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independency from respective applications,
optimization is often regarded as a complex and
independent field of action. Thereby, commercial tools,
such as modeFRONTIER, are readily available for use
since a long time. Such tools allow to setup, perform
and automate optimization analyses in an easy way.
The optimization level (and, hence, potential savings)
depends to some degree on the development status of
a company. On the one hand, it is possible to perform
optimization on a relatively low level for the
Figure 6: Optimization of a support roller of a paper machine
parameters of a single product. On the other hand,
optimization can be considered as a tool of process
integration and automation, hence, to enable the
mapping and simulation of the complete process and
design chain.
Optimization of a bicycle frame
Figure 4 illustrates an optimization of a bicycle frame with
relatively traditional optimization objectives in structural
mechanics: The goal here is to minimize the stresses
caused by different loading conditions; at the same time,
the weight of the frame should be minimized. Moreover,
requirements regarding limits for maximum stresses
(tensile strength and fatigue resistance) have to be
observed.
In this example, the available geometric optimization
variables are some lengths, the thicknesses of the tubes
and their radial dimensions. In fact, with modeFRONTIER
the present problem can be described in a single run and
by integrating a single FEA application, as shown in Figure
5. Here, after an automatic analysis of the problem
structure, modeFRONTIER recommends to run the
optimization with a certain algorithm - in the present
case a Multi-Objective Genetic Algorithm MOGA-II, with
an appropriately generated DOE.
The optimization run takes place automatically and allows
a systematic Illustration of the results as, for example, by
using a Bubble Chart as shown in Figure 5 (b). Here, the
optimal solutions on the Pareto Frontier are clearly visible.
In this example, the automation enabled the engineer to
Newsletter EnginSoft Year 6 n°4 - 27
compute 300 designs within a few minutes time. Hence,
the design time was shortened, instead of wasting time
for multiple manual variations. Additionally, the
performance of the bicycle frame with respect to stresses
could be improved, while achieving significantly lower
weight conditions, which also led to lower material costs.
Design Chain Optimization
The relatively simple optimization approach applied to the
design of the bicycle frame already delivered significant
savings. This approach however is based on the (mostly
feasible) assumption that existing residual stresses, σ0,
inside the device can be neglected. These stresses derive
from upstream manufacturing processes. With regard to
the bicycle frame, we could consider such stresses being
related to welding, heat treatment, and quasi-static
bending (straightening) processes of the frame. If
available, this data could be used in a subsequent stress
analysis to take into account real initial stress conditions
and thus provide a far more accurate optimization. This
way, we would obtain a process chain with four different
applications which also can be mapped and optimized in
modeFRONTIER.
As another similar example, we can take a closer look at a
roller support of a paper machine, as illustrated in Figure
6. The roller support is manufactured by a casting process,
the weight of the first design was 476 kg. The
optimization goal here was to minimize the weight and
deformation at the same time. In addition, the castability
of the final form had to be guaranteed.
In this example, the sole and initially performed
optimization of the geometry (variation of 13 parameters)
with respect to the most extreme load-case delivered a
weight reduction from 476 kg to 360 kg, while the
deformation was reduced slightly. The verification of the
castability was performed using the software tool
MAGMASOFT (sand casting) in a second step after
optimization.
Analyzing the casting simulation, the results additionally
revealed zones with non-homogeneous microstructure and