Making Industrial Processes More Cost Efficient

Copper Precipitation Hardening

Nonlinear modeling speeds up process development of precipitation hardening of chromium‑zirconium alloyed copper

Process development is conventionally carried out by a relatively large number of trial and error experiments in the metal industry. This is not very efficient since a large number of experiments are carried out, from which very limited amount of knowledge is derived, and it is not easy to find process conditions close to the optimum. Efficient process development can be performed with much less but systematic experimentation, followed by nonlinear modeling, as demonstrated in this article.

To be able to determine the optimal operating conditions, it is necessary to have a good quantitative knowledge of the effects of process variables on the final consequences of the process, like product properties, energy consumption, production rate, etc. Such mathematical models can be developed with different approaches which are suitable in different situations. Physical modeling is particularly suitable when no experiments can be carried out and no production data is available. However, it is not particularly suitable for prediction of material properties without involving a lot of empiricism. Empirical modeling is suitable when it is easy to carry out experiments or if plenty of production data is easily available. Empirical modeling has been carried out conventionally using linear statistical techniques, which have their limitations because nothing in nature is absolutely linear. New techniques of nonlinear modeling have proved to be particularly effective for metallurgical processes, which have otherwise been considered difficult to model. This article contains a nice example which demonstrates how nonlinear modeling has been effective at speeding up process development of a precipitation hardening process for a copper alloy.

Good process development can result in better production economics than can be achieved by operating in countries with low labour costs. To be able to produce the product most cost efficiently while fulfilling the requirements on product properties and other constraints, it is very advantageous to have mathematical models which relate the important variables in the process.

Process development of metallurgical processes is often carried out by performing a large number of experiments, for the simple reason that development of mathematical models of most metallurgical processes is too complicated. Physical modeling is not very effective, neither is empirical modeling with conventional linear statistical techniques. New techniques of nonlinear modeling have altered this situation entirely, and offer a tremendous advantage in quantitatively describing complicated metallurgical processes. Nonlinear models have successfully been used for a large number of processes in various industrial sectors.

How these models in combination with appropriate mathematical tools help in efficient process development with much less experimentation is demonstrated with an example. Besides a little bit of theory, the article also explains the strengths and limitations of these new techniques.