英文文献以及翻译Boolean operations for 3D simulation of CNC machining.docx

英文文献以及翻译Boolean operations for 3D simulation of CNC machining.docx

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英文文献以及翻译Booleanoperationsfor3DsimulationofCNCmachining

Booleanoperationsfor3DsimulationofCNCmachining

ofdrillingtools

DaniTost*,AnnaPuig,Lluı´sPe´rez-Vidal

SoftwareDepartment,PolytechnicalUniversityofCatalonia,SpainAccepted25April2003

Abstract

ThispaperaddressesthesimulationofdrillingtoolsCNCmachining.Itdescribesanovelapproachforthecomputationoftheboundaryrepresentationofthemachinedtools.MachiningconsistsofasequenceofBooleanoperationsofdifferencebetweenthetoolandthegrindingwheelsthroughtime.TheproposedmethodperformsthedynamicBooleanoperationsoncrosssectionsofthetoolanditreconstructsthe3Dmodelbytilingbetweenthecrosssections.Themethodisbasedonclassicalcomputationalgeometryalgorithmssuchasintersectiontests,hullcomputations,2DBooleanoperationsandsurfacetiling.Thisapproachisefficientanditprovidesusercontrolontheresolutionoftheoperations.AbstractThispaperaddressesthesimulationofdrillingtoolsCNCmachining.Itdescribesanovelapproachforthecomputationoftheboundaryrepresentationofthemachinedtools.MachiningconsistsofasequenceofBooleanoperationsofdifferencebetweenthetoolandthegrindingwheelsthroughtime.TheproposedmethodperformsthedynamicBooleanoperationsoncrosssectionsofthetoolanditreconstructsthe3Dmodelbytilingbetweenthecrosssections.Themethodisbasedonclassicalcomputationalgeometryalgorithmssuchasintersectiontests,hullcomputations,2DBooleanoperationsandsurfacetiling.Thisapproachisefficientanditprovidesusercontrolontheresolutionoftheoperations.

q2003ElsevierLtd.Allrightsreserved.

Keywords:

CNCsimulations;Boresmachining;Computationalgeometry;Booleanoperations;Surfacetiling

1.Introduction

MostoftheresearchonCNCinCADiscenteredontheautomaticcomputationoftoolpaths[5,13].Givenafinaltooldesign,theoptimaltrajectoriesofthetoolandthegrindingwheelsmustbecomputedyieldingasfinalresulttheCNCcode.Machiningsimulationandverificationhasexactlytheoppositegoal:

tocalculatethetoolstartingfromtheCNCcodeandfromageometricalmodelofthemachine,thewheelsandthetoolbeforemachining.Thissimulationhasthreemainapplications[6].First,itdetectseventualcollisionsbetweenthetooloranyofthegrindingwheelsandtherestofthemachine.Itisimportanttoavoidcollisionsbecauseseriousdamagestothemachinescanfollow.Next,simulationprovidesameansofvisuallyverifyingtheefficiencyofthetrajectories,whichmayresultinfasterandcheaperprocesses.Finally,thesimulationallowsuserstocheckifthesurfaceoftheresultingtooliseffectivelythedesiredone.Intheroutinepracticeofmachining,experiencedoperatorshaveenoughskillstoimaginethetoolfinalshapebyonlyreadingtheCNCcode.

However,theyaregenerallynotabletodosowithnewornon-standarddesigns.Therefore,theuseofasimulationsystemdecreasesconsiderablythetoolproductioncostbecauseitavoidsthetrialanderrorprocessontherealmachinewithcostlymaterialsthatisotherwisenecessary.

ThispaperaddressesaparticulartypeofCNCmachiningsimulation:

thegrindingofboresandcutters.ConventionalCADsystemsdonotprovideameansofrealizingthistypeofsimulationsandspecificapplicationsareneeded.Untilrecently,mostofthesimulationapplicationsdealtonlywiththemachiningof2Dcross-sectionsofthetoolsandtheywererestrictedtothemainflutingoperation[3].Threedimensionalapplicationsareratherrecent[4,23].Theyprovideamachiningsimulationforspecific5-axesmachinesandtheyarenotapplicabletogeneralmovements.Thispaperpresentsanovelapproachforthecomputationoftheexternalshapeofthetoolsthroughasequenceofcoordinatedmovementsofthetoolandthewheelsonmachinesofupto6-axes.Theproposedmethodreducesthe3Dproblemto2DdynamicBooleanoperationsfollowedbyasurfacetiling.The2Dsolutioninvolvesdifferenttechniquesofplanarcomputationalgeometry:

fromintersectionstohullcomputations.

Thepaperisstructuredasfollows.InSection2wereviewpreviousapproachesonmachiningsimulations.Section3describesbrieflythecontourconditionsofthesimulation.Finally,Section4describesthecomputationofBooleanoperationsandtheresultsoftheimplementationareshowninSection5.

2.Previouswork

MachiningcanbeconsideredadynamicBooleanoperationofdifferencebetweenthegrindingwheelandthetool.Itisdynamic,becauseboththetoolandthewheelsmovealongtimethroughrotationsandtranslations.

TheVectorCut[8,10],isprobablythemostreferencednumericalcontrolsimulationmethod.Itisanapproximatesolutionthatrepresentsthefrontierasasetofpointsandnormalvectorsthatwillbecutalongthepathofthegrindingwheel.Thismethodiseffectiveforthesimulationofsculpturedsurfacepolishing,butitisnotextensibletocomplexmotionsofthetooland/orthegrindingwheels.Itismainlyusefultodetectmistakesinthepathsuggestedbythepresenceofabnormallyhighorsmallcutvectors.Besides,exceptfortheextensionofRef.[16],itdoesnotyielddirectlyamodelofthebittobemachined.

Analternativestrategyformachiningsimulationconsistsofrealizingasequenceof3DstaticBooleanoperationsthroughtime.Themaindrawbackofthisstrategyisitshighcomputationalcost.AccordingtoRef.[11],thisisproportionaltothenumberofdiscretepositionstothefourth.Thisputsitoutofquestion,inpracticalterms.Anotherproblemitshowsisthegranularityofthetemporaldiscretization:

itmustbeveryfineifprecisioninthefinaltoolisrequired.ThismeansthatverylittlematerialiscutoffineachBooleanoperation,andthatmayentailrobustnessproblemsinthecomputations.Apossiblemethodtoavoidbothproblemsistodiscretizetheinitialtoolmodelintoavoxeloranoctreemodel,[20],toperformallthesequenceofBooleanoperationsonthediscretemodelandthenreconstructthemachinedsurface,attheend.ThisapproachbenefitsfromthefactthatthecostofdiscreteBooleanoperationsismuchlowerandthereconstructionphaseattheendoftheprocessisdoneaslateaspossible.Thisoptionrequiresthesequenceofmovementstobespecifiedintermsofrelativemotionofthegrindingwheel,whilethetoolanditsdiscretizationremainfixed.Thisprerequisiteisnotalwaysvalidand,inparticular,itdoesnotholdforthegeneralcaseof6-axesmachines.

Finally,anotheroptiontakenintoaccountisthatofthecomputationofthevolumesweptbythetoolandthegrindingwheelintheirmotions.AgeometricrepresentationofthisvolumewouldallowperformingonlyoneBooleandifferenceoperationbetweenthetwovolumes.Themaindifficultyofthisoptionisthecomputationofsweptvolumes.Thereareseveralreferences[1,2,21]onthissubject,thatcontainmethodsgenerallyappliedinCADforextrusions,collisiondetection,andotherproblemsbutnoneofthemcanbeappliedtothenon-trivialcaseofsimultaneousmotionofthetwosolidsinplay.

Thestrategyproposedhereinovercomesthedisadvantagesofthesemethods.Itconsistsofadoublediscretizationoffourdimensionalspace（3Dþtime）thatreducesthegeneralproblemtoasequenceof2DBooleanoperationsand3Dgeometricreconstructions.Thisalgorithmisfastanditprovidesuser-controlonsimulationaccuracy.

3.Scenemodel

Therearedifferenttypesofmachinetoolsforthefabricationofboresandcutters.Theysharethesamegeneralstructurebuttheydifferinthenumberofdegreesoffreedom.Themethodproposedhereindealswithmachinesuptosixdegreesoffreedom.Thesemachineshaveastaticverticalaxis（ZinFig.1onwhichthegrindingwheelsetcanmoveupanddown.Onetoolisplacedonaspindle（thetoolholder）,thatmaytranslateonthreeaxes（X;YandU）androtateontwoaxes（WinrelationtothewheelaxisandArelativetoitsownaxis）.Atthebeginningoftheprocess,atoolhasapiecewisecylindricalorconicalshape.Itsfinalshapeistheresultofasequenceofmachiningoperationsconsistingofsimultaneousmovementsofthetoolandthewheels.Thewheelshapeisalsopiecewisecylindricalorconical.Itremainsunchangedduringtheprocess.

Themachiningprocessisdividedintoasetofoperations,eachonewithaspecificnameinCNCjargon.Eachoperationisperformedusingaspecificwheel.ThisinformationiswrittenintheCNCfile.

Specifically,themainoperationsare（intheirusualorder）:

Fig.1.6-Axesmachinetool.

Fig.2.Machiningoperationsonatool.

*Fluting:

performingthelateralhelicoidalofstraightgrooves

*Gashing:

cutsinthetoolhead

*Outerdiametersharpening:

edgesharpeningofthelateralgrooves

*Endfacesharpening:

edgesharpeningofthetoolheadcuts

*Notching:

directcutinthetoolhead.

Fig.2showsarealboreanditindicatestheoperationsthathavegivenitsshape.

Eachoperationperformsseveralsymmetricalcutsinthetoolshape.ThetoolshowninFig.2,forinstance,hasthreelateralgroovesrealizedduringthe‘Fluting’operation.Eachcutisperformedthroughasequenceofmovements.IntheCNCcode,eachmovementcorrespondstoalineinstructionspecifyingthemotionaxes（X;Y;U;A;orWforthetoolandZforthewheel）alongwiththeamountofrotationortranslationtobeperformedforeachedge.

4.Machiningsimulation

4.1.Overview

Ourapproachusesthefactthatthetoolshaveatubularshape.Itconsistsofdiscretizingthetoolinaxialsections,performingthemachiningoperationsonthesecrosssectionsandfinally,reconstructingthesurfaceof