Non Circular Arc Temper Rolling Model Considering Radial And Circumferential Work Roll Displacements

Abstract

Compared to usual cold rolling conditions the length of contact between work roll and strip is very short in case of temper rolling. As a consequence, work roll flattening becomes critical even for small contact pressures, and the simplifying assumption of a “circular arc” contour of the deformed work roll cannot be justified anymore. A new temper rolling model is presented applying a non circular arc theory using a semi‐analytical procedure for the calculation of the elastic work roll deformations based on numerical superposition of influence functions. In addition to the radial displacements of the work roll, also the circumferential displacements, generated mainly by the shear stresses acting on the work roll surface, are taken into account. The circumferential displacements heavily affect the relative speed (slip speed) between the surfaces of work roll and strip, this speed being a crucial input parameter for any friction law. Hence, the evolution of the shear stresses in the roll gap is re‐affected by these circumferential displacements. Their influence is increasing with decreasing temper degrees and cannot be neglected in such cases. The formation of a neutral zone instead of a neutral point is a natural consequence of this approach. The model for the strip is based on Karman’s theory. In addition to the elastic compression‐, elastic recovery‐ and plastic zone, also elastic regions are allowed to arise between plastic zones (Internal Elastic Zones). The consequence is that the case of contained plastic flow will appear automatically without additional simplifying assumptions. Simulation results from the new model are presented and discussed. Their comparison with results from FE‐simulations shows very good agreement. The model was calibrated against practical data from an existing temper rolling mill. For this purpose extensive temper rolling tests were performed.