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MILLINGAMSTERCOMPRISINGTOOLLIFECOMPAREDTOBALLMILLSH208514H20852IPANDLOFTUSH208515H20852DEMONSTRATEDTHECOMPETENCYOFANINCLINEDENDMILLMACHININGSTRATEGYON3AXISMACHINESINPRODUCINGLOWCURVATURESURFACESHOWSURFACEISDECOMPOSEDINTOTRIANGULARPATCHESANOCCUPANCYTESTOFTHEPATCHESISCONDUCTEDONATRIANGULARREPRESENTEDUNITSPHEREDOWNLOADED11DEC2009TO222190117204REDISTRIBUTIONSUBJECTTOASMELICENSEORCOPYRIGHTSEEHTTP/WWWASMEORG/TERMS/TERMS_USECFMEVER,TOMACHINEASURFACEWITHLARGECURVATUREVARIATION,ITISNECESSARYTODETERMINEASETOFMACHININGORIENTATIONSANDCARRYOUTMULTIPLE3AXISMACHININGOPERATIONSINASEQUENTIALMANNERWITHRESPECTTOEACHOFTHOSEORIENTATIONSTHEREFORE,ANEFFECTIVEMACHINABILITYANALYSISISOFCRITICALIMPORTANCETOTHESUCCESSFULIMPLEMENTATIONOFMULTIPLEORIENTATION3AXISMACHININGFORCREATINGCOMPLEXPARTSMANYRESEARCHERSHAVESTUDIEDMACHINABILITYANALYSISANDITSCLOSELYRELATEDWORKPIECESETUPPROBLEMMOSTOFTHEAPPROACHESAREBASEDONVISIBILITY,WHICHISESSENTIALLYLINEOFLIGHTACCESSIBILITYSUANDMUKERJEEH208516H20852PRESENTEDAMETHODTODETERMINEMACHINABILITYOFPOLYHEDRALOBJECTSACONVEXENCLOSINGOBJECTISCONSTRUCTEDTOMAKEEACHFACEOFTHEPARTORTHOGONALLYVISIBLETOTOGENERATEGLOBALVISIBILITYDHALIWALETALH2085115H20852PRESENTEDASIMILARAPPROACHFORCOMPUTINGGLOBALACCESSIBILITYCONESFORPOLYHEDRALOBJECTS,BUTWITHEXACTMATHEMATICALCONDITIONSANDALGORITHMSBALASUBRAMANIAMETALH2085116H20852ANALYZEDVISIBILITYBYUSINGCOMPUTERHARDWAREH20849GRAPHICSCARDSH20850FRANKETALH2085117H20852ANALYZEDTWODIMENSIONALH208492DH20850GLOBALVISIBILITYONSTEREOLITHOGRAPHYH20849STLH20850SLICESANDSEARCHEDTHENECESSARYMACHININGORIENTATIONSFORFOURTHAXISINDEXABLEMACHININGBYEXECUTINGAGREEDYSEARCHALGORITHMALLTHESEVISIBILITYBASEDAPPROACHESDETERMINETHENECESSARYCONDITIONFORMACHINABILITYHOWEVER,THEYIGNORETOOLGEOMETRYAND,THEREFORE,TRUEACCESSIBILITYH20849MACHINABILITYH20850ISNOTGUARANTEEDFIGURE1SHOWSTHATTHEACCESSIBILITYCONEH20849H9251,H9252H20850BASEDONLINEOFLIGHTVISIBILITYCANNOTGUARANTEETHETRUEACCESSIBILITYUSINGASIZEDTOOLINMACHININGASEGMENTIJSUANDMUKERJEEH208516H20852TOOKINTOACCOUNTTHECUTTERINFORMATIONBYCONSTRUCTINGANEWPARTMODELTHROUGHOFFSETTINGTHEORIGINALPARTSURFACEBYTHEAMOUNTOFTHECUTTERRADIUSMACHINABILITYWASFURTHERGUARANTEEDBYCHECKINGTHETOPOLOGYOFTHISOFFSETPARTCONTRIBUTEDBYTHEMANUFACTURINGENGINEERINGDIVISIONOFASMEFORPUBLICATIONINTHEJOURNALOFMANUFACTURINGSCIENCEANDENGINEERINGMANUSCRIPTRECEIVEDOCTOBER13,2004FINALMANUSCRIPTRECEIVEDAUGUST8,2005REVIEWCONDUCTEDBYDWCHO454/VOL128,MAY2006COPYRIGHT2006BYASMETRANSACTIONSOFTHEASMEYELIEMAILYELIIASTATEEDUMATTHEWCFRANKDEPARTMENTOFINDUSTRIALANDMANUFACTURINGSYSTEMSENGINEERING,IOWASTATEUNIVERSITY,AMES,IA50011MACHINABILITYFLATENDTHISPAPERPRESENTSOFTHESTRATEGYDETERMINES3AXISMACHININGOPERATIONSFILEGEOMETRYFROMAOFTHELINESEGMENTSORTHOGONALTOTHEAXISMACHINABILITYANALYSISRESPECTIVELYTHISMACHINABILITYANALYSISFORTHERAPIDMACHININGH20851DOI101KEYWORDSMACHINABILITY,1INTRODUCTIONMACHINABILITYANALYSISISTAKINGANINCREASINGLYIMPORTANTROLEASCOMPLEXSURFACESAREUSEDINTHEDESIGNOFAWIDEVARIETYOFPARTSCURRENTCOMPUTERAIDEDMANUFACTURINGH20849CAMH20850SOFTWAREISREADILYCAPABLEOFGENERATINGTOOLPATHSGIVENASETOFSURFACESOFAPARTANDACUTTINGORIENTATIONH208493AXISMACHININGH20850HOWEVER,DETERMININGTHESETUPORIENTATIONCANBEDIFFICULTANDMOREOVER,ITMAYBEVERYCHALLENGINGTODETERMINEIFTHEPARTCANBECREATEDUSINGMACHININGATALLANAPPROPRIATESETUPORIENTATIONCANGUARANTEEANEFFECTIVECUTTINGOFTHESURFACE,WHEREASANINAPPROPRIATEONEWILLLEAVETOOMUCHMATERIALINCERTAINREGIONSTHEADVANCEMENTOF5AXISCOMPUTERNUMERICALLYCONTROLLEDH20849CNCH20850MILLINGMACHINESSEEMSTOALLEVIATETHISSITUATIONHOWEVER,OFTENTHECOSTAND/ORDIFFICULTYOFPROGRAMMINGA5AXISMACHINEHAVELIMITEDTHEIRWIDESPREADUSETHREEAXISMACHINES,ASECONOMICALANDTECHNOLOGICALLYMATUREPIECESOFEQUIPMENT,HAVEBEENPAIDSPECIALATTENTIONWITHRESPECTTOCOMPLEXSURFACEMACHININGIFASSISTEDWITHMULTISETUPDEVICESH20849EG,APROGRAMMABLEINDEXERH20850SUHANDLEEH208511H20852USEDA3AXISMACHINEWITHAROTARYTILTTYPEINDEXERTOPROVIDEANALTERNATIVETO5AXISBALLENDMILLINGSUHETALH208512H20852PROVIDEDATHEORETICBASISFORMACHININGWITHADDITIONALAXESRECENTLY,FRANKETALH208513H20852EMPLOYEDA3AXISMILLINGCENTERWITHAFOURTHAXISINDEXERASANEFFECTIVERAPIDPROTOTYPINGMACHINEENDMILLSHAVEBEENSHOWNTOOFFERABETTERMATCHTOTHEPARTSURFACEGEOMETRY,AHIGHERMATERIALREMOVALRATE,ANDALONGERANALYSISFOR3AXISETHODFORGEOMETRICMACHINABILITYANALYSISTHEIMPLEMENTATIONTHEMACHINABILITYOFAPARTBEINGPROCESSEDUSINGAPLURALITYOFABOUTASINGLEAXISOFROTATIONFORSETUPORIENTATIONSSLICEEOLITHOGRAPHYMODELISUSEDTOMAPMACHINABLERANGESTOEACHTHEPOLYGONALCHAINSOFEACHSLICETHESLICESARETAKENOFROTATION,HENCE,BOTHTWOANDTHREEDIMENSIONAL2DAND3DISCALCULATEDFORPERPENDICULARANDOBLIQUETOOLORIENTATIONS,APPROACHEXPANDSUPONEARLIERWORKON2DVISIBILITYMANUFACTURINGANDPROTOTYPINGOFCOMPONENTSUSINGCNC115/12137748H20852TOOLACCESSIBILITY,CNCMACHINING,SLICEGEOMETRYTHEPLANESOFTHEENCLOSINGOBJECTTHEPARTISTHENCONSIDEREDTOBEMACHINABLEFROMTHENORMALVECTORDIRECTIONSOFTHEENCLOSINGOBJECTPLANESLATER,COMPUTATIONALGEOMETRYONTHESPHEREWASUTILIZEDTOANALYZEVISIBILITYBYCHENANDWOOH208517H20852WHOPERFORMEDPIONEERINGWORKONCOMPUTATIONALGEOMETRYALGORITHMSTHATCOULDBEUSEDFOR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