Civil Engineering Reference
In-Depth Information
FIGURE 5.10
Backward tracing method for the preform design of an axisymmetrical part—left: backward simu-
lation starting from the final part—right: forward simulation using the preforming tool derived from the obtained
prefom (a-c) preforming operation (d-e) finishing operation [41] (with permission).
This powerful method has some important shortcomings which have motivated some of its users to
move to more general optimization methods [69]. First, it does not actually suggest a design of the
preforming tools, but the shape of the preform itself. So there is no guarantee that this preform can be
produced by forging, and that the preforming tools might not be too complex. In fact, it seems difficult
to introduce shape constraints for the preforming tools. Second, it is not possible to know whether the
proposed preform is optimal or not with respect to the design objectives. This way, this method can be
rather considered as an efficient way to suggest new preform shapes, which will be further investigated
and optimized by finite element direct simulations. The concurrent optimization methods, although they
look less advanced today, have much more potential.
Design Techniques Based on Optimization Methods
These methods are based on the direct numerical simulation of the process. Using optimization tech-
niques, several designs are tested in order to find the best one. In a first step, it is necessary to identify
the various parameters, (
p
)
,
, of the process which have to be optimized. Npar is the number of
k
k
1
Npar
such parameters and
is the vector of the parameter values. As mentioned earlier, the
possible parameters are: the shape of the initial billet, the shape of the dies of the preforming tools, the
process parameters such as the dies velocities and temperatures, the billet temperature, etc. In a second
step, a mathematical function, the objective function
p
(
p
)
k
k
1,Npar
, has to be defined in order to measure the quality
of the design for a given set of parameters. For instance,
can be the distance between the obtained and
the desired part, the severity of the forming defects such as folds, the forming energy, the metallurgical
qualities of the final part, etc. Eventually, the design has to obey a certain number of constraints. There
can be both equality C
constraints, such as geometrical constraints regarding the shape
of the preforming dies, the maximal values of the forming velocities and pressures, or any of the funda-
mental quality requirements such as the absence of defects. So, the problem can be summarized as:
and inequality C
1
2
find
p
such that:
()
p
MIN
()
p
C
1
p
()
0
(5.1)
p
,
()
C
2
p
0
