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10.1
Introduction
and
synopsis
These case studies illustrate how the techniques described in the previous chapter really work. Two
'were sketched out there: the light, stijJ; strong beam, and the light, cheap, stiff beam. Here we
develop four more. The first pair illustrate multiple constraints; here the active constraint method is
used. The second pair illustrate compound objectives; here a value function containing an exchange
constant. £$, is formulated. The examples are deliberately simplified to avoid clouding the illustra
tion with unnecessary detail. The simplification
is not nearly as critical as it may at first appear:
the choice of material is determined primarily
by the physical principles of the problem, not by
details of geometry .The
principles remain the same when much of the detail is removed so that
the selection is largely independent of these.
Further case studies can be found in the sources listed under Further reading.
conrods
for
10.2
Multiple
constraints

highperformance
engines
A connecting rod in a high perfonnance engine, compressor or pump is a critical component: if
it fails, catastrophe follows. Yet to
minimize inertial forces and bearing loads it
must weigh
as little as possible, implying
the use of light, strong materials, stressed near their limits. When
cost, not perfonnance, is the design goal, conrods are frequently made of cast iron, because it is
so cheap. But what are the best materials for conrods when performance is the objective?
The
model
Table 10.1 sultlmarizes the design requirements for a connecting rod of minimum
weight with
two constraints: that it must carry a peak load F without failing either by fatigue or by buckling
elastically. For simplicity, we assume that the shaft has a rectangular section A = bw (Figure 10.1).
The objective function is an equation for the mass which we approximate as
m = fJALp
(10.1)
where L is the length of the conrod and p the density of the material of which it is made, A the
crosssection of the shaft and .8 a constant multiplier to allow for the mass of the bearing housings.
Case studies: multiple constraints
and compound objectives
10.1
Introduction and synopsis
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229
Table 10.1
The design requirements: connecting rods
Function
Objective
Minimize mass
Constraints
Connecting rod for reciprocating engine or pump
(a) Must not fail by highcycle fatigue, or
(b) Must not fail by elastic buckling
(c) Stroke, and thus conrod length
L,
specified
Fig. 10.1
A connecting rod. The rod must not buckle, fail by fatigue or
by fast fracture (an example of multiple constraints). The objective is to
minimize mass.
The fatigue constraint requires that
F
A

<
0,
(10.2)
where
CT~
is the endurance limit of the material of which the conrod is made. (Here, and elsewhere,
we omit the safety factor which would normally enter an equation of this sort, since it does not
influence the selection.) Using equation (10.2) to eliminate
A
in equation (10.1) gives the mass of
a conrod which will just meet the fatigue constraint:
ml
=
BFL
(:)
(10.3)
pi
MI
=

(10.4)
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 Spring '07
 MILLER

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