FEM Analysis of Rolling Pressure Along Strip Width in Cold Rolling Process

Available online at www.sciencedirect.comScienceDirectJOURNAL OF IRON AND STEEL RESEARCH , INTERNATIONAL 2007 ,14(5 ):22-26FEM Analysis of Rolling Pressure Along Strip Width inCold Rolling ProcessLIU Xiang-hua'，SHI Xu2，LI Shan-qing2，XU Jian-yong'，WANG Guo-dong'( 1. State Key Laboratory of Rolling and Automation , Northeastern University , Shenyang 110004 , Liaoning , China ;2. Research and Development Center , Baoshan Iron and Steel Co Ltd , Shanghai 201900 , China ;3. Baosteel Branch Co , Baoshan lron and Steel Co Ld , Shanghai 201900 , China )Abstract : Using 3-D elastic-plastic FEM ,the cold strip rlling process in a 4-high mill was simulated. The elastic deforma-tion of rolls , the plastic deformation of the strip , and the pressure between the work roll and the backup roll were taken intoaccount. The distribution of rolling pressure along the strip width was obtained. Based on the simulation results , the peakvalue of rolling pressure and the location of the peak were analyzed under different rolling conditions. The effects of the rollbending force and the strip width on the distribution of rlling pressure along the width direction were determined.Key words : thin strip ; cold rlling ; elastic-plastic FEM ; pressure distributionTo meet the user 's requirements of high quality anddeformation of the rolls cannot be neglected , and the 3-low cost for cold strip product ,it is very important to ob-D elastic-plastic FEM plays an important role in the coldtain high precision models for the calculation of the roll-strip rolling simulation.ing parameters. The rolling pressure and its distributionThere are two aspects on the research of rollinghave efcts on the thickness and shape of the strip ; thepressure : one is the prediction of the rolling force ; this .research on the rolling pressure is more important thanmainly deals with the setup calculation accurately andthe other parameters.rapidly, and the main research is the distribution ofThe main research methods of the deformation andthe rolling pressure along the rolling direction. Many a-the stress of the rolls are the influence function methodcademicians , specifically Miguel A , Angelov T，Yuen .and the FEM , which have been developed recently. The W Y D ,Liu Y J ,ZHU Guang-ming , and SUN Deng-influence function method has been widely used to solveyue , have done considerable work using the FEM to dis-the deformation and the stress of rolls , but it has a limita- cuss the distribution of rolling pressure along the rollingtion that using the model , the influence coefficients weredirection8-13. The other aspect is the research on thecalculated based on the equations for deflection of a sim-rolling pressure distribution along the strip width and theple beam1. 2-D FEM can be used to obtain the rollingentire contact areas ; Lin Zone-Ching , XIE Hong-biaopressure ,but it is not a method to simulate the rllingXU Zhi-rang , and ZHANG Guo-ming have done consid-pressure along the strip width direction. 3-D FEM pro-erable work“-1 on this aspect , and it is important tovides a possibility to obtain a better solution of the physi-control the strip shape , edge drop , wear , and spalling ofcal component for an investigated system. The 3-D rigidthe rol|[ 18]FEM has the characteristic of high efficiency in computa-中国煤化Iling proces in a four-tion , and has been widely applied in the hot rollinghigh stMYHC N M H G elastic-plastic FEM u-processIn cold strip rolling process , the elasticsing the Marc software. In the model , the elastic de-Foundation Item :Item Sponsored by Hi-Tech Research and Development Program of China ( 2003 AA33G010 ) ; National Basic ResearchProgram of China ( G2000067208-4 )Biography LIU Xiang-hud( 1953- ) , Male , Doctor , Professor; E-mail : sx-1jy@ 163. com; Revised Date : April 6 ,2006No. 5FEM Analysis of Rolling Pressure Along Strip Width in Cold Rolling Process23.formation of the work roll and the backup roll , the elas-gential vector in the direction of the relative velocity ;tic-plastic deformation of the strip , and the pressure be-and D, is relative sliding velocity.tween the work roll and the backup roll were taking intoIn Eqn.( 2 ) , the value of t will change positively oraccount. Based on the simulation , the characteristic ofnegatively with U, , and hence the friction stress/ force isthe rolling pressure along the strip width was analyzed ，discontinuous( Fig. 1 ,0。 =0 ). When the value of u, isand the change characteristic was obtained in differentzero( that is , stick-slip ) , the friction is discontinuous.rolling parameters of bending force and strip width.This discontinuity in the value of σ, can result in diffi-culties of calculation and can cause the phenomenon of1 Introduction of Modelnon-convergence in the numerical computation ; hence,1.1 FE modela modified shear friction model is implemented using theSince the rolling conditions and the geometric pa-arc tangent function :rameters are symmetrical ，a quarter of the geometricσ:≤-m°σ，2arctan(3 )model is selected to be the simulated object. The geo-metric parameters of the model are shown in Table 1.where v。is the value of the relative velocity when slidingThe model uses the Update Lagrange Method , the Vonoccurs.Mises yield criterion , and the large deformation method.The value of v。is important in determining howFriction is a complex physical phenomenon that in-closely the mathematic model represents the step func-volves the characteristics of the surface , such as , thetion. A very large value of D。 results in a reduced valuesurface roughness，normal stres，and the relative veloc- of the efective friction. A very small value results inity. The most popular friction model is the coulomb fric-poor convergence. In the present study , the value of Dtion model. However ,this model often does not correlateis 0.08. The selected stick-slip approximation( m'well with the experimental observations when the normal3force/ stress becomes large. If the normal stress becomes=1 ,1tl=1 ) and the shear friction are shown in Fig. 1. .large , the coulomb model may predict that the frictionalshear stresses increase to a level that can exceed the flow1.2 FEM meshesstress or the failure stress of the material. As this isThe roll system is regarded as an elastic body , andphysically possible , the choice is to use the cohesivethe strip is regarded as an elastic-plastic body. To de-shear based friction model.crease the amount of elements , the possible contact areaThe shear friction model states that the frictionalof the roll system and the strip are divided denselystress is a fraction of the equivalent stress in the materi-( Fig.2 ). The element of 20-node , isoparametric , arbi-al :trary hexahedron was used for the strip and the possibleσ≤-m(1)contact area of the roll system , and the 8-node elementwas used for the remaining rolls.0Compared with the 8 -node element , the 20-node(2)|o,Ielement can simulate the real curve better( Fig.3 ).where σ; is tangential friction stress ,MPa ;m is frictionThe 20-node element uses tri-quadratic interpolationcoefficient ;σ is equivalent stress ,MPa it is tan-.2厂0.8 tTable 1 Geometric parameters of modelmm0.4Roll diameter1 200Backup rollBarrel length中国煤化工Roll neck diameter700470MYHCNMHG....... v_=0.08Work roll151015- 10-551015285Relative sliding velocity/(mm-s )Fig.1 Curve of shear frictionThickness1.0StripWidth700 ,960 ,1 230. 24+.Jourmal of Iron and Steel Research , InternationalVol. 14Table 2 Physical properties of roll and stripYoung modulus/ MPa2. 156x 105Poisson ratio0.3Density/( kg; m -3 )7.85x1032. 156 x 105Backup rollStripDensity/( kg" m ~ 3 )Table 3Rolling conditionsBending force/kN0 ,200 ,400Work rollForward tension/ MPa246Backward tension/ MPa147Friction cofficient0.05Fig. 2 Finite element modelRolling velocity/( mm" s-1 )8 050b)2 ResultsBased on the simulation results of the rollingprocess under different roll bending forces ( three levels :0 ,200 , and 400 kN ) and strip widths ( three levels :700 ,960 ,and 1 230 mm ) , the distribution of rollingpressure along the strip width was obtained.( a)20-node element ; ( b)8-node elementFig. 3 Isoparametric arbitrary hexahedral element2.1 Characteristic of rolling pressure along stripwidthfunctions to represent the coordinates and displace-The distribution of the rolling pressure in the con-ments ;thus , it allows for an accurate representation oftact area is shown in Fig. 5.the strain fields in elastic analyses. The 8-node elementAs seen in Fig. 5( a ) , without the bending force ,uses tri-linear interpolation functions ; the strains tend toat the entry side , the rolling pressure increases from thebe constant throughout the element , which results in :center to the edge and reaches a peak value near thepoor representation of the shear or the bending behavior.strip edge ;at the neutral point , the pressure shows a lit-tle variation in the center area and decreases at the strip1.3 Rolling conditionsedge ; and at the exit side , the pressure variation is simi-The material of the strip is selected as the C-Mnlar to the pressure variation at the entry side. It is seensteel in some factory , and the curve of plastic strain offrom Fig. 5( b ) that the bending force causes the rollingthe strip is shown in Fig. 4. The physical properties ofpressure to be flatting along the width direction.the model are shown in Table 2 , and the rolling parame-2.2 Influence of strip width on distribution of totalters are shown in Table 3.rolling pressure650The total rolling pressure is obtained by the sum00 tforce in the rolling direction. The distribution of the total50 trolling中国煤化工for different strip width500is showMHCN M H GFig 6 ,without the ben-ding force , the rolling pressure increases from the strip450.51.01.52.0center to the edge , and with the increase in the stripStrainwidth , the increment and the peak value of the rollingFig. 4 Curve of plastic strainpressure decrease accordingly.No. 5FEM Analysis of Rolling Pressure Along Strip W idth in Cold Rolling Process25.a)| (b)1 2000.76' 0.343.550谷F 6.7509018027609.2012024036048000 10.00Distance in widh/mmDistance? in widtV/nm .(a) Strip width of 700 mm , no bending force; ( b) Strip widh of 1 230 mm ,bending force of 400 kNFig.5 Rolling pressure in contact area700it is about 60 mm to the edge of the strip ; when the stripwidth is 1 230 mm , the rolling pressure begins to in-500'crease at the position where it is about 135 mm to theedge of the strip , and the rolling pressure reaches theSurip widh 700 mm9641230 Ipeak value at the position where it is about 75 mm to the100edge of the strip.As seen from the above data , without the bending000500Distance in width/mmforce , the rolling pressure increases since the edge of theFig. 6 Rolling pressure along strip width forstrip has no relationship with the width of the strip. Fordifferent strip widthdifferent strip width , the peak value of the rolling pres-sure is at a position where it is about 140 mm to the edgeBy analyzing the data of the simulation results , whenof strip , and with the increase in the strip width , thethe strip width is 700 mm , the rolling pressure begins todistance of the peak value location to the edge also in-increase at the position where it is about 140 mm to thecreases , but the increment is very limited.2.3Influence of bending force on distribution ofpeak value at the position where it is about 50 mm to thetotal rolling pressureedge of the strip ; when the strip width is 960 mm , theThe distribution of the total rolling pressure alongrolling pressure begins to increase at the position where itthe strip width under different roll bending forces isis about 150 mm to the edge of the strip , and the rollingshown in Fig. 7.As seen from Fig. 7 ,it is clear that the bendingpressure reaches the peak value at the position wherea) Strip width 700 mm(b) Strip width 1 230 mm8233002 100中国煤化工200400MYHCNMHG.600Distance in width/mi1-No bending force; 2- Bending force of 200 kN; 3- -Bending force of 400 kNFig. 7 Rolling pressure along strip width under different bending forcesJourmal of Iron and Steel Research , InternationalVol. 14force influences the rolling pressure distribution at theRolling Process During Width Reduction by Full Three-Dimen-sional Rigid-Plastic Finite Element Method[ J ] Jourmal of Ma-area near the strip edge , and with the increase in theterials Engineering and Performance , 1997 ,6 :757-765.bending force ,the increment of the rlligg pressure be- [5] Cao HRamalingm sC, Baher GC,et al. 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