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Research on the influence of nonlocal effect on specific roll pressure by nonlocal stress gradient model in strip rolling

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Abstract

In this paper, a nonlocal stress gradient model based on nonlocal theory has been developed to research the influence of the nonlocal effect on the specific roll pressure in strip rolling. In order to obtain the higher-order stress terms in the nonlocal stress gradient model, the local stress in Eringen’s nonlocal integral model is expressed as the form of a series by Taylor expansion. By comparisons of the experimental data with the results predicted by the nonlocal stress gradient model and the local model, it is found that the application of the nonlocal stress gradient model can lead to a better solution. Meanwhile, the effect of the material characteristic parameter, the friction coefficient, and the reduction on the non-dimensional pressure difference (nonlocal effect) is discussed.

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References

  1. Karman TV (1925) On the theory of rolling. Z Angew Math Mech 5:130–141

    Google Scholar 

  2. Orowan E (1943) The calculation of roll pressure in hot and cold flat rolling. Proc Inst Mech Eng 150(1):140–167. https://doi.org/10.1243/PIME_PROC_1943_150_025_02

    Article  Google Scholar 

  3. Sims RB (1954) The calculation of roll force and torque in hot rolling mills. Proc Inst Mech Eng 168(1):191–200. https://doi.org/10.1243/PIME_PROC_1954_168_023_02

    Article  Google Scholar 

  4. Bland DR, Ford H (1948) The calculation of roll force and torque in cold strip rolling with tensions. Proc Inst Mech Eng 159(1):144–163. https://doi.org/10.1243/PIME_PROC_1948_159_015_02

    Article  Google Scholar 

  5. Li S, Wang Z, Ruan J, Liu C, Xu Z (2017) Hydrodynamics method and its application in hot strip rolling. Steel Res Int 88(4). doi:https://doi.org/10.1002/srin.201600220

  6. Li S, Wang Z, Liu C, Ruan J, Xu Z (2017) A simplified method to calculate the rolling force in hot rolling. Int J Adv Manuf Technol 88(5):2053–2059. https://doi.org/10.1007/s00170-016-8890-z

    Article  Google Scholar 

  7. Dixit US, Chandra S (2003) A neural network based methodology for the prediction of roll force and roll torque in fuzzy form for cold flat rolling process. Int J Adv Manuf Technol 22(11–12):883–889. https://doi.org/10.1007/s00170-003-1628-8

    Article  Google Scholar 

  8. Hua L, Deng J, Qian D, Ma Q (2015) Using upper bound solution to analyze force parameters of three-roll cross rolling of rings with small hole and deep groove. Int J Adv Manuf Technol 76(1–4):353–366. https://doi.org/10.1007/s00170-014-6107-x

    Article  Google Scholar 

  9. Eringen AC (1972) On nonlocal fluid mechanics. Int J Eng Sci 10(6):561–575. https://doi.org/10.1016/0020–7225(72)90098-5

    Article  MathSciNet  MATH  Google Scholar 

  10. Eringen AC, Edelen DGB (1972) On nonlocal elasticity. Int J Eng Sci 10(3):233–248. https://doi.org/10.1016/0020–7225(72)90039-0

    Article  MathSciNet  MATH  Google Scholar 

  11. Eringen AC (1981) On nonlocal plasticity. Int J Eng Sci 19(12):1461–1474. https://doi.org/10.1016/0020–7225(81)90072-0

    Article  MathSciNet  MATH  Google Scholar 

  12. Eringen AC (1983) Theories of nonlocal plasticity. Int J Eng Sci 21(7):741–751. https://doi.org/10.1016/0020–7225(83)90058-7

    Article  MATH  Google Scholar 

  13. Polizzotto C, Fuschi P, Pisano AA (2006) A nonhomogeneous nonlocal elasticity model. Eur J Mech A Solid 25(2):308–333. https://doi.org/10.1016/j.euromechsol.2005.09.007

    Article  MathSciNet  MATH  Google Scholar 

  14. Tuna M, Kirca M (2016) Exact solution of Eringen’s nonlocal integral model for bending of Euler–Bernoulli and Timoshenko beams. Int J Eng Sci 105:80–92. https://doi.org/10.1016/j.ijengsci.2016.05.001

    Article  MathSciNet  Google Scholar 

  15. Tuna M, Kirca M (2016) Exact solution of Eringen’s nonlocal integral model for vibration and buckling of Euler–Bernoulli beam. Int J Eng Sci 107:54–67. https://doi.org/10.1016/j.ijengsci.2016.07.004

    Article  Google Scholar 

  16. Shaat M, Abdelkefi A (2017) New insights on the applicability of Eringen’s nonlocal theory. Int J Mech Sci 121:67–75. https://doi.org/10.1016/j.ijmecsci.2016.12.013

    Article  Google Scholar 

  17. Voyiadjis GZ, Pekmezi G, Deliktas B (2010) Nonlocal gradient-dependent modeling of plasticity with anisotropic hardening. Int J Plast 26(9):1335–1356. https://doi.org/10.1016/j.ijplas.2010.01.015

    Article  MATH  Google Scholar 

  18. Miandoab EM, Yousefi-Koma A, Pishkenari HN (2014) Nonlocal and strain gradient based model for electrostatically actuated silicon nano-beams. Microsyst Technol 21(2):457–464. https://doi.org/10.1007/s00542-014-2110-2

    Article  Google Scholar 

  19. Challamel N, Wang CM, Elishakoff I (2016) Nonlocal or gradient elasticity macroscopic models: a question of concentrated or distributed microstructure. Mech Res Commun 71:25–31. https://doi.org/10.1016/j.mechrescom.2015.11.006

    Article  Google Scholar 

  20. Ebrahimi F, Barati MR (2017) A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams. Compos Struct 159:174–182. https://doi.org/10.1016/j.compstruct.2016.09.058

    Article  Google Scholar 

  21. Xu XJ, Wang XC, Zheng ML, Ma Z (2017) Bending and buckling of nonlocal strain gradient elastic beams. Compos Struct 160:366–377. https://doi.org/10.1016/j.compstruct.2016.10.038

    Article  Google Scholar 

  22. Oden JT, Pires EB (1983) Nonlocal and nonlinear friction laws and variational principles for contact problems in elasticity. J Appl Mech-T ASME 50(1):67–76. https://doi.org/10.1115/1.3167019

    Article  MathSciNet  MATH  Google Scholar 

  23. Mahrenholtz O, Bontcheva N, Iankov R (2005) Influence of surface roughness on friction during metal forming processes. J Mater Process Technol 159(1):9–16. https://doi.org/10.1016/j.jmatprotec.2003.10.009

    Article  Google Scholar 

  24. Lenard JG (1992) Friction and forward slip in cold strip rolling. Tribol Trans 35(3):423–428. https://doi.org/10.1080/10402009208982138

    Article  MathSciNet  Google Scholar 

  25. Zhao ZY (1994) Metal plastic deformation and rolling theory. Metallurgical Industry Press, Beijing, pp 275–279 (in Chinese)

    Google Scholar 

  26. Hitchcock J (1935) Elastic deformation of rolls during cold rolling. ASME Report of Special Research Committee on Roll Neck Bearings 33–41

  27. Wang CM, Reddy JN, Noël C, Challamel N (2016) Eringen’s stress gradient model for bending of nonlocal beams. J Eng Mech 142(12):04016095. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001161

    Article  Google Scholar 

  28. Liu YM, Zhang DH, Zhao DW, Sun J (2015) Analysis of vertical rolling using double parabolic model and stream function velocity field. Int J Adv Manuf Technol 82(5–8):1153–1161. https://doi.org/10.1007/s00170-015-7393-7

    Google Scholar 

  29. Zhang DH, Liu YM, Sun J, Zhao DW (2015) A novel analytical approach to predict rolling force in hot strip finish rolling based on cosine velocity field and equal area criterion. Int J Adv Manuf Technol. https://doi.org/10.1007/s00170-015-7692-z

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

    Article  Google Scholar 

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Li, S., Wang, Z., Ruan, J. et al. Research on the influence of nonlocal effect on specific roll pressure by nonlocal stress gradient model in strip rolling. Int J Adv Manuf Technol 94, 1857–1862 (2018). https://doi.org/10.1007/s00170-017-0994-6

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