Page 151 - Analysis and Design of Machine Elements

A 2 Belt Drives 129
Slack side
F B 1 F 2 C 2 F
F 2 2
1
dλ 2
n 2
dλ 2
O 1 O 2
C 1
dλ 1 n 1 dλ 1
F 1
F+dF A 1 F 1 F+dF
Tight side
B 2
Figure 6.8 Belt elastic creep.
gradually increases from F to F , resulting in a gradual increase in elastic deformation
2 1
of belt along the active arc C B . The belt elongates forward relative to the driven pulley,
2 2
leading to a higher belt speed v than the linear speed of driven pulley v .
2
This slight relative sliding between the belt and pulleys due to different tensions on the
tight and slack side is called elastic creep. It is the result of minute stretch or contraction
of belt as its tension various between F and F while the belt going through contact
1 2
arcs, causing a loss of driven speed. Since it is essential for different tensions to exist
in order to exert a tangential force on the driven pulley, elastic creep is an inevitable
physical phenomenon in belting. Except for timing belts, there is always elastic creep
in belt drives. Compared with V-belts, flat belts are most affected by this phenomenon.
Because of elastic creep, the speed ratio of belt drive is neither constant nor exactly

equal to the ratio of two pulley diameters. Therefore, belt drives cannot be used where
a constant output speed is required.

6.2.3.2 Slippage of Belts
The contact arc includes the idle arc and active arc. In the driving pulley, when the belt
works normally elastic creep only happens within the active arc C B where the belt
1 1
leaves. If the effective tension exceeds the sum of limited frictional force, the length of
active arc C B will increase. If the active arc extends to the whole contact arc, that is,
1 1
point C overlaps with point A , a total slippage of belt relative to the pulley occurs. This
1
1
will cause excessive wear and must be avoided.
6.2.3.3 Speed Ratio
Most prime movers rotate at higher speeds than are desirable for driven machines. The-
oretically, in the absence of slippage, the linear speeds of driving and driven pulleys are
equal to the belt speed, v. Therefore
D n D n
1 1
2 2
v = v =
1 2
60 × 1000 60 × 1000
Since
v = v = v 2
1
The speed ratio, i,isexpressed as:
n 1 D 2
i = =
n D
2 1