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DOI10.1007/s00170-004-2374-2ORIGINALARTICLEIntJAdvManufTechnol(2006)28:370378C.L.LiK.M.YuY.H.LeeAutomaticdatumdimensioningforplasticinjectionmoulddesignandmanufacturingReceived:7May2004/Accepted:10August2004/Publishedonline:20April2005Springer-VerlagLondonLimited2005AbstractDatumdimensioning(orordinatedimensioning)tech-niqueisverypopularinplasticinjectionmoulddrawingswherethelocationdimensionsofalargenumberofholefeaturesmustbespecifiedinthedrawingsofthemouldplates.Althoughcom-mercialCAD/CAMsystemsprovidesemi-automatictoolstoas-sistthedesignerinthedimensioningprocess,itisstillaverytediousprocess,astheuserhastospecifythelocationofeachdi-mensiontag.Thispaperreportsacompletelyautomaticmethodwhereoptimalplacementsofthedimensiontagscanbedeter-mined.Themethodemploysdynamicprogrammingtechniquetooptimizethedimensionprocesswithrespecttoseveralcriteriathatcanbeselectedbytheuser.Themethodhasbeenimple-mentedandincorporatedintoacommercialCAD/CAMsystem,andexamplesaregiventoillustratetheimportantfeaturesoftheprogram.KeywordsAutomaticdimensioningDatumdimensioningDynamicprogrammingOptimaldimensioningOrdinatedimensioning1IntroductionCAD/CAMsystemsarenowwidelyusedintheplasticinjec-tionmould-makingindustry.Manycompaniesareusingasolidmodelingsystemtodesigntheinjectionmould.TheyuseaCADsystemtomodelnotonlythecoreandcavityinsertsofthemould(whicharethemostimportantcomponentsthatformtheim-pressionofthemould),butalsoallothercomponentsintheC.L.Li(a117)Y.H.LeeDepartmentofManufacturingEngineeringandEngineeringManagement,CityUniversityofHongKong,TatCheeAvenue,Kowloon,HongKongE-mail:.hkTel.:+8-52-27888432Fax:+8-52-27888423K.M.YuDepartmentofIndustrialandSystemsEngineering,TheHongKongPolytechnicUniversityentiremouldassembly.WiththeadvanceinInternettechnologyandtherecentdevelopmentofInternet-enabledCAD,thede-signinformationoftheinjectionmouldcanbecommunicatedelectronicallybetweentheproductengineer(whodesignstheplasticpart)andthetoolingengineer(whodesignstheinjectionmould),eventhoughtheymaybelocatedindifferentgeographicregionsoftheworld.Whileflowofdesigninformationbetweenproductdesignandtoolingdesignarecommunicatedeffectivelythroughanelectronicmeans,thecommunicationofmanufac-turinginformationtotheshopfloorisdonebybothelectronicandtraditionaltechniques.ComputerNumericalControl(CNC)machiningtoolpathorinspectioninstructionscanbegenerateddirectlyfromtheCAD/CAMsystemanddownloadedthroughanetworktotheCNCcontrollerforthemachiningorinspectionoperations.However,set-upinstructionsforaparticularmachin-ingjobmaybespecifiedinanengineeringdrawing.Moreover,notallmachiningtasksaredoneusingCNCmachinetools.Sometraditionalmachiningprocesses,suchasdrillingandgrinding,aredoneusingconventionalmachinetoolsbecauseofcostcon-sideration.Conventionalengineeringdrawingsarethusstillplay-inganimportantroleincommunicatingengineeringinformationtotheshopfloor.TheorthographicprojectionsinengineeringdrawingscanbegeneratedautomaticallyfromtheCADmodeloftheparts.AutomatictoolsfordimensioningofthepartsarealsoprovidedbymanycommercialCADsystems.However,aspointedoutbyChenetal.1,thoseautomaticdimensioningtoolsarenotabletogeneratedimensionsaccordingtothedraw-ingstandardsandengineeringpracticesadoptedintheshopfloor.Inthespecificapplicationofinjectionmoulddesign,datumdimensioning(orordinatedimensioning)ofholefeaturesareusedextensively.Figure1showsatypicaldetaildrawingthatcanbefoundontheshopfloorofamouldmakingcompany.Showninthefigurearetheholefeaturesanddatumdimensionswhichareusedtospecifythelocationsoftheholes.Itcanbeseenthatthedimensionsareverycrowdedanditisatedioustasktomanuallyadjusttheplacementofallthedatumdimensions.Thequalityofthefinalfully-dimensioneddrawingthusdependsverymuchontheexperienceofthedraftsmanwhoproducesthedraw-ing.Thepurposeofthisresearchistodevelopatoolthatcan371Fig.1.Useofdatumdimensioninginadrawingofaplasticinjectionmouldpartgeneratethedatumdimensionsautomaticallyfromagivenpartoftheinjectionmould.Theresultingdimensionsmustsatisfytwoobviousrequirements:first,thatnotwodimensiontagsmayoverlap；andsecond,thatadimensiontagbeplacedascloseaspossibletothefeaturebeingdimensioned.Thekeyissueinthisresearchistodevelopamethodthatcanoptimizetheplacementofthedatumdimensions.2RelatedworkWhiledimensioningandtolerancingaretwocloselyrelatedpro-cessesinspecifyingthesizeandlocationinformationofthefeaturesinamechanicalpartoranassembly,mostofthepastresearchworkhasfocusedontolerancing.Themajorresearchissuesintolerancingarerepresentation,analysisandsynthesis.Tolerancingrepresentationisconcernedwiththeincorporationoftoleranceinformationintoaproductmodelingscheme.Exam-plesincludethesolidoffsetapproachdevelopedbyRequicha2,thefeasibilityspaceapproachproposedbyTurner3,andtheTTRSbyDesrochersandClement4.MoredetailedreviewcanbefoundinRoyetal.5andYuetal.6.Toleranceanaly-sisaimstodeterminethecombinedeffectofparttolerancesontheassemblytolerance.Itcanbeusedtoverifythefunctional-ityofadesigngivenknownorassumedvariationsofindividualpartdimensions.Examplesoftechniqueintoleranceanalysisin-cludeMonteCarlosimulation7andthedirectlinearizationmethod8.Themainobjectiveoftolerancesynthesisortol-eranceallocationistoallocateparttolerancesbasedongivenfunctionalrequirementsoftheassembly.Recently,Islam9re-portedaconcurrentengineeringapproachtoaddressthisprob-lem.Basedonasystemicanalysisofthefunctionalrequirementsfromdifferentcustomerrequirementsandthetechnicalrequire-mentsfromengineeringconsiderations,amethodologyforex-tractingdimensionalrequirementsisdeveloped.Asoftwarepro-totypeFDT10isalsodevelopedforsupportingtheimplemen-tationofthemethodology.FDTprovidestoolsforrepresentingthefunctionalrequirements,dimensions,tolerancesandprocesscapabilityintoafunctionalrequirement/dimensionsmatrix.Thefunctionalequationscapturedinthematrixarethenseparatedintogroups,andeachgroupisthensolvedusingasolutionstrat-egyspecifictothefunctionalrequirementandthetolerancingprobleminvolved.MoredetailedreviewintoleranceanalysisandsynthesiscanbefoundinRoyetal.5,NgoiandOng11andHongandChang12.Severalmethodshavebeendevelopedforgeneratingdimen-sionsautomaticallyfromtheCADmodelofapart.Yuenetal.13reportedanearlyattemptinautomaticdimensioningofpartsrepresentedinConstructiveSolidGeometry(CSG)solidmodelingtechnique.Pointsfromplanarfacesandaxesofcylin-dersareextractedfromthesolidmodel.Thecoordinatesofthepointsarearrangedinatreestructuretogeneratelineardimen-sionsinthethreeprincipaldirections.Asimpletechniquefordiametricandradialdimensionswasalsoreported.OtherearlyworksinautomaticdimensioninghavebeensummarizedbyYuetal.6.Recently,Chenetal.1,14reportedamorein-depthstudyofautomaticdimensioning.Theirmethodanalyzeddi-mensionredundancy,determineddimensioningschemesthatarespecifictofeaturepatterns,selectedappropriateviewsforspec-ifyingthedimension,anddeterminedtheappropriatelocationofthedimensionusinganexpertsystemapproach15.Theex-pertsystemanalysesthegeometryandtopologyofthefeaturetobedimensioned,anddeterminedapositionforplacingthedimensionbasedonasetofrulesthatisrelevanttothecur-rentdimensioningfeature.Withtheplacementofonedimension,aforbiddenregionisconstructedsothatallsubsequentdimen-sionswillnotbeplacedinthisregion.Thisavoidsoverlaporintersectionbetweentwodimensions.372Alimitationintheexistingapproachfortheplacementofthedimensionisduetothesequentialnatureofthemethod.Forexample,inChens1,14methodthefeaturestobedimen-sionedareprioritized,andthepositionsofthedimensionsaredeterminedoneafteranother.Theapproachisnotappropriatefordeterminingtheplacementofdatumdimensions,especiallywhenthedimensionsareverycrowded,asinthecaseofinjectionmouldplates.Thisisbecausetheplacementofonedatumdi-mensionmayhaveaneffectontheplacementofanotherdimen-sionthatmaybelocatedfarawayfromthecurrentdimension.Thispaperreportsourworkinsolvingtheplacementproblemindatumdimensioning.Themajorcontributionofourworkisthedevelopmentofanewmethodthatdeterminestheoptimalplacementofeachdatumdimension.Usingthedynamicpro-grammingapproachtooptimization,thisnewmethodovercomesthelimitationofthesequentialapproachusedintheexistingmethod.3BasiccharacteristicofdatumdimensioningIndatumdimensioning,thelocationofafeatureisspecifiedbythehorizontalandverticaldistancesfromthereferencelo-cationofthefeatureandareferencedatum.ThedefaultformofdatumdimensionisshowninFig.2a.Whentheverticaldis-tancebetweentwofeaturestobedimensionedislessthanthedimensiontagsize(i.e.thesumofthedimensiontextheightandtheminimumspacingbetweenadjacentdimensiontexts),Fig.2.BasiccharacteristicsofdatumdimensioningthealternativeformsshowninFig.2barerequired.1Thedi-mensiontagsareshiftedupwardordownwardfromthedefaultlocationtopreventoverlap.AsshowninFig.2c,theshiftingofthedimensiontagisachievedbybreakingthesingleexten-sionlineofthedimensionintothreesegments:twohorizontalsegmentswhichareconnectedbyoneinclinedsegment.Theex-tenttowhichadimensiontagcanbeshiftedisgovernedbythreeparameters:(i)thedoglegangle,whichistheanglebe-tweentheinclinedsegmentandthehorizontalsegmentsofthedimensionline；(ii)themargindistancembetweenthedimen-siontextandthepartboundary；and(iii)thelocation(xfi,yfi)ofthefeaturefi.Thetwoextremepositions(i.e.theuppermostpos-itionymaxiandlowermostpositionymini)ofthedimensiontagaregivenby:ymaxi=yfi+(xfi+m)tanymini=yfi(xfi+m)tan(1)4AutomaticdatumdimensionTheobjectiveoftheautomaticdatumdimensioningsystemistofindanoptimalpositionforeachdatumdimension.Theprocessconsistsoftwophasesofoperation:thepreparationphaseandtheoptimizationphase.Inthepreparationphase,majorparam-etersthatfacilitatetheoptimizationprocesswillbeestablished.Feasibilityforplacingthedimensionsforallthefeaturesusingthegivendoglegangle,marginoffsetanddimensiontagsizewillalsobetested.Intheoptimizationphase,adynamicpro-grammingapproachisused.Thedimensiontaglocationscanbeoptimizedwithrespecttodifferentsetsofcriteria,includingtheminimizationoftheshiftofeverydimensionfromtheirdefaultlocations,ormaximizationoftheuseofthedefaultformasmuchaspossible.4.1ThepreparationphaseThefeaturestobedimensionedarefirstgroupedintooneormorefeaturesets.Foreachfeatureinafeatureset,thereexistatleastoneotherfeatureinthesetsuchthattheverticaldis-tancebetweenthemislessthanthedimensiontagsize.Inotherwords,thefeaturesinafeaturesetcannotbedimensionedusingthedefaultformexclusivelywithoutoverlapbetweenadjacentdimensiontags.Instead,atmostonefeaturecanusethede-faultformwhileallothersrequiretheuseofthealternativeform.Thesetofdimensiontagsassociatedwithafeaturesetiscalledadimensionblock.Theconfigurationofadimensionblockreferstotheformsandlocationsofeachdatumdimen-sionwithinthedimensionblock.Foreachpositionofadimen-sionblock,itsconfigurationisuniquelydefined.Figure3showstwofeaturesetsandtheirdimensionblocksattwodifferentconfigurations.1Tosimplifytheexplanationofthetechnique,onlyverticaldimensionsplacedonthelefthandsideofthepartarediscussed.Themethoddevelopedisgeneralandcanbeappliedtotheothersidesofthepart.373Fig.3.Featuresetsanddifferen