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FRICTION (applications of friction)
Compiled by: RAMAKANT RANA
Q. 1:
What is belt? How many types of belt are used for power transmission?
Solution:
The power or rotary motion from one shaft to another at a considerable distance is usually
transmitted by means of flat belts, V
contain some friction.
Types of Belts: Important types of belts are:
Flat Belt: The flat belt is mostly used in the factories and workshops.
of power is to be transmitted, from one pulley to another,
10m apart.
V-Belt: The V-belt is mostly used where a great amount of power is to be transmitted, from one pulley to
another, when the two pulleys are very near to each other.
Circular Belt or Rope: The circular belt or rope is mostly used where a great amount of
one pulley to another, when the two pulleys are more than 5m apart.
Q. 2:
Explain how many types of belt drive used for power transmission? Also derive their
velocity ratio.
Solution:
There are three types of belt drive:
1) Open belt drive
2) Cross belt drive
3) Compound belt drive
FRICTION (applications of friction)
What is belt? How many types of belt are used for power transmission?
The power or rotary motion from one shaft to another at a considerable distance is usually
by means of flat belts, V-belts or ropes, running over the pulley. But the pulleys
The flat belt is mostly used in the factories and workshops. It is used where a moderate amount
transmitted, from one pulley to another, when the two pulleys are not more than
belt is mostly used where a great amount of power is to be transmitted, from one pulley to
when the two pulleys are very near to each other.
r rope is mostly used where a great amount of power is to be transmitted from
to another, when the two pulleys are more than 5m apart.
Explain how many types of belt drive used for power transmission? Also derive their
There are three types of belt drive:
MAIT
Page 1
The power or rotary motion from one shaft to another at a considerable distance is usually
But the pulleys
here a moderate amount
when the two pulleys are not more than
belt is mostly used where a great amount of power is to be transmitted, from one pulley to
power is to be transmitted from
Explain how many types of belt drive used for power transmission? Also derive their
FRICTION (applications of friction)
Compiled by: RAMAKANT RANA
(1) Open Belt Drive When the shafts are arranged in parallel and rotating in the same direction, open belt drive is
obtained. In the following diagram
with the rotating shaft.
Velocity Ratio (V.R.) for Open Belt Drive
Consider a simple belt drive (i.e., one driver and one follower) as shown in
Let
D1 = Diameter of the driver
N1 = Speed of the driver in R.P.M.
D2, N2 = Corresponding values for the follower
Length of the belt, that passes over the driver, in one minute =
Similarly,
Length of the belt, that passes over the follower, in one minute =
FRICTION (applications of friction)
When the shafts are arranged in parallel and rotating in the same direction, open belt drive is
m, pulley 'A' is called as driver pulley because it is attached
Velocity Ratio (V.R.) for Open Belt Drive:
Consider a simple belt drive (i.e., one driver and one follower) as shown in above
= Speed of the driver in R.P.M.
= Corresponding values for the follower
that passes over the driver, in one minute = Π.D1.N1
hat passes over the follower, in one minute = Π.D2.N2
MAIT
Page 2
When the shafts are arranged in parallel and rotating in the same direction, open belt drive is
pulley 'A' is called as driver pulley because it is attached
above fig:
FRICTION (applications of friction)
Compiled by: RAMAKANT RANA
Since the length of belt, that passes over the driver in one minute is equal to the length of belt that
follower in one minute, therefore:
Π.D1.N1 = Π.D2.N2
Or, velocity ratio = N2/N
If thickness of belt 't' is given then
V.R = N2/N1 = (D1 + t)
(2) Cross Belt Drive: When the shafts are rotating in
opposite direction, cross belt drive is
obtained.
In the diagram, pulley 'A' is called as
driver pulley because it is attached
with the rotating shaft.
Velocity ratio is same as for open belt
V.R. = N2/N1 = D1/D2
If thickness of belt 't' is given then
V.R = N2/N1 = (D1 + t)/(D2 + t)
(3) Compound Belt Drive: When a number of pulleys are used to transmit power from one shaft to another then a compound belt drive is
obtained.
Velocity Ratio for Compound Belt Drive
N4/N1 = (D1.D3)/(D2.D4)
Q. 3:
What is slip of the belt? How slip of belt affect the velocity ratio?
Solution:
FRICTION (applications of friction)
h of belt, that passes over the driver in one minute is equal to the length of belt that
/N1 = D1/D2
+ t)/(D2 + t)
When a number of pulleys are used to transmit power from one shaft to another then a compound belt drive is
Ratio for Compound Belt Drive
What is slip of the belt? How slip of belt affect the velocity ratio?
MAIT
Page 3
h of belt, that passes over the driver in one minute is equal to the length of belt that passes over the
When a number of pulleys are used to transmit power from one shaft to another then a compound belt drive is
FRICTION (applications of friction) MAIT
Compiled by: RAMAKANT RANA “[email protected]” Page 4
When the driver pulley rotates, it carries the belt, due to a firm grip between its surface and the
belt. The firm between the pulley and the belt is obtained by friction. This firm grip is known as
frictional grip. But sometimes the frictional grip is not sufficient. This may cause some forward
motion of the driver pulley without carrying the belt with it. This means that there is a relative
motion between the driver pulley and the belt. The difference between the linear speeds of the
pulley rim and the belt is a measure of slip. Generally, the slip is expressed as a percentage. In
some cases, the belt moves faster in the forward direction, without carrying the driver pulley
with it. Hence in case of driven pulley, the forward motion of the belt is more than that of driver
pulley.
Slip of belt is generally expressed in percentage (%).
Let v = Velocity of belt, passing over the driver pulley/min
N1 = Speed in R.P.M. of driver
N2 = Speed in R.P.M. of follower
S1 = Slip between driver and belt in percentage
S2 = Slip between follower and belt in percentage
The peripheral velocity of the driver pulley
Now due to Slip between the driver pulley and the belt, the velocity of belt passing over the
driver pulley will decrease
Velocity of belt
Now with this velocity the belt pass over the driven pulley,
Now
Velocity of Driven = Velocity of Belt - Velocity of belt X (S2 /100)
This formula is used when total slip in % is given in the problem
NOTE:
If Slip and thickness both are given then, Velocity ratio is,
FRICTION (applications of friction)
Compiled by: RAMAKANT RANA
Q. 4: Write down different relations used in belt drive.
Solution:
Let: D1 = Diameter of the driver
N1 = Speed of the driver in R.P.M.
D2 = Diameter of the driven or Follower
N2 = Speed of the driven or follower in R.P.M.
R1 = Radius of the driver
R2 = Radius of the driven or Follower
t = Belt thickness (if given)
X = Distance between the centers of two pu
α = Angle of lap (Generally less than 10º)
θ = Angle of contact (Generally greater than 150º) (always express in radian.)
µ = Coefficient of friction s = Total slip in percentage (%)
L = Total length of belt
FORMULA FOR
Velocity Relation:
Thickness is considered
Slip is considered
Slip and thickness both are
considered
Angle of contact
Angle of lap
Length of belt
Q. 5: Prove that the ratio of belt tension is given
Solution:
Let
T1 = Tension in the belt on the tight side
T2 = Tension in the belt on the slack side
θ = Angle of contact
µ = Co-efficient of friction between the belt and pulley.
α = Angle of Lap Consider a driven or follower pulley. Belt remains in contact with EBF.
Let T1 and T2 are the tensions in the tight side and slack side.
Angle EBF called as angle of contact =
Consider a driven or follower pulley.
Belt remains in contact with NPM. Let T
tight side and slack side.
FRICTION (applications of friction)
Q. 4: Write down different relations used in belt drive.
= Diameter of the driven or Follower
= Speed of the driven or follower in R.P.M.
X = Distance between the centers of two pulleys
= Angle of lap (Generally less than 10º)
= Angle of contact (Generally greater than 150º)
FORMULA FOR OPEN BELT DRIVES
V.R = N2/N1
Thickness is considered
Slip is considered
Slip and thickness both are
considered
θ = Π – 2α
Sinα = (r1–r2)/X
Prove that the ratio of belt tension is given by the T1/T2 = eµq
= Tension in the belt on the tight side
= Tension in the belt on the slack side
efficient of friction between the belt and pulley.
Belt remains in contact with EBF.
in the tight side and slack side.
Angle EBF called as angle of contact = Π.–2α Consider a driven or follower pulley.
Belt remains in contact with NPM. Let T1 and T2 are the tensions in the
MAIT
Page 5
BELT DRIVES
FRICTION (applications of friction) MAIT
Compiled by: RAMAKANT RANA “[email protected]” Page 6
Let T be the tension at point M & (T + δT) be the tension at point N. Let d? be the angle of contact of the element
MN. Consider equilibrium in horizontal Reaction be 'R' and vertical reaction be µR.
Since the whole system is in equilibrium, i.e.,
∑V = 0;
Tsin (90 – δθ/2) + µR - (T + δT)sin(90 – δθ/2) = 0
Tcos (δθ/2) + µR = (T + δT) cos (δθ/2)
Tcos (δθ/2) + µR = Tcos(δθ/2) + δTcos(δθ/2)
µR = δTcos(δθ/2)
Since δθ/2 is very small & cos0° = 1, So cos(δθ/2) = 1
µR = δT ...(i)
∑H = 0;
R–Tcos(90 – δθ/2)–(T + δT)cos(90 – δθ/2) = 0
R = Tsin(δθ/2) + (T + δT)sin(δθ/2)
Since δθ/2 is very small So sin(δθ/2) = δθ/2
R = T(δθ/2) + T(δθ/2) + δT(δθ/2)
R = T.δθ + δT(δθ/2)
Since δT(δθ/2) is very small So δT(δθ/2) = 0
R = T.δθ ...(ii)
Putting the value of (ii) in equation (i)
µ.T.δθ = δT
or, δT/T = µ.δθ
Integrating both side: Where θ = Total angle of contact
ln(T1/T2) = µ.θ
or, T1/T2 = eµ.θ
Ratio of belt tension = T1/T2 = eµθ
Belt ratio is also represent as 2.3log(T1/T2) = µ.θ
Note that θ is in radian
In this formula the main important thing is Angle of contact(θ)
For Open belt drive:
Angle of contact (θ) for larger pulley = Π + 2α
Angle of contact (θ) for smaller pulley = Π – 2α
For cross belt drive:
Angle of contact (θ) for larger pulley = Π + 2α
Angle of contact (θ) for smaller pulley = Π + 2α (i.e. for both the pulley, it is same)
But for solving the problems, We always take the Angle of contact (θ) for smaller pulley
Hence,
Angle of contact (θ) = Π – 2α – for open belt
Angle of contact (θ) = Π + 2α – for cross belt