Universiti Tun Hussein Onn Malaysia

Mechanical EngineeringMechanics of Machine

BYKhairulnizam Bin Othman

Mohd Hadri Bin Mohamed NorNoraniah Binti Kassim

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CHAPTER 2POWER TRANSMISSION

BELT DRIVE

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LEARNING OUTCOMES

• IDENTIFY AND SOLVE PROBLEMS RELATED TO TYPES OF POWER TRANSMISSION SYSTEM.

• APPLY KINEMATICS PRINCIPLE TO SOLVE FLAT AND V-BELT PROBLEMS.

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CONTENTS• CENTRIFUGAL & CENTRIPETAL FORCE• CLASSIFICATION OF POWER DRIVE• BELT DRIVE SYSTEM• BELT DRIVE ARRANGMENT• BELT TYPES• VELOCITY RATIO• EFFECT OF SLIP ON VELOCITY RATIO• ANGLE OF CONTACT• LENGTH OF BELT• TENSION RATIO IN A BELT DRIVE• BELT SYSTEM POWER TRANSMISSION• EFFECT OF CENTRIFUGAL TENSION• BELT CREEP

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CENTRIFUGAL & CENTRIPETAL FORCE

According to Newton’s Third Law, all forces have reactions of the same magnitude but act in the opposite direction. Since a rotating body experiences centripetal force, its reaction acts in the opposite direction. This reaction is known as centrifugal force and its direction is outwards from the axis of rotation.

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CENTRIFUGAL & CENTRIPETAL FORCE

• Centripetal force is force that acts by pulling a rotating mass towards the axis of rotation. Consider a mass m moving around a circle of radius r at angular velocity . Its normal acceleration directed towards the center of the circle is:

• Therefore, the centripetal force that acts on the body is:

• The magnitude of centripetal and centrifugal force is same but opposite direction.

ran2

rmmaF nn2

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CLASSIFICATION OF POWER DRIVE

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POWER DRIVE

FLEXIBLE DRIVE DIRECT DRIVE

BELT DRIVECHAIN DRIVEROPE DRIVE

GEAR DRIVECAM DRIVE

BELT DRIVE SYSTEM

• Consists of two or more pulleys (sheaves) connected with belts

• The pulleys are mounted on shafts that are supported by bearings

• Purpose: to transmit power and motion between shafts

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BELT DRIVE SYSTEMAdvantages: • Up to 95% efficient • Designed to slip when an overload occurs • Resist abrasion (friction)• Require no lubrication (no metal to metal contact) • Smooth running • Quiet • Can transmit motion and power over long distances • Operate effectively at high speeds • Flexible shaft center distances • Inexpensive (when compared to other drive systems such as chain or gear

drives) • Easy to assemble and install • Have flexible tolerances • Absorb shock well • Easy and inexpensive to maintain

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BELT DRIVE ARRANGEMENT• Machines operated by belt drives must have an idler, an

adjustable base, or both • Idler is use to help maintain constant tension on the belt

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BELT TYPES

• Flat Belt • V Belt• Synchronous Belt

(timing belt)

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BELT TYPES

Uses/advantages of flat belt:• where high-speed applications (up to 140,000 rpm) are

more important than power transmission • long center distances are necessary • where drives with non-parallel shafts are required (belt can

be twisted) • applications requiring small pulley diameters (as small as

3/8")

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BELT TYPES

Disadvantages of flat belt:• tend to slip under load • lower efficiency at moderate speeds • must be kept under tension to function

(require tensioning devices); causes high bearing loads

• require friction for proper functioning • stretch over time

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BELT TYPESUses/advantages of V-belt:• useful in automotive, household, industrial, and

agricultural applications • easy to install and replace • low maintenance • provide shock absorption between driver and driven

shafts • useful with temperature range of 1oC to 82oC • are 90-98% efficient • maximum satisfactory speed ratio is approximately

6:1

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BELT TYPES

Disadvantages of V-belt:• improper belt tension can reduce service life • belt life at increased temperatures (above

82oC) is significantly shorted • require friction for proper functioning

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BELT TYPES

Uses/advantages of synchronous belt:• useful in operations requiring high efficiency, timing or

constant velocity • no slippage• will not stretch • required belt tension is very low • speed is transmitted uniformly

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BELT TYPES

Disadvantages of synchronous belt:• shorter center distance required than

flat belts • used on parallel shafts only• cost

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VELOCITY RATIO

[rpm] ;2

1

1

2 Ndd

NNn

• By assuming that there is no slipping and that the belt is inelastic, we can write v1 = v2 which brings us to the relations:

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[rad/s][m],[m/s], ;ocitydriver velocitydriven vel

22

11

1

2 rv

rr

vvn

VELOCITY RATIO

)(2

1

1

2 tutoriltdtd

NNn

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• If the thickness of the belt, t, is countered in the calculation, we add this value to the diameter, so we have:

EFFECT OF SLIP ON VELOCITY RATIO

• Although belt-drive depends on friction for power transmission, there are factors that contribute to the inefficiency of the drive. This inefficiency is known as belt slip where frictional force is not strong enough to hold the belt in its place, causing the sheaves to rotate without affecting the belt.

• When there is insufficient friction between a belt and the pulley, the belt cannot take up more loads; it results in the belt slipping over the pulley, the phenomenon is called belt slip. Belt slip results in loss of motion and power.

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EFFECT OF SLIP ON VELOCITY RATIO

• Normally belt slip is expressed as a percentage and denoted by G :• G1 = Percentage of slip between belt and driver sheave• G2 = Percentage of slip between belt and driven sheave• G = Total percentage slip = G1 + G2

• Again, by considering the thickness of the belt, t, then the velocity ratio:

100G-1

2

1

1

2

dd

NNn

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An engine, running at 150rpm, drives a line shaft by means of a belt. The engine pulley is 750mm diameter and the pulley on the line shaft being 450mm. A 900mm diameter pulley on the line shafts drives a 150mm diameter pulley keyed to a dynamo shaft. Fine the speed of the dynamo shaft, when:

1. There is no slip

2. There is a slip of 2% at each drive

Example 1.1

ANGLE OF CONTACT

[radian] ;21 X

rropen

[radian] ;2 contact, of Angle open23

OPEN BELT DRIVEOPEN BELT DRIVE

ANGLE OF CONTACT

[radian] ;21 X

rrcross

[radian] ;2 contact, of Angle cross24

CROSS BELT DRIVECROSS BELT DRIVE

TENSION RATIO IN A BELT DRIVE

[radian] ],[ ;2

1 NTeTT

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FLAT BELT DRIVEFLAT BELT DRIVE

TT11 == Tension on the Tension on the tight side of the belttight side of the belt

TT22 == Tension on the Tension on the slack side of the beltslack side of the belt

θθ = Angle of contacts= Angle of contacts

= Coefficient of = Coefficient of friction between friction between pulley and beltpulley and belt

TENSION RATIO IN A BELT DRIVE

[degree][radian], ],[ ;cossin

2

1

NTeeTT ec

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V-BELT DRIVEV-BELT DRIVE

BELT SYSTEM POWER TRANSMISSION

][ ; que,Driven tor

][ ; que,Driver tor2212

1211

NmrTTNmrTT

[Watt] ; Power, 21 PvTTP

ve

TP

ve

TP

sin1drivebelt -V

1drivebelt Flat

11

11

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EFFECT OF CENTRIFUGAL TENSION

][ ;2 NTmvT cc

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Since the belt has mass and as the belt rotates, there is a tendency for the belt to be ‘thrown out’ of the belt causing the tension in the belt to increase and the centrifugal force, Fc will be exist.

eTTTT

c

c

2

1

sin

2

1 eTTTT

c

c

FOR FLAT BELTFOR FLAT BELT

FOR V-BELTFOR V-BELT

m =m = mass of belt per unit mass of belt per unit lengthlength

TTcc = = centrifugal tensioncentrifugal tensionFC

EFFECT OF CENTRIFUGAL TENSION

cTT 2

ve

TTP

ve

TTP

c

c

sin1drivebelt -V

1drivebelt Flat

11

11

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cTT 1 &&

As a conclusion, when the mass of the belt is considered, the centrifugal force would be exist and the effective driving tensions:

And the power transmitted by a belt drive:

EFFECT OF CENTRIFUGAL TENSION

131 TTc

mT

eTP

311

32 1

sin1drive)belt -(Vmax

2mvTc 1

2

31Tmv

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For the maximum power transmitted by a belt drive, centrifugal tension is:

As we know that , so:

And:

mT

eTP

311

32 1

1drive)belt (Flat max

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Find the power transmitted by a belt running over a pulley of 600mm diameter at 200rpm. The coefficient of friction between the belt and pulley is 0.25, angle of lap 160º and maximum tension in the belt is 2500N.

Example 1.2

LENGTH OF BELT

X

rrXrrLopen

221

21 2

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OPEN BELT DRIVEOPEN BELT DRIVE

LENGTH OF BELT

X

rrXrrLcross

221

21 2

33

CROSS BELT DRIVECROSS BELT DRIVE

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A shaft which rotates at a constant speed of 160rpm is connected by belting to a parallel shaft 720mm apart, which has to run at 60, 80 and 100rpm. The smallest pulley on the driving shaft is 40mm in radius. Determine the remaining radii of the two stepped pulleys for:

1. A crossed belt

2. An open belt

(Neglect belt thickness and slip)

Example 1.3

BELT CREEP

][pulley ofvelocity ]drive[belt of elasticity of modulus

][ drivebelt of areasection cross

1

1

2

2

21

1

2

msvmNE

mAEATT

vv

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Belt creep happens due to the elasticity of belt. It can be defined as a situation in which a portion of the belt elongated while the other does not.

Due to elastic condition , v1 ≠ v2

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The power is transmitted from a pulley 1m diameter running at 200rpm to a pulley 2.25m by means of belt. Find the speed lost by the driven pulley as a result of creep, (if the stress on the tight and slack side of the belt is 1.4MPa and 0.5MPa respectively. The Young modulus for the material of the belt is 100MPa.

Example 1.4

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A flat belt type is used for a belt drive system connecting two pulleys 1.2m apart. The driver pulley with diameter 40cm is rotating with speed 350 rpm, while diameter of driven pulley is 100cm. Coefficient of friction of the contact surface between belt and pulley is 0.3. Maximum allowable tension is 600N. Find:

1. Power transmitted by the belt

2. Initial tension of the belt

3. If the flat belt is replaced by the V-belt with groove angle of 30º, find the power transmitted by the belt.

Example 1.5

Now, using the same data as example 1.5, treat now the belt is elastic, given that mass per unit length is 0.4kg/m, cross section of belt is 320mm2, and modulus of elasticity of 300MN/m2, find the power delivered by the system.

Example 1.6

THANK YOU

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