Unit 8 Power Transmission1

Power Transmission UNIT 8

POWER TRANSMISSIONPower is transmitted from the prime mover to machines by mans of intermediate mechanisms called transmission systems / drives.Transmission systems are classified depending on 1. Distance between them2. Speed3. Power as

Belt drives Rope drives Chain drives Gear drives

Belt drives: are used to transmit power or motion between two parallel shafts. Belt drive consists of two pulleys over which an endless belt is passed encircling both of them.

The arrangement consists of two pulleys mounted on two different shafts. One shaft called the driving shaft which receives the power from the mains and transmit to another shaft called driven shaft .The pulley mounted on the driving shaft is called driving pulley or driver, while the other pulley mounted on a shaft to which power is to be transmitted is called the driven pulley or follower. The belt passed over the pulley is kept in tension so as to avoid slip over the pulley. This helps in transmitting power effectively from one shaft to another .The portion of the belt which is having less tension is called slack side ad one which has higher tension is called tight side.

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Applications: To transmit power from prime mover to any device To transmit rotational motion to various parts of the machine. It is used when the distance between the two shafts is not very

large.Materials:Generally made from

Leather: are made from hide and can be used in both dry and wet conditions.

Rubber belts: used when the belts are exposed to damp conditions.

Canvas: is used when atmospheric conditions affect leather or rubber belt.

Balata: made from cotton and balata.

Types of Belt drives:1. Open Belt Drive2. Cross Belt Drive

Open Belt Drive: Open belt drives are employed when two parallel shafts have to rotate in the same direction.

When the shafts are placed far apart, the lower side of the belt should be the tight side and the upper side must be the slack side, because it will sag due to its own weight and thus increases the arc of contact which in turn increases the capacity of the drive.

Shaft axes should be horizontal or inclined. They should never be vertical.



Cross Belt Drive: are used to connect two shafts that are parallel and rotating in opposite direction. At the junction where the belt crosses, it rubs against itself and wears off. To avoid excessive wear the shafts must be placed at a maximum distance from each other and operated at very low speeds,

Length of Belt for open belt drive:Let the two pulleys connected by an open belt as shown in the Fig.Let, r1 = Radius of the driver (larger) pulley. r2 = Radius of the driven (smaller) pulley. C = Centre distance between the two pulleys.L= Length of the belt.L1 = Length of the belt in contact with larger pulleyL2 = Length of the belt in contact with Smaller pulleyL3 = Length of the belt which is not in contact with either of the pulleys.



L = L1 + L2 + L3 ……………………………. (1)

From the geometry of the figure L1 = ( + 2 ) r1 …………………………………………………(2)

L2 = ( - 2 ) r2 ……………………………..………………..(3)

To Calculate L3,

From O2, a line O2P is drawn parallel to the belt, which is not in contact with either of the pulleys.From triangle O1O2P,



Expanding the term in brackets using binomial theorem and neglecting the higher powers, we have

Substituting eauation (2),(3), and (5) in (1)

……(6)But = ?

From triangle O1O2P,

Sin = O1P / O1O2

= r1 – r2/ CFor small values of , Sin =

= r1 – r2/ C …………………..(7)Substituting (7) in (6)



The above equation can be used to calculate the length of the belt for an open belt drive.

Length of belt for cross belt drive:

Let r1 = Radius of the driver (larger) pulley r2 = Radius of the driven (smaller) pulley Let C = Centre distance between the two pulleysL= Length of beltL1 = Length of the belt in contact with larger pulleyL2 = Length of the belt in contact with Smaller pulleyL3 = Length of the belt which is not in contact with either of the pulleys.



L = L1 + L2 + L3 ……………………………. (1)

To Calculate L3,

From O2 draw a line O2P parallel to the belt, which is not in contact with either of the pulleys.From triangle O1O2P,

Expanding the term in brackets using binomial theorem and neglecting the higher powers, we have

Substituting eauation (2),(3), and (5) in (1)



But = ?From triangle O1O2P,

Sin = O1P / O1O2

= r1 + r2/ CFor small values of , Sin =

= r1 + r2/ C …………………..(7)Substituting (7) in (6)

The above equation can be used to calculate the length of the belt for a cross belt drive.Velocity Ratio: Defined as the ratio of the speed of the driven pulley (follower) to the speed of the driver pulley (Driving).Let d1 and d2 be the diameters of the driving and the driven pulley resp.



Let N1 and N2 be the speeds of the driving and the driven pulley in rpm.Assuming there is no slip between the belt and the pulley rim, the linear speed at every point on the belt must be the same. Hence circumferential speed at driver and driven and linear speed of the belt are equal.

Liner speed = d1 N1 = d2 N2 or d1 N1 = d2 N2

Effect of thickness of belt on the Velocity Ratio:When the thickness of the belt is considered the circumferential speed should be the mean speed reckoned at the centre of the belt thickness.

(d1 + t) N1 = (d2+ t ) N2

Speed of driven/ Speed of driver = diameter of driver/diameter of driven

Creep: In belt drives, driver pulls the belt from driven and hence receives more length of the belt. The belt gets stretched as it comes out of the driving pulley. Driven pulley receives less length of belt as it comes out of the driven pulley and hence there is a contraction in the belt. The belt being in elastic material stretches out more compared to contraction and hence the increase in length of the belt results in relative motion between the belt and the pulley surface. The relative



motion is called creep of the belt. The creep results in the loss of power ad decrease in the velocity ratio.

Slip: The power transmitted from one shaft to another depends on the frictional grip between the belt and the pulley rim. There is always some amount of slip between the belt and the pulley rim that results in slight reduction in the velocity ratio of the belt drive.

Slip may be defined as the relative motion between the pulley and the belt passing over it.Velocity ratio = N2/N1 = (d2/d1) *(100 - S)/100 Where S= % slipIf thickness of the belt is considered,Velocity ratio = N2/N1 = ((d2 + t)/ (d1 +t) *(100 - S)/100)

Types of Pulleys: Idler/ Rider /Jockey Pulley Fast and loose pulley Steeped pulley

Idler/ Rider /Jockey Pulley:When the diameter of the pulleys used in a belt drive is too small or the centre distance between the pulleys is small then the arc of contact of the smaller pulley reduces. This results in less tension in belt. In such cases jockey/ idler pulley are used to increase the arc of contact and tension in the belt.

Idler pulley is placed on the slack side of the belt, exerts pressure on the belt there by increasing the arc of conduct and also tension in the belt. Thus the power transmitted also increases.



IDLER PULLEY

Fast and loose pulleyIt is also called tight and loose pulley, used in belt drives in case when one of the driven shaft is to be started or stopped without starting or stopping the driving shaft.

It consists of two pulleys. Fast pulley is keyed to the driven shaft, while the loose pulley fitted with a tight fitting brass bush is mounted on the same shaft but without rigidly securing it. Hence the loose pulley rotates freely on the driven shaft .The driving pulley is also



keyed to the driving shaft and hence it rotates along with it. Belt will always be on the driving pulley and will be either on the fast pulley or on the loose pulley. When the belt is on the fast pulley, the power is transmitted to the machine shaft. When the machine shaft is to be brought to rest, the belt is to be shifted from fast to loose pulley.

Fast and loose pulleyStepped pulley: is used for changingthe speed of the driven shaft, while the driving shaft runs at constant speed.

It is a cast iron pulley having several steps of different diameters mounted on two parallel shafts, such that the smallest step of one pulley is opposite to the largest step of the other. The velocity ratio of the belt drive can be varied by shifting the belt from one step of the pulley to the other.



Stepped pulleyPower Transmitted: The effective turning force acting on the circumference of the follower is the difference in tensions on the tight side T1 and the slack side T2 of the belt.

F = (T1 – T2) NF = (T1 – T2) / 1000 K N

Power = P = F * VVelocity = ( d N) / 60 m/s

P = F = (( T1 – T2 ) * v ) / 1000 KWAdvantages of Belt Drive:

Higher belt efficiency. Simplicity. Durability of flat belts. Suitable for large centre distances. Speed can be varied by varying the diameter of the pulleys.



Disadvantages: Not suitable for small centre distances. Slip and creep cause power loss. High power can not be transmitted. Exact velocity ratio can not be maintained

V-Belts V-Belts are widely used in high power transmission. V-belts are trapezoidal in section. They are moulded as endless loops from rubber reinforced with fibrous material. They run in the V-grooves made in the pulleys, the wedging action of the belts in the V-grooves enables them to transmit higher torques. The power transmitted by a V-belt drive can be increased by operating with several belts placed side by side. This form of drive is used extensively in all classes of machineries transmitting power from 0.5 kW up to 150 kW.

Advantages of V-Belt Drives

1.V-Belts can transmit higher power.2. V-Belts can be used for small centre distances.3. V-Belts permit large speed ratios.4. There is no slipping of the belt from the pulley in V- Belt drives.5. In an emergency it is possible to continue the drive temporarily even if one of the belts snap.6. It is possible to operate with the shaft axes in any position.7. Several machines can be driven from a single driving shaft.8. Because they are moulded as endless loops, maintenance is less since belts do not snap as in the case of flat belts.



Disadvantages of V-belt drives

1. The pulley construction is more complex in a V-belt drive when compared to flat belt drive.2. Durability of V-belts is less compared to flat belts.3. V-Belts are not suitable for large center distances.4. V-Belt is a costlier system than flat belt drives

FORMULAST1/T2 =e

T1 = tension in tight side of the belt.T2 = tension in slack side of the belt. = angle of contact between the belt and pulley rim. = coefficient of friction.For open belt drive

= (180 – 2 sin-1(r1 – r2)/c)) /180 radians

For cross belt drive, = (180 + 2 sin-1(r1 + r2)/c)) /180 radiansIntial tension in belt = T0 = T1 + T2 /2

GEARSA wheel provided with teeth is called a GEAR. Gears are toothed wheel used to transmit power o motion from one shaft to another where the distance between the two shafts is relatively small.

Gears are generally used for To reverse the direction of rotation. To increase or decrease the speed of rotation. To move rotational motion to different axis. To keep the rotation of two axes synchronized.



Spur gear Terminology: Pitch circle: It is a theoretical or an imaginary circle upon which all computations are made.

Addendum:

The radial distance between the Pitch Circle and the top of the teeth.

Backlash: Play between mating teeth.

Base Circle:

The circle from which is generated the involute curve upon which the tooth profile is based.

Center Distance: The distance between centers of two gears.

Circular Pitch: Millimeter of Pitch Circle circumference per tooth.

Circular Thickness:

The thickness of the tooth measured along an arc following the Pitch Circle

Clearance:

The distance between the top of a tooth and the bottom of the space into which it fits on the meshing gear.

Dedendum:

The radial distance between the bottoms of the tooth to pitch circle.

Diametrical Pitch: Teeth per mm of diameter.

Face:

The working surface of a gear tooth, located between the pitch diameter and the top of the tooth.

Face Width: The width of the tooth measured parallel to the gear axis.



Flank:

The working surface of a gear tooth, located between the pitch diameter and the bottom of the teeth

Land: The top surface of the tooth.

Module: Millimeter of Pitch Diameter to Teeth.

Pitch Circle:

The circle, the radius of which is equal to the distance from the center of the gear to the pitch point.

Diametrical pitch: Teeth per millimeter of pitch diameter.

Root Circle:

The circle that passes through the bottom of the tooth spaces.

Root Diameter: The diameter of the Root Circle.

Working Depth:

The depth to which a tooth extends into the space between teeth on the mating gear.

Spur gear terminology



Spur Gears When the axes of the driving and driven shafts are parallel and co-planar and the teeth of the gear wheels are parallel to the axis, the gears are called spur gears. Teeth of the spur gears are cut on the circumference of the cylindrical discs. The contact between the mating gears will be along a line; hence spur gears can transmit higher powers. Spur gears are widely used in machine tools, wind up alaram clocks, watches, and in all general cases of power transmission where gear drives are preferred.

Advantages of Spur Gears

Spur gears are easy to find, inexpensive, and efficient.



Disadvantages of Spur Gears

Spur gears generally cannot be used when a direction change between the two shafts is required. Spur gears are not used in automobiles because each time a gear tooth engages a tooth on the other gear, the teeth collides and this impact makes a noise.

Bevel Gears When the axes of the two shafts are inclined to one another, and intersect when produced, bevel gears are used. Teeth of the bevel gears are cut on the conical surfaces. The most common examples of power transmission by bevel gears are those in which the axes of the two shafts are at right angles to each other. When two bevel gears have their axis at right angles and are of equal sizes they are called mitre gears.

Straight spur gears have the same problem as straight spur gears teeth. Solution to this problem is to curve the teeth and such gears are called spiral bevel gears.



Helical Gears Helical gears are similar to the spur gears except that the teeth are cut in the form of the helix around the gear. Helical gears are used for transmitting power between two parallel shafts and also between non parallel, non-intersecting shafts. The tooth contact is progressive, i.e., first at one end of a pair of engaging teeth, then, a little further along and so on, progressively to the end of the particular tooth. By this time, the next pair of teeth will be in contact so that engagement is continuous, backlash is greatly reduced and strength enhanced. Helical gears are preferred to spur gears in automobile power transmission where smooth and quiet running at higher speeds are necessary. The main disadvantage of the helical gears is that it produces end thrusts on the driving and driven shafts.


http://drives.themetalmachine.com/index.html%00%E5%A1%B9%EF%92%81%E1%B4%BB%E4%A1%BF%E2%B2%AF%E5%B6%82%E8%97%84%E6%8C%A7%00%00%EA%AE%A5


Worm and Worm Wheel:

Worm gears are used to transmit power between the driving and driven shafts having their axes at right angles and non-coplanar. A worm drive consists essentially of a worm which may have one or more helical threads and a worm wheel a gear wheel, which engages with the worm. Worm gears are suitable for transmission of power when a high velocity ratio as 60:1 is required. worm gear drives are generally employed in machine tools, like lathe, milling, drilling machines to get large speed reduction. Another important characteristic of the worm and worm wheel drive is that it offers self locking facility between the driven and the driving units.


http://drives.themetalmachine.com/index.html%00%E5%A1%B9%EF%92%81%E1%B4%BB%E4%A1%BF%E2%B2%AF%E5%B6%82%E8%97%84%E6%8C%A7%00%00%EA%AE%A5


Rack and Pinion

When a rotary motion is to be converted into a linear motion, rack and pinion arrangement is used. Rack is a rectangular bar with a series of straight teeth cut on it. Theoretically rack is considered to be a spur gear of infinite diameter. Rack and pinion arrangement, find their application in machine tools, such as, lathe, drilling,

planning machine.



Different Types of Gear Trains

Different types of gear trains are as follows

1. Simple Gear Train2. Compound Gear Train3. Reverted Gear Train4. Epicyclic gear train

Simple Gear Train In a simple gear train, a series of gear wheels are mounted on different shafts between the driving and driven shafts, each shaft carrying only one gear as shown in the figure. A is the Driving gear C is the driven gear and B is the Intermediate gear. The intermediate gear B is also called idler gears, because the velocity ratio depends only upon the numbers of teeth on the driving and driven gears. The idler gears act as the intermediate gears to establish the drive between the driving and the driven gears, but they change the direction of rotation of the driven gear. Even number of of idler gears will rotate the driven gear in the direction opposite to that of the driving gear. Odd number of idler gears will

rotate the driven gear is the same direction as that of the driving gear.


http://drives.themetalmachine.com/Gear_Drives/Reverted_Gear_Train.html

http://drives.themetalmachine.com/Gear_Drives/Compound_Gear_Train.html

http://drives.themetalmachine.com/Gear_Drives/Simple_Gear_Train.html


Velocity ratio of simple gear train:

Let N1 ,N2 ,N3 and N4 be the speeds and T1 ,T2,T3 and T4 be the number of teeth on gear 1 2 3 and 4 resp.

Gear 1 drives gear 2 Velocity ratio = N2 / N1 = T1 / T2 ………………………………….1

Gear 2 drives gear 3Velocity ratio = N3 / N2 = T2 / T3 …………………………………2

Gear 3 drives gear 4Velocity ratio = N4 / N3 = T3 / T4 …………………………………3

The velocity ratio of gear train is obtained by multiplying the equation 1, 2 and 3

Velocity ratio = N4 / N1 = T1/ T4



Compound Gear Train In a compound gear train, the intermediate shaft carries two gears which are keyed to it. When the velocity ratio is very high, a simple gear train becomes practically impossible owing to the difficulty of connecting the driving and driven gears because the given centre distance is small. In such cases a compound gear train is used. In given Compound gear train A is the driving gear, D is the driven gear and gears B and C keyed to an intermediate shaft and are called compound gears. Since gears B and C are mounted on the same shaft, they rotate at the same speed.

Velocity ratio of gear drives: Gear A meshes with gear B and Gear C meshes with gear D and B & C are compound gears.

Velocity ratio = NB/NA = TA/TB …………………….1

Velocity ratio = ND/NC = TC/TD …………………………..2



Multiplying 1 and 2(NB/NA ) * (ND/NC ) =( TA/TB ) * (TC/TD ) ……..3

Since B and C are mounted on the same shaft speed of both the gears are same. NB = NC

Then equation 3 reduces toND / NA = =( TA/TB ) * (TC/TD )

Velocity Ratio =

Problems1. A shaft running at 150 rpm drives another shaft at 250 rpm to

transmit a power of 20 kw .The diameter on the output shaft of the driven is 0.6 m and the distance between centers of the two shafts is 2.7 m .Assume the coefficient of friction between the belt and the pulley rim as 0.25.Determine the length of the belt and belt tensions for A) Open belt drive B) Cross belt drive.

Solution:Data: n1 = 150 rpm n2 = 250 rpm d2 = 0.6 m d1 = ?C= 2.7 m μ = 0.25 P = 20kw



W.K.T,P = (( T1 – T2 ) * v ) / 1000 KW

V = Π d1 n1/60 = Π d2 n2/60 V= Π d2 n2/60 = Π *0.6*250/60 = 7.85 m/s

20 = (( T1 – T2 ) * 7.85 ) / 1000 ( T1 – T2 ) = 2547 N ---------------(1)

A) Open belt drive

r1 =? n2/n1 = d1/d2 => d1 =1m r1 = 0.5 m L =2(2.7) + Π (0.5+0.3) + [0.5 – 0.3]2/2.7

L = 7.92 m for open belt driveT1/T2 =e

Θ = ? = (180 – 2 sin-1(r1 – r2)/c)) /180 radians

= (180 – 2 sin-1(0.5-0.3)/2.7)) /180 radians = 3 radiansT1/T2 =e0.25(3)

T1 = 2.117 T2 Substitutung in equation 1 (2.117 T2 - T2) = 2547 T2 = 2280.2 N

T1 = 4827.18 N B) Cross belt drive

L = 2(2.7)+ Π *(0.5+0.3) + (0.5+0.3)2/2.7L= 8.15 m for cross belt drive

T1/T2 =e



= ? = (180 + 2 sin-1(r1 + r2)/c)) /180 radians

= (180+ 2 sin-1(0.5+0.3)/2.7)) /180 radians =3.74 radians

T1/T2 =e0.25(3.74)

T1 = 2.54 T2 Substitutung in equation 1 (2.54 T2 - T2) = 2547 T2 = 1646.4 N

T1 = 4193.3 N 2. A compound gear train consists of wheels A,B,C and D have

15,30,20, and 40 teeth resp. The wheels B and C are keyed to the same spindle.If the wheel A runs at 400 rpm ,find the speed of wheel D.Sketch the arrangement if B meshes with A and C meshes with D.

Solution: Data:TA= 15 TC = 20 TB=30 TD = 400NA= 400

ND / NA = =( TA/TB ) * (TC/TD )ND/400 = 15(20)/30(40)

ND = 100 rpm speed of wheel D



3. A simple gear train consists of 3 gears .The number of teeth on the driving gear is 60 and on the idler is 40 and on the driven gear is 80.Find the velocity ratio, if the driving gear rotates at 1200 rpm.Calculate the speed of the driven gear.

T1= 60 T2 = 40 T3 = 80N1= 1200 rpm N3 =?

N3 / N1 = T1 / T3

N3 /1200 = 60/80N3 = 900 rpm

b) velocity ratio

N3 / N1 = 900/1200 =3/4 = 3:4

4. The velocity ratio of a gear is 2. The driving wheel has 16 teeth and turns at 120 rpm.Find the rpm and the number of teeth on the driven wheel.

T1= 16 T2 = ? N1= 120 rpm N2 =?

N2 / N1 = T1 / T2

N2 / 120 = 16 / 8

N2 = 240 rpm



Question Bank1. Briefly explain the following gear drives with neat sketches.

a. Spur gearb. Helical gearc. Bevel geard. Rack and pinione. Worm and worm wheel

2. Distinguish between open belt drive and cross belt drive3. Write short notes on gears.4. What are the advantages and disadvantages of gear drives over

belt drives.5. Write short notes on types of pulley with neat sketches.6. Distinguish between simple and compound gear train.7. Derive the equation for length of open belt drive and cross belt

drive.


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