Reliability-Based Optimal Cluster Mill Pass Scheduling

Optimal pass-scheduling on cluster-type cold rolling mills, use to process flat metals, presents added challenges over conventional (vertical-stack) mills due to the complexity of roll arrangements. Cluster-type rolling mills not only pose difficulties in modeling deflections occurring in the multi-roll stack, they also impose the burden of modeling more sophisticated mechanisms used to adjust rolling force distribution and achieve desired strip flatness. In a competitive global market for very thin gauge strip, an advantage is gained through use of efficient mathematical set-up models that can adequately optimize the flatness actuators according to the target gauge reductions for each rolling pass. The mill’s process control computer should therefore determine a gauge reduction schedule leading to minimum number of passes, while simultaneously assigning nominal flatness control actuator set-points. Although recent developments in roll-stack deflection modeling using simplified, mixed finite element techniques have enabled more efficient roll-stack deflection modeling in 20-high and other cluster mills, the optimal pass-schedule problem is still complicated by the abundance of geometric and mechanical property variations in the strip or sheet to be processed. Furthermore, problems with strip flatness frequently arise because of uncertainties in roll diameter profiles resulting from variations in the roll grinding and roll wear patterns. In this paper, we extend recent work in pass schedule optimization (through improved rollstack deflection) by applying First Order Reliability Methods to rigorously account for various rolling process uncertainties. The results allow predictive probability constraints for strip flatness to be included in the optimization problem, thus enabling mill operators some insight and control into the likelihood of achieving desired strip flatness for a given rolling pass schedule.