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外文翻译--包络法的资产负债.doc

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外文翻译--包络法的资产负债.doc

英文原文AENVELOPEMETHODOFGEARINGFOLLOWINGSTOSIC1998,SCREWCOMPRESSORROTORSARETREATEDHEREASHELICALGEARSWITHNONPARALLELANDNONINTERSECTING,ORCROSSEDAXESASPRESENTEDATFIGA1X01,Y01ANDX02,Y02ARETHEPOINTCOORDINATESATTHEENDROTORSECTIONINTHECOORDINATESYSTEMSFIXEDTOTHEMAINANDGATEROTORS,ASISPRESENTEDINFIG13ΣISTHEROTATIONANGLEAROUNDTHEXAXESROTATIONOFTHEROTORSHAFTISTHENATURALROTORMOVEMENTINITSBEARINGSWHILETHEMAINROTORROTATESTHROUGHANGLEΘ,THEGATEROTORROTATESTHROUGHANGLEΤR1W/R2WΘZ2/Z1Θ,WHERERWANDZARETHEPITCHCIRCLERADIIANDNUMBEROFROTORLOBESRESPECTIVELYINADDITIONWEDEFINEEXTERNALANDINTERNALROTORRADIIR1ER1WR1ANDR1IR1W−R0THEDISTANCEBETWEENTHEROTORAXESISCR1WR2WPISTHEROTORLEADGIVENFORUNITROTORROTATIONANGLEINDICES1AND2RELATETOTHEMAINANDGATEROTORRESPECTIVELYFIGA1COORDINATESYSTEMOFHELICALGEARSWITHNONPARALLELANDNONINTERSECTINGAXESTHEPROCEDURESTARTSWITHAGIVEN,ORGENERATINGSURFACER1T,ΘFORWHICHAMESHING,ORGENERATEDSURFACEISTOBEDETERMINEDAFAMILYOFSUCHGENERATEDSURFACESISGIVENINPARAMETRICFORMBYR2T,Θ,Τ,WHERETISAPROfiLEPARAMETERWHILEΘANDΤAREMOTIONPARAMETERSR1R1T,ΘX1,Y1,Z1X01COSΘY01SINΘ,X01SINΘY01COSΘ,P1ΘA,10,,111TYTXTR0,COSSIN,SINCOS0101011TYTXTYTXA20,,0,,01010111XYYXRA3COSSIN,SINCOS,,,,,1111122222ZYZYCXZYXTRR202020202,SINSIN,SINCOSPYXYXA42020202022222,SINCOS,SINSIN,,PYXYXPXYRSINCOS,COSSIN,COSSIN121211CXPCXPYPA5THEENVELOPEEQUATION,WHICHDETERMINESMESHINGBETWEENTHESURFACESR1ANDR20222RRTRA6TOGETHERWITHEQUATIONSFORTHESESURFACES,COMPLETESASYSTEMOFEQUATIONSIFAGENERATINGSURFACE1ISDEfiNEDBYTHEPARAMETERT,THEENVELOPEMAYBEUSEDTOCALCULATEANOTHERPARAMETERΘ,NOWAFUNCTIONOFT,ASAMESHINGCONDITIONTODEFINEAGENERATEDSURFACE2,NOWTHEFUNCTIONOFBOTHTANDΘTHECROSSPRODUCTINTHEENVELOPEEQUATIONREPRESENTSASURFACENORMALAND∂R2∂ΤISTHERELATIVE,SLIDINGVELOCITYOFTWOSINGLEPOINTSONTHESURFACES1AND2WHICHTOGETHERFORMTHECOMMONTANGENTIALPOINTOFCONTACTOFTHESETWOSURFACESSINCETHEEQUALITYTOZEROOFASCALARTRIPLEPRODUCTISANINVARIANTPROPERTYUNDERTHEAPPLIEDCOORDINATESYSTEMANDSINCETHERELATIVEVELOCITYMAYBECONCURRENTLYREPRESENTEDINBOTHCOORDINATESYSTEMS,ACONVENIENTFORMOFTHEMESHINGCONDITIONISDEfiNEDAS0211111RRTRRRTR(A7)INSERTIONOFPREVIOUSEXPRESSIONSINTOTHEENVELOPECONDITIONGIVESTYYTXXPPXC1111211COT0COT12111TXCPTYPPA8THISISAPPLIEDHERETODERIVETHECONDITIONOFMESHINGACTIONFORCROSSEDHELICALGEARSOFUNIFORMLEADWITHNONPARALLELANDNONINTERSECTINGAXESTHEMETHODCONSTITUTESAGEARGENERATIONPROCEDUREWHICHISGENERALLYAPPLICABLEITCANBEUSEDFORSYNTHESISPURPOSESOFSCREWCOMPRESSORROTORS,WHICHAREELECTIVELYHELICALGEARSWITHPARALLELAXESFORMEDTOOLSFORROTORMANUFACTURINGARECROSSEDHELICALGEARSONNONPARALLELANDNONINTERSECTINGAXESWITHAUNIFORMLEAD,ASINTHECASEOFHOBBING,ORWITHNOLEADASINFORMEDMILLINGANDGRINDINGTEMPLATESFORROTORINSPECTIONARETHESAMEASPLANARROTORHOBSINALLTHESECASESTHETOOLAXESDONOTINTERSECTTHEROTORAXESACCORDINGLYTHENOTESPRESENTTHEAPPLICATIONOFTHEENVELOPEMETHODTOPRODUCEAMESHINGCONDITIONFORCROSSEDHELICALGEARSTHESCREWROTORGEARINGISTHENGIVENASANELEMENTARYEXAMPLEOFITSUSEWHILEAPROCEDUREFORFORMINGAHOBBINGTOOLISGIVENASACOMPLEXCASETHESHAFTANGLEΣ,CENTREDISTANCEC,ANDUNITLEADSOFTWOCROSSEDHELICALGEARS,P1ANDP2ARENOTINTERDEPENDENTTHEMESHINGOFCROSSEDHELICALGEARSISSTILLPRESERVEDBOTHGEARRACKSHAVETHESAMENORMALCROSSSECTIONPROfiLE,ANDTHERACKHELIXANGLESARERELATEDTOTHESHAFTANGLEASΣΨR1ΨR2THISISACHIEVEDBYTHEIMPLICITSHIFTOFTHEGEARRACKSINTHEXDIRECTIONFORCINGTHEMTOADJUSTACCORDINGLYTOTHEAPPROPRIATERACKHELIXANGLESTHISCERTAINLYINCLUDESSPECIALCASES,LIKETHATOFGEARSWHICHMAYBEORIENTATEDSOTHATTHESHAFTANGLEISEQUALTOTHESUMOFTHEGEARHELIXANGLESΣΨ1Ψ2FURTHERMOREACENTREDISTANCEMAYBEEQUALTOTHESUMOFTHEGEARPITCHRADIICR1R2PAIRSOFCROSSEDHELICALGEARSMAYBEWITHEITHERBOTHHELIXANGLESOFTHESAMESIGNOREACHOFOPPOSITESIGN,LEFTORRIGHTHANDED,DEPENDINGONTHECOMBINATIONOFTHEIRLEADANDSHAFTANGLEΣTHEMESHINGCONDITIONCANBESOLVEDONLYBYNUMERICALMETHODSFORTHEGIVENPARAMETERT,THECOORDINATESX01ANDY01ANDTHEIRDERIVATIVES∂X01∂TAND∂Y01∂TAREKNOWNAGUESSEDVALUEOFPARAMETERΘISTHENUSEDTOCALCULATEX1,Y1,∂X1∂TAND∂Y1∂TAREVISEDVALUEOFΘISTHENDERIVEDANDTHEPROCEDUREREPEATEDUNTILTHEDIFFERENCEBETWEENTWOCONSECUTIVEVALUESBECOMESSUFFICIENTLYSMALLFORGIVENTRANSVERSECOORDINATESANDDERIVATIVESOFGEAR1PROfiLE,ΘCANBEUSEDTOCALCULATETHEX1,Y1,ANDZ1COORDINATESOFITSHELICOIDSURFACESTHEGEAR2HELICOIDSURFACESMAYTHENBECALCULATEDCOORDINATEZ2CANTHENBEUSEDTOCALCULATEΤANDfiNALLY,ITSTRANSVERSEPROfiLEPOINTCOORDINATESX2,Y2CANBEOBTAINEDANUMBEROFCASESCANBEIDENTIfiEDFROMTHISANALYSISIWHENΣ0,THEEQUATIONMEETSTHEMESHINGCONDITIONOFSCREWMACHINEROTORSANDALSOHELICALGEARSWITHPARALLELAXESFORSUCHACASE,THEGEARHELIXANGLESHAVETHESAMEVALUE,BUTOPPOSITESIGNANDTHEGEARRATIOIP2/P1ISNEGATIVETHESAMEEQUATIONMAYALSOBEAPPLIEDFORTHEGENERATIONOFARACKFORMEDFROMGEARSADDITIONALLYITDESCRIBESTHEFORMEDPLANARHOB,FRONTMILLINGTOOLANDTHETEMPLATECONTROLINSTRUMENT122AENVELOPEMETHODOFGEARINGIIIFADISCFORMEDMILLINGORGRINDINGTOOLISCONSIDERED,ITISSUFFCIENTTOPLACEP20THISISASINGULARCASEWHENTOOLFREEROTATIONDOESNOTAFFECTTHEMESHINGPROCESSTHEREFORE,AREVERSETRANSFORMATIONCANNOTBEOBTAINEDDIRECTLYIIITHEFULLSCOPEOFTHEMESHINGCONDITIONISREQUIREDFORTHEGENERATIONOFTHEPROfiLEOFAFORMEDHOBBINGTOOLTHISISTHEREFORETHEMOSTCOMPLICATEDTYPEOFGEARWHICHCANBEGENERATEDFROMITBREYNOLDSTRANSPORTTHEOREMFOLLOWINGHANJALIC,1983,REYNOLDSTRANSPORTTHEOREMDEfiNESACHANGEOFVARIABLEΦINACONTROLVOLUMEVLIMITEDBYAREAAOFWHICHVECTORTHELOCALNORMALISDAANDWHICHTRAVELSATLOCALSPEEDVTHISCONTROLVOLUMEMAY,BUTNEEDNOTNECESSARILYCOINCIDEWITHANENGINEERINGORPHYSICALMATERIALSYSTEMTHERATEOFCHANGEOFVARIABLEΦINTIMEWITHINTHEVOLUMEISVVDVTTB1THEREFORE,ITMAYBECONCLUDEDTHATTHECHANGEOFVARIABLEΦINTHEVOLUMEVISCAUSEDBY–CHANGEOFTHESPECIfiCVARIABLEM/INTIMEWITHINTHEVOLUMEBECAUSEOFSOURCESANDSINKSINTHEVOLUME,TDVWHICHISCALLEDALOCALCHANGEAND–MOVEMENTOFTHECONTROLVOLUMEWHICHTAKESANEWSPACEWITHVARIABLEINITANDLEAVESITSOLDSPACE,CAUSINGACHANGEINTIMEOFFORΡVDAANDWHICHISCALLEDCONVECTIVECHANGETHEfiRSTCONTRIBUTIONMAYBEREPRESENTEDBYAVOLUMEINTEGRALDVTVB2WHILETHESECONDCONTRIBUTIONMAYBEREPRESENTEDBYASURFACEINTEGRALADAVB3THEREFOREAVVVDAVDVTDVDTDTB4WHICHISAMATHEMATICALREPRESENTATIONOFREYNOLDSTRANSPORTTHEOREMAPPLIEDTOAMATERIALSYSTEMCONTAINEDWITHINTHECONTROLVOLUMEVMWHICHHASSURFACEAMANDVELOCITYVWHICHISIDENTICALTOTHEFLUIDVELOCITYW,REYNOLDSTRANSPORTTHEOREMREADSDAWDVTDDTDTAMVMVMVMVB5IFTHATCONTROLVOLUMEISCHOSENATONEINSTANTTOCOINCIDEWITHTHECONTROLVOLUMEV,THEVOLUMEINTEGRALSAREIDENTICALFORVANDVMANDTHESURFACEINTEGRALSAREIDENTICALFORAANDAM,HOWEVER,THETIMEDERIVATIVESOFTHESEINTEGRALSAREDIFFERENT,BECAUSETHECONTROLVOLUMESWILLNOTCOINCIDEINTHENEXTTIMEINTERVALHOWEVER,THEREISATERMWHICHISIDENTICALFORTHEBOTHTIMES

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