POWER TRANSMISSION

Introduction
The rotational motion can be transmitted from one mechanical element to the other with
the help of certain systems known as power transmission systems. The one that drives is called
driving
system and the other which is driven is called driven system. The methods of power transmission
are:
i. Belt drive.
ii. Gear drive.
iii. Rope drive.
iv. Chain drive.
Belt Drives
It is one of the most common and effective devices of transmitting motion from one
shaft to another by means of a thin inextensible band running over two pulleys. Belt drive is
generally employed whenever rotary motion is to be transmitted between two parallel shafts.
They are generally used when the driving and driven ends are far apart. The drive consists of 2
pulleys over which an endless belt is passed encircling both of them. The power is transmitted
from driving pulley to driven pulley because of the frictional grip that exists between the belt
and pulley.

Belt Drive

1
In the above figure when the system is stationary the belt will be slightly in a stretched condition
due to the initial tension To prevailing in the belt. As soon as the driving pulley rotates in the
clockwise direction it pulls the belt from its lower side due to the friction prevailing between the
belt and the pulley surface and the tension on the lower side increases from To to T1 and the belt
becomes tight. Hence it is called as the tight side of the belt. The driving pulley delivers the belt
to the upper side where the tension in the belt decreases from To to T2. This is known as the slack
side of the belt. Here (T1 – T2) is the effective force driving the belt drive. As long as the
frictional force required to cause relative movement between the belt and either the driving or
driven pulley surface is greater than (T1 – T2) the slipping of the belt does not take place and
power is transmitted from driving pulley to driven pulley. If (T1 – T2) is greater than the
frictional force the belt slips. Hence higher coefficient of friction is an advantage in case of a belt
drive.
Belt materials of power transmission belts are generally made from leather, rubber
canvas etc. and are used in mills & factories. Advantage is low cost, low maintenance, and long
life. Limitations are not a Positive Drive, less efficiency due to Slip and Creep and not suitable
for shorter distances.
Types of Belt drives
Open Belt Drive: This type of belt drive shown in figure below is employed when the 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, so that
when the upper side becomes the slack side it will sag due to its own weight thereby increasing
the arc of contact which in turn increases the capacity of the drive.

Open Belt Drive

Flat belt drives of the open system should always have their shaft axes horizontal. They should
never be vertical, for if so arranged the centrifugal force developed in the belt combined with the

2
force of gravity causes the bell to stretch and tend to leave the rim of the pulleys, thereby losing
contact with their rim surfaces.
Crossed Belt Drive: This type of belt drive shown in figure below is employed when two
parallel shafts have to rotate in the 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.

Crossed Belt Drive

3
Velocity Ratio of a Belt Drive:
The velocity ratio of a belt drive is defined as the ratio of the speed of the driven pulley to
the speed of the driving pulley.

Velocity Ratio = N2 / N1 = d1 / d2

Velocity Ratio = =

Stepped Cone Pulley (Speed Cone)

Stepped/Speed Cone Pulley

A stepped cone pulley is an Integral casting having three or more number of pulleys of
different diameters one adjacent to the other as shown in figure above. One set of stepped cone
pulley is mounted on the driving shaft and other set is mounted in the reverse direction on the
driven shaft. An endless belt is wrapped around one pair of pulleys. By shifting the belt from one
pair of pulleys to the other, the speed of the driven
shaft can be varied. The diameters of the driving and driven pulleys are such that the same
belt will operate when shifted on different pairs of pulleys.
It is used when speed of the driven shaft is to be changed very frequently as in the case of
machine tools such as lathe, drilling machine etc.

4
Fast and loose pulley:
When many machines obtain the drive from a main driving shaft, it may be required to
run some machines intermittently without having to start or stop the main driving shaft. Fast and
loose pulley arrangement shown in the figure below is used for this purpose. It consists of two
pulleys mounted on the driven shaft, a fast pulley which is securely keyed to the driven shaft and
a loose pulley which is mounted with a brass bush and is free to rotate on the driven shaft or the
machine shaft. The main driving pulley is slightly larger in width and is securely keyed to the
driving shaft. The belt will always be on the driving pulley and either on the fast pulley or loose
pulley depending upon the requirement. When the belt is on the fast pulley power is transmitted
to the machine shaft and when the machine shaft is to be brought to rest belt is shifted from fast
pulley to loose pulley.

shaft.
Fast and Loose Pulley

5
Length of Belt
Length of Open Belt
L = length of the belt = π (r1+r2) + (r1-r2)2 / X + 2X
where,
r1 = Radius of the larger pulley P
r2 = Radius of the smaller pulley Q and
X = Distance between the centers of the pulleys.

Angle of lap = θ = π – 2φ
where

Open Belt Drive

Length of Crossed Belt
L = length of the belt = π (r1+r2) + (r1+r2)2 / X + 2X
Where,
r1 = Radius of the larger pulley P
r2 = Radius of the smaller pulley Q and
X = Distance between the centers of the pulleys.
Angle of lap = θ = π +2φ
Where

6
 Crossed Belt Drive

Ratio of Tensions in belt drive:

𝑻𝟏
Ratio of Tensions = = 𝒆𝝁𝜽
𝑻𝟐
where, T1 = Tight side tension
T2 = Slack side tension
µ = coefficient of friction
θ = angle of contact

7
Slip in a belt drive:
A belt drive transmits power as long as the frictional force required to create relative movement
between the belt and either the driving or driven pulley surface is greater than (T1 – T2). When
this condition exists the friction prevailing between the belt and the pulley surface will provide
the necessary grip to prevent the sliding of the belt over the pulley. When (T1 – T2) is greater
than the frictional grip between the belt and the pulley surface then the belt begins to slide over
the pulley surface causing relative motion between the pulley surface and the belt. This
phenomena is called slip in a belt drive. It tends to decrease the velocity ratio.

Velocity Ratio = N2 / N1 = d1 / d2 [100-S/100]

where, S = % Slip
Slip mainly occurs when the difference between tensions in the tight and the slack side is very
large or when the coefficient of friction between the belt and the pulley surface decreases owing
to stretching of the belt or when the smoothness of the pulley surface is more or due to a layer of
air trapped between the pulley rim and the belt.
Creep in a belt drive:
In a belt drive the belt is alternatively subjected to higher and lower tensions. The portion of the
belt between the driving and driven pulley has lower tension and the portion of the belt between
the driven and driving pulley has higher tension. Thus the belt undergoes alternate stretching and
contraction. While passing from slack side to tight side the belt extends and while passing from
tight side to slack side the belt contracts. Due to this alternate stretching and contraction over a
period of time the length of the belt increases leading to relative
motion between the belt and the pulley surface. This relative motion is called creep which results
in loss of power and decreases the velocity ratio.

Initial Tension in Belt:

It is the uniform tension that exists initially when the drive
is not in motion. It is given by making the free length of the belt slightly shorter than what is
required as per geometrical calculations. It is designated as To.
Initial Tension in Belt = To = (T1+T2) / 2

8
Power transmitted by a belt drive: The power transmitted by a belt drive is given by the
relation
P = (T1 - T2) v / 60000 kW,
Where
T1 & T2 are tight and slack side tensions in newtons and
v is the linear velocity of the belt drive = π d1 N1 = π d2 N2
where d1 & d2 are the diameters of driving and driven pulleys in metres.
and N1 and N2 are the speed of driving and driven pulleys in RPM.

Chain Drives:
Chain drives are positive drives having no slip and velocity ratio remaining
constant. Chain drives are suitable for small centre distances and can be used generally up to
3metre but in special cases even up to 8 meters. The velocity ratio can be as high as 8:1.
Chain drives are employed in bicycles, motor cycles, rolling mills, agricultural
machineries, machine tools, conveyors etc.
A chain drive consists of a chain and two sprockets. The sprockets are teethed wheels over
which an endless chain fitted.

Roller Chain

Driven Sprocket
Driving Sprocket
Roller Chain

Advantages
• Positive non-slip drives
• Efficiency is high
• Employed for small as well as large centre distances up to 8m.
• Permit high velocity ratio up to 8:1

9
 • Transmit more power than belt drives
• They produce less load on shafts compared to belt drives
• Maintenance is low
Disadvantages
• Driving and driven shafts should be in perfect alignment.
• Requires good lubrication
• High initial cost

Rope Drives
Used when centre distances are greater than 10m and power to be transmitted is more than
200 HP. Used in lifts, hoists etc. Ropes can be made from nylon or metal wires.

Gear Drives:
Gear drives find a very prominent place in mechanical power transmission. Gear drives
are preferred when considerable power needs to be transmitted over a short distance positively
and with a constant velocity ratio.
Types Gears:
There are different types of gears to suit various applications. They differ in the shape of
the gear wheel like cylindrical or conical, the orientation of their axes and the angle
at which the teeth mesh. Gear drives transmit power between the shafts when their axes are:
i) Parallel ii) Intersecting iii) Neither parallel nor intersecting.
The different types of gears used are:
1. Spur Gears - For Parallel Axes shafts.
2. Helical Gears - For both Parallel and Non-parallel and Non-intersecting Axes shafts.
3. Bevel Gears - For Intersecting Axes shafts.
4. Worm Gears - For Non-Parallel and Non-co-planar Axes shafts.
5. Rack and Pinion - For converting rotary motion into linear motion.

10
 Different types of Gears
1. 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 axes, the gears are called spur gears. The contact between the
mating gears will be along a line, hence spur gears can transmit higher power. Because of the
instantaneous line contact when the teeth mesh, noise will be very high. They are widely used in
machine tools, automobile gear boxes and in all general cases of power transmission where gear
drives are preferred.

Spur Gears

11
2. 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. The teeth are cut at an angle to the axis of the gear. Helical gears are used
for transmitting power between two parallel shafts and also between non parallel, non-
intersecting shafts. The contact between the mating gears will be along a curvilinear path. Helical
gears are preferred to spur gears when 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. Generally they are used in automobile power transmission.

Helical Gears

3. Bevel gears:
When the axes of the two shafts are inclined to one another, and intersect when produced
bevel gears are used. The angle of intersection can be right angle, acute or obtuse. 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. Teeth of the bevel gears are cut on the conical surfaces
and the width of the teeth is less at the front end as compared to the rear end. When two bevel
gears have their axes at right angles and are of equal sizes, they are called miter gears. They are
used in automobile power transmission, machine tools and industrial machinery.

12
 Bevel Gears

4. Worm Gear:
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 of a worm (essentially a screw) which
may have one or more number of helical threads cut on it 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 high as 300:1 is required. They are generally employed in machine tools like
lathe, milling, drilling machines etc. to get large speed reduction.

Worm and Worm Wheel

13
5. 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, planing machines, and in automobile steering
systems.

Rack and Pinion

Advantages and Disadvantages of Gear Drives:

Advantages:
1. They are positive non-slip drives.
2. Most convenient for very small centre distances.
3. By using different types of gears, it will be possible to transmit the power when the axes
of the shafts are not only parallel, but even when nonparallel, intersecting, non-
intersecting and co- planar or non-coplanar.
4. The velocity ratio will remain constant throughout.
5. They can be employed conveniently for low, medium and high power transmission.
6. They have very high transmission efficiency.
7. Gears can be cast in a wide range of both metallic and non-metallic materials.
8. If required gears may be cast integral with the shafts.
9. Gears are employed for wide range of applications like in watches, precision measuring
instruments, machine tools, gear boxes fitted in automobiles, aero engines, etc.

14
Disadvantages:
1. They are not suitable for shafts of very large centre distances.
2. They always require some kind of lubrication.
3. At very high speeds noise and vibrations will be more.
4. They are not economical because of the increased cost of production of precision gears.
5. Use of large number of gear wheels in gear trains increases the self-weight of the
machine.

Nomenclature:
Circular Pitch (Pc) : It is the distance measured along the circumference of the pitch circle of
a gear from a point of one tooth to the corresponding point on the adjacent tooth. It is the width
of a tooth and a space, measured on the pitch circle

D
Pc
T
Where D is the pitch circle diameter and T is the number of teeth.
Diametrical pitch (Pd): It is defined as the number of teeth per unit length of pitch circle
diameter.

T
Pd 
D
Where, Pd = Diametrical pitch, T = number of teeth &D = pitch diameter

Module (m): It is the ratio of the pitch circle diameter to the number of teeth. Module is the
inverse of diametrical pitch

m = D/T
m= 1/Pd

15
Velocity Ratio of Gear drive:
The velocity ratio of a gear drive is defined as the ratio of the speed of the driven gear to
the speed of the driving gear.
𝑵𝟐 𝒅𝟏 𝑻𝟏
Velocity Ratio of a gear drive = =
𝑵𝟏 𝒅𝟐 𝑻𝟐
where,
N1 & N2 are the RPM’s of driver and driven gears respectively.
d1 & d2 = Pitch circle diameter of the driver and driven gears respectively.
T1 & T2 = no. of teeth on the driver and driven gears respectively
Gear Train:
A gear train is an arrangement of number of successively meshing gear wheels through
which the power can be transmitted between the driving and driven shafts. The gear wheels used
in gear train may be spur, bevel or helical etc.
The widely used gear trains are:
1. Simple gear train.
2. Compound gear train.

1. Simple gear train:

In a simple gear train a
series of gear wheels arc mounted
on different shafts between the
driving and driven shafts each shaft
carrying only one gear. In the
figure, A is the driving gear. B and
C are intermediate gears and D is
the driven gear. Intermediate gears
in a simple gear train do not
influence the velocity ratio but only
the direction of rotation of the
Simple Gear Train
driven gear.

16
 𝑵𝑫 𝑻𝑨
Velocity Ratio = =
𝑵𝑨 𝑻𝑫
Where, N & T = speed (in rpm) and no. of teeth on respective gears.
2. Compound gear train:
A compound gear train is one in which except the driving and driven shaft each shaft
carries two gears. Figure below represents a compound gear train in which gears Band C
constitute compound gears. It is used when a large velocity ratio is required and there is as
restriction on centre distance between driver and driven shafts.

Compound Gear Train

𝑵𝑫 𝑻𝑨 𝑻𝑪
Velocity Ratio = = .
𝑵𝑨 𝑻𝑩 𝑻𝑫
where, N & T = speed (in rpm) and no. of teeth on respective gears.

SIMPLE GEAR TRAIN COMPOUND GEAR TRAIN

Each shaft carries only one gear wheel. Except the first and last shaft each shaft
carries two gear wheels.
Velocity ratio is lower Velocity ratio is higher
Velocity ratio is independent of intermediate Velocity ratio is depends on intermediate
gears gears
Intermediate gears influence only the Intermediate gears influence not only the

17
direction of rotation of the last gear. direction of rotation of the last gear but also
the velocity ratio.
Occupies more space Occupies less space.
Gears used should be of the same type Different types of gears can be used but
meshing gears should be of the same type.
Gears used should be of the same module Gears having different module can be used
but meshing gears should be of the same
module.

18