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外文翻译--工业机器人 英文版.pdf

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外文翻译--工业机器人 英文版.pdf

JOURNALOFOPTOELECTRONICSANDADVANCEDMATERIALSVOL8,NO5,OCTOBER2006,P17361740THERESIDUALSTRESSESOFFEBSITYPEINANINGOTMOULDIAŞTEFĂNOAEI,DRADU,HCHIRIACAABA“ALICUZA”UNIVERSITY,CAROLIBLVD,11,700506,IASI,ROMANIABNATIONALINSTITUTEOFRESEARCHANDDEVELOPMENTFORTECHNICALPHYSICS,47MANGERONBLVD,700050IASI,ROMANIAINTHISPAPERWEANALYSEDTHEINTERNALRESIDUALSTRESSESTHATAPPEARDURINGTHERAPIDCOOLINGOFAFEBSITYPEALLOY,LAININTHEINTERIORCHANNELOFANINGOTMOULDWHOSEEXTERIORWALLSAREMAINTAINEDATTHEROOMTEMPERATURETHETHEORETICALMODELPRESENTEDINTHEPAPEREMPHASIZESINACOMPLETEANDSYNTHETICALMANNER,THESPATIOTEMPORALDISTRIBUTIONOFTHEINDUCEDSTRESSESINAFEBSITYPEALLOYDURINGITSCOOLINGTOTHEROOMTEMPERATURE,TAKINGINTOACCOUNTBOTHTHETHERMALBEHAVIOUROFTHEALLOYANDTHESUPPLEMENTARYSTRESSESINDUCEDBYTHEINGOTMOULD,ASARESULTOFTHEDIFFERENCEBETWEENTHETHERMALEXPANSIONCOEFFICIENTSOFTHETWOMATERIALSINCONTACTRECEIVEDSEPTEMBER6,2006;ACCEPTEDSEPTEMBER13,2006KEYWORDSRESIDUALSTRESSES,INGOTMOULD,THERMALGRADIENTS1INTRODUCTIONTHEAIMOFTHISPAPERISTOEVALUATEOFTHETHERMALSTRESSESDURINGTHECOOLINGOFANALLOYINTHEINNERVERTICALCHANNELOFANINGOTMOULD,WHOSEEXTERIORWALLSAREMAINTAINEDATTHEROOMTEMPERATURE,MOREPRECISELY,OURPURPOSEISTODETERMINETHESPATIOTEMPORALDISTRIBUTIONOFTHESTRESSESTHATAPPEARDURINGTHERAPIDCOOLINGOFTHEWHOLEMATERIALTOTHETEMPERATURETHISMODELCONTAINSTWOIMPORTANTTASKS1THEEVALUATIONOFTHESPATIOTEMPORALTEMPERATURE’SDISTRIBUTIONDURINGTHERAPIDCOOLING1,2,3OFTHEMATERIALTOTHEROOMTEMPERATUREFORDIFFERENTVALUESOFTHERADIUSOFTHEINNERCHANNEL,TAKINGINTOACCOUNTTHETHERMALCONDITIONSONTHEALLOYINGOTMOULDINTERFACE,WEANALYZEDTHESPATIALANDTEMPORALEVOLUTIONOFTHETEMPERATURE;2STARTINGFROMTHESPATIOTEMPORALDISTRIBUTIONOFTHETEMPERATURE,ONECANOBTAINTHESTRESSESDUETOBOTHRAPIDCOOLINGBIGTHERMALGRADIENTSANDCONSTRAINTSPRODUCEDTOTHEALLOYBYTHECOOLEDINGOTMOULDASARESULTOFADIFFERENCEBETWEENTHETHERMALEXPANSIONCOEFFICIENTSOFTHETWOMATERIALS300WTKWTTHETHEORETICALMODELPRESENTEDHEREISBASEDONTHEFOLLOWINGWORKINGHYPOTHESESITHEFORMTHEGEOMETRYOFTHEFLOWINGCHANNELOFTHEMELTEDMETAL/ALLOYWITHACYLINDRICALSYMMETRYDEMANDSACYLINDRICALCOORDINATESSYSTEM,,RΘZ,WITHTHEAXISPOINTEDVERTICALLYDOWNWARD,ALONGWITHTHEINGOTMOULDCHANNELANDTHEZRCOORDINATEALONGITSRADIALDIRECTION;IIWECONSIDERTHELENGTHLOFTHEINGOTMOULDFLOWINGCHANNELMUCHBIGGERTHANITSRADIUS,,2R2LR;IIITHEMATERIALMADEFROMAFEBSIALLOYHASATTHEINITIALMOMENTTHETEMPERATUREANDIVWEASSUMETHATTHEREARENOTEMPERATUREGRADIENTSALONGTHEINGOTMOULDCHANNELTHECHARACTERISTICSOFTHEALLOYARE2,3ISTHESPECIFICHEAT,ISTHETHERMALCONDUCTIBILITY,1200MTKKK3530/PCJKG130/KWM37210/MKGMΡ⋅ISTHEMASSDENSITY,112210/ALLOYENM⋅ISTHEYOUNG’SMODULUSANDISTHETHERMALEXPANSIONCOEFFICIENTTHECHARACTERISTICOFTHEINGOTMOULDARE2,368710ALLOYKΑ−−⋅1MK2383/KWISTHETHERMALCONDUCTIBILITY,15LCMISTHELENGTH,61710CU1KΑ−−⋅ISTHETHERMALEXPANSIONCOEFFICIENT,1021310/INGOTENM⋅ISTHEYOUNG’SMODULUS,11RMMISTHERADIUSOFTHEINNERVERTICALCHANNELAND25RMMISTHETOTALRADIUS2THERAPIDCOOLINGPROCESSOFTHESOLIDIFIEDALLOY21THETEMPERATUREDISTRIBUTIONINTHEALLOYINGOTMOULDSYSTEMTEMPERATUREDISTRIBUTIONINTHEALLOYINTHEFOLLOWINGITISANALYSEDTHERAPIDCOOLINGOFTHESOLIDIFIEDMETALFROMTHETEMPERATURETOTHEROOMTEMPERATUREASITWILLBESHOWN,FROMAMATHEMATICALPOINTOFVIEW,WEMAYCONSIDERTHISASAPROBLEMOFCONDUCTIONANDTHERMALTRANSFERWITHASOURCE,ANDITIMPLIESTHEDETERMINATIONOFTHESPATIOTEMPORALDISTRIBUTIONOFTHETEMPERATUREGT1TR,TOFTHESOLIDIFIEDMATERIAL,WHICHHASINTHECENTEROFTHEINGOTMOULD’SCHANNELTHETEMPERATUREGTGT800KISTHESOLIDIFICATIONTEMPERATURE;THESOURCEISDISTRIBUTEDONTHEINNERSURFACEOFTHEINGOTMOULD’SWALL,HAVINGTHETEMPERATURETHEHEATLOSSESOFTHEALLOYDUETOITSFORCEDCOOLINGMAYBECONSIDEREDASUNIFORMLYDISTRIBUTEDNEGATIVESOURCESTHEDETERMINATIONOFTHETEMPERATUREDEMANDSTOFINDTHESOLUTIONOFTHETHERMALBALANCEEQUATIONFORTHEMATERIALSUBMITTEDTOARAPIDCOOLINGPROCESSWT1TR,TTHERESIDUALSTRESSESOFFEBSITYPEINANINGOTMOULD17372111121WTTTABTTRRR⎛⎞∂∂∂−−⎜⎟∂⎝⎠1RR≤≤,FOR0,1WHERE1/ΡMPAKC,,/BAPLV21ARΠ,12PRΠANDLISTHEINGOTMOULD’SLENGTHTHEGENERALSOLUTIONOFEQ1ISOFTHEFORM2210,/−−MATWTRTTCIRBAME,WHEREISANINTEGRATIONCONSTANT,C20/−IRBAMAREMODIFIEDBESSELFUNCTIONSOFTHEZEROORDERANDTHECONSTANTWILLBEDETERMINEDFROMTHETHERMALCONDITIONSONTHEINTERFACEALLOY–INGOTMOULDBYIMPOSINGTHEPARTICULARCONDITIONSM10,0GTRTTAND100TRR∂∂ONECANOBTAINTHEEXPRESSIONFORTHECONSTANTCGWCTT−,WHICHLEADSUSTOTHEEXPRESSIONOFTHETEMPERATUREDISTRIBUTIONINTHEMATERIAL2210,/MATWGWTRTTTTIRBAME−−−2THETEMPERATUREDISTRIBUTIONINTHEINGOTMOULD’SWALLDURINGTHECOOLINGPROCESS,THEINGOTMOULD’SWALLRECEIVESTHEHEATAMOUNTFROMTHECOOLINGALLOYWEWILLCONSIDERTHETEMPERATUREDISTRIBUTIONINTOTHEINGOTMOULD’SWALLOFTHEFORM421,LNTRTARA2,3WHERE1AAND2AAREVARIABLESDEPENDINGONTHETIMET11AAT≡,22AAT≡BOUNDARYCONDITIONSFORTHEALLOY–INGOTMOULDINTERFACEINORDERTODETERMINETHEFINALEXPRESSIONSOFTHETEMPERATURESANDWEMUSTUSETHEFOLLOWINGBOUNDARYCONDITIONS1,TRT2,TRTITHEHEATFLUXFROMTHEALLOYISRECEIVEDBYTHEINGOTMOULDTHISHEATFLUXFROMTHEALLOYINGOTINTERFACEMUSTBECONTINOUSSO,FOR,WEMUSTHAVE1RR1211∂∂TTRRRRRRKK,4WHEREANDARETHECOEFFICIENTSOFTHERMALCONDUCTIVITYOFTHEALLOYANDINGOTMOLD,RESPECTIVELY;1K2KIIONTHEALLOYINGOTINTERFACE,THETEMPERATURESFROMTHEADJACENTREGIONSMUSTBEEQUAL1RR112TRRTRR1,5IIIONTHEOUTERSURFACEOFTHEINGOTMOULD,WECONSIDERTHATWEHAVETHEROOMTEMPERATURE,THATIS22WTRRT6USINGTHEBOUNDARYCONDITIONSGIVENBY4AND6,WEOBTAINTHEFOLLOWINGEXPRESSIONSFOR1AAND2A211212211///−−−−GWATKKRTTBAMIRBAMEXPAMT,72212122112///LN−−−−−WGWATTKKRTTBAMIRBAMREXPAMT,8ANDFROMCONDITIONS5WEOBTAINTHECONSTANTASTHESOLUTIONOFEQUATIONM220111221112////LN/−−−IRBAMKRKBAMIRBAMRR,9WHERE211/−IRBAMAREMODIFIEDBESSELFUNCTIONSOFTHEFIRSTORDERINORDERTODETERMINETHESTRESSESWHICHAPPEARDURINGTHECOOLINGPROCESSOFTHEALLOYPLACEDINTOTHEINGOTMOULD,WEWILLCONSIDERTHETEMPERATUREDISTRIBUTIONINTHEALLOY2,WHERETHECONSTANTISGIVENBYTHESOLUTIONOFEQ9M22THEINTERNALSTRESSESWHICHAPPEARDURINGTHEFORCEDCOOLINGPROCESSINTHISSECTION,OURPURPOSEISTOANALYZETHESTRESSESWHICHAPPEARBOTHDUETOTHETHERMALGRADIENTSANDFROMTHECONSTRAINTSPRODUCEDONTHEALLOYBYTHECOOLEDINGOTMOULD’SWALLASARESULTOFTHEDIFFERENCEBETWEENTHETHERMALEXPANSIONCOEFFICIENTSOFTHETWOMATERIALSINCONTACTTHERADIALTEMPERATUREGRADIENTSLEADTOTHEAPPEARANCEOFSOMEDISPLACEMENTS,BOTHINALLOYANDANDINTHEWALLOFTHEINGOTANDTHESEDISPLACEMENTSSATISFYTHEDIFFERENTIALDISPLACEMENTS’EQUATIONINCYLINDRICALCOORDINATESTHESEEQUATIONSREADS5ALLOYRUALLOYZUINGOTRUINGOTZU11,111ALLOYRALLOYDURDTRTDDRRDRDRΑ⎡⎤⎢⎥−⎣⎦,2,ALLOYZDUCONSTDZ10FORALLOYANDIAŞTEFĂNOAEI,DRADU,HCHIRIAC1738110INGOTRDURDDRRDR⎡⎤⎢⎥⎣⎦,2,INGOTZDUCONSTDZ11FORTHEINGOTMOULD’SWALLINTHEABOVERELATIONSALLOYΑISTHEALLOY’STHERMALEXPANSIONCOEFFICIENTSANDISTHEPOISSON’SCOEFFICIENTITISASSUMEDTHATTHEVALUESOFPOISSON’SCOEFFICIENTFORALLOYANDINGOTMOULDARETHESAME1/3ALLOYINGOT6ASITWILLBESHOWNINSECTION3,THETHERMALGRADIENTSINTOTHEINGOTMOULD’SWALLARESMALL,COMPAREDTOTHETHERMALGRADIENTSINTHEALLOY;THISALLOWSUSTOFURTHERCONSIDER,INTHECALCULATIONOFTHESTRESSES,ONLYTHECONSTRICTION/DILATATIONEFFECTSOFTHEINGOTMOULDOVERTHEALLOY,DUETOTHEDIFFERENTCOOLINGOFTHETWOMATERIALSINCONTACTTHESOLUTIONSOFEQS10AND11REPRESENTINGBOTHTHERADIALANDTHEAXIALDISPLACEMENTSINTHEALLOYANDANDRESPECTIVELY,THERADIALANDAXIALDISPLACEMENTSINTHEINGOTMOULDANDLEADUS6TOTHEFOLLOWINGEXPRESSIONSOFTHESTRESSESFORTHEALLOYANDFORTHEINGOTMOULD’SWALLALLOYRUALLOYZUINGOTRUINGOTZU1120,,1RALLOYALLOYALLOYRRALLOYERTECRTRTDRRΑΣ−−∫,11,,1ALLOYZZALLOYALLOYALLOYRTECETRTΣΑ−−1211201,,1,1RALLOYALLOYALLOYALLOYALLOYALLOYERTECRTRTDRRETRTΘΘΑΣΑ−−∫−,222,1INGOTRRINGOTINGOTRTECECRΣ⎡⎤−⎣⎦,223,1INGOTINGOTINGOTRTECECRΘΘ⎡⎣⎤⎦,132,2INGOTZZINGOTRTECΣWHEREANDARETHREEINTEGRATIONCONSTANTSWHICHWILLBECALCULATEDFROMTHEEQUILIBRIUMCONDITIONSANDFROMTHECONDITIONWHICHCONSIDERSTHEDIFFERENTTHERMALBEHAVIOUROFTHETWOMATERIALSINCONTACTTHERESULTANTSTRAINDUETOTHECOOLINGOFTWOMATERIALSWITHDIFFERENTTHERMALEXPANSIONCOEFFICIENTSWHICHAREINCONTACTDURINGTHEENTIRECOOLINGPROCESSISGIVENBYTHERELATION1,C2C3CALLOYINGOTALLOYINGOTTΕΕΕΑΑ∆−−INOURCASE,FORTHEALLOYWEHAVEALLOYALLOYTΕΑ∆ANDFORTHEINGOT’SWALL,INGOTINGOTTΕΑ∆,WHEREALLOYΕANDINGOTΕARETHESTRAINSDUETOTHETHERMALCONTRACTIONINTHEALLOYANDINGOTRESPECTIVELLYANDINGOTΑISTHETHERMALEXPANSIONCOEFFICIENTOFTHEINGOTINTHISCASE,ISTHEDIFFERENCEBETWEENTHET∆GTANDTHEROOMTEMPERATURE,INORDERTODETERMINE,ANDWEMUSTFINDTHEVALUESOFTHECONSTANTSANDFORTHEALLOY–INGOTMOULDINTERFACEWEIMPOSETHEFOLLOWINGCONDITIONSWT,ALLOYRRRTΣ,ALLOYRTΘΘΣ,ALLOYZZRTΣ1,C2C3C1THESTRAINSTHATAPPEARINTHISPROCESSAREDUEONLYTOTHEDIFFERENCEBETWEENTHETHERMALEXPANSIONCOEFFICIENTSOFTHEALLOYANDINGOT11ALLOYINGOTRRURRURRR−Ε11;142THEEQUILIBRIUMCONDITIONSATTHEALLOY–INGOTMOULDINTERFACE1,,ALLOYINGOTRRRRRRTRRTΣΣAND153ONTHEEXTERIORSURFACEOFTHEINGOTMOULD2RR2,INGOTRRRRTΣ0FROMTHESETHREEPARTICULARCONDITIONS,ONECANOBTAINTHENUMERICALVALUESFORTHECONSTANTSANDWHICHALLOWUSTODETERMINETHESTRESSES12INTHEALLOY,DURINGTHECOOLING,1C2C3C3RESULTSANDDISCUSSIONFORTHEGIVENABOVECHARACTERINSTICSOFTHEFEBSITYPEALLOYANDOFANINGOTMOULDWITHCOPPERWALL2,WECALCULATEDTHECONSTANTS1AAND2A,ANDWEALSODETERMINEDTHECONSTANTBYSOLVINGEQ9INTHEFOLLOWING,WEWILLCONSIDERANINGOTMOULDWITHTHEINNERCHANNEL’SRADIUSM11RMANDTHETHICKNESSOFTHEWALL;THUS,WEWILLCALCULATETHERADIALTEMPERATUREDISTRIBUTIONATDIFFERENTMOMENTSFIG1SHOWSTHESHAPEOFTHERADIALDISTRIBUTIONOFTHETEMPERATURE,BOTHINTHETRANSVERSALSECTIONOFTHEALLOYTHEREDCURVESANDINTHEINGOTMOULD’SWALLTHEBLUECURVES,ATTHREEDIFFERENTMOMENTS,IE202TSANDRESPECTIVELYASTHISFIGURESHOWS,THEREISADIFFERENCEINTHETEMPERATUREBETWEENTHECENTEROFTHECHANNELANDITSINNERSURFACE;THISDIFFERENCEISBIGGERINTHEFIRSTSTAGESOFTHECOOLINGPROCESSANDITBECOMESLESSSIGNIFICANTATTHEENDOFTHEPROCESSFIG1THERADIALDISTRIBUTIONOFTHETEMPERATUREINTHEMOULD’STRANSVERSALSECTIONONECANOBSERVETHATINTHEFIRSTMOMENTSOFTHEALLOY’SCOOLING,THEAMOUNTOFHEATDELIVEREDISBIGGER;THISTHERESIDUALSTRESSESOFFEBSITYPEINANINGOTMOULD1739SLEADSTOBIGGERTEMPERATUREGRADIENTSFORDIFFERENTVALUESOF,THERADIALDISTRIBUTIONOFTEMPERATUREINTHEINGOTMOULD’SWALLEVOLVESASFOLLOWSAFTERTHETIMET101T,THEDIFFERENCEOFTEMPERATUREBETWEENTHEINNERWALLOFTHEINGOTMOULDANDTHEEXTERIORONEIS,WHILEFOR1227RRT∆KS303T,THISDIFFERENCEISMUCHSMALLERFIG2SHOWSTHERADIALDISTRIBUTIONOFTEMPERATUREINTHEINGOTMOULD’SSECTIONBOTHINTHEALLOY’STRANSVERSALSECTIONANDINTHEINGOTMOULD’SWALLATATIME124RRT∆KS101T,FORTHREEVALUESOFTHERADIUSOFTHEINNERCHANNEL11RMM,13RMMAND14RMMRESPECTIVELYFIG2THE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