Page 159 - Analysis and Design of Machine Elements

Belt Drives
diameter is specified as the datum diameter d , the belt length is termed datum length 137
d
L . Since the datum diameter d is identical to the sheave diameter D, for an open-belt
d
d
′
drive in Figure 6.6, the preliminary belt length L is given by
d
(D − D ) 2
2
1
′
L = 2a + (D + D )+ (6.26)
d 0 2 1 2 4a 0
(3) Select belt datum length, L d
V-belts are of closed loop and made in standard lengths. The belt datum length L of
d
Types A, B and C belt can be selected from Table 6.1, close to the preliminary calculation
′
of L . The corresponding length correction factor K can be found in Figure 6.11.
d L
(4) Compute the actual centre distance, a
The actual centre distance a is calculated by
L − L ′ d
d
a ≈ a + (6.27)
0
2
Considering the installation adjustment and pretension compensation to take up slack
in belts due to stretch and wear, the variation of centre distance is given as
a = a − 0.015L
min d
a max = a + 0.03L d
6.4.3.5 Compute Contact Angle on the Small Sheave, 1

Since belts transmit power by friction against sheaves, large values of equivalent coeffi-
cient of friction f and contact angle favour power transmission capacity. The contact
v
∘
angle should be greater than 120 to ensure adequate contact and frictional force, that
is, the contact angle on the small sheave must satisfy
1
∘ D − D 1 ∘ ∘
2
= 180 − × 57.3 ≥ 120 (6.28)
1
a
6.4.3.6 Compute the Number of Belts Required to Carry the Design Power
If a single V-belt has insufficient capacity, multiple belts may be used. The number of
belts required is calculated from
P ca P ca
z = = ≤ 10 (6.29)
P (P +ΔP )K K
r 0 0 a L
The number of belts required is normally less than 10 to ensure each belt carries a
similar load. When one belt needs replacement, a complete new set should be installed.
6.4.3.7 Decide Initial Tension, F
0
Belts must be installed with an initial tension recommended by manufacturers. From
Eqs. (6.9) and (6.11), and considering the centrifugal force and the effect of contact angle,
the initial tension can be estimated by [6]
( )
P ca 2.5
F = 500 − 1 + qv 2 (6.30)
0
zv K a