Analysis of flatness control capability based on the effect function and roll contour optimization for 6-h CVC cold rolling mill

The 6-high continuously variable crown (6-h CVC) cold rolling mill shows limited capability to control coupled edge and center waves for both narrow strip and ultra-wide strip production. In order to solve this problem, an integrated three-dimensional (3D) elastic-plastic finite element model (FEM) of rolls and strip is built to calculate the effect functions in consideration of work roll bending (WRB), intermediate roll bending (IMRB), and CVC intermediate roll shifting (IMRS) with different strip widths. A set of orthogonal vectors which is defined as eigenvectors is proposed to analyze the similarities and the complementarities of the effect functions. It is applied to study the flatness control characteristics of the cold rolling mill. Based on the analysis of flatness stress characteristics of different strip widths in the production, it is found that the similarities between the flatness stress and the eigenvectors of different strip widths are relative low. The flatness defects are difficult to be eliminated. From the relationship between IMRS and strip widths, a segmented CVC intermediate roll contour is then proposed and experimented in an industrial production. The proportion of coupled edge and center waves is decreased by 15.2%, and the overall flatness is reduced by 0.7 IU.