Thermal-Mechanical Modelling of the Flat Rolling Process

Computer control of strip and plate rolling equipment requires the use of a predictive -adaptive mathematical model of the process and of the equipment. The purpose of the predictive portion is to compute the process parameters, given the desired mechanical and metallurgical properties and the final dimensions of the product along with its initial metal­lurgical make-up. The adaptive part should be designed to make use of the results of the predictive model, analyze them in combination with data supplied by the sensors and monitor and correct the settings of the mill parameters during rolling. Further, it should have a learning component, storing all relevant information during production runs, for future use.

The equations describing the thermal and mechanical events in the roll gap need to be supplemented with appropriate boundary and initial conditions. For the mechanical component these include the resistance to deformation of the metal to be rolled, the frictional forces at the roll-strip interface and the shape of the deformed contact surface. Knowledge of the interface heat transfer coefficient is essential in order to formulate the boundary conditions applicable to the thermal component of the model.

There are three sections in this chapter. The first includes the description of the conventional mathematical models applicable for cold and hot rolling, developed by Orowan, Sims, Bland and Ford, Ford and Alexander and Tselikov. In the second a refinement of the one-dimensional models is presented and a new philosophy guiding the improvement of computational accuracy and consistency is described. The third section contains an assessment of the assumptions introduced in various models and experimental substantiation.

The conventional analytical methods discussed in the previous chapters accounted for mechanical events in the deformation zone. Thermal phenomena were considered only by introducing the temperature-dependent properties of the rolled metal. Realistic analysis of the flat rolling process indicates however, that the events taking place during a pass should be properly looked at as a thermal-mechanical problem. Arbitrary separation of these components may lead to erroneous appreciation of the variables and parameters that characterize the process. A list of the most important of these combined phenomena includes:

A common feature of some metal forming operations, such as rolling, drawing or extrusion, is the flow of metal through a converging channel. Changes in the displacement and velocity components are unavoidable in the material travelling through this channel. These changes also tend not to be the same for all particles of the material. When they differ, as they generally do, gradients of strain and strain rate are the result.

Mathematical modelling of the flat rolling process has been considered in this book with the emphasis placed on experimental substantiation of the predictions of the models. A general formulation of the problem has been presented in Chapter 1. In Chapter 2, phenomena, common to both one and two-dimensional analyses, have been discussed, these being the interfacial forces during rolling and the material’s resistance to deformation. The traditional models, based on equilibrium considerations, have been treated next. Thermal-mechanical modelling and a description of the role of the shape coefficient are included in the following chapters.