A Response Surface Exit Crown Model Built from the Finite Element Analysis of a Hot-Rolling Mill
Stewart, William Elliott
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Nine independent and four dependent variables are used to build a response surface to calculate strip crown using the difference in the industry standard strip height measurements. The single element response surface in use provides the advantages of continuous derivatives and decouples rolling load from the determination of exit height. The data points to build the response surface are the product of a calibrated finite element model. The rolling dynamics in the finite element model creates a transient that requires nonlinear regression to find the system steady-state values. Weighted-least squares is used to build a response surface using isoparametric interpolation with the non-rectangular domain of the mill stands represented as a single element. The regression statistics, the 1-D projections, comparisons against other response surface models and the comparisons against an existing strip crown model are part the validation of the response surface generated. A four-high mill stand is modeled as a quarter-symmetry 3-D finite element model with an elastic-plastic material model. A comparison of the pressure distribution under the arc of contact with existing research supports the pressure distribution found with experiments conducted by Siebel and Lueg  and it also suggests the need for one improvement in the initial velocity for the strip in the finite element model. The strip exit heights show more sensitivity to change than strip exit crown in seven out of the nine independent variables, so a response surface built with the strip exit height is statistically superior to using the derived dependent variable strip exit crown. Sensitivity of strip exit crown and the strip exit heights to changes in work-roll crown are about equal. Backup-roll diameter sensitivity is small enough that oversampling for the mean trend has to be considered or ignore backup-roll altogether. Strip entry velocity is a new independent variable, unless the response surface is built from the derived variable, strip exit crown. A problem found is that the sensitivity of strip entry crown and work-roll crown requires a larger than typical incremental change to get a reliable measure of the change strip exit crown. A narrow choice of high and low strip entry crowns limits the usefulness of the final response surface. A recommendation is to consider the use of the strip cross-section as an exit crown predictor.
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