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DOI10.1007/s0017000423742ORIGINALARTICLEIntJAdvManufTechnol200628370–378C.L.LiK.M.YuY.H.LeeAutomaticdatumdimensioningforplasticinjectionmoulddesignandmanufacturingReceived7May2004/Accepted10August2004/Publishedonline20April2005©SpringerVerlagLondonLimited2005AbstractDatumdimensioningorordinatedimensioningtechniqueisverypopularinplasticinjectionmoulddrawingswherethelocationdimensionsofalargenumberofholefeaturesmustbespecifiedinthedrawingsofthemouldplates.AlthoughcommercialCAD/CAMsystemsprovidesemiautomatictoolstoassistthedesignerinthedimensioningprocess,itisstillaverytediousprocess,astheuserhastospecifythelocationofeachdimensiontag.Thispaperreportsacompletelyautomaticmethodwhereoptimalplacementsofthedimensiontagscanbedetermined.Themethodemploysdynamicprogrammingtechniquetooptimizethedimensionprocesswithrespecttoseveralcriteriathatcanbeselectedbytheuser.ThemethodhasbeenimplementedandincorporatedintoacommercialCAD/CAMsystem,andexamplesaregiventoillustratetheimportantfeaturesoftheprogram.KeywordsAutomaticdimensioningDatumdimensioningDynamicprogrammingOptimaldimensioningOrdinatedimensioning1IntroductionCAD/CAMsystemsarenowwidelyusedintheplasticinjectionmouldmakingindustry.Manycompaniesareusingasolidmodelingsystemtodesigntheinjectionmould.TheyuseaCADsystemtomodelnotonlythecoreandcavityinsertsofthemouldwhicharethemostimportantcomponentsthatformtheimpressionofthemould,butalsoallothercomponentsintheC.L.Lia117Y.H.LeeDepartmentofManufacturingEngineeringandEngineeringManagement,CityUniversityofHongKong,TatCheeAvenue,Kowloon,HongKongEmailmecllicityu.edu.hkTel.85227888432Fax85227888423K.M.YuDepartmentofIndustrialandSystemsEngineering,TheHongKongPolytechnicUniversityentiremouldassembly.WiththeadvanceinInternettechnologyandtherecentdevelopmentofInternetenabledCAD,thedesigninformationoftheinjectionmouldcanbecommunicatedelectronicallybetweentheproductengineerwhodesignstheplasticpartandthetoolingengineerwhodesignstheinjectionmould,eventhoughtheymaybelocatedindifferentgeographicregionsoftheworld.Whileflowofdesigninformationbetweenproductdesignandtoolingdesignarecommunicatedeffectivelythroughanelectronicmeans,thecommunicationofmanufacturinginformationtotheshopfloorisdonebybothelectronicandtraditionaltechniques.ComputerNumericalControlCNCmachiningtoolpathorinspectioninstructionscanbegenerateddirectlyfromtheCAD/CAMsystemanddownloadedthroughanetworktotheCNCcontrollerforthemachiningorinspectionoperations.However,setupinstructionsforaparticularmachiningjobmaybespecifiedinanengineeringdrawing.Moreover,notallmachiningtasksaredoneusingCNCmachinetools.Sometraditionalmachiningprocesses,suchasdrillingandgrinding,aredoneusingconventionalmachinetoolsbecauseofcostconsideration.Conventionalengineeringdrawingsarethusstillplayinganimportantroleincommunicatingengineeringinformationtotheshopfloor.TheorthographicprojectionsinengineeringdrawingscanbegeneratedautomaticallyfromtheCADmodeloftheparts.AutomatictoolsfordimensioningofthepartsarealsoprovidedbymanycommercialCADsystems.However,aspointedoutbyChenetal.1,thoseautomaticdimensioningtoolsarenotabletogeneratedimensionsaccordingtothedrawingstandardsandengineeringpracticesadoptedintheshopfloor.Inthespecificapplicationofinjectionmoulddesign,datumdimensioningorordinatedimensioningofholefeaturesareusedextensively.Figure1showsatypicaldetaildrawingthatcanbefoundontheshopfloorofamouldmakingcompany.Showninthefigurearetheholefeaturesanddatumdimensionswhichareusedtospecifythelocationsoftheholes.Itcanbeseenthatthedimensionsareverycrowdedanditisatedioustasktomanuallyadjusttheplacementofallthedatumdimensions.Thequalityofthefinalfullydimensioneddrawingthusdependsverymuchontheexperienceofthedraftsmanwhoproducesthedrawing.Thepurposeofthisresearchistodevelopatoolthatcan371Fig.1.Useofdatumdimensioninginadrawingofaplasticinjectionmouldpartgeneratethedatumdimensionsautomaticallyfromagivenpartoftheinjectionmould.Theresultingdimensionsmustsatisfytwoobviousrequirementsfirst,thatnotwodimensiontagsmayoverlapandsecond,thatadimensiontagbeplacedascloseaspossibletothefeaturebeingdimensioned.Thekeyissueinthisresearchistodevelopamethodthatcanoptimizetheplacementofthedatumdimensions.2RelatedworkWhiledimensioningandtolerancingaretwocloselyrelatedprocessesinspecifyingthesizeandlocationinformationofthefeaturesinamechanicalpartoranassembly,mostofthepastresearchworkhasfocusedontolerancing.Themajorresearchissuesintolerancingarerepresentation,analysisandsynthesis.Tolerancingrepresentationisconcernedwiththeincorporationoftoleranceinformationintoaproductmodelingscheme.ExamplesincludethesolidoffsetapproachdevelopedbyRequicha2,thefeasibilityspaceapproachproposedbyTurner3,andtheTTRSbyDesrochersandClement4.MoredetailedreviewcanbefoundinRoyetal.5andYuetal.6.Toleranceanalysisaimstodeterminethecombinedeffectofparttolerancesontheassemblytolerance.Itcanbeusedtoverifythefunctionalityofadesigngivenknownorassumedvariationsofindividualpartdimensions.ExamplesoftechniqueintoleranceanalysisincludeMonteCarlosimulation7andthedirectlinearizationmethod8.Themainobjectiveoftolerancesynthesisortoleranceallocationistoallocateparttolerancesbasedongivenfunctionalrequirementsoftheassembly.Recently,Islam9reportedaconcurrentengineeringapproachtoaddressthisproblem.Basedonasystemicanalysisofthefunctionalrequirementsfromdifferentcustomerrequirementsandthetechnicalrequirementsfromengineeringconsiderations,amethodologyforextractingdimensionalrequirementsisdeveloped.AsoftwareprototypeFDT10isalsodevelopedforsupportingtheimplementationofthemethodology.FDTprovidestoolsforrepresentingthefunctionalrequirements,dimensions,tolerancesandprocesscapabilityintoafunctionalrequirement/dimensionsmatrix.Thefunctionalequationscapturedinthematrixarethenseparatedintogroups,andeachgroupisthensolvedusingasolutionstrategyspecifictothefunctionalrequirementandthetolerancingprobleminvolved.MoredetailedreviewintoleranceanalysisandsynthesiscanbefoundinRoyetal.5,NgoiandOng11andHongandChang12.SeveralmethodshavebeendevelopedforgeneratingdimensionsautomaticallyfromtheCADmodelofapart.Yuenetal.13reportedanearlyattemptinautomaticdimensioningofpartsrepresentedinConstructiveSolidGeometryCSGsolidmodelingtechnique.Pointsfromplanarfacesandaxesofcylindersareextractedfromthesolidmodel.Thecoordinatesofthepointsarearrangedinatreestructuretogeneratelineardimensionsinthethreeprincipaldirections.Asimpletechniquefordiametricandradialdimensionswasalsoreported.OtherearlyworksinautomaticdimensioninghavebeensummarizedbyYuetal.6.Recently,Chenetal.1,14reportedamoreindepthstudyofautomaticdimensioning.Theirmethodanalyzeddimensionredundancy,determineddimensioningschemesthatarespecifictofeaturepatterns,selectedappropriateviewsforspecifyingthedimension,anddeterminedtheappropriatelocationofthedimensionusinganexpertsystemapproach15.Theexpertsystemanalysesthegeometryandtopologyofthefeaturetobedimensioned,anddeterminedapositionforplacingthedimensionbasedonasetofrulesthatisrelevanttothecurrentdimensioningfeature.Withtheplacementofonedimension,aforbiddenregionisconstructedsothatallsubsequentdimensionswillnotbeplacedinthisregion.Thisavoidsoverlaporintersectionbetweentwodimensions.372Alimitationintheexistingapproachfortheplacementofthedimensionisduetothesequentialnatureofthemethod.Forexample,inChens1,14methodthefeaturestobedimensionedareprioritized,andthepositionsofthedimensionsaredeterminedoneafteranother.Theapproachisnotappropriatefordeterminingtheplacementofdatumdimensions,especiallywhenthedimensionsareverycrowded,asinthecaseofinjectionmouldplates.Thisisbecausetheplacementofonedatumdimensionmayhaveaneffectontheplacementofanotherdimensionthatmaybelocatedfarawayfromthecurrentdimension.Thispaperreportsourworkinsolvingtheplacementproblemindatumdimensioning.Themajorcontributionofourworkisthedevelopmentofanewmethodthatdeterminestheoptimalplacementofeachdatumdimension.Usingthedynamicprogrammingapproachtooptimization,thisnewmethodovercomesthelimitationofthesequentialapproachusedintheexistingmethod.3BasiccharacteristicofdatumdimensioningIndatumdimensioning,thelocationofafeatureisspecifiedbythehorizontalandverticaldistancesfromthereferencelocationofthefeatureandareferencedatum.ThedefaultformofdatumdimensionisshowninFig.2a.Whentheverticaldistancebetweentwofeaturestobedimensionedislessthanthedimensiontagsizei.e.thesumofthedimensiontextheightandtheminimumspacingbetweenadjacentdimensiontexts,Fig.2.BasiccharacteristicsofdatumdimensioningthealternativeformsshowninFig.2barerequired.1Thedimensiontagsareshiftedupwardordownwardfromthedefaultlocationtopreventoverlap.AsshowninFig.2c,theshiftingofthedimensiontagisachievedbybreakingthesingleextensionlineofthedimensionintothreesegmentstwohorizontalsegmentswhichareconnectedbyoneinclinedsegment.Theextenttowhichadimensiontagcanbeshiftedisgovernedbythreeparametersithedoglegangleα,whichistheanglebetweentheinclinedsegmentandthehorizontalsegmentsofthedimensionlineiithemargindistancembetweenthedimensiontextandthepartboundaryandiiithelocationxfi,yfiofthefeaturefi.Thetwoextremepositionsi.e.theuppermostpositionymaxiandlowermostpositionyminiofthedimensiontagaregivenbyymaxiyfixfimtanαyminiyfi−xfimtanα14AutomaticdatumdimensionTheobjectiveoftheautomaticdatumdimensioningsystemistofindanoptimalpositionforeachdatumdimension.Theprocessconsistsoftwophasesofoperationthepreparationphaseandtheoptimizationphase.Inthepreparationphase,majorparametersthatfacilitatetheoptimizationprocesswillbeestablished.Feasibilityforplacingthedimensionsforallthefeaturesusingthegivendoglegangle,marginoffsetanddimensiontagsizewillalsobetested.Intheoptimizationphase,adynamicprogrammingapproachisused.Thedimensiontaglocationscanbeoptimizedwithrespecttodifferentsetsofcriteria,includingtheminimizationoftheshiftofeverydimensionfromtheirdefaultlocations,ormaximizationoftheuseofthedefaultformasmuchaspossible.4.1ThepreparationphaseThefeaturestobedimensionedarefirstgroupedintooneormorefeaturesets.Foreachfeatureinafeatureset,thereexistatleastoneotherfeatureinthesetsuchthattheverticaldistancebetweenthemislessthanthedimensiontagsize.Inotherwords,thefeaturesinafeaturesetcannotbedimensionedusingthedefaultformexclusivelywithoutoverlapbetweenadjacentdimensiontags.Instead,atmostonefeaturecanusethedefaultformwhileallothersrequiretheuseofthealternativeform.Thesetofdimensiontagsassociatedwithafeaturesetiscalledadimensionblock.Theconfigurationofadimensionblockreferstotheformsandlocationsofeachdatumdimensionwithinthedimensionblock.Foreachpositionofadimensionblock,itsconfigurationisuniquelydefined.Figure3showstwofeaturesetsandtheirdimensionblocksattwodifferentconfigurations.1Tosimplifytheexplanationofthetechnique,onlyverticaldimensionsplacedonthelefthandsideofthepartarediscussed.Themethoddevelopedisgeneralandcanbeappliedtotheothersidesofthepart.373Fig.3.FeaturesetsanddifferentconfigurationsofdimensionblocksDefinition1Validityofaconfiguration.Aconfigurationofadimensionblockisvalidifthereisnooverlapbetweenanydimensiontagsinthedimensionblock,andeachdimensiontaglieswithinitsextremepositions.TheconfigurationsofthedimensionblocksshowninFig.3barevalid.TwoexamplesofinvalidconfigurationareshowninFig.4.TheconfigurationshowninFig.4aisinvalidbecausetwoofthedimensiontagsoverlap.FortheconfigurationshowninFig.4b,theextensionlineofthedimensiontag14.00isatitslowermostposition,whiletherequiredpositionforthedimensiontagisbeyondthislowermostposition.Fig.4.InvalidconfigurationsofadimensionblockFig.5.DimensionblockatextremeconfigurationsDefinition2Extremeconfigurations.Therearetwoextremeconfigurationstheuppermostandlowermostconfigurations.Adimensionblockisatitsuppermostlowermostconfigurationifthedimensionblockisvalidandisatapositionsuchthatanyotherhigherlowerpositionresultsinaninvalidconfiguration.TheextremeconfigurationsofadimensionblockdiaredenotedbyYmaxiandYmini.Figure5ashowsadimensionblockatitsuppermostconfiguration.Itcannotmovefurtherupwardbecausethedimensiontag29.5isatitshighestposition.Figure5bshowsadimensionblockatitslowermostconfiguration.Itcannotmovefur
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