Chapter11-Worm-Gears-機(jī)械零件設(shè)計(jì)英文全套教案

Chapter9Springs

9.1TypesandCharacteristicsofSprings9.2PotentialFailureModes9.3SpringMaterials

9.4AxiallyLoadedHelical-CoilSprings;Stress9.5DeflectionandSpringRate9.6BucklingAnalysisofHelicalCompressionSprings9.7ProcedureandGeneralGuidelinesforSpringDesignChapter9Springs9.11

9.1TypesandCharacteristicsofSpringsSpringsmaybebroadlydefinedasstructuresordevicesthatexhibitelasticdeformationwhenloaded,andrecovertheirinitialconfigurationwhentheloadisremoved.Usuallythetermspringdenotesaresilientdevicespeciallyconfiguredtoexertdesiredforcesortorques,toprovideflexibility,ortostorepotentialenergyofstrainforreleaseatalatertime.Springsincludehelicallycoiledwireloadedbyaforcealongtheaxisofthehelixorbytorsionalmomentsabouttheaxisofthehelix,thinflatbeamsloadedinbending,androundbarsortubesloadedintorsion.9.1TypesandCharacteristics2Thecommonlyusedmechanicalspringshelical-coilspringsspiraltorsionspringMultileafspringsRubberspringsPneumaticspringsringspringBellevillewashers(coned-disksprings)Thecommonlyusedmechanica3Chapter11-Worm-Gears-機(jī)械零件設(shè)計(jì)英文PPT全套教案4Chapter11-Worm-Gears-機(jī)械零件設(shè)計(jì)英文PPT全套教案5MusicwireOil-temperedsteelvalvespringwireOil-temperedsteelspringwireHard-drawnsteelwireAlloysteelwireStainless-steelwireBerylliumcopperwireNickelalloywireSpringwirematerialsthatarewidelyusedMusicwireSpringwiremateria6Strengthpropertiesofmanymaterialsarestronglysizedependent,ultimatestrengthpropertiesformanyofthesematerialsmaybecloselyapproximatedbytheempiricalexpression

Sut=Bda(9-1)whereSut

=ultimatestrengthintension

d=wirediameter

a=exponent

B=coefficientTheexponentaandcoefficientBmaybeevaluatedforfiveofthematerials,asshowninTable9.1.Strengthpropertiesofmanyma7

9.4AxiallyLoadedHelical-CoilSprings;StressThedesignofhelical-coilspringsinvolvesselectionofamaterial,anddeterminationofthewirediameter,d,meancoilradius,R,numberofactivecoils,N,andotherspringparameters(seeFigure9.2)sothatthedesiredforce-deflectionresponseisobtained,withoutexceedingthedesignstressunderthemostsevereoperatingconditions.9.4AxiallyLoadedHelic8Foropen-coilaxiallyloadedhelicalsprings

Theprimarystressdevelopedinthewireistorsion,whethertheloadproducesextensionorcompression.Thefreebodythatresultswhenasectioniscutthroughthehelicallycoiledbar,asshowninFigure(b),indicatesthatthebarexperiencesatorsionalmomentT=FR,andinaddition,atransverseshearforceF.Foropen-coilaxiallyloadedh9TorsionalshearingstressesThetorsionalshearingstressesinducedinthewirearetheprimarystresses,buttransverseshearingstressesinhelical-coilspringsareimportantenoughtoconsider.Themaximumtorsionalshearingstressoverthesurfaceofthewireis

Thetransverseshearingstresshasbeenshowntoreachamaximumvalueatthemidheightofthewirecrosssection,andtohavethemagnitudeTorsionalshearingstressesThe10Becauseofcoilcurvature,aslightlylargershearingstrainisproduced(bythetorsion)attheinner(shorter)fiberofthecoilthanattheouter(longer)fiber,inducingaslightlyhighertorsionalshearingstressattheinnerfiber.Thisstress-increasingcurvaturefactor,Kc,maybeestimatedas

wherethespringindex,c,isdefinedtobe

CurvatureeffectBecauseofcoilcurvature,as11Themaximumshearingstressoccursatthemid-heightofthewireattheinnercoilradius,andmaybeestimatedby:

ThemaximumshearingstressFormostsprings,cwillrangefrom4to12.

Themaximumshearingstressoc12Theendloopsofhelical-coilextensionspringsmustbeseparatelyanalyzedbecausestressconcentrationatthepointwheretheendloopis"bentup"[seeFigure9.4(b)],andattheinnerradiusofthehook[seeFigure9.4(a)].StressconcentrationeffectattheendloopTheendloopsofhelical-coil13

9.5DeflectionandSpringRateAxialdeflectionofahelical-coilspringunderaxialloadmaybefoundbyfirstdeterminingthemagnitudeoftherelativeangularrotationbetweentwoadjacentcrosssectionsofthewire,spacedadistancedLapart,producedbyanappliedtorqueT=FR.9.5Deflectio14ThetotalaxialdeflectionandthespringrateExtendingtheresultsforthesmallsegmenttotheentireflexiblespring,wecanobtainthetotalaxialdeflectionandthespringrate,respectively:Thetotalaxialdeflectionand15Forhelical-coilcompressionsprings,Nt,isdeterminedbyaddingthenumberofinactivecoils,Ni,tothenumberofactivecoilsN,toobtainFigure9.6givesthenumberofinactivecoilsassociatedwitheachofthemorecommonendconditionsusedforhelical-coilcompressionsprings.Endcoilconfigurationinfluences

onoverallspringflexibilityForhelical-coilcompressions16Forthecaseofextensionsprings,theendloopscontributeadditionalelasticitytothesprings,dependingupontheend-loopconfiguration.Theeffectivenumberofactivecoils,N,isobtainedbyaddingtheequivalentcoilsforbothendloops,Ne,tothenumberofcoilsinthelengthovercoils,Nc,toobtainN=Nc+Ne

Forthecaseofextensionspri17Helical-coilspringsloadedincompressionwillbuckleifaxialdeflectionsbecometoolarge.Equationsforpredictionofcriticalbucklingdeflection,ycr,developedinamannersimilartocolumn-bucklingequations,maybeexpressedintermsoffreelengthLy,meancoilradiusR,andthemethodofconstrainingtheendsofthespring(seeTable9.2).9.6BucklingAnalysisofHelicalCompressionSpringsHelical-coilspringsloadedin18Fig.9.8showscriticaldeflectionratioplottedversusslendernessratioforspringswithbothendshinged(α=1)andspringswithbothendsfixed(α=0.5).PotentialbucklingfailureshouldbecheckedusingthecurvesofFig.9.8.Ifthedeflectionratiofortheproposedspringexceedsthecriticalvaluereadfromthecurve,thespringshouldberedesigned.Fig.9.8showscriticaldeflect19Tocontainthespringinsideacloselyfittingguidecylinder;Toinsertaninternalcylindricalguidemandrel;Adiametralclearanceofapproximately10percentofthecylinderormandreldiameteriscommonlyusedtoavoidrubbingbetweenthespringanditsguide.AnalternativebucklingsolutionTocontainthespringinsidea201)DesignProcedures(1)Basedonfunctionalspecificationsandcontemplatedsystemconfiguration,generateafirstconceptualsketchfortheproposedspring,approximatelytoscale.(2)Identifypotentialfailuremodes(3)Selectatentativespringmaterial(4)Selectanappropriatedesignsafetyfactor(5)Calculatethedesignstress9.7ProcedureandGeneralGuidelinesforSpringDesign1)DesignProcedures9.7Proced21(6)Determinewirediameter,d,meancoilradius,R,andnumberofactivecoils,N,sothatshearingstressanddeflectionareindependentlysatisfied.(7)Usingthetentativevaluesofd,R,andN,determinespringrate,k,andchecktoassurethatitalsomeetsanyotherfunctionalrequirementsfork.(8)Selectanappropriateendconfigurationanddeterminethenumberofinactivecoils(forcompressionsprings)orequivalentextracoils(forextensionsprings).Calculatetotalnumberofcoilsinthespring.(6)Determinewirediameter,d22(9)Determinesolidheight,freeheight,andoperationaldeflectiontomakesurethatnodesignrequirementsareviolated.(10)Checkpotentialbucklingofcompressionsprings.(11)Continuetoiterateuntilalldesignrequirementsaresatisfied.Summarizethefinalspecificationsformaterial,heattreatment,anddimensions.(9)Determinesolidheight,fr23a.Ifthespringisguided(topreventbuckling),allowaminimumdiametralclearancebetweenthespringandtheguidingholeormandrel,orapproximately10percentofthecoildiameter.b.Calculatematerialstrengthdatawith(9-1),ifapplicable.Otherwise,useproceduresformultiaxialstatesofnonzero-meancyclicstresstodeterminefailurestrength.

c.Forinitialselectionofwirediameter,dandmeancoilradius,R,trytoproportionthespringsothatspringindexcwilllieintherangebetween4and12;2)Experience-basedguidelines

a.Ifthespringisguided(to24d.Ifdesigningacompressionspring,closedandgroundendsareusuallyagoodchoice.Ifdesigninganextensionspring,theuseoffullendloops,overcenterisusuallyagoodchoice,unlessminimumcostisessential.e.Allowaclearancebetweencoilswhenthespringisatitsm