Metal Foams: A Design Guide

204 Metal Foams: A Design Guide
and rate, (2) a dedicated cost/unit of production which varies as the reciprocal
of the production volume (1/ Pn), and (3) a gross overhead/unit of production
which varies as the reciprocal of the production rate (1/ Pn). Plotted against
the production volume, n, thecost,C, has the form shown in Figure 16.2.
When the production volume, n, is small, the cost per kg of foam is totally
dominated by the dedicated tooling costs Ct. As the production volume grows,
the contribution of the second term in the cost equation diminishes. If the
process is fast, the cost falls until, often, it flattens out at about twice that of
the constituent materials.
1000
C
(Relative cost)
1
0
Tooling cost
dominates
50,000
100,000
Production volume
Variation of cost
with production
Material plus overhead
dominate
150,000
200,000
Figure 16.2 The variation of material cost with production volume
Technical cost modeling
Equation (16.3) is the first step in modeling cost. Greater predictive power is
possible by introducing elements of technical cost modeling or TCM (Field
and de Neufville, 1988; Clark et al., 1997), which exploits the understanding
of the way in which the control variables of the process influence production
rate and product properties. It also uses information on the way the capital
cost of equipment and tooling scale with output volume. These and other
dependencies can be captured in theoretical and empirical formulae or look-up
tables which are built into the cost model, giving greater resolution.
The elements of a TCM for liquid-state foaming of aluminum
Consider a cost model for the production of panels of a SiC-stabilized
aluminum-based metallic foam by the process illustrated in Figure 16.3 and
described in Chapter 2. There are four steps: