Send Orders for Reprnts to reprnts@benthamscence.ae The Open Mechancal Engneerng Journal, 215, 9, 111-116 111 Open Access Research and Applcaton of Work Roll Contour Technology on Thn Gauge Stanless Steel n Hot Rollng Shao Jan *,1, He Anru 1, Kong Fanfu 1, Xang Yang 2 and Zhou Zhou 3 1 Natonal Engneerng Research Center of Advanced Rollng Technology, Unversty of Scence and Technology Bejng, Bejng, 183, Chna 2 Hot Strp Mll of Schuan Southwest Stanless Steel Co., Ltd, Leshan, 61492, Chna 3 Hot Strp Mll of Beha Chende Stanless Steel Co., Ltd, Beha, 536, Chna Abstract: Shape control s the key technology for thn gauge stanless steel n hot rollng. Because of hgh rollng force, work roll can suffer from serous uneven wears, edge drop of strp temperature and so on. And n turn these mperfectons lead to defects n thn gauge stanless steel producton, such as bg crown value, quarter wave, edge profle anomales, poor rollng stablty. In order to mprove shape the control ablty, one wll have to elmnate the quarter wave, make roll wear unform, ncrease rollng stablty n the thn gauge stanless steel producton, use hgh performance varable crown technology n upstream stands, use mxed varable crown technology n last stand, and use conventonal work roll wth varable shftng stroke strategy n other downstream stands. The above technologes have been successfully appled n several stanless steel productons, whch have completely ndependent ntellectual property rghts, and the crown control precson of thn gauge stanless s 98.1%, flatness control precson s 97.5%, also a 126 mm 1.6 mm ultra-thn gauge stanless steel was successfully developed. Keywords: Hot rollng, stanless steel, shape control, work roll contour, quarter wave. 1. INTRODUCTION Stanless steel s wdely used n aerospace, petroleum, mechancal, chemcal ndustry, bology and other felds because t s corroson resstant, has hgh toughness and plastcty, and t s non-magnetc etc. The thn stanless steel raw materal can gve more flexble schedule for cold rollng, and can even take the place of cold rollng producton, whch s a developng trend for stanless steel rollng technology. Due to greater deformaton resstance and poor hot ductlty, bg rollng force and fast temperature drops are a sgnfcant characterstc of the thn gauge stanless steel n hot rollng, ths leads to serous shape problem and poor rollng stablty, such as large crown value, anomales at strp edge area and quarter wave. Work roll contour s the most mportant factor of the shape control, and many outstandng shape control technologes are based on work roll contour desgn [1, 2]. In upstream stands of hot strp fnshng mll, the man functon s crown control, and flatness control s requred n downstream stands [3]. Therefore, the work roll desgn targets are dfferent between upstream and downstream stands accordng to dfferent requrements. In order to mprove the shape control capablty, elmnate the quarter wave, make unform work roll wear, and ncrease rollng stablty n the thn gauge stanless steel producton. The hgh performance varable crown work roll was developed and used n upstream stands, whereas the mxed varable crown work roll was developed and used n last stand, conventonal work roll was used n the other stands wth varable stroke shftng strategy technology. 2. HIGH PERFORMANCE VARIABLE CROWN WORK ROLL Work roll bend s serous n stanless steel hot rollng because of hgh deformaton resstance, and n order to get the profle target a good crown control capablty s demanded. Varable crown work roll wth axal shftng represented by three order curve can provde strong shape control capablty [4-6]. As we all known, the shape control capablty s nversely proportonal to the strp wdth, whch s smlar to work roll bendng, and poor capablty can only be provded n narrow strp rollng wth shftng n the lmt poston [7, 8]. Consderng ncreasng shape control capablty on varous strp wdth, a new varable crown work roll was developed. Varable crown work roll wth axal shftng needs to satsfy the odd symmetrcal condtons. Takng the mdpont of work roll as the orgn coordnate and usng polynomal expressons, the upper work roll radus curve functon can be expressed as: m y t (x) = a ( x s ) + sgn x s =1,3,5, n (1) ( ) a j ( x s ) j j=2,4,6, 1874-155X/15 215 Bentham Open
112 The Open Mechancal Engneerng Journal, 215, Volume 9 Jan et al. where y t (x) s the radus curve functon of the upper work roll, a s the roll curve coeffcent, s s the offset of roll curve, x s abscssa of work roll, sgn(x-s ) s the sgn functon shown as follow: 1 x s < sgn(x s ) = x s 1 x s > The upper work roll s symmetrcal wth s, and the lower work roll radus curve functon can be expressed as: m y b (x) = a ( x + s ) sgn x + s =1,3,5, n ( ) a j ( x + s ) j j=2,4,6, (2) (3) where y b (x) s the radus curve functon of lower work roll. Usng the bnomal theorem, the arbtrary odd (x-s ) and (x+s ) can be expressed as: y t ( x) = y 3 ( ) + a 2 ( x s ) 3 x X 1 ( x) = a 3 ( x s ) + a 4 sgn( x s )( x s ) 2 x X 2 ( x) = a 5 ( x s ) + a 6 ( x s ) 3 x X 3 ( x) = a 1 x s The work roll equvalent crown adjustng ablty s expressed as: C r 3 2 a ( s + s 2 )w2, w < L c ( s, w) = ( s + s) 3 2 a 2L 2 c + 2a 4 ( w L c ), L c w L q ( s + s) 3 2 a Lc2 2 + 2a 4 ( L q L c ) + 3 2 a 6 w2 2 ( L q ), w > L q (8) (9) ( x s ) = C k x k s k= ( ) k = x C 1 x 1 s + C 2 x 2 s 2 C 3 x 3 s 3 + s (4) ( x + s ) = C k x n k k s k= = x + C 1 x 1 s + C 2 x 2 s 2 + C 3 x 3 s 3 + + s The roll gap functon constructed by odd tems can be expressed as: G ( x) = 2a C k x k k s (6) k=1,3,5, where G (x) s the roll gap functon, C s coeffcent of the bnomal theorem expresson. In the roll gap functon constructed by odd tems, the hghest order term s 2a C 1 x - 1 s, and f neglectng the hgher order terms, the roll gap functon s ( 1) order wth the abscssa of work roll, therefore, the relatonshp between work roll equvalent crown and strp wdth s the same. Smlarly, the work roll equvalent crown constructed by even tems s (-1) order wth strp wdth. Accordng to the roll gap formng prncple, work roll contour can be composed of pecewse functons. As shown n Fg. (1), two order polynomal curve was used n the specfed wdth nterval [L c, L q ], and three order polynomal curve was used n others. The domans of pecewse functon are as follows: [ ] X 1 = s.5l c, s +.5L c X 2 = s.5l q, s.5l c ) ( s +.5L c, s +.5L q X 3 =.5L, s.5l q ) ( s +.5L q,.5l The pecewse functon of work roll curve can be shown as follow: (5) (7) Fg. (1). Pecewse functon of work roll contour. In equaton (9), the relatonshp between equvalent crown adjustng ablty and strp wdth s lnear n [L c, L q ], whle n other wdth range, the relatonshp s square. Accordng to the crown adjustng ablty characterstc, a hgh performance varable crown (HVC) was developed. As shown n equaton (8), there are seven parameters, s, a 1, a 2, a 3, a 4, a 5, a 6, and so seven equatons are requred n roll contour desgn. In roll contour desgn, there are some known condtons, such as work roll length (L), shftng lmt poston (s m ), lnear wdth range (L c and L q ), work roll equvalent crown based on shftng lmt poston (C r1 and C r2 ). Accordng to equaton (9), C r1 and C r2 are gven as follows: C r1 = C r ( s m, L) C r2 = C r ( s m, L) (1) Based on contnuty requrements of HVC work roll pecewse functon, the followng equatons can be acheved: ( s +.5L c ) = ( s +.5L c ) ( ) = ( ) s +.5L c s +.5L c ( s +.5L q ) = y 3 ( s +.5L q ) ( s +.5L q ) = y 3 ( s +.5L q ) (11) (12)
Research and Applcaton of Work Roll Contour Technology The Open Mechancal Engneerng Journal, 215, Volume 9 113 The mnmum devaton dameter or axal force of work roll s a desgn objectve, and t can establsh an equaton wth the same roll devaton dameter under the man rollng wdth w m : ( ) = y(.5w m ) (13) y.5w m From the seven nonlnear equatons (1-13), seven roll parameters can be solved, and the HVC work roll contour can also be establshed. Consderng the work roll length as (L=255 mm), shftng lmt poston as (s m =15 mm), lnear wdth range as (L c =12 mm, L q =2 mm), and equvalent crown as (C r1 =-.9 mm, C r2 =.5 mm), the three order work roll and HVC were desgned and the crown adjustng ablty was compared under varous strp wdth, as shown n Fg. (2). The crown adjustng ablty / mm.6.4.2 -.4 -.6 -.8-1 3 order curve HVC Capacty Increment 6 9 12 15 18 21 -.2 Strp wdth /mm Fg. (2). Crown adjustng ablty comparson between HVC and 3 order curve. As shown n Fg. (2), along wth the drop of strp wdth, HVC work roll equvalent crown adjustng ablty decreases slowly than thrd order curve work roll because of the lnear relatonshp between equvalent crown and wdth. HVC contour adopt pecewse functon, makes the equvalent crown not only lnearly proportonal to shft poston, but also to strp wdth n specfed range, therefore, enhances overall shape control capacty of mlls. HVC contour has a stronger crown adjustment capacty than 3 order curve work roll, especally for the narrow strp. 3. MIDDLE VARIABLE CROWN WORK ROLL 15% 13% 11% 9% 7% 5% 3% 1% -1% Quarter wave s the man hgh order shape defect n thn gauge stanless steel rollng, as shown n Fg. (3). The reasons for hgh order shape defect are manly as follows: 1) strp factors, such as transverse uneven temperature, transverse uneven alloy components, profle anomales and so on. 2) Roll factors, such as roll transverse serous uneven wear, roll transverse uneven temperature dstrbuton, roll grndng precson and so on. 3) Roll deformaton factors, such as hgh order bendng of work roll and backup roll under hgh rollng forces. Some of the above factors can be avoded or lessened n the producton process, such as the profle anomales, roll grndng precson, uneven alloy components and so on, but the others cannot be solved due to equpment problems. Therefore, work roll compensaton technology has been consdered to elmnate the quarter wave. Capacty ncrement Fg. (3). Quarter wave n thn gauge stanless steel rollng. In the roll length range, parabolc flatness was consdered to desgn work roll conventonal curve. If center buckle s the man shape defect of stanless steel, desgnng parabolc curve for work roll, makng work roll ntermedate dameter small and both ends of the roll dameter larger. If edge wave s famlar, then the adjustment wll be opposte. Parabolc curve equaton of the work roll s as follows: y( x) = k 2 x 2.5L x.5l (14) where L s work roll length, x s work roll abscssa wth the mdpont of orgn, y(x) s parabolc work roll radus curve, k 2 s parabolc curve parameter. If asymmetrc flatness appears n dfferent poston on ether sde of strp center lne, or dfferent flatness appears n the same poston, then two sxth order curves are desgned on the bass of wave defect locaton and sze on both sdes of strp, as shown n Fg. (4). Sx order curve /µm Fg. (4). Sx order curve for compensaton. In the range of [-.5w, ] and (,.5w], parabolc curve by supermposng two sx order curves, mddle varable crown (MVC) work roll s obtaned, as shown n Fg. (5), and the formula s as follow: y( x) = x 1 25 2 15 1 5-6 -4-2 2 4 6 Strp wdth /mm ( ).5w x k 2 x 2 + b 2 x 2 + b 4 x 4 + b 6 x 6 k 2 x 2 + ( c 2 x 2 + c 4 x 4 + c 6 x 6 ) < x.5w k 2 x 2.5L x <.5w,.5w < x.5l (15) where L s the work roll length, w s the strp wdth, y(x) s the MVC radus curve, b 2, b 4, b 6, c 2, c 4, and c 6 are the parameters of the sx order curve whch satsfy the followng equatons: x 2
114 The Open Mechancal Engneerng Journal, 215, Volume 9 Jan et al. b 2 x 2 1 + b 4 x 6 1 + b 6 x 6 1 = 2b 2 + 4b 4 x 2 1 + 6b 6 x 4 1 b 2 (.5w) 2 + b 4.5w c 2 x 2 2 + c 4 x 6 2 + c 6 x 6 2 = 2c 2 + 4c 4 x 2 2 + 6c 6 x 4 2 c 2 (.5w) 2 + c 4.5w ( ) 4 + b 6 (.5w) 6 ( ) 4 + c 6 (.5w) 6 (16) (17) where, x 1, x 2 are the dstance from the strp center of asymmetry hgh order wave,, are the maxmum values for the sxth order radus curve, whch s used to compensate for the asymmetry hgh order wave, usually, the values of, are between 2 µm and 5 µm, the quarter wave s larger, and the and are bgger. MVC work roll curve/µm 5-5 -1-15 -2-25 Conventonal work roll MVC -1-5 5 1 work roll length /mm Fg. (5). MVC work roll curve for stanless steel rollng. As shown n Fg. (6), after usng MVC work roll technology n the last stand of hot rollng, a good shape was acheved, and quarter wave was elmnated by work roll compensaton technology. campagn, the profle anomales becomes more and more obvous. Conventonal work roll wth shftng along the axal drecton can unform a work roll wear and get a good profle [12, 13]. Shftng strategy for conventonal work rolls ncludes three parameters: shftng step t s, shftng stroke k s and shftng frequency f s, whch respectvely refers to the magntude of shftng, the maxmum value of shftng, towards the operaton sde or drvng sde and the calculaton frequency of shftng setup. At the begnnng of the rollng campagn, the amount of work roll wear s small, then as the shftng stroke s operated at a maxmum value, wear wdth B w s made larger, wear anomales heght H c grows smaller and the edge wear of the work roll s unform. Wth an ncrease of work roll wear, shftng stroke changes to mnmze nfluence the loadng gap profle and quarter wave caused by shftng. Varyng shftng stroke strategy algorthm s as follows: 1) If L L s where L s the rollng klometers of last stand n fnshng mll, L s s rollng klometers when the shftng stroke begns to change. When, L L s, the work roll shftng can be calculated by the same parameters as shftng strategy and s expressed as follows: N = 1 > N and % f s 1 + D r t s > N and % f s (18) where, N s the strp number for begnnng shftng and values range from 1 to 3 generally. D r s the shftng begnnng drecton and ntal values are ±1 generally. The comparon between shftng and shftng stroke k s requres the followng relatonshp: k s = k s > k s < k s (19) 2) If L >L s when L >L s, calculate the permssble shftng stroke k of the strp. Δk s = k s1 k s2 (2) k = Δk s L m (21) Fg. (6). Good shape qualty n thn gauge stanless steel rollng after usng MVC. 4. VARYING SHIFTING STROKE STRATEGY OF CONVENTIONAL WORK ROLL Accordng to dfferent contour curves, work roll shftng technology n hot strp mlls can be dvded nto a conventonal work roll shftng strategy (such as sne curve, parabolc curve, etc.) and hgh order work roll shftng strategy (such as CVC, Smart Crown, etc.) [9, 1]. Work roll wear n stanless steel rollng s 1.5-2. tmes than the plan carbon steel because of ts hgh rollng force [11], transverse serous uneven temperature, and n the later stages of rollng k = k s1 k ( L L s ) (22) where, k s1 s ntal shftng stroke, k s2 s shftng stroke n the end of rollng, Δk s s the dfference between k s1 and k s2, k s the varaton coeffcent of shftng stroke, L m s rollng klometers when the shftng stroke change to k s2. After establshng the value of k, we can get by usng formula (18) and S meets the demands below: k > k = (23) k < k varyng shftng stroke strategy has been used n the fnshng mlls of hot strp mlls. Operator can choose the shftng mode on the human machne nterface (HMI). By confgurng the shftng step t s, shftng stroke k s and the
Research and Applcaton of Work Roll Contour Technology The Open Mechancal Engneerng Journal, 215, Volume 9 115 shftng frequency f s, good profle and rollng stablty were acheved. Varyng shftng stroke strategy n a rollng unt s shown n Fg. (7). Work roll shftng / mm 1 5-5 -1 2 4 6 8 1 Fg. (7). Varyng shftng stroke strategy n a rollng unt. 5. INDUSTRIAL APPLICATION 145 mm hot strp mll of Schuan southwest stanless steel, 163 mm hot strp mll of Beha Chengde southwest stanless steel, 178 mm hot strp mll of Dngxn southwest stanless steel were put nto operaton n 28, 212 and 214 respectvely. In 145 mm hot strp mll, the quarter wave was serous and rollng stablty was poor because of ts hgh rollng force, the edge temperature drop and so on, by usng HVC, MVC, and varyng shftng stroke strategy of conventonal work roll, the problem has been resolved effectvely, and ths technology has also been appled n the other two stanless steels. For example, 163 mm hot rollng mll s a modern wde stanless steel producton lne whch has been ndependently ntegrated domestcally. It s man equpment s nclude: Two walkng beam furnaces, one rough descalng devce wth hgh pressure water, one four hgh reversble rough rollng mll wth vertcal rolls, one colbox wth double-workng poston, one flyng shear, 8 stands four hgh fnshng mlls, two down colers, one col conveyer, bndng machne and weghng machne. The desgned annual producton capacty s 1.6 mllon ton, ncludng 2 and 3 seres austentc stanless steel, 4 seres ferrte and martenstc stanless steel, and the scope of product specfcaton s 1.6~8. mm 83~152 mm. In order to mprove ts shape control ablty, elmnate quarter wave, make unform work roll wear, and ncrease rollng stablty n thn gauge stanless steel producton, HVC technology s used n upstream stands, MVC s used n last stand, and conventonal work roll (CON) wth varable shftng stroke strategy s used n other downstream stands, as shown n Fg. (8). F1 F2 F3 Strp number n a rollng unt F4 HVC HVC HVC HVC CON CON CON F5 F6 Shftng F7 F8 MVC results. As shown n Fg. (9), the number of stanless steel s 449, and more than 49.67% steel thckness s less than 2.2 mm. 124 mm 1.6 mm ultra-thn gauge stanless steel n hot rollng s also developed. Thckness of stanless steel / mm 3.5 3. 2.5 2. 1.5 1. Fg. (9). Thckness of stanless steel rollng. The crown ht rate of stanless steel reaches 98.1% n absolute error range of ±15 µm, and the flatness ht rate reaches 97.5% n absolute error range of ±25IU, at the same tme, quarter wave had been elmnated after usng MVC work roll technology. CONCLUSION Due to hgh rollng force, serous edge temperature drop, hgh order roll bendng and so on, quarter wave, bad profle and poor rollng stablty are common problems n stanless steel rollng. Under the premse of lmted condtons, as mentoned above, the work roll technology s the key to solvng these problems. HVC enhances the shape control capacty of the mlls, especally for the narrow strp. MVC elmnates the quarter wave by supermposng the sxth order curve, and conventonal work roll wth shftng along the axal drecton can make the work roll wear unform and obtan a good profle. The applcaton on hot strp mlls for stanless steel rollng ndcates that work roll technologes acheved the desred results n both shape control and rollng stablty. CONFLICT OF INTEREST The authors confrm that ths artcle content has no conflct of nterest. ACKNOWLEDGEMENTS 1.6mm 1 2 3 4 Rollng number of stanless steel Ths work was supported by Bejng Hgher Educaton Young Elte Teacher Project (YETP413) and Technology Development Plan of Guangx Provnce (213AA11). REFERENCES Fg. (8). Work roll technology usng n 163 mm hot strp mll for stanless steel rollng. Usng work roll technology, the producton process stablty s mproved and the product qualty acheved good [1] A. Selnger, A. Mayrhofer, and A. Kanz, SmartCroum - A new system for mproved profle and flatness control, Alumnum Internatonal Today, vol. 15, pp. 26-28, March 23. [2] W. Bald, G. Besemann, H. Feldmann, and T. Contnuously varable crown (CVC) rollng, Iron and Steel Engneerng, vol.22, pp.32-4, March 1987.
116 The Open Mechancal Engneerng Journal, 215, Volume 9 Jan et al. [3] J. G. Cao, J. Zhang, X. L. Chen, G. C. We, P. Song, and Y. Su, Selecton of strp mll confguraton and shape control, Iron and Steel, vol.4, pp.4-43, June 25. [4] H. B. L, J. Zhang, J. G. Cao, Z. M. Wang, Q. Wang, and S. S. Zhang, Analyss and selecton of crown control ranges for CVC work rolls n CSP hot rollng, J. Unversty of Scence and Technology Bejng, vol. 32, pp.118-122, Januar1. [5] J. Zhang, X. L. Chen, Y. H. Xu, and Y. Zhang, Roll contour desgn of 4-hgh mll wth varable crown by axal shftng, J. Unversty of Scence and Technology Bejng, vol.16, pp.98-11, November 1994. [6] H. B. L, J. Zhang, J. G. Cao, X. M. S, and S. X. Zhang, Control characterstcs contrast among cubc CVC, quntc CVC and SmartCrown roll controus, Chna Mechancal Engneerng, vol.2, pp.237-24, Januar9. [7] A. R. He, Q. Yang, X. L. Chen, L. Zhao, H. R. Dong, and Y. Q. Xu, Development and applcaton of lnearly varable crown work roll n hot strp mlls, Chnese Journal of Mechancal Engneerng, vol.44, pp.255-259, November 28. [8] R. Z. Wang, A. R. He, Q. Yang, L. Zhao, and H. R. Dong, Profle control capablty of LVC work roll contour, Iron and Steel, vol.41, pp.41-44, Ma6. [9] G. C. We, J. G. Cao, J. Zhang, J. W. Hao, and G. Chen, Optmzaton and applcaton of CVC work roll contour on 225 hot strp mlls, Journal of Central South Unversty (Scence and Technology), vol.38, pp.937-942, October 27. [1] J. Shao, A. R. He, Q. Yang, and N. A. Sh, Smulaton and applcaton of shape setup control system n hot strp mll, Journal of Iron and Steel Research, vol.2, pp.53-56, June 28. [11] J. Shao, A. R. He, Q. Yang, and H. W. Guo, Research on work roll wear predcton model takng n account lubrcaton n hot rollng, Chna Mechancal Engneerng, vol.2, pp. 361-364, Februar9. [12] X. W. Kong, J. Z. Xu, D. Y. Gong, and G. D. Wang, Optmum shft scheme of SFR realzed by adoptng flat roll, J. Northeastern Unversty, vol. 23, pp. 2-22, December 22. [13] Q. D. Zhang, A. R. He, L. W. Huang, X. L. Chen, G. C. We, and S. Q. Huang, shape control n schedule free hot strp rollng, Iron and Steel, vol.36, pp.72-75, Februar1. Receved: January 8, 215 Revsed: Januar5, 215 Accepted: Januar6, 215 Jan et al.; Lcensee Bentham Open. Ths s an open access artcle lcensed under the terms of the Creatve Commons Attrbuton Non-Commercal Lcense (http://creatvecommons.org/lcenses/by-nc/3./) whch permts unrestrcted, non-commercal use, dstrbuton and reproducton n any medum, provded the work s properly cted.