Online calculation model of rolling force for cold rolling mill based on numerical integration

Based on comprehensive consideration of elastic and plastic deformation of both strip and work roll, an online rolling force model for tandem cold rolling mill has been developed by numerical integration method in this paper. According to the load equilibrium equation and the boundary condition, the vertical stress of every unit can be obtained. The rolling force in the plastic deformation zone can be calculated via the sum of vertical stress of every unit, and the total rolling force can be obtained by summing rolling force of elastic and plastic deformation zones. In addition, the suitable mathematic models of friction coefficient and strip deformation resistance were also established. In accordance with the coupling problem between the flatten roll radius and rolling force, the iterative procedure by computer was built. This rolling force model has been applied to a 5-stand tandem cold mill and the relative error of rolling force prediction is within ±4.1%, which proves the model is accurate and meets the requirement of online process control.