Rolling process – Modelling objectives and stakes

In the never-ending race for productivity and quality, the rolling mill industry makes extensive use of models of all kinds. From "on-line" computer models used to operate furnaces or rolling mills, to the most sophisticated "off-line" software, running on the latest generation of parallel computers and designed to increase technical knowledge, all degrees of complexity are represented, as are many disciplinary fields: thermics, fluid mechanics, solid mechanics, acoustics and vibrations, mechanics of materials, solid physics, chemical engineering, corrosion...

The aim of this article is to show what types of models are required to understand, individually or in their interactions, the various processes involved in metal deformation in a rolling mill, with a view to optimizing them in order to reduce costs - the ultimate objective of all these analyses. The aim here is not to detail the derivation and equations of these models (which can be found in the references cited), but to analyze their hypotheses in the light of physical realities, and thereby judge their practical contributions, actual or potential.

Rolling mills are rarely modeled for the sheer pleasure of knowledge. We generally seek to understand in order to improve the process, ensure product quality, make a plant more profitable, or guide future investments. It is therefore essential to optimize the quality/price ratio of the modeling itself. The first step in this article is therefore to categorize the multiple rolling operations (flat/long products, hot/cold rolling, thin/thick products), which have very specific thermomechanical characteristics and therefore require different modeling methods. The defects (geometric, metallurgical, surface) that need to be corrected constitute the second stage of the analysis, which leads to an overview of the modeling topics and the fields of physics that will be called upon. It then remains to analyze the mathematical methods that meet these specifications, depending on the precise nature of the objectives (stationary models / extremity modeling), the variables to be accessed, the time available (very fast "on line" models / knowledge-based "off line" models) and the quality of the physical data available.

A glossary and table of symbols are provided at the end of the article.