... !¼6:344lb-ftð6-6Þ¼76:130lb-in:whereni=1/5.488fortheendrollersandni=1/1.254fortheintermediaterollers.Ifthebrakehadbeenmountedoneitheroftheendrollershafts,equation(6-6)wouldhavebeenreplacedbyT¼4:1140:1553"2ð0:0759Þþ20ð0:000556Þð4:375Þ2þ23032:24:375122#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 ... 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,T¼2Apmaxwr2osinfo2ð8-8Þforeithertwoopposinginternalorexternallinearlyactingbrakeshoes,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...