Skip to main content
SpringerLink
Log in

A coupling model of vertical rolling process based on upper bound method and elastic theory

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

A mathematical model of vertical rolling process with the consideration of mechanism displacement is proposed. Using Γ function and parabola function to describe edge deformation, the corresponding 3D velocity field, strain rate field and total power functional are derived. Simultaneously, an analysis method of mechanism deformation is proposed. The deflection of vertical roller and the radial displacement of support bearings are calculated by applying superposition principle and Palmgren’s modified formula respectively. The coupling calculation of slab deformation and mechanism displacement is realized through minimizing the total functional and repeated iteration. The accuracy of the presented model is verified by comparison with other models and factory measurements. Subsequently, the influences of main rolling parameters on edge deformation, rolling force and mechanism displacement are analyzed. The proposed model could provide some references for the optimization of vertical rolling process and the improvement of slab quality and yield ratio.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Data availability

The authors assure the transparency and availability of data and material, and adhere to discipline-specific rules for acquiring, selecting and processing data.

Code availability

The authors make sure we have permissions for the use of software, and the availability of the custom code.

References

  1. Liu YM, Wang ZH, Wang T, Sun J, Hao JP, Zhang DH, Huang QX (2022) Prediction and mechanism analysis of the force and shape parameters using cubic function model in vertical rolling. J Mater Process Technol 303:117500. https://doi.org/10.1016/j.jmatprotec.2022.117500

    Article  Google Scholar 

  2. Okado M, Ariizumi T, Noma Y, Yabuuchi K, Yamazaki Y (1981) Width behaviour of the head and tail of slabs in edge rolling in hot strip mills. Tetsu-to-Hagane 67(15):2516–2525

    Article  Google Scholar 

  3. Xiong SW, Zhu XL, Liu XH, Wang G, Zhang Q, Li H, Meng X, Han L (1997) Mathematical model of width reduction process of roughing trains of hot strip mills. Shanghai Metals 19:39–43

    Google Scholar 

  4. Shibahara T, Misaka Y, Kono T, Koriki M, Takemoto H (1981) Edger set–up model at roughing train in hot strip mill. Tetsu-to-Hagane 67(15):2509–2515. https://doi.org/10.2355/tetsutohagane1955.67.15_2509

    Article  Google Scholar 

  5. Tazoe N, Honjyo H, Takeuchi M, Ono T (1984) New form of hot strip mill width rolling installations. AISE spring conference. Dearborn, Assn Iron Steel Engineers, Pittsburgh, pp 85–88

    Google Scholar 

  6. Ginzburg VB, Kaplan N, Bakhtar F, Tabone CJ (1991) Width control in hot strip mills. Iron Steel Eng 68(6):25–39

    Google Scholar 

  7. Huisman HJ, Huètink J (1985) A combined Eulerian-Lagrangian three–dimensional finite–element analysis of edge–rolling. J Mech Work Technol 11(3):333–353. https://doi.org/10.1016/0378-3804(85)90005-1

    Article  Google Scholar 

  8. Chung WK, Choi SK, Thomson PF (1993) Three–dimensional simulation of the edge rolling process by the explicit finite–element method. J Mater Process Technol 38(1–2):85–101. https://doi.org/10.1016/0924-0136(93)90188-C

    Article  Google Scholar 

  9. Xiong SW, Liu XH, Wang GD, Zhang QA (2000) Three–dimensional finite element simulation of the vertical–horizontal rolling process in the width reduction of slab. J Mater Process Technol 101(1–3):145–151. https://doi.org/10.1016/S0924-0136(00)00439-8

    Article  Google Scholar 

  10. Yu HL, Liu XH, Chen LQ, Li CS, Zhi Y, Li XW (2009) Influence of edge rolling reduction on plate–edge stress distribution during finish rolling. ISIJ Int 16(1):22–26. https://doi.org/10.1016/S1006-706X(09)60005-4

    Article  Google Scholar 

  11. Yun DJ, Kim YK, Hwang SM (2011) A FE–based model for predicting roll force in a vertical rolling process. Trans Mater Process 20(8):548–554. https://doi.org/10.5228/KSTP.2011.20.8.548

    Article  Google Scholar 

  12. Zhang SH, Deng L, Tian WH, Che LZ, Li Y (2022) Deduction of a quadratic velocity field and its application to rolling force of extra-thick plate. Comput Math Appl 109:58–73. https://doi.org/10.1016/j.camwa.2022.01.024

    Article  MathSciNet  MATH  Google Scholar 

  13. Lundberg SE (1986) An approximate theory for calculation of roll torque during edge rolling of steel slabs. Steel Res Int 57(7):325–330. https://doi.org/10.1002/srin.198600773

    Article  Google Scholar 

  14. Lundberg SE, Gustafsson T (1993) Roll force, torque, lever arm coefficient, and strain distribution in edge rolling. J Mater Eng Perform 2(6):873–879. https://doi.org/10.1007/BF02645688

    Article  Google Scholar 

  15. Lundberg SE (2008) A model for prediction of roll force and torque in edge rolling. Steel Res Int 78(2):160–166. https://doi.org/10.1002/srin.200705874

    Article  Google Scholar 

  16. Yun D, Lee D, Kim J, Hwang SM (2012) A new model for the prediction of the dog–bone shape in steel mills. ISIJ Int 52(6):1109–1117. https://doi.org/10.2355/isijinternational.52.1109

    Article  Google Scholar 

  17. Liu YM, Ma GS, Zhang DH, Zhao DW (2015) Upper bound analysis of rolling force and dog–bone shape via sine function model in vertical rolling. J Mater Process Technol 223:91–97. https://doi.org/10.1016/j.jmatprotec.2015.03.051

    Article  Google Scholar 

  18. Zhang YF, Zhao MY, Li X, Di HS, Zhou XJ, Wen P, Zhao DW, Zhang DH (2022) Optimization solution of vertical rolling force using unified yield criterion. Int J Adv Manuf Tech 119(1–2):1035–1045. https://doi.org/10.1007/s00170-021-08333-3

    Article  Google Scholar 

  19. Liu YM, Zhang DH, Zhao DW, Sun J (2016) Analysis of vertical rolling using double parabolic model and stream function velocity field. Int J Adv Manuf Tech 82(5–8):1153–1161. https://doi.org/10.1007/s00170-015-7393-7

    Article  Google Scholar 

  20. Cao JZ, Liu YM, Luan FJ, Zhao DW (2016) The calculation of vertical rolling force by using angular bisector yield criterion and Pavlov principle. Int J Adv Manuf Tech 86(9–12):2701–2710. https://doi.org/10.1007/s00170-016-8373-2

    Article  Google Scholar 

  21. Li X, Wang H, Liu Y, Zhang DH (2016) Analysis of edge rolling based on continuous symmetric parabola curves. J Braz Soc Mech Sci 39(4):1259–1268. https://doi.org/10.1007/s40430-016-0587-6

    Article  Google Scholar 

  22. Ding JG, Wang HY, Zhang DH, Zhao DW (2017) Slab analysis based on stream function method in chamfer edge rolling of ultra–heavy plate. P I Mech Eng C-J Mec 231(7):1237–1251. https://doi.org/10.1177/0954406216646400

    Article  Google Scholar 

  23. Zhang SH, Deng L, Che LZ (2022) An integrated model of rolling force for extra-thick plate by combining theoretical model and neural network model. J Manuf Process 75:100–109. https://doi.org/10.1016/j.jmapro.2021.12.063

    Article  Google Scholar 

  24. Liu YM, Sun J, Zhang DH, Zhao DW (2018) Three–dimensional analysis of edge rolling based on dual–stream function velocity field theory. J Manuf Process 34:349–355. https://doi.org/10.1016/j.jmapro.2018.06.012

    Article  Google Scholar 

  25. Liu YM, Hao PJ, Wang T, Run ZK, Sun J, Zhang DH, Zhang SH (2020) Mathematical model for vertical rolling deformation based on energy method. Int J Adv Manuf Tech 107(1–2):875–883. https://doi.org/10.1007/s00170-020-05094-3

    Article  Google Scholar 

  26. Yang BX, Xu HJ, An Q (2022) Analysis of 3D plastic deformation in vertical rolling based on global weighted velocity field. Int J Adv Manuf Tech 120:6647–6659. https://doi.org/10.1007/s00170-022-09190-4

    Article  Google Scholar 

  27. Zhang SH, Song BN, Wang XN, Zhao DW (2014) Analysis of plate rolling by MY criterion and global weighted velocity field. Appl Math Model 38(14):3485–3494. https://doi.org/10.1016/j.apm.2013.11.061

    Article  MathSciNet  Google Scholar 

  28. Zhao DW, Xie YJ, Liu XH, Wang GD (2004) New yield equation based on geometric midline of error triangles between Tresca and twin shear stress yield loci. J Northeastern Univ 25(2):121–124

    Google Scholar 

  29. Zhang DH, Cao JZ, Xu JJ, Peng W, Zhao DW (2014) Simplified weighted velocity field for prediction of hot strip rolling force by taking into account flattening of rolls. J Iron Steel Res Int 21(7):637–643. https://doi.org/10.1016/S1006-706X(14)60099-6

    Article  Google Scholar 

  30. Zhang SH, Zhao DW, Gao CR (2012) The calculation of roll torque and roll separating force for broadside rolling by stream function method. Int J Mech Sci 57(1):74–78. https://doi.org/10.1016/j.ijmecsci.2012.02.006

    Article  Google Scholar 

  31. Zhang SH (2016) Mechanical principle of plastic forming. Metallurgical Industry Press, Beijing (in Chinese)

    Google Scholar 

  32. Wang TP, Qi KM (2012) Metal plastic process: rolling theory and technology. Metallurgical Industry Press, Beijing (in Chinese)

    Google Scholar 

  33. Zhou XW, Zhu QY, Wen BG, Zhao G, Han QK (2019) Experimental investigation on temperature field of a double–row tapered roller bearing. Tribol T 62(6):1086–1098. https://doi.org/10.1080/10402004.2019.1649509

    Article  Google Scholar 

  34. Liu HW (2011) Mechanics of Materials. Higher Education Press, Beijing (in Chinese)

    Google Scholar 

  35. Ma ZH, Wang R, Zhao HT, Huang L, Meng FM (2022) Coupling behavior of lubrication and dynamics for tapered roller bearing. Tribology 42(1):55–64. https://doi.org/10.16078/j.tribology.2020278

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai, 200237, People’s Republic of China

    Boxin Yang, Haojie Xu & Qi An

Authors
  1. Boxin Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haojie Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qi An
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qi An.

Ethics declarations

Ethics approval

The authors declare that the submitted work is original. Neither the entire paper nor any part of its content has been published or has been accepted elsewhere. It is not being submitted to any other journal.

Consent to participate

The authors confirm that this research does not involve Human Participants and/or Animals.

Consent for publication

The authors consent for publication in The International Journal of Advanced Manufacturing Technology exclusively.

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, B., Xu, H. & An, Q. A coupling model of vertical rolling process based on upper bound method and elastic theory. Int J Adv Manuf Technol 128, 715–728 (2023). https://doi.org/10.1007/s00170-023-11712-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-023-11712-7

Keywords

Search

Navigation