35050627 Belt Drive Chapter 2

832019 35050627 Belt Drive Chapter 2

httpslidepdfcomreaderfull35050627-belt-drive-chapter-2 151

CHAPTER 2

BELT DRIVES SYSTEM



APPLICATIONS OF BELT DRIVES

VEHICLES

INDUSTRIAL

AUTOMATION



Another method widely used in engineering practice in transmitting powerbetween shafts is belt drive system

Basic arrangement of a belt drive system consists of driver sheave driven sheaveand belting material such as ropes rubber bands or chain

The operation of belt drives depends fully on the friction generated from contactsurface between the belt and sheaves Thus any slip occurrence on the contactsurface will reduce the efficiency of the power transmitted

The choice of type of belt to be used is important so that the required power can bedelivered efficiently Some of the factor to be considered in selecting a suitable belttype to be used for a particular application is

- Speed of driver and driven sheaves

- Required velocity ratio- Distance between the driver sheave and driven sheave- Workspace constraint- Total power to be transmitted

INTRODUCTION TO BELT DRIVE





BELT DRIVE ARRANGEMENTS

Compound Belt Drives




Stepped Cone Pulley

Step or cone pulley is used forchanging speed of driven shaftwhile the driver shaft runs atconstant speed

This is achieved by shifting thebelt from one part of the step to

the other



TYPES OF BELT AND MATERIAL

Flat belt ndash Most commonly used in factories workshops Used when moderatepower is to be transmitted Limitation for centre distance is not more than 8meter

V-Belts ndash Commonly used in factories workshops and is used when great

amount of power is to be transmitted when the centre distance is near to eachother

Circular belt Rope ndash Used when great amount of power is to be transmittedwhen centre distance for both pulleys are more than 8 meter apart



Material used for belts must be strong durable and flexible It must have highcoefficient of friction micro The material used are

1 Leather belt

2 Rubber belt

3 Cotton fabric belts

The coefficient of friction of belts depends upon factors such as belt materialpulley material slip of belt and speed of belt Table shows some of micro value for

belt and pulley material



VELOCITY RATIO FOR BELT DRIVE SYSTEM



SLIP IN BELT DRIVE SYSTEM





ANGLE OF LAP

It is the enclosed angle in which the belt and surface of pulley are in contact

It is important for determining the right setting of driver and driven pulley toguarantee an effective power transmission

For Open belt arrangement



For Cross belt arrangement



OVERALL LENGTH OF BELT DRIVE SYSTEM

For Open Belt arrangement




For Cross Belt arrangement



Belt tension in a belt drive system can be expressed in terms of ratio betweentension on the tight side and the slack side of the same belt when it was operating

In order for the belt to produce torque on the wheel (whether or not it is rotating)there must be tension in both ends

The tension in one end must be greater than the tension in the other hand Let thetension T+dT is larger than T where dT is the small increment in tension Consideran elementary length of the belt on the pulley

BELT RATIO



BELT RATIO



BELT RATIO





BELT RATIO FOR VEE BELT SYSTEM

For Vee Belt system the samederivation technique can be

applied to get the Belt Ratio forVee Belt system

The wedging effect of the beltincreases the reaction forcebetween the pulley and the belt

Total reaction force R is R=2R rsquo sin β

Previously dT =microRrsquo but for Vee Belt dT = 2 microRrsquo

Thus

sinsin2

22 R R

RdT

For complete derivation integrating between the limits as previous approach

sin

2

1e

T

T



Case Study CVT vs Gears Technology

Traditional car manufacturer uses gears as the primary drive train These gearswill have interlocking toothed wheels that help transmit and modify rotary motion

and torque A combination of planetary gears creates all of the different gearratios that the transmission can produce When this type of transmission cyclesthrough its gears the driver can feel jolts as each gear is engaged

Continuously Variable Transmissions(CVT) dont have a gearbox with set ofgears

The most common type of CVToperates on an ingenious pulley

system that allows an infinite variabilitybetween highest and lowest gears withno discrete steps or shifts




The simplicity and steeples nature of CVT make them an ideal transmissionfor a variety of machines and devices not just cars CVT have been usedfor years in power tools and drill presses Theyve also been used in avariety of vehicles including tractors and motor scooters



So whats different about these CVT-based cars -- cars like the Saturn Vue theAudi A4 and A6 the Nissan Murano and the Honda Insight

The animation below which compares the acceleration of a car with a CVT to onewithout can give a good feel for the experience

PLAY THE ANIMATION



Example 1

Two pulleys one 450mm dia and the other 200 mm dia on parallel shaft 195mapart are connected by a crossed belt Find the length of the belt required andthe angle of contactlap between the belt and each pulley



Solution





Example 2

A compound belt drive will have these properties

a) Find the speed of follower pulley D in terms of above properties

b) Find the speed of follower pulley D in terms of above properties if thethickness of belt and slip is taken into consideration Assume S is thetotal slip for all pulley



Solution



POWER TRANSMISSION OF BELT DRIVES

The tension in a belt pulley increases with torque and power The maximum powerthat a pulley system can transmit is limited by the strength of the belt material

If this is a problem then more than one belt should be used to share the loadFor power to be delivered to the driven pulley thus the driver pulley will pull the belt(tight side) and delivers it to the other side (slack side) Thus the tight side will havetension greater than the slack side

Thus the effective driving force is the difference between tight and slack side

tension (T1-T2)



MAXIMUM POWER WITH NO BELT SLIP

v

e

T P

sin

1

11

For Vee Belt power is

Watt



EFFECT OF CENTRIFUGAL FORCE

C O C G O C












MAXIMUM POWER WITH CENTRIFUGAL EFFECT INCLUDED




Earlier we have shown that how to achieve maximum power at no slip condition(ideal condition) However in practice centrifugal force effect exist for high speedapplication system of belt drive This will cause slippage likely to occur since

centrifugal force tends to lift the belt off the pulley

So how do we maximize the full power of the belt drive system by takingconsideration on the centrifugal effect









Example 3 A leather belt with cross sectional area of 2250mm2 is used to drive a cast ironpulley 900 mm in diameter at 336 rpm If the angle of lap is 120deg and the stressin the tight side is 2 MPa find

a) Effective tension on the tight side of belt

b) Centrifugal force acting on the belt

c) Effective tension on the slack side of the belt

d) Power capacity of the belt

The density of the leather is 980 kgm3 and the coefficient of friction is

035





Solution













INITIAL TENSION OF BELT DRIVES








CREEP OF BELT DRIVES




When power is transmitted by a belt or rope there is always a difference betweenthe peripheral speed of the driving pulley and that of driven pulley Because ofdifferent tensions on the two sides of the pulley the stretch in the belt will be

different

Consider one metre length of belt when unstressed Because of tension T 1 onthe tight side the length of the belt is (1 + x1) metre where x1 is the stretchSimilarly due to tension T2 on the slack side the length of the belt is (1 + x2) metre where x2 is the stretch Obviously x1 is greater than x2

A length (1 + x1) metre has approached the driver but only (1 + x2) metre hasmoved off the driver Thus the length of belt that leaves the driver pulley is lessthan that which has approached it

Thus there is some relative motion of the belt on the pulley and the belt is saidto creep The effect of creep in belt is to reduce the speed of the follower andreduce the power output





E ample 4



Example 4





Example 5



Example 5

Design a rubber belt to drive a dynamo generating 20 kW of power at 2250 rpmand fitted with a pulley 200 mm diameter Assume dynamo efficiency to be 85The data given are

Allowable stress for belt = 21 MPa

Density of rubber belt = 1000 kgm3

Angle of lap for dynamo pulley = 165deg

Coefficient of friction between belt and pulley = 03

Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1

Design a belt drive that can transmit 110 kW power for a system consisting of twopulleys of diameter 09 m and 12 m center distance of 36 m belt speed of 20ms coefficient of friction 03 a slip of 12 at each pulley and the belt drive iscapable to carry an overload torque of 866 Nm You can assume the safe stressof the belt is around 15 to 25 MPa You must design the belt system by finding

- Type of belt drive to be use

-Speed for driver and driven pulley

-Required design torque to compensate the extra loading of 866 Nm

-Angle of lap

-Length of belt required

-The sizing of belt (cross sectional area)

-Centrifugal force effect (if exist)





APPLICATIONS OF BELT DRIVES

VEHICLES

INDUSTRIAL

AUTOMATION



















Stepped Cone Pulley



the other











1 Leather belt

2 Rubber belt














ANGLE OF LAP




















BELT RATIO



BELT RATIO



BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap
























Stepped Cone Pulley



the other











1 Leather belt

2 Rubber belt














ANGLE OF LAP




















BELT RATIO



BELT RATIO



BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap















Stepped Cone Pulley



the other











1 Leather belt

2 Rubber belt














ANGLE OF LAP




















BELT RATIO



BELT RATIO



BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap













Stepped Cone Pulley



the other











1 Leather belt

2 Rubber belt














ANGLE OF LAP




















BELT RATIO



BELT RATIO



BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap









Stepped Cone Pulley



the other











1 Leather belt

2 Rubber belt














ANGLE OF LAP




















BELT RATIO



BELT RATIO



BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap
















1 Leather belt

2 Rubber belt














ANGLE OF LAP




















BELT RATIO



BELT RATIO



BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap









1 Leather belt

2 Rubber belt














ANGLE OF LAP




















BELT RATIO



BELT RATIO



BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap
















ANGLE OF LAP




















BELT RATIO



BELT RATIO



BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap













ANGLE OF LAP




















BELT RATIO



BELT RATIO



BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap










ANGLE OF LAP




















BELT RATIO



BELT RATIO



BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap








ANGLE OF LAP




















BELT RATIO



BELT RATIO



BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap






















BELT RATIO



BELT RATIO



BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap



















BELT RATIO



BELT RATIO



BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap















BELT RATIO



BELT RATIO



BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap











BELT RATIO



BELT RATIO



BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap








BELT RATIO



BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap








BELT RATIO











Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap
















Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap














Thus

sinsin2

22 R R

RdT


sin

2

1e

T

T

















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap






















PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap














PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap










PLAY THE ANIMATION



Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap








Example 1




Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap








Solution





Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap










Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap








Example 2






Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap








Solution







tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap












tension (T1-T2)




v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap









v

e

T P

sin

1

11


Watt




C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap









C O C G O C

































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap






































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap


































035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap






























035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap


























035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap



















035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap















035





Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap









Solution


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap






























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap


























different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap






















different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap


















different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap














different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap










different








E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap









E ample 4



Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap








Example 4





Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap










Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap








Example 5



Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap








Example 5






Solution

GROUP PROJECT 1



GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap








GROUP PROJECT 1

DESIGN PROJECT 1





-Angle of lap








35050627 Belt Drive Chapter 2

Documents