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ShaftSolidshafts. Asamachinecomponentashaftiscommonlyacylindricalbarthatsupportsandrotateswithdevicesforreceivinganddeliveringrotarymotionandtorque.Thecrankshaftofareciprocatingenginereceiveitsrotarymotionfromeachofthecranks,viathepistonsandconnectingroads(theslider-crankmechanisms),anddeliversitbymeansofcouplings,gears,chainsorbeltstothetransmission,camshaft,pumps,andotherdevices.Thecamshafts,drivenbyagearorchainfromthecrankshaft,hasonlyonereceiverorinput,buteachcamontheshaftdeliversrotarymotiontothevalve-actuatingmechanisms.Anaxleisusuallydefinedasastationarycylindricalmemberonwhichwheelsandpulleyscanrotate,buttherotatingshaftsthatdrivetherearwheelsofanautomobilearealsocalledaxles,nodoubtacarryoverfromhorse-and-buggydays.Itiscommonpracticetospeakshortshaftsonmachinesasspindles,especiallytool-carryingorwork-carryingshaftsonmachinetools.Inthedayswhenallmachinesinashopweredrivenbyonelargeelectricmotororprimeitwasnecessarytohavelonglineshaftsrunninglengthoftheshopandsupplyingpower,bybelt,toshortercoutershafts,jackshafts,orheadshafts.Theselineshaftswereassembledformseparatelengthsofshaftingclampledtogetherbyrigidcouplings.Althoughitisusuallymoreconvenienttodriveeachmachinewithaseparateelectricmotor,andthepresent-daytrendisinthisdirection,therearestillsomeoilenginereceivesitsrotarymotionfromeachofthecranks,viathepistonsandconnectingroads(theslider-crankmechanisms),anddeliversitbymeansofcouplings,gears,chainsorbeltstothetransmission,camshaft,pumps,andotherdevices.Thecamshafts,drivenbyagearorchainfromthecrankshaft,hasonlyonereceiverorbuteachcamontheshaftdeliversrotarymotiontothevalve-actuatingmechanisms.Anaxleisusuallydefinedasastationarycylindricalmemberonwhichwheelsandpulleyscanrotate,buttherotatingshaftsthatdrivetherearwheelsofanautomobilearealsocalledaxles,doubtacarryoverfromhorse-and-buggydays.Itiscommonpracticetospeakshortshaftsonmachinesasspindles,especiallytool-carryingorwork-carryingshaftsonmachinetools.Inthedayswhenallmachinesinashopweredrivenbyonelargeelectricmotororprimeitwasnecessarytohavelonglineshaftsrunninglengthoftheshopandsupplyingpower,bybelt,toshortercoutershafts,jackshafts,orheadshafts.Theselineshaftswereassembledformseparatelengthsofshaftingclampledtogetherbyrigidcouplings.Althoughitisusuallymoreconvenientdriveeachmachinewithaseparateelectricmotor,andthepresent-daytrendisinthisdirection,therearestillsomesituationinwhichagroupdriveismoreeconomical.Asingle-throwcrankshaftthatcouldbeusedinasingle-cylinderreciprocatingengineorpumpisshowninFigure21.ThejournalsAandBrotateinthemainbearings,CisthecrankpinthatfitsinabearingontheendoftheconnectingrodandmovesonacircleofradiusRaboutthemainbearings,whileDandEarethecheeksorwebs.ThethrowRisonehalfthestroksofthepiston,whichisconnected,bythewristpin,totheotherendoftheconnectingrodandguidedsoastomoveonastraightpathpassingthrowtheXX.Onamultiple-cylinderenginethecrankshafthasmultiplethrows---eightforastraightandforaV-8---arrangedinasuitableangularrelationship.Stressandstrains.Inoperation,shaftsaresubjectedtoashearingstress,whosemagnitudedependsonthetorqueandthedimensionsofthecrosssection.Thisstressisameasureofresistancethattheshaftmaterialofferstotheappliedtorque.Allshaftsthattransmitatorquearesubjectedtotorsionalshearingstresses.Inadditiontotheshearingstresses,twistedshaftsarealsosubjectedtoshearingdistortions.Thedistortedstateisusuallydefinedbytheangleoftwistperunitlength;i.e.,theretationofcrosssectionofashaftrelativetoanothercrosssectionataunitdistancefromit.Shaftsthatcarrygearsandpulleysarebentaswellastwisted,andthemagniudeofthestresses,whicharetensileontheconvexsideofthebendandcompressiveontheconcaveside,willdependontheload,thedistancebetweenthebearingsoftheshaftcrosssection.Thecombinationofbendingandtwistingproducesastateofstressintheshaftthatismorecomplexthanthestateofpureshearsproducedbytorsionaloneorthestateoftension-compressionproducedbybendingalone.Tothedesignerofshaftitisimportanttoknowiftheshaftislikelytofailbecauseofanexcessivenormalstress.Ifapieceofchalkistwisted,itwillinvariablyruptureonaplaneatabout45degreestotheaxis.Thisisbecausethemaximumtensilestressesactonthisplane,andchalkisweakintension.Steelshaftingisusuallydesignedsothatthemaximumshearingstressproducedbendingandtorsionislessthanaspecifiedmaximum.Shaftswithcircularcrosssectionsareeasiertoproduceinthesteelmill,easiertomachine,andeasiertosupportinbearingsthanshaftswithothercrosssection;thereisseldomanyneedfornoncircularshapes.Inaddition,thestrengthandstiffness,bothinbendingandtorsion,aremoreeasilycalculatedforcircularshafts.Lastly,foragivenamountofmaterialsthecircularshaftshasthesmallestmaximumshearingstressforagiventorque,andthehighesttorsionalrigidity.Theshearinginacircularshaftishighestatthesurfaceanddropsofftozeroattheaxis.meansthatmostofthetorqueiscarriedbythematerialonandnearthesurface.Criticalspeeds.Inthesamewaythataviolinstringvibrateswhenstrokedwithabow,acylindricalshaftsuspendedbetweentwobearingshasanaturalfrequencyoflateralvibration.Ifthespeedofrevolutionoftheshaftcoincideswiththenaturalfrequency,theshaftexperienceawhirlingcriticalspeedandbecomenoisy.Thesespeedsaremorelikelytooccurwithlong,flexibleshaftsthanwithshort,stiffones.Thenaturalfrequencyofashaftcanberaisedbyincreasingitsstiffness.Ifaslenderrodisfixedtotheceilingtaoneendandsupportsaheavydiskattheotherend,thediskwilloscillatebackandfortharoundtherodaxislikeatorsionpendulumifgivenaninitialandletgo.Thefrequencyoftheoscillationswilldependonthetorsionalstiffnessoftherodandtheweightofthedisk;thestiffertherodandthelighterthediskthehigherthefrequency.Similartorsionaloscillationscanoccurinthecrankshaftsofreciprocatingengines,particularlythosewithmanycrankthrowsandaheavyflywheel.Eachcrankthrowandpartoftheassociatedconnectingrodactslikeasmallflywheel,andforthecrankshaftasawhole,thereareanumberofwaysormodesinwhichtheresmallflywheelscanoscillatebackandfortharoundtheshaftaxisinoppositiontooneanotherandtothemainflywheel.Foreachofthesemodestherecorrespondsanaturalfrequencyofoscillation.Whentheengineisoperatingthetorquesdeliveredtothecrankshaftbytheconnectingrodsfluctuate,andifthecrankshaftspeedissuchthatthesefluctuatingimpulsesaredeliveredataspeedcorrespondingtooneofthenaturaltorsionalfrequenciesoftheshaft,torsionaloscillationswillbesuperimposedontherotarymotionoftheshafts.Suchspeedareknownastorsionalcriticalspeeds,andtheycancauseshaftfailures.Anumberofdevicestocontroltheoscillationsofcrankshaftsbeeninvented.Flexibleshafts. Aflexibleshaftconsistsofanumberofsuperimposedtightlywoundright-andleft-handlayersofhelicallywoundwireswrappedaboutasinglecenterwireormandrel.Theshaftisconnectedtosourceofpowerandthedrivenmemberbyspecialfittingsattachedtotheendofshaft.Flexibleeasingsofmetallicornonmetallicmaterials,whichguideandprotecttheshaftretainthelubricant,arealsoavailable.Comparedwithsolidshafts,flexibleshaftscanbebenttomuchsmallerradiiwithoutbeingoverstressed.Fortransmittingpoweraroundcornersandforconsiderabledistancesflexibleshaftsareusuallycheaperandmoreconvenientthanbelts,chains,orgears.Mostspeedometersonautomobilesaredrivenbyflexibleshaftsrunningfromthetransmissiontothedashboard.Whenavalve,aswitch,orothercontroldevicesisinahard-to-reachlocation,itcanbeoperatedbyaflexibleshaftfromaconvenientposition.Forportabletoolssuchassanders,grinders,anddrillingmachines,flexibleshaftsarepracticallyindispensable.KEY,SPLINESANDPINSKeys,splines,andpins.Whenpowerisbeingtransmittedfromamachinemembersuchasacoupling,agear,aflywheel,orapulleytotheshaftonwhichitismounted,meansmustbeprovidedforpreventingrelativemotionbetweentheshaftandthemember.Onhelicalandbevelgears,relativemovementalongtheshaftcausedbythethrust(axial)loadsispreventedbyastepintheshaftorbyhavingthegearcontactthebearingdirectlyorthroughatubularspacer.Whenaxialareincidentalandofsmallmagnitude,themembersarekeptfromslidingalongtheshaftbymeansofasetscrew.Theprimarypurposeofkeys,splines,andpinsistopreventrelativerotarymovement.Acommonlyusedtypeofkeyhasasquarecrosssectionandissunkhalfintheshaftandhalfinthehuboftheothermember.Ifthekeyismadeofsteel(whichiscommonlythecase)ofthesamestrengthastheshaftandhasawidthanddepthequaltoonefourthoftheshaftdiameter(thisproportioniscloselyapproximatedinpractice)thenitwillhavethesametorquecapacityasthesolidshaftifitslengthis1.57timesthatoftheshaftdiameter.Anothercommontypeofkeyhasarectangularcrosssectionwithadepthtowidthratioof0.75.Bothofthesekeysmayeitherbestraightortaperedindepth.Thestraightkeysfitsnuglyonthesidesofthekeywaysonly,thetaperedkeysonallsides.Gib-headkeysaretaperedkeyswithaprojectionononeendtofacilitateremoval.Woodruffkeysarewidelyusedonmachinetoolsandmotorvehicles.Thekeyisasegmentofadiskandfitsinakeywayintheshaftthatiswithaspecialmillingcutter.Thoughtheextradepththesekeysweakenstheshaftconsiderably,itpreventsanytendencyofthekeytorotateormoveaxially.Woodruffkeysareparticularlysuitablefortaperingshaftends.Becausetheyweakentheshaftsless,keyswithstraightortaperedcircularcrosssectionsaresometimesusedinplaceofsquareandrectangularkeys,butthekeyways,halfintheshaftandhalfintheshaftandhalfinthehub,mustbecutwithadrillafterassembly,andinterchangeabilityofispracticallyimpossible.Whenalargegearblankismadebyshrinkingahigh-strengthrimonacheapercastcenter,circularkeys,snuglyfitted,arefrequentlyusedtoensureapermanentconnection.Splinesarepermanentkeysintegralwiththeshaft,fittinginkeywayscutinthehub. Thedimensionsofsplinedfittingsarestandardizedforbothpermanent(press)fitsandslidingfits.Theteethhaveeitherstraightorinvoluteprofiles;thelatterarestronger,moreeasilymeasured,andaself-centringactionwhentwisted.Taperedcircularpinscanbeusedtorestrainshaft-mountedmembersfrombothaxialandrotarymovement.Thepinfitssnuglyinareamedtaperedholethatisperpendiculartotheshaftsurface.numberofstraightpinsthatgripbydeformingelasticallyorplasticallywhendrivenintostraightholesarecommerciallyavailable.Allthekeysandpinsthathavebeendescribedarestandarddrivingdevices.Insomecasestheyinadequate,andunorthodoxmeansmustbeemployed.Fordrivingsmallgearinwhichthereisnoroombetweentheboreandtherootsoftheteethforalongitudinalkeyway,atransverseradialslotontheendofthegearcanbemadetofitaradialprotuberanceontheshaft.Fortransmittingmoderateloads,acheaperandeffectiveconn