A Statistical-Based Model of Roll Force During Commercial Hot Rolling of Steel

This research introduces a new model to predict the roll force during hot rolling of steel, based on a statistical analysis of approximately 38,980 sets of measurements in a commercial mill with five finishing stands. The study includes ten different steel grades and features models of both single grades and the entire dataset. Three models are developed and compared: a temperature-dependent strain rate model (M1), a strain rate model (M2), and a simplified strain rate model (M3). The decrease in temperature with roll stand has a strong cross-correlation with compensating decreases in strain and contact length by roll stand, such that both the temperature and strain terms are statistically insignificant. The final model (M3)—<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mrow><mo>[</mo><mi mathvariant="normal">N</mi><mo>]</mo></mrow><mo>=</mo><mn>113.1</mn><mo>·</mo><mover accent="true"><mi>ϵ</mi><mo>˙</mo></mover><msup><mrow><mo>[</mo><msup><mi mathvariant="normal">s</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>]</mo></mrow><mrow><mn>0.3141</mn></mrow></msup><mo>·</mo><mi>w</mi><mrow><mo>[</mo><mi>mm</mi><mo>]</mo></mrow><mo>·</mo><mo>ℓ</mo><mrow><mo>[</mo><mi>mm</mi><mo>]</mo></mrow></mrow></semantics></math></inline-formula>—relates force (<i>F</i>) to strain rate (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>ϵ</mi><mo>˙</mo></mover></semantics></math></inline-formula>), width (<i>w</i>), and contact length (<i>ℓ</i>) and achieves an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>R</mi><mn>2</mn></msup></semantics></math></inline-formula> fit of 0.946 over all 10 steel grades. Although the single-grade models show slightly higher accuracy, the final model retains robust predictive capability with only two fitting parameters. This model enables fast and easy estimation of roll force for commercial hot rolling of low-carbon, medium-carbon, and high-strength–low-alloy steels.