Mathematical modelling of the interrelated electric and mechanical systems of continuous sub-group of the rolling mill stands. Part 1. Development of the mathematical model

The paper considers development of the mathematical model of the interrelated stands of the continuous sub-group belonging to the roughing train of the wide-strip hot-rolling mill. The paper substantiates the task of studies on repeated dynamic processes occurring in the electromechanical systems of the universal mill stand edging rolls at the strip gripping by rolls of the tandem horizontal roll stand. The dynamic torque is registered to be 2 to 2.5 times greater than the steady mill torque in this mode. The main reason for occurring repeated shock loads is incoordination of the speed of the strip leaving the edging stand rolls and linear speed of the horizontal stand rolls. To study the transfer of the kinetic energy to the motor shaft of the previous stand it is proved that developing the improved mathematical model of the deformation zone is reasonable. We propose to develop this model in reliance on the equation of the energy conservation at rolling. In the paper there is the structural diagram of the mathematical model of the interrelated electric drives of the edging and horizontal rolls of the three-stand 2,000 mm mill trains of OJSC Magnitogorsk Iron and Steel Works. The paper offers analytic expressions for calculation of the power supplied to the deformation zone from the roll drive motor side, the power supplied due to the metal front tension (looping) and rear looping (tension), the power consumed at gauge forming and power of the slipping friction power. In connection with it, the metal behavior in the deformation zone has been studied; mathematical expressions of the changing elementary velocities of points on the surfaces of the entrance and exit sections are provided. The paper gives dependencies of the metal sliding related to the rolls and slipping friction powers for lead and lag areas obtained with regard to the changing area of the proceeded metal and its resistance to deformation. Based on the obtained expressions, the structural diagram of the deformation zone model has been developed. Analytical and operator expressions for modeling tension and looping forces, as well as structure of the model describing elastic properties of the strip in the inter-stand space are presented. The paper delivers the structure of the mathematical model for electric drive speed control system based on the known equations of the anchor chain of the DC motor. After the comparison of the transient processes of the electric drive coordinates and rolling settings obtained at the modeling and oscillography at the mill the conformity of the developed model to the studied object has been proved. The provided mathematical model is recommended to be applied for examination of the power interaction of the electromechanical rolling mill systems, as well as for the analysis of the dynamical modes at the strip gripping by the edging and horizontal stand rolls.