Tài liệu Clutches and brakes design and selection P4 pdf

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 may be used to force the shoes outwardly against the drum. The cylin-
ders or cams also serve as anchors to prevent rotation and react against the
vehicle frame. The springs shown are to retract the shoes when the brake
is released.
A collection of segmented brake pads (backing plate plus lining) along
the entire circumference of the drum may be arranged as in Figure 3 to move
outwardly against a drum, as in Figure 3a, or inwardly against a drum, as in
Figure3b.Thebrakepads,orshoes,arethemselvesconstrainedagainst
Copyright © 2004 Marcel Dekker, Inc.
rotationbyanchorpinsthatfitintoshortradialslotsbetweentheshoesand
areattachedtotherimofthecircularframe,asshowninFigure3a.Brake
actuationisaccomplishedbyusingairtoexpandthenormallyflatelasto-
meric-fabricannulartubeshowninthatfigurebetweenthebrakepadsandthe
circularframe.Whendesignedtomoveinwardlyagainstadrum,asinFigure

3b,thebrakeliningisrivetedtoadifferentlycontouredbackingplatewhich
hasshouldersateachendtoresistatwistingtorqueandwhichisfittedwitha
centralslotthatacceptstheanchorpintotheouterframeateachsideofthe
shoe.Thisradialslotallowsthepadtomoverapidlyinwardbutprevents
tangentialmotion.
F
IGURE
1Linearlyacting,centrallypivotedshoebrake.(CourtesyoftheHindon
Corp., Charleston, SC)
Chapter 468
Copyright © 2004 Marcel Dekker, Inc.
I.BRAKINGTORQUEANDMOMENTSFORCENTRALLY
PIVOTEDEXTERNALSHOES
Tocalculatethetorque,wemustfirstfindanexpressionfortheliningpres-
sure.GuidedbythegeometryshowninFigure4,weseethattheliningpres-
surewillbegivenby
p¼kDcosuð1-1Þ
intermsoftheliningdeformationDiftheshoeanddrumareassumedtobe
absolutelyrigid.Maximumpressureoccurswhenu
g
0,sothatp
max
=kD.
Thusequation(1-1)becomes
p¼p
max
cosuð1-2Þ
andtheincrementaltangentialfrictionforceisgivenby
dF¼Ap
max

cosurwduð1-3Þ
F
IGURE
2Linearlyacting,twin-shoe,internaldrumbrakewithpneumaticactiva-
tion (Girling Twinstop). (Reprinted with permission. n1977 Society of Automotive
Engineers, Inc.)
Linearly Acting External and Internal Drum Brakes 69
Copyright © 2004 Marcel Dekker, Inc.
sothebrakingtorquebecomes
T¼Ap
max
r
2
w
Z
u
2
u
1
cosudu¼Ap
max
r
2
wðsinu
2
Àsinu
1
Þð1-4Þ
IndesignsdifferentfromthoseshowninFigure1itmayprove
convenienttohavetheshoepivotedaboutapointataradialdistanceRon

theaxisofsymmetry,suchaspointAinFigure4.ThemomentM
p
duetothe
pressureontheliningiszeroaboutpointAbecauseofthesymmetryofthe
shoeaboutthispoint.NosuchsymmetryexistsforthefrictionmomentM
f
,
however,sofromtheincrementalmomentduetofriction
dM
f
¼ðAp
max
rwcosuduÞðRcosuÀrÞ
F
IGURE
3Rimbrakeswithpneumaticactivation(alsousedasrimclutches).
(Courtesy of Eaton Corp., Airflex Division, Cleveland, Ohio.)
Chapter 470
Copyright © 2004 Marcel Dekker, Inc.
it follows that
M
f
¼ Ap
max
rw
Z
u
2
u
1

R cos
2
u À r cos u
ÀÁ
du
¼ Ap
max
rw R
f
0
2
þ
1
4
ðsin 2u
2
À sin 2u
1
Þ
!&
ð1-5Þ
À rðsin u
2
À sin u
1
Þ
'
where f
0
= u

2
À u
1
. The expression in equation (1-5) may be simplified by
observing that the symmetry of the shoe about A requires that
À u
1
¼ u
2
¼
B
0
2
ð1-6Þ
where B
0
is the angle subtended by the lining. Substitution of these values into
equation (1-5) leads to
M
f
¼ Ap
max
rw
R
2
ðf
0
þ sin f
0
ÞÀ2r sin

f
0
2
!
ð1-5aÞ
F
IGURE
3 Continued.
Linearly Acting External and Internal Drum Brakes 71
Copyright © 2004 Marcel Dekker, Inc.
whichsuggeststhatmomentM
f
willvanishiftheshoeispivotedat
R¼r
4sinðf
0
=2Þ
f
0
þsinf
0
ð1-7Þ
UponplottingR/rweobtainFigure5,whereintheratioincreases
smoothlyfrom1.0atf
0
=0to1.273atf
0
=krad.=180j.Thisclearly
indicatesthatitisimpossibletofindapivotpointforwhichM
f

=0foran
internallinearlyactingshoe.Thisconclusionis,ofcourse,unaffectedbythe
F
IGURE
4Geometryusedfortheanalysisofalinearlyactingexternalshoe.
Chapter 472
Copyright © 2004 Marcel Dekker, Inc.