Kinematics and Theory of Machines

203109207
Dr. Bhakti Patel, Assistant Professor
Mr. Manoj Nehe, Assistant Professor
Mechanical Engineering Department, PIET
 CHAPTER-6
Friction Devices
I. Clutches

 The clutch is a mechanical device used to connect or disconnect driven shaft

from the driving shaft as per the will of operator.

 In automobiles, where vehicle can be stopped for a while or to change the gear,
requirement is that the driven shaft should stop but the engine should run
naturally under the no load condition. This is achieved by using clutch mounted
between engine shaft and gearbox shaft and which is operated by a lever.
A. Classification of Clutches

Clutches

Positive Clutches Friction Clutches

Jaw Clutch Plate clutch Cone clutch Centrifugal clutch

Single plate clutch Multi plate Clutch

1. Positive Clutch
 Jaw clutch consist of two segments as shown in Figure One segment is
permanently fastened to the driving shaft and the other segment is free to slide
axially on the splined driven shaft, thus permitting it to be engaged or disengaged
by sliding.
 The shapes of the jaws may be square, gear toothed or spiral.
1. Positive Clutch
 Advantages
1) Positive clutches do not slip.
2) No heat is generated at clutch surface during the engagement.

 Disadvantages
1) Shock and noise is there when engaged in motion.
2) They cannot be engaged at high speeds and sometimes cannot be engaged at
rest unless the jaws are aligned.

 Applications
 In agricultural equipment like tractor, thresher etc.
2 . Friction Clutches
 It consists of two plates. One of them is keyed to the driving shaft and other is
free to slide axially on the driven splined shaft. Friction lining is provided on the
driven shaft. Axial force applied by the compression spring will held the two
plates together.
 The torque or power is transmitted between driving and driven shaft because of
frictional force in between surfaces in contact.
 It can be engaged while the driving
member is rotating and the member
is stationary.

https://isccompanies.com/parts-distribution/clutches-brakes/friction-brakes-clutches/
2. Friction Clutches
 Advantages
1) Frequent engagement and disengagement is possible.
2) It can transmit partial or full power.
3) It can be engaged when driving shaft is rotating and driven shaft is stationary.
4) It is very easy to operate.

 Disadvantages
1) It will not give positive engagement.
2) Due to slip between contacting surfaces, heat is generated during engagement
i. Single Plate Clutch
 A single disc or plate clutch as
shown in figure, consist of a
clutch plate whose both sides are
faced with the friction material
(usually ferrodo).

 It is mounted on the hub which is

free to move axially along the
splines of the driven shaft. The
pressure plate is mounted inside
the clutch body which is bolted
to the flywheel.

Theory of Machines – R.S. Khurmi, S. Chand

i. Single Plate Clutch
 Disengaging the clutch: When the clutch pedal is pressed down, its linkage
forces the thrust bearing to move towards the flywheels and pressing the
pressure plate away from the flywheel thereby the compression springs are
compressed. This action removes the pressure from the clutch plate and the
driving shaft comes to a stationary position.

 Engaging the clutch: On the other hand, when the foot is taken off from the
clutch pedal, the thrust bearing moves back by levers this action allows the
springs to extend, and thus the pressure plate pushes the clutch plate back
towards the flywheel. The clutch is engaged and power is transmitted from
Torque transmitting Capacity of Single plate clutch
Let T = Torque transmitted by the clutch,   Coefficien t of friction
p = Intensity of axial pressure with which the contact surfaces are held together,
r 1 and r2 = External and internal radii of friction faces, and
Consider an elementary ring of radius r and thickness ‘dr’ as shown in Figure
We know that ,
 Area of contact surface ‘ dA’ or friction surface
dA  2 r dr
 Normal or axial force on the ring
W  p  2 r dr
 and the frictional force on the ring acting
tangentially at radius ‘r’

F r    W   p  2 r dr
Torque transmitting Capacity of Single plate clutch
Therefore, Frictional torque acting on the ring , (Tr)
T r  F r r   p  2 r dr  r  2pr 2 dr

To find out total we shall now consider the following two cases :
1. When there is a uniform pressure (Uniform Pressure theory ), and
2. When there is a uniform wear. (uniform wear Theory)
1. Uniform Pressure theory
When the pressure is uniformly distributed over the entire area of the friction face,
then the intensity of pressure
W
p

 r1 2  r2 2 
Where W= Axial thrust with which the contact surfaces are held together
Torque transmitting Capacity of Single plate clutch
As we have the frictional torque on the elementary ring of radius r and thickness dr
is
T r 2pr dr2

Integrating above equation within the limits from r2 to r1 for the total frictional
torque.
Total frictional torque acting on the friction surface or on the clutch
2 r1
r 
r2

T   2pr 2 dr  2p  
r1  3 r 2

2  r1 3  r2 3 
After substituting the value of P, T   W  2 2
3 
 1r   r2  
2  r1 3  r2 3  Where R= Mean radius of Friction surface
T   W  2 2 
 W R
3  r1   r2  
2  r 3
 r 3

R   2 1 2

3  r1   r2 2 
Torque transmitting Capacity of Single plate clutch
2. Uniform wear Theory
let p be the normal intensity of pressure at a distance r from the axis of the clutch.
Since the intensity of pressure varies inversely with the distance, therefore
p.r = C (C = Constant)
and the normal force on the ring,
C
W  p 2  r. dr   2 C. dr  2C.dr
r
Therefore Total force acting on the friction surface,
r2

W   2C dr  2C (r1  r2 )

r1

Now, W
C
2 (r1  r2 )
Torque transmitting Capacity of Single plate clutch
We know the friction torque acting on the ring
T r 2pr 2 dr
C
 2   r 2 dr  2 C r dr
r
 Total frictional torque acting on the friction surface or on the clutch
r1
 r2 
r2

T   2 C r dr  2 C  
r1  2  r2
 After substituting the value of C ( As per the UWT)

T     W r1  r2 
1
or T  .W .R
2
R
r1  r2 
where R= Mean radius of contacting surfaces
2
Torque transmitting Capacity of Single plate clutch
 Note
In general, total frictional torque acting on the friction surface (or on the clutch) is given by
T  n..W .R
n = Number of pairs of friction or contact surfaces, and
2  r1   r2  
3 3
R = Mean radius of friction surface (According to UPT)
R   2 
3  r1   r2 2 

R
r1  r2  (According to UWT)
2
 For a single disc or plate clutch, normally both sides of the disc are effective.
Therefore, a single disc clutch has two pairs of surfaces in contact, i.e. n = 2.
 For new clutch use Uniform Pressure Theory (UPT)
 For old clutch use Uniform Wear Theory (UWT)
ii. Multi Plate Clutch
 A multi-plate clutch is a type of clutch
in which the multiple clutch plates
are used to make frictional contact
with the flywheel of the engine in
order to transmit power between the
engine shaft and the transmission
shaft of an automobile vehicle.
 In bikes and scooter multi-plate
clutch is used due to the limitation of
compact gearbox used in bikes and
scooter.

Theory of Machines – R.S. Khurmi, S. Chand

Torque transmitting Capacity of Multi plate clutch
 We can use the formulae of Torque transmitting capacity of single plate clutch to
find Torque transmitting capacity of multi plate clutch only we have find out the
multiply factor ‘n’ ( total number of contacting surfaces.)
Let n1 = Number of disc on the driving shaft, and
n2 = Number of disc on the driving shaft,
therefore , Number of pairs of contact surfaces,
n = n1+n2-1
 total frictional torque acting on the friction surfaces or on the clutch
T  n..W .R
n = Number of pairs of friction or contact surfaces,
2  r1   r2   (According to UPT)
3 3
R = Mean radius of friction surface
R   2 
3  r1   r2 2 

R
r1  r2 
(According to UWT)
2
iii. Cone clutch
 It consists of one pair of friction surface only.
 In a cone clutch, the driver is keyed to the driving shaft by a sunk key and has an
inside conical surface or face which exactly fits into the outside conical surface of
the driven. The driven member resting on the feather key in the driven shaft, may
be shifted along the shaft by a
forked lever provided at B, in
order to engage the clutch by
bringing the two conical surfaces
in contact.
 Torque transmitting capacity is
More than the plate clutch
 Cone clutches are used in
power boats

Theory of Machines – R.S. Khurmi, S. Chand

iv. Centrifugal clutch
 Centrifugal clutch consists of a number of shoes on the inside of a rim of the pulley
 The outer surface of the shoes are covered with a friction material.
 These shoes, which can move radially in guides, are held against the against the
boss (or spider) on the driving shaft by means of springs.
 The magnitude of this centrifugal force depends upon the speed at which the shoe
is revolving.
 Engagement and disengagement
depends on magnitude of
centrifugal force and
restoring spring force.
 Centrifugal clutch found
application in the chain saw,
lawn movers and moped

Theory of Machines – R.S. Khurmi, S. Chand

II. Brakes
 Brake is a device by means of which an artificial frictional resistance is applied to
a moving body in order to retard or stop the motion of a body.

 During braking process, the brake absorbs either kinetic energy or potential
energy or both by an object. In automobiles brake absorbs kinetic energy of
moving vehicles. In case of elevators and hoists brake absorb potential energy
released by the objects during braking period.

 The energy absorbed by the brake is converted in the form of heat which is
dissipated to the surrounding air or water which is circulated through the
passage in the brake drum.
A. The capacity of brake depends on
1) Unit pressure between braking surfaces,
2) Coefficient of friction
3) Peripheral velocity of brake drum
4) Projected area of friction surfaces
5) Heat dissipating capacity of the brake
B. Properties of brake lining materials
1) It should have high coefficient of friction. It should remain constant with
change in temperature.
2) Low wear rate.
3) High heat resistance.
4) High heat dissipation capacity.
5) Adequate mechanical strength.
C. Materials used for braking lining
1) Bronze on cast iron
2) Steel on cast iron
3) Wood on cast iron
4) Fibre on metal
5) Asbestos on metal
D. Classification of Brakes

Brakes

Internal
Band and
Shoe brakes Band brakes expanding
block brakes
shoe brake

differential
Single shoe double shoe pivoted shoe simple band
band
IIl. Belt and Rope drive
 The belts or ropes are used to transmit power from one shaft to another by
means of pulleys which rotate at the same speed or at different speeds
1) The amount of power transmitted depends upon the following factors :
2) The velocity of the belt.
3) The tension under which the belt is placed on the pulleys.
4) The arc of contact between the belt and the smaller pulley.
5) The conditions under which the belt is used.
A. Selection of belt drive
 Following are the various important factors upon which the selection of a belt
drive depends:
1) Speed reduction ratio,
2) Power to be transmitted,
3) Centre distance between the shafts,
4) Positive drive requirements,
5) Shafts layout,
6) Space available
B. Types of belt drive
1) Light drives : used to transmit small powers at belt speeds up to about 10 m/s,
as in agricultural machines and small machine tools.
2) Medium drives: used to transmit medium power at belt speeds over 10 m/s
but up to 22 m/s, as in machine tools.
3) Heavy drives: used to transmit large powers at belt speeds above 22 m/s, as in
compressors and generators.
C. Types of belt
 Round Belt: Round belts are generally made of rubber. This type of belt is
generally used for light loads, such as in a sewing machine or a vacuum cleaner
C. Types of belt
 V belts : are arguably the most widely used belts in industry. V belts have a V
shaped cross-section, which against the side of V pulley under tension.
 The V shaped cross-section prevents belt from slipping off.
C. Types of belt
 Flat belts: are designed for light-duty power transmission and high-
performance conveying. They are best-suited for applications with smaller
pulleys and large central distances.

 Flat belts can connect inside and outside pulleys and can come in both endless
and jointed construction. They have a high power transmission efficiency, are
cost effective, and are easy to use and install.
C. Types of belt
 Timing/ Toothed belt: It is a flexible belt with teeth moulded onto its inner
surface. It is designed to run over matching toothed pulleys or sprockets.
Toothed belts are used in a wide array of in mechanical devices, where high-
power transmission is desired
D. Belt Material
1) Leather: The leather is the most significant material for flat belts. Leather belts
are made from steer leather (cut from either side of the backbone of a steer)..
2) Cotton or fabric belts: The fabric belts are commonly used for temporary
application. Most fabric belts are made by the folding cotton duck to three or
more layers and stitching together..
3) Rubber belt: They are made by impregnating fabric or canvas with rubber and
have a thin layer of rubber on the surface of the belt. These types of the belt
are very flexible
4) Balata belts: They are similar to the rubber belt but stronger than rubber belt.
In this type, balata gum is used instead of rubber. Balata belt is waterproof and
has high resistance to acidic, alkaline materials, so they are used for food
packing conveyor.
E. Types of Flat belt drive
 Open belt drive: The open belt drive, as shown in Figure is used with shafts
arranged parallel and rotating in the same direction.

Theory of Machines – R.S. Khurmi, S. Chand

E. Types of Flat belt drive
 Crossed belt drive :The crossed or twist belt drive, as shown in Figure, is used
with shafts arranged parallel and rotating in the opposite directions.

Theory of Machines – R.S. Khurmi, S. Chand

E. Types of Flat belt drive
 Quarter turn belt drive: The quarter turn belt drive also known as right angle
belt drive, a shown in Figure, is used with shafts arranged at right angles and
rotating in one definite direction.

Theory of Machines – R.S. Khurmi, S. Chand

E. Types of Flat belt drive
 Compound belt drive: A compound belt drive, as shown in Figure, is used when
power is transmitted from one shaft to another through a number of pulleys.

Theory of Machines – R.S. Khurmi, S. Chand

E. Types of Flat belt drive
 Stepped or cone pulley drive: A stepped or cone pulley drive, as shown in
Figure issued for changing the speed of the driven shaft while the main or
driving shaft runs at constant speed. This is accomplished by shifting the belt
from one part of the steps to the other

Theory of Machines – R.S. Khurmi, S. Chand

F. Advantages of belt drive
1) Belt drives are simple and economical than ropes and chains.
2) They don’t need parallel shafts.
3) Belts drives are provided with overload and jam protection.
4) Noise and vibration are damped out. Machinery life is increased because load
fluctuations are shock-absorbed.
5) They are lubrication-free. They require less maintenance cost.
6) Belt drives are highly efficient in use (up to 98%, usually 95%).
7) They are very economical when the distance between shafts is very large
G. Disadvantages of belt drive
1) In Belt drives, angular velocity ratio is not necessarily constant or equal to the
pulley diameters, because of slipping and stretching.
2) Heat build up occurs. Speed is limited to usually 35 m/sec.
3) Power transmission is limited to 370 kilowatts.
4) Operating temperatures are usually restricted to –35 to 85°C.
5) Some adjustment of centre distance or use of an idler pulley is necessary for
wearing and stretching of belt drive compensation.
6) Belts can be noisy; also loose or worn belts can be a major cause of machinery
vibration.
7) Belts are easily damaged by oil, grease, abrasives, some chemicals, and heat
H. Rope drive
1) The rope drives are widely used where a large amount of power is to be
transmitted, from one pulley to another, over a considerable distance.
2) It may be noted that the use of flat belts is limited for the transmission of
moderate power from one pulley to another when the two pulleys are not
more than 8 metres apart.
3) If large amounts of power are to be transmitted, by the flat belt, then it would
result in excessive belt cross-section wear.
I. Type of Rope drive
1) Fibre Ropes:
 The ropes for transmitting power are usually made from fibrous materials such
as hemp, manila and cotton. Since the hemp and manila fibres are rough,
therefore the ropes made from these fibres are not very flexible and possesses
poor mechanical properties
 In order to minimize this defect, the rope fibres are lubricated with a tar, tallow
or graphite.
I. Type of Rope drive
2) Rope Ropes:
 Wire rope is several strands of metal wire twisted into a helix forming a
composite "rope", in a pattern known as "laid rope". Larger diameter wire rope
consists of multiple strands of such laid rope in a pattern known as "cable laid".
J. Advantages of Rope drive
1) Significant power transmission.
2) It can be used for long distance.
3) Ropes are strong and flexible.
4) Provides smooth and quiet operation.
J. Disadvantages of Rope drive
1) Internal failure of the rope has no sign on external, so it if often get unnoticed.
2) Corrosion of wire rope
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