Journal of Materials Processing Technology 209 (2009) 48504856

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Journal of Materials Processing Technology

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Resear forproces

Jinmao Jia School of Mec 240, Pb Baoshan Iron

a r t i c l

Article history:Received 25 JuReceived in reAccepted 10 Ja

Keywords:Cage roll formERW round piNon-bending aFinite element methodLongitudinal strain

orminprocedgezes. Twith

, duesed dplastiestig

phenomenon is found, and the ranges of the non-bending area at different forming stands are obtained.In addition, the longitudinal strain at the inside edge and center are predicted, and by comparison, it canbe known that the deformation of the strip edge is usually larger and edge buckling ismost likely to occurat the entry sides of No.1No.3 n-pass stands. Finally, the circumferential length, opening distance andthe proles of the deformed strip are measured on the cage roll-forming mill. There is a good agreement

1. Introdu

In cold rdeformed inseries of roltion. As anforming is ptrial elds, agauge sectiowelded squ

At preseducing elecconventionventional ststepwise behorizontalBecause theall the formdifferent oudowntime a

CorresponE-mail add

0924-0136/$ doi:10.1016/j.jbetween the experimental and simulated results. 2009 Elsevier B.V. All rights reserved.

ction

oll-forming processes, metal sheets are progressivelyto products with required cross-sectional proles by a

ls installed at the tandems along the longitudinal direc-economical metal sheet forming technology, cold rolllayingmore andmore important roles in various indus-nd many products are manufactured by it, such as lightn steels, electricwelded round pipes and tubes, electricare and rectangular pipes, etc.nt, there are two main roll-forming processes for pro-tric resistance welded (ERW) pipes, which are theal step roll forming and cage roll forming. In the con-ep roll-forming process of ERW pipes, a metal sheet isnt into round shape using contoured rolls (vertical androlls) mounted on different stands, as shown in Fig. 1.formedstrip is shapedasdenedby the contourof rolls,ing rolls have to be changed every timewhenpipeswithter diameters are manufactured, which leads to longnd high roll costs. Moreover, edge buckling and spring

ding author. Fax: +86 21 34206313.resses: void@sjtu.edu.cn, erwok@hotmail.com (J. Jiang).

back are prone to occur during the conventional forming process,especially as the ratio of the outside diameter to wall thickness (D/tratio) increases. In consideration of these problems, the conven-tional roll-forming mill is changed into the cage roll-forming mill(Michitoshi et al., 2004).

In the cage roll-forming process of ERW pipes, a metal sheet iscontinuously deformed into a round pipe by using a set of smallcage rolls arranged along the outer surface of the steel strip. Thosesmall cage rolls can realize abendingprocess by applying thedown-hill forming before the n-pass stands. As shown in Fig. 2, the cageroll-forming mill consists of ve parts, which are pinch roll unit,edge-bending stand, pre-forming section, linear forming section(No.1No.3 linear forming section) and n-pass stands (No.1No.3n-pass stand). The pinch roll unit serves for feeding the strip intothe forming mill and for providing main drive forces during pro-duction. The edge-bending stands are arranged after the pinch rollstand to bend strip edge on both sides by an upper and a lowerbending roll. The pre-forming section consists of two outer formingroll groups equipped with 13 non-driven cage rolls, inner formingtools (upper roll 1upper roll 4), and a breakdown stand. The linearforming section serves for further forming of the strip before then-pass stands, and comprises three (No.1No.3) linear formingsub-sections (each sub-section consists of two outer forming rollgroups equipped with 1012 non-driven cage rolls), inner forming

see front matter 2009 Elsevier B.V. All rights reserved.matprotec.2009.01.011ch on strip deformation in the cage roll-s of ERW round pipes

anga,, Dayong Lia, Yinghong Penga, Jianxin Lib

hanical Engineering, Shanghai Jiaotong University, 800 Dongchuan Road, Shanghai 200& Steel Co. Ltd., Shanghai 201900, PR China

e i n f o

ne 2008vised form 6 January 2009nuary 2009

ingpesrea

a b s t r a c t

Cage roll forming is an advanced roll-fround pipes. In the cage roll-formingthe deformable strip to bend the stripused for forming pipes of different siimprove forming quality, as comparedcan be found about cage roll formingon experience rather than science-bais simulated with the explicit elasticcage roll-forming process has been invlocate / jmatprotec

ming

R China

g technique tomanufacture electric resistancewelded (ERW)ess, many small rolls are arranged along the outer surface ofin a more smooth way. Furthermore, these small rolls can beherefore, cage roll forming can reduce roll change time andthe conventional step roll forming. However, very few studiesto its complexity, and the industrial practice depends greatlyesign today. In this work, the whole cage roll-forming processc nite element method, and the strip deformation during theated in detail. Through the simulation, the non-bending area

J. Jiang et al. / Journal of Materials Processing Technology 209 (2009) 48504856 4851

tools (uppestands are tsheet weldelower roll, aterized by thcage rolls, wwithout charesult, the ctime signithe deform

Many reroll-forminsemi-analytforming prbetween twand an autoKiuchi andformed a gdeformed gusing this g

deformed skelp. Nefussi andGilormini (1993) described themiddlesurface of thedeformed strip byusing a Coons Patch, andpredictedthe optimal shape and the deformed length of a strip before the rstroll stand. Liu et al. (1996) and Han et al. (2004) developed a nitestripmethopipes basedmethod reshave an advods are basshape of thand the stri

In recenin the analysented a corigid-viscopsheet deforet al. (2000ysis of thesections. Inalized planwas startedKim et al. (pass conven

ge sionsto-ptmeg proe rolform, proinin

mentoug

rmintudietionanal

rial egreacatell foroll foFig. 1. A conventional roll-forming mill.

r roll 5upper roll 8) and the support rolls. The n-passhe last roll-forming sections before the shaped metald, and each n-pass stand comprises an upper roll, and two side rolls. This cage roll-forming mill is charac-e feature that it is equippedwith several dozen pairs ofhich can be used for manufacturing pipes of any sizesnging and ensure smooth forming of strip edge. As aage roll forming can not only reduce the roll changingcantly, but also prevent edge buckling and spring back ofed strip, compared with the conventional roll forming.searchers have done many studies on the conventionalg process of ERW pipes. Kiuchi (1973) rstly applied aical method (SAM) to simulate the conventional roll-ocess by dening the deformed surface of the sheeto adjacent stands as a set of sinusoidal shape functions,mated design system of roll proles was developed byKoudabashi (1984). Walker and Pick (1990, 1991) per-

the edregress3D elaexpliciforminon cagthe dehistorydetermexperi

Althroll-fovious sconvenon theindust20m),complicage rocage reneral modeling technique by describing the complexeometry of the skelp with B-splines and a method ofeometric description to dene the strain state in the

Fig. 2. A cage roll-forming mill.

FEM is seleof ERW piping memor1990). Theusing explicment methdeformatioprocess. Inthe deformduring theof non-benaddition, thcenter are pbuckling ardistance anmeasured a

2. Finite el

An elastmill, whichter, has beeforming secd (FSM) to analyze the cold roll-forming process of ERWon total-Lagrangian method and updated-Lagrangian

pectively. The above two methods SAM and FSM bothantage of low computational cost, but these two meth-ed on the geometric assumption of the deformatione strip and neglect the contact between forming rollsp, which decrease the accuracy of analysis.t years, the nite element method has also been appliedsis of the roll-forming process. Kim and Oh (1999) pre-mputational method based on the three-dimensionallastic nite element method to investigate the steelmation in the conventional roll-forming process. Hong) developed a 3D FEM program (SHAPE-RF) for anal-cold roll-forming process of channel and circular tubeSHAPE-RF, initial geometrywas calculatedwith gener-e-strain assumption, and then the 3D FEM simulationwith the initial geometry and boundary conditions.

2003) established a nite element model of the multi-tional roll-formingprocess of ERWpipes, andpredicted

hapes of initial strip with second-degree polynomialmethod. Kiuchi and Wang (1999) developed 2D andlastic FEM codes based on static implicit and dynamicthods, andmade a comprehensive study on exible roll-cess of ERW pipe. To obtain fundamental knowledge

l-forming process, Yokoyama et al. (1981) investigatedation behavior of steel sheet as expressed in strainjection trace and forming owers and methods ofg forming load at n-pass rolls and squeeze rolls bys.h there have been many researches on the analysis ofg process by various simulation techniques,most of pre-s focusedondeformation features ofmetal sheets in theal roll-forming process. Few reports have been foundysis of the cage roll-forming process, except for somexperiment. Due to the quite long forming zone (almostt number of forming rolls (approximately 80 rolls), andcontact status between the deformed strip and rolls inming, the computation cost for simulation of the wholerming is formidable. Therefore, the dynamic explicitcted to simulate the whole cage roll-forming processes, due to its high efciency in reducing CPU time, sav-y and dealing with the contact (Lindgren and Edberg,modeling of the cage roll-forming process is proposedit code LS-DYNA based on 3D elasticplastic nite ele-od. The work presented here aims to investigate then characteristics of steel strip in the cage roll-formingparticular, through analyzing the relative curvature ofed strip, the non-bending area phenomenon is foundcage roll-forming process of ERW pipes, and the rangesding area at different forming stands are obtained. Ine distribution of longitudinal strains at inside edge andredicted and the positionsmost likely subjected to edgee located. Finally, the circumferential length, openingd cross-section congurations of the deformed strip arend compared with the simulation results.

ement modeling of the cage roll-forming process

icplastic nite element model of the cage roll-formingis used to produce pipes of 325mm in outer diame-

n established. The FE models about pre-forming, lineartion, and n-pass stands are shown in Figs. 35 respec-

4852 J. Jiang et al. / Journal of Materials Processing Technology 209 (2009) 48504856

Fig. 3. The FE model of pre-forming section in the cage roll-forming process.

Fig. 4. The FE

tively. Thed(length)1X-60 steel.sheet speedbeen tried

Fig. 5. T

and the comto symmetrof the cage

2.1. Materia

elasa aned inll-fo

he shThe210GPdepictcage rowith tmodel of linear forming section in the cage roll-forming process.

imensionof theoriginal strip tobe formed is 21,000mm018mm (width)10.3mm (thickness). The material isIn this study, different element types, element sizes,, sheet length, typeofvelocityboundaryconditionshaveto get a good balance between the required CPU time

he FE model of n-pass stands in the cage roll-forming process.

bodies.

2.2. Finite e

In the nto generatements are uinside andthe steel strwhole stripand all the felements. Tcient is seof the formcertain speeforming dirjected to ano motion ia satisfactobe rationalof metal sh(Zhang et atual velocitkinetic ene

3. Discussi

Throughforming pro

3.1. Deform

As showshapes at thtions; EE rFig. 6. Stressstrain curves for X-60 steel.

putation accuracy. Only half of the model is used duey. The detailed information of the nite element modelroll-forming process is described as follows.

l properties

tic modulus (E) and Poissons ratio () of X-60 steel ared 0.3, respectively. The stressstrain curve for X-60 isFig. 6. The deformation of all the forming rolls in therming process of ERW pipes is very tiny as comparedaped steel strip, so all of them are assumed as rigid

lement modeling

ite element model, eight-node brick elements are usedthe mesh for the steel strip, and four-node shell ele-sed to model the roll surfaces. In order to simulate theoutside bending deformation of strip more accurately,ip is divided into two layers through the thickness. Theconsists of 231,132 nodes and 150,500 brick elements,orming rolls consist of 278,280 nodes and 269,384 shellhe coulombs friction law is used and the frictional coef-t to 0.1. For simplicity, all six degrees of freedom of alling rolls are xed and the steel strip is pulled with ad through a series of xed forming rolls arranged in theection. A set of nodes at the center of the strip is sub-symmetrical condition constraint in the yz plane, i.e.s allowed for y translation, x and z rotation. For keepingry precision for simulation, the virtual velocity shouldly controlled to ensure that the virtual kinetic energy

eet should be less than 7% of the total internal energyl., 2006). As a result, in the nal 3D simulation, the vir-y of steel strip is set to 12m/s, which results in its virtualrgy being 5.8% of the total internal energy.

on of simulation results

the nite element simulation, the whole cage roll-cess of ERW round pipe is investigated.

ation features of steel strip

n in Fig. 7, AA, BB, CC and DD represent the sectione outlet of pre-forming, No.1No.3 linear forming sec-epresents the section shape at the No.1 n-pass stand.

J. Jiang et al. / Journal of Materials Processing Technology 209 (2009) 48504856 4853

eet in the different forming positions.

The non-becanbe clearare those rpassing throing directiothe No.1 npass standsthe steel ststand (as sforming rolleads to inadeformedstsqueeze-bethe constradeformed sforming roleliminated

Throughbending aresections, sonon-bendinthe non-benis dened athe radius ocurvature is

In orderduring the walong transtypical formthe edge-beoutlet of prsection (Lf1No.3 linearn-pass sta

Fig. 9 shdeformed stion. As sh

Fig. 8.

elative curvature of the cross-sectionof deformed strip at different positionshe pre-forming section.

ed strip is 5072% relative distance from the center of stripthe pre-forming section.10 shows the relative curvature of the cross-section of theed strip at different positions during the linear forming sec-Fig. 7. Schematic illustration of non-bending area of steel sh

nding areas of steel sheet in different forming positionsly observed fromFig. 7. The so-callednon-bending areasegions on the strip that remain almost straight afterugh forming rolls. According to Fig. 7, along the form-n, the non-bending area is always in existence prior to-pass stand and eliminated after passing through n-. The reason for having the non-bending area is thatrip is shaped by air-bending before the No.1 n-passhown in Fig. 8(a)). In air-bending the steel sheet andls are under an incomplete contact state, which usuallydequate bending due to the lack of constraints. As therip ispassing through then-pass stands, it is shapedbynding (shownas Fig. 8(b)),which can greatly strengthenints. Moreover, in squeeze-bending the shape of thetrip is generally dependent on the geometry of thels. Therefore, the non-bending area of the steel strip isat the n-pass rolls.above analysis, it just can be found that the non-a usually occurs at the pre-forming and linear formingit is still very necessary to investigate the ranges of theg area at different forming positions. In the next study,ding area is indicated by the relative curvature, whichs the ratio of bending radius of the deformed sheet tof the nal product. Usually the region where relativeless than 0.1 can be taken as non-bending area.to get the detailed information of the non-bending areahole cage roll-forming process, the relative curvature

verse proles of the deformed sheet is calculated at theing positions. These typical forming positions includending stand (ED), upper roll 2 (R2), upper roll 4 (R4),e-forming section (Prf), outlet of No.1 linear forming), outlet of No.2 linear forming section (Lf2), outlet offorming section (Lf3), No.1 n-pass stand (Fp1), No.2nd (Fp2) and No.3 n-pass stand (Fp3).ows the relative curvature of the cross-section of the

Fig. 9. Rduring t

deformduring

Fig.deformtrip at different positions during the pre-forming sec-own in Fig. 9, the range of non-bending area of the

Schematic illustration of air-bending and squeeze-bending.Fig. 10. Relatitions during thve curvature of the cross-section of deformed strip at different posi-e linear forming section.

4854 J. Jiang et al. / Journal of Materials Processing Technology 209 (2009) 48504856

Fig. 11. Relative curvature of the cross-section of deformed strip at different posi-tions during the n-pass stands.

tion. As shown in Fig. 10, during the No.1 and No.2 linear formingsections th5272% relalinear formthe center o

Fig. 11 shstrip at diffethe non-benafter the NoFig. 7.

In orderand correspgral of relaof strip atintegral ofat differentear formindeformed sthe formingthe edge-beis that the bwhile the d

Fig. 12. Integrforming positi

Fig. 13. Longicage roll-form

tions is smoin-pross-atio

rminby sqecom

ngitu

racts ofave

ll occof the13 sedgeal die mathe

whicucklcursdowe range of non-bending area of the deformed strip istive distance from the center of strip and after the No.3ing section its range is 6368% relative distance fromf strip.ows relative curvature of the cross-section of deformedrent positions at then-pass stands. As shown in Fig. 11,ding area of the deformed strip disappears completely.1 n-pass stand, which has also been demonstrated in

to evaluate the contribution of different forming standsonding bending degree to the deformed strip, the inte-tive curvature with respect to distance from the centerdifferent positions is calculated. Fig. 12 depicts the

relative curvature of the deformed strip cross-sectionforming positions. During the pre-forming and lin-

g sections, the integral of relative curvature of thetrip cross-section increases linearly and smoothly along

direction; an obvious increment can be observed atnding (ED) and No.1 n-pass (Fp1) stands. The reasonending deformation at ED and Fp1 stands is very large,eformation at the pre-forming and linear forming sec-

(No.3 Fstrip cdeformroll-fopletedstrip b

3.2. Lo

In pprocesedge wlingwistrain

Fig.insidegitudinand thmeansedge,edge btion ocbreakal of relative curvature of the deformed strip cross-section at differentons.

tions. In this observed

It shouldsile deformregion fromstand.

The longthe No.1N2.0%, 2.3% adeformatioously, edgeNo.1No.3

Fig. 14 sinside centestrain at theNo.1 n-paand linear fthe longituremain wittudinal strain of the deformed strip at inside edge during the entireing process.

oth and uniform. In addition, at the last forming standass) the integral of relative curvature of the deformedsection reaches about 0.65, which means the bendingn of the at strip has been done 65% after the entire cageg process. The remaining 35% deformation will be com-ueeze-weldingandsizing sections, before thedeformedes the nal product.

dinal strain

ice, the most common defect in the cage roll-formingERW round pipes is edge buckling, which is so-called. Once the edge elongation is excessive, the edge buck-ur. Therefore, it is necessary to analyze the longitudinalskelp during the cage roll-forming process.

hows the longitudinal strain of the deformed strip atduring the entire cage roll-forming process. In the lon-rection, tensile strain at the edge shows a great increaseximum strain is about 1.65% at edge-bending stand. Itedge-bending rolls exert a strong bending on the striph is helpful to increasing the rigidity and preventinging. After edge-bending rolls, small plastic deforma-on the strip edge at the inlet of pre-forming section,

n stand, the outlet of No.1No.3 linear forming sec-

e cage zone, little variation in the longitudinal strain.be noticed that the edge is subjected to a slight ten-

ation and then a large compressive deformation in thethe last cage roll to the entrance of the No.1 n-pass

itudinal strain at the edge shows a great increase ato.3 n-pass stands and the maximum strains are aboutnd3.2% respectively,whichmeans that the relative largen of the strip edge occurs at the n-pass stands. Obvi-buckling is mostly likely to appear at the entry side ofn-pass stands.hows the longitudinal strain of the deformed strip atr part during the entire cage roll-formingprocess. As forcenter part, small plastic deformation occurs after the

ss stand and the longitudinal strain in the pre-formingorming sections are less than 0.2%, which indicates thatdinal deformation in the cage zone is small enough tohin the elastic scope.

J. Jiang et al. / Journal of Materials Processing Technology 209 (2009) 48504856 4855

Fig. 14. Longitcage roll-form

Table 1Comparisons ostrip.

Measured pos

EDPrfLf1Lf2Lf3

4. Compar

In orderferential lenthe deformforming mipositions h(ED), pre-foforming sectively.

Table 1 sferential lenat the diffelated resultthe outsidethe maximcircumferenrespondingsection. As srelative err

Table 2Comparisons o

Measured pos

EDPrfLf1Lf2Lf3

Fig. 15. Prole comparison at the exit of edge-bending stand.udinal strain of the deformed strip at inside center during the entireing process.

f measured and simulated results of the circumferential length of

itions Circumferential length l (mm) l (mm) l (%)

Simulated Measured

1026.5 1030.5 4 0.3881031.8 1036.2 4.4 0.4251035.5 1039.4 3.9 0.3751037.5 1043.1 5.6 0.5371041.5 1047 5.5 0.525

isons with experimental measurementsto calibrate the nite element simulation, the circum-gth, opening distance and the section congurations ofed strip have been measured on an industrial cage roll-ll. As shown as in Fig. 7, for convenience, ve measuredave been chosen, which are the exit of edge bendingrming section (Prf), linear forming section 1 (Lf1), lineartion 2 (Lf2) and linear forming section 3 (Lf3), respec-

hows themeasuredand simulated results of the circum-gth (l) of the deformed strip along the outside surface

rent positions. Table 2 shows the measured and simu-s of the opening distance (d) of the deformed strip atsurface at the different positions. As shown in Table 1,um absolute error (l) and relative error (l) of thetial length is 5.6mm and 0.537% respectively. The cor-positions are located at the exit of No.2 linear forminghown in Table 2, themaximum absolute error (d) andor (d) of the opening distance is 20.2mm and 4.514%

f measured and simulated results of the opening distance of strip.

itions Opening distance d (mm) d (mm) d (%)

Simulated Measured

979.1 986.2 7.1 0.720778.6 785.5 6.9 0.878572.6 585.8 13.2 2.253427.3 447.5 20.2 4.514184.6 190.3 5.7 2.995

Fig. 1

respectivelyNo.2 linear

Figs. 15of the deforlinear formrespectivelyresults and

Fig6. Prole comparison at the exit of the pre-forming section.

. The corresponding position is located at the exit offorming section.19 show the comparison of the section congurationsmed strip at the exit of edge bending, pre-forming, No.1ing, No.2 linear forming and No.3 linear forming section. Good agreement is shown between the experimentalsimulation results.

. 17. Prole comparison at the exit of No.1 linear forming.

4856 J. Jiang et al. / Journal of Materials Processing Technology 209 (2009) 48504856

Fig

Fig

5. Summa

In this pcage roll-fodeformatiosimulationdrawn:

(1) The steeNo.1 nthe nonn-passof the ddifferenthe desforming

(2) By computing the integral of relative curvature with respect todistance from the center of strip at different positionswith thetrapezoidalmethod, not only the forming contribution of differ-ent forming stands but also the bending degree of the deformedstrip in different forming sections are predicted. It is helpfulto evaluate the forming capability of different forming sectionsandadjust formingparametersmore reasonablyduring thecageroll-forming process.

(3) Through analyzing the strain distribution of the deformed stripin the forming direction, the characteristics of longitudinaldeformation at edge and center parts are obtained. At the sametime, the positions most likely subjected to edge buckling havebeen located.

(4) The circumferential length, opening distance and the proles ofdefo

l-forme a g

wled

autf Na010,7XDy Exc

nces

., Liuretica. 18. Prole comparison at the exit of No.2 linear forming.

therolhav

Ackno

Theport o50634(Nos. 0Centur

Refere

Han, Z.Wtheo. 19. Prole comparison at the exit of No.3 linear forming.

ry and conclusion

aper, the elasticplastic FEM model about the wholerming ERW pipe mill has been established. The

n behavior of steel sheet has been analyzed throughof the forming process. The following conclusions are

l strip is subjected to anair-bendingdeformationbefore-pass stand in the cage roll-forming process. As a result,-bending area phenomenon can be found before No.1stand.After calculating the relative curvatureofproleseformed strip, the ranges of the non-bending area att forming positions are obtained, which is instructive toign of pass-schedules and roll proles in the cage roll-process.

of MateriaHong, S.M., Ki

lation proAnnual M

Kiuchi,M., 197of Industr

Kiuchi,M., Koucold roll foMetalwork

Kiuchi, M., Wmill/proce

Kim, N., Oh, S.-element m

Kim, N., Kang,for thick tProcessing

Liu, C., Zhou,nite strip

Lindgren, L.-Kin simulat

Michitoshi, T.,Hikari 24

Nefussi, G., Giforming. I

Walker, T.R., Piroll formin

Walker, T.R., Ppipe skelp

Yokoyama, E.,sheet defoforming E

Zhang, D.J., Cuspringback(10), 1636rmed strip have been measured on the 325mm cageing mill, and the experimental and simulated results

ood agreement.

gements

hors would like to acknowledge the nancial sup-tional Natural Science Foundation of China (Nos.50375095), Shanghai Science & Technology Projects14016, 06QA14026, 05JC14022), and Program for Newellent Talents in University (NCET-07-0545).

, C., Lu, W.P., Ren, L.Q., Jin, T., 2004. Experimental investigation andl analysis of roll forming of electrical resistance welded pipes. Journalls Processing Technology 145, 311316.m, D.S., Yoon, H.J., Kim, N., 2000. Development of roll forming simu-gram. In: Transactions of the Korean Society of CAD/CAM Engineerseeting, pp. 417423.3. Analytical study on cold roll forming process. Report of the Instituteial Science 23 (1), 143.dabashi, T., 1984. Automated design systemof optimal roll proles forrming. In: Proceedings of the 3rd International Conference on Rotarying Processes, pp. 423436.ang, F.Z., 1999. FEM simulation of roll-forming of ERW pipes andss design. In: Proceedings of the 6th ICTP, pp. 1924.I., 1999. Analysis tool for roll forming of sheetmetal strips by the niteethod. CIRP Annals-Manufacturing Technology 48 (1), 235238.B., Lee, S., 2003. Prediction and design of edge shape of initial stripube roll forming using nite element method. Journal of MaterialsTechnology 142, 479486.

Y., Lu, W.P., 1996. Numerical simulation of roll-forming by B-splinemethod. Journal of Materials Processing Technology 60, 215218.

., Edberg, J., 1990. Explicit versus implicit nite element formulationion of rolling. Journal of Materials Processing Technology 24, 8594.Isamu, K., Osamu, S., 2004. Outline of new forming equipment forERW Mill, Nippon Steel Technical Report, No. 90, pp.122126.lormini, P., 1993. A simplied method for the simulation of cold rollnternational Journal of Mechanical Sciences 35 (10), 867878.ck, R.J., 1990. Approximation of the axial strains developed during theg of ERW pipe. Journal of Materials Processing Technology 22, 2944.ick, R.J., 1991. Developments in the geometric modeling of an ERW. Journal of Materials Processing Technology 25, 3554.Toyooka, T., Ejima, A., Yoshimoto, Y., Kawate, T., Kumata, K., 1981. Steelrmation behavior and forming load determination in the 26-inch cageRW pipe mill, Kawasaki steel technical report, No.4, pp. 7283.i, Z.S., Li, Y.Q., Ruan, X.Y., 2006. Effect of virtual kinetic energy onsimulation accuracy. Journal of Harbin Institute of Technology 38

1639.

Research on strip deformation in the cage roll-forming process of ERW round pipesIntroductionFinite element modeling of the cage roll-forming processMaterial propertiesFinite element modeling

Discussion of simulation resultsDeformation features of steel stripLongitudinal strain

Comparisons with experimental measurementsSummary and conclusionAcknowledgementsReferences