Page 152 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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where
−1
v , v 2 — linear speed of driving and driven pulleys, respectively, m s ;
1
n , n — rotational speed of driving and driven pulleys, respectively, rpm;
1 2
D , D — diameter of driving and driven pulleys, respectively, in mm.
1 2
That is, the speed ratio of driving and driven pulleys is inversely proportional to the
ratio of their diameters. However, except for timing belts, there is always elastic creep
between the belts and pulleys. Creep causes a small reduction in speed, that is, the linear
speed of driven pulley is slightly smaller than that of the driving pulley. The difference
is measured by a slip ratio, , defined as
v − v 2
1
= × 100% (6.14)
v
1
Since slip ratio varies from 1 to 2%, it can therefore be neglected. We then have speed
ratio, i, approximately expressed as:
n 1 D 2 D 2
i = = ≈ (6.15)
n (1 − )D D
2 1 1
6.2.4 Stress Analysis
As discussed before, a working V-belt is subject to tension, bending and centrifugal
forces. Consequently, stresses in a belt include normal tensile stress, bending stress and
centrifugal stress.

6.2.4.1 Tensile Stress in Tight Side, , and Slack Side, 2
1
The tensile stresses caused by belt tensions are normal stresses, with a larger value on
the tight side,
F 1
Tight side =
1
A
F 2
Slack side = (6.16)
2
A
6.2.4.2 Centrifugal Stress, c
The centrifugal stress is a normal stress caused by centrifugal tension as belts move
around sheaves, expressed as
F c qv 2
= = (6.17)
c
A A
6.2.4.3 Bending Stress, b
In addition to tensile stresses, belts are also subject to cyclic bending stresses when in
contact with sheaves. The outer and inner faces of a belt are in tension and compression,
respectively. Between these two faces, there is a neutral section that is neither in tension
nor in compression. The bending stress is expressed as [6, 7]
h
≈ E (6.18)
b
D