机械设计外文翻译英文原文1

Studyoncascadedwhole-leafspringoscillationmechanismformouldincontinuouscastingL.-P.Zhang*1,X.-K.Li2,Y.-F.Yao2andL.-D.Yang3Adesignmethodofacascadedwhole-leafspringmechanismisproposed,whichisanewoscillationguidancedeviceforthemouldincontinuouscasting.Thenitsprototypedesignedinthispaperisproducedinthelab,ofwhichkinematicsanddynamicssimulationsarecarriedoutbasedontherigid–flexiblecouplingvirtualmodel.Simulationcurvesofthedisplacementandvelocityofthemouldarealmostconsistentwiththeidealones,whichverifiesthemodelbuiltinthispaperisrational.Furthermore,naturalfrequenciesandmodeshapesofthemechanismarecalculatedbydynamicssimulation,andforcesappliedonleafspringsandrevolutejointsareanalysedandeffectsofthebasicparametersontheseforcesarealsostudied,whichestablishthebasisforfurtherstudiesandnextapplicationofthismechanism.Keywords:Continuouscasting,Mould,Cascadedwhole-leafspringoscillationmechanism,Designmethod,DynamicsanalysisIntroductionTheoscillationsystemforthemouldisthekeyequipmenttothemoderncontinuouscastingtechnol-ogy,ofwhichthetechnicalperformanceandreliabilitydirectlyaffectthequalityandproductionofcontinuouscastingslabs.Theoscillationsystemiscomposedoftheoscillationgeneratingdeviceandguidingmechanism,andthelatterisstudiedinthispaper.Duringcontinuouscasting,theoscillationguidingmechanismplaysaguidanceroleinthemotionofthemould.Onlywhenthemouldvibratesalongthecorrecttrack,thequalityofthestrandcanbeensured.Sothestrandrequiresveryhighguidanceaccuracyoftheoscillationguidingmechanismforthemould.Butforinevitablegapandwearofthebearings,thefour-eccentricaxesandfour-barlinkageoscillationmechanismswidelyusedinmoderncastingwillcauseuncontrolleddeviationinmotionsofthemould,whichbadlyaffectsthequalityofthestrand.1Therefore,thesemi-andwhole-leafspringmechanismsaregraduallyusedasguidancemechanismsforthemouldinbilletandslabcontinuouscasting.2,3Inrecentyears,withfurtherdevelopmentofthesemi-andwhole-leafspringoscilla-tionmechanisms,thecascadedwhole-leafspringoscilla-tionmechanismisdevelopedabroad,4whichhasalongerlife,higherlateralrigidityandreliabilityandsoon.However,untilnow,reportsonthisoscillationmechanismarefew.5,6Itsworkingprinciplehasbeenproposedbytheauthors,7basedonwhichdesignmethodofthecascadedwhole-leafspringoscillationmechanismisproposedinthispaperanditsexperi-mentalprototypeismanufactured.Furthermore,therigid–flexiblecouplingvirtualmodelofthecascadedwhole-leafspringoscillationmechanismisbuiltanditskinematicsanddynamicssimulationsareanalysedusingmanytypesofsoftware,suchasANSYS.Systemmodesandtheforcesappliedonleafspringsandrevolutejointsofthemechanismareanalysed,whichestablishthebasisforfurtherstudiesandapplicationofthismechanism.Workingprincipleofcascadedwhole-leafspringguidancemechanismThestructureofthecascadedwhole-leafspringoscilla-tionmechanismisshowninFig.1.Itmainlyconsistsofthecascadedleafspring,vibrationtableandframe,whichcanbedrivenbymachinery(Fig.1a,orhydraulicsservo(Fig.1b,generatingdeviceofsinusoi-dalornon-sinusoidaloscillation.Andthecascadedleafspringiscomposedoffoursteelplatespringsdividedintotwosets.Allleafsprings’extensionlinesjointothecirculararccentreofthecontinuouscasterandtheirendsareseparatelyconnectedtothevibrationtableandtheframe,asshowninFig.2,andthentwosetsofleafsprings,thevibrationtableandtheframeformtwofour-barlinkageguidancedevices.Duringthemouldvibrat-ing,flexibleleafspringsproduceelasticdeformations,whichmaketwoleafspringfour-barlinkageguidancedevicesalternatelyplayaguidanceroleinthemouldwithoutanyinterferencebythegeneratingdevice.71TheMechatronicsandInformationEngineeringSchool,FoshanUniversity,Foshan528000,China2CollegeofMechanicalEngineering,YanshanUniversity,Qinhuangdao066004,China3No.2ResearchDevelopmentDepartment,Xi’anHeavyMachineryResearchInstitute,Xi’an710032,China*Correspondingauthor,emailzhanglpok@204ß2010InstituteofMaterials,MineralsandMiningPublishedbyManeyonbehalfoftheInstituteReceived14November2008;accepted16September2009DOI10.1179/030192309X12573371383677IronmakingandSteelmaking2010VOL37NO3Designofcascadedwhole-leafspringoscillationmechanismFromworkingprincipleofthecascadedwhole-leafspringoscillationmechanism,itcanbeseenthattwoleafspringfour-barlinkagescarryontheguidancetothemould.Ifdesignisunreasonable,themotionofthetwoleafspringfour-barlinkageswillinterfereduringvibration,whichwillblockthemould.Therefore,howtodesignthesetwoleafspringfour-barlinkagesbecomesthekeyproblem.Designmethodofcascadedwhole-leafspringoscillationmechanismAccordingtothecharactersofthecascadedwhole-leafspringmechanismdevelopedfromtheshort-armfour-barlinkage,itsdesignmethodisproposedasfollowing:(ibasedonthedesignprinciplesoftheshort-armfour-barlinkagesimulatingarc,8designtworigidfour-barlinkagesunderthesamebasicpara-metersofthemouldbyoptimumdesign,whichfulfiltherequirementforguidingaccuracyofthemouldsimulatingarc(iiforsettlinginterferenceofthetwofour-barlinkages,rigidlinkagesoptimisedinstep(iaresubstitutedbysteelplatespringswithelasticdeformationandthenformtwoleafspringfour-barlinkages(iiibasedonthebasicprinciplesoftheshort-armfour-barlinkage,arrangetwoleafspringfour-barlinkagesaccordingtoFig.2.Thatis,end-pointsA1,C1andA2,C2arefixedontheframe;endpointsB1,D1andB2,D2areconnectedtothevibrationtableofthemould.Inthisway,twoleafspringfour-barlinkagesarecascaded,soacascadedwhole-leafspringmechanismisdesigned.CalculationexampleCalculationsofparametersandguidanceaccuracyofrigidfour-barlinkagesAccordingtothegeometryrelationsandthemovementrelationshipsofthefour-barlinkageguidancedevicesofthearccaster(seeFig.2,thepositionofanypointonthemouldcanbecalculatedduringthemouldvibration.Inthispaper,takenthebottompointEontheouterarcofthemouldasanexample,formulasofthetrackandtheguidingaccuracyofpointEarededuced,aslistedinTable1,withonlyonerigidfour-barlinkageguidingforthemould.Tocalculateconveniently,itisassumedthatl1,l2,l3andl4arerespectivelythelengthsoflinkagesofA1C1,A1B1,B1D1andC1D1,andA2C2,A2B2,B2D2andC2D2;Sistheamplitudeofthemould;DQistheswingangleofthelinkageofB1D1andB2D2underthemaxdisplace-mentofthemoulddownward;Risthecaster’sbasicradius;R1andR2areradiusrespectivelyfromthearccentretotwoendpointsoflinkagesA1C1,B1D1,A2C2andB2D2;H1andH2aretheheightsofbothsidestothehorizontalcenterlineofthemould;aistheincludedanglebetweenOEandthehorizontalcentrelineofthearccasterwhenthemouldisatequilibriumposition;h1,h2,r1andr2arerespectivelytheincludedanglesbetweenlinkagesofA1C1,A2C2,B1D1,B2D2andthehorizontalcentrelineofthecaster;DREisthesimulatedarcerrorofthemould.MathematicalmodelandoptimisationoflinkagesOscillationparametersofthemouldandtheinstallationpositionsoflinkagesaretheprimarydesigningtermsoftheguidancemechanism.Takingarccasterforexample,outsidepenaltyfunctionoptimisationmethodisadoptedinoptimumdesignofthetworigidfour-barlinkages.Infour-barlinkagesdesign,itisthegoalthatthetrajectoryerrorofthemouldmeetstherequirementforguidingaccuracy.Sotheobjectivefunctionoftheoptimisationmathematicalmodelcanbewrittenbyf(x~DRE~OE’{R¡0:02(1AccordingtoTable1,itcanbeseenthatthedesignoptimisationvariablesarex~R,S,h,r,R1,R2½T(2Byexperience,geometricdimensionsandinstallationpositionsoftwofour-barlinkagesmustmeetthefollowingconstraints2Layoutofcascadedwhole-leafspringamechanicdriven;bhydraulicsservodriven1Cascadedwhole-leafspringoscillationmechanismZhangetal.Cascadedwhole-leafspringoscillationmechanismformouldincontinuouscastingIronmakingandSteelmaking2010VOL37NO320530D¡R¡50D2¡Sjj¡10R1w0,hw0R2wR1,rwh0:91R¡R2vR0:82R¡R1¡0:91R(3whereDisthethicknessofbillet;handrareincludedanglesbetweenlinkagesandhorizontalcentrelineofthecaster.Basedontheobjectivefunction(equation(1,optimisationvariables(equation(2andconstraintsestablishedinequation(3,optimisationprocedureofoutsidepenaltyfunctioniscompiledbyClanguageandtwofour-barlinkagesareseparatelyoptimumdesigned.OptimisationresultsInoptimisation,itisassumedthatthemouldisarrangedsymmetricallyaboutitsequilibriumpositionanditsheightH1zH25900mm;thethicknessofthebilletD5150mm;theguidingaccuraciesoftworigidfour-barlinkagesDRE50?02mm.Therefore,thegeometricalparametersandtheguidingaccuraciesofthetworigidfour-barlinkagesareoptimumdesigned(Table2.Bytheoptimisedresults,rigidlinkagesaresubstitutedbyleafspringsarrangedaccordingtoFig.2;thenacascadedwhole-leafspringmechanismisdesigned.Experimentalprototypeofcascadedwhole-leafspringoscillationmechanismBasedontheoptimisedresults,theexperimentalproto-typeofthecascadedwhole-leafspringoscillationmechan-ismforthemouldismanufactured,asshowninFig.3,inwhichleafspringfour-barlinkageA1C1B1D1iscomposedofleafsprings1and4;andleafspringfour-barlinkageA2C2B2D2ismadeupofleafsprings2and3.Leafspringfour-barlinkagesA1C1B1D1andA2C2B2D2arelocatedatbothsidesofthemouldintheverticaldirectionofcasting.AndparametersoftheprototypeareroundednumbersofTable2andguidanceaccuracyiscalculatedafterround-ing,aslistedinTable3.FlexiblemultibodytheoryVectorsoflocation,velocityandaccelerationofpointonflexiblebodyBasedonthesmalldeformationtheory,complicatedmotionoftheflexiblebodycanbedecomposedtoseveralTable2Optimisedresultsoftworigidfour-barlinkagesFour-barlinkageA1B1C1D1Four-barlinkageA2B2C2D2R,mm5974.695902.74S,mm¡3.33¡3.19h,rad0.050.08r,rad0.170.14R1,mm5219.795233.23R2,mm5490.995505.41DR,mm20.020.0193ExperimentalprototypeTable1Formulasofparametersoftworigidfour-barlinkagesanderrorofbottompointEonmouldFour-barlinkageA1B1C1D1Four-barlinkageA2B2C2D2l15l35R22R1l15l35R22R1a5arcsin(H2/Ra5arcsin(H2/RDQ52arcsin(S/2l1cosr1DQ52arcsin(S/2l1cosr1l252R1sin[(r12h1/2]l252R1sin[(r12h1/2]l452R1sin[(r12h1/2]l452R1sin[(r22h2/2]D1E~½R22zR2{2R2Rcos(r1{a1=2D2E~½R21zR2{2R1Rcos(r2{a1=2C1E~½R22zR2{2R2Rcos(h1{a1=2C2E~½R21zR2{2R1Rcos(h2{a1=2A1D1’~fl21zl22z2l1l2sin½(r1{h1=2zDQg1=2A2D2’~fl21zl22{2l1l2sin½(r2{h2=2{DQg1=2c~arccos½(l24zD1E2{C1E2(2l4:D1Ec~arccos½(l24zD2E2{C2E2(2l4:D2Ev~arccos½(l24zAD1’2{l23.(2l4:AD1’v~arccos½(l24zAD2’2{l23.(2l4:AD2’b~arccos½(l21zAD1’2{l22.(2l1:AD1’b~arccos½(l21zAD2’2{l22.(2l1:AD2’OD1’~½R21zl21z2R1l1cosDQ1=2OD2’~½R22zl21{2R2l1cosDQ1=2w~arccos½(OD1’2zl21{R21.(2OD1’:l1w~arccos½(OD2’2zl21{R22.(2OD2’:l1d5wzczvzbd5wzc2(vzbOE’~½D1E2zOD1’2{2D1E:OD1’:cosd1=2OE’~½D2E2zOD’22{2D2E:OD2’:cosd1=2DRE5OE92RDRE5OE92RTable3ParametersofprototypeLeafspringfour-barlinkageA1B1C1D1Leafspringfour-barlinkageA2B2C2D2R,mm6000.006000.00S,mm¡3.00¡3.00h,u3.005.00r,u10.008.00R1,mm5220.005235.00R2,mm5490.005505.00DR,mm20.0160.018Zhangetal.Cascadedwhole-leafspringoscillationmechanismformouldincontinuouscasting206IronmakingandSteelmaking2010VOL37NO3simplemotions.Sothelocationvectorofanypointontheflexiblebodycanbeexpressedasequation(4.9rp~r0zA(sPzuP(4whereAisthematrixofdirectioncosine;rPisthevectorofpointPintheinertialcoordinatesystem;r0isthevectoroftheoriginofmovingcoordinateintheinertialcoordinatesystem;sPisthevectorofpointPinmovingcoordinatesystemwhentheflexiblebodyisundeformed;anduPistherelativedeflectionofpointPexpressedbymodalcoordinatesnamelyuP5WPq(whereWPistheassumedmodalmatrixandqisthegeneralisedcoordinateofdeformation.Differentiatingequation(4withrespecttotime,vectorsofvelocityandaccelerationarecalculated:rp~:r0z:A(sPzuPzAWP:q::rp~::r0z::A(sPzuPz2:AWP:qzAWP::q(5FlexiblemultibodydynamicequationConsideringthelocation,directionandmodeofpointPontheflexiblebody,thegeneralisedcoordinateisselected,asinequation(6.j~xyzyhwqi(i~1,:::,M½T~ryq½T(6ThemotionequationofflexiblebodyisdeducedfromdLL:{LLzlLyT{Q~0y~08><>:(7whereyisrestraintequation;lisLagrangemultipliercorrespondingtorestraintequation;Qisgeneralisedforceprojectedtogeneralisedcoordinatej;LisLagrangeitemwithL5T2W,andTandWrespectivelydenotekineticenergyandpotentialenergy.ThekineticenergyofflexiblebodyiscalculatedbyT~12:jTM(j:j(8whereM(jismassmatrixandM(j~MttMtrMtmMTtrMrrMrmMTtmMTrmMmm2435;subscriptst,randmrespectivelydenotetranslation,revolutionandmodalfreedom.Thepotentialenergyofflexiblebodyincludesthegravitationalpotentialenergyandtheelasticpotentialenergy,thatisW~Wg(jz12jTKj(9whereKisgeneralisedstiffnessmatrixcorrespondingtomodalcoordinatesandisaconstant.Becausethemassoftheflexibleleafspringsisverysmallcomparingtootherpartsoftheoscillationmechanismwithcascadedwhole-leafspring,itspotentialenergycouldbeignored.Sosubstitutingequations(8and(9intoequation(7,differentialequationofmotionoftheflexiblebodyiswrittenasfollowsM::jz:M:j{12LMLj:jT:jzKjzlLyLjjT~Q(10Kinematicssimulationofcascadedwhole-leafspringoscillationmechanismBasedontheflexiblemultibodytheory,thevirtualdesignandthenkinematicssimulationoftheexperi-mentalprototypeofthecascadedwhole-leafspringoscillationmechanismforthemouldwithnon-sinusoi-daloscillationarecarriedoutusingmanytypesofsoftwares,suchasANSYS,10,11andcurvesofdisplace-mentandvelocityofthemouldareobtainedandcomparedwiththeidealones.SimulationmodelBasedonthestructuralcharacteristicofthecascadedwhole-leafspringoscillationmechanism,itisassumedasfollows:(ithevibrationtableissymmetricaboutx–yplaneanddirectionof–yisthecastingdirection,withthecoordinateasshowninFig.4(iileafspringswithelasticdeformationareregardedasflexiblebodies.Eccentricshaft,connectingrod,vibrationtableandframewithbigstiffnessaretakenforrigidbodies.Sothesimulationmodeloftheexperimentalprototypeisbuilt,inwhichleafsprings1and4arecomposedoftwogroupsofleafspringfour-barlinkageA1C1B1D1;andleafsprings2and3areformedbytwogroupsofleafspringfour-barlinkageA2C2B2D2(Fig.4.KinematicssimulationandresultsTosimulatetheactualnon-sinusoidalmotionlawofthemouldwiththeguidanceofthecascadedwhole-leafspringmechanism,anon-uniformrotationalspeedisimposedontheeccentricshaft,asshowninFig.4,inwhichthefrequencyf52Hz,thedeflectionratioofoscillationa530%andtheamplitudeofthemouldh53mm.Thedisplacementandvelocitycurvesofthevibrationtable(i.e.movementcurvesofthemouldareshowninFig.5,ofwhichtheerrorscomparedwiththeidealcurvesareshowninFig.6.FromFig.5,itcanbeseenthevirtualvibrationtablecanmovealongthegivennon-sinusoidalrule.Althoughtheoscillationwaveformofthemouldinsimulationhaserrorcomparedwiththeidealcurves(Fig.6,themaximumerrorsofthedisplacementandthevelocityareverysmall(0?0068mmand0?1287mms21respec-tively,andcanbeignored.Therefore,itisconcludedthatthevirtualmodelisrationalandcanbeusedfor4SimulatingmodelZhangetal.Cascadedwhole-leafspringoscillationmechanismformouldincontinuouscastingIronmakingandSteelmaking2010VOL37NO3207furtherstudyonthecascadedwhole-leafspringmechanism.DynamicssimulationofoscillationmechanismBasedonthedynamicsimulationofthecascadedwhole-leafspringoscillationmechanism,systemmodalandtheforcesappliedonleafspringsandrevolutejointsareanalysed.ModalanalysisofoscillationmechanismUsingtheinstantaneousfreezingmethodofmechan-ism,12modalanalysisofthecascadedwhole-leafspringguidancemechanismiscarriedout,fromwhichsystemmodalsandnaturalfrequenciesareobtained.Forthefrequencyofnon-sinusoidaloscillationincontinuouscastingisnotveryhigh,13naturalfrequenciesandmodeshapesfromthefirsttothefifthareemphasisedinthispaperwithrelatedinformationofthemodalslistedinTable4.Limitedbyspace,onlythefirsttothethirdmodeshapesareshowninFig.7.Frommodalanalysisofthemechanismabove,itisknownthatthefirstandthesecondnaturalfrequenciesarelowerandresonancemayoccuronthemouldincontinuouscasting.14Whenresonanceoccurs,themouldwilldeflectfromthecorrecttrajectory,whichbadlyimpactsonthequalityofstrand.Soitmustbeensuredthattheworkingfrequencyincontinuouscastingisfarfromthefirstandthesecondnaturalfrequenciesofthecascadedwhole-leafspringoscillationmechanism.AnalysisofforcesappliedonleafspringsOwingtothesymmetryaboutthex–yplane,leafspringsinbothsidesofthecascadewhole-leafspringoscillationmechanismhavethesameforcesanddeformations,onlytheoneatthepositiveaxisofzisanalysed.Forthecascadewhole-leafspringmechanism,leafspringfour-barlinkageA1C1B1D1andA2C2B2D2alternatelyplaytheguidanceroleonthemouldandforcesappliedontheleafspringandtheirdeformationsareverycomplicated.Soitisdifficulttoanalyseleafspringswellonlybyexperimentsandcomputersimulationhasimportantsignificance.Inthispaper,basedonthevirtualproto-typetechnology,dynamicssimulationiscarriedout,bywhichforcescurvesofleafspringsareobtainedduringthemouldmovement.Furthermore,effectsofbasicoscillationparametersontheseforcesareanalysed,whichestablishthebasisforfurtherstudyonthereliabilityofthemechanism.5adisplacementandbvelocitycurvesofvibrationtableTable4NaturalfrequenciesandmodesshapesfromfirsttofifthorderModalityorderNaturalfrequency,HzModeshapes172058Verticalvibrationofthevibrationtablealongthecastingdirection(–y211.4723Deviatedswingofthevibrationtableabouttheaxisofx323.7038Vibrationofleafspring1423.7068524.0872Transversevibrationofthevibrationtablealongthezaxiszvibrationofleafspring17afirstandbsecondmodalmodeshapesofsystemZhangetal.Cascadedwhole-leafspringoscillationmechanismformouldincontinuouscasting208IronmakingandSteelmaking2010VOL37NO3Zhangetal.Cascadedwhole-leafspringoscillationmechanismformouldincontinuouscastingaleafspring1;bleafspring4;cleafspring2;dleafspring38ForcesappliedonleafspringsatdifferentamplitudesForcesappliedonleafspringsatdifferentamplitudesTounderstandtheforcesappliedonleafspringsunderdifferentamplitudes,themotionofthemouldwithdifferentlengthsoftheeccentricshaftrespectivelyh53mmandh52mm(thatistheamplitudesofthemouldaretakenforexampletosimulateinwhichthedeflectionratioofoscillationandthefrequencyarethesametothoseinthesectionon‘Kinematicssimulationandresults’.Forcesappliedalongthelengthdirectionofleafsprings,forexample,areanalysedinthispaper.Basedonthedynamicsimulations,forcesappliedontheendsofleafsprings1,4and2,3inaperiodareobtainedasshowninFig.8.Itcanbeseenthattheforcesappliedontheendsofleafsprings1and4aresimilarandvaryatnonsinusoidalrules.Whenthemouldworksaboveitsequilibriumpositionatthefirsthalf-period,twoleafspringsarecompressedontheactionofnegativeforces;whenthemouldmovesundersideofitsequilibriumpositionatthesecondhalf-period,thesetwoleafspringsaretensionedwithpositiveforces.Furthermore,thevaluesofforcesaredirectlyproportionaltothedistanceofthemoulddepartingfromitsequilibriumposition.Whenthemouldmovestoitsmax.displacement,bothleafspringswillbearthelargestforces.Andforcesappliedontheleafspringsgetbiggerastheamplitudeofmouldincreases.Forcesappliedonleafsprings2and3varywiththesamelaw,yetoppositetothoseofleafsprings1and4.Whenthemouldisaboveitsequilibriumpositionatthefirsthalf-period,leafsprings2and3beartensileforces;however,attheotherhalf-period,bothleafspringsbearpressure.Similarlythevaluesofforcesareproportionaltothedistanceofthemouldoffitsequilibriumpositionandtheforcesgetbiggerastheamplitudesofthemouldincrease.ForcesappliedonleafspringsatdifferentdeflectionratioofoscillationWiththesamefrequencyandamplitudeinthesectionon‘Kinematicssimulationandresults’,basedonthedynamicsimulationsatdifferentdeflectionratiosofoscillationa1510%,a2530%,a3550%,forcecurvesofeachleafspringareobtained,asshowninFig.9.FromFig.9,itcanbeseenthatwiththesamefrequencyandamplitudeofoscillation,deflectionratiosoftheforcecurvesofleafspringsbecomebiggerasthedeflectionratioofoscillationenlarges,buttheamplitudesofforcesappliedoneveryleafspringkeepconstant.Atthesametimethereareforcesappliedinthenormaldirectionofthelengthofleafspring,whichvarywiththesameruletotheforcesalongthelengthdirection.Ingeneral,forcesappliedonleafspringsperiodicallyvarywiththesameperiodicitytothesystem’sduringthemouldvibration,thevaluesofwhichareproportionaltothedistanceofthemoulddepartingfromitsequilibriumpositionandgetbiggerastheamplitudeofthemouldincreases.Deflectionratiosofaleafspring1;bleafspring2;cleafspring3;dleafspring49ForcesappliedonleafspringsatdifferentdeflectionratioIronmakingandSteelmaking2010VOL37NO3209Zhangetal.Cascadedwhole-leafspringoscillationmechanismformouldincontinuouscastingtheforcecurvesofleafspringsbecomebiggerwiththedeflectionratioofoscillationenlarging,buttheamplitudesofforcesofeveryleafspringareinvariant.EffectofbasicoscillatoryparametersonjointforcesThebasicoscillatoryparametersareoftenadjustedtomeetdifferenttechnologiesincontinuouscasting,whichwillaffectthejointforcesofkinematicpairsandthenthedynamiccharacteristicofthemechanism.Therefore,jointforcesareanalysedofthecascadewhole-leafspringoscillationmechanism,whichshowsthatamplitudeanddeflectionratioofoscillationaffectjointforceswiththesimilarlawtoforcesappliedonleafsprings.Jointforcesgetbiggerastheamplitudeofthemouldincreasesanddeflectionratiosofjointforcecurvesbecomebiggerwithincreasingthedeflectionratioofoscillation;however,theamplitudesofjointforcesareconstant.Basedonanalysesabove,thecascadedwhole-leafoscillationmechanismcanbeproperlydesignedforthemouldincontinuouscastingaccordingtopracticalconditions,whichcanmakethemouldvibratealongthecorrecttrackwithbetterperformanceandhigherreliabilityofproduction.Therefore,thetheorybasisforapplicationisestablished.4.Theamplitudesofforcesappliedonleafspringsandrevolutejointsareonlydeterminedbytheamplitudeofthemouldandenlargewiththeamplitudesofthemouldincreasing;andasthedeflectionratioofoscillationincreases,thedeflectionofforcecurvesbecomesgreater.OutlookSuchasystemisnowbeingplannedforuseinindustry.References1.Y.G.YanandX.J.Wang:‘Erroranalysisandcomparisonoftwotypicalmoldoscillators’,HeavyMach.,2006,3,46–48,54.2.in‘800problemso