Analytical model for temperature prediction of hot-rolled strip based on symplectic space Hamiltonian system

Abstract

The cooling process of hot-rolled strip has an important influence on the mechanical and metallurgical properties of the final product. In particular, the uneven temperature of the hot-rolled strip in the run-out table cooling after rolling will lead to the formation of residual stress and eventually cause the flatness defects. Therefore, this study focused on the temperature distribution prediction of steel strips during run-out table cooling. For this purpose, an analytical model for calculating temperature distribution of strip width and thickness is presented. It is different from the traditional analytical models, this study introduces the two-dimensional heat conduction equation with an internal heat source under the traditional Lagrange system into the symplectic space Hamiltonian system to obtain the symplectic dual equations. Meanwhile, symplectic superposition method is used to deal with complex cooling boundary conditions. The symplectic analytical solution of the two-dimensional temperature field is calculated by strict derivation without any assumptions or predetermination of the solution forms. In order to verify the accuracy of the symplectic analytical solution, a temperature−phase transformation coupled finite element model for run-out table cooling of hot strip was established. Then the accuracy of the finite element model is verified by the measured data. Finally, it has been determined that the symplectic analytical solution exhibits a high degree of consistency with the computed results obtained from the finite element model.