Short Notes: Brakes and Clutches | Design of Machine Elements - Mechanical Engineering PDF Download

 Page 1


Brakes and Clutches 
Brake: A brake is a device by means of which artificial frictional resistance is 
applied to a moving machine member, in order to retard or shop the motion of a 
machine. The most commonly brakes use friction to convert kinetic energy into 
beat, though other methods of energy conversion may be employed.
Single Block or Shoe Brake
It consists of a block or shoe which is passed against the rim of revolving brake 
wheel drum. The block is made of a softer material than the rim of the wheel.
Let, P = Force applied at the end of the lever 
r = Radius of the wheel
RN = Normal force pressing the block on the wheel
Ft = Tangential braking or frictional force acting at the contact surface of the block 
and wheel
20 = Angle of contact surface of the block 
p = Coefficient of friction
If the angle of contact is less than 60° then, it may be assumed that normal 
pressure or force between the block and the wheel is uniform.
The following are cases to describe the location of line of action of tangential 
braking force with respect to fulcrum point 0.
Page 2


Brakes and Clutches 
Brake: A brake is a device by means of which artificial frictional resistance is 
applied to a moving machine member, in order to retard or shop the motion of a 
machine. The most commonly brakes use friction to convert kinetic energy into 
beat, though other methods of energy conversion may be employed.
Single Block or Shoe Brake
It consists of a block or shoe which is passed against the rim of revolving brake 
wheel drum. The block is made of a softer material than the rim of the wheel.
Let, P = Force applied at the end of the lever 
r = Radius of the wheel
RN = Normal force pressing the block on the wheel
Ft = Tangential braking or frictional force acting at the contact surface of the block 
and wheel
20 = Angle of contact surface of the block 
p = Coefficient of friction
If the angle of contact is less than 60° then, it may be assumed that normal 
pressure or force between the block and the wheel is uniform.
The following are cases to describe the location of line of action of tangential 
braking force with respect to fulcrum point 0.
A schematic diagram of shoe brake
Case I: When the line of action of tangential braking force passes through the 
fulcrum 0 of the lever.
Then, there are two cases
• If wheel is rotating in clockwise direction then, Free Body Diagram (FBD) of 
wheel and block is
Rn
• If wheel is rotating in anticlockwise direction then, FBD of wheel and block is
Wheel is rotating anti clockwise
Now, taking moment about fulcrum 0 
clockwise direction.
Rx x x = P x l
Braking force
M y = '
uPl
Braking torque
<r,)= r x 
Braking force
direction
of the lever when wheel is rotating in
uPlr
X
Page 3


Brakes and Clutches 
Brake: A brake is a device by means of which artificial frictional resistance is 
applied to a moving machine member, in order to retard or shop the motion of a 
machine. The most commonly brakes use friction to convert kinetic energy into 
beat, though other methods of energy conversion may be employed.
Single Block or Shoe Brake
It consists of a block or shoe which is passed against the rim of revolving brake 
wheel drum. The block is made of a softer material than the rim of the wheel.
Let, P = Force applied at the end of the lever 
r = Radius of the wheel
RN = Normal force pressing the block on the wheel
Ft = Tangential braking or frictional force acting at the contact surface of the block 
and wheel
20 = Angle of contact surface of the block 
p = Coefficient of friction
If the angle of contact is less than 60° then, it may be assumed that normal 
pressure or force between the block and the wheel is uniform.
The following are cases to describe the location of line of action of tangential 
braking force with respect to fulcrum point 0.
A schematic diagram of shoe brake
Case I: When the line of action of tangential braking force passes through the 
fulcrum 0 of the lever.
Then, there are two cases
• If wheel is rotating in clockwise direction then, Free Body Diagram (FBD) of 
wheel and block is
Rn
• If wheel is rotating in anticlockwise direction then, FBD of wheel and block is
Wheel is rotating anti clockwise
Now, taking moment about fulcrum 0 
clockwise direction.
Rx x x = P x l
Braking force
M y = '
uPl
Braking torque
<r,)= r x 
Braking force
direction
of the lever when wheel is rotating in
uPlr
X
T
13 ~
X
Case II: When the line of acting of the tangential braking force (Ft) passes through 
a distance a below the fulcrum 0. Then, there are two cases:
When wheel is rotating in anticlockwise direction then, the braking torque is same
as above
*v =
If wheel rotates in clockwise direction then, the FBD of block is
PI
x + /ja
Braking force
uPl
F, = uRx = —
x + fia
Braking torque
fjPlr
T b =
x + fiia
r«----------------
- * 1
__________ i
n r z z
0 at
> r n
--------fe- C.
k -------^
Ry =
FBD of block
If wheel rotates in anticlockwise direction then, FBD of block is given as
PI
x - fia 
Braking force
F ,= — —
x — ua
Braking torque
uPlr
T s =
x - ua
(as Tb = Ft x r)
FBD of block
Case III: When the line of action of tangential braking force (Ft) passes through a 
distance 'a' above the fulcrum 0.
Then, there are two cases:
Page 4


Brakes and Clutches 
Brake: A brake is a device by means of which artificial frictional resistance is 
applied to a moving machine member, in order to retard or shop the motion of a 
machine. The most commonly brakes use friction to convert kinetic energy into 
beat, though other methods of energy conversion may be employed.
Single Block or Shoe Brake
It consists of a block or shoe which is passed against the rim of revolving brake 
wheel drum. The block is made of a softer material than the rim of the wheel.
Let, P = Force applied at the end of the lever 
r = Radius of the wheel
RN = Normal force pressing the block on the wheel
Ft = Tangential braking or frictional force acting at the contact surface of the block 
and wheel
20 = Angle of contact surface of the block 
p = Coefficient of friction
If the angle of contact is less than 60° then, it may be assumed that normal 
pressure or force between the block and the wheel is uniform.
The following are cases to describe the location of line of action of tangential 
braking force with respect to fulcrum point 0.
A schematic diagram of shoe brake
Case I: When the line of action of tangential braking force passes through the 
fulcrum 0 of the lever.
Then, there are two cases
• If wheel is rotating in clockwise direction then, Free Body Diagram (FBD) of 
wheel and block is
Rn
• If wheel is rotating in anticlockwise direction then, FBD of wheel and block is
Wheel is rotating anti clockwise
Now, taking moment about fulcrum 0 
clockwise direction.
Rx x x = P x l
Braking force
M y = '
uPl
Braking torque
<r,)= r x 
Braking force
direction
of the lever when wheel is rotating in
uPlr
X
T
13 ~
X
Case II: When the line of acting of the tangential braking force (Ft) passes through 
a distance a below the fulcrum 0. Then, there are two cases:
When wheel is rotating in anticlockwise direction then, the braking torque is same
as above
*v =
If wheel rotates in clockwise direction then, the FBD of block is
PI
x + /ja
Braking force
uPl
F, = uRx = —
x + fia
Braking torque
fjPlr
T b =
x + fiia
r«----------------
- * 1
__________ i
n r z z
0 at
> r n
--------fe- C.
k -------^
Ry =
FBD of block
If wheel rotates in anticlockwise direction then, FBD of block is given as
PI
x - fia 
Braking force
F ,= — —
x — ua
Braking torque
uPlr
T s =
x - ua
(as Tb = Ft x r)
FBD of block
Case III: When the line of action of tangential braking force (Ft) passes through a 
distance 'a' above the fulcrum 0.
Then, there are two cases:
When wheel rotates in clockwise direction then, FBD of block is Taking
moment about point 0,
we get
Rx =
Pi
x - ua
Braking force
F =
uPl 
x - t Lia
Braking torque
_ fiP lr 
3 x - (ia
(Tb = Ft x r)
FBD of 
block 
P
ft
rn
? Fi
4
r
M ---------------
I — —
FBD of block
• When wheel rotates in anticlockwise direction then, FBD of block is:
Pi
x - fua
Braking force
F = - ^ ~ 
x + p a
Braking torque
fiPir
T* =
x - /ua
P
FBD of block
When the frictional force helps to apply the brakes then, such type of brakes are 
said to self-energizing brakes.
When P is negative or equal to zero then, these are known as self-locking brakes.
Bearing pressure on shoe
where, w = Width of shoe
2r sin0 = Projected length of shoe
Pivoted Block or Shoe Brake
When the angle of contact is greater than 60° then, the unit pressure normal to the 
surface of contact is less at ends than at the centre. In this case, the block or shoe
Page 5


Brakes and Clutches 
Brake: A brake is a device by means of which artificial frictional resistance is 
applied to a moving machine member, in order to retard or shop the motion of a 
machine. The most commonly brakes use friction to convert kinetic energy into 
beat, though other methods of energy conversion may be employed.
Single Block or Shoe Brake
It consists of a block or shoe which is passed against the rim of revolving brake 
wheel drum. The block is made of a softer material than the rim of the wheel.
Let, P = Force applied at the end of the lever 
r = Radius of the wheel
RN = Normal force pressing the block on the wheel
Ft = Tangential braking or frictional force acting at the contact surface of the block 
and wheel
20 = Angle of contact surface of the block 
p = Coefficient of friction
If the angle of contact is less than 60° then, it may be assumed that normal 
pressure or force between the block and the wheel is uniform.
The following are cases to describe the location of line of action of tangential 
braking force with respect to fulcrum point 0.
A schematic diagram of shoe brake
Case I: When the line of action of tangential braking force passes through the 
fulcrum 0 of the lever.
Then, there are two cases
• If wheel is rotating in clockwise direction then, Free Body Diagram (FBD) of 
wheel and block is
Rn
• If wheel is rotating in anticlockwise direction then, FBD of wheel and block is
Wheel is rotating anti clockwise
Now, taking moment about fulcrum 0 
clockwise direction.
Rx x x = P x l
Braking force
M y = '
uPl
Braking torque
<r,)= r x 
Braking force
direction
of the lever when wheel is rotating in
uPlr
X
T
13 ~
X
Case II: When the line of acting of the tangential braking force (Ft) passes through 
a distance a below the fulcrum 0. Then, there are two cases:
When wheel is rotating in anticlockwise direction then, the braking torque is same
as above
*v =
If wheel rotates in clockwise direction then, the FBD of block is
PI
x + /ja
Braking force
uPl
F, = uRx = —
x + fia
Braking torque
fjPlr
T b =
x + fiia
r«----------------
- * 1
__________ i
n r z z
0 at
> r n
--------fe- C.
k -------^
Ry =
FBD of block
If wheel rotates in anticlockwise direction then, FBD of block is given as
PI
x - fia 
Braking force
F ,= — —
x — ua
Braking torque
uPlr
T s =
x - ua
(as Tb = Ft x r)
FBD of block
Case III: When the line of action of tangential braking force (Ft) passes through a 
distance 'a' above the fulcrum 0.
Then, there are two cases:
When wheel rotates in clockwise direction then, FBD of block is Taking
moment about point 0,
we get
Rx =
Pi
x - ua
Braking force
F =
uPl 
x - t Lia
Braking torque
_ fiP lr 
3 x - (ia
(Tb = Ft x r)
FBD of 
block 
P
ft
rn
? Fi
4
r
M ---------------
I — —
FBD of block
• When wheel rotates in anticlockwise direction then, FBD of block is:
Pi
x - fua
Braking force
F = - ^ ~ 
x + p a
Braking torque
fiPir
T* =
x - /ua
P
FBD of block
When the frictional force helps to apply the brakes then, such type of brakes are 
said to self-energizing brakes.
When P is negative or equal to zero then, these are known as self-locking brakes.
Bearing pressure on shoe
where, w = Width of shoe
2r sin0 = Projected length of shoe
Pivoted Block or Shoe Brake
When the angle of contact is greater than 60° then, the unit pressure normal to the 
surface of contact is less at ends than at the centre. In this case, the block or shoe
pivoted to the lever gives the uniform wear of the brake lining in the direction of thfj 
applied force.
In this case, 
Braking torque
T,~M 'R x r
A p L sin 6 * •
26 - s in 20
(where. 26 > 60°)
where, p’ = Equivalent coefficient of friction 
p = Actual coefficient of friction
These brakes having more lie and provide a higher braking torque.
Simple Band Brake
A band brake consists of a flexible band of leather, one or more ropes, or steel lined 
with friction material, which embraces a part of the circumference of the drum is 
called simple band brake.
• When wheel rotates in the clockwise direction then, the end of the band 
attached to B is in tight side and end of the band attached to fulcrum 0 is in 
slack side.
• When wheel rotates in the anticlockwise direction then, the end of the band 
attached to B is in slack side and end of the band attached to the fulcrum 0 is 
in tight side.
Let, T -i = Tension in the tight side of the band 
72 = Tension in the slack side of the band. 
t = Thickness of the band 
0 = Angle of lap
p = Coefficient of friction between band and the drum 
r = Radius of the drum 
rc = r + t/2 = Effective radius of the drum 
We know,