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EXERCISES

CONTENTS

Chapter1FundamentalPrinciplesofMachineDesign

Chapter2FundamentalsofTransmissionDesign

Chapter3FlexibleTransmissions

Chapter4GearTransmission

Chapter5WormGearTransmission

Chapter6Shafting

Chapter7BallandRollerBearings

Chapter8SlidBearings

Chapter9BoltConnectionsandScrew

Chapter10Springs

Chapter11MechanicalConstructionDesign

Chapter1FundamentalPrinciplesofMachineDesign

EX.1.1Afterbeingdrawnupsnug,inFig.1-1,thenutM20isgiven120additionalturn.Findtheforceinthepipeandthebolt.Theboltismadeofsteelandthepipeismadeofbrass.Outdiameterofthepipeis32mmandinternaldiameteris22mm,lengthofthepipeis200mm.

EX.1.2Ifthethicknessofthelinkis35mm.,F=30kN.DeterminethewidthboftheoffsetlinkofFig.1-2,ifthepermissiblevalueoftheworkingstressis68MPa.

Fig.1-1Fig.1-2

EX.1.3AuniformbarintensionifF=5000N,F=2000N.MaterialofthebarisQ235.TakethefactorofsafetyS=1.6,basedontheyieldpoint,findthediameterofthebar.Thebarhasamachinedsurface,calculatethefactorofsafetyforinfinitelife.

EX.1.4SupposethelifeNofthepartunderheavytestloadis20hr.ThelifeNundercombinedloadingwas32hr,ofwhich14hrwasatthenormalloadand18hrwasattheheavytestload.FindtheexpectedlifeNunderthenormaloperatingload.

EX.1.5InFig.1-3,theleafspringisstraightandunstressedwhenthecamandshaftareremoved.Thematerialofthespringis65Mn.Notanystressconcentration.Springsurfacesareground.Ifthecamrotatescontinuously,findthesafefactorfortheleafspring.Thicknessofthespringis=3mmandwidthb=25mm.

EX.1.6AmachineelementshowninFig.1-4ismadefrom40Cr.ItissubjecttofluctuatingbendingwithamaximumloadofF=4000N,aminimumloadofF=600N.Caculatethefactorofsafetyforinfinitelifeforthepart.

Fig.1-3Fig.1-4

EX.1.7Acircularshaftofanelectricmotoris750mmfrombearingtobearing.Theweightoftherotoris6000N.Thematerialis45steel.Forsimplicity,wewillassumetheforceofgravityconcentratedatmidpoint.Thesurfaceisground.lightshock,nostressconcentration.Calculatetheshaftdiameter.

EX.1.8ThethreegearsshowninFig.1-5havetherespectivetoothnumberZ、Z、Z.AninputtorqueTisappliedtotheendAoftheshaftThetorsionalspringconstantoftheshaftsarek、k、krespectively.AssumetheshaftisfixedatendB.CalculatethetorsionalspringrateoftheentiresystembaseduponadeflectionmeasuredatA.

EX.1.9AsizeNU216EcylindricalrollerbearingshowninFig.1-6withoutsidediameterD=140mm,borediameterd=80mm..Thediameteroftherollersis16mm,theracewaycontactdiameteroftheinnerringandouterringare94mmand126mmrespectively,lengthoftherolleris20mm.NumberofrollersZ=15.Determinethemaximumrollerforceandcontactstress,underthestaticradialloadF=100kN..

Hint:themaximumrollerforceF=4.08F/Z(forrollerbearing)

Fig.1-5Fig.1-6

EX.1.10Calculatethestressincreasesper100Ctemperaturerisefortherestrictedrod,whenthematerialiscarbonsteel.

Chapter2FundamentalsofTransmissionDesign

EX.2.1TheFig.2-1illustratesadouble-reductiongeartrain.Shaftaisdrivenbya1.25kWsourceat1,470rpm.Thereductionbetweenshaftsaandbis3:1andbetweenshaftsbandcitis4:1.Thepiniononshaftahas20teeth,andthegearonshaftc,120teeth.

Findthetoothnumberforthegearonshaftb.

Findthespeedofshaftsbandc.

Ifthepowerlossis4percentateachmesh,findthetorqueateachshaft.

Fig.2-1Fig.2-2

EX.2.2Anoverheadcranewithaprojectedliftingcapacityof450kNandatravelspeedof1.2m/shasamassof7000kg.Thismotor-driven,bridgelikesteelstructurerunsontwoelevatedrailsandissupportedbyfoursteelwheels.Coefficientofrollingfrictionis0.018.Assumeanefficiencyofthedrivemechanismis0.68.Forfullload,.answerthefollowingquestions:

Whatpowerisneedforthecranetravel?

b)Ifthecraneistobebroughttoastopfromfullspeedin10s,howmachenergymustthebrakesdissipateasheatandwhatwillthestopdistancebe?

c)Whereshouldthebrakebelocatedformaximumefficiencyandminimumsize?

EX.2.3Arubberbeltconveyorisdrivenbyelectricmotor.V-beltandgeartransmission.DiameterofthedramD=400mm,speedoftheconveyorbeltv=1.2m/sandeffectivetensionF=2000N.

Selectasuitableelectricmotor

b)Determinethetransmissionsystem

c)Calculatethepowerandtorqueofeachshaft.

EX.2.4.A10kW1500rpmgeneratoristobedrivenbya“low-head”waterturbinewitharegulatedoptimumspeedofapproximately30rpm.

Forahorizontalturbineshaft,designacombinedbeltandchaindrive.Makeakinematicdiagram.Givethediametersofthepulleysandnumberofteethofthesprockets.

Foraverticalturbineshaft,designabevelgearandcylindricalgeartrain.Givethenumberofteethofeachgearandakinematicdiagram..

EX.2.5Fig.2-2showsaplatformthatcanbeelevatedandloweredwhilecarryingaheavyloadF.Theweightoftableandloadis45kN,assumethattheloadconcentratedatthecenterofthetable.Theplatformassumedrigid,istobeliftedbytwoverticalscrewsataspeed4m/min.ThescrewsareturnedbytwosetsofbevelgearsforwhichZ=22,Z=50,thethreadofscrewsaretrapezoidTr609.Thecoefficientofthreadfrictionf=0.08.Calculatethefollowing:

Thenecessaryspeedoftheshaft.

b)Thepowernecessarytoelevatethetableatconstantspeed.

c)Thediameterofthedriveshaftbetweenthetwobevelgears.Assumetheallowablestressoftorsion[]=18MPa

d)Thedifferenceinelevationofthetwosidesduetotheangulardisplacementofthehorizontaldriveshaft.Assumealengthof3m..

e)Whatsortofpowersourcewouldyousuggestforthisplatform?Givethereasonsforyourchoice.

f)Woulditbeadvantageoustospecifyballscrew?

EX.2.6Aflatbeltconveyorisrequiredtotransportpartsatarateof120m/min.ThediameteroftheheadshaftpulleyD=250mm.ThenominalpoweroftheelectricmotorisP=7.5kW,andfullloadspeedis970rpm.Servicetimeis4h/day,5day/wk,50wk/yr.Selectseveral(atleast3)suitabledrives.Giveakinematicdiagramforeachscheme.

EX2.7Alathewasusedincuttingthreads.InboththeEnglishandmetricunits,theconversionfrominchestomillimeters(1inch=25.4mm)wasdonebymeansofasinglepairoflathechangegearsconnectingthelathespindlewiththelathescrew.Findsuchapair,Itmusthaveacenterdistancenotexceed90mmandfindasuitablemodule.

EX.2.8Apinionrunsat630rpm,drivingagearat210rpm,centerdistanceisfixedat130mm.Findthenumberofteethrequiredforgearrotationin(a)oppositedirections,(b)thesamedirections..Theerrorofspeedratiolessthan5%.Makeasimplesketchofbotharrangements.

EX.2.9Ahelicalgearpairhasaspeedratioi=4.3andcenterdistancea=150mm.Findthenumberofteeth,helixangleandnormalmodule.Theerrorofspeedratiomustbelessthan5%.

EX.2.10Apairofspurgearswithaspeedratioof4,andacenterdistanceof10in.Istobereplacedbyapairofpairofmodule-basedgears.Specifysuchgearswhen(a)exactcenterisimportant,and(b)exactspeedratioisimportant..

EX.2.11Thegateofasluicevalveweighting6t.Israisedbymeansofacast-ironrackandasteelpinion.Designatrainofgears,includingtherack,sothatthegatemayberaisedbytwomenworkingon,400mmcrankhandlesandexertingapressure150Neach.Givealsothelinearspeedoftherackmotionassumingthatthehandcrankturnsby20rpm.

EX.2.12AsshowninFig.2-3,whereasingle-startthreadofleadS=4mmisbeingcutbyanenginelathewhoseleadscrew(single-startthread)hasaleadofS=8mm.DeterminethenumberofteethofgearsZ、Z、Z、Z.

EX.2.13.InFig.2-3,ifS=4mm,S=8mm,DeterminethenumberofteethofgearsZ、Z、Z、Z.

Hint::22/7=3.14286,355/113=3.1415929

Fig.2-3

Chapter3FlexibleTransmissions

EX.3.1DesignaV-beltdrivefora64kWcentrifugalwaterpumprunningat1200rpmanddrivenbyanoilenginerunningat350rpm.Maketheshortestpossiblecenterdistance.

EX3.2DesignaV-beltdrivefora5.5kWmotorruningat1440rpmdrivinganaircompressorat520rpm.

EX.3.3TheweightinFig3-1mustberaisedattherateof3m/s.Assumeaservicefactorof1.6willcareforimpacteffectsandfrictionofthesystem.Efficiencyofthissystemis85%.DesigntheV-belttransmission.

EX.3.4Aflatbelttransmitspowerbetweentwo700mmdiameterpulleys.Theshaftloadisnotexceed1200N.FindthelimitingvaluesoftightsidetensionFandslacksidetensionF.Disregardservicefactor.

EX.3.5AflatbelttransmissionD=125mmandD=400mm,centerdistancea=1400mm.Calculatethespeedofdrivenshaftiftheinputshaftis1440rpm.Ifthereisacreeprateof3%,howtocompensatetheslip?

Fig.3-1Fig.3-2

EX.3.6Whatisthemaximumspeedratioofabeltdrivewhentheangleofwrapis150degreeandthecenterdistanceis400mm?Confirmyourcalculationwithasuitablelayout.

EX.3.7ThebandbrakeshowninFig3-2isoperatedwithafootpedalforceF=50N.Ifcoefficientoffrictionf=0.30,whattorqueisdevelopedonthedrumwhenitsenseis(a)clockwise?(b)counterclockwise?(c)whatchangeinonedimensionwillmakethebrakeself-locking?

EX.3.8Designarollerchaindriveforasmallfan.Themotorspeedis900rpm,thedesiredfanspeedis500rpm,thepowerrequirementis435kW.

EX.3.9Determinethepowerwhichcanbetransmittedbyadoublerollerchain16A,thesmallsprockethas21teethdrivenbyamotorat1460rpm,thelargesprockethas64teeth.

EX.3.10Designarollerchaindrivetotransmit120kW,thedriversprocketspeedof420rpm,thedrivenspeedof120rpm;uniformpowerrequirement,12hr.perdayoperation.

Chapter4GearTransmission

EX.4.1ThegearshownintheFig.4-1haveamoduleof3mmand20pressureangle,andareinthesameplaneorcanbeassumedtobe.Thepinionrotatescounterclockwiseat650rpmandtransmits10kWthroughtheidlertothe28-Tgearonshaftc.Calculatetheforceonthe36-Tidler.

EX4.2Ageartrainiscomposedoffourhelicalgearswiththeshaftaxesinasingleplane.Thegearshavea20normalpressureangleanda15helixangleandanormalmoduleofmn=2mm.Gear1iscutright-handedandhas16teeth.Thegearsonshaftbhave56and27teethrespectively..Gear4has60teeth.Thedriverrotatesat970rpmandtransmits5kW.(Fig4-2)

Calculatethecenterdistancebetweenshaftsa,bandb,c.

Calculatethepitchdiameterofeachgear.

Findthetangential、radicalandthrustforcesoneachgearofshaftb.

Fig.4-1Fig.4-2

EX4.3IntheFig.4-3,gear1has28teeth,anormalmoduleof2mm.Gear2has70teethandgear3,126teeth.Gear1isthedriverandtransmits5.5kW,at960rpm.Centerdistanceabetweengear1and2is100mmandais200mm.

Calculatethehelicalangleandpitchdiameterofeachgear.

Findthedirectionoftheforcesshowninthefigure.

Tellifshaftbissubjectedtobendingmomentandtorque.

Tellwhetherthebearingofshaftbissubjectedtoradialforceandaxialforce.

EX4.4Thefigure(Fig.4-4)showsageartraincomposedofapairofstraightbevelgearsandapairofhelicalgears.Shaftaistheinputshaftofthetrainanddelivers17kWataspeedof720rpm.Thebevelgearshaveamoduleof5mmandafacewithofgearis50mm.Thehelicalgearshaveanormalmoduleof6mm.

Ifthethrustforcesonshaftbcounteract,findthehelixangleofthehelicalgear.

Indicatethehandofthehelicalgears.

Fig.4-3Fig.4-4

EX4.5Designatrainofgearstotransmit650kWfromashaftrunningat1460rpmtoonerunningat300rpm,useherringbonegears,selectthematerialsandheattreatments.Makeasketchofthelargegearassumingthataweldedconstructionisused.

EX4.6FindthetoothloadsshowninFig4.5.Allgearsare20normalpressureanglewithnormalmodulem=3mm,numberofteethZ=21,Z=64,centerdistancea=130mm.Calculatethereferencecirclesofpinionandgear.Theforceactingonthepiniondenotebythreecomponents:tangentialforceF,axialforceF,radialforceF.Assumethefrictionlossestobenegligible

Fig4-5Fig.4-6

EX4.7Twoparallelshaft360mmapart,areconnectedbytwoparallelhelicalgears(Fig.4-6).Thedriveshaftrunningat800rpm,willtransmit80hptothedrivenshaft,withaspeedreductionof3:1.

Findthenormalmodule,thehelixangleandthenumberofteethinbothgearandpinion.

b)Calculatethepitchdiameters.

c)Determinetheforcecomponentsandthetotaltoothload.

Hint::1hp(horsepower)=550ft.lbf/s=0.746kW

EX4.8Designageartransmission,thegearis45steelnormalizedandthepinionis40Crtobequenchedandtempered.Pinionturns820rpm,Z=23,Z=85,facewidthb=50mm.Findthepowerthatthegearsaretransmitting.Servicelifeis10years,16hr/day.

EX4.9Apairofhelicalgearsaremadeofinductionhardenedsteel.Speedratioi=3.2.pinionturns1440rpm.Ifthegearsarecarrying100kW,findsuitablevaluesforZ,Z,b,a,m.

EX4.10Designanopengearpairtotransmit15kW,thespeedofpinionis200rpmandthegear65rpmnotanyshockaction.

EX4.11Designapairofbevelgeartotransmit16kW,fromadrivingshaftmaking400rpmtoapumpmaking1000rpm.Theoperationistobeconsideredcontinuous.

EX4.12Anopenbevelgearpair,thegearismadeofcast-irontotransmit25kW,thespeedofthedrivingshaftis500rpm,ofthedriven180rpm.Servicetimeis10yr,and2hr/day,5day/wk,50wk/yr,

EX4.13Apairofbevelgearconsistsofpinionof19teethandagearof55teeth,modulem=8mm,thefacewidthoffaceb=70mm,thematerialofgeariscaststeel,andthepinionis40Cr.Theservicetimeis10years.,8hrperday,accompaniedbylightshock.Findwhatpowercanbetransmittedifthepinionspeedis450rpm.

Chapter5WormGearTransmission

EX.5.1AwormgearsetisshownintheFig.5-1.Therighthand2-toothwormhasamoduleof6.3mmandatransmits3kWat960rpmtoa31-toothwormwheel.Thediameterofthewormreferencecircleis63mm.Thecoefficientoffrictionfis5percent.

a)Determinetheefficiency.

b)Determinetheradial,tangentialandaxialforcesofthewormwheel.

c)Indicatethedirectionsoftheforcesinthefigure.

EX.5.2Awormgearandhelicalgeartrain(Fig.5-2),determinethehandofthehelixangleofthecylindricalgear,inorderthattheaxialforceisminimum.

EX.5.3Designawormgearingtotransmit15kWfromaelectricmotorrunningat1440rpmtoacompressorwhichshouldrunat60rpm..

EX.5.4Designawormdriveforaspeedreducertotransmit30kW,atawormspeedof620rpm.Thedesiredspeedratioisi=25.Assumethatthewormismadeofhardenedsteelandthematerialofwormgearisbronze.

Fig.5-1Fig.5-2

EX5.5Anelevatorcageisliftedattherateofv=1.0m/s,theelevatordrumdiameteris620mmandtheloadtobeliftedisQ=1000kg.Awormgeariskeyedtothedrumshaft.Assumingaspeedofthedrivingmotorof960rpm,determine:a)thewormandgearproportionsb)therequiredpowerofthemotor.

Hint:therequiredpowerofthemotorcanbecalculatedbythefollowingformula:

P=whereisefficiencyofthetransmission,forthestraightsidedaxialworm=0.5~0.55;Kp(=0.45~0.50)istheliftbalancefactor.

EX5.6Awormgearingtotransmit11kWfromanelectricmotorrunningatn=1460rpm.Itisknownthatm=10mm,d=90mm,Z=2,Z=40,thewormismadeof20Crsteelcarburized,hardened,andground,thewormgearismadeofbronzeZCuSn10P1.Calculatetheefficiencyofthewormgear..Checkthewormdriveforoverheating.

EX.5.7Aright-anglewormgearspeedreducerhasaquadruple-threadedwormandan89toothgear.Thewormhasanaxialmodulem=10mmandapitchdiameterof90mm.Thecoefficientoffrictionis0.025.Calculate(a)efficiency,(b)outputiftheinputis25kW.

EX.5.8A2-toothwormdrivesagearhaving47teeth.Theaxialmodulem=12.5mm,andthepitchdiameterofthewormis112mm.Theinputpoweris15kWat970rpm.Calculatethepoweroutputandthetransmittedforces(bythreecomponents).Assumeacoefficientoffrictionof0.032.Willtheunitback-drive?

EX5.9Awormdrivesagearwith49teeth.Theaxialmoduleis6.3mmandthepitchdiameterofthewormis80mm.thecoefficientoffrictionis0.15.Calculateandplottheleadangleandtheefficiencyasthenumberofteethinthewormvariesfrom1to6.

EX5.10Adouble-threadwormmesheswitha60teethwheelm=8mm.Pitchdiameterofthewormis80mm.Wormturns960rpm.Findthepowerbasedoncoolingfortemperatureriseof45℃.

Chapter6Shafting

EX.6.1FindthevalueofdimensioncinFig.6-1thatcausestheslopeoftheshafttobezeroatthebearings.

Fig.6-1

EX.6.2Alineshaftrotatingat450rpmmusttransmit80hp.Assumingthattheshaftismadeofalloysteel40Crdetermine(a)thenecessarydiameter.(b)theangleoftwistofshaftinalengthof1.5m.

Hint::1hp(horsepower)=550ft.lbf/s=0.746kW

EX.6.3Ashaftcarriesasteadytorqueof200kNm,theshaftismadeof45steel.Calculatethediameteroftheshaft.

EX.6.4Ashaftspeed360rpmandtransmit25kWismadeof45steel.Determinethediameteroftheshaftthattheangleoftwistis(a)1inl=25d(wherel_lengthoftheshaft;d_diameteroftheshaft),(b)0.5permeteroftheshaft.

EX.6.5Findthediameterofashippropellertotransmit1500hp.at100rpm.Thethrustfromthepropelleris150kN,thetorqueisuniform.

EX.6.6Findtheoutsidediameterofahollowshaft,transmit1000kWat85rpm,assumingthattheinnerdiameterisabout0.6oftheoutsidediameter,andcalculatethesavinginweightascomparedwiththesolidshaft.

EX.6.7Calculatethediameteroftheshaftinexercise6.4,using37SiMn2MoV.

EX.6.8Ahollowshafthasaholeofdiameterkd,wheredistheoutsidediameterandkisaconstant.Calculatethevalueoftheratioofdtothediameterdofasolidshaftforequalshearingstressescausedbythesametorquefork=0.5.

EX.6.9Ashafthasadiameter105mm,showninFig.6.2,withresistance-wirestraingagesgivingdeformationat45withtheshaftaxisareattachedatAandB.Leadwiresarecarriedfromthegagesthroughslipringsandbrushestoelectricinstruments,whichpermitthedeformationtobedetermined.Theshaftcarriestorqueonly.FinditsvalueiftheelongationatAinx-directionis0.0005mm/mmpositive,andelongationatBinthey-directionisthesameamountbutnegative.=0.3,E=2.110MPa.

EX.6.10FindthereactionsanddrawthebendingmomentdiagramandthetwistingmomentdiagramfortheshaftofFig.6-3Determinethediameteroftheshaft.

Fig6-2Fig.6-3

Chapter7BallandRollerBearings

EX.7.1Acertainapplicationrequiresaballbearingtolastfor2500hwithareliabilityof98%.Whatshouldbetheratedlifeofthebearingselectedforthisapplication?

EX.7.2Ifadeepgrooveballbearingcarriesaradialload5000Nandaaxialload1200N,speedoftheshaft800rpm,theliferequiredis10000h,selectthenumberofthebearing.

EX.7.3Ifa6208ballbearingloadedbyaradialforceF=10kNandaaxialforceF=5kN,findtheratinglifeinhours.Shaftspeedis1200rpm,andthebearingissubjectedtolightshock.

EX.7.4ShowninFig7.1theriseis50mmverticallyfor150mmhorizontally.Ateachenda2310bearingisinstalledTheshaftrotates1460rpmloadissteady.Makeadiagramandshowthereactionsateachend.Calculatetheexpectedaveragelifeoftheliftbearing.

EX.7.5Whatchangeinthelifeofarollerbearingwillcausetheratinglifetobedoubled?

EX.7.6ThegearreductionunitshowninFig.7.2isarrangedtorotatethecup,whiletheconeisstationary.BearingAhasaradialloadof1200Nandthethrustloadof320N.BearingBissubjectedtoaradialloadof700N.thedesiredlifeLis15000h.Selectsuitabletaperedrollerbearingusinganapplicationfactorof1.2.

Fig/7-1Fig.7-2

EX.7.7Adesignerneedsaballbearingwithacapacityratingof45kNtoachieveadesiredlifeof15000h.theshaftdiameterisnolessthan55mm.Whatbearingshouldbeselected?

EX.7.8Agivendeepgrooveballbearing6307hasaradialloadof14kNandathrustloadof6kN,lightrock.Whatistheequivalentradialload?Whatisthebearinglifeiftherotatingspeedoftheshaftis960rpm.?Whatisthelifewiththrustloadremoved?

EX.7.9Anastronomicalobservatoryusesaprotectingdomehavingaweightof45kN.Itissupportedby20steelballs,eachhavingadiameterof120mm.Theballsareconfinedbetweentwosteelguidewaywitha5mpitchdiameter.thecoefficientofrollingfrictionis0.18/R.Whatforceattheraceperipheryisrequiredtorotatethedome?Whatpowerisrequiredtorotatethedomeataspeedof0.1rpm.

EX.7.10Inredesigningamachine,arollerbearingisfoundtohaveanincreasedspeedof25%,andandecreasedloadof15%.Whatchangeofcapacityisrequiredtomaintainthesamehours?

Chapter8SlidBearings

EX.8.1ThelinerofaplainjournalbearingismadeoftinbronzeZCuSn10P1,itcarriesaradialloadof10kNandthespeedofshaft900rpm.Determinethediameterandwidthofthisbearing.

EX.8.2Aplainjournalbearingofboundarylubrication,carriesaradialforceof300kNandthespeedofshaft1420rpm.Determinethematerialanddimensionsofthebearing.

EX.8.3Aplainthrustbearingofacraneloadedbyaaxialforce16kN.Thisbearingturnsveryslowly,.The.O.D.=1.5I.D.ofthebearing.Determinethematerial,lubricantanddimensionsofthebearing.Makeadrawingofthebearing.

EX.8.4Themaximumloadwhichistakenbythebearingsofapunchpressis100t.Assumingthatthisloadisdistributedequallybetweenthetwobearings,oneontheeachsideoftheeccentric,determineminimumdiameterandlengthofthebearings.

EX.8.5Ajournalbearing1.5in.indiameterand2inlongsupportsaloadof216lbf.Whatisthepvfactorat1460rpm?Whichporousmetalbearingsaresturdyenoughforthisapplication?

Hint:1lbf=0.4536kgf1in=25.4mm,1lbf/in=6.89510MPa(N/mm)

EX.8.6Inajournalbearingtheshaftisoperatingataneccentricityof0.036mm.Theradialclearanceis0.060mmCalculateminimumoilfilmthicknessandtheeccentricityratioofthisbearing.

EX.8.7Inafoodmachinethereisabearingtosupportaloadof450N.Theshafthasadiameterof25mmandrotatingspeed55rpm.Itwillbeonlylightlylubricated.Selectasuitableporousmetalbearinganddeterminethebearinglength.

EX.8.8Atanaveragetemperatureof60℃whatoilinGB(nationalstandardoftheP.RofChina)shouldbeusedtogetaviscosityofabout25cSt?

EX.8.9Designahydrodynamiclubricatedsleevebearingloadedbyradialforce25kN.Theshaftturnsat1460rpm.

EX.8.10Afulljournalbearingis75mmlongand60mmdiameter.Thebearingloadis4kNandthejournalrunsat1440rpm.Usingaclearance0.03mmandanaverageviscosityof0.2Pa.S,findthefrictionpower

Chapter9BoltConnectionsandScrew

EX.9.1Thefigure9-1showsthattwocolddrawnbarsof45steelareboltedtogetherbytwoM16boltsgrade6.8toformalapjoint.Thecoefficientoffrictionbetweenthebarsis0.2.DeterminetheforceFcanbecarriedbythisconnection.

EX.9.2AcolddrawnsteelbeamistobefastenedusingfourM10grade8.8boltstothe180709-GB707-1988channelshownintheFig.9-2.Thecoefficientoffrictionis0.18.WhatmaximumforceFcanbeappliedtothecantilever?Donotconsiderthechannel.

EX.9.3AsshownintheFig.9-3,abeamisconnectedbythreefinefittedboltsgrade8.8andsupportsastaticloadofF=15kN..Calculatetheminimumsizeofthebolt.

EX.9.4TheFig.9-4showsacastbracketwhichistosupportaforceF=5000N.Thebracketistobeboltedtoasmoothverticalface,notshown,bymeansoffourbolts.Coefficientoffrictionis0.12.Calculatethesizeofthebolts.

EX.9.5TheFig.9-5showsahydrauliccylinder,inwhichouterdiameterofthecylinderd=144mm,interdiameterd=120mm,lengthL=400mm,thicknessofthecoverb=20mm.Boththebracketsandthecylinderaremadeofsteel.Workingpressureis1to5MPa.SixM16metricgrade8.8gradeboltsareused.

Calculatethestiffnessoftheboltandthecylinder,assumingthattheendbracketsareperfectlyrigidandtheentirecylinderiscompresseduniformly.

Findthemeanandalternatingstressesinthebolt.

Checkthestrengthofthebolts.

Fig.9-1Fig.9-2

EX.9.6Apressurecylinderofinternaldiameter420mm.Atotalof16boltsistobeusedtoresistapressurethatvariesfrom0to3.2MPa..Findtheproperboltpreloadandthedimensionofthebolts.

EX.9.7FindtheforceoftensioninanM10bolt.Ifitistightenedbyawrenchwithatorqueequalto35Nm.Assumethecoefficientoffrictionforthescrewandthecollaristhesame,andmakecomputationforcoefficientsof0.08,0.12.,and0.18.

Fig.9-3.Fig.9-4.

Fig.9-5.

EX.9.8Aloadof40000Niscarriedbya70mmdiametertrapizoidalsingle-threadscrewofstandardproportions.TheODofcollaris100mm,andtheIDis75mm.

(a)Ifthecoefficientoffrictionofthethreadandthecollaristhesamef=0.15.findpowerrequiredtorotatethescrewiftheweightistoberaisedattherateof20mm/s.

(b)Findthepowerrequiredtolowertheloadatthesamerate.

(c)Whatisthe