Tài liệu Clutches and brakes design and selection P8 ppt

... 301References 316Chapter 14 Engineering Standards for Clutches and Brakes 317I. SAE Standards 317II. American National Standards Institute (ANSI) 320III. Other Standards Organizations 320Bibliography ... according to the SAE J661 standard. Field perform-Friction Materials 92Band Brakes Band brakes are simpler and less expensive than most other braking devices,with shoe brakes, as perhaps their ... derive, where possible, the design formulas for the major types of clutches and brakes listed in the contents and to display an example of their use in a typical design. Some pertinentcomputer...

... pressure upon the lining.Band Brakes 23Copyright © 2004 Marcel Dekker, Inc.2BandBrakesBandbrakesaresimplerandlessexpensivethanmostotherbrakingdevices,withshoebrakes,asperhapstheirnearestrival.Becauseoftheirsimplicity,theymaybeproducedeasilybymostequipmentmanufacturerswithouthavingtopurchasespecialequipmentandwithouthavingtousefoundryorforgingfacilities.Onlytheliningmustbepurchasedfromoutsidesources.Bandbrakesareusedinmanyapplicationssuchasinautomatictransmissions(Figure1)andasbackstops(Figure5—devicesdesignedtopreventreversalofrotation),forbucketconveyors,hoists,andsimilarequipment.Theyareespeciallydesirableinthelast-mentionedapplicationbecausetheiractioncanbemadeautomaticwithoutadditionalcontrols.I.DERIVATIONOFEQUATIONSFigure2showsthequantitiesinvolvedinthederivationoftheforcerelationsused ... Quantities and geometry used in the derivation of the band-brake design relations.Band Brakes 19Copyright © 2004 Marcel Dekker, Inc.To ensure clearance, let the drum diameter be 32 in., and design ... pressure betweenthe drum and the lining, and w represents the width of the band. Uponsimplifying equations (1-1) and (1-2) and remembering that as the element ofband length approaches zero,...

... in lb, and the adjusting link isExternally and Internally Pivoted Shoe Brakes 57Copyright © 2004 Marcel Dekker, Inc.V. DESIGN OF SINGLE-ANCHOR TWIN-SHOE DRUM BRAKES Internal shoe drum brakes ... Marcel Dekker, Inc.3ExternallyandInternallyPivotedShoe Brakes TypicalexternallyandinternallypivotedshoebrakesareshowninFigures1 and 2. In all but extremely rare designs, equal forces act upon ... Inc.Thislinkforceandtheactivatingmomentbothactonthesecondaryshoe,sothattheforceandmomentequationsofequilibriumforthesecond-aryshoebecomeFr2¼ÀrwZf2f1pcosfdfþArwZf1f2psinfdfþFlsinf2þh2ð5-7ÞFu2¼ÀrwZf2f1psinfdfþArwZf2f1pcosfdfþFlcosf2þh2ð5-8Þwhere2histheanglesubtendedbytheadjustinglink.Next,Ma2¼Mp2þMf2À2RFlsinf22sinf22þh2ð5-9ÞwhereMp2andMf2areagaingivenbyequations(5.1 )and( 5.2)intermsofthepressuredistributiononthesecondaryshoe.TorqueforeithershoemaybecalculatedfromT¼ArwZf2f1pdfð5-10ÞEventhoughtheseequationsdonotuniquelydeterminethepressuredistributionoverthebrakelining,theyarestillofusebecausetheyallowthedesignengineertocomparetheeffectsofdifferentrealisticpressuredistribu-tionandtodesigndrumsandshoeswhoserigiditywillinduceparticularpressuredistributionsovertheprimaryandsecondaryshoes.Thefirstofthetwopressuredistributionsconsideredisasynthesisof(1)thesinusoidaldistributionassociatedwithanondeformingdrumandshoe,generallyassociatedwithalightlyloadedbrake ,and( 2)theforcepeaksthatoccurattheendsofload-bearingmembersincontact.Thesecondofthetwoisasysthesisof(1)theconstantdistributionsaidtobeassociatedwithmoreheavilyloadedbrakes ,and( 2)thepreviouslynotedforcepeaks.Thusthepressuredistributionswillberepresentedeitherbypp0¼eÀc1c=f0ðÞcoscf0kc2þc3c¼fÀf1ð5-11Þorbypp0¼eÀc1c=f0ðÞcoscf0kc2þc3sincþf1ðÞð5-12Þfortheprimaryshoes,wherethepeakpressureoneachshoeoccursattheheelbecauseitspivotcannotsustainaradialforceintheoutwarddirection.TheserelationsproducethepressuredistributionsshowninFigures1 4and1 5forthe...

... Inc.4LinearlyActingExternalandInternalDrumBrakesLinearlyactingdrumbrakesarethosefittedwithshoeswhich,whenacti-vated,approachthedrumbymovingparalleltoaradiusthroughthecen-teroftheshoe.TypicallinearlyactingdrumbrakesareillustratedinFigures1–3.Analysisoflinearlyactingbrakesincludesthoseinwhichthecentrallypivotedshoesareattachedtopivotedlevers,asinFigure1.Includingbrakesofthisdesignwithinthecategoryoflinearlyactingbrakesisjustifiediftheyaredesignedsothattheappliedforcesontheshoesandliningsactalongtheradiioftheshaftsthattheygripwhenthebrakesareapplied.Brakesofthistypemayacteitheruponbrakedrumsordirectlyuponrotatingshaftsandaresuitableforuseinheavy-dutyapplications,suchasfoundinminingandconstructionequipmentandinmaterials-handlingmachinery.Internallinearlyactingdrumbrakes,suchasusedontrucksinEurope,maybedesignedasinFigure2.Eitherpneumaticorhydrauliccylindersorcams ... Inc.4LinearlyActingExternalandInternalDrumBrakesLinearlyactingdrumbrakesarethosefittedwithshoeswhich,whenacti-vated,approachthedrumbymovingparalleltoaradiusthroughthecen-teroftheshoe.TypicallinearlyactingdrumbrakesareillustratedinFigures1–3.Analysisoflinearlyactingbrakesincludesthoseinwhichthecentrallypivotedshoesareattachedtopivotedlevers,asinFigure1.Includingbrakesofthisdesignwithinthecategoryoflinearlyactingbrakesisjustifiediftheyaredesignedsothattheappliedforcesontheshoesandliningsactalongtheradiioftheshaftsthattheygripwhenthebrakesareapplied.Brakesofthistypemayacteitheruponbrakedrumsordirectlyuponrotatingshaftsandaresuitableforuseinheavy-dutyapplications,suchasfoundinminingandconstructionequipmentandinmaterials-handlingmachinery.Internallinearlyactingdrumbrakes,suchasusedontrucksinEurope,maybedesignedasinFigure2.Eitherpneumaticorhydrauliccylindersorcams ... f0Þsin aLinearly Acting External and Internal Drum Brakes 81Copyright © 2004 Marcel Dekker, Inc.4LinearlyActingExternalandInternalDrumBrakesLinearlyactingdrumbrakesarethosefittedwithshoeswhich,whenacti-vated,approachthedrumbymovingparalleltoaradiusthroughthecen-teroftheshoe.TypicallinearlyactingdrumbrakesareillustratedinFigures1–3.Analysisoflinearlyactingbrakesincludesthoseinwhichthecentrallypivotedshoesareattachedtopivotedlevers,asinFigure1.Includingbrakesofthisdesignwithinthecategoryoflinearlyactingbrakesisjustifiediftheyaredesignedsothattheappliedforcesontheshoesandliningsactalongtheradiioftheshaftsthattheygripwhenthebrakesareapplied.Brakesofthistypemayacteitheruponbrakedrumsordirectlyuponrotatingshaftsandaresuitableforuseinheavy-dutyapplications,suchasfoundinminingandconstructionequipmentandinmaterials-handlingmachinery.Internallinearlyactingdrumbrakes,suchasusedontrucksinEurope,maybedesignedasinFigure2.Eitherpneumaticorhydrauliccylindersorcams...

... Inc.5DryandWetDiskBrakesandClutchesThischapterondiskbrakesandclutcheswillconsiderannularcontactdiskclutchesandbothcaliperandannularcontactdiskbrakes,asillustratedinFigures1,2 ,and3 .Caliper disk brakes, ... Airflex Division, Cleveland, OH.)Dry and Wet Disk Brakes and Clutches 93Copyright © 2004 Marcel Dekker, Inc.used on large earth-moving equipment, on mine shuttle cars, and similarequipment ... multiple-disk brakes and clutches, illustrated in Figure 3, havesimilar multiple-disk construction, but operate in an oil bath. Thus these brakes are isolated from dirt and water, and the circulation...

... sin aÞð1-10ÞCone Brakes and Clutches 109Copyright © 2004 Marcel Dekker, Inc.II.FOLDEDCONEBRAKEPrototypeconebrakeshavebeendesignedandtestedforarangeofvehiclesizes,fromtractorsandtrailerstosubcompactautomobiles[1].Boththelargeandsmallsizesusedafoldedconedesign,asillustratedinFigures 5and6 ,eachwitha=27j.Althoughtheconebrakehasfewerpartsthandrum brakes, thisadvantagemustbebalancedagainstthedisadvantageofrequiringanoutboardwheelbearing.Analysisofthefoldedconebrakewithasectorshoe,showninFigure5,toobtaindesignformulasforthetorquecapabilityandtherequiredactiva-tionforceisquitesimilartothatusedforsimpleconebrakesandclutches.SincethebrakesillustratedinFigures 5and6 useasectorpad,webegintheanalysisbyobservingfromFigure7(a)thatanelementofareaontheconicalsurfacemaybewrittenasda¼rdudrsinað2-1ÞFIGURE4DesignregionsintheA,aplaneforconeclutches /brakes. Cone ... Inc.II.FOLDEDCONEBRAKEPrototypeconebrakeshavebeendesignedandtestedforarangeofvehiclesizes,fromtractorsandtrailerstosubcompactautomobiles[1].Boththelargeandsmallsizesusedafoldedconedesign,asillustratedinFigures 5and6 ,eachwitha=27j.Althoughtheconebrakehasfewerpartsthandrum brakes, thisadvantagemustbebalancedagainstthedisadvantageofrequiringanoutboardwheelbearing.Analysisofthefoldedconebrakewithasectorshoe,showninFigure5,toobtaindesignformulasforthetorquecapabilityandtherequiredactiva-tionforceisquitesimilartothatusedforsimpleconebrakesandclutches.SincethebrakesillustratedinFigures 5and6 useasectorpad,webegintheanalysisbyobservingfromFigure7(a)thatanelementofareaontheconicalsurfacemaybewrittenasda¼rdudrsinað2-1ÞFIGURE4DesignregionsintheA,aplaneforconeclutches /brakes. Cone ... Inc.II.FOLDEDCONEBRAKEPrototypeconebrakeshavebeendesignedandtestedforarangeofvehiclesizes,fromtractorsandtrailerstosubcompactautomobiles[1].Boththelargeandsmallsizesusedafoldedconedesign,asillustratedinFigures 5and6 ,eachwitha=27j.Althoughtheconebrakehasfewerpartsthandrum brakes, thisadvantagemustbebalancedagainstthedisadvantageofrequiringanoutboardwheelbearing.Analysisofthefoldedconebrakewithasectorshoe,showninFigure5,toobtaindesignformulasforthetorquecapabilityandtherequiredactiva-tionforceisquitesimilartothatusedforsimpleconebrakesandclutches.SincethebrakesillustratedinFigures 5and6 useasectorpad,webegintheanalysisbyobservingfromFigure7(a)thatanelementofareaontheconicalsurfacemaybewrittenasda¼rdudrsinað2-1ÞFIGURE4DesignregionsintheA,aplaneforconeclutches /brakes. Cone Brakes and Clutches 113Copyright © 2004 Marcel Dekker, Inc.where we again use the pressure p and element of area da...

... Inc.Beyondthispointthetorquedecreasesrapidly,asshowninthesliptorqueversusspeedcurveinFigure13(a).ComparisonwithFigure13(b)correctlyimpliesthattheshapeofthedecreasing-torqueportionofthecurvetotherightofthecriticalpointreflectsboththechangeinthehysteresisloopwithincreasingtemperatureandtheheattransfercharacteristicsofthecoolingsystem(i.e.,whetherairorliquidandthetemperatureandvelocityofthecoolingmedium).Whentheseconditionsarefixedtheshapeofthecurveremainsqualitativelyinvariant.Thus,asthebraketorqueincreasesfromonesizeofbraketoanother,thatportionofthecurvetotheleftofthecriticalpointdecreasesunlessimprovedcoolingisusedtomovetheconcaveportionofthecurveupwardandtotheright,thusmovingthecriticalpointtotheright.ThemagnitudeofthatportionofthecurvewhichisindependentofrotationalspeedtotheleftofthecriticalpointinFigure14ais,ofcourse,alsodeterminedbythetorqueversuscontrolcurrentcurveshowninFigure14b.ThedifferencebetweenthetorqueobtainedfromincreasinganddecreasingcontrolcurrentisshowninFigure2.Useofthetermsliptorque,incidentally,istoemphasizethatthetorqueactsbetweentwomechanicalpartswhichmaybemovingrelativetooneanotherbecausethesebrakesmaybeusedastensioncontroldevicesaswellasameansofstoppingtherotationentirely.FIGURE9Torque-slipspeedcurvesfordryfrictionandmagneticparticlebrakes(also clutches) .Magnetic Particle, Hysteresis and Eddy-Current Brakes 137Copyright © 2004 Marcel Dekker, Inc.7MagneticParticle,Hysteresis ,and Eddy-CurrentBrakesandClutchesAllthreeofthesebrakeorclutchtypeshavenowearingpartsbecausethetorqueisdevelopedfromelectromagneticreactionsratherthan ... Hysteresis and Eddy-Current Brakes 143Copyright © 2004 Marcel Dekker, Inc.IV. EDDY-CURRENT BRAKES AND CLUTCHES Construction of eddy-current brakes is physically similar to that of hysteresis brakes. ... Hysteresis and Eddy-Current Brakes 127Copyright © 2004 Marcel Dekker, Inc.II.MAGNETICPARTICLEBRAKESANDCLUTCHESThesebrakesareavailableinarangeofsizesthatincludethe100-lb-ftmodelshowninFigure3andthe8-lb-ftmodelshowninFigure4.Sincethesecon-figurationsareequallysuitedforclutches,theymaybecombinedtoformclutch-brakecombinations,asinFigure5.Whenusedasaclutch,theunithastwomovingparts;whenusedasabrakeithasonlyone.Whenusedasaclutch,theconfigurationisasrepresentedbythesche-maticinFigure6(a).Theinputshaftisattachedtoacylindricaldrum,termedthe...

... Inc.Thekineticenergiesmaybefoundfromn14¼116n24¼13:2n34¼13:2m1¼1278m2¼276m3¼721m4¼231r1g¼0:81r2g¼0:17r3g¼0:32r4g¼0:09Ig1¼m1r21gIg2¼m2r22gIg3¼m3r23gIg4¼m4r24gId¼mdr2dgked¼12Idn214keg1¼12Ig1n214keg2¼12Ig2n224keg3¼12Ig3n234keg4¼12Ig4wherem1throughm4arethemassesofgears1through4,respectively,andr1gthroughr4garetheirrespectiveradiiofgyration.Thus,KEd¼kedN2m¼185:5N-mKEL¼12mLv2c¼957:3N-mKEr¼12mrv2c¼49:2N-mKEg1¼keg1N2m¼4224:5N-mKEg2¼keg2N2m¼1004:7N-mKEg3¼keg3N2m¼9299:2N-mKEg4¼keg4N2m¼2413:3N-mAdditionofthesegivesKE¼ðkeg1þkeg2þkeg3þkeg4þkedÞN2mþKELþKEr¼18;133:6N-mSouponaddingthistothetotalpotentialenergyofPE¼23;202:3N-mthetorquerequiredmaybefoundfromTo¼PEþKEðNm=2Þt¼813:9N-mð8-6ÞinwhichtheaveragemotorspeedduringbrakingwastakentobeNm/2.Thebrakingrequirementof813.9N-mmaybemetbyusingavarietyof brakes, suchasband,externallinear,annularcaliper,andannulardisk brakes. Tochooseamongthese,recallequation(1-10)fromChapter1,equa-tion(2-1)fromChapter4,andequations(1-7 )and( 3-5)fromChapter5corresponding ... Inc.theannularcaliperandannulardiskbegivenbyequation.Accordingly,eval-uatetheformulasT¼pmaxwr2oð1ÀeÀAfÞð8-7Þforabandbrake,T¼2Apmaxwr2osinfo2ð8-8Þforeithertwoopposinginternalorexternallinearlyactingbrakeshoes,T¼2Apmaxr3o3ffiffiffi3pfoð8-9Þfortwoopposingdiscbrakepads,eachsubtendingangleBo ,and T¼4kApmaxr3o3ffiffiffi3pð8-10ÞfortwocompleteannularpadsinwhichBo=2kinequation(8-9).WeshallalsoconsideranexternalpivoteddrumbrakewithaleadingandtrailingshoethatmaybeevaluatedbyinvokingtheprogramusedinChapter3.Inallofthesecalculationsassumeafrictioncoefficientof0.3 ,and setthewidthfortheband,thelinearlyactingdrumbrake,andtheexternallypivotedbraketo5cm.Limitthemaximumliningpressureforthebandbrakeandfortheexternallypivotedbraketo2.0MPa,andlimitthepressurefortheotherliningsto3.0MPa,whichmaybeeitherformedorsolid.Liningpressurefortheexternallypivotedbrakewastakentobe2.0MPa,merelyforcomparisonwiththebandbrake.Figure11(a)showsthetorquecapacityinnewton-metersasafunctionofangleBsubtendedbyeachshoeforadrumdiameterof300mm,andFigure11(b)showsthetorquecapacityinnewton-metersforband,linearlyacting,caliper,andannularbrakesasafunctionofthedrumordiscdiameterinmillimeters.AlthoughthelinearlyactingdrumbrakeisclearlymoreeffectivethantheotherbrakesshowninFigure11(b),itandalloftheotherthreebrakesinthatfigurerequiremorehardwarethandoesthebandbrake.Therefore,selectthebandbrake,becauseitcanprovidethenecessarytorquecapabilitywithmechanicalsimplicity.Externaldual-shoedrumbrakesarethenextsimplest.Increasingthemaximumliningpressureto3.0MPaforanexternallypivoteddual-shoebrakeallowsthedrumdiametertobereducedto170mmandtheradialdistancetotheshoepivottobereducedto100mm,fromthe150mmas-sociatedwithFigure11(a),togetatorquevs.anglecurvesimilarinshapeandmagnitudetothatinFigure11(a).Thus,eitheranexternallypivotedChapter8174Copyright ... !¼6:344lb-ftð6-6Þ¼76:130lb-in:whereni=1/5.488fortheendrollersandni=1/1.254fortheintermediaterollers.Ifthebrakehadbeenmountedoneitheroftheendrollershafts,equation(6-6)wouldhavebeenreplacedbyT¼4:1140:1553"2ð0:0759Þþ20ð0:000556Þð4:375Þ2þ23032:24:375122#¼34:811lb-ftð6-7Þandthebrakingtorquerequirementwouldhavebeenn=5.488timeslargerthanthatfoundbyequation(6-6).Thiscomparisonisanexampleofthegen-eralrulethatthebrakeshouldusuallybeplacedinthefastershaft.VII.EXAMPLE3:ROTARYKILNThecurvesinFigure6clearlyimplythatefficientuseofaclutchbyreducingthepowerlossduetoheatgeneration,alongwithwear,requiresthatthespeedsofitsinputandoutputshaftsshouldbenearlyequal.Accordingly,dependinguponthepowersource(electricorhydraulicmotor,turbine,orinternalcombustionengine),aclutchmaybeusedtochangegearratios,tochangefromonepowersourcetoanotherwhenthespeedsarenearlyequal,ortodisconnectthepowersourcebeforebraking.Thisexamplewillconsideraloadthatisessentiallyrotationalinordertoconcentrateonclutchandbrakeselectionwhendynamictorqueandbrakeheatingcurvesareavailable.Bothclutchandbrakeanalyseswilldisplaysomeofthecalculationinvolvedwhenthespeedsoftheinputandoutputshaftsarenotalmostequal.Arotarykilnistobedrivenbya15-hpthree-phasemotoroperatingat870rpmandratedtodeliveratorqueof240lb-ftwithaKfactor(overloadfactorforstarting)of2.64.Themotor,clutch,geartrainwitha28.4speed-reductionratio,androtarykilnarearrangedasshowninFigure7.Theoveralldamping...

... 1 and 230j between detents 2 and 3130j between detents 8 and 3 and that the angular separation between detent centers 1 and 5 is given by25j between detents 1 and 230j between detents 2 and ... detents 3 and 440j between detents 4 and 5130j between detents 1 and 5The second instance occurs when balls 8 and 1 engage detents 1 and 5,where ball centers 8 and 1 are separated by 75j and detent ... Inc.MaximumpressureontheliningmaybefoundfromF¼rowZfo=2Àfo=2pcosfx¼rowpmaxZfo=2Àfo=2cosðfÞ2df¼pmax2rowðfoþsinfoÞð1-8Þuponusingthepressuredistributionfromequation(1-2)inChapter4.Hence,pmax¼2FrowðfoþsinfoÞð1-9ÞTheangularvelocityoftheinputshaftwhentheweightsmakeinitialcontactwiththedrummaybefoundbysettingthesquarebracketinequation(1-6)equaltozero.Substitutionofx=2kn/60,wherenisinrpm,followedbysolvingtheresultingexpressionforn,yieldsn¼k30ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffingrcðhÞþyð1þDÞrð1-10ÞTheroleofparametershandEinequation(1-5)uponforceF,equation(1-3),andthereforeuponpmax,equation(1-9)andthespeedatwhichtheyfirstcontactthedrumareshowninFigures2(a)through(d).Observethatthevariationofthepressure,andhencetheforce,thateachweightexertsagainstthedrumisalinearfunctionofparameterEandthatitbecomesanearlylinearfunctionofh,andhenceofri,forhgreaterthanabout0.3.Thedependenceofthewidthofeachweight,however,becomesincreas-inglynonlinearashincreasesandasEdecreases.Therotationalspeedforinitialcontactisalsonearlylinearforh<0.6,especiallyforthelargervaluesofE.ExampleDesignacentrifugalclutchtoprovideatorqueof2400N-mwhentherota-tionalspeedreaches870rpmusingsectorweightshavingthegeometryshowninFigure3(a).Preferredcharacteristicsarethatinitialcontactbetweenweightsanddrumoccuratbetween22 0and2 30rpmandthatthewidthoftheweightsbelessthan30cm.Assumealiningcoefficientoffrictionof0.35anddesign foraninsidedrumradius(minustheliningthickness)of15cm,adisplacementyof3mmforthe...

... Nd1ld1ln1tan2f and Nn2¼Ndrd2rn2¼ Ndld 2ln2tan2fð3-1Þwhere rd1 and rnlare the radii of the driver and driven cones, respectively, atpoint 1, rd 2 and rn2are driver and driven ... Inc.setofunitstobeusedforeachratio,andtheresultingratiosareindependentoftheunitsused.Relativelybroadcurvesareshowninthefollowingcomputer-generatedgraphsforeasyreadingtoshowcharacteristicbehaviorandtoprovidecontrastagainstthegridlines.Associatedroutines,suchasMathcadTrace,appeartoreadthemfromtheoriginatingdata,therebyeliminatingtheread-ingerrorsassociatedwithtracewidths.I.BELTDRIVESEquipmentusingnonmetallicbeltdrivesmayincludetheclutchcapabilitybymountingthemotor(becauseitisusuallysmallerthanthedrivenmachine)eitheruponahingedbaseoruponaslidingbasefittedwithaleveroralinkagethatpermitsthemotortobemovedtoandfromthedrivenmachineinordertoapplyandrelievethebelttensionandtherebygiveclutching(applyingbelttension)anddeclutching(relievingbelttension)capability.Thesedesignseliminatetheneedforamechanicalclutch.Theirsim-plicityisachieved,however,attheriskofintroducingthepossibilitythatfrictionalheatingofthebeltduringidling,whenthebelt(orbelts)mayrestonthemotor’srotatingsheave(pulley).Thatmaygenerateenoughheattocausebeltingmaterialstoslowlyshrink.Thisreductioninthecenterdistancebetweenthedrivinganddrivenpulleys,orsheaves,maybegreatenoughtocauseanunintendedre-engagementofthemotorandthedrivenmachine.Itmayalsoinhibittheirdisengagement.Consequently,somebeltmanufacturersproducebeltsthatresistshrinkageduetoheatingforuseintheseclutchinganddeclutchingapplications.Torquecapabilityforthesedrivesisaseparatecalculationtobeperformedaccordingtotheproceduresgivenbythebeltmanufacturers.Therefore,itwillnotbeconsideredinthefollowingdiscussion.A.HingedBaseAtfirstglanceitmayappearthatmovingamotorbymountingiteitheronahingedbaseoronaslidingbaseissosimplethatnoanalysisisnecessary.Ananalysis,however,doesbringforthseveralconsiderationsthatmaybemissedinselectingthedimensionsofthebaseplate,inlocatingthepositionofthebaseplatehinge,orindesigningthelinkagefortheslidingbaseplate.Twosimilar,butdistinct,mountingdesignsforhingedbaseswillbeconsidered.Intheseconfigurationsitistheweightofthemotoralonethatprovidesthebelttension.ThetensionvectorshowninFigure1(a )and( b)acting ... Inc.maximuminFigure16,setg=13.52j,asreadusingtheMathcadTracefeature.Evaluationofequation(1-13)forn=0.2,g=180,U=0.3,a=14j,andh=20foru=13.52jandforu=20jgivesadetentforceof4.544lb,whichiswithintheacceptablerange.Substitutionofg=180andq=1/32in.intoa=gq=180/32=5.625in.enablesdeterminationofrfromr=Ua=0.(5.625)=1.688in.Withlengthlgivenbyl=r/n=1.688/0.2=8.44in.,itfollowsthattheclearancegivenbylÀr=8.440À1.688=6.752in.exceedsthatspecified.Thisclearancerequirementmaybesatisfiedbyincreasingthemagni-tudeofnandreducingthemagnitudeofg.Thus,ifn=0.28andg=150,thedetentforcebecomes4.702lb,aisreducedto4.688in.,andrbecomes1.406in.Thesevaluesgivel=5.021in.,sotheclearanceis5.021À1.406=3.615in.,whichiswithinthedesiredrange.VI.EXAMPLE3:CONEDRIVESelectaconedriveforacombinationgolfcardandaproposedcongestedareacommutercartforuseincommunitiesthatacceptthem.Analysisoftorquetransmissiononthebasisofthedynamiccoefficientsoffrictionforacceptableliningsindicatesthata2.00-in.overlapwouldbesufficient.Forcomparison,consideronedesignwiththedriverconehavinganapexhalf-angleof40janddrivenconeshavingapexhalf-anglesof50jandaseconddesigninwhichboththedriveranddrivenconeshaveapexhalf-anglesof45j.Inbothcasesinitiallyselectaconegeneratorlengthof6.00in.toallowtheoverlaptobegreaterthan2.00in.intheeventthattheprototypeshouldrequiremodification.Beginwiththe40j,50jcombinationandturntoFigure11toselectthedimensionsoftheconesbyenteringthecurveatz=6andreadinguptothe40jline.Theprincipalradiusofcurvatureatthatpointis5.0346.Sincezismeasuredininches,theprincipalradiusofcurvatureis5.0346in.ReadingtotheleftatthisvalueofUyieldsthatatz=4.25in.,theprincipalradiusofcurvatureofthe50jhalf-angleconeis5.0650in.Aplotofthex-dimensionforeachcone,showninFigure17(a),confirmsthatthetwoconesshouldrollwithout...