CASE STUDY OF A DIPOLE MODEL MAGNET - A ROXIE WORKEDEXAMPLE

C. VollingerCERN,1211Geneva 23,Switzerland

AbstractThe intentionof this chapteris to introducethe ROXIE programpackagetonew andpotentialusersby meansof a worked example. It startswith the2dgenerationof a dipole magnetgeometry, 2d field optimization,followed bycoil-endoptimizationandendspacerdesign,bothfor symmetricandasymmet-ric cases.Finally anexampleof asimpleiron yoke is discussed.

1 Intr oduction

Theintentionof this tutorial is to introducetheROXIE programpackageto new andpotentialusersbymeansof a worked example. It is recommendedto follow the stepsindicatedin the boxes. To workthroughthis examplethe ROXIE version6.0 is required,featuringa graphicalTCL/TK userinterface(Xroxie). More informationon theinterfacecanbefoundin the‘Xroxie UserDocumentation’.

2 Running ROXIE for the first time

ROXIE is startedby typingthecommand’Xroxie’. Thiswill loadtheROXIE programandstartthemainROXIE window with aclearform containingno input data,shown in Fig. 1.

Fig. 1: ROXIE mainmenu(clearform)

Thelayoutof themainwindow follows theblock structureof theROXIE input datafile. Thewindow issplit into sectionsthatcanbeopenedaspull-down menusby left-clicking with themouseon thebuttonat the left handsideof thesectionlabel. SincetheROXIE datafile containsa considerableamountof

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informationit is notpossibleto displayall dataatoncein awindow environment.Thesolutionis to alloweachsectionof theform to be’rolled up’, if notneeded.If theuserchangesa globaloption,Xroxie willadda new sectionto theform sothat it is possibleto edit andspecifynecessarydata.It is alsopossibleto startROXIE by typing ’Xroxie [filename.data]’.In this caseROXIE will loadthechosenfile for thestartup.

StarttheROXIE programby typingXroxie

Beforeyou starteditingyour first ROXIE file you shouldsetthepathsfor theROXIE databasefiles byopeningthepull-down menu‘Run-SetPaths’. The initial window is shown in Fig. 2. Hereall optionsshouldbesetlike usedprinters,theeditoryou preferandalsothepathsto all materialdatafiles ROXIEpossiblyneedswhile running.

Fig. 2: Settingpathfor theROXIE databasefiles

3 2d geometrycreation

To createa new input file, you canedit the clear form or you canusean existing samplefile. If thesamplefile is not availabletype-inthedataasshown in Fig. 3. It is not necessaryto typeall linesin theBlock Data2d section.A pull down menucanbeopenedby clicking on thebuttonabove thescroll barto theright handsideof thesectiontableandchoose’Duplicatemultiple lines...’. In thesamepull-downmenuyou canrenumberthenew duplicatedentries,sortor deletethem. You shouldthenalso’auto fit’thetablesize. Sincewe wantto designa symmetriccoil first, thetogglebutton’Symmetriccoil’ in thesection’Main options’hasto beturnedon. Notethedifferentcablenamesdefiningthecablein theinnerlayerblocks3-6andouterlayerblocks1 and2.

Generateform asshown in Fig. 3

In a latercasewe will defineasymmetriccoils. In thiscasethetogglebutton’Symmetriccoil’ hasto besetto false.In case,you areswitchingon thetogglebutton’2D-Peakfield in coil (LPEAK) asshown infig. 3, youalsohave to specifytheblocksin whichyouwantthepeakfield to becalculatedandprinted.

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Fig. 3: 2D Block definition

4 The Preview Window

It is not necessaryto run theprogramandimmediatelyproducepostscriptplots to displaythecoil ge-ometry. You canalsoopena preview window asshown in Fig. 4, usingthemenuoption ’Run – Openpreview window’ command.

Openapreview window

� Thebuttons’XY’, ’YZ’ and’SZ’ allow theuserto changetheactualview of thecrosssection.Thepreview window shown in Fig. 4 presentsaquaterof thecoil transversalcrosssection(XY-View).Theactualview is shown on theleft handsideof thepreview window. Thebuttons’YZ’ and’SZ’(notavailableat currentstate)areonly usedin the3d case.

� ’1,2...’ will cycle betweenshowing no numbering,showing block numberingandshowing cablenumberingon theimage.As shown in Fig. 4 block numberingis activated.

� ’Cable’ will togglebetweendisplayingthecablebareor insulated.Thecurrentstateis shown ontheleft handsideof thepreview window also.

� Thebuttons’Imag’, ’Layer’ and’Edge’ (notavailableatcurrentstate)areonly usedin the3dcase.

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Fig. 4: Preview window (invertedcolourrepresentation)

� ’Update’ will updatethe imagesaccordingto thecurrentstateof the form given to ROXIE. Thisbuttonwill needto beusedif theROXIE form is modifiedor anew form is loaded.

� ’Close’ will closethepreview window.

� Whenthe mouseis directedto oneof the coil’s conductors,the appropriatedconductoris high-lightedandits coordinatesareshown on theleft handsideof thepreview window.

5 Producing Postscript Plots

SettingLPLOT=true(clicking on thetogglebutton ’Postscriptplots’ in section’Main options’)createsthenew section’Plotting Information2D’ asshown in Fig. 5. Heretheuserhasto specifytheplots tobeproducedby ROXIE. It is not possibleto producepostscriptswhile runninganoptimization.Figure5 shows a selectionof availableplots. Thecolumns’No’,’X-axis’, ’Colour’ and’360deg’ do not needany explanation.Righthandclicking with themousein thecellsof thecolumn’Field’ shows thecurrentplotting possibilities.

Fig. 5: 2D Plotdefinitionwindow

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If field valuesare to be displayedin the coil the blocks in which the fields arecalculatedhave to bespecifiedin thesection’Blocks(Peakfields,FEM plots)’ asdonein thesampleinputfile (seeFig. 5).

Edit your input file accordingto thesampleshown in Fig. 5

If youpressthetogglebutton’Display graphaxis’ thehorizontalaxiswill beplottedasshown in Fig. 6.It is alsopossibleto displaya legendby settingthetogglebutton ’Display legend’ to true. Pressingthebutton ’Run ROXIE’ startstheprogram.If you have not yet saved thefile, ROXIE will requestsavingfirst. To save thefile, youcanequallyusethecommand’Save form as...’ in thepull-down menu’File’.

Runyourfirst ROXIE input file

SinceROXIE will checkfor missinginformationin a form beforeit is savedor ROXIE is run, you canusuallynot misstheinput dataof wholesections.ROXIE hashowever only a limited numberof checksfor physicalvalidity of inputdata.

Fig. 6: Postscriptplot of thecoil cross-section

You canseetheresultsby pressingthebutton’V iew Postscripts’.Fig. 6 shows the5th postscript-plotasseenusingghostview. It shows thecross-sectionof thedipolemagnet.

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6 2-dimensionaloptimization

ROXIE offersseveralalgorithmsfor differentoptimizationproblems.To run anoptimization,you haveto turn on theoption ’Optimizationalgorithms(LALGO)’ in section’Main options’andsettheoption’Postscriptplots (LPLOT)’ to falseasshown in Figure7. This createsnew sections’DesignVariables’and’Objectives’ asshown in Fig. 7, automatically. Youhave to specifyin thesection’DesignVariables’thestartingpoint andtheupperandlower boundfor eachdesignvariableto beappliedto thecoil. Thesection’Objectives’ containsdatadefiningtheobjective functionsetup.Theentriesin the ’String’ and’Oper’ fieldsin thetablecanalsobeselectedfrom amenuby right-clicking in theappropriatecell. Theydefinethe way the objective function is setup, e.g. the usageof objective weightingresp. constraintformulationof theobjective function.ROXIE alsooffersahelpmenuactivatedby left-clicking with themouseon thestringto which thefurtherinformationis needed.

Fig. 7: Window for thedefinitionof designvariablesandobjectivesfor theoptimizationproblem

For our casestudyshown in Fig. 7 the positioninganglesof blocks2, 5 and6 ’PHI0’ aredeclaredasdesignvariables,while thegoal is to reducetherelative field components(harmonics

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Note, that the weighting factorsallow the userto definepreferencesfor the objectives andallow forscalingof thedifferentobjectivesbecauseof their differentnumericalvalue.An optimizationalgorithmhasto be chosenin section’Global Information’. Left-clicking with the mouseon the button ’Opti-mizationalgorithm’ in this sectionwill show all availablealgorithms.For this casestudythealgorithm’EXTREM’ shouldbeused.

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Edit your input file as shown in Fig. 7 and run your first optimizationwith ROXIE. Donot forget to chosean optimizationalgorithm. Make surethe 2d peakfield calculationisswitchedoff

Startingtheoptimizationyieldsanoutputfile called’filename.output’.Theoptimalvaluesfor theposi-tioning angleshave to betransferredby handto a new input file for ’post-processing’of theresults(Xsin the designvariableblock). To readthe outputfile you canuseany editor of your choiceavailableon your platforme.g. ’emacs’or ’nedit’. During the run of anoptimizationwith theplotting informa-tion switchedoff, all datain thesection’Plotting Information2D’ is storedin thebackgroundalthoughthesectionitself is not displayedin thewindow. Thestoreddatacanbereactivatedafter theoptimiza-tion is finished. Although it is not possibleto producepostscriptplots of the coil geometryduring anoptimization,ROXIE producestwo postscriptplotsaftereachoptimizationrun. Theseplotscontaintheconvergencecurvesof thedifferentobjectivesdeclaredandcanbeopenedwith pressingthebutton’V iewPostscripts’.

Startasecondrunwith theoptimizedvaluesfor theanglesandproducethepostscriptplotsof thefinal design.

Fig. 8 shows the6th postscriptplot asseenusingghostview. It shows themagneticfield modulusinsidethecoil blocks.

Fig. 8: PostscriptPlotof thefield insidethecoil blocks

By switchingon the option ’Design VariablePrintout(LINPUT)’, it is alsopossibleto producea file[filename.scan]that allows theuserto read-inan optimizedsetof variablesasnew input file. To readin the designset the userhasto pressthe button above the scroll bar in section’Design Variables’andchoosing’Readin designset...’. This is in particularusefulwhenthe numberof designvariablesincreases.

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7 Coil enddesign

To designa 3-dimensionalcoil end,the useof ROXIE is very similar to the 2-dimensionalcase.Theeasiestway to startis to usea 2-dimensionalcaseandsave it with a differentfile name.Turn on ’Coilenddesign(LEND)’ in section’Main options’. This yieldstwo new sections:’Global Information3D’and’Block Data3D’ asshown in Fig. 9. Section’3D Block Data’ containsall informationwhichhastobedefinedin additionto the2d datadescribedin chapter3.

Fig. 9: 3D Block definitionwindow

Changeyour 2D caseto thenew 3D caseusing’File save as’ in thepull down menu’File’asshown in Fig. 9. Do not forgetto changethefilenamebeforesaving.

In ’Global Information3D’ thespecialinformationandoptionsrequiredto configureROXIE for 3D coilendcalculationsis defined.

� ’Numberof blocksin theouterlayer’ is to bedeclaredfor endspacerdesignin orderto keepthenumberingof theend-piecesconsistent.Notethatthecentralpostandthehead-spacershave onlyonemachinedsurface. In thesymmetriccasetwo layerscanbetreatedat thesametime whereasin theasymmetriccasetheblockson onesidehave to be groupedas’outer layercoil blocks’ to

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Fig. 10: Postscriptplot of thesymmetriccoil end(innerlayer)

Fig. 11: Postscriptplot of thesymmetriccoil end(outerlayer)

guaranteethenumberingof blocksandendspacersremainsconsistent.In theartistsview, theouterlayercoil blocksappearin bluecolourandtheinnerlayercoil blocksin orange.For instance,theinnerandtheouterlayerof acoil endareshown in Fig. 10 andin Fig. 11,respectively.

� ’Cablesizeincr., lessend-comp.’ givestheincreaseof insulationthickness(azimuthal)in thecoilendsdueto lesscompression.

� ’Number of cuts in Z-plane’ meansthe numberof cuts in the z-directionbetweenthe xy-cross-sectionandtheyz-cross-section.Usuallyabout20 cutswill besufficient. Themaximumnumberis 25.

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� ’Length of extensioninto -z direction’ meansthelengthof straightsectioninto -z direction(seenfrom theonsetof thecoil endat z=0). Note, that if thecoil is imagedat z=0 thestraightsectionhasalwaysto bezero.

A detailedhelpmenuto all expressionsis offeredandactivatedby left-clicking with themouseon theexpression.Thereforea detailedexplanationof the input datais omittedhere. If you want to produce3-dimensionalpostscriptplots you have to edit section’Plotting Information3D’ asshown in Fig. 12.Theinstructionswill producethe3D-postscriptplotsof theinnerandouterlayerof thecoil.You will geta selectionmenuwith pre-definedsymbolsby right-clicking with themousein theappro-priatecell. Again, it is notnecessaryto producepostscriptplotsto preview thecoil geometry. As for the2d casesapreview window is offeredin 3D.

Runthe3-dimensionalcase

8 Integrated 3d field harmonics

For thecalculationof the3d field harmonicsthe togglebutton ’3D Harmonics’hasto be switchedon.This createsthenew section’Integral field 3D’ which is alsoshown in Fig. 12. Togetherwith thestartandendof theintegrationpath,theonsetof theiron yoke hasto bespecified.As theimagingmethodisusedto calculatetheeffectof theiron yoke,saturationinducedeffectsareneglected.It is alsonecessarythat thestartandendof the integrationpathis sufficiently far away from any discontinuityin the ironyoke.

9 The Preview Window for the 3D Case

ROXIE offers the useof a preview window in the 3-dimensionalcase,too. To activate it, openthepull-down menuandpress’Run – Openpreview window’. Figure13 andFig. 14 bothshow anopenedpreview window for the3d coil endgeometry.

Therearedifferentviews availableandit is possibleto togglebetweenthem:

� Thebutton’XY’ openstheview on thecoil transversalcrosssection.

� Thebutton’YZ’ openstheview on thecoil longitudinalcrosssectionasshown in Fig. 13.

� Pressingthebutton ’SZ’ presentstwo differentviews on thecoil asshown in Fig. 14. The lowerpartof theFigureshows onehalf of thecoil endseenasartistview. Theupperpartof theFigureshows thesamecoil endwhile theviewer seesthelower radiusof thecoil.

Thenumberingof theblocksandconductorscanbe shown by pressingthebutton ’1,2...’ asshown inFig.13andFig.14. Moving themouseononeof theconductorsdisplaysthecoordinatesontheleft handsideof thewindow. To closethepreview window pressthebutton’Close’.

10 3-dimensionalOptimization

As mentionedin chapter6, you have to set ’Postscriptplots (LPLOT)’ to falsewhile turning the op-tion ’OptimizationAlgorithm (LALGO)’ to true. Theactionsto betakento run a 3D optimizationwith

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Fig. 12: 3D integral field calculationwindow

ROXIE are identical to the 2-dimensionalcase. You have to edit the sections’Design Variables’and’Objectives’ asshown in Fig. 15.

As anexamplefor a 3-dimensionaloptimizationuseDZZ0 asa designvariable. ThevalueDZZ0 rep-resentsthe straightsectionof the coil end. In the samplefile shown in Fig. 15 the valuesof B3R areoptimizedwith a distancefunctionmethod.B3R representstheaveragefield componentsalongthecoilend(hereof order3,5,7and9). Again,rightclickingwith themousein thecellsof thecolumn’String’ ac-tivatespull-down menuscontainingthepre-defineddesignvariablesor objectives.Thevaluesin column’Weight’ aretheweightingfactorsmentionedin chapter6.

Do not forget to chosean optimizationalgorithmin section’Global Information’ beforestartingyourROXIE run. It is also recomendedto reducethe discretization of the cable i.e. group 4 strandstogether to oneline current, 1:9 insteadof 2:18 in the Block Data 2d widget.

11 3D Endspacerdesign(symmetric)

ROXIE offers a completetool to designsymmetricandasymmetriccoil endspacersincluding an in-terfacefor CNC machining. You canstartwith the 3D samplefile producedin chapter7. First turnon ’Wedge/Endspacerdesign(LEND)’ in section’Main Options’asshown in Fig. 16. Make surethat’Postscriptplots(LPLOT)’ is activatedand’Optimizationalgorithms(LALGO)’ in ’Main Options’is setto false.To produceendspacerplotsyou canedit section’Plotting information3D’ asshown in Fig. 16.Thecolumn’View’ givesa descriptionof whatview anglesof thecoil endarepossible.Rightclickingwith the mousein the appropriatecells will show a list of availableoptions. Note that for plotting ofendspacersthepolygonscreatedfor CNC machiningareneeded.Soyouhave to turn on ’CNC Machin-ing (LCNC)’ in section’Interfaceoptions’asshown in Fig. 16, too. While creatingaCNC file, thecoldcontractionfactorin section’Global Information’hasto bezero.

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Fig. 13: YZ crosssectionof thedipolecoil end(invertedcolourrepresentation)

Fig. 14: SZplaneof thedipolecoil end(invertedcolourrepresentation)

Edit andrun theinput file for endspacerdesign

Fig.17shows the 27th of the postscript-plotsasseenusingghostview. It shows the endspacersof theouterlayer in symmetriccaseseenfrom thetop while fig. 18 shows theendspacersof theinnerlayer insymmetriccase.

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Fig. 15: 3D optimizationdata

12 3D Coil and endspacerdesign(connectionside)

Todesignasymmetriccoilsandendspacersusethesamplefile youcreatedin chapter11andsaveit with adifferentfile name.Youfirst haveto settheoption’Symmetriccoil (LSYMM)’ in section’Main options’to false.Thentwo new columns’Imag’ and’Turn’ appearin section’Block Data2D’ automaticallyasshown in Fig.19:

� The’Imag’ field is usedto mirror blocksatthex-axis.Youcanchosebetweenthesetting’Imag’=1(imagedat thex-axis)or ’Imag’=0 (not imaged).

� The’Turn’ field is usedto shift blockswith anazimuthalanglein mathematicalpositive direction.Setting’Turn’ to 0 meanstheblock won’t beshifted.Thegivenvaluesareexpectedin degrees.

Type-inthemissingdataof thesamplefile asshown in Fig.19

Makesurethat’CNC Machining’ in section’InterfaceOptions’is still activated.In theasymmetriccaseonly onelayercanbetreatedat thetime. The turnswhich cross-over from onecoil block to anotherinendhave to bedefinedasasingleblockasshown in fig. 20. Thelayerdefinitionsarethenusedto defineleft andright sideof thecoil, e.g.definingleft sideas”outer layer”.If theblocksareconnectedin thexy cross-section,thedefinition of relative anglesPHIR andALPHRasshown in fig. 19 canbe useful. It is possibleto determinethe anglesin section’Design Variables’in column’string’. Right clicking with the mousein this columngivesall availablepossibilities. Thearguments’PHIR’ and’ALPHR’ canbefoundchoosingthemenu’2D Block positions- PHIR’ or ’2D

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Fig. 16: 3D plot definitionsin caseof endspacerdesign

Block positions- ALPHR’, respectively. In this casePHIR of the n-th block refersto the positioninganglerelative to block numbern-1, while ALPHR is the relative inclination angle. In fig. 19 e.g. therelative angleof block no. 2 with respectto blockno. 1 is chosenas’0’.Fig.20and21show thecoil in theXY andSZ planesasdisplayedin thepreview window.In the asymmetriccaselayer by layer (with upperandlower edgesof the cable)or both layersat thesametimecanbedisplayed.In thelattercaseonly theupperedgesor theloweredgesaredisplayed.

It is possibleto producepostscriptplotsof thedesignedasymmetricendspacersin variousviews. Fig. 22shows a selectionof availableplots. In column’View’ is an integervalueexpected,that representsthesingleviews. Fig.23shows the31thpostscriptplot of theendspacersfor theasymmetriccaseasshownusingghostview. This specialplot refersto No.2 in section’Plotting Information3D’.

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Fig. 17: Postscriptplot of thesymmetriccoil endspacers(outerlayer)

Fig. 18: Postscriptplot of thesymmetriccoil endspacers(innerlayer)

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Fig. 19: Window for anasymmetriccoil end

Fig. 20: Cross-sectionof asymmetriccoil end(invertedcolourrepresentation)

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Fig. 21: SZ planedisplayof asymmetriccoil end(invertedcolourrepresentation)

Fig. 22: 3D Plottinginformationfor asymmetricendspacers

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Fig. 23: Postscriptplot of theasymmetriccoil andendspacers

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13 Ir on cross-sectiondefinition

To calculatetheinfluenceof theiron yokeon thefield, e.g.saturationinducedfield errors,ROXIE offerstheusertwo differentcalculationmethods.Thefirst methodusesa reducedvectorpotentialformulationandsolves the problemwith the finite-elementmethodimplementedin the FEM2D program( c

�TU-

Graz/Austria).Thesecondmethodworkswith a total vectorpotentialformulationandsolvesthefieldproblemusingacoupledboundaryelement/ finite elementmethod( c

�TU-Stuttgart/Germany). Charac-

teristic for bothmethodsis that thecoils aren’t representedin thefinite elementmesh.This allows theuserto modelthecoil andiron yoke separately.

Fig. 24: Definitionof theiron yoke

Thereforetheinputfile ’[filename.data]’remainsthesamewith only smallchangesandthefinite elementmeshis definedin a separatefile named’[filename.iron]’. The syntaxof the iron file is explainedindetail lateron.

First stepin thesettingup of a finite elementmethod(FEM) or a coupledBEM-FEM calculationis tospecifythe entirecoil without the useof symmetriesby settingthetogglebutton’LSYMM’ in section’Main options’to false.Thenyou caneitherdefineeachsinglecoil block in the2d coil block definitionwindow or declarelayersto which singleblocksrefer. If you want to uselayers,switch on the togglebutton’Definition of layers’asshown in fig. 24. Thiscreatesthenew section’Layer’ automatically.

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� ’No’ is thenumberingof theLayers.

� ’Symm’ is thedefault geometricsymmetryof thelayer. For thedipolecasetheno. ’2’ shouldbechoosenasshown in fig. 24.

� ’Blocks’ lists theblock numberswhicharerelatedto theappropriatelayer.

Then you have to specifythe maximum angleof the harmonic analysiswithin the FEM meshareain section’Design Variables’ while setting the variable ’SYMMR’=90 . In thesamesection,youalsocandeclaretheradiusof thefringing field calculationasshown in fig. 24, if you wanta fringing field tobecalculated.

Type-inthemissingdatafor theiron casestudyasshown in fig. 24

As mentionedbefore,theiron geometryis modelledin theiron file ’[filename.iron]’whichcanbeeditedwith aneditorof yourchoice.Makesurethatthefilenamecorrespondsto theappropriatedatafile. In theiron file you defineyour geometryusingkeypointsandlinesto modelthegeometricalshape.Linescanbestraightlines,arcsor elliptic arcs.A specialeditorcalled’Xhermes’editoris offeredto createanironinput file. It is alsopossibleto createtheinput file with usualeditors.Furthermore,ROXIE supportstheuseof macrosto createmorecomplicatediron models.Theuseof theXhermeseditor is explainedinsection15. While you aremodelling,switchoff thetogglebutton’FEM calculation(LFEM)’ in section’Main Options’ and turn on the button ’Iron Modeller (LIRON)’. All valuesgiven in the iron file areexpectedin m. It is thereforeusefulto usecapitallettersfor symbolsdefinedin mmandsmalllettersforsymbolsdefinedin m.

14 Generatinga new iron file

Fig. 25: Inputfile for simpleiron yoke

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Userscancreatenew iron files usingan usualtext editor. The creatediron file needto have a name’[filename.iron]’ accordingto theexistingdatafile named’[filename.data]’.

Firststepis to declaretheprincipalstructureof theyokeby definingsocalledkeypoints. Thesekeypointsshouldsketchthegeometry, additionalkeypoints,linesandmaterialareascanbedefinedeitherdirectlyin theiron file or by usingtheXhermeseditorlater. If youaredefiningkeypoints,linesandareaswithoutusingtheXhermeseditor, beawareof thecorrectsyntaxasexplainedin ’THE HermesPREPROCESSORFOR FEM2D. Fig. 25 shows the syntaxto definekeypoints. It is possibleto type in the x- and y-coordinatesor radiusandangleto specifya point uniquely. As shown in thesamplefile, declarationofsymbolsis allowed. To specifykeypoints,you canalsousecoordinatesof keypoints that arealreadyexistingasdonewith keypointno.2,e.g.

15 The Xhermeseditor

To edit anexisting iron file with theXhermeseditor, opentheGraphicalFEM viewer by choosingthemenu’Iron - opengraphicalFEM viewer’. If youopentheiron previewer for thefirst time,ROXIE willaskyouto confirmthecreationof thepreview file andopenthepreview window afteryourconfirmation.Pressingthe button ’Edit...’ in the GraphicalFEM viewer opensthe Xhermeseditor. The appearingdisplayof the Xhermeseditor dependson the currentdisplaymodeof the preview viewer. Therearethreedifferentpossibilitiesasshown in fig. 26. Userswill gettheleft window whenopeningtheXhermeseditor in nodeediting modus,the window in the middle in line editing modusandthe window on theright handsidein areaeditingmodus.

Fig. 26: Xhermeseditormodes

� To add nodes, it is possibleto go into the nodeediting modusand pressthe button ’Add’ inthe appropriatesection. This opensa small window whereyou can type-in the new nodes. Tosave the new nodespressthe button ’Apply’. This runs the hermespreprocessorandsaves allchangesyou made. With the sameprocedureuserscanaddsymbolsusingthe Xhermeseditor.

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It is assumed,that the syntaxcorrespondsto the definitionsof keypointsasdescribedin ’THEHermesPREPROCESSORFORFEM2D by J.Lucas.

� Lines betweenkeypointscanbeaddedby changingthepreview window stateinto line modethatalsochangestheXhermeseditormode.Firstpressthebutton’Add lines’. Thischangesthedisplayof themousecursor. Leftclicking with themouseon keypointsconnectsthemwith lines. To savethechangesclick the right mousebuttonandpressthebutton ’Apply’ afterwards. Thenthenewlinesareaddedto theiron file. To unselectthemclick on oneof theselectedlines.

With thesameprocedurearcsor ellipsiscanbeadded.Thenusersalsohave to specifytheradiusof thearc in cell ’rad’ or click on a third point to describetheellipsis, respectively. Note, that itis not possibleto add different line typesin oneoperation. Xhermesseriellynumbersthelinenamesasdefault but it is alsopossibleto give userdefinednamesby typing thenamein thecell’Name’ andpressing’Return’. Furthermore,line nameshaveto beuniqueandXhermeswill deletethefirst line if you usethenameof a line twice. If you wantto changetheboundaryconditionofa line, click on thetogglebuttonof theappropriateboundarybeforeyouapplythechanges.

To deletelines(straightlines,arcsor ellipsis),selecttheline andpressthebutton’Delete’. Linescanonly get deletedif they arenot part of a materialarea. If they are,you have to deletetheconnectedareafirst. It is possibleto selectanddeletemorethanoneline by holdingthe’Ctrl’ keyon thekeyboardwhile left-clicking on theappropriatelines.

� Ar eascanbeaddedor deletedin themacroelementmodeof thegraphicalFEM viewer. Thereforepressthebutton’Macro EM’ to changeto macroelementmode.Type-inthematerialwishedto bereferredto thenew areaandpressthe’Return’ key to confirmthechangeof material.Thenpressthebutton ’Add macroelement’andselectthenew area.Again it is possibleto selectmorethanoneareaby holdingthe’Ctrl’ key. Right-clickingwith themouseconfirmsall selectedareasandpressingthebutton’Apply’ savesthechangesto theiron file. To deletea materialarea,selecttheareaandpressthebutton’Delete’. Thenpress’Apply’ to save thechanges.

� Pressingthebutton’Reload’updatesthecurrentview andshows all changesmade.

� Thebutton’Close’ closesthegraphicalFEM viewer.

Notethat theiron file differsdependingon thechoosenmethodto solve thefield problem.Makesure,thatthedeclarationof boundariesis correctandthattheiron file containsnoair areasin caseof theBEM/FEM couplingmethod.

16 The preview window for the ir on model

Startinga ROXIE run with an existing iron file ’[filename.iron]’ createsa meshthat canbe previewedby openingthepull-down menu’Iron - OpenGraphicalFEM viewer’. Existingiron files canbeopenedusingthemenuitem ’View Iron file’ in thesamepull-down menu,too.

� ’Hide Labels’:Pressingthisbuttontogglesbetweenshowing theappropriatelabelsfor nodes,linesor areasandhiding them.Thebuttonindicationchangesaccordingto theactualstate.

� ’Zooming’,’Auto-fit’: Leftclicking with the mousein the iron preview window zoomsan area,markedwhile moving themouse.Usingthebutton’Auto-fit’ reproducestheoriginal size.

� Pressingthebutton’Nodes’shows thenodes.This is thedefault view, shown by ROXIE whenthewindow is openedfor thefirst time.

� Pressingthebutton’Lines’ showsthedeclarednodesandthelineswith theappropriateline names.In additionthechosenboundariesaremarked.

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Fig. 27: Preview window for simpleiron yoke (invertedcolourrepresentation)

� Thebutton’Macro EM’ (MacroElements)presentsthemacroelementnumberingandthechosenmacroelements.Again differentboundariesaremarked. In this mode,RXIE alsoshows you thedifferentmaterialsused:they aremarkedwith differentcolours.

� Pressingthebutton’Finite EM’ displaysthefinite elementmesh.

� Pressingthebutton’Edit...’ openstheXhermeseditorasadditionalwindow on theright handsideof thepreview window. Xhermesgivestheuserthepossibility to changetheyoke geometryveryeasilyandis explainedin detailin section15.

� After changeingthe actualgeometry, pressthe button ’Reload’ to reloadthe file andupdatetheview.

� ’Close’ will closetheiron preview window.

17 FEM calculationsconsideringthe ir on yoke

Fig. 28: Choosingcoupledboundary- finite elementmethod

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After modellingthe iron file, the usershave to choosethe solving algorithm: switchingon the togglebutton ’FEM calculation(LFEM)’ in section’Main options’ asshown in fig. 24 for solving the fieldproblemwith thefinite elementmethodor choosethetogglebutton’BEM-FEM coupling(LBEMFEM)’in section’InterfaceOptions’asshown in fig. 28for solvingthefield problemwith thecoupledboundary- finite elementmethod.StarttheROXIE programby pressingthebutton’Run ROXIE’.

0

20 40 60�

80�

100 120 140 160 180 200 220

0.58761 0.4408-

0.4408 0.88101-

0.88101 1.32122-

1.32122 1.76143-

1.76143 2.20164-

2.20164 2.64184-

2.64184 3.08205-

3.08205 3.52226-

3.52226 3.96247-

3.96247 4.40268-

4.40268 4.84289-

4.84289 5.2831-

5.2831 5.72331-

5.72331 6.16352-

6.16352 6.60373-

6.60373 7.04394-

7.04394 7.48415-

7.48415 7.92436-

7.92436 8.36457-

|Btot| (T)

FEM ROXIE6.02D *

Fig. 29: Total field consideringthesimpleiron yoke,FEM calculation

Fig.29showsthetotalfield calculatedby ROXIE usingthereducedvectorpotentialformulationandcon-sideringthesimpleiron yoke while fig. 30 shows thedistribution of thetotal vectorpotentialcalculatedwith thecoupledBEM/FEM method.

Runthefirst FEM calculation

249

0

20�

40�

60�

80�

100�

120�

140�

160�

180�

200�

220�

0. 0.01412-

0.01412 0.02824-

0.02824 0.04236-

0.04236 0.05648-

0.05648 0.07059-

0.07059 0.08471-

0.08471 0.09883-

0.09883 0.11295-

0.11295 0.12707-

0.12707 0.14119-

0.14119 0.15531-

0.15531 0.16943-

0.16943 0.18355-

0.18355 0.19767-

0.19767 0.21178-

0.21178 0.2259-

0.2259 0.24002-

0.24002 0.25414-

0.25414 0.26826-

AR (Tm)

BEMFEM ROXIE6.0*

Fig. 30: Totalvectorpotentialconsideringthesimpleiron yoke,coupledBEM/FEM calculation

18 Calculation of transfer functions

ROXIE offers a specialtool to calculatethe transferfunction of a magnetwhile ramping. To producethetransferfunction,switchon thetogglebutton ’FEM TransferFunction(LEXIT)’ in section’GlobalInformation’. This yields to a new section’Transferfunction (CurrentFactors)’. In this sectionuserscanspecifythebasepointswherethetransferfunctionwill becalculated.If nothingis specifiedin thissection,ROXIE calculatesautomatically10aquidistantbasepointsbetweenthe0andthenominalcurrentvalue,thatis definedin section’Block Data2D’. If theuserdeclarescurrentfactors,ROXIE will multiplythe specifiedfactor with the nominal currentand calculatethe transferfunction only at the specifiedvalues. In both casesan additionalplot asshown in fig. 32 is createdandshows the transferfunctionsthatarespecifiedin sectionin section’Objectives’ (seefig. 31). Theplot canbedisplayedby pressingthebutton’V iew Postscripts’

Fig. 31: Objectivesfor thetransferfunction

250

While calculatinga transferfunction, the toggle button ’PostscriptPlots (LPLOT)’ in section’MainOptions’shouldbeswitchedoff.

2000�

4000�

6000�

8000�

10000 12000

-2

0�

2

4

6�

8�

Fig. 32: Transferfunctionof theiron case

251