Engineering Mechanics

(^690) „„„„„ A Textbook of Engineering Mechanics
33.19.INITIAL TENSION IN THE BELT
When a belt is wound round the two pulleys (i.e., driver and follower), its two ends are jointed
together; so that the belt may continuously move over the pulleys. Since the motion of the belt (from the
driver) and the follower (from the belt) is governed by a firm grip due to friction between the belt and the
pulleys, therefore the belt is tightened up, in order to keep a proper grip of the belt over the pulleys.
Initially, even when the pulleys are stationary the belt is subject to some tension, called initial tension.
Let T 0 = Initial tension in the belt,
T 1 = Tension in the tight side of the belt,
T 2 = Tension in the slack side of the belt, and
μ= Coefficient of increase of the belt length per unit force.
A little consideration will show, that increase of tension in the tight side
=T 1 – T 0
and increase in the length of the belt on the tight side
=μ (T 1 – T 0 ) ...(i)
Similarly, decrease in tension in the slack side
=T 0 – T 2
and decrease in the length of the belt on the slack side
=μ (T 0 – T 2 ) ...(ii)
Assuming the length of the belt to be constant, when it is at rest or in motion, therefore increase
in length on the tight side is equal to decrease in the length on the slack side. Therefore, equating
(i) and (ii),
μ (T 1 – T 0 )=μ (T 0 – T 2 )or T 1 – T 0 = T 0 – T 2
∴ T 0 =^12
2
TT+
Note: If centrifugal tension is taken into consideration, then
T 0 =^1212
2
22
C
C
TT T TT
T
++ +
=+
Example 33.13. Two parallel shafts whose centre lines are 4·8 m apart are connected by an
open belt drive. The diameter of the larger pulley is 1·5 m and that of the smaller pulley is 1m. The
initial tension in the belt, when stationary, is 3·0 kN. The mass of the material is 1·5 kg/m length and
the coefficient of friction between the belt and the pulley is 0·3. Calculate the power transmitted,
when the smaller pulley rotates at 400 r.p.m.
Solution. Given: Distance between the centres of shafts (l) = 4·8 m; Diameter of the
larger pulley (d 1 ) = 1·5 m or radius (r 1 ) = 0·75 m; Diameter of the smaller pulley (d 2 ) = 1 m
or radius (r 2 ) = 0·5 m; Initial tension in the belt (T 0 ) = 3 kN; Mass of the material (m) = 1·5 kg/m;
Coefficient of friction (μ) = 0·3 and speed of the smaller pulley (N 2 ) = 400 r.p.m.
Fig. 33.12.