20-High rolling mills process high strength and/or very thin non-ferrous and ferrous metals using a complex, cluster arrangement of rolls. The 20-high roll cluster arrangement achieves specific flatness goals in the thin sheet by delivering maximum rolling pressure while minimizing the deflections of the small diameter rolls. 20-high mills also employ flatness control mechanisms with sophisticated actuators, such as those to shift intermediate rolls and deflect backup bearing shafts. The purpose of this is to compensate for variations in strip dimensional and mechanical properties which can cause poor flatness control quality from discrepancies in work-roll gap profile and distribution of rolling force. This suggests that the random property differences in the rolling parameters that substantially affect the flatness must be directly accounted for in flatness control algorithms in order to achieve strict flatness quality. The use of accurate mathematical models that account for the rolling pass target gage reduction can optimize the flatness control actuators and help gain an advantage in the thin gauge strip competitive global market. Based on the expected process parameter variations and nominal mill set-points (speed, tension, gage reduction, etc.), the mill’s process control computer should determine the probability that target flatness control quality will be met for a required length of strip. The process computer should then either modify the number of rolling passes or adjust the thickness reduction schedule before rolling begins to secure an improved flatness probability estimate if the probability of achieving target strip flatness is too low for the required deliverable quality. Therefore, this research integrates 1) 20-high roll-stack mill mathematical modeling, 2) probability distribution data for random important rolling parameters, 3) reliability-based models to predict the probability of achieving desired strip flatness, and 4) optimization examples. The results can be used to reduce wasted rolled metal from poor flatness before rolling.

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