Page 154 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
132
Since F = A, and using Eq. (6.20), we then have
1
1
( 1 )
F =([ ]− − )A 1 − (6.21)
ec b1 c f
e
Thisisthe maximumeffectivetensionwithinthe rangeofwhich no slippage and
fatigue will occur.
6.3.2 Power Transmission Capacity of a Single V-Belt
6.3.2.1 The Basic Power Rating of a Single Standard V-Belt, P 0
The power transmitted by a belt is the product of the maximum effective tension and
belt speed. Substituting f by the equivalent coefficient of friction of a V-belt f in Eq.
v
(6.4), we have the basic power rating for a single standard V-belt as
( )
1
([ ]− − )Av 1 −
F v b1 c e f v
ec
P = = kW (6.22)
0
1000 1000
The basic power rating a single standard V-belt can transmit is obtained under spe-
cific test conditions. The test condition specifies as a moderate length belt running on
identical diameter sheaves, transmitting a steady load. Due to limited space, this book
only presents data for Type A, B and C V-belts. Detailed data for other belt types can be
found in standards or design handbooks [8].
The basic power ratings of single standard Type A, B and C V-belts as thefunctionof
pitch diameter of small sheave and selected rotational speeds of 700, 1450 and 2800 rpm
are presented in Figure 6.9. The abscissas of the points in the figure give pitch diameters
of small sheaves, which can be referred to in Table 6.1. The basic power ratings at other
rotational speeds can be obtained by interpolation.
6.3.2.2 The Actual Power Rating of a Single V-Belt, P
r
In practice, deviations from these specific test conditions are acknowledged by introduc-
ing correction factors. A given belt can carry a greater power as the speed ratio increases.
The increment of transmitted power ΔP , as listed in Figure 6.10, is added to the basic
0
power rating to take this factor into account.
Since contact angles affect frictional force and ultimately the transmitted power, a
∘
correction factor K is introduced for contact angles other than 180 . Corresponding to

∘
∘
∘
∘
contact angles of 180 , 150 , 120 and 90 , the correction factor K canbeselectedas

1.0, 0.92, 0.82 or 0.69 [4], respectively. The correction factor K for other contact angles

can be obtained by interpolation.
Similarly, if a belt length is different from the specified belt length when the basic
power rating is obtained, a belt length correction factor K is introduced, as illustrated
L
in Figure 6.11. After incorporating these correction factors, the actual power rating of a
single V-belt is adjusted as
P =(P +ΔP )K K (6.23)
r 0 0 L
where
P r — actual power rating of a single standard V-belt;
P 0 — basic power rating of a single standard V-belt, see Figure 6.9;
ΔP — increment of the basic power rating of a single standard V-belt, see Figure 6.10;
0
K — correction factor for contact angle;

K — correction factor for belt length, see Figure 6.11.
L