Design of rope, belt and chain by Aliyi Umer

Design of
Belt, Rope, and Chain drives
Prepared by Aliyi Umer
Aliyi Umer 1

INTRODUCTION
Belts, ropes, chains, and other similar elastic or flexible machine
elements are used in conveying systems in the transmission of power
over comparatively long distances.
 These elements can be used as a replacement for gears, shafts,
bearings, and other relatively rigid power-transmission devices.
 Power is transmitted from the prime mover to a machine by means
of intermediate mechanism called drives.
This intermediate mechanism is known as drives may be belt or chain
or gears.
 Belt is used to transmit motion from one shaft to another shaft with
the help of pulleys Aliyi Umer 2

Types of Belts
• Though there are many types of belts used these days, yet the following
Three types of belt drives are commonly used important from the subject
point of view: They are:
- Flat belt drive
-V-belt drive
-Rope or circular belt drive
Figure 1 Types of belt
1. Flat belt. The flat belt as shown in above fig.1 (a), is mostly used in the
factories and workshops, where a moderate amount of power is to be
transmitted, from one pulley to another when the two pulleys are around 10
metres apart. Aliyi Umer 4

. Belt may be arranged in two ways
Open belt drive
Cross belt drive
 When the direction of rotation of both the pulleys are
required in the same direction, we use open belt drive.
 Where as the direction of rotation of pulleys are
required in opposite direction then cross belt is used.
Aliyi Umer 5

 The pulleys which drives the belt is known as driver and the pulley
which follows driver is known as driven or follower.
Figure 2 open and cross arrangements of belt
Aliyi Umer 6

MERITS AND DEMERITS OF FLAT BELT DRIVE
Merits:
 Simplicity, low cost, smoothness of operation, ability to absorb
shocks, flexibility and efficiency at high speeds.
 Protect the driven mechanism against breakage in case of sudden
overloads owing to belt slipping.
 Simplicity of care, low maintenance and service.
 Possibility to transmit power over a moderately long distance.
Demerits:
 It is not a positive drive and comparatively large size.
 Stretching of belt calling for resewing when the center distance is
constant.
 Not suitable for short center distance.
 Belt joints reduce the life of the belt.
Aliyi Umer 7

Velocity Ratio of a Belt Drive
Aliyi Umer 8

Considering a pulleys in which pulley 1 drives pulley 2 where
pulley 2 and 3 are keyed to the same shaft there fore pulley 1 also
drives pulley 3 which in turn drives pulley 4.
Figure 3 compound arrangements of belt
Aliyi Umer 9

Slip in Belts
 Consider an open belt drive rotating in clockwise direction, this
rotation of belt over the pulleys is assumed to be due to firm
frictional grip between the belt and pulleys.
 When this frictional grip becomes insufficient, there is a possibility
of forward motion of driver without carrying belt with it and there is
also possibility of belt rotating without carrying the driver pulley
with it, this is known as slip in belt.
Aliyi Umer 11

Therefore slip may be defined as the relative motion between the
pulley and the belt. This reduces velocity ratio and usually expressed
as a percentage and If thickness of the belt (t) is considered, then
...(where s = s1 + s2 i.e. total percentage of slip)
Creep of Belt
When the belt passes from the slack side to the tight side, a certain
portion of the belt extends and it contracts again when the belt passes
from the tight side to the slack side. Due to these changes of length,
there is a relative motion between the belt and the pulley surfaces.
Aliyi Umer 12

This relative motion is termed as creep. The total effect of creep is to
reduce slightly the speed of the driven pulley or follower. Considering
creep, the velocity ratio is given by
Note: Since the effect of creep is very small, therefore it
is generally neglected.
Aliyi Umer 13

Length of open belt drive
Aliyi Umer 14

Length of cross belt drive
Aliyi Umer 15

Power Transmitted by a Belt
Aliyi Umer 16

power transmitted = (T1 – T2) ν N-m/s equal to W
Ratio of driving tension for flat belt drive
Consider a driven pulley rotating in the clockwise direction as shown
in Fig. below.
Now consider a small portion of the belt PQ, subtending an angle δθ at
the center of the pulley as shown in Fig. above.The belt PQ is in
equilibrium under the following forces:
Aliyi Umer 17

Let T1 = Tension in the belt on the tight side,
T2 = Tension in the belt on the slack side,
θ = Angle of contact in radians (i.e. angle subtended by the
arc AB, along which the belt touches the pulley, at the
center).
μ = the coefficient of friction between the belt
and pulley.
𝑇1
𝑇2
= 𝑒𝜇.𝜃
Aliyi Umer 18

Notes : 1.While determining the angle of contact, it must be remembered
that it is the angle of contact at the smaller pulley, if both the pulleys are
of the same material. We know that
2. When the pulleys are made of different material (i.e. when the
coefficient of friction of the pulleys or the angle of contact are different),
then the design will refer to the pulley for which μ.θ is small.
Aliyi Umer 19

Centrifugal Tension
 Since the belt continuously runs over the pulleys, therefore, some centrifugal
force is caused, whose effect is to increase the tension on both the tight as well
as the slack sides. The tension caused by centrifugal force is called centrifugal
tension. At lower belt speeds (less than 10 m/s), the centrifugal tension is very
small, but at higher belt speeds (more than 10 m/s), its effect is considerable and
thus should be taken into account.
Aliyi Umer 20

TC = mv2
m = Mass of belt per unit length in kg,
v = Linear velocity of belt in m/s,
r = Radius of pulley over which the belt runs in meters,
= Centrifugal tension acting tangentially at P and Q in newton's.
𝑇𝐶
Aliyi Umer 21

Maximum Tension in the Belt
Aliyi Umer 22

V-Belt Drives:
On account of the wedging action of a V-belt in the
groove of the sheave or pulley, the traction force
(force transmitting power) is greater than in a flat belt
running on a flat face pulley. To ensure wedging action
in the groove, the belt should make contact with the
sides of the groove but not the bottom. It is evident
that the wedging action and the traction force are large
for small groove angles ; however, the force required
to pull the belt out of the groove as it leaves the
sheave is large for :small groove angles, resulting in
loss of power and excessive wear of the belt.
Aliyi Umer 25

Figure Cross-sections of v belt
The :selected groove angle is therefore a compromise to secure large
traction force without unduly large force to pull the belt from the
groove. The groove angle in the sheave is less than the belt angle to
allow for change in shape. Groove angles of 32° to 38° are used.
Aliyi Umer 26

Standard sizes of belts for power transmission have been
adopted and designated by sizes A,B,C,D, and E. For low
bending stresses as the belt wraps around the sheave , small belts
are better for long belt life; however a large number of small
belts requires a wider sheave which increases the load overhang
( distance from the belt force to the bearing), which in turn
increases the shaft stresses and bearing loads, all of which raises
the cost of the drive. A moderate number of belts desirable so
that if one belt fails or stretches excessively, the remaining belts
may carry the load until the replacement of the belts can be
made. In replacing the belts, a complete set of new belts should
be used rather than replacing a single damaged belt, since a new
(upstretched) would carry more than its share of the load and
would have a short life. Thus optimum design requires
compromises in belt selection.
Aliyi Umer 27

Table 4.1. Dimensions of standard V-belts
Table 4.2. Dimensions of standard V-grooved pulleys
Aliyi Umer 28

Advantages
1. The V-belt drive gives compactness due to the small distance
between centers of pulleys.
2. The drive is positive, because the slip between the belt and the pulley
groove is negligible.
3. Since the V-belts are made endless and there is no joint trouble,
therefore the drive is smooth.
4. It provides longer life, 3 to 5 years.
5. The belts have the ability to cushion the shock when machines are
started.
6. The high velocity ratio (maximum 10) may be obtained.
7. The V-belt may be operated in either direction, with tight side of the
belt at the top or bottom. The center line may be horizontal, vertical
or inclined.
Aliyi Umer 29

Disadvantages
1. The V-belt drive can not be used with large center
distances, because of larger weight per unit length
2. The V-belts are not so durable as flat belts.
3. The construction of pulleys for V-belts is more
complicated than pulleys of flat belts.
4. Since the V-belts are subjected to certain amount of
creep, therefore these are not suitable for constant
speed applications such as synchronous machines and
timing devices.
5. The belt life is greatly influenced with temperature
changes, improper belt tension and mismatching of
belt lengths.
6. The centrifugal tension prevents the use of V-belts at
speeds below 5 m / s and above 50 m / s
Aliyi Umer 30

Rope Drives
Rope Drives; The drives are widely used where a large amount of power
is to be transmitted from one pulley to another over a considerable
distance. Frictional grip is more than that in v drive. Number of separate
drives can be taken from one driving pulley.
Types of Rope Drive
The following two types of Rope drive,
1. Fiber Rope Drives These operate successfully when the pulleys are
about 60 m apart.
2. Wire Rope Drives These operate successfully when the pulleys are up
to 150 m apart.
Aliyi Umer 31

Advantages of Rope Drive
1. They give smooth, steady and quite service.
2. They are little affected by outdoor conditions.
3. Their shafts may be out of straight alignment.
4. These are more durable,
5. They do not fail suddenly,
6. The efficiency is high,
7. The cost is low.
Aliyi Umer 32

Applications of Rope Drive
1. These are used as haulage ropes in mines, tramways,
power transmission.
2. Also used for hoisting purpose in mines, quarries, cranes,
dredges, elevators well drilling etc.
3. As hoisting ropes in steel mill ladles, high speed elevators.
4. Used in hand operated hoisting machinery and as tie ropes
for fitting tackles, hooks.
Aliyi Umer 33

Table Steel wire ropes for haulage purposes in mines.
Table Steel wire suspension ropes for lifts, elevators and hoists.
Aliyi Umer 34

Table Diameter of wire and area of wire rope.
Table Factor of safety for wire ropes.
Aliyi Umer 35

Stresses in Wire Ropes
2. Bending stress when the rope winds round the sheave or drum. When a wire
rope is wound over the sheave, then the bending stresses are induced in the wire
which is tensile at the top and compressive at the lower side of the wire.
Aliyi Umer 36

While designing a wire rope, the sum of these stresses should be
less than the ultimate strength divided by the factor of safety.
Aliyi Umer 39

Procedure for Designing a Wire Rope
1. First of all, select a suitable type of rope from tables for the given application.
2. Find the design load by assuming a factor of safety 2 to 2.5 times the factor of
safety given in Table.
3. Find the diameter of wire rope (d) by equating the tensile strength of the rope
selected to the design load.
4. Find the diameter of the wire (dw) and area of the rope (A) from table.
5. Find the various stresses (or loads) in the rope.
6. Find the effective stresses (or loads) during normal working, during starting
and during acceleration of the load.
7. Find the actual factor of safety and compare with the factor of safety table. If
the actual factor of safety is within permissible limits, then the design is safe.
Aliyi Umer 40

We have seen in previous chapters on belt and rope drives that slipping
may occur. In order to avoid slipping, steel chains are used. The chains
are made up of number of rigid links which are hinged together by pin
joints in order to provide the necessary flexibility for wraping round
the driving and driven wheels. These wheels have projecting teeth of
special profile and fit into the corresponding recesses in the links of the
chain as shown in Fig. below. The toothed wheels are known as
*sprocket wheels or simply sprockets. The sprockets and the chain are
thus constrained to move together without slipping and ensures perfect
velocity ratio.
Chain Drives
Aliyi Umer 41

Fig Sprockets and chain.
The chains are mostly used to transmit motion and power from one shaft
to another, when the centre distance between their shafts is short such as
in bicycles, motor cycles, agricultural machinery, conveyors, rolling
mills, road rollers etc. The chains may also be used for long centre
distance of up to 8 metres. The chains are used for velocities up to 25 m /
s and for power upto 110 kW. In some cases, higher power transmission
is also possible.
Aliyi Umer 42

Merits and demerits of Chain Drive over Belt or Rope Drive
Merits of Chain Drive
1. As no slip takes place during chain drive, hence perfect velocity ratio
is obtained.
2. Since the chains are made of metal, therefore they occupy less space
in width than a belt or rope drive.
3. It may be used for both long as well as short distances.
4. It gives a high transmission efficiency (up to 98 percent).
5. It gives less load on the shafts.
6. It has the ability to transmit motion to several shafts by one chain
only.
7. It transmits more power than belts.
8. It permits high speed ratio of 8 to 10 in one step.
9. It can be operated under adverse temperature and atmospheric
conditions.
Aliyi Umer 43

Demerits of Chain Drive
1. The production cost of chains is relatively high.
2. The chain drive needs accurate mounting and careful
maintenance, particularly lubrication and slack
adjustment.
3. The chain drive has velocity fluctuations especially
when unduly stretched.
Aliyi Umer 44

Terms Used in Chain Drive
1. Pitch of chain. It is the distance between the hinge center of a link and the
corresponding hinge center of the adjacent link, as shown in Fig. It is usually
denoted by p.
2. Pitch circle diameter of chain sprocket. It is the diameter of the circle on which
the hinge centers of the chain lie, when the chain is wrapped round a sprocket. The
points A, B, C, and D are the hinge centers of the chain and the circle drawn
through these centers is called pitch circle and its diameter (D) is known as pitch
circle diameter. Aliyi Umer 45

Relation Between Pitch and Pitch Circle Diameter
A chain wrapped round the sprocket is shown in Fig. above. Since the links of the
chain are rigid, therefore pitch of the chain does not lie on the arc of the pitch circle.
The pitch length becomes a chord. Consider one pitch length AB of the chain
subtending an angle θ at the center of sprocket (or pitch circle),
Aliyi Umer 46

Velocity Ratio of Chain Drives
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Length of Chain and Centre Distance
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Table , Characteristics of roller chains according to IS: 2403 -1991.
Table , Power rating (in kW) of simple roller chain.
Aliyi Umer 49

Design Procedure of Chain Drive
1. First of all, determine the velocity ratio of the chain drive.
2. Select the minimum number of teeth on the smaller sprocket or pinion from table.
3. Find the number of teeth on the larger sprocket.
4. Determine the design power by using the service factor, such that
Design power = Rated power × Service factor
5. Choose the type of chain, number of strands for the design power and r.p.m. of the
smaller sprocket from table .
6. Note down the parameters of the chain, such as pitch, roller diameter, minimum
width of roller etc. from table.
7. Find pitch circle diameters and pitch line velocity of the smaller sprocket.
8. Determine the load (W) on the chain by using the following relation, i.e.
9. Calculate the factor of safety by dividing the breaking load (WB) to the load on the
chain ( W ). This value of factor of safety should be greater than the value given in
table.
10. Fix the center distance between the sprockets.
11. Determine the length of the chain.
Aliyi Umer 50

Design of rope, belt and chain by Aliyi Umer

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