Rolling processes - 2D thermomechanical analysis and application to flat products

Rolling mills are extremely diverse. The reason for this is that the rolled products themselves form very different families in terms of geometry (long and flat products, tubes, rings, etc.), dimensions (from thick sheet for shipbuilding to thin aluminum foil for food use), metals and alloys used (few are not rolled), and temperatures of course (cold rolling, hot rolling, and the hot of aluminum is not the same as the hot of steel). This leads to a diversity of stresses, temperature ranges and precision requirements, all of which call for very different tools and machines.

Beyond these differences, the behavior of all these rolled products and the behavior of rolling mills follow immutable laws: those of plastic deformation of metals, those of elastic deformation of structures and those of heat transfer. The ambition of this text is to highlight the common features of all rolling operations conferred by these universal laws, while showing how these physical laws, each responding in their own way to the size and time scales present in rolling mills, lead to highly typified behaviors.

We therefore focus exclusively on the mechanical and thermal aspects of rolling flat products, as these are simpler to analyze and therefore more instructive. We compare them with practical experience, and show how various types of model enable us to move from a general view of the process to a more intimate look at the behavior of this complex system. The aim is to explain why a particular type of stand is chosen for a given rolling operation, how the interweaving of economic considerations and technical arguments leads to the design of a different range for different metals, and how these choices then condition product quality. Over and above the immediate technical aspects, we make the choice of a model adapted to a given objective more concrete. Ultimately, the aim is to highlight the current state of theoretical knowledge and modeling methods used to advance rolling processes.

A glossary, a table of symbols and a table of indices are presented at the end of the article.