THREE-DIMENSIONAL MODEL OF EQUIVALENT ROLL GAP OF CVC MILL UNDER CONDITIONS OF ROLL CROSSING AND NO LOAD
Keywords:
roll crossing, nonlinear transformation, equivalent three-dimensional roll gap, asymmetrical distribution
Abstract
Traditional roll technologies focus solely on the contour of the roll gap at the outlet under ideal conditions. However, upon roll crossing, the three-dimensional distribution of the deformation zone becomes asymmetrical, leading to an adverse impact on the rolling pressure in the deformation zone. To study the screw-down load deviation of plate mills, it is necessary to accurately calculate the equivalent three-dimensional roll gap in the deformation zone under roll-crossing conditions. In this paper a model for calculating the equivalent three-dimensional roll gap under the conditions of roll crossing and no load was established based on the method of the coordinate nonlinear transformation of the spatial rectangular coordinate system. Based on this model, the influences of roll-crossing angles and translation parameters on the symmetry of the equivalent three-dimensional roll gap were analyzed. The distribution of the three-dimensional equivalent roll gap was calculated with different roll lengths, roll radii, and the roll gap’s nominal thickness. The intuitive contour map reveals that under the same condition of crossing angle and translation parameters, the larger the roll length and roll radii and the smaller the roll gap’s nominal thickness are, the greater the influence of the roll crossing on the asymmetrical distribution of roll gap is. It put forward a quantitative calculation method for evaluating the symmetrical distribution of the roll gap, and the calculation results can provide the equivalent roll profile for the roll-deformation model.
References
[1] S. Omori, T. Kajiwara, H. Hino and H. Goto, Analysis of rolling load generated by pair crossing rolling mill, Ironmak. Steelmak. 31 (1) (2013) 71-80. https://doi.org/10.1179/030192304225012088
[2] J. G. Ding, Y.H.C. He, M.X. Song, Z.J. Jiao and W. Peng, Roll crown control capacity of sextic CVC work roll curves in plate rolling process, Int. J. Adv. Manuf. Technol. 113 (2021) 87–97. https://doi.org/10.1007/s00170-020-06536-8
[3] J. G. Cao, S. J. Liu, J. Zhang, P. Song, T. L. Yan and Y. Z. Zhou, ASR work roll shifting strategy for schedule-free rolling in hot wide strip mills, J. Mater. Process. Technol. 211 (11) (2011) 1768-1775. https://doi.org/10.1016/j.jmatprotec.2011.05.025
[4] X. B. Ma, D. C. Wang, H. M. Liu, C.C. Wen and Y. Zhou, Large concave roll technology for hot rolled silicon steel, Ironmak. Steelmak. 45(1) (2018) 66-75. https://doi.org/10.1080/03019233.2016.1240841
[5] A. R. He, J. Shao, W. Q. Sun C. L. Guan, X. Y. Shen and J. P. Zhang, Transverse thickness deviation control of non-oriented silicon steel during cold rolling, J. Mech. Eng. 47 (10) (2011) 25-30. DOI:10.3901/jme.2011.10.025
[6] A. Seilinger, A. Mayrhofer and A. J. Kainz, SmartCrown - A new system for improved profile and flatness control in strip mills, Steel Times Int. 26 (10) (2002)11-12.
[7] H. N. He, J. Shao, X. C. Wang, Q. Yang, Y. Liu, D. Xu and Y.Z. Sun, Research and application of approximate rectangular section control technology in hot strip mills, J. Iron Steel Res. Int. 28(3) (2021) 279-290. https://doi.org/10.1007/s42243-021-00558-6
[8] A. R. He, Q. Yang, X. L. Chen, L. Zhao, H. R. Dong and Y. Q. Xu, Development and application of linearly variable crown work roll in hot strip mills, J. Mech. Eng. 44 (11) (2008) 255-259. DOI：10.3901/jme.2008.11.255
[9] G. M. Liu, H. S. Di, A. Chang and Z. Y. Hou, Discussion on design of CVC roll contour and its equivalent crown, J. Northeast. Univ., Nat. Sci. 29 (10) (2008) 1443-1446. https://xuebao.neu.edu.cn/natural/EN/Y2008/V29/I10/1443
[10] H. B. Li, J. Zhang, J. G. Cao, F. W. Cheng, W. D. Hu and Y. Zhang, Roll contour and strip profile control characteristics for quintic CVC work roll, J. Mech. Eng. 48 (12) (2012) 24-30. DOI：10.3901/JME.2012.12.024
[11] F. Schausberger, A. Steinboeck and A. Kugi, Mathematical modeling of the contour evolution of heavy plates in hot rolling, Appl. Math. Model. 32 (15) (2015) 4534-4547. https://doi.org/10.1016/j.apm.2015.01.017
[12] H. B. Lu, Tandem rolling and its equivalent roll crown curve, Baosteel Technology, (02) (1995) 50-53.
[13] B. L. Lu, Single cross rolling and equivalent crown, Iron Steel, 35 (01) (2000) 32-34.
[14] W. M. Li, Z. B. Liu, L. Y. Ni and Y. S. Long, Technological principle on shape control by single declining roller in asymmetrical PC rolling mill, J. Iron Steel Res. 14 (02) (2002) 13-17.
[15] M. Abbaspour and A. Saboonchi, Work roll thermal expansion control in hot strip mill, Appl. Math. Model. 32 (12) (2008) 2652-2669. https://doi.org/10.1016/j.apm.2007.09.011
[16] R. Servin Castañeda, F. Equihua Guillen, R. Torres Gonzalez and I. A. Facundo Arzola, Development of simple equation for calculating average wear of hot strip mill work rolls, Ironmak. Steelmak. 41 (5) (2014) 369-376. https://doi.org/10.1179/1743281213Y.0000000162
[17] S. M. Hwang, C. G. Sun, S. R. Ryoo and W. J. Kwak, An integrated FE process model for precision analysis of thermo-mechanical behaviors of rolls and strip in hot strip rolling, Comput. Method Appl. Mech. Eng. 191 (37) (2002) 4015-4033. https://doi.org/10.1016/S0045-7825(02)00298-0
[18] X. D. Wang, Q. Yang, A. R. He and R. Z. Wang, Comprehensive contour prediction model of work roll used in online strip shape control model during hot rolling, Ironmak. Steelmak. 34 (4) (2007) 303-311. https://doi.org/10.1179/174328107X168011
[19] Z. F. Chen, Theoretical and experimental research on roll of four-high strip mill, Doctor Dissertation, Shanghai Jiao Tong University, Shanghai, China, 2003.
[20] X. D. Shu and G. X. Shen, The test of work roll axial force about 2350 aluminium foil mill and the shorter longevity analysis of end thrust bearing, Metall. Equip. (5) (2001) 1-5.
[21] G. X. Shen, M. Li, R. Shi and J. Yanagimoto, Indeterminacy of the offset mechanism and microscale static determinacy of roll system in four-high mill, J. Mech. Eng. 46 (10) (2010) 69-74. DOI：10.3901/JME.2010.10.069
[22] G. X. Shen, Y. J. Zheng, M. Li, Development of statically determinate plate rolling mills that maintain the rolls parallel, J. Manuf. Sci. Eng. 135 (3) (2013) 922-926. https://doi.org/10.1115/1.4024039
[23] G. X. Shen, M. Li, Statically determinate characteristics of microdisplacement in a four-high mill, J. Mater. Process. Technol. 209 (11) (2009) 5002-5007. https://doi.org/10.1016/j.jmatprotec.2009.01.023
[24] T. Kiefer, A. Kugi, An analytical approach for modelling asymmetrical hot rolling of heavy plates, Math. Comp. Model. Dyn. Systems 14 (14) (2008) 249-267. https://doi.org/10.1080/13873950701844915
[25] X. Liu, X. H. Liu, M. Song and L. Z. Liu, Theoretical analysis of minimum metal foil thickness achievable by asymmetric rolling with fixed identical roll diameters, Transactions of Nonferrous Metals Society of China, 26 (2) (2016) 501-507. https://doi.org/10.1016/S1003-6326(16)64138-9
[26] J. J. Minton, C. J. Cawthorn and E. J. Brambley, Asymptotic analysis of asymmetric thin sheet rolling, Int. J. Mech. Sci. 113 (2016) 36-48. https://doi.org/10.1016/j.ijmecsci.2016.03.024
[27] X. B. Ma, H. M. Liu, J. L. Sun and Z. Z. Zhang, Screw-down load deviation model of 5m heavy plate mill based on influence of back-up roll axial force, Ironmak. Steelmak. 43 (2) (2016) 112-120. https://doi.org/10.1179/1743281215Y.0000000055
[28] X. H. Zhou, J. X. Zhao and T. D. Lu, Transforming between spatial rectilinear coordinate system and non-linear coordinate system, Beijing Surv. and Mapp. (1) (2005) 33-35.
[2] J. G. Ding, Y.H.C. He, M.X. Song, Z.J. Jiao and W. Peng, Roll crown control capacity of sextic CVC work roll curves in plate rolling process, Int. J. Adv. Manuf. Technol. 113 (2021) 87–97. https://doi.org/10.1007/s00170-020-06536-8
[3] J. G. Cao, S. J. Liu, J. Zhang, P. Song, T. L. Yan and Y. Z. Zhou, ASR work roll shifting strategy for schedule-free rolling in hot wide strip mills, J. Mater. Process. Technol. 211 (11) (2011) 1768-1775. https://doi.org/10.1016/j.jmatprotec.2011.05.025
[4] X. B. Ma, D. C. Wang, H. M. Liu, C.C. Wen and Y. Zhou, Large concave roll technology for hot rolled silicon steel, Ironmak. Steelmak. 45(1) (2018) 66-75. https://doi.org/10.1080/03019233.2016.1240841
[5] A. R. He, J. Shao, W. Q. Sun C. L. Guan, X. Y. Shen and J. P. Zhang, Transverse thickness deviation control of non-oriented silicon steel during cold rolling, J. Mech. Eng. 47 (10) (2011) 25-30. DOI:10.3901/jme.2011.10.025
[6] A. Seilinger, A. Mayrhofer and A. J. Kainz, SmartCrown - A new system for improved profile and flatness control in strip mills, Steel Times Int. 26 (10) (2002)11-12.
[7] H. N. He, J. Shao, X. C. Wang, Q. Yang, Y. Liu, D. Xu and Y.Z. Sun, Research and application of approximate rectangular section control technology in hot strip mills, J. Iron Steel Res. Int. 28(3) (2021) 279-290. https://doi.org/10.1007/s42243-021-00558-6
[8] A. R. He, Q. Yang, X. L. Chen, L. Zhao, H. R. Dong and Y. Q. Xu, Development and application of linearly variable crown work roll in hot strip mills, J. Mech. Eng. 44 (11) (2008) 255-259. DOI：10.3901/jme.2008.11.255
[9] G. M. Liu, H. S. Di, A. Chang and Z. Y. Hou, Discussion on design of CVC roll contour and its equivalent crown, J. Northeast. Univ., Nat. Sci. 29 (10) (2008) 1443-1446. https://xuebao.neu.edu.cn/natural/EN/Y2008/V29/I10/1443
[10] H. B. Li, J. Zhang, J. G. Cao, F. W. Cheng, W. D. Hu and Y. Zhang, Roll contour and strip profile control characteristics for quintic CVC work roll, J. Mech. Eng. 48 (12) (2012) 24-30. DOI：10.3901/JME.2012.12.024
[11] F. Schausberger, A. Steinboeck and A. Kugi, Mathematical modeling of the contour evolution of heavy plates in hot rolling, Appl. Math. Model. 32 (15) (2015) 4534-4547. https://doi.org/10.1016/j.apm.2015.01.017
[12] H. B. Lu, Tandem rolling and its equivalent roll crown curve, Baosteel Technology, (02) (1995) 50-53.
[13] B. L. Lu, Single cross rolling and equivalent crown, Iron Steel, 35 (01) (2000) 32-34.
[14] W. M. Li, Z. B. Liu, L. Y. Ni and Y. S. Long, Technological principle on shape control by single declining roller in asymmetrical PC rolling mill, J. Iron Steel Res. 14 (02) (2002) 13-17.
[15] M. Abbaspour and A. Saboonchi, Work roll thermal expansion control in hot strip mill, Appl. Math. Model. 32 (12) (2008) 2652-2669. https://doi.org/10.1016/j.apm.2007.09.011
[16] R. Servin Castañeda, F. Equihua Guillen, R. Torres Gonzalez and I. A. Facundo Arzola, Development of simple equation for calculating average wear of hot strip mill work rolls, Ironmak. Steelmak. 41 (5) (2014) 369-376. https://doi.org/10.1179/1743281213Y.0000000162
[17] S. M. Hwang, C. G. Sun, S. R. Ryoo and W. J. Kwak, An integrated FE process model for precision analysis of thermo-mechanical behaviors of rolls and strip in hot strip rolling, Comput. Method Appl. Mech. Eng. 191 (37) (2002) 4015-4033. https://doi.org/10.1016/S0045-7825(02)00298-0
[18] X. D. Wang, Q. Yang, A. R. He and R. Z. Wang, Comprehensive contour prediction model of work roll used in online strip shape control model during hot rolling, Ironmak. Steelmak. 34 (4) (2007) 303-311. https://doi.org/10.1179/174328107X168011
[19] Z. F. Chen, Theoretical and experimental research on roll of four-high strip mill, Doctor Dissertation, Shanghai Jiao Tong University, Shanghai, China, 2003.
[20] X. D. Shu and G. X. Shen, The test of work roll axial force about 2350 aluminium foil mill and the shorter longevity analysis of end thrust bearing, Metall. Equip. (5) (2001) 1-5.
[21] G. X. Shen, M. Li, R. Shi and J. Yanagimoto, Indeterminacy of the offset mechanism and microscale static determinacy of roll system in four-high mill, J. Mech. Eng. 46 (10) (2010) 69-74. DOI：10.3901/JME.2010.10.069
[22] G. X. Shen, Y. J. Zheng, M. Li, Development of statically determinate plate rolling mills that maintain the rolls parallel, J. Manuf. Sci. Eng. 135 (3) (2013) 922-926. https://doi.org/10.1115/1.4024039
[23] G. X. Shen, M. Li, Statically determinate characteristics of microdisplacement in a four-high mill, J. Mater. Process. Technol. 209 (11) (2009) 5002-5007. https://doi.org/10.1016/j.jmatprotec.2009.01.023
[24] T. Kiefer, A. Kugi, An analytical approach for modelling asymmetrical hot rolling of heavy plates, Math. Comp. Model. Dyn. Systems 14 (14) (2008) 249-267. https://doi.org/10.1080/13873950701844915
[25] X. Liu, X. H. Liu, M. Song and L. Z. Liu, Theoretical analysis of minimum metal foil thickness achievable by asymmetric rolling with fixed identical roll diameters, Transactions of Nonferrous Metals Society of China, 26 (2) (2016) 501-507. https://doi.org/10.1016/S1003-6326(16)64138-9
[26] J. J. Minton, C. J. Cawthorn and E. J. Brambley, Asymptotic analysis of asymmetric thin sheet rolling, Int. J. Mech. Sci. 113 (2016) 36-48. https://doi.org/10.1016/j.ijmecsci.2016.03.024
[27] X. B. Ma, H. M. Liu, J. L. Sun and Z. Z. Zhang, Screw-down load deviation model of 5m heavy plate mill based on influence of back-up roll axial force, Ironmak. Steelmak. 43 (2) (2016) 112-120. https://doi.org/10.1179/1743281215Y.0000000055
[28] X. H. Zhou, J. X. Zhao and T. D. Lu, Transforming between spatial rectilinear coordinate system and non-linear coordinate system, Beijing Surv. and Mapp. (1) (2005) 33-35.
Published
2024-04-03
How to Cite
1.
Ma X, Yuan P, Li F, Ji J. THREE-DIMENSIONAL MODEL OF EQUIVALENT ROLL GAP OF CVC MILL UNDER CONDITIONS OF ROLL CROSSING AND NO LOAD. MatTech [Internet]. 2024Apr.3 [cited 2024Dec.10];58(2):193–202. Available from: https://mater-tehnol.si/index.php/MatTech/article/view/1047
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