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An improved method for calculating roll deformation of six-high rolling mill: enhances computation speed and accuracy

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Abstract

The roll deformation model of the six-high rolling mill is one of the core models of the strip shape control theory. The influence function method (IFM) is a numerical method applied to solve the roll deformation problem. This study aims to address the problems of slow calculation speed and insufficient calculation accuracy of IFM in calculating the roll deformation of the six-high rolling mill. Three optimization measures are proposed, namely, optimizing the iterative calculation order of the roll deformation to improve the calculation efficiency; introducing the Adam (Adaptive Moment Estimation) gradient descent optimization algorithm to enhance the stability of the iterative process; and introducing a high-precision rolling force model based on the XGBoost (eXtreme Gradient Boosting) algorithm to improve the calculation accuracy of flatness in the IFM. Parallel experimental results show that by applying the three optimization measures simultaneously, improving the iterative calculation order of the roll deformation can improve the calculation speed by about 7.64 times; introducing the Adam algorithm can reduce the oscillation range of roll contact pressure by an average of 50.4%, increasing the stability of the calculation process; and introducing a high-precision rolling force model based on the XGBoost algorithm can improve the flatness calculation accuracy by about 39.1%. This study provides an effective method to improve the calculation speed and accuracy of the roll deformation in a six-high rolling mill, which has important academic application value.

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Data availability

All data generated or analyzed during this study are included in this manuscript.

Code availability

Not applicable.

Abbreviations

W, I, B :

Work roll, intermediate roll, support roll

L, R :

Left, right

F W, F I :

Work roll bending force and intermediate roll bending force

A:

Unit column vector, A = [111…1]T

P L, P R, P :

The vector of rolling force of the work roll on the left side, right side, and overall

Y WL, Y WR, Y W :

The elastic bending of the work roll on the left side, right side, and overall

Y IL, Y IR, Y I :

The elastic bending of the intermediate roll on the left side, right side, and overall

Y BL, Y BR, Y B :

The elastic bending of the support roll on the left side, right side, and overall

Q WIL, Q WIR, Q WI :

The vector of contact pressure between the work roll and the intermediate roll on the left side, right side, and overall

Q IBL, Q IBR, Q IB :

The vector of contact pressure between the intermediate roll and the support roll on the left side, right side, and overall

G WL, G WR :

The influence function matrix of the bending on the left and right sides of the work roll

G IL, G IR :

The influence function matrix of the bending on the left and right sides of the intermediate roll

G BL, G BR :

The influence function matrix of the bending on the left and right sides of the support roll

G FWL, G FWR :

The influence function matrix of bending roll force on the left and right sides of the intermediate roll

G IWL, G IWR :

The influence function matrix of bending roll force on the left and right sides of the intermediate roll

Y WI, Y IB, Y WS :

The elastic flattening between the work roll and the intermediate roll, elastic flattening between the intermediate roll and the backup roll, and elastic flattening of the work roll caused by rolling force

G WI, G IB, G WS :

The influence function matrix of elastic flattening between the work roll and the intermediate roll, influence function matrix of elastic flattening between the intermediate roll and the backup roll, and influence function matrix of elastic flattening of the work roll caused by rolling force

M W, M I, M B :

The curvature vector of the work roll, intermediate roll, and backup roll

Y WI 0, Y IB 0, Y WS 0 :

YWI, YIB, and YWS located at the center of the strip

H, H C :

Strip thickness vector after rolling, half of the thickness at the center point of the strip

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Funding

This work was supported by the Natural Science Foundation of Liaoning Province (Grant No. 2020-MS-094). Moreover, the authors are very grateful to Yilin Zhou, chief engineer of the Cold Rolling Mill of Panzhihua Steel and Vanadium Co., Ltd., for providing production rolling data and suggestions.

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Authors and Affiliations

  1. State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang, 110819, China

    Yafei Chen, Pingjie Feng, Jihan Zhou, Lianggui Peng & Changsheng Li

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  1. Yafei Chen
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  2. Pingjie Feng
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  3. Jihan Zhou
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  4. Lianggui Peng
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  5. Changsheng Li
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All authors contributed to the study conception. The manuscript has been written by all authors. All authors read and approved the final manuscript.

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Correspondence to Lianggui Peng or Changsheng Li.

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Chen, Y., Feng, P., Zhou, J. et al. An improved method for calculating roll deformation of six-high rolling mill: enhances computation speed and accuracy. Int J Adv Manuf Technol 130, 3755–3770 (2024). https://doi.org/10.1007/s00170-024-12950-z

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