机械毕业设计英文外文翻译一种关于粗糙集改进注射模具浇道的报告.docx

机械毕业设计英文外文翻译一种关于粗糙集改进注射模具浇道的报告.docx

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机械毕业设计英文外文翻译一种关于粗糙集改进注射模具浇道的报告

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AnImprovedRoughSetApproachtoDesignofGatingSchemeforInjectionMoulding

F.Shi,1Z.L.Lou,1J.G.Lu2andY.Q.Zhang11DepartmentofPlasticityEngineering,ShanghaiJiaotongUniversity,P.R.China;and2CenterofCAD,NanjingUniversityofChemicalTechnology,P.R.China

Thegateisoneofthemostimportantfunctionalstructuresinaninjectionmould,asithasadirectinfluenceonthequalityoftheinjectionproducts.Thedesignofagatingschemeincludestheselectionofthetypesofgateandcalculationofthesizesanddeterminationofthelocation,whichdependsheavilyonpriorexperienceandknowledgeandinvolvesatrial-and-errorprocess.Duetothevaguenessanduncertaintyinthedesignofagatingscheme,classicalroughsettheoryisnoteffective.Inthispaper,afuzzyroughsetmodelisproposed,whichisnotbasedonequivalentrelationshipsbutonfuzzysimilarityrelationships.Aninductivelearningalgorithmbasedonthefuzzyroughsetmodel（FRILA）isthenpresented.Comparedtodecisiontreealgorithms,theproposedalgorithmcangeneratefewerclassificationrules;moreover,thegeneratedrulesaremoreconcise.Finally,anintelligentprototypesystemforthedesignofagatingschemebasedonaninducedfuzzyknowledgebaseisdeveloped.Anillustrativeexampleprovestheeffectivenessoftheproposedmethod.

Keywords:

Fuzzyroughset;Gatingscheme;Injectionmold;

Intelligentdesign;Knowledgeacquisition

1.Introduction

Themanufacturingindustryforplasticproductshasbeengrowingrapidlyinrecentyears,andplasticsareusedwidelytosubstituteformetals.Theinjectionmouldingprocessisthemostpopularmouldingprocessformakingthermoplasticparts.Thefeedingsystem,whichisoneoftheimportantfunctionalstructures,comprisesasprue,aprimaryrunner,asecondaryrunnerandagate.Themoltenplasticflowsfromthemachinenozzlethroughthesprueandrunnersystemandintothecavitiesthroughthegate.Actingastheconnectionbetweentherunnerandthecavity,thegatecaninfluencedirectlythemouldventing,theoccurrenceofjetting,thelocationofweldlines,andwarpage,shrinkageandresidualstresses.Hence,thegatedesignisimportantforassuringthequalityofthemould.

Thedesignofagateincludestheselectionofthetypeofgate,calculationofthesizeanddeterminationofthelocation.Andthedesignofagateisbasedontheexperienceandknowledgeofthedesigners.Thedeterminationsofthelocationandsizesaremadebasedonatrial-and-errorprocess.Inrecentyears,afeature-modellingenvironmentandintelligenttechnologyhavebeenintroducedforgatedesign.LeeandKiminvestigatedgatelocationsusingtheevaluationcriteriaofwarpage,weldlinesandizodimpactstrength.Alocalsearchwasusedtodeterminethenodesofthelocationofthegate[1].SaxenaandIraniproposedaframeforanon-manifoldtopology-basedenvironment.Aprototypesystemforgatelocationdesignwasdeveloped.Thecriteriaforevaluationwerebasedongeometry-relatedparameters[2].Linselectedtheinjectionlocationandsizeofthegateasthemajorcontrolparameters,andchosetheproductperformance（deformation）astheoptimisingparameter.Combiningthetechnologiesofabductivenetworksandsimulationannealingoptimisationalgorithms,theoptimalmodelforthelocationandsizeofthegatewasconstructed[3,4].Zhouetal.establishedarulesetfordeterminingthelocationofthegatebasedonanalysisoftheplasticparts.Thelocationofthegatewasdeterminedthroughreasoningwithrules[5].Pandelidisetal.developedasystemwhichcanoptimisegatelocationbasedontheinitialgatingplans.ThesystemusedMOLDFLOWsoftwareforflowanalysis,andcontrolledthetemperaturedifferentialandthenumberofelementsoverpackedwithanoptimisationstrategy[6].

DengusedID3anditsmodifiedalgorithmstogeneratetherulesetfortheselectionofthegatetypes[7].However,therearemanyfuzzyorvagueattributesintheselectionofthetypes,suchastheattributeoflossofpressurethathastwofuzzylinguisticvariablesi.e.canbehighandmustbelow.TheID3algorithmscannotdealwithfuzzyor“noise”informationefficiently.Itisalsodifficulttocontrolthesizeofthedecisiontreeextractedbythealgorithmsandsometimesverylargetreesaregenerated,makingcomprehensibilitydifficult[7,8].

Roughsettheoryprovidesanewmathematicalapproachtovagueanduncertaindataanalysis[9,10].Thispaperintroducesthetheoryofroughsetsforthedesignofagatingscheme.Theselectionofthetypeofgateisbasedonthetheoryofroughsets.Consideringthelimitationsofroughsets,thispaperproposesanimprovedapproachbasedonroughsettheoryforthedesignofthegatingscheme.Theimprovedroughsetapproachtotheschemedesignwillbegivenfirst.Afuzzyrough-set-basedinductivelearningalgorithm（FRILA）,whichisappliedintheimprovedapproach,willthenbepresented.Anexampleofthedesignofagatewillfinallybegiven.

Table1.Classificationcriteria.

Conditionattributes

Fuzzylinguisticvariables

Styleofplasticparts（p）

（Deep,Middle,Shallow）Shell,（Deep,Middle,Shallow）Tube,（Deep,Middle,Shallow）

Ring

Numberofcavities（n）

Single-cavity,Multi-cavity

Lossofpressure（l）

Canbehigh,Mustbelow

Conditionofseparatinggatefromparts（q）

Mustbeeasy,Notrequestspecially

Machiningperformance（m）

Mustbeeasy,Notrequestspecially

2.ARoughSetApproachtoGatingSchemeDesign

2.1DesignoftheGatingScheme

Themodelofthegatingschemedesigncanbedescribedasfollows.Adecisiontablewith4-tuplescanberepresentedasT=（U,C,D,T）.whereUistheuniverse.C={C1,C2,…,Ck}isthesetofconditionattributes,eachofwhichmeasuressomeimportantfeatureofanobjectintheuniverseU.T（Ck）={Tk1,T2k,...,TkSk}isthesetofdiscretelinguisticterms.Inotherwords,T（Ck）isthevaluesetoftheconditionattributes.D={D1,D2,…,Dl}isthesetofdecisionattributes,thatis,eachobjectintheuniverseisclassifiedbythesetD.

Generally,theconditionattributescanbeclassifiedasfivesets,includingstyleofplasticparts,numberofcavities,lossofpressure,conditionofseparatinggatefrompartsandmachineperformance.ThedetailsofthefiveconditionattributesandcorrespondingvariablesofthefuzzylinguisticareshowninTable1.

Fromthetable,itcanbeseenthatmostoftheattributesarevaguesincetheyrepresentahumanperceptionanddesire.Forinstance,shell,tubeandringareselectedfortheclassificationofplasticpartsandtheirfuzzylinguisticvaluesare“deep”,“middle”and“shallow”,respectively.Fortheattributelossofpressure,“canbehigh”and“mustbelow”areselectedtoapproximatethefuzzyattribute.

Afuzzyruleforgatingschemedesigncanbewritteninthefollowingform:

IF（C1isT1i1）AND…（CkisTik）THEN（DisDj）

（1）whereTkikisthelinguistictermofconditionattributeCk,andDjisaclasstermofthedecisionattributeD.

FuzzyruleswiththeformofEq.

（1）areusedtoperformmin-maxfuzzyinference.LetckbethemembershipvalueofanobjectinTkanddbetheforecastvalueofDj,whered=ikmin（ck）andministheminimumoperator.Iftwoormoreruleshavethesameconclusion,theconclusionwiththelargestvalueofd,whichisalsonamedthecertaintyfactorischosen.

Fortheproblemofthegatingschemedesign,afuzzydesignrulecanbedescribedasfollows.

IF（Typeofplasticpart=middleshell）

AND（Numberofcavities=single）

AND（Conditionofseparatinggatefrompart=notrequestespecially）

（2）

THEN（Gatingscheme=straightgate）

CF=0.825

Fromtheaboverule,thegatingschemeofthestraightgatewillbeselectedisswithacertaintyfactorof0.825,ifthetypeofpartismiddleshellandthenumberofcavitiesissingleandtheconditionofseparatinggatefrompartisnotrequired.Theaboveisjustlikehumanlanguageandiseasytounderstand.

2.2BasicConceptsofRoughSets

Inrecentyears,theroughset（RS）theory,proposedbyPawlak,hasbeenattractingtheattentionoftheresearchers.ThebasicideaofRSistoclassifytheobjectsofinterestintosimilarityclasses（equivalentclasses）containingindiscernibleobjectsviatheanalysisofattributedependencyandattributereduction.Theruleinductionfromtheoriginaldatamodelisdata-drivenwithoutanyadditionalassumptions.Roughsetshavebeenappliedinmedicaldiagnosis,patternrecognition,machinelearning,andexpertsystems[10,11].

Adecisiontablewitha4-tuplecanberepresentedasT=,whereUistheuniverse,

CandDarethesetsofconditionanddecisionattributes,respectively,VisthevaluesetoftheattributeainA,andfisaninformationfunction.

Assumingasubsetofthesetofattributes,twoobjectsxandyinUareindiscerniblewithrespecttoPifandonlyif

.TheindiscernibilityrelationiswrittenasIND（P）.U/IND（P）isusedtodenotethepartitionofUgiventheindiscernibilityrelationIND（P）.

Aroughsetapproximatestraditionalsetsbyapairofsets,whicharethelowerandtheupperapproximationsofthesets.ThelowerandupperapproximationsofasetY.UgivenanequivalencerelationIND（P）aredefinedasfollows:

Thedefinitionofthelowerapproximationofasetinvolvesaninclusionrelationwherebytheobjectsinanequivalenceclassoftheattributesareentirelycontainedintheequivalenceclassforthedecisioncategory.Thisisthecaseofaperfectorunambiguousclassification.Fortheupperapproximation,theobjectsarepossiblyclassifiedusingtheinformationinattributesetP.