The prediction of applied force and torque during flat hot rolling.

A mathematical model has been used to calculate the roll force and torque produced under a wide range of flat hot rolling conditions.The technique used is based on the numerical solution to the Von Karman equation developed by Alexander and applied to cold rolling conditions. In the present work, extensions have been made that allow the use of a yield .stress which is dependent upon temperature, rate of deformation and extent of inhomogeneity of the deformation process. Like Alexander, the present model considers also the effect of both: the elastic zone at each end of the deformation region and of roll flattening on force and torque. A prerequisite for these calculations has been the experimental determination of the temperature gradients in the plate during rolling, the coefficient of friction between plate and rolls and the flow stress of the material at relevant temperatures and strain rates; the last named data being supplemented by published data on similar material. The results have been compared with experimentally determined force and torque required to roll mild steel plates at temperatures between 900C and 1200C, under uniubricated conditions.The coefficients of friction associated with percentage reductions of between 30 and were within the range 0.2--0.5. The thickness of the scale, the rolling velocity and the temperatures at the plate surface appeared to control the magnitude of the coefficient of friction. The peripheral layers of the plates underwent a severe quench, caused by rapid heat transfer to the rolls: the associated temperature reduction increased with increasing roll pressures and contact time. The resulting temperature gradient was implied in the calculation using a geometric mean of the individual temperature measurements. At rolling temperatures between 900 °C and 1000°C and reductions up to 35 the degree of agreement between the experimental and calculated roll forces and torques were +/-1 Jfo and +/-1% respectively, although the use of Suzuki's flow stress data reduced these discrepancies to about4 6% and4 11% respectively in most cases. However the use of higher reductions or higher, temperatures led to poorer agreement between calculation and experiment 2% and 4 35- in the case of roll force and torque respectively).