clutches and brakes design and selection rar

... 301 References 316 Chapter 14 Engineering Standards for Clutches and Brakes 317 I. SAE Standards 317 II. American National Standards Institute (ANSI) 320 III. Other Standards Organizations 320 Bibliography ... according to the SAE J661 standard. Field perform- Friction Materials 9 2 Band 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 pertinent computer...

... Inc. suchasbronze,glass,andgraphite,significantlyaddtothewearresistanceof PTFE[3].Glassappearstobethemostcommonlyused. B.Kevlar KevlaristheDuPonttradenameforanaramid(aromaticpolyamidefiber) thathasatensilestrengthgreaterthansomesteels,i.e.,someofthesefibers haveamodulusupto27 Â 10 6 psi(1.86 Â 10 5 Mpa).Neverthelesstheyare flexibleenoughtobewovenandprocessedastextiles,soKevlarbrakelinings andclutchfacingsareavailableineitherwovenornonwovenforms.Theyare usedalongwithproprietarypolymerbindersinthemanufactureofbrake liningsandclutchfacingsforbothwet(oilbath)anddryclutchapplications. Indrybrakeandclutchapplications,aflexible,nonwovenformcan withstanddynamicpressureupto3100kPa(450psi),arenonabrasivetoiron, steel,andcoppersurfaces,anddisplayandnominalcoefficientoffrictionof 0.36F0.1,asstatedbyonemanufacturer.Thismanufactureralsostatesthat inadryenvironmentthesebrakeliningsshowsignificantfadeat260jC (500jF)thatbecomesgreaterat370jC(700jF)[7].Hence,theymaybeused inthoseindustrial,marine,andoff-roadapplicationswherefadeisnota limitingfactor;applicationscanincludeagricultural,industrial,marine ,and off-roadequipment. Inwetapplicationsthisnonwovenformoffacingmaterialissaidto withstanddynamicpressureupto2760kPa(400psi)withanominal coefficientoffrictioninthe0.10–0.15rangewhendissipating23–290W/ cm 2 (0.2–2.5hp/in 2 )[7].Ambientoperatingtemperaturesarereplacedby powerperunitareaattheliningfaceinwetapplicationsbecausethe envelopingfluidbathcoolstheliningasittransferstheheattocoolingfins ortoanoilcooler.Clutchfacingsandbrakeliningsthatcontainnometal reinforcingwiresorsegmentsprovidelowwearonmatingsurfacesand eliminatethepossibilityofmetalfragmentsincoolingsystemfilters. Kevlarhasalsobeenusedinaproprietarysolidformtoobtainhigher coefficientsoffrictioninawovenmaterialinwhichKevlarfibersaremixed withotherorganicandinorganicfibersthatenclosebrasswireyarnsto producealiningthatmaybeusedasadirectreplacementforolderliningsthat containasbestos[8].Becauseofthebrasswireandinorganicfibers,these liningmaybemoreabrasivethanthosewithoutthesematerials.Thisis,of course,anaturalconsequenceofhavinghigherfrictioncoefficientsonthe ordersof0.40dynamicand0.42static. Representativesecondfadeandsecondrecoverycurvesofthefriction coefficientvs.temperatureofarepresentativeofsuchliningsareshownin Figure4,asdeterminedaccordingtotheSAEJ661standard.Fieldperform- Friction ... Inc. indicatesachangeinAfromapproximately0.45toapproximately0.07,fora changeof84.4%.Incontrasttothis,Figure7forsteelbrakeswithsintered liningsshowsachangeinAfromamidrangevalueofabout0.25toamidrange valueofabout0.14,forachangeof44%.However,carbon–carbonbrakes arelighterthansteelbrakesandcanbemadefromasinglematerial[11]. F.OtherProprietaryMaterials Frictionmaterialsproducedbymostmanufacturersareproprietarytothe extentthatnotalloftheiringredientsaredisclosed.Noneoftheingredients maybelistedforthoseliningmaterialsthatperformsatisfactorilywithout componentsprovidedbyothers,suchasKevlar.Absenceofasbestosalways willbenotedbyU.S.suppliers. Manymanufacturersofentirelyorpartiallyproprietaryliningsprovide dataonthenominalfrictioncoefficients,wear,andrecommendedtemper- aturerangesoftheirproducts,althoughafewwillsupplydataonlytoa manufacturingcustomer.Thisdatamaybeineithertabularorgraphical form.Typicaltabulardatafordryliningmaterialsmaybesimilartothat showninTable2,andtypicaldataforwet(oil,transmissionfluid)lining materialsmaybesimilartothatshowninTable3fortwodifferentlining materials.Thefirstofthese,GL483-110,isdescribedasalayeredKevlarmat withembeddedcarbonparticlesthatarehighlywearresistant.Thislayered compositionisboundtogetherwithahighstrength,temperatureresistant phenolicsresin.Thesecond,GL383-114,isanon-asbestos,cellulosefiber compositefrictionpaperthatissaturatedwithasimilarphenolicsresin.(See Fig.1.) Datainbothtableswereobtainedfromconditionsthatmaydifferfrom those ... material and carbon–carbon composites are widely used in brakes for large aircraft, such as long-range commercial jets, and in military aircraft. Their typical construction is shown in Figure 6. Brakes...

... pressure upon the lining. Band Brakes 23 Copyright © 2004 Marcel Dekker, Inc. 2 BandBrakes Bandbrakesaresimplerandlessexpensivethanmostotherbrakingdevices, withshoebrakes,asperhapstheirnearestrival.Becauseoftheirsimplicity, theymaybeproducedeasilybymostequipmentmanufacturerswithout havingtopurchasespecialequipmentandwithouthavingtousefoundryor forgingfacilities.Onlytheliningmustbepurchasedfromoutsidesources. Bandbrakesareusedinmanyapplicationssuchasinautomatic transmissions(Figure1)andasbackstops(Figure5—devicesdesignedto preventreversalofrotation),forbucketconveyors,hoists,andsimilar equipment.Theyareespeciallydesirableinthelast-mentionedapplication becausetheiractioncanbemadeautomaticwithoutadditionalcontrols. I.DERIVATIONOFEQUATIONS Figure2showsthequantitiesinvolvedinthederivationoftheforcerelations used ... Quantities and geometry used in the derivation of the band-brake design relations. Band Brakes 19 Copyright © 2004 Marcel Dekker, Inc. To ensure clearance, let the drum diameter be 32 in., and design ... pressure between the drum and the lining, and w represents the width of the band. Upon simplifying equations (1-1) and (1-2) and remembering that as the element of band length approaches zero,...

... Marcel Dekker, Inc. 3 ExternallyandInternallyPivotedShoe Brakes TypicalexternallyandinternallypivotedshoebrakesareshowninFigures1 and 2. In all but extremely rare designs, equal forces act upon ... in lb, and the adjusting link is Externally and Internally Pivoted Shoe Brakes 57 Copyright © 2004 Marcel Dekker, Inc. V. DESIGN OF SINGLE-ANCHOR TWIN-SHOE DRUM BRAKES Internal shoe drum brakes ... Inc. Thislinkforceandtheactivatingmomentbothactonthesecondary shoe,sothattheforceandmomentequationsofequilibriumforthesecond- aryshoebecome F r 2 ¼Àrw Z f 2 f 1 pcosfdfþArw Z f 1 f 2 psinfdfþF l sinf 2 þ h 2  ð5-7Þ F u 2 ¼Àrw Z f 2 f 1 psinfdfþArw Z f 2 f 1 pcosfdfþF l cosf 2 þ h 2  ð5-8Þ where2histheanglesubtendedbytheadjustinglink.Next, M a 2 ¼M p 2 þM f 2 À2RF l sin f 2 2 sin f 2 2 þ h 2  ð5-9Þ whereM p 2 andM f 2 areagaingivenbyequations(5.1 )and( 5.2)intermsofthe pressuredistributiononthesecondaryshoe.Torqueforeithershoemaybe calculatedfrom T¼Arw Z f 2 f 1 pdfð5-10Þ Eventhoughtheseequationsdonotuniquelydeterminethepressure distributionoverthebrakelining,theyarestillofusebecausetheyallowthe designengineertocomparetheeffectsofdifferentrealisticpressuredistribu- tionandtodesigndrumsandshoeswhoserigiditywillinduceparticular pressuredistributionsovertheprimaryandsecondaryshoes. Thefirstofthetwopressuredistributionsconsideredisasynthesisof(1) thesinusoidaldistributionassociatedwithanondeformingdrumandshoe, generallyassociatedwithalightlyloadedbrake ,and( 2)theforcepeaksthat occurattheendsofload-bearingmembersincontact.Thesecondofthetwois asysthesisof(1)theconstantdistributionsaidtobeassociatedwithmore heavilyloadedbrakes ,and( 2)thepreviouslynotedforcepeaks.Thusthe pressuredistributionswillberepresentedeitherby p p 0 ¼e Àc 1 c=f 0 ðÞ cos c f 0 k         c 2 þc 3 c¼fÀf 1 ð5-11Þ orby p p 0 ¼e Àc 1 c=f 0 ðÞ cos c f 0 k         c 2 þc 3 sincþf 1 ðÞð5-12Þ fortheprimaryshoes,wherethepeakpressureoneachshoeoccursattheheel becauseitspivotcannotsustainaradialforceintheoutwarddirection.These relationsproducethepressuredistributionsshowninFigures1 4and1 5for the...

... Inc. 4 LinearlyActingExternalandInternal DrumBrakes Linearlyactingdrumbrakesarethosefittedwithshoeswhich,whenacti- vated,approachthedrumbymovingparalleltoaradiusthroughthecen- teroftheshoe.TypicallinearlyactingdrumbrakesareillustratedinFigures 1–3. Analysisoflinearlyactingbrakesincludesthoseinwhichthecentrally pivotedshoesareattachedtopivotedlevers,asinFigure1.Includingbrakes ofthisdesignwithinthecategoryoflinearlyactingbrakesisjustifiedifthey aredesignedsothattheappliedforcesontheshoesandliningsactalongthe radiioftheshaftsthattheygripwhenthebrakesareapplied.Brakesofthis typemayacteitheruponbrakedrumsordirectlyuponrotatingshaftsandare suitableforuseinheavy-dutyapplications,suchasfoundinminingand constructionequipmentandinmaterials-handlingmachinery. Internallinearlyactingdrumbrakes,suchasusedontrucksinEurope, maybedesignedasinFigure2.Eitherpneumaticorhydrauliccylindersor cams ... Inc. 4 LinearlyActingExternalandInternal DrumBrakes Linearlyactingdrumbrakesarethosefittedwithshoeswhich,whenacti- vated,approachthedrumbymovingparalleltoaradiusthroughthecen- teroftheshoe.TypicallinearlyactingdrumbrakesareillustratedinFigures 1–3. Analysisoflinearlyactingbrakesincludesthoseinwhichthecentrally pivotedshoesareattachedtopivotedlevers,asinFigure1.Includingbrakes ofthisdesignwithinthecategoryoflinearlyactingbrakesisjustifiedifthey aredesignedsothattheappliedforcesontheshoesandliningsactalongthe radiioftheshaftsthattheygripwhenthebrakesareapplied.Brakesofthis typemayacteitheruponbrakedrumsordirectlyuponrotatingshaftsandare suitableforuseinheavy-dutyapplications,suchasfoundinminingand constructionequipmentandinmaterials-handlingmachinery. Internallinearlyactingdrumbrakes,suchasusedontrucksinEurope, maybedesignedasinFigure2.Eitherpneumaticorhydrauliccylindersor cams ... f 0 Þsin a Linearly Acting External and Internal Drum Brakes 81 Copyright © 2004 Marcel Dekker, Inc. 4 LinearlyActingExternalandInternal DrumBrakes Linearlyactingdrumbrakesarethosefittedwithshoeswhich,whenacti- vated,approachthedrumbymovingparalleltoaradiusthroughthecen- teroftheshoe.TypicallinearlyactingdrumbrakesareillustratedinFigures 1–3. Analysisoflinearlyactingbrakesincludesthoseinwhichthecentrally pivotedshoesareattachedtopivotedlevers,asinFigure1.Includingbrakes ofthisdesignwithinthecategoryoflinearlyactingbrakesisjustifiedifthey aredesignedsothattheappliedforcesontheshoesandliningsactalongthe radiioftheshaftsthattheygripwhenthebrakesareapplied.Brakesofthis typemayacteitheruponbrakedrumsordirectlyuponrotatingshaftsandare suitableforuseinheavy-dutyapplications,suchasfoundinminingand constructionequipmentandinmaterials-handlingmachinery. Internallinearlyactingdrumbrakes,suchasusedontrucksinEurope, maybedesignedasinFigure2.Eitherpneumaticorhydrauliccylindersor cams...

... Inc. 5 DryandWetDiskBrakesandClutches Thischapterondiskbrakesandclutcheswillconsiderannularcontactdisk clutchesandbothcaliperandannularcontactdiskbrakes,asillustratedin Figures1,2 ,and3 . Caliper disk brakes, ... Airflex Division, Cleveland, OH.) Dry and Wet Disk Brakes and Clutches 93 Copyright © 2004 Marcel Dekker, Inc. used on large earth-moving equipment, on mine shuttle cars, and similar equipment ... multiple-disk brakes and clutches, illustrated in Figure 3, have similar multiple-disk construction, but operate in an oil bath. Thus these brakes are isolated from dirt and water, and the circulation...

... sin aÞð1-10Þ Cone Brakes and Clutches 109 Copyright © 2004 Marcel Dekker, Inc. II.FOLDEDCONEBRAKE Prototypeconebrakeshavebeendesignedandtestedforarangeofvehicle sizes,fromtractorsandtrailerstosubcompactautomobiles[1].Boththelarge andsmallsizesusedafoldedconedesign,asillustratedinFigures 5and6 , eachwitha=27j.Althoughtheconebrakehasfewerpartsthandrum brakes, thisadvantagemustbebalancedagainstthedisadvantageofrequiring anoutboardwheelbearing. Analysisofthefoldedconebrakewithasectorshoe,showninFigure5, toobtaindesignformulasforthetorquecapabilityandtherequiredactiva- tionforceisquitesimilartothatusedforsimpleconebrakesandclutches. SincethebrakesillustratedinFigures 5and6 useasectorpad,webeginthe analysisbyobservingfromFigure7(a)thatanelementofareaontheconical surfacemaybewrittenas da¼rdu dr sina ð2-1Þ F IGURE 4DesignregionsintheA,aplaneforconeclutches /brakes. Cone ... Inc. II.FOLDEDCONEBRAKE Prototypeconebrakeshavebeendesignedandtestedforarangeofvehicle sizes,fromtractorsandtrailerstosubcompactautomobiles[1].Boththelarge andsmallsizesusedafoldedconedesign,asillustratedinFigures 5and6 , eachwitha=27j.Althoughtheconebrakehasfewerpartsthandrum brakes, thisadvantagemustbebalancedagainstthedisadvantageofrequiring anoutboardwheelbearing. Analysisofthefoldedconebrakewithasectorshoe,showninFigure5, toobtaindesignformulasforthetorquecapabilityandtherequiredactiva- tionforceisquitesimilartothatusedforsimpleconebrakesandclutches. SincethebrakesillustratedinFigures 5and6 useasectorpad,webeginthe analysisbyobservingfromFigure7(a)thatanelementofareaontheconical surfacemaybewrittenas da¼rdu dr sina ð2-1Þ F IGURE 4DesignregionsintheA,aplaneforconeclutches /brakes. Cone ... Inc. II.FOLDEDCONEBRAKE Prototypeconebrakeshavebeendesignedandtestedforarangeofvehicle sizes,fromtractorsandtrailerstosubcompactautomobiles[1].Boththelarge andsmallsizesusedafoldedconedesign,asillustratedinFigures 5and6 , eachwitha=27j.Althoughtheconebrakehasfewerpartsthandrum brakes, thisadvantagemustbebalancedagainstthedisadvantageofrequiring anoutboardwheelbearing. Analysisofthefoldedconebrakewithasectorshoe,showninFigure5, toobtaindesignformulasforthetorquecapabilityandtherequiredactiva- tionforceisquitesimilartothatusedforsimpleconebrakesandclutches. SincethebrakesillustratedinFigures 5and6 useasectorpad,webeginthe analysisbyobservingfromFigure7(a)thatanelementofareaontheconical surfacemaybewrittenas da¼rdu dr sina ð2-1Þ F IGURE 4DesignregionsintheA,aplaneforconeclutches /brakes. Cone Brakes and Clutches 113 Copyright © 2004 Marcel Dekker, Inc. where we again use the pressure p and element of area da...

... Inc. Beyondthispointthetorquedecreasesrapidly,asshownintheslip torqueversusspeedcurveinFigure13(a).ComparisonwithFigure13(b) correctlyimpliesthattheshapeofthedecreasing-torqueportionofthecurve totherightofthecriticalpointreflectsboththechangeinthehysteresisloop withincreasingtemperatureandtheheattransfercharacteristicsofthe coolingsystem(i.e.,whetherairorliquidandthetemperatureandvelocity ofthecoolingmedium).Whentheseconditionsarefixedtheshapeofthe curveremainsqualitativelyinvariant.Thus,asthebraketorqueincreases fromonesizeofbraketoanother,thatportionofthecurvetotheleftofthe criticalpointdecreasesunlessimprovedcoolingisusedtomovetheconcave portionofthecurveupwardandtotheright,thusmovingthecriticalpointto theright. Themagnitudeofthatportionofthecurvewhichisindependentof rotationalspeedtotheleftofthecriticalpointinFigure14ais,ofcourse,also determinedbythetorqueversuscontrolcurrentcurveshowninFigure14b. Thedifferencebetweenthetorqueobtainedfromincreasinganddecreasing controlcurrentisshowninFigure2. Useofthetermsliptorque,incidentally,istoemphasizethatthetorque actsbetweentwomechanicalpartswhichmaybemovingrelativetoone anotherbecausethesebrakesmaybeusedastensioncontroldevicesaswellas ameansofstoppingtherotationentirely. F IGURE 9Torque-slipspeedcurvesfordryfrictionandmagneticparticlebrakes (also clutches) . Magnetic Particle, Hysteresis and Eddy-Current Brakes 137 Copyright © 2004 Marcel Dekker, Inc. 7 MagneticParticle,Hysteresis ,and Eddy-CurrentBrakesandClutches Allthreeofthesebrakeorclutchtypeshavenowearingpartsbecausethe torqueisdevelopedfromelectromagneticreactionsratherthan ... Hysteresis and Eddy-Current Brakes 143 Copyright © 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 127 Copyright © 2004 Marcel Dekker, Inc. II.MAGNETICPARTICLEBRAKESANDCLUTCHES Thesebrakesareavailableinarangeofsizesthatincludethe100-lb-ftmodel showninFigure3andthe8-lb-ftmodelshowninFigure4.Sincethesecon- figurationsareequallysuitedforclutches,theymaybecombinedtoform clutch-brakecombinations,asinFigure5.Whenusedasaclutch,theunithas twomovingparts;whenusedasabrakeithasonlyone. Whenusedasaclutch,theconfigurationisasrepresentedbythesche- maticinFigure6(a).Theinputshaftisattachedtoacylindricaldrum,termed the...

... Inc. Thekineticenergiesmaybefoundfrom n 14 ¼ 1 16 n 24 ¼ 1 3:2 n 34 ¼ 1 3:2 m 1 ¼1278m 2 ¼276m 3 ¼721m 4 ¼231 r 1g ¼0:81r 2g ¼0:17r 3g ¼0:32r 4g ¼0:09 I g1 ¼m 1 r 2 1g I g2 ¼m 2 r 2 2g I g3 ¼m 3 r 2 3g I g4 ¼m 4 r 2 4g I d ¼m d r 2 dg ke d ¼ 1 2 I d n 2 14 ke g1 ¼ 1 2 I g1 n 2 14 ke g2 ¼ 1 2 I g2 n 2 24 ke g3 ¼ 1 2 I g3 n 2 34 ke g4 ¼ 1 2 I g4 wherem 1 throughm 4 arethemassesofgears1through4,respectively,andr 1g throughr 4g aretheirrespectiveradiiofgyration.Thus, KE d ¼ke d N 2 m ¼185:5N-mKE L ¼ 1 2 m L v 2 c ¼957:3N-m KE r ¼ 1 2 m r v 2 c ¼49:2N-mKE g1 ¼ke g1 N 2 m ¼4224:5N-m KE g2 ¼ke g2 N 2 m ¼1004:7N-mKE g3 ¼ke g3 N 2 m ¼9299:2N-m KE g4 ¼ke g4 N 2 m ¼2413:3N-m Additionofthesegives KE¼ðke g1 þke g2 þke g3 þke g4 þke d ÞN 2 m þKE L þKE r ¼18;133:6N-m Souponaddingthistothetotalpotentialenergyof PE¼23;202:3N-m thetorquerequiredmaybefoundfrom T o ¼ PEþKE ðN m =2Þt ¼813:9N-mð8-6Þ inwhichtheaveragemotorspeedduringbrakingwastakentobeN m /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)fromChapter5 corresponding ... Inc. theannularcaliperandannulardiskbegivenbyequation.Accordingly,eval- uatetheformulas T¼p max wr 2 o ð1Àe ÀAf Þð8-7Þ forabandbrake, T¼2Ap max wr 2 o sin f o 2  ð8-8Þ foreithertwoopposinginternalorexternallinearlyactingbrakeshoes, T¼2Ap max r 3 o 3 ffiffiffi 3 p f o ð8-9Þ fortwoopposingdiscbrakepads,eachsubtendingangleB o ,and T¼4kAp max r 3 o 3 ffiffiffi 3 p ð8-10Þ fortwocompleteannularpadsinwhichB o =2kinequation(8-9). Weshallalsoconsideranexternalpivoteddrumbrakewithaleading andtrailingshoethatmaybeevaluatedbyinvokingtheprogramusedin Chapter3.Inallofthesecalculationsassumeafrictioncoefficientof0.3 ,and setthewidthfortheband,thelinearlyactingdrumbrake,andtheexternally pivotedbraketo5cm.Limitthemaximumliningpressureforthebandbrake andfortheexternallypivotedbraketo2.0MPa,andlimitthepressureforthe otherliningsto3.0MPa,whichmaybeeitherformedorsolid.Liningpressure fortheexternallypivotedbrakewastakentobe2.0MPa,merelyfor comparisonwiththebandbrake. Figure11(a)showsthetorquecapacityinnewton-metersasafunction ofangleBsubtendedbyeachshoeforadrumdiameterof300mm,andFigure 11(b)showsthetorquecapacityinnewton-metersforband,linearlyacting, caliper,andannularbrakesasafunctionofthedrumordiscdiameterin millimeters. Althoughthelinearlyactingdrumbrakeisclearlymoreeffectivethan theotherbrakesshowninFigure11(b),itandalloftheotherthreebrakesin thatfigurerequiremorehardwarethandoesthebandbrake.Therefore,select thebandbrake,becauseitcanprovidethenecessarytorquecapabilitywith mechanicalsimplicity. Externaldual-shoedrumbrakesarethenextsimplest.Increasingthe maximumliningpressureto3.0MPaforanexternallypivoteddual-shoe brakeallowsthedrumdiametertobereducedto170mmandtheradial distancetotheshoepivottobereducedto100mm,fromthe150mmas- sociatedwithFigure11(a),togetatorquevs.anglecurvesimilarinshape andmagnitudetothatinFigure11(a).Thus,eitheranexternallypivoted Chapter8174 Copyright ... ! ¼6:344lb-ftð6-6Þ ¼76:130lb-in: wheren i =1/5.488fortheendrollersandn i =1/1.254fortheintermediate rollers. Ifthebrakehadbeenmountedoneitheroftheendrollershafts, equation(6-6)wouldhavebeenreplacedby T¼ 4:114 0:1553 " 2ð0:0759Þþ20ð0:000556Þð4:375Þ 2 þ 230 32:2 4:375 12  2 # ¼34:811lb-ftð6-7Þ andthebrakingtorquerequirementwouldhavebeenn=5.488timeslarger thanthatfoundbyequation(6-6).Thiscomparisonisanexampleofthegen- eralrulethatthebrakeshouldusuallybeplacedinthefastershaft. VII.EXAMPLE3:ROTARYKILN ThecurvesinFigure6clearlyimplythatefficientuseofaclutchbyreducing thepowerlossduetoheatgeneration,alongwithwear,requiresthatthe speedsofitsinputandoutputshaftsshouldbenearlyequal.Accordingly, dependinguponthepowersource(electricorhydraulicmotor,turbine,or internalcombustionengine),aclutchmaybeusedtochangegearratios,to changefromonepowersourcetoanotherwhenthespeedsarenearlyequal,or todisconnectthepowersourcebeforebraking. Thisexamplewillconsideraloadthatisessentiallyrotationalinorderto concentrateonclutchandbrakeselectionwhendynamictorqueandbrake heatingcurvesareavailable.Bothclutchandbrakeanalyseswilldisplaysome ofthecalculationinvolvedwhenthespeedsoftheinputandoutputshaftsare notalmostequal. Arotarykilnistobedrivenbya15-hpthree-phasemotoroperatingat 870rpmandratedtodeliveratorqueof240lb-ftwithaKfactor(overload factorforstarting)of2.64.Themotor,clutch,geartrainwitha28.4speed- reductionratio,androtarykilnarearrangedasshowninFigure7.Theoverall damping...

... 1 and 2 30j between detents 2 and 3 130j between detents 8 and 3 and that the angular separation between detent centers 1 and 5 is given by 25j between detents 1 and 2 30j between detents 2 and ... detents 3 and 4 40j between detents 4 and 5 130j between detents 1 and 5 The 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. Maximumpressureontheliningmaybefoundfrom F¼r o w Z f o =2 Àf o =2 pcosf x ¼r o wp max Z f o =2 Àf o =2 cosðfÞ 2 df ¼ p max 2 r o wðf o þsinf o Þ ð1-8Þ uponusingthepressuredistributionfromequation(1-2)inChapter4.Hence, p max ¼ 2F r o wðf o þsinf o Þ ð1-9Þ Theangularvelocityoftheinputshaftwhentheweightsmakeinitial contactwiththedrummaybefoundbysettingthesquarebracketinequation (1-6)equaltozero.Substitutionof x =2kn/60,wherenisinrpm,followedby solvingtheresultingexpressionforn,yields n¼ k 30 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n g r c ðhÞþy ð1þDÞ r ð1-10Þ TheroleofparametershandEinequation(1-5)uponforceF,equation (1-3),andthereforeuponp max ,equation(1-9)andthespeedatwhichtheyfirst contactthedrumareshowninFigures2(a)through(d). Observethatthevariationofthepressure,andhencetheforce,thateach weightexertsagainstthedrumisalinearfunctionofparameterEandthatit becomesanearlylinearfunctionofh,andhenceofr i ,forhgreaterthanabout 0.3.Thedependenceofthewidthofeachweight,however,becomesincreas- inglynonlinearashincreasesandasEdecreases.Therotationalspeedfor initialcontactisalsonearlylinearforh<0.6,especiallyforthelargervalues ofE. Example Designacentrifugalclutchtoprovideatorqueof2400N-mwhentherota- tionalspeedreaches870rpmusingsectorweightshavingthegeometryshown inFigure3(a).Preferredcharacteristicsarethatinitialcontactbetween weightsanddrumoccuratbetween22 0and2 30rpmandthatthewidthof theweightsbelessthan30cm.Assumealiningcoefficientoffrictionof0.35 anddesign foraninsidedrumradius(minustheliningthickness)of15cm,a displacementyof3mmforthe...

... N d1 l d1 l n1 tan 2 f and N n2 ¼ N d r d2 r n2 ¼ N d l d 2 l n2 tan 2 f ð3-1Þ where r d1 and r nl are the radii of the driver and driven cones, respectively, at point 1, r d 2 and r n2 are driver and driven ... Inc. setofunitstobeusedforeachratio,andtheresultingratiosareindependent oftheunitsused. Relativelybroadcurvesareshowninthefollowingcomputer-generated graphsforeasyreadingtoshowcharacteristicbehaviorandtoprovide contrastagainstthegridlines.Associatedroutines,suchasMathcadTrace, appeartoreadthemfromtheoriginatingdata,therebyeliminatingtheread- ingerrorsassociatedwithtracewidths. I.BELTDRIVES Equipmentusingnonmetallicbeltdrivesmayincludetheclutchcapabilityby mountingthemotor(becauseitisusuallysmallerthanthedrivenmachine) eitheruponahingedbaseoruponaslidingbasefittedwithaleveroralinkage thatpermitsthemotortobemovedtoandfromthedrivenmachineinorder toapplyandrelievethebelttensionandtherebygiveclutching(applyingbelt tension)anddeclutching(relievingbelttension)capability. Thesedesignseliminatetheneedforamechanicalclutch.Theirsim- plicityisachieved,however,attheriskofintroducingthepossibilitythat frictionalheatingofthebeltduringidling,whenthebelt(orbelts)mayreston themotor’srotatingsheave(pulley).Thatmaygenerateenoughheattocause beltingmaterialstoslowlyshrink.Thisreductioninthecenterdistance betweenthedrivinganddrivenpulleys,orsheaves,maybegreatenoughto causeanunintendedre-engagementofthemotorandthedrivenmachine.It mayalsoinhibittheirdisengagement.Consequently,somebeltmanufacturers producebeltsthatresistshrinkageduetoheatingforuseintheseclutching anddeclutchingapplications. Torquecapabilityforthesedrivesisaseparatecalculationtobe performedaccordingtotheproceduresgivenbythebeltmanufacturers. Therefore,itwillnotbeconsideredinthefollowingdiscussion. A.HingedBase Atfirstglanceitmayappearthatmovingamotorbymountingiteitherona hingedbaseoronaslidingbaseissosimplethatnoanalysisisnecessary.An analysis,however,doesbringforthseveralconsiderationsthatmaybemissed inselectingthedimensionsofthebaseplate,inlocatingthepositionofthe baseplatehinge,orindesigningthelinkagefortheslidingbaseplate. Twosimilar,butdistinct,mountingdesignsforhingedbaseswillbe considered.Intheseconfigurationsitistheweightofthemotoralonethat providesthebelttension.ThetensionvectorshowninFigure1(a )and( b) acting ... Inc. maximuminFigure16,setg=13.52j,asreadusingtheMathcadTrace feature.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.,it followsthattheclearancegivenbylÀr=8.440À1.688=6.752in.exceeds thatspecified. Thisclearancerequirementmaybesatisfiedbyincreasingthemagni- tudeofnandreducingthemagnitudeofg.Thus,ifn=0.28andg=150,the detentforcebecomes4.702lb,aisreducedto4.688in.,andrbecomes1.406in. Thesevaluesgivel=5.021in.,sotheclearanceis5.021À1.406=3.615in., whichiswithinthedesiredrange. VI.EXAMPLE3:CONEDRIVE Selectaconedriveforacombinationgolfcardandaproposedcongestedarea commutercartforuseincommunitiesthatacceptthem.Analysisoftorque transmissiononthebasisofthedynamiccoefficientsoffrictionforacceptable liningsindicatesthata2.00-in.overlapwouldbesufficient. Forcomparison,consideronedesignwiththedriverconehavingan apexhalf-angleof40janddrivenconeshavingapexhalf-anglesof50janda seconddesigninwhichboththedriveranddrivenconeshaveapexhalf-angles of45j.Inbothcasesinitiallyselectaconegeneratorlengthof6.00in.toallow theoverlaptobegreaterthan2.00in.intheeventthattheprototypeshould requiremodification. Beginwiththe40j,50jcombinationandturntoFigure11toselectthe dimensionsoftheconesbyenteringthecurveatz=6andreadinguptothe 40jline.Theprincipalradiusofcurvatureatthatpointis5.0346.Sincezis measuredininches,theprincipalradiusofcurvatureis5.0346in.Readingto theleftatthisvalueofUyieldsthatatz=4.25in.,theprincipalradiusof curvatureofthe50jhalf-angleconeis5.0650in.Aplotofthex-dimensionfor eachcone,showninFigure17(a),confirmsthatthetwoconesshouldroll without...

... 2004 Marcel Dekker, Inc. 11 FluidClutchesandBrakes Fluidclutchesandbrakesmaybedividedintotwogroups:thosecontaininga fluidonlyandthosecontainingamixtureoffluidsandsolids.Thosecon- tainingonlyafluidrelyprimarilyuponthemassofthefluidandsecondarily uponitsviscositytotransmittorque.Unitscontainingbothafluidandasolid inaparticulateformrelyuponthesuspendedsolidstoprovidethemajor bondbetweenthecomponentsthateithertransmitorresisttorquewhenun- dertheinfluenceofanexternalelectromagneticfield. Theadvantageoffluidclutchesandbrakesisthatthereisnoliningto wearandreplace.This,however,isobtainedattheexpenseofsomepowerloss inthetransmissionoftorqueandthedistinctneedforsomesortoffluid coolingforbothfluidclutchesandfluidbrakes.Moreover,occasionalfluid sealreplacementmayalsoberequired. I.FLUIDCOUPLINGSASCLUTCHES Fluidcouplingsmayserveassoftstartclutchesandastorquelimiting clutches. Atypicalfluidcouplingconsistsofaninputshaftattachedtoan impellerandanoutputshaftattachedtoarunner,withbothencasedwithina closedhousingandorientedasshowninFigure1.Animpellermaydiffer fromarunnerintheshapeoftheradialvanesofthesortshowninFigure2 andmaybeattachedto,androtatewith,thehousingthatcontainsboththe impellerandtherunner.AsindicatedinFigure1,theshaftsaresupportedby bearingsatthehousingandbybearingsatthefarendsofeachshaftthatin turnaresupportedbyanenclosure,asshowninFigure3.Eachimpellerand Copyright ... Inc. 11 FluidClutchesandBrakes Fluidclutchesandbrakesmaybedividedintotwogroups:thosecontaininga fluidonlyandthosecontainingamixtureoffluidsandsolids.Thosecon- tainingonlyafluidrelyprimarilyuponthemassofthefluidandsecondarily uponitsviscositytotransmittorque.Unitscontainingbothafluidandasolid inaparticulateformrelyuponthesuspendedsolidstoprovidethemajor bondbetweenthecomponentsthateithertransmitorresisttorquewhenun- dertheinfluenceofanexternalelectromagneticfield. Theadvantageoffluidclutchesandbrakesisthatthereisnoliningto wearandreplace.This,however,isobtainedattheexpenseofsomepowerloss inthetransmissionoftorqueandthedistinctneedforsomesortoffluid coolingforbothfluidclutchesandfluidbrakes.Moreover,occasionalfluid sealreplacementmayalsoberequired. I.FLUIDCOUPLINGSASCLUTCHES Fluidcouplingsmayserveassoftstartclutchesandastorquelimiting clutches. Atypicalfluidcouplingconsistsofaninputshaftattachedtoan impellerandanoutputshaftattachedtoarunner,withbothencasedwithina closedhousingandorientedasshowninFigure1.Animpellermaydiffer fromarunnerintheshapeoftheradialvanesofthesortshowninFigure2 andmaybeattachedto,androtatewith,thehousingthatcontainsboththe impellerandtherunner.AsindicatedinFigure1,theshaftsaresupportedby bearingsatthehousingandbybearingsatthefarendsofeachshaftthatin turnaresupportedbyanenclosure,asshowninFigure3.Eachimpellerand Copyright ... Inc. 11 FluidClutchesandBrakes Fluidclutchesandbrakesmaybedividedintotwogroups:thosecontaininga fluidonlyandthosecontainingamixtureoffluidsandsolids.Thosecon- tainingonlyafluidrelyprimarilyuponthemassofthefluidandsecondarily uponitsviscositytotransmittorque.Unitscontainingbothafluidandasolid inaparticulateformrelyuponthesuspendedsolidstoprovidethemajor bondbetweenthecomponentsthateithertransmitorresisttorquewhenun- dertheinfluenceofanexternalelectromagneticfield. Theadvantageoffluidclutchesandbrakesisthatthereisnoliningto wearandreplace.This,however,isobtainedattheexpenseofsomepowerloss inthetransmissionoftorqueandthedistinctneedforsomesortoffluid coolingforbothfluidclutchesandfluidbrakes.Moreover,occasionalfluid sealreplacementmayalsoberequired. I.FLUIDCOUPLINGSASCLUTCHES Fluidcouplingsmayserveassoftstartclutchesandastorquelimiting clutches. Atypicalfluidcouplingconsistsofaninputshaftattachedtoan impellerandanoutputshaftattachedtoarunner,withbothencasedwithina closedhousingandorientedasshowninFigure1.Animpellermaydiffer fromarunnerintheshapeoftheradialvanesofthesortshowninFigure2 andmaybeattachedto,androtatewith,thehousingthatcontainsboththe impellerandtherunner.AsindicatedinFigure1,theshaftsaresupportedby bearingsatthehousingandbybearingsatthefarendsofeachshaftthatin turnaresupportedbyanenclosure,asshowninFigure3.Eachimpellerand Copyright...

... between values E 1 and E 2 , in which E 1 may be 10% and E 2 may be 20%, for example. This may be achieved by returning to equation (1-4) and solving for v 1 and then replacing v 1 and v 0 with the ... slip and v 0 represents the actual vehicle velocity. Associated wheel angular velocities are represented by N 1 and N 0 . For additional information on published details of ABS and TCS designs, ... such as Ref. 9, and from other automotive engineering journals. Example 1 To demonstrate that equation (4-5), (4-6), (4-9), and (4-10) yield the angular and linear accelerations and the magnitude...

... the brake assembly (drum, backplate, shoes, and lining in the case of drum brakes and disk and caliper in the case of disk brakes) as it vibrates and have shown that brake vibration is the result ... Inc. II.RECENTEXPERIMENTALDATA Usingexperimentaltechniquesnotavailableinthe1960sfortheexamination ofbothdiscanddrumbrakevibration,Felske,Hoppe,andMattha ¨ iemployed holographicinterferometrytodemonstrateconclusivelythatitisthecaliper vibrationthatisthemajorcontributortobrakenoisefromdiskbrakes[11] andthebackplatevibrationthatisthemajorcontributorfromdrumbrakes [12].Typicalstandingwaveshapes,orthenodalpatterns,forthediskare showninFigures 2and3 .VibrationofthecaliperisshowninFigures 4and5 . Thealternatingblackandwhitelineboundariesrepresentcontourlines,or elevationlines,onthecaliperanddiskandconsequentlymeasurethede- flectionofthediskandcaliperinadirectionperpendiculartotheplaneofthe photograph,asindicatedinFigure6foranantinodeonthedisk. F IGURE 3 ... Inc. II.RECENTEXPERIMENTALDATA Usingexperimentaltechniquesnotavailableinthe1960sfortheexamination ofbothdiscanddrumbrakevibration,Felske,Hoppe,andMattha ¨ iemployed holographicinterferometrytodemonstrateconclusivelythatitisthecaliper vibrationthatisthemajorcontributortobrakenoisefromdiskbrakes[11] andthebackplatevibrationthatisthemajorcontributorfromdrumbrakes [12].Typicalstandingwaveshapes,orthenodalpatterns,forthediskare showninFigures 2and3 .VibrationofthecaliperisshowninFigures 4and5 . Thealternatingblackandwhitelineboundariesrepresentcontourlines,or elevationlines,onthecaliperanddiskandconsequentlymeasurethede- flectionofthediskandcaliperinadirectionperpendiculartotheplaneofthe photograph,asindicatedinFigure6foranantinodeonthedisk. F IGURE 3...

... Performance Standard, Power Press Brakes R(2002). BSMI B2004400: Hand Brakes for Bicycles. BSMI B4003700: Axles with Brakes of Trailer for Power Tiller. Engineering Standards for Clutches and Brakes ... rNormung(DIN). Italy:EuteNazionaleItalianodiUnificazione(UNI). Japan:JapaneseIndustrialStandards(JIS). Korea:KoreanStandardsAssociation(KSA). Malaysia:StandardsandIndustrialResearchofMalaysia(SIRIM). Netherlands:NederlandsNormalisatie-Instituut(NEN). Norway:NorwegianStandardsAssociation(—) Slovenia:StandardsandMetrologyInstitute(SMIS). Taiwan:BureauofStandardsandMetrologyInstitute(BSMI). UnitedStates:DepartmentofDefense(DoD—STD—),(MIL—). A.SelectedStandardsfromtheseOtherOrganizations ThetitlesofthefollowingstandardswerecopiedfromtheNSSNWebsiteasa partialindicationofthetopicsandapplicationsconsidered.Atthistimeof thiswriting,thestandardslistedbyNSSNmaybefoundbygoingtowww. ossn.org,wherealeft-clickofacomputermouseonthewordsSearchfor Standards,whicharedirectlyunderthewordswww.NSSN.ORGatthetop left ... that standard. JIS D 4421:1996: Method of Hardness Test for Brake Linings, Pads and Clutch Facings for Automobiles. JIS D 0152:1997: Clutches and Brakes Vocabulary. ASME B5.55M: Specification and...