Thermal expansion and crown evaluations in rolling processes

An understanding of thermal expansion of work rolls is essential for proper control of flatness of a rolled strip in operating a modern, high-speed rolling mill. In this paper, an analytical solution has been developed to provide thermal displacements and expansions of the roll. The thermal expansion data, in turn, can be utilized to estimate thermal crown for shape control and contributes to alleviation of many shape problems of the rolled product. The thermal displacement potential function has been used to solve the governing partial differential equations for the thermal displacements. The general stress function was then obtained to modify the displacement potential solution, to satisfy the boundary conditions of the free roll surface. To demonstrate the accuracy and reliability of the solution developed, the results of the present solution have been compared with previously published numerical and experimental results at typical rolling conditions; good agreement is found between them. A parametric study is then performed to provide needed information for proper control of the roll and strip shape in operating a high-speed rolling mill.