Modelling of Spread and Side-Form Function in Hot Rolling by Different Upper-Bound Approaches

Physically based models for predicting the spread behaviour in hot rolling are developed. The energy minimisation method the upper-bound technique is used to take advantage of an analytical formulation of the problem and its fast calculation compared to numerical methods like the finite-element method. It is shown that the formulation of the velocity field, the equation for the transition function from rollgap entry to exit, and the accurateness of the consideration of the boundary conditions for the velocities influence the result considerably.

Moreover, the model shall fulfil the practical needs in industry. Here, the conditions of a roughing stand are of highest interest. This means that with several passes the roll-gap aspect ratio and the reduction are varied. Additionally the model shall describe the situation of different thickness-width ratios. The application of this model to industrial hot rolling demands a sufficiently good assumption for the flow stress with respect to the material and the strain, strain rate and temperature.

In this paper the highest stress is laid on the comparison of the different approaches. Velocity discontinuities at the entry to the plastic zone as well as at the exit should be avoided or at least it must be judged how big their influence is. First attempts are carried out by introducing a weighted function in the equation for the longitudinal velocity.

All results are compared to experiments performed in the laboratory mill of Max Planck Institute for Iron Research. A special attention is laid on a good accordance of the computer results with those gained in an industrial plant.