Belt friction lecture_new

emech

1. 11/29/2013
1
Applications
Engineering Mechanics: Belt Friction
Band brakes
Torque
Transmission
Capstan
(Use less smaller force to
holdloads)
Pulley
(Raising or lowering
loads)
Theory
•Relate T
1and T
2when belt is about to slide to right.
Engineering Mechanics: Belt Friction

2. 11/29/2013
2
2 1
T / T es
 

Condition for impending slip for
belt about to slide toward right
(T
2> T
1)
T
2= Tension in the belt that pulls
T
1=Tension in the belt that resist
Engineering Mechanics: Belt Friction
Theory
Angle of contact shall be expressed in
radian
The formula can be applied for
impending slip condition for
problems involving:
1.Flat belt passing over a fixed
cylindrical drum
2.Ropes/Belt wrapped around a
post or capstan or pulleys
3.Belt drives, both pulley and
belt rotate
2 1
T / T ek


If the belt or rope is actually
slipping (relative slip between
belt/rope and drum/pulley)
Problem-1
Acordiswrappedtwicearounda
capstanAandthreetimesaround
secondcapstanB.Finallycordgoes
overahalfbarrelsectionandsupports
amassMof500kg.WhatistensionT
requiredtomaintainthisload?Take
coefficientoffriction0.1forall
surfacesofcontact.
Engineering Mechanics: Belt Friction
Maximumvalueoftensioncanbe
foundoutbyupwardimpending
motionofmass‘M’forwhich
Mg<T.
Minimumvalueoftensioncanbe
foundoutbytheimpending
downwardmotionof‘M’for
whichMg>T.
Solution:

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Problem-1
For 181.15 <T<132811.04 N, the load will be
held in place .
Engineering Mechanics: Belt Friction
For impending downward motion of M ,
Mg > T
2>T
1> T
M=500 Kg, β
A=4π,β
B=6π,β
pulley=0.5πSOLUTION:
0.20
s
 0.15
k

A cable passes around three 2-in.-radius
pulleys and supports two blocks as
shown. Two of the pulleys ( D and E) are
locked to prevent rotation, while the third
pulley is rotated slowly at a constant
speed. Knowing that the coefficients of
friction between the cable and the pulleys
are
determine the largest weight which can
be raised if pulley Cis rotated clockwise
.
Problem-2
Engineering Mechanics: Belt Friction
Solution:
Impending slip at C
Slips at D and E

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4
Note:
1
sin 30 rad,
2 6
r
r



   
2
,
2 6 3
C D E
  
       
2
,
s C
A
W T e
 


1 2 1 , 16 lb
k D k E
T T e T e
   
 

 

 
5 2
3 3
0.15 0.20
16 lb 16 lb 11.09 lb
k E D s C
A
W e e e e
 
    
 
   
C is rotated clockwise slowly
Engineering Mechanics: Belt Friction
Problem-2
Belt Drives
Driver Pulley
T
2>T
1
Driven pulley
M1
Engineering Mechanics: Belt Friction
Connected to electric motor (say).
An external torque (M) is applied
Connected to a machine tool (say).
Torque transferred to the pulley by the
machine tool is M1
Torque Transmitted
M1= (T2-T1)*0.2

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Problem-3
AflatbeltconnectspulleyA,which
drivestheamachinetool,topulleyB
,whichisattachedtoshaftofanelectric
motor.Thecoefficientsoffrictionare
s
=0.25and
k=0.20betweenboth
pulleysandthebelt.Knowingthatthe
maximumallowabletensioninthebeltis
600N,determinethelargesttorque
whichcanbeexertedbythebelton
pulleyA.
Engineering Mechanics: Belt Friction
Solution:
Sinceslippingdependsuponangleof
contactandcoefficientoffriction,pulley
‘B’willslipfirst.(Sinceitishavingsame
coefficientoffrictionbutsmallerangleof
contactthanpulley‘A’).
Forthemaximumtensioninonesideof
beltofpulley‘B’,resistancetensionin
othersideshouldbefoundout.
Frommomentaboutcenterofpulley‘A’
,maximumallowabletorquecanbefound
out.
Fornoslipat‘A’,µ
s<(µ
s)
maxcondition
shouldbesatisfiedatpulley‘A’.
Problem-3
.
Pulley-B
Engineering Mechanics: Belt Friction
SOLUTION:


0 25
240 4 3
120 2 3
s
o
A
o
B
.
 
 

 
 

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Problem-3
Here couple M
Ais applied to the pulley by the
machine tool to which it is attached and is equal
and opposite to the torque exerted by the belt.
Pulley-A
Engineering Mechanics: Belt Friction
Problem-4
Adifferentialbandbrakeisusedtocontrol
thespeedofadrumwhichrotatesata
constantspeed.Knowingthatthecoefficient
ofkineticfrictionbetweenthebeltandthe
drumis0.30andthatacoupleofmagnitude
125lb-ftisappliedtothedrum,determine
thecorrespondingmagnitudeoftheforceP
thatisexertedonendDoftheleverwhen
thedrumisrotating(a)clockwise,(b)
counterclockwise.
Solution
•Relative slip between belt and
drum
•Moment equilibrium of drum
about center of drum will give
tension generated in both side of
the drum.
•Again moment equilibrium of
lever about point B will give the
force ‘P’
Engineering Mechanics: Belt Friction

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Problem-4
SOLUTION:
Engineering Mechanics: Belt Friction
Problem-4
Lever
Engineering Mechanics: Belt Friction