Page 161 - Analysis and Design of Machine Elements

Solution Belt Drives 139

Steps Computation Results Units
1. Compute the design Select service factor K from Table 2.1 as K = 1.1, therefore P = 8.25 kW
A A ca
power P the design power is
ca
P = K P =1.1×7.5=8.25 kW
A
ca
2. Determine Select the diameter of the driving sheave as D = 100 mm D = 100 mm
1 1
the diameters of the according to Table 6.1. Select slip ratio = 1.5%, the diameter
sheaves of the driven sheave can be calculated by Eq. (6.15)
D = i(1 − )D =3.5×(1 −1.5%) × 100 = 344.8mm
2
1
Select D = 355 mm according to Table 6.1. D = 355 mm
2
2
Check the speed of the belt by
D n × 100 × 1450 v = 7.59 ms −1
v = 1 1 = = 7.59 < 25 m∕s
60 × 1000 60 × 1000
The speed of the belt is acceptable.
Check the error of speed ratio
|D ∕D − 3.5| | 355∕100 − 3.5 |
2
1
Δi = | | × 100%= | | = 1.43% < 5%
| 3.5 | | 3.5 |
| | | |
The speed ratio is acceptable.
3. Confirm centre Specify a trial centre distance according to
distance a and belt 0.7(D + D ) < a < 2(D + D )
datum length L d 1 2 0 1 2
The initial centre distance is selected as a = 500 mm.
0
The preliminary belt length is calculated by Eq. (6.26)
(D − D ) 2

′
L = 2a + (D + D )+ 2 1
d 0 2 1 2 4a
[ 0 2 ]
(355 − 100)
= 2 × 500 + ×(100 + 355)+ = 1747mm
2 4 × 500
L = 1750 mm
d
Select the belt datum length from Table 6.1 as L = 1750 mm. a = 502 mm
d
The actual centre distance a is calculated from Eq. (6.27)
L d −L ′ ( 1750 − 1747 )
a ≈ a + 2 d = 500 + 2 ≈ 502 mm a min = 476 mm
0
a min = a − 0.015L = 502 − 0.015 × 1750 = 476 mm a max = 555 mm
d
a max = a +0.03L = 502 + 0.03 × 1750 = 555 mm
d
4. Compute From Eq. (6.28) we have = 150.9 ∘
∘
the contact angle = 180 − D − D 1 × 57.3 ∘
2
on the driving sheave 1 a
∘ 355 − 100 ∘ ∘ ∘
= 180 − × 57.3 = 150.9 > 120
502
So the contact angle on the driving sheave is acceptable.
5. Compute From Eq. (6.29)
the number of belts z = P ca
required to carry (P +ΔP )K K L
0
0
a
the design power
Since n = 1450 rpm, D = 100 mm, i = 3.5, from Figures 6.9
1 1
and 6.10a, we have P = 1.32 kW, ΔP = 0.17 kW
0 0
Select K = 0.92. From Figure 6.11, select K = 1.00
L
8.25
z = = 6.02
(1.32 + 0.17)× 0.92 × 1.00
Select z = 7 z = 7