Page 148 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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6.2.2.1 Force Analysis of an Element of Belt
Figure 6.7b illustrates an element of flat belt acting on a pulley by a radial force Q.The
frictional force on the flat belt working surface is
F = fN = fQ (6.2)
f
Figure 6.7c illustrates a segment of a V-belt acting on a sheave by the same amount of
radial force Q, ignoring friction in the radial direction, the frictional force on the V-belt
working surfaces is
f
F = 2fN = Q = f Q (6.3)
v
f
sin
2
Consequently, the equivalent coefficient of friction of V-belt f is
v
f
f = (6.4)
v
sin
2
Obviously, the equivalent coefficient of friction on a V-belt drive f is greater than that
v
on a flat belt drive f . This is called the wedge effect. Because of the increased friction
resulting from wedge effect, V-belt drives provide a better overall power transmission
capability than a flat belt drive in terms of both low cost and space. The following analysis
is on flat belts for simplicity. For V-belts, the coefficient of friction is substituted by f .
v
6.2.2.2 Relations Between Tight Tension F , Slack Tension F , Initial Tension F 0
2
1
and Effective Tension F e
Assume the total length of belt keeps constant. Therefore, the increase of belt length
in the tight side is the same as the decrease of belt length in the slack side; that is,
F – F = F – F . Hence, we have the initial tension as
0
1
0
2
1
F = (F + F ) (6.5)
0 1 2
2
Summing torque with respect to the centre of driving pulley in Figure 6.7a, we have
D D D
∑ 1 1 1
T = F f + F 2 − F 1 = 0
2 2 2
F = F − F 2
1
f
The effective tension on the belt drive, which is related to the pulley torque, is the sum
of distributed frictional forces at the interface between belt and pulley, thus,
F = F = F − F 2 (6.6)
1
e
f
Incorporating Eq. (6.5), the tight tension F and slack tension F are given by
1 2
F e
F = F + (6.7)
1
0
2
F e
F = F − (6.8)
2 0
2
The power transmission capacity, P,ofabelt is
F v
e
P = (6.9)
1000