Rapid prediction model for symmetric and asymmetric flatness of 20-high mills

20-high mills often face various flatness problems in the production of cold-rolled stainless steel thin strips. The flatness prediction model is essential for flatness control techniques. A novel rapid prediction model for flatness in a 20-high mill is proposed based on a model coupling method capable of forecasting the flatness of cold-rolled stainless steel thin strips under symmetric and asymmetric rolling conditions. The model integrates deformation coordination equations between rolls, force and moment balance equations, strip exit transverse displacement equations, and no-load roll gap equations into a unified set of linear equations. This solution process avoids repeated iterations between the elastic deformation model of the roll system and the plastic deformation model of the strip, which is a limitation of the traditional method and significantly improves the calculation speed and stability. The accuracy of the model was verified via a ZR22B-52 Sendzimir 20-high mill. The measured and calculated flatness values highly coincided, confirming the model’s accuracy. Rolling calculations of 304 stainless steel thin strips demonstrate that the new model results are consistent with those of the traditional method. The calculation time of the new model is only approximately 0.04%-0.35% that of the traditional method. On this basis, the impact of common flatness control methods on the flatness has been analyzed.