Mechanisms and control strategies for spatial crossing of working rolls in S6-high cold rolling mills

As the primary equipment for producing high-strength thin strips, the S6-high cold rolling mill offers excellent thinning capabilities, but its unique floating working roll structure inevitably introduces complex product quality control challenges under load conditions. To address the tendency of floating small-diameter working rolls in S6-high cold rolling mills to undergo spatial crossing, which induces asymmetric flatness and transverse thickness deviation, an integrated roll and strip three-dimensional elastoplastic finite element model was developed and its accuracy validated. Two key parameters were examined, working roll cross angle and crossing centre offset. A closed-form expression was derived for the lateral distribution of the crossing-induced roll gap, and an analytical limit for the intermediate roll crossing angle was obtained from a minimum distance geometric constraint (limit 3.23°). Multi-condition simulations and mechanistic analysis indicate that a larger cross angle markedly amplifies asymmetric flatness and transverse thickness deviation, and that defects caused by positive versus negative angles exhibit mirror symmetry. Lateral displacement of the crossing centre further aggravates asymmetry, increasing the maximum transverse thickness deviation from 0.049 mm to 0.40 mm. Based on these results, the compensation mechanism between intermediate roll crossing and working roll crossing was elucidated, presetting the intermediate roll crossing state limited the profile error to RMSE 4.9 μm and MAE 3.9 μm. A process window using second and fourth order crown terms of the roll gap provides a visual control map linking crossing parameters to flatness response, offering a practical basis for stable thin gauge rolling and high-quality production in S6-high cold rolling mills.