Degree Name

Doctor of Philosophy


Department of Mathematics


The high quality requirements of sheet metal (eg steel, aluminium) and the modern trends towards computer control of sheet rolling have placed an increasing emphasis on a thorough understanding of the physics of the flat rolling process. The examination of the thermal behaviour of the rolls and rolled product, as the latter is deformed in a rolling stand, is integral to an understanding of rolling. The thermal process occurring in the rolling stands affects the mechanical and metallurgical properties of the material, governs the roll cooling requirements, and influences the overall flatness of the rolled product. This thesis is primarily concerned with the prediction of the short-time variation of the temperature field of the rolls and rolled product, as the latter is deformed in a rolling stand. The effect of an oxide layer, which often exists in hot rolling of steel, on the thermal process has been studied in detail. It is demonstrated that, under normal rolling conditions, the thermal process occurring in rolling can be reduced by perturbation methods to one of heat transfer between three slabs with plane parallel boundary contact. As a result, the reduction in heat loss to the rolls and the increase in temperature of the rolled product due to the insulating effect of the oxide layer can be quantified. The contribution of each heat source term, namely, that arising from the effect of the bulk temperature difference between the roll and rolled product, frictional heating at the roll/rolled product contact region, and deformation heating in the rolled product within the roll gap, to the overall thermal process is estimated for both hot and cold rolling conditions.