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4. Case studies
This chapter will present a number of real industrial applications where all the aspects
described and commented in the previous sections have been applied. Most of them come
from our personal experience, as acquiring enough, reliable and trustable details from other
people is usually difficult.
4.1 Prediction of Jominy profiles of steels
The
Jominy profile
of a steel is a curve obtained in a test, where a small cylindrical specimen
of steel is kept at a very high temperature (usually more than 1500 °C) and one end of the
specimen is cooled by quenching it for at least 10 min. in a water stream, while the other
specimen end is cooled in air. This treatment causes a cooling rate gradient to develop over
the length of the specimen, with the highest cooling rate corresponding to the quenched
end. This procedure affects the steel micro-structure along the length of the specimen and,
as a consequence, the steel hardness in the diverse portions of the test bar. The Jominy
profile is built by measuring the specimen hardness values
h
i
on the Rockwell C scale at
increasing distances
d
i
from the quenched end. Several studies investigated the correlation
between the shape of such curve and the steel chemistry (Doane & Kirkaldy, 1978) and some
of them applied neural networks to this purpose, such as (Vermeulen et al., 1996).
In particular Colla et al. (Colla et al., 2000) propose a parametric characterization of the
profile, namely the approximation of the generic profile with a parametric curve, and then
predict the shape of each profile through a neural network which links the steel chemistry to
the curve parameters.
This approach proved to be successful when the “shape” of the profile is constant (which
happens, for instance, when dealing with the same steel grades produced by one single
manufacturer). On the other hand, when facing the prediction of the Jominy curve of many
different steel grades manufactured by different steel producers, the actual shape of the
curve might considerably vary and the parametric approach is no more successful.
Fig. 1. Conceptual scheme of the sequential predictor of Jominy curves.
In fact, a different approach to the same problem has been proposed by Marin et al. (Marin
et al. 2007), where a neural sequential predictor has been proposed: here, apart from the first
two points of the curve (i.e. the ones corresponding to the lowest distance values from the
quenched end), each single point of the Jominy profile is singularly predicted by a neural
