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.In the rolling mill industry, 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 is possible. The interstand tensions couple the effects of subsequent roll gaps and should therefore by known for a holistic recalculation of the process. It is straightforward to calculate the effects of the tensions on roll forces, torques and the stock velocity. The inverse problem of calculating the acting interstand tensions including their effects from the process parameters is of greater interest but also of a higher complexity, because the interactions between all the stands in the rolling mill must be regarded. The present paper aims at filling this research gap by presenting a mathematical model to solve the inverse problem by a linearization of the tensions influences in the rolling mill. The present model does not require measured roll forces or torques to find the interstand tensions, only the rotational velocities of the rolls and the rolling parameters (material, temperature, pass schedule or pass design) must be known. Tension-dependent spread is considered by an empirical sub-model. Results are shown for the tension distributions in strip and rod mills. The results indicate that the present friction conditions and the entry size of the rolled stock have a high impact on the tension distributions.