5 FRICTION APPLICATIONS

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


“[email protected]”

What is belt? How many types of belt are used for power transmission?


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.


There are three types of belt drive:

MAIT


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




(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 =



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

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:



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:



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

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]”

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,



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.



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

BELT DRIVES

FRICTION (applications of friction) MAIT

Compiled by: RAMAKANT RANA “[email protected]”

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

5 FRICTION APPLICATIONS

Documents

Transcript of 5 FRICTION APPLICATIONS