Page 150 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
128
The maximum effective tension F and the torque are in proportion to the initial ten-
ec
sion F . With the increase of initial tension F , the drive capacity may increase. However,
0
0
too large an initial tension is not necessary, as increasing F will inevitably increase
0
tight tension F and slack tension F , which will in turn reduce belt fatigue life. For a
1 2
belt drive to transmit power satisfactorily, a proper initial tension must be provided and
maintained.
Additionally, increasing contact angle will increase contact surfaces, and conse-
quently increase total frictional force. Usually, contact angles should be no less than
∘
120 . Similarly, increasing the coefficient of friction f will increase total frictional force
and eventually increase the power carrying capacity of a belt drive.
6.2.2.4 Centrifugal Tension, F
c
For a greater power transmitting capacity, most belt drives operate at relatively high
speeds. In such cases, as the belt travels around a part of circumference of pulley, cen-
trifugal force acting on the belt creates centrifugal tension F . Considering a differential
c
element of belt shown in Figure 6.7e, according to Newton’s second law, the differential
centrifugal force dC canbeexpressed as
v 2 v 2 2
dC = m = rd • q • = qv d
r r
where q is themassofbeltper unit length, v for belt speed and r the pulley radius.
From the force equilibrium condition in the radial direction and considering a small
angle d ,wehave

{ d
2
2F sin = qv d
c
2
sin d ≈ d
2 2
Therefore, the centrifugal tension F is
c
F = qv 2 (6.12)
c
When the centrifugal tension is sufficiently large, it should be considered in both F
1
and F in Eq. (6.10) and expressed as [5]
2
F − qv 2
1 = e f (6.13)
F − qv 2
2
6.2.3 Kinematic Analysis
6.2.3.1 Elastic Creep
When a belt drive is in operation in Figure 6.8, the belt first contacts the driving pulley
at point A with tight tension F at speed v,which is thesameasthe linear speed of
1
1
driving pulley v . The belt then passes through the idle arc of A C with no changes in
1
1
1
F and v. As the belt moves along the active arc C B , the tension on a differential belt
1
1 1
element close to the tight side is greater than that close to the slack side, resulting in
the elastic deformation near the tight side d greaterthanthatonthe slackside d .
2
1
The belt contracts backward relative to the driving pulley and elastic creep begins. At
the end of the active pulley arc C B at point B , the belt leaves the pulley with the
1 1
1
slack tension F and a reduced speed v. Similarly, for the driven pulley, the belt tension
2