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11/29/2013
1
ApplicationsEngineering Mechanics: Belt Friction
Band brakes
Torque Transmission
Capstan(Use less smaller force to hold loads)
Pulley(Raising or lowering loads)
Theory• Relate T1 and T2 when belt is about to slide to right.
Engineering Mechanics: Belt Friction
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2 1T / T e s
Condition for impending slip for belt about to slide toward right (T2 > T1 )
T2 = Tension in the belt that pullsT1 =Tension in the belt that resist
Engineering Mechanics: Belt Friction Theory
Angle of contact shall be expressed in radianThe 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 pulleys3. Belt drives, both pulley and
belt rotate 2 1T / T e k
If the belt or rope is actually slipping (relative slip between belt/rope and drum/pulley)
Problem-1A cord is wrapped twice around acapstan A and three times aroundsecond capstan B. Finally cord goesover a half barrel section and supportsa mass M of 500 kg. What is tension Trequired to maintain this load? Takecoefficient of friction 0.1 for allsurfaces of contact.
Engineering Mechanics: Belt Friction
Maximum value of tension can befound out by upward impendingmotion of mass ‘M’ for whichMg<T.
Minimum value of tension can befound out by the impendingdownward motion of ‘M’ forwhich Mg>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 > T2>T1> T
M=500 Kg, βA=4π, βB=6π, βpulley=0.5 πSOLUTION:
0.20s 0.15k
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 C is rotated clockwise .
Problem-2Engineering Mechanics: Belt Friction
Solution:Impending slip at C
Slips at D and E
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Note: 1sin 30 rad,2 6rr
2 ,2 6 3C D E
2 ,s CAW T e
1 2 1, 16 lbk D k ET T e T e
5 23 30.15 0.20
16 lb 16 lb 11.09 lbk E D s CAW e e e e
C is rotated clockwise slowly
Engineering Mechanics: Belt Friction
Problem-2
Belt Drives
Driver Pulley
T2 >T1
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 TransmittedM1= (T2-T1)*0.2
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Problem-3A flat belt connects pulley A, which
drives the a machine tool, to pulley B,which is attached to shaft of an electricmotor. The coefficients of friction are s= 0.25 and k = 0.20 between bothpulleys and the belt. Knowing that themaximum allowable tension in the belt is600 N, determine the largest torquewhich can be exerted by the belt onpulley A.
Engineering Mechanics: Belt Friction
Solution:Since slipping depends upon angle ofcontact and coefficient of friction ,pulley‘B’ will slip first.(Since it is having samecoefficient of friction but smaller angle ofcontact than pulley ‘A’).
For the maximum tension in one side ofbelt of pulley ‘B’, resistance tension inother side should be found out.
From moment about center of pulley ‘A’,maximum allowable torque can be foundout.
For no slip at ‘A’ , µs < (µs) max conditionshould be satisfied at pulley ‘A’.
Problem-3
.
Pulley-B
Engineering Mechanics: Belt Friction
SOLUTION:
0 25
240 4 3
120 2 3
so
Ao
B
.
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Problem-3Here couple MA is 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
A differential band brake is used to controlthe speed of a drum which rotates at aconstant speed. Knowing that the coefficientof kinetic friction between the belt and thedrum is 0.30 and that a couple of magnitude125 lb-ft is applied to the drum, determinethe corresponding magnitude of the force Pthat is exerted on end D of the lever whenthe drum is rotating (a) clockwise, (b)counter clockwise.
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-4SOLUTION:
Engineering Mechanics: Belt Friction
Problem-4
Lever
Engineering Mechanics: Belt Friction