Page 147 - Analysis and Design of Machine Elements

Belt Drives
The contact angle is one of several factors determining the power transmission capac- 125
∘
ity of a belt drive. It is equal to 180 only when the speed ratio is one (i.e. no speed
∘
change). The contact angle on the small pulley is always less than or equal to 180 ,or
π rad.
6.2.2 Force Analysis
The mechanics of belt drives can be explained by Figure 6.7a. Initially, the belt is installed
by placing it around two pulleys loosely with a reduced centre distance. The two pulleys
are then moved apart to a desired centre distance. The belt thus clamps firmly against the
pulley surface with an initial tension F . This initial tension is critical because it ensures
0
the belt works properly under design loads.
Due to initial tension F , normal force N generates at the interface between the belt
0
and pulleys in the radial direction. When the driving pulley rotates at a rotational speed
n in the clockwise direction, the belt applies frictional force to the driving pulley in
1
the anticlockwise direction. In return, the driving pulley applies the same amount of
frictional force F in the opposite direction, that is, in the clockwise direction, to the belt.
f
The belt is thus driven by this frictional force. Similarly, when the belt moves around
the driven pulley, the frictional force acting on the driven pulley by the belt is in the
clockwise direction. This frictional force acts as tangential force and the driven pulley is
thus driven by this force and rotates at a rotational speed n . Hence, the belt drives use
2
friction as a useful agent to transmit power.
From startup to operating speed, the tensile force in the bottom strand of belt
increases from initial tension F to tight tension F ; while the tensile force in the
0
1
upper strand drops from F to a smaller value of F , termed slack or loose tension.
0 2
Correspondingly, the bottom strand of belt is termed the tight side, while the upper
strand is the slack side.
F 2
F 2 F f
F f 1 2
A-A α 2
A A
Q N dα α 1 o 1 n 1 o 2 n 2
F 1
(b) F 1
(a)
N
Q
φ F
f dN F dα c dα
N 2 2
(c) dα dα
dN dC

dα dα
2 2
F+dF F c
(d) (e)
Figure 6.7 Force analysis of a belt drive.