A mathematical model for longitudinal temperature evolution in strip deformation zone during cold rolling

Abstract

Strip temperature is a critical control factor in the cold rolling process. In previous, most attention is paid to the total temperature rise in the strip rolling deformation zone, i.e., temperature grows approximately linearly from the entry to the exit. However, the rolling pressure, friction stress and contact condition show different characteristics in different longitudinal zones, which make the heat generation and transfer states different, so the strip temperature undergoes a complex change process. Here, an improved rolling pressure calculation model is proposed at first, where the entry-elastic and exit-elastic zones are added and the Karman differential equation is re-derived in the plastic zone. On this basis, a longitudinal temperature evolution model is proposed, which includes the temperature changes caused by the plastic deformation heat, the friction heat and the contact heat loss. Then, the effectiveness of the proposed model is verified by cold rolling plant experiments and finite element method, the results show that the new model has higher prediction accuracy in rolling force and temperature and can be applied to online control of cold rolled strip. Finally, the effects of different rolling parameters on total temperature are studied, and the results show that the temperature rise of friction heat increases slowly in the front of the rolling deformation zone, so the appearance of maximum temperature is closely related to the increment of the temperature rise of deformation heat against the temperature drop of contact heat loss. To avoid the maximum temperature appearing in the middle of deformation zone, it is useful to appropriately increase the rolling speed, reduce the strip entry temperature.