Development of a stream function-upper bound analysis applicable to the process of plate rolling

Abstract

Purpose – The purpose of this paper is to develop a mathematical solution to estimate the deformation pattern and required power in cold plate rolling using coupled stream function method and upper bound theorem. Design/methodology/approach – In the first place, an admissible velocity field and the geometry of deformation zone are derived from a new stream function. Then, the optimum velocity field is obtained by minimizing the corresponding power function. Also, to calculate the adiabatic heating during high speed rolling operations, a two-dimensional conduction-convection problem is sequentially coupled with the mechanical model. To verify the predictions, rolling experiments on aluminum plates are conducted and also, a finite element analysis is performed by Abaqus/Explicit. The predicted deformation zone is then compared with the experimentally measured region as well as with the results of the finite element analysis. Findings – The results show that the predicted deformation zone and the temperature distribution fit reasonably with the experimental data while much lower computational cost needs comparing to the fully finite element analysis. Originality/value – A new stream function is proposed to properly describe the velocity field and deformation pattern during plate rolling considering the neutral point. Furthermore, the employed algorithm can be simply coupled with the thermal finite element analysis.