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17/12/2013, 11:15
... 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 ... Letusdenetheeciencyofabrakeastheratioofthetorqueprovided
bythebraketothetorquethatcouldbehadbyapplyingtheforcedirectlyto
thedrum,orshaft.Accordingtothisdenition,theeciencybecomes
T
F
s
r
ẳ
Ap
max
r
2
wsinu
2
sinu
1
ị
1=2ịp
max
r
2
wf
0
ỵsinf
0
ị
ẳ2A
sinu
2
sinu
1
f
0
ỵsinf
0
1-10ị
Uponsubstitutingforu
1
andu
2
inequation(1-8)andrecallingequations(1-6)
and( 1-7)wendthat
T
F
s
r
ẳ
4Asinf
0
=2ị
f
0
ỵsinf
0
ẳA
R
r
1-11ị
wheretheright-handsidehasalreadybeenplottedinFigure5.Fromthat
gurewendthatalthoughmaximumeciencymaybeachievedonlyifeach
shoeandliningextendoverhalfofthedrum,orshaft,relativelylittleeciency
islostiftheliningextendsoveronly160jinsteadof180j.This,togetherwith
thenearimpossibilityofmaintaininggoodcontactbetweentheliningand
thedrumneartheendsofashoesubtending180jatthecenterofthedrum,
accountsfortheangulardimensionsofthebrakeliningsshowninFigure1.
Finally,itfollowsfromequation(1-11)thatiftheshoeissymmetrically
pivotedandifequation(1-7)holds,theappliedtorqueisgivenby
TẳARF
s
1-12ị
II.BRAKINGTORQUEANDMOMENTSFORSYMMETRICALLY
SUPPORTEDINTERNALSHOES
Pressurepandbrakingtorqueareagaingivenbyequations(1-2 )and( 1-4),
respectively,foraninternalshoemovedagainstarotatingdrumalongaline
paralleltoitsaxisofsymmetry,lineOB,inFigure6.Inthefollowinganalysis
it ... Letusdenetheeciencyofabrakeastheratioofthetorqueprovided
bythebraketothetorquethatcouldbehadbyapplyingtheforcedirectlyto
thedrum,orshaft.Accordingtothisdenition,theeciencybecomes
T
F
s
r
ẳ
Ap
max
r
2
wsinu
2
sinu
1
ị
1=2ịp
max
r
2
wf
0
ỵsinf
0
ị
ẳ2A
sinu
2
sinu
1
f
0
ỵsinf
0
1-10ị
Uponsubstitutingforu
1
andu
2
inequation(1-8)andrecallingequations(1-6)
and( 1-7)wendthat
T
F
s
r
ẳ
4Asinf
0
=2ị
f
0
ỵsinf
0
ẳA
R
r
1-11ị
wheretheright-handsidehasalreadybeenplottedinFigure5.Fromthat
gurewendthatalthoughmaximumeciencymaybeachievedonlyifeach
shoeandliningextendoverhalfofthedrum,orshaft,relativelylittleeciency
islostiftheliningextendsoveronly160jinsteadof180j.This,togetherwith
thenearimpossibilityofmaintaininggoodcontactbetweentheliningand
thedrumneartheendsofashoesubtending180jatthecenterofthedrum,
accountsfortheangulardimensionsofthebrakeliningsshowninFigure1.
Finally,itfollowsfromequation(1-11)thatiftheshoeissymmetrically
pivotedandifequation(1-7)holds,theappliedtorqueisgivenby
TẳARF
s
1-12ị
II.BRAKINGTORQUEANDMOMENTSFORSYMMETRICALLY
SUPPORTEDINTERNALSHOES
Pressurepandbrakingtorqueareagaingivenbyequations(1-2 )and( 1-4),
respectively,foraninternalshoemovedagainstarotatingdrumalongaline
paralleltoitsaxisofsymmetry,lineOB,inFigure6.Inthefollowinganalysis
it...