(^692) A Textbook of Engineering Mechanics
- A belt connects two pulleys A and B 4 m apart. The pulley A is 1 m diameter, whereas the pulley
B is 50 cm diameter. If the coefficient of friction between the belt and the pulleys is 0·32, find
the ratio of the tensions, when the drive is (i) an open belt drive ; and (ii) cross belt drive.
[Ans. 2·623 ; 3·084] - The initial tension in a flat belt drive is 1800 N. The angle of lap on the smaller diameter is
170°. The coefficient of friction between the belt and pulley surface is 0·25. The pulley has a
diameter of 0·9 m and it runs at 540 r.p.m.
Determine the power that can be transmitted at the above speed. Neglect the centrifugal ten-
sion. [Ans. 32·5 kW] - A flat belt 7·5 mm thick and 100 mm wide transmits power between two pulleys, running at
1600 r.p.m. The mass of the belt is 0·9 kg/m length. The angle of lap on the smaller pulley is
165° and the coefficient of friction between the belt and pulleys is 0·3. If the maximum permis-
sible stress in the belt is 2 MN/m^2 , find (i) maximum power transmitted ; and (ii) initial tensions
in the belt. [Ans. 15·44 kW ; 710·5 N]
33.20.ROPE DRIVE
Sometimes, the power, from one shaft to another, is transmitted by
rope drive, instead of belt drive. This method is specially used when the
shafts are a long distance apart or a considerable power is to be transmitted.
The only difference between the belt drive and rope drive is that in the case
of belt drive, the belt runs over the pulleys, whereas in the case of rope
drive, the rim of the pulley is grooved, in which the rope runs.
The effect of the groove is to increase the frictional grip of the rope
on the pulley, and thus to reduce the tendency of slipping. To have a good
grip on the pulleys, the rope is in contact with side faces of the groove and
not at the bottom approximately V-shaped as shown in Fig. 33·13.33.21.ADVANTAGES OF ROPE DRIVE
Following are the advantages of a rope drive over belt drive:- The rope drive is particularly suitable, when the distance between the shafts is large.
- The frictional grip in case of rope drive is more than that in the belt drive.
- The net driving tension (i.e., difference between the two tensions) in the case of rope drive is
more than the belt drive (because the ratio of tensions in the case of rope drive is
cosec α times more than that in the belt drive.)
33.22.RATIO OF TENSIONS IN ROPE DRIVE
We have already discussed in Art. 33·14 the ratio of tensions
in a belt drive. The same principle may be used for the determination
of ratio of tensions in case of a rope drive. Now consider a rope
running in a groove as shown in Fig. 33·14.
Let R 1 = Normal reactions between rope and
sides of the groove.
R= Total reaction in the plane of the
groove.
2 α= Angle of the groove.
μ= Coefficient of friction between rope
and sides of the groove.Fig. 33.13. Rope drive.Fig. 33.14. Ratio of tensions
in rope drive.