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The 20-high mills often face various flatness problems in the production of cold-rolled stainless steel thin strips. In the proposed model coupling method, the roll-stack elastic deformation equations and the strip plastic deformation equations are assembled into a single system of linear equations and solved simultaneously. This avoids the repeated iterative exchange between the two sub-models used in the conventional method, thereby significantly improving computational speed and numerical stability. Rolling calculations of 304 stainless steel thin strips show that the model coupling results agree with those of the traditional method. The root mean square error (RMSE) values for all variables are very small. Compared with the traditional method, the model coupling method gives very small RMSEs. For the symmetric shifting case, the RMSE is 5.48 × 10−4 mm for exit thickness and 3.61 I for flatness. For the asymmetric shifting case, the corresponding RMSEs are 3.80 × 10−5 mm and 5.57 I, respectively. Additionally, the influence of the first intermediate roll on symmetric and asymmetric roll shifting and ASU (Adjustable Support Unit) control on flatness was analyzed. For both symmetric and asymmetric roll shifting, the inter-roll pressure remains non-uniform and exhibits peaks. Adjusting the ASU can, to some extent, suppress many defects. However, ASU adjustment alone cannot completely eliminate high-order defects.
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Ren et al. (2026) studied this question.
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