Numerical Assessment of Interstand Tensions in Continuous Hot Rolling Processes of Flat and Long Products

The paper deals with the calculation of interstand tensions in continuous rolling mills for flat and long products. In the rolling mill industry, the digitization has reached a state in which a continuous measurement and data collection of roll forces, roll torques, temperatures and roll velocities is possible. However, the important process parameter of interstand tensions is not directly measurable and no direct calculation of the interstand tensions in the form of mechanical stresses is possible. A fast calculation method for the interstand tensions from measurable process quantities is a critical point to enable the construction of digital twins for the rolling process of continuous rolling mills.
It is straightforward to calculate the effects of the tensions on roll forces, torques and the strip or bar velocity. However, the inverse problem of calculating the acting interstand tensions including their effects from the process parameters is of much greater interest but also of a higher complexity, because the interactions between all of the stands in the continuous rolling mill must be taken into account.
The present paper aims at filling this research gap by presenting a mathematical model to solve the inverse problem by subsequent linearization of the tensions influences in the rolling mill. Extra nonlinearities are taken into account by modeling the tension-dependent spread by an empirical model. The overall model is solved by an iteration method to yield a fully compatible solution for the constant volume flux as well as the force and torque equilibria in the roll gaps. Results are shown for the tension distributions in strip and rod mills. The results indicate that the present friction conditions and the spreading behaviour of the rolled material have a high impact on the tension distributions.