20 Introduction to Optimization
Figure 1.10 Step-cone pulley.
SOLUTION The design vector can be taken as
X=
d 1
d 2
d 3
d 4
w
wherediis the diameter of theith step on the output pulley andwis the width of the
belt and the steps. The objective function is the weight of the step-cone pulley system:
f (X)=ρw
π
4
(d 12 +d 22 +d 32 +d^24 +d 1 ′^2 +d 2 ′^2 +d 3 ′^2 +d′ 42 )
=ρw
π
4
{
d 12
[
1 +
(
750
350
) 2 ]
+d 22
[
1 +
(
450
350
) 2 ]
+d 32
[
1 +
(
250
350
) 2 ]
+d^24
[
1 +
(
150
350
) 2 ]}
(E 1 )
whereρis the density of the pulleys andd′iis the diameter of theith step on the input
pulley.