Tài liệu CLUTCHES AND BRAKES Design and Selection

... and Eddy-CurrentBrakes and Clutches 125I. Theoretical Background 126II. Magnetic Particle Brakes and Clutches 130III. Hysteresis Brakes and Clutches 132ContentsxIV. Eddy-Current Brakes and Clutches ... Collection 81Chapter 5 Dry and Wet Disk Brakes and Clutches 83I. Caliper Disk Brakes 84II. Ventilated Disk Brakes 91III. Annular Contact Disk Brakes and Clutches 92IV. Design Examples 99V. Notation ... together the formulas for thedesign and selection of a variety of brakes and clutches. The second is toprovide flowcharts and programs for programmable calculators and personalcomputers to facilitate...

... 2BandBrakesBandbrakesaresimplerandlessexpensivethanmostotherbrakingdevices,withshoebrakes,asperhapstheirnearestrival.Becauseoftheirsimplicity,theymaybeproducedeasilybymostequipmentmanufacturerswithouthavingtopurchasespecialequipmentandwithouthavingtousefoundryorforgingfacilities.Onlytheliningmustbepurchasedfromoutsidesources.Bandbrakesareusedinmanyapplicationssuchasinautomatictransmissions(Figure1)andasbackstops(Figure5—devicesdesignedtopreventreversalofrotation),forbucketconveyors,hoists,andsimilarequipment.Theyareespeciallydesirableinthelast-mentionedapplicationbecausetheiractioncanbemadeautomaticwithoutadditionalcontrols.I.DERIVATIONOFEQUATIONSFigure2showsthequantitiesinvolvedinthederivationoftheforcerelationsused ... the lining material and the drum, p represents the pressure betweenthe drum and the lining, and w represents the width of the band. Uponsimplifying equations (1-1) and (1-2) and remembering that ... the element ofband length approaches zero, sin(du/2) approaches du/2, cos(du/2)FIGURE2 Quantities and geometry used in the derivation of the band-brake design relations.Band Brakes 19Copyright...

... f0ð1-14ÞExternally and Internally Pivoted Shoe Brakes 37Copyright © 2004 Marcel Dekker, Inc.3ExternallyandInternallyPivotedShoe Brakes TypicalexternallyandinternallypivotedshoebrakesareshowninFigures1 and ... brake life, heatdissipation, fading, and braking torque capability.III. DESIGN OF DUAL-ANCHOR TWIN-SHOE DRUM BRAKES For both external and internal shoes and for either direction of rotation ... Inc.rotatesawayfromthepivot,self-lockingcanbeavoidedifMf/MpisalwaysgreaterthanÀ1.Similarcriteriaholdforinternalbrakesexceptthatthedirectionsofrotationarereversedforthesamealgebraicsigns.Sincemostbrakesaredesignedforrotationinbothdirections,itisgenerallyconvenienttocombinethesecriteriaintoasinglecriterion,whichisthatself-lockingofbothinternalandexternaldrumbrakesmaybeavoidedifÀ1VMfMpVþ1ð3-3ÞSelectionofshoeanddrumanglesanddimensionsinaccordancewiththiscriterionmaybeaidedbyconstructionofdesigncurvessuchasillustratedinFigures 7and8 ,inwhichtheratioMf/AMpisplottedagainstanglef2forselectedvaluesofthecoefficientoffriction.ExternalshoesarecharacterizedbyR/rratiosgreaterthanunityandinternalshoesbyr/Rratioslessthanunity.TheratioMf/AMphasbeenplottedinsteadofMf/MpinFigures 7and8 because...

... 4LinearlyActingExternalandInternalDrumBrakesLinearlyactingdrumbrakesarethosefittedwithshoeswhich,whenacti-vated,approachthedrumbymovingparalleltoaradiusthroughthecen-teroftheshoe.TypicallinearlyactingdrumbrakesareillustratedinFigures1–3.Analysisoflinearlyactingbrakesincludesthoseinwhichthecentrallypivotedshoesareattachedtopivotedlevers,asinFigure1.Includingbrakesofthisdesignwithinthecategoryoflinearlyactingbrakesisjustifiediftheyaredesignedsothattheappliedforcesontheshoesandliningsactalongtheradiioftheshaftsthattheygripwhenthebrakesareapplied.Brakesofthistypemayacteitheruponbrakedrumsordirectlyuponrotatingshaftsandaresuitableforuseinheavy-dutyapplications,suchasfoundinminingandconstructionequipmentandinmaterials-handlingmachinery.Internallinearlyactingdrumbrakes,suchasusedontrucksinEurope,maybedesignedasinFigure2.Eitherpneumaticorhydrauliccylindersorcams ... 4LinearlyActingExternalandInternalDrumBrakesLinearlyactingdrumbrakesarethosefittedwithshoeswhich,whenacti-vated,approachthedrumbymovingparalleltoaradiusthroughthecen-teroftheshoe.TypicallinearlyactingdrumbrakesareillustratedinFigures1–3.Analysisoflinearlyactingbrakesincludesthoseinwhichthecentrallypivotedshoesareattachedtopivotedlevers,asinFigure1.Includingbrakesofthisdesignwithinthecategoryoflinearlyactingbrakesisjustifiediftheyaredesignedsothattheappliedforcesontheshoesandliningsactalongtheradiioftheshaftsthattheygripwhenthebrakesareapplied.Brakesofthistypemayacteitheruponbrakedrumsordirectlyuponrotatingshaftsandaresuitableforuseinheavy-dutyapplications,suchasfoundinminingandconstructionequipmentandinmaterials-handlingmachinery.Internallinearlyactingdrumbrakes,suchasusedontrucksinEurope,maybedesignedasinFigure2.Eitherpneumaticorhydrauliccylindersorcams ... 4LinearlyActingExternalandInternalDrumBrakesLinearlyactingdrumbrakesarethosefittedwithshoeswhich,whenacti-vated,approachthedrumbymovingparalleltoaradiusthroughthecen-teroftheshoe.TypicallinearlyactingdrumbrakesareillustratedinFigures1–3.Analysisoflinearlyactingbrakesincludesthoseinwhichthecentrallypivotedshoesareattachedtopivotedlevers,asinFigure1.Includingbrakesofthisdesignwithinthecategoryoflinearlyactingbrakesisjustifiediftheyaredesignedsothattheappliedforcesontheshoesandliningsactalongtheradiioftheshaftsthattheygripwhenthebrakesareapplied.Brakesofthistypemayacteitheruponbrakedrumsordirectlyuponrotatingshaftsandaresuitableforuseinheavy-dutyapplications,suchasfoundinminingandconstructionequipmentandinmaterials-handlingmachinery.Internallinearlyactingdrumbrakes,suchasusedontrucksinEurope,maybedesignedasinFigure2.Eitherpneumaticorhydrauliccylindersorcams...

... Inc.Evaluationoftheseintegralsiseasiestforbrakepadswithradialandcircularboundaries,asinFigure4,forwhichequation(1-4 )and( 1-5)maybewrittenusingadummyvariablefasF¼pmaxriZA1rda¼pmaxriZr0riZu0dfdrð1-6Þ¼pmaxriuðr0ÀriÞ and T¼ApmaxriZAda¼ApmaxriZrorirdrZu0dfð1-7Þ¼Apmaxriu2r2oÀr2iÀÁFromequation(1-7)wefindthatforthepressuredistributiongivenbyrela-tion(1-3)thetorquemaybeeasilycalculatedforanybrakepadwhoseareaisFIGURE2Combinationdiskbrakeanddiskclutch,bothdry.(CourtesyofMinsterMachine Co., Minster, OH.)Chapter 586Copyright © 2004 Marcel Dekker, Inc.5DryandWetDiskBrakesandClutchesThischapterondiskbrakesandclutcheswillconsiderannularcontactdiskclutchesandbothcaliperandannularcontactdiskbrakes,asillustratedinFigures1,2 ,and3 .Caliper ... Inc.5DryandWetDiskBrakesandClutchesThischapterondiskbrakesandclutcheswillconsiderannularcontactdiskclutchesandbothcaliperandannularcontactdiskbrakes,asillustratedinFigures1,2 ,and3 .Caliper disk brakes, as shown in Figure 1, are used on aircraft, auto-motive, industrial, and mining ... MI.)Dry and Wet Disk Brakes and Clutches 87Copyright © 2004 Marcel Dekker, Inc.Evaluationoftheseintegralsiseasiestforbrakepadswithradialandcircularboundaries,asinFigure4,forwhichequation(1-4 )and( 1-5)maybewrittenusingadummyvariablefasF¼pmaxriZA1rda¼pmaxriZr0riZu0dfdrð1-6Þ¼pmaxriuðr0ÀriÞ and T¼ApmaxriZAda¼ApmaxriZrorirdrZu0dfð1-7Þ¼Apmaxriu2r2oÀr2iÀÁFromequation(1-7)wefindthatforthepressuredistributiongivenbyrela-tion(1-3)thetorquemaybeeasilycalculatedforanybrakepadwhoseareaisFIGURE2Combinationdiskbrakeanddiskclutch,bothdry.(CourtesyofMinsterMachine...

... 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.comparisonofthethreefigures,theminimumdescribedbyequation(1-16)andplottedinFigure4isqualitativelyevidentinFigures 3and4 .It is Figure 4 that is directly useful in the design of cone brakes and clutches, because we find from equation (1-19) that the regions to the left ofthe solid curve (regions 2 and ... 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.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.IV. EDDY-CURRENT BRAKES AND CLUTCHES Construction ... Hysteresis and Eddy-Current Brakes 129Copyright © 2004 Marcel Dekker, Inc.II.MAGNETICPARTICLEBRAKESANDCLUTCHESThesebrakesareavailableinarangeofsizesthatincludethe100-lb-ftmodelshowninFigure3andthe8-lb-ftmodelshowninFigure4.Sincethesecon-figurationsareequallysuitedforclutches,theymaybecombinedtoformclutch-brakecombinations,asinFigure5.Whenusedasaclutch,theunithastwomovingparts;whenusedasabrakeithasonlyone.Whenusedasaclutch,theconfigurationisasrepresentedbythesche-maticinFigure6(a).Theinputshaftisattachedtoacylindricaldrum,termedthe ... the design practices as-sociated with these brakes. They are often designed in the laboratory by acombination of theory and trial and error because our present theory is notadequate to handle...

... !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 ... 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...

... 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 ... 3 and 4 areChapter 9222Copyright © 2004 Marcel Dekker, Inc.separated by 35j and 4 and 5 are separated by 40j for a combined separationof 75j. The third and last instance is when balls 7 and...

... Inc.Thistypeofdriveisaninexpensivealternatetobevelgearsforaright-angledrive,aclutch,andareversingmechanism.Whentheright-handconeinFigure8ismoveddownwardtocontacttheupperhalfofthedoubleconeandtheleft-bandconeismovedupwardtocontactthelowerhalfofthedoublecone,boththeleft-andright-handconesrotateinthesamedirection.Iftheright-andleft-handconesdrivetheright-andleft-handwheelsofalawnmower,themowermovesforward.Iftheright-handconeismoveddownwardandtheleft-handremainsdownward,thewheelstheydriveturninoppositedirectionsandthemowerrotatesinitsownlengthtoprovidethezeroturningradius.(Theunpoweredfrontwheelsareoncasters.)Finally,iftheright-handconeremainsdownwardandtheleft-handconeismovedupward,themowermovesinreverse.Contactbetweenconeswouldbealongalinewherethegeneratorsofeachconeareincontactiftheconeswereabsolutelyrigid.However,theelasticityoftherelativelysofterconeliningsformacontactstripcenterdalongwhatwouldhavebeenthecontactline.Againtherearetwopossiblemodesoftorquetransfer;onewithnoslipatsomepointortransverselinewithinthecontactregionandslipelsewhere,andtheotherwithslipeverywherewithinthecontactarea.AsillustratedinFigure9,ifslippageatallbutonepointorlineisassumedtooccurwhentworotatingconesareincontact,thenthespeedofthedrivenconewilldependuponthelocationoftheno-slippointortransverseline.FromFigure9itisevidentthatwitheitherpointorlinecontact,theangularvelocityoftheoutputconesmayfallsomewherebetweenthelimitsdeterminedbythelocationofthatpoint,orline,withinthecontactstripwhereFIGURE8Conefrictiondriveschematic.Centraldoubleconedrivesoutputconeson ... Inc.Substitutionfromtherelationsforr1andr2yieldsr2Àr1¼l2Àl1ðÞsinfandr2þr1¼l2þl1ðÞsinfSowithpw(l2Àl1)=N=VsinfwehaveT¼AVl2þl12sin2fð3-13ÞIV.EXAMPLEI:BELTDRIVE,HINGEDMOTORMOUNTWouldyouapproveamotormountasillustratedinFigure1(a)forclutchinganddeclutching?Themassofthemotoris18.6kgandthecenterofthemotorshaftis12cmabovethebottomofthemotor’sbase,whichis17.8cmwide.Center-to-centerdistancebetweentheshaftofthemotorandtheshaftofthedrivenmachineistobe50cm.Belttensionistobe298.5N,thebeltshouldbereplacedafterthecenterdistanceincreases2.4cm,theangleofthelinebetweencentersmaybefrom15jto20jwiththehorizontal,andtheshaftofthedrivenmachineisaboveandtotherightofthemotorshaft.ThegravitationalforceonthemotorisgivenbyW=mgintermsofthemassofthemotorandtheaccelerationofgravity.ThusW¼18:69:8067ðÞ¼182:4NtogiveT/W=1.637.Fromthemotorspecifications,b=12cmandamustbeequaltoorlargerthan17.8/2=8.9cm.Asanaidtoselectingavaluefora,plotT/Wasafunctionofsforf=20jand30jandforu=20jand30j,asshowninFigure14.Selectf=20jandcomparedesignsusingu=20jandu=30j.Useoff=15jwasrejectedinordertoavoidexcessivebelttensionasthebeltstretches.Considers=0.2tohavealargerT/Wratioandconsiders=0.685,correspondingtoa=13cm,togetamorecompactmounting.Thusa=44.5mmfors=0. 2and1 3mmfors=0.685.SincebeltelongationduringusecanalterthegeometryshowninFigure15bychangingangleuandtherebychangingthebelttension,calculatethe ... 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...