magtest,db ! Resume half Model parres,new

!! Delete Bottom half of model and all loading attatched to bottom nodes

/prep7

allsel nummrg,all

csys,1

nsel,s,loc,x,r5

D,all,az,0 ! AZ = 0 on outside nodes of arc D,all,temp,25

!! Define Coils on Half Model

!Coil 1 ASEL,S,LOC,X,r3,r4 ASEL,R,LOC,Y,0,alpha esla,s CM,COIL1,ELEMENT

!Coil 2 ASEL,S,LOC,X,r3,r4

ASEL,R,LOC,Y,beta,(180-beta) esla,s

CM,COIL2,ELEMENT

!Coil 3

ASEL,S,LOC,X,r3,r4 ASEL,R,LOC,Y,(180-alpha),180 esla,s

CM,COIL3,ELEMENT

!! Apply bfe loads to Half Model coils

cmsel,s,COIL1

bfe,all,js,,,,i2

cmsel,s,COIL2

bfe,all,js,,,,i1

cmsel,s,COIL3 bfe,all,js,,,,(-i2)

!!!Apply cyclic - create cyclic model with two sectors

allsel csys,0 cyclic,2

/solution

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!!! Plot Out Contour Line Plot of Equipotentials plf2d

FINISH

Figure 7.30: Vector Plot of Cyclic Flux Density (B) - Half Model

Figure 7.31: Contour Line Plot of Equipotentials