... 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 ... inertia Ii, n weights Wˆi and theirelevation changes, and including nonzero values of velocity vi, and angularrotation Ni.III. BRAKING AND CLUTCHING TIME AND TORQUEWork done by a brake ... !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...