BELT DRIVE CLASS NOTES

FOR MECHANICAL ENGINEERING

 Belts, chains and gears transmit power

from one shaft to the another shaft.

Use belts and ropes where distance

between the two shafts is large. The chains are

used for intermediate distances. The gears are

used for shorter distance between the shafts.

Gear drive is a positive drive because there is no slip.

Belts(or ropes) transmit power because of friction

between the belt (or rope) and the pulley. Due to slip

and creep in belts, this drive is not a positive drive.

Thus it finds limited applications.

BELT DRIVE

Belt drive consists of
(i) Driver and driven pulleys
(ii) Motor and machine shafts
(iii) Two keys
(iv) One belt
TYPES OF BELT DRIVE
Open Belt Drive
Cross Belt Drive
Compound Belt Drive (3 shafts and two belts, four shafts and three belts)
Quarter turn belt drive

Definition of a belt 

Belt is in the form of a loop. It connects mechanically two shafts for transmitting power smoothly. A belt drive consists of shafts, pulleys and a belt.

Material Of Belts

(I) Leather

(ii) Rubber

(iii) Fiber/cotton

(iv) Balata

Standard Thicknesses of belts

5, 6.5, 8, 10 and 12 mm are the standard thicknesses.

Standard widths of flat belts

25, 32, 40, 50, 63, 71, 80, 90, 100, 112,

125, 140, 160, 180, 200, 224, 250, 280,

315, 400, 450, 500, 560 and 600 mm

Types Of Flat Belts

1. Based on Orientation

   1. Horizontal

   2. Vertical

   3. Quarter –turn

   4. Right-angled

   5. Crossed

   6. Reversed drive

2. Based on power transmitted

Sr. No.	DUTY or LOAD	Power	Peripheral velocity
1.	Light load	7.5 kW	12 m/s
2.	Medium Load	7.5 to 15 kW	>12
3.	Heavy load	> 15 kW	>24 m/s

 Important terminology for belts

(i) Speed ratio

Neglecting the slip and thickness of the belt.

Speed ratio= diameter of bigger pulley/diameter of smaller pulley

Hence Speed ratio = N₁/N₂

Where N₁ is the motor or engine speed OR higher speed

N₂ is the machine speed or lower speed

(ii) Center distance

(iii) Peripheral velocity

 LAW OF BELTING

The center line of belt as it approaches the pulley must coincide with the central plane of that pulley. Otherwise belt will fly away from the pulley.

TYPES OF PULLEYS USED WITH BELTS

There are of two types.

(I) Flat pulleys——–Used with flat belts.

(ii) Grooved pulleys—–Used with V-belts. Grooved pulleys are sheaves.

Belt Drive and its Types

A belt drive consists of two shafts, two pulleys and a belt. On one shaft, mount the electric motor. On the other shaft, mount the machine. Belt drive transmits power from the motor to the machine shaft. It can be from the engine to the machine shaft. This can also be from turbine to generator.

Motor speed and Pulleys sizes

Normally speed of the motor is high because high speed motors are more efficient. Therefore,  motor shaft is the driving shaft and the machine shaft is the driven shaft. Thus, in most of the cases the machine has Lesser RPM than that of the motor. Hence, pulley on motor will be smaller pulley and the pulley on the machine shaft will be a larger pulley. Belts do not transmit with 100 % efficiency because of SLIP and stretching of the belt. There are two types of belt drive, namely flat belt drive and V-belt drive. The flat belt drive is of further two types, Open and cross belt drives.

 Open Belt Drive

 Both drive and driven shafts run in the same direction in case of an open belt drive. For smooth power transmission, belt on one side is more tight than the other side. In a horizontal drive, keep the tight side as the lower side.  The sag of the upper side slightly increases the angle of contact of the belt on the two pulleys. More angle of contact means more power transmission.

Cross Belt Drive

In case of cross belt drive, both drive and driven shafts run in the opposite directions. But the more angle of contact (angle of wrap) increases power transmission. Chances of slip of belt are not there.

Rope Belt Drive

In this, use a rope instead of a belt. But these not very common in industries.

 Advantages of a belt drive

1. Belt drive  is a simple drive.

2. It is cheap.

3. No lubrication required.

4. Have high efficiency.

5. Requires less maintenance.

6. Some misalignment is adjustable without loss in efficiency.

7. Durable and has long life.

8. Used for parallel and non parallel shafts.

9. Easy to reduce vibrations and noise.

 Disadvantages of a belt drive

1. Velocity ratio is not truly constant because of slip and stretching.

2. Heating occurs due to friction. It disturbs its perfect working at higher temperatures.

3. There is a speed limit of 35 m/s.

4. Requires center distance adjustment due to stretching.

PRACTICAL APPLICATIONS OF A FLAT BELT DRIVE

(I) Farming

(ii) Water pumps

(iii) Mining

(iv) Saw mills

(v) Electrical generators

PRACTICAL APPLICATIONS OF A V- BELT DRIVE

(i) Stone crushers

(ii) Machine tools

(iii) Paper industry

(iv) Textile industry

(v) High power mills

(vi) Refrigeration and air conditioning machinery

(vii)  Cars

ANALYSIS OF FLAT BELT DRIVE

OPEN FLAT BELT DRIVE
Neglecting centrifugal tension
T₁ / T₂ = e^µθ
T1 Tight side tension in Newton (N)
T2 Slack side tension in Newton (N)
µ = Coefficient of friction between the pulley and belt materials    

θ = Angle of contact=angle of lap on the SMALLER PULLEY
Initial tension = Ti = (T₁ + T₂)/2
Power transmitted = (T₁ –T₂) v            Watts (W)
v is the linear velocity of the belt in meters
Hence v =πD N/60
Where N is RPM and D is the diameter of the pulley in meters

Considering centrifugal tension 
T_c = m v²
Where m is mass of belt PER UNIT LENGTH, kg/m
Initial tension = T_i = ((T₁ + T₂)/2 + T_c)
Firstly        T_tight = T₁ + T_c
Secondly  T_slack = T₂ + T_c
Thirdly      T_tight / T_slack = e^µθ
Power transmitted = (T_tight — T_slack) v         Watt

CONDITION FOR MAXIMUM POWER WITH CENTRIFUGAL TENSION (T_c)
Firstly T_max = 3 m v²

Secondly T₁ = (2/3) T_max

Thirdly T₂ = (1/3) T_max

V = (T_max/3 m) ^0.5

Max Power = (2/3) T_max (1 — e^µθ)( (T_max/3 m)^0.5)            Watts

SLIP AND CREEP

Slip is there when belt does not grip pulley fully and perfectly. Thus,  there is not full friction between the pulley and the belt. Thus, there will be slip between the driver pulley and belt. There will be slip between the belt and driven pulley.

SLIP BETWEEN DRIVER PULLEY AND BELT

This slip is the difference between the linear velocities of driver pulley and belt. Express it in terms of driver linear velocity.
Linear velocity of driver pulley = [(πd₁N₁)/60)

Where

d₁ is the diameter of the driver pulley

N₁ is the RPM of the driver pulley
Linear velocity of belt = v
Let S₁ = % slip between driver pulley and the belt

S₁ =% of linear velocity of driver velocity

=[(πd₁N₁)/60) (S₁/100)

∴[(πd₁N₁)/60)] (S₁/100) = [(πd₁N₁)/60)]-v

∴v = [(πd₁N₁)/60)] [1 — S1/100]              (i)

SLIP BETWEEN BELT AND DRIVEN PULLEY

This slip is the difference between the linear velocities of belt and the driven pulley. Express it in terms of linear belt velocity.

Let d₂ be diameter of the driven pulley

N₂ is the RPM of the driven pulley
S₂ = % slip between the belt and driven pulley

=in terms of velocity of belt

=v x S₂/100

Slip = = v — πd₂N₂/60

v x S2/100 = v — πd₂N₂/60

v(1 — S2/100 ) = πd₂N₂/60

Substituting the value of v from equation (i), we get

[(πd₁N₁)/60)] [1 — S1/100] (1 — S2/100) = πd₂N₂/60

Multiply brackets containing terms S1 and S2

[(πd₁N₁)/60)] [1 — S1/100 — S2/100 + S1S2/10000 )= πd₂N₂/60

Neglecting S1S2/10000, we get

[(πd₁N₁)/60)] [1 — S1/100 — S2/100)= πd₂N₂/60

[(πd₁N₁)/60)] [1 – (S1+S2)/100)= πd₂N₂/60

Let Total % slip = S = S1+S2, then

[(πd₁N₁)/60)] [1 – S/100)= π d₂N₂/60

DIFFERENCE BETWEEN SLIP AND CREEP IN A BELT DRIVE

SLIP

Slip Is due to incorrect tensions in the belt. Due to slip driver pulley moves and the driven pulley does not move. It is more prominent in a V-belt drive than a flat belt drive. It is due to insufficient friction.

CREEP

Belt material is of low modulus. Change in length on tight and slack side are different. Hence creep occurs. It also occurs because of pulleys not being parallel to each other. It is more prominent in a flat belt drive. To avoid creep, crown the pulleys in the center. It results in no relative motion between the pulley and the belt. Both slip and creep cause relative motion between the pulley and belt. Both reduce power transmission. Reduce these to the minimum.

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