Two shafts, 1.67 ft apart, are connected by an open belt. The input shaft has a speed of 350 rpm and the output shaft should be capable of running at speeds of 950 rpm, 650 rpm, 450 rpm, 250 rpm, and 150 rpm. If the diameter of the smallest pulley on the driven shaft is 2 inches, calculate the length of the belt and the diameters of each pulleys attached at the shafts.

Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
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Chapter2: Axially Loaded Members
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Two shafts, 1.67 ft apart, are connected by an open belt. The input shaft has a speed of 350 rpm and the output shaft should be capable of running at speeds of 950 rpm, 650 rpm, 450 rpm, 250 rpm, and 150 rpm. If the diameter of the smallest pulley on the driven shaft is 2 inches, calculate the length of the belt and the diameters of each pulleys attached at the shafts.

W
W
No, = 150
No2 = 250
Noz = 450
No4 = 650
No, = 850
Cs
Ni = 350
The design variables are d;, the diameter of the ith step, and w the width of the belt
and each step. The objective of this system is to minimize the weight of the step-
cone pulley.
The weight (W) is found by the following equation
W = pw÷(d + d; + d; + d?+ d? + d?,+d? ,+ d? + d?n+ d?
in,4
in,5
'in,1
"in,2
"in,3
The diameters of the input pulley (din) are found by using the ratio between the
input shaft rpm and the target output rpm.
No;
dini = d;-
Nin
Transcribed Image Text:W W No, = 150 No2 = 250 Noz = 450 No4 = 650 No, = 850 Cs Ni = 350 The design variables are d;, the diameter of the ith step, and w the width of the belt and each step. The objective of this system is to minimize the weight of the step- cone pulley. The weight (W) is found by the following equation W = pw÷(d + d; + d; + d?+ d? + d?,+d? ,+ d? + d?n+ d? in,4 in,5 'in,1 "in,2 "in,3 The diameters of the input pulley (din) are found by using the ratio between the input shaft rpm and the target output rpm. No; dini = d;- Nin
The belt lengths required for the desired output speeds are determined by the
following equation:
No;
-1
Nin
d?
Td;
C; -
2
No;
1+
+
Nin
i = 1,2, 3, 4, 5
4а
The angle of the lap of the belt over the ith pulley step is:
No;
d;
Nin
0; = T – 2sin
2a
The tension on the tight side of the ith step is given by:
Ti = stw
The tension of the loose side of the ith step is given by
Tii
The belt length values are subject to the following constraints:
C1 – C2 = 0
C1 – C3 = 0
C1 – C4 = 0
C1 – C5 = 0
The constraint on the power transmitted is given by:
(Tii – Ti) rdin,i(350)
33000
The constraint on tension ratio can be given by:
> 2
Transcribed Image Text:The belt lengths required for the desired output speeds are determined by the following equation: No; -1 Nin d? Td; C; - 2 No; 1+ + Nin i = 1,2, 3, 4, 5 4а The angle of the lap of the belt over the ith pulley step is: No; d; Nin 0; = T – 2sin 2a The tension on the tight side of the ith step is given by: Ti = stw The tension of the loose side of the ith step is given by Tii The belt length values are subject to the following constraints: C1 – C2 = 0 C1 – C3 = 0 C1 – C4 = 0 C1 – C5 = 0 The constraint on the power transmitted is given by: (Tii – Ti) rdin,i(350) 33000 The constraint on tension ratio can be given by: > 2
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