2. Finite Element Modelling and Validation
To clearly analyse the strip deformation behaviour under asymmetric control, this paper constructs a static implicit finite element model of a 1450 S6-High mill based on ABAQUS 2022 software. The model contains seven components: a back-up roll, intermediate roll, work roll, side support roll, back-up bearing roll, a core shaft, and a strip. The rolls and back-up bearing roll are elastomeric, and the strip is constructed using an elastoplastic model [
16]. Since the side support roll system is assembled in a separate frame, the core shaft is set as a rigid body. The parameters of the roller system are given in
Table 1. To improve the accuracy of the finite element calculation, the positions of the contact zone between the rolls and the contact zone between the rolls and the strip have been refined. For load application, the rolling force is applied in the same way as in the real world, and the rolling simulation is performed by pressing down. For the application of bending roll forces, the effect of asymmetric bending rolls is considered. Therefore, four positions, WS (work side), DS (drive side), the upper roll system, and the lower roll system, are applied separately. The IRS are assembled according to a fixed spatial relationship between their positions. The model as a whole is shown in
Figure 1.
The movement of the model is divided into several steps: pressing down, applying bending rolls and tension, and rotating the roll. The main purpose of the model is to simulate the real rolling process of pressing down, building tension, and rolling after threading. The strip after the rotary rolling is taken as the research position. The specific rolling parameters of the model are shown in
Table 2, where taper coverage refers to the size of the tapered part of the roll covering the edge of the strip during the intermediate roll shifting. The rolled steel grade is 65 Mn with a more prominent asymmetric shape problem.
Simulation and validation of the model: In this paper, the accuracy of the model was verified by means of two verification modes: strip thickness reduction and side support roll pressure. For the actual production requirements, the required thickness reduction tolerance is usually within 10 μm. The actual thickness reduction was 0.579 mm, and the model simulation result was 0.571 mm, showing an error of 1.4%.
The same needed to be verified for the side support roll system, which is unique to the S6-High mill. Firstly, we constructed the numerical force model of the S6-High rolling mill roll system, as shown in
Figure 2.
Through calculations, the coordinates of the work roll positions for the S6-High rolling mill can be determined as shown in Equations (1) and (2) due to the control mechanisms.
where
and
is the centre position of the work roll;
is the radius of the work roll in millimetres;
is the radius of the side support roll in millimetres;
h is the thickness of the strip at the exit in millimetres; and
is the angle between the side support axis and the horizontal in degrees.
Simultaneously, based on the overall force balance of the roll system and the local force balance of the work roll, the force exerted on the side support can be calculated as shown in Equation (3).
where
represents the rolling pressure, kN;
is the exit tension, kN;
is the entry tension, kN;
denotes the work roll shifting angle;
is the angle between the line connecting the radius of friction circle between the intermediate roll and the work roll (N1) and the vertical;
represents the angle between the rolling support reaction force and the perpendicular line;
is the angle between the line connecting the centre of the work roll and the centre of the side support roll and the horizontal line; and
is the angle between the line connecting the radius of friction circle between the side support roll and the work roll (N2) and the horizontal.
In the actual production, the force of the side support roll is 223 kN, the finite element simulation result is 207 kN, and the numerical simulation result is 214 kN. The finite element simulation’s error is 7.2%. This indicates that the model can effectively represent the unique work roll shifting of the S6-High rolling mill during the rolling process. It is capable of studying the variation in the effectiveness of asymmetric control power with actual strip shape control parameters. The model’s accuracy meets the requirements of the simulation.
Author Contributions
Conceptualization, T.Y. (Tieheng Yuan) and T.Y. (Tingsong Yang); methodology, W.S. and T.Y. (Tieheng Yuan); software, T.Y. (Tieheng Yuan); validation, R.G.; formal analysis, R.G. and T.Y. (Tieheng Yuan); investigation, T.Y. (Tieheng Yuan) and T.Y. (Tingsong Yang); resources, W.S.; data curation, R.G.; writing—original draft preparation, T.Y. (Tieheng Yuan); writing—review and editing, T.Y. (Tingsong Yang); visualization, T.Y. (Tieheng Yuan); supervision, W.S. and R.G.; project administration, W.S.; funding acquisition, T.Y. (Tingsong Yang). All authors have read and agreed to the published version of the manuscript.
Funding
This research was funded by the National Key Technologies Research and Development Program (Grant Number: 2023YFB3812602), and the recipient of the funding is Tingsong Yang.
Data Availability Statement
The data presented in this study are available on request from the corresponding author due to privacy.
Conflicts of Interest
The authors declare no conflicts of interest.
References
- Wang, X.C.; Liang, Z.G.; Yang, Q.; Du, X.Z.; Liu, H.Q.; Zhang, Y. Asymmetric shape control theory and practice in cold strip mills. Adv. Mater. Res. 2011, 145, 204–209. [Google Scholar] [CrossRef]
- Xu, Y.; Wang, D.; Liu, H.; Duan, B.; Yu, H. Flatness Defect Recognition Method of Cold Rolling Strip with a New Stacked Generative Adversarial Network. Steel Res. Int. 2022, 93, 2200284. [Google Scholar] [CrossRef]
- Wen, J.; Zhang, Q.D.; Zhang, X.F.; Ye, X.W. Influence of roll profile configuration on high-strength strip flatness control performance in tandem cold rolling. Adv. Mater. Res. 2011, 145, 210–215. [Google Scholar] [CrossRef]
- Jiang, Z.Y.; Du, X.Z.; Du, Y.B.; Wei, D.B.; Hay, M. Strip shape analysis of asymmetrical cold rolling of thin strip. Adv. Mater. Res. 2010, 97, 81–84. [Google Scholar] [CrossRef]
- Chen, Y.; Peng, L.; Wang, Y.; Zhou, Y.; Li, C. Prediction of tandem cold-rolled strip flatness based on Attention-LSTM model. J. Manuf. Process. 2023, 91, 110–121. [Google Scholar] [CrossRef]
- Park, J.; Kim, B.; Han, S. Reinforcement Learning With Model-Based Assistance for Shape Control in Sendzimir Rolling Mills. IEEE Trans. Control Syst. Technol. 2022, 31, 1867–1874. [Google Scholar] [CrossRef]
- Valigi, M.C.; Papini, S. Analysis of chattering phenomenon in industrial S6-high rolling mill. Diagnostyka 2013, 14, 3–8. [Google Scholar]
- Wu, S.; Shao, Y.; Wang, L.; Yuan, Y.; Mechefske, C.K. Relationship between chatter marks and rolling force fluctuation for twenty-high roll mill. Eng. Fail Anal. 2015, 55, 87–99. [Google Scholar] [CrossRef]
- Wang, Z.H.; Gao, Q.J.; Chao YA, N.; Xia, Z.Y.; Zhang, Y.B. Calculation and Analysis of Force in Roll System of 20-High Sendzimir Mill. J. Iron Steel Res. Int. 2013, 20, 33–39. [Google Scholar] [CrossRef]
- Zhou, G.; He, A.; Liu, C.; Zhou, M.; Qin, J.; Liu, Z. Modeling and Simulation of Wide Commercial Pure Titanium Strip Rolling on Sendzimir 20-high Mill. Rare Met. Mater. Eng. 2020, 49, 2333–2339. [Google Scholar]
- Zhang, Y.; Yang, Q.; Wang, X.C. Control strategies of asymmetric strip shape in six-high cold rolling mill. J. Iron Steel Res. Int. 2011, 18, 27–32. [Google Scholar] [CrossRef]
- Yan, Z.W.; Bu, H.N.; Li, H.; Hong, L. Numerical simulation analysis of the rolling process based on the particle swarm hybrid algorithm. Ironmak. Steelmak. 2023, 50, 1321–1330. [Google Scholar] [CrossRef]
- Wang, P.F.; Zhang, W.X.; Wang, Y.H.; Zhang, D.H. Analysis of Actuator Performance Based on Actuator Efficiency in Flatness Control of Cold Rolling Mill. Adv. Mater. Res. 2011, 154, 344–348. [Google Scholar] [CrossRef]
- Prinz, K.; Steinboeck, A.; Müller, M.; Ettl, A.; Kugi, A. Automatic gauge control under laterally asymmetric rolling conditions combined with feedforward. IEEE Trans. Ind. Appl. 2017, 53, 2560–2568. [Google Scholar] [CrossRef]
- Alvarez, J.C.; Diez, A.B.; Alvarez, D.; Gonzalez, J.A.; Obeso, F. Thick unevenness compensation in a hot rolling mill having automatic gage control. IEEE Trans. Ind. Appl. 2002, 38, 559–564. [Google Scholar] [CrossRef]
- Cao, J.G.; Chai, X.T.; Li, Y.L.; Kong, N.; Jia, S.H.; Zeng, W. Integrated design of roll contours for strip edge drop and crown control in tandem cold rolling mills. J. Mater. Process. Tech. 2018, 252, 432–439. [Google Scholar] [CrossRef]
- Hai, Y.; Yang, T.; Wang, H.; Xu, Z.; Fan, M. Roll profile preset and control based on electronic temperature control technology. Metall. Res. Technol. 2022, 119, 512. [Google Scholar] [CrossRef]
- Sun, J.; Shan, P.F.; Wei, Z.; Hu, Y.H.; Wang, Q.L.; Peng, W.; Zhang, D.H. Data-based flatness prediction and optimization in tandem cold rolling. J. Iron Steel Res. Int. 2021, 28, 563–573. [Google Scholar] [CrossRef]
- Bu, H.N.; Zhou, H.G.; Yan, Z.W.; Zhang, D.H. Multi-objective optimization of bending force preset in cold rolling. Eng. Comput. 2019, 36, 2048–2065. [Google Scholar] [CrossRef]
- Wang, P.; Jin, S.; Li, X.; Huang, H.; Wang, H.; Zhang, D.; Yao, Y. Optimization and prediction model of flatness actuator efficiency in cold rolling process based on process data. Steel Res. Int. 2022, 93, 2100314. [Google Scholar] [CrossRef]
- Wang, Q.L.; Li, X.; Hu, Y.J.; Sun, J.; Zhang, D.H. Numerical analysis of intermediate roll shifting–induced rigidity characteristics of UCM cold rolling mill. Steel Res. Int. 2018, 89, 1700454. [Google Scholar] [CrossRef]
- Song, M.; Liu, H.; Xu, Y.; Wang, D.; Huang, Y. Decoupling adaptive smith prediction model of flatness closed-loop control and its application. Processes 2020, 8, 895. [Google Scholar] [CrossRef]
- Chen, L.; Sun, W.; He, A.; Liu, C.; Qiang, Y. Study on quarter-wave generation mechanism in DP980 steel during cold rolling. Int. J. Adc. Manuf. Tech. 2022, 120, 313–327. [Google Scholar] [CrossRef]
Figure 1.
Finite element model assembly.
Figure 2.
Schematic diagram of side support, work roll positions, and forces.
Figure 3.
Comparison of different fitting orders.
Figure 4.
Schematic diagram of asymmetric shape fitting.
Figure 5.
Section shape after rolling: (a) IRB = −100 kN; (b) IRB = 0 kN; (c) IRB = 100 kN; (d) IRB = 200 kN.
Figure 6.
Comparison of shape after rolling under symmetrical working conditions.
Figure 7.
Efficacy of asymmetric IRB of each order: (a) ; (b) ; (c) ; (d) .
Figure 8.
Section shape after rolling. (a) Schematic diagram of asymmetric IRS; (b) S = 70 mm; (c) S = 100 mm; (d) S = 130 mm.
Figure 9.
Efficacy of asymmetric IRS of each order: (a) ; (b) ; (c) ; (d) .
Figure 10.
The control ability of asymmetric IRB under different IRS.
Figure 11.
The control ability of asymmetric IRS under different IRBs.
Figure 12.
Comparison of equivalent shape control efficacy.
Figure 13.
Comparison of strip shape after rolling with equivalent working conditions.
Figure 14.
Comparison of strip shape after rolling for superimposition working conditions.
Figure 15.
Equivalent Relationship between IRB and IRS.
Figure 16.
S6-High Cold Rolling Mill.
Figure 17.
Flatness during actual production (a) before optimization and (b) after optimization.
Table 1.
Roller system parameter configuration.
Roll | Length/mm | Diameter/mm |
---|
Back-up Roll (Body/Neck) | 1450/580 | 1200/690 |
Intermediate roll (Body/Neck) | 1720/450 | 370/230 |
Work Roll (Body/Neck) | 1450/335 | 170/120 |
Side Support Roll (Body/Neck) | 1450/90 | 168/90 |
Back-up Bearing Roll | 75 × 15 | 150 |
Table 2.
Rolling parameters.
Rolling Parameters | Value | Rolling Parameters | Value |
---|
Rolling Pass | 1 | Strip width (mm) | 1250 |
Rolling Force (kN) | 8455 | Strip thickness (mm) | 4.3 |
IRB (kN) | 180 | Front unit tension (MPa) | 3.5 |
Taper coverage (mm) | 100 | Back unit tension (MPa) | 12.1 |
Table 3.
Asymmetric IRB working conditions design.
IRB/kN | DIRB/kN |
---|
−100 | −100, −50, 0, 50, 100 |
0 | −100, −50, 0, 50, 100 |
100 | −100, −50, 0, 50, 100 |
200 | −100, −50, 0, 50, 100 |
Table 4.
Asymmetric IRS working conditions design.
Coverage of IMR Taper/mm | Coverage Difference/mm |
---|
70 | −20, −10, 0, 10, 20 |
100 | −20, −10, 0, 10, 20 |
130 | −20, −10, 0, 10, 20 |
Table 5.
Equivalent IRS and IRB working conditions design.
Working Condition | IRB/kN | DIRB/kN | S/mm | DS/mm |
---|
A1 | 0 | −40 | 100 | 6 |
A2 | −100 | −50 | 100 | 8 |
A3 | 100 | −80 | 100 | 11 |
A4 | 200 | −90 | 100 | 12 |
Table 6.
Superimposition relationship of asymmetric IRS and IRB working conditions design.
IRB/kN | DIRB/kN | S/mm | DS/mm | Theory DCw2/mm |
---|
0 | 60 | 100 | 10 | ≈0.017 |
0 | 0 | 100 | 19 | ≈0.017 |
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