Optimization of a two-high cambered mill for the foil rolling

Rolling is one of the fundamental metals forming processes used for producing metallic foils with extensive industrial and commercial applications. In this study, the optimal curvature of rolls in a two-high foil-rolling system employing identical cambered rolls was determined through a comprehensive mathematical model. The foil–roll contact pressure distribution along the roll axis was obtained by accounting for both elastic deflection and local flattening of the rolls through an iterative computational approach. Because elastic roll deformation causes non-uniform foil thickness across the width, cambered rolls were adopted to minimize this variation. Two key design parameters—the curvature radius of the cambered roll and the roll-edge gap—were optimized through four iterative cycles to achieve a uniform thickness distribution. For a 36% thickness reduction of aluminum foil with an initial thickness of 100 μm, the optimal curvature radius and edge gap were determined as 59 m and 57 μm, respectively. Under these optimized conditions, the foil thickness variation decreased from 4.9 μm (in cylindrical rolling) to 1.3 μm, with a maximum deviation from the target thickness limited to 1 μm. These findings demonstrate that a two-high mill can achieve comparable uniformity in foil thickness through proper selection of the roll-edge gap and curvature radius.