Abstract
It is well known that there are sharp peaks (friction hills) in the specific roll pressure curves predicted by Sims formula and Цeликoв formula which result in large errors for hot rolling. In this paper, a new specific roll pressure formula is derived from the Navier-Stokes equation (N-S equation) by the hydrodynamics method (HM) with assumptions that strip materials take the characteristics of viscous fluid during plastic deformation of hot rolling processes. Results predicted by this HM formula, Sims formula, and Цeликoв formula were compared with experimental data. It was found the friction hills in the specific roll pressure curves predicted by Sims formula and Цeликoв formula are smoothed by this newly established formula and higher accuracy can be achieved in the calculation of the unit width rolling force.
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References
Karman TV (1925) On the theory of rolling. Z Angew Math Mech 5:130–141
Orowan E (1943) The calculation of roll pressure in hot and cold flat rolling. Proc Inst Mech Eng 150(1):140–167. doi:10.1243/PIME_PROC_1943_150_025_02
Sims RB (1954) The calculation of roll force and torque in hot rolling mills. Proc Inst Mech Eng 168(1):191–200. doi:10.1243/PIME_PROC_1954_168_023_02
Qwamizadeh M, Kadkhodaei M, Salimi M (2014) Asymmetrical rolling analysis of bonded two-layer sheets and evaluation of outgoing curvature. Int J Adv Manuf Technol 73(1–4):521–533. doi:10.1007/s00170-014-5825-4
Lundberg SE, Överstam H (2007) Modeling of stress state, centre consolidation and roll force in billet rolling. Steel Res Int 78(6):492–501
Oluwole OO, Olaogun O (2011) Slip line field solution for second pass in lubricated 4-high reversing cold rolling sheet mill. Engineering 3(12):1225–1233. doi:10.4236/eng.2011.312152
Sun JL, Peng Y, Liu HM, Liu G (2012) Rolling theory analysis and forces calculation of heavy cylinder rolling mill with two drive rolls. Adv Mater Res 572:13–18
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. doi:10.1016/j.jmatprotec.2015.03.051
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. doi:10.1007/s00170-014-6107-x
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. doi:10.1007/s00170-015-7393-7
Bogatov AA, Nukhov DS, P’yankov KP (2015) Finite-element modeling of plate-rolling. Metallurgist 59(1–2):113–118. doi:10.1007/s11015-015-0069-6
Lenard JG (2014) An advanced finite element model of the flat, cold rolling process. In: Lenard JG (ed) Primer on flat rolling, 2nd edn. Elsevier, Oxford, pp 113–123. doi:10.1016/B978-0-08-099418-5.00006-8
Mei RB, Li CS, Cai B, Zhang G, Liu XH (2013) Prediction of initial velocity field for fast solution of rolling force by FEM in strip rolling. AIP Conf Proc 1532(1):574–580. doi:10.1063/1.4806878
Ruan JH, Zhang LW, Wang ZG, Wang T, Li YR, Hao ZQ (2015) Finite element simulation based plate edging model for plan view pattern control during wide and heavy plate rolling. Ironmak Steelmak 42(8):585–593. doi:10.1179/1743281215Y.0000000002
Hum B, Colquhoun HW, Lenard JG (1996) Measurements of friction during hot rolling of aluminum strips. J Mater Process Technol 60(1–4):331–338. doi:10.1016/0924-0136(96)02350-3
Daniel WP, Alain E, Nicolas L (2011) A new sensor for the evaluation of contact stress by inverse analysis during steel strip rolling. J Mater Process Technol 211(9):1500–1509. doi:10.1016/j.jmatprotec.2011.03.025
Daniel WP, Alain E, Nicolas L (2013) Evaluation of contact stress during rolling process, by three dimensional analytical inverse method. Int J Solids Struct 50(20–21):3319–3331. doi:10.1016/j.ijsolstr.2013.06.005
Wang Q, Jiang Z, Zhao J, Fang M (2013) Multi-factor coupling system characteristic of the dynamic roll gap in the high-speed rolling mill during the unsteady lubrication process. Tribol Int 67:174–181. doi:10.1016/j.triboint.2013.07.010
Le HR, Sutcliffe MPF (2002) Rolling of thin strip and foil: application of a tribological model for “mixed” lubrication. J Tribol 124(1):129–136. doi:10.1115/1.1402179
He YX (2010) Rolling engineering. Chemical Industry Press, Beijing (in Chinese)
Ding Z, Li B, Liang S (2015) Maraging steel phase transformation in high strain rate grinding. Int J Adv Manuf Technol 80(1–4):711–718. doi:10.1007/s00170-015-7014-5
Saboori M, Champliaud H, Gholipour J, Gakwaya A, Savoie J, Wanjara P (2015) Extension of flow stress–strain curves of aerospace alloys after necking. Int J Adv Manuf Technol 83(1–4):313–323. doi:10.1007/s00170-015-7557-5
Yu J, Jiang F, Rong Y, Xie H, Suo T (2014) Numerical study the flow stress in the machining process. Int J Adv Manuf Technol 74(1–4):509–517. doi:10.1007/s00170-014-5966-5
Anand L, Zavaliangos A, von Turkovich BF (1990) Hot working—constitutive equations and computational procedures. CIRP Ann Manuf Technol 39(1):235–238. doi:10.1016/s0007-8506(07)61043-9
Ji S, Wang Y, Liu J, Meng X, Tao J, Zhang T (2015) Effects of welding parameters on material flow behavior during linear friction welding of Ti6Al4V titanium alloy by numerical investigation. Int J Adv Manuf Technol 82(5–8):927–938. doi:10.1007/s00170-015-7408-4
Rakhshkhorshid M (2014) Modeling the hot deformation flow curves of API X65 pipeline steel. Int J Adv Manuf Technol 77(1–4):203–210. doi:10.1007/s00170-014-6447-6
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Li, S., Wang, Z., Liu, C. et al. A simplified method to calculate the rolling force in hot rolling. Int J Adv Manuf Technol 88, 2053–2059 (2017). https://doi.org/10.1007/s00170-016-8890-z
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DOI: https://doi.org/10.1007/s00170-016-8890-z