Semi-Analytical Model for Predicting Roll Forces in the Finishing Stage of H-Beam Rolling and Its Application to determine Setup Roll Gap

Abstract

This study presents a semi-analytical model to accurately predict roll force and setup roll gap (G_set) in the finishing stage of H-beam rolling. The model modifies Sims' classical strip rolling formula to capture the unique geometric and deformation characteristics of H-beam sections. The cross-section is divided into web and flange regions using a rectangular approximation. A geometry-dependent correction function is then introduced to account for the effects of reduction ratio, reduction balance, and contact geometry. This function is calibrated through finite element (FE) simulations under varying rolling conditions. Parameters such as web and flange thickness reduction, junction radius, and flange inclination are systematically adjusted, and the resulting roll forces are used to optimize the function via the Nelder–Mead method.

The model is validated using two H-beam specifications from Hyundai Steel. Compared to the company's empirical model, the proposed model reduces web and flange thickness deviations by up to 71%, demonstrating improved prediction accuracy. Statistical analysis also shows substantial reductions in standard deviation and mean error, confirming better dimensional control. This semi-analytical model provides a fast, reliable alternative to full FE simulations and manual adjustment procedures, improving both efficiency and product quality in industrial H-beam rolling.