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8/10/2019 MECH2400 5400 Belt Drives Flat Belt Drives 2014
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8/10/2019 MECH2400 5400 Belt Drives Flat Belt Drives 2014
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FlatBelting
isstill
the
logical
selection
to
agreat
many
basic
driving
problems.Itstillremainsthemajormeansoftransmittingpowerintraditionalolderstyle
ofmachinery.
ThetwokeyadvantagesofusingFlatBeltingare:
1. Maybeusedonverylongcentre distancearrangements.2. Relativelyinexpensive.
FlatBeltDrives
SometypicalarrangementsinFlatBeltdrivesinclude:
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GeneralTheoryonDesignofBeltDrives
Difference
in
Belt
Tensions
(Effective
Pull)
NotethatthebelttensionTlispullingthepulleyinananticlockwisedirectionwhilethebelttensionT2ispullingthepulleyintheclockwisedirection,butasTl islargerthanT2thepulleywillrotateinan
anti
clockwise
direction.
1
2
=(T1T2)
Indesigningabelttheaimisto
maketheturningeffectandhencethedifference(T1T2)aslargeaspossible.
Thedifferenceinbelttension(T1T2)isknownastheeffectivepullTEofthebelt.
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GeneralTheoryonDesignofBeltDrives
Sum
of
Tensions
Thepulleyisheldinpositionbyashaftmountedinbearings.
TheloadontheshaftwillbethesumofthetensionsT1+T2whentheslacksideandtightsideofthebeltareparallel(evenwhenthesidesarenotparallel;thisisroughlytrue).
HenceitisdesirabletokeepthesumofthetensionsTl +T2assmallaspossible.
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GeneralTheoryonDesignofBeltDrives
Tension
RatioOfcourseT1+T2isalwayslargerthanTlT2,butthesetworequirements(T1T2largeandTl+T2small)arefulfilledwhenthetensionratioT1/T2ismadeaslargeas
possible.Considertwoexamples,bothhavingthesameeffectivepull:
Example1:
T1/T2=2
LetT1=6 T2=3
T1 T2=3T1+T2=9
Example2:
T1/T2=4
LetT1=4 T2=1
T1 T2=3T1+T2=5
Itcanbeseenthatthesetwodriveswouldtransmitthesamepoweratthesamespeed(sinceT
lT
2isthesameinboth
cases).But,inExample1,theloadontheshaftsandbearingsisnearlytwiceasgreatasin2,alsoin1themaximumtensioninthebeltT1is50%greater. Hence,whenthe
tensionratio
islower
(Ex.
1)
the
shafts,
bearings,belts,andperhapspulleyswouldallneedtobestrongerandmoreexpensive.
NOTE:
Shouldalways
be
kept
large.
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GeneralTheoryonDesignofBeltDrives
General
FormulaThetensionratiowhenthebeltisjustonthepointofslippingis,
Where e=2.718(baseofnaturallogs)=Coefficientoffrictionbetweenbeltandpulley
=Arcofcontact(rads)=2arcos
Forthetensionratio
tobelarge,mustbelarge;
Thismeansthatbothandshouldbeaslargeapossible.
iscontrolledbythematerialsofthebeltandpulley,itcanbeslightlyincreasedforleatherbeltsbyusingabeltdressing.
isalways
smaller
on
the
small
pulley
so
the
belt
will
slip
there
first.
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Thearcofcontact()canbeimprovedby:1. Havingasmallratiobetweenthetwopulleys2. Havingalongcentredistancebetweenpulleys3. Usingajockeypulleyarrangement
4. Usingacrossedbeltarrangement
GeneralTheoryonDesignofBeltDrives
Arrangements
Arcof
Contact
( )
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GeneralTheoryonDesignofBeltDrives
Arrangements
PowerThepowertransmittedbyabeltisproportionaltotheproductoftorqueandspeed(R.P.M.).i.e..
P=
Henceatlowspeeds,thefasterthebeltruns,
themorepoweritwilltransmit.
Athigherspeeds,theeffectofthecentrifugaltensionbecomessolargethatthepowertransmittedbeginstodecreasesharplyasthe
beltspeedincreases.
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Wherethespeedofbeltingisabove900m/min allowanceshouldbemadefortheeffectofcentripetalforce.Thecentrifugalforcepermetre lengthofarcwillbegivenby;
f=
TheseradialforceswillhavearesultantRdirectedtowardstheleftandwillbebalancedbytensionsTcinthebelt,whichareinadditiontothoserequiredfordrivingpurposes.
Thecaseisanalogoustoaboilershellsubjectedtointernalpressure.
R=f2r=
2r=2mv2
Also2Tc=R,
Tc=mv2
GeneralTheoryonDesignofBeltDrivesArrangements DeterminationofTc
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GeneralTheoryonDesignofBeltDrives
Power
Formula for
a
Flat
Belt
1
=0
i.e.
1 3=0
i.e.mv2 =
1
orTc=
1
P= 1 1
v
Thepowerformulaforaflatbeltdrivemaybewritten:
Thispowerisamaximumwhen: ServiceFactors(S.F.):
DesignPower =motorpowerxS.F.
Prime
Mover Uniform Moderate HeavyShock Shock
ElectricalMotor 1.20 1.40 1.60MultiCylinderICengine 1.25 1.50 2.00SingleCylinderICengine 1.50 1.75 2.25
Careshouldbetakentokeepmaximumbelttensionduringtheaccelerationperiodwithinacceptablelimits.
Theapplicationofthecorrectservicefactoratthedesignstagehelpsinavoidinganyproblem.
Ifthestartingtorqueissevere,thebeltmanufacturercanprovidemaximumpermissibleaccelerationtensionsformoreprecisecalculations.
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GeneralTheoryonDesignofBeltDrives
Good
Practice1. Theslacksideofthebeltshouldbekepttothetopsothattheforceofgravity
increasesthewrapofthebeltaroundthepulleys.
2. Becauseofbeltslipandcreepthedrivenpulleywillrotateataslightlyslowerspeedthanthepulleyratioswouldindicate.
3. Thevelocityratiodoesnotremainquiteconstant.
4. Allowanceforbeltslipandcreepcanbemadebysmallchangeinoneofthepulleydiameters.
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GeneralTheoryonDesignofBeltDrives
Length
of
Belt
LengthofBelt(exact)=2Ccos+
1 2 +
1 2
LengthofBelt(approx)=
1 2 +2C+
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GeneralTheoryonDesignofBeltDrivesLimitsonSizes
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Generallywithtransmissionbeltingalonglengthofunsupportedbeltapproachesthepulley.Undertheseconditionscrowninghelpsthebelttotrackcorrectly.
Thiseffectisduetothetendencyofthetwosidesofthebeltsection,viewedseparately,torideintowardsthehighpointonthepulley,whichisthecrownof
thecamber.
Wherepulleycamberistoogreat,thebeltwillintimeacquireaglazedsurfaceinthecentre,asaresultofcarryingthewholeloadandslipping,becausetheedgesofthebeltarenotincontactwiththepulley.
BeltDrives CrowningofPulleys
Note:Excessivecrowningisdetrimentaltothebeltandresultsinuneventensiondistribution.Withsometypesofbeltingmaterials,suchasnylon,flatfacedpulleys(orpulleyswithaverysmallamountofcrowning)arepreferred.Alwayscheckwiththe
beltmanufacturer.
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BeltDrives PossibleModesofMisalignment