Theoretical Investigation on the Critical Thickness Conditions and Development of a Minimal Producible Thickness Model for Thin Strip Rolling

The growing demand for high-precision thickness control in cold rolling of metal strips calls for continuous improvement in rolling force prediction models. Classical thin-strip rolling theories, notably the Stone model, are based on the assumption of a circular roll arc profile within the contact deformation zone. In practice, however, this assumption often becomes invalid owing to the emergence of a neutral zone under specific rolling conditions, which introduces considerable errors in force calculation and compromises model applicability. To address this issue, the present study develops a numerical analysis framework for thin-strip rolling processes across a range of initial thicknesses and reductions. The proposed method quantitatively captures the effects of single-pass reduction on roll shape evolution and contact pressure distribution along the deformation arc. In addition, a limiting producible thickness model is proposed by incorporating the deformation efficiency of the strip material. This approach enables the precise delineation of a neutral-zone-free deformation regime and establishes a criterion for determining the optimal single-pass reduction based on the ratio of initial thickness to Stone minimum rolling thickness. For given initial thickness and process parameters, a critical single-pass reduction exists that eliminates the neutral zone, yielding a characteristic curve that divides the rolling regimes: above it, the neutral zone vanishes, the Stone model applies, and efficiency is high; below it, a finite neutral zone persists, partially dissipating rolling force in elastic deformation, though rolling remains viable within limits. These findings provide a robust basis for improving rolling force accuracy and pass optimization, ultimately enhancing product quality and forming efficiency in precision strip manufacturing.