Research ArticleOne-Time Roll-Forming Technology for High-Strength SteelProfiles with ldquo日rdquo Section

Jicai Liang12 Chuandong Chen13 Ce Liang 13 Yi Li 13 Guangyi Chen 4

Xiaoming Li 13 and Aicheng Wang 12

1Key Laboratory of Automobile Materials (Jilin University) Ministry of Education Changchun 130025 Jilin China2Roll Forging Institute Jilin University Changchun 130025 Jilin China3College of Materials Science and Engineering Jilin University Changchun 130025 Jilin China4School of Automotive Engineering Dalian University of Technology Dalian 116024 Liaoning China

Correspondence should be addressed to Ce Liang liangcejlueducn and Guangyi Chen chengy0721163com

Received 30 January 2019 Revised 6 August 2019 Accepted 29 August 2019 Published 22 September 2019

Academic Editor Gianfranco Palumbo

Copyright copy 2019 Jicai Liang et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Roll forming is an important processing method for the production of commercial vehicle anticollision beams and edge bucklingis one of the common defects in roll-forming process In this paper the ldquo日rdquo shape section of roll forming is studied and first theb-shaped section is formed by roll forming and the internal weld line is automatically welded while forming then the long side ofthe b-shaped section is bent into the ldquoUrdquo shape and the external weld line is welded while forming e profile is cut off and thenbent at both ends to form a commercial vehicle anticollision beam e ABAQUS finite element software is used to model andanalyze the factors affecting the ldquoedge bucklingrdquo defect of roll-formed products is paper uses three factors and three levels oforthogonal simulation experiments to study the problem e results show that the effect of the factors of flange height sheetthickness and forming speed on the formation of edge buckling is in the order of sheet thicknessgt flange heightgt forming speede edge buckling size of the vertical edge of b-shaped tube decreases with the increase of sheet thickness and increases with theincrease of flange height

1 Introduction

Roll forming is a plastic processing method for graduallyforming a metal strip into a desired product section throughmulti-pass rolls [1] and its schematic diagram is shown inFigure 1

Roll forming has many advantages such as high pro-duction efficiency good forming effect and saving formingmaterial [2] is processing method is widely used in au-tomobile parts track bus brackets oil and gas pipelinesbuilding components and other aspects [3] e sheet metalis constantly subjected to complex bending and shearingforces during the forming process which makes the formingmechanism particularly complicated and the forming law isextremely difficult to grasp e main defects of the formedparts are distortion warpage fracture edge bucklingspringback and so on [4]

By using ABAQUS finite element software for numericalsimulation it is convenient and efficient to study theforming law of roll-forming process master the techno-logical conditions affecting its forming effect avoid the wastecaused by ldquotrial and error methodrdquo effectively improve theproduct forming quality and create greater production value[5] Domestic and foreign scholars have carried out a lot ofresearch work on this and have achievedmany achievementsin the aspects of roll-formingmechanism process parametercontrol and finite element simulation Heislitz and Duggalet al [6 7] began to simulate the simple U-shaped channelsteel by finite element method to predict the stress-straindistribution and geometric shape after forming McClureand Li [8] used ABAQUSrsquos implicit algorithm to simulate theroll forming of the channel section ey compared thecalculated longitudinal strain with the experimental resultsof Bhattacharyya and Smith [9] to demonstrate the validity

HindawiAdvances in Materials Science and EngineeringVolume 2019 Article ID 6505914 10 pageshttpsdoiorg10115520196505914

of the finite element simulation Tehrani et al [10 11] con-ducted a finite element simulation study on the phenomenonof edge buckling in the roll-forming process and found that ifthe bending angle of the sheet metal in the first formingprocess exceeded a specific limit it would appear edge bucklingin the subsequent second roll-forming process Kim et al [12]studied the shape of the edge of the sheet before welding Inorder to ensure the weld quality of the ERW pipeline anoptimized edge shape was obtained by preprocessing the edgeto ensure a good welding effect Wang and Fei [13] studied theeffect of sheet thickness arc radius side leg height andbending arc length on side leg wrinkling through orthogonalsimulation experiments which provided a basis for the for-mulation of roll-forming process and finite element model

As an important component product of automobile thecommon anticollision beam is commonly used in the shapeof rectangle U-shape and complex section as shown inFigure 2

e research content of this paper is to study the roll-forming process of anticollision beam with complex ldquo日rdquoclosed section because the section needs to be further weldedafter forming the forming effect of its edge will seriously affectthe next step of production so its profile welding edge-forming accuracy is particularly important Edge buckling isone of the common forming defects in the roll-formingprocess which cannot be eliminated but can be minimized byprocess optimization design In this paper COPRA a pro-fessional roll-forming software of German Data M Companyis used to carry out inverse modeling and analysis of roll-forming parts and their forming methods [14] e accuracyof the simulation model is verified by simulation and ex-periment comparisone section nodes of tube after formingare compared with the section of test results so as to masterthe forming law of closed section e effects of differentprocess conditions on the edge buckling of roll forming arestudied to determine the process conditions for reducing thelongitudinal strain and optimize the forming scheme so as toprovide guarantee for improving the product quality

2 Experimental Design

21 Experimental Method e ldquo日rdquo shape section is one ofthe typical product shapes of automobile anticollision beamand its section shape is shown in Figure 3

Due to the complexity of the roll-forming process thedesign of the roll flower is cumbersome and difficult toprocess and the processing pass is more than that of thegeneral shapee processing sequence is shown in Figure 4

e traditional ldquo日rdquo shape tube processing method isdivided into two types e first type is carried out in threesteps (1) two U-shaped channel steels are processed by roll-forming equipment (2) cut out a rectangular baffle and (3)weld two U-shaped channel steels with a rectangular baffleas shown in Figure 5(a)e second is done in two steps (1)a rectangular tube and a U-shaped tube are manufacturedby roll-forming equipment and (2) the rectangular tubeand the U-shaped tube are weld as shown in Figure 5(b)e welding process of the above two methods is verycomplex requiring repeated welding to achieve theforming effect which not only increases the workload ofworkers but also has low production efficiency and poorproduct quality e mechanical properties of the productsare difficult to guarantee In this paper one-time rollforming is used to form the anticollision beam of com-mercial vehicle which is a challenging forming method asshown in Figure 5(c) First of all the b-shaped tube is rolledout by the roll-forming equipment and the side position isautomatically welded to complete the internal weld linethen the b-shaped tube is rolled again to make the verticaledge roll into a U-shaped tube to obtain the ldquo日rdquo shapetube finally the curved edge position is welded to completethe external weld line as shown in Figure 5(d) is notonly reduces the manufacturing process and improves thematerial utilization and production efficiency but alsoensures the mechanical properties of the product such astensile strength flexural strength and impact toughnessbecause it is the roll forming-internal welding-roll form-ing-external welding continuous roll forming

In this paper the vertical edge buckling of b-shaped tubeis studied e section size of the b-shaped tube is shown inFigure 6 e forming material of the b-shaped tube is thebeam high strength steel B700L which is commonly used inthe automobile field e forming angle of each pass cannotbe too large and the b-shaped tube needs to be weldedautomatically in time after forming erefore the re-quirements for the accuracy of the roll-forming sectionespecially the ldquoedge bucklingrdquo control accuracy should beensured e product is produced on the self-invented roll-forming production line as shown in Figure 7 e distancebetween rolls is 350mm In the roll-forming process thelower rolls are used as the driving rolls and the upper rollsare used as the passive rolls

22 e Flower Pattern for b-Shaped Tube Section Flowerpattern is a cross-sectional diagram describing the roll-forming process of the sheet metal e forming sequence ofthe b-shaped tube is designed by COPRArsquos roll designmodule As shown in Figure 8 the outer side angle is firstformed to 75deg for 6 passes en the inner corners areformed and the inner corners are finally formed to 90degrees for 6 passes Finally the remaining unformed outercorners are formed forming 75deg per pass for 2 passes

Fin-pass stands

Linear forming

Preforming

Roll-forming direction

Figure 1 Schematic diagram of roll forming

2 Advances in Materials Science and Engineering

(a) (b) (c) (d)

Figure 2 Cross section of the roll forming of the traditional commercial vehicle anticollision beam

Figure 3 Schematic diagram of the ldquo日rdquo cross section

Figure 4 Processing sequence diagram of ldquo日rdquo shape cross-section products

Welding spot

(a)

Welding spot

(b)

Internal welding line External welding line

(c) (d)

Figure 5 (a) ldquo日rdquo shape tube traditional forming method I (b) ldquo日rdquo shape tube traditional forming method II (c) New roll-formingmethod (d) Product photo

Advances in Materials Science and Engineering 3

23 Design of Orthogonal Experiment In the longitudinaldirection of the sheet the strain occurring in the formingzone is different which is easy to produce the defect of edgebuckling e standard deviation Δε of longitudinal strain ofeach node on the edge of channel steel is usually taken as acriterion to measure the magnitude of edge buckling ebigger the standard deviation the more serious the edgebuckling at the edge of the forming part the smaller thestandard deviation the smaller the edge buckling (1) is theformula for calculating the standard deviation Δε [15]

Δε

1n

1113944

n

i1εi minus ε( 1113857

2

11139741113972

(1)

ε ε1 + ε2 + ε3 + middot middot middot + εn

n (2)

where n is the number of vertical nodes of the measurementposition εi is the longitudinal strain of each node and ε isthe average value of the longitudinal strain

ere are many factors that affect the buckling defects ofthe edge of b-shaped tube roll-forming process amongwhich the factors such as flange height sheet thickness andforming speed have a great effect on the forming defects ofthe sheet metal is paper mainly investigates the effect of

various factors on the edge buckling of the b-shaped tube ofthe high-strength beam steel B700L material during the roll-forming process In order to ensure the rationality of theexperiment three factors and three levels are selected for theorthogonal experimental design e flange height of thematerial is 60 70 and 80mm the thickness of the sheetmetal is 2 25 and 3mm and the forming speed is 50 100and 150mms e orthogonal table of the three factors andthree levels that affect the edge buckling during the b-shapedtube roll forming process is shown in Table 1

3 Material Properties

Some material parameters of beam high-strength steelB700L are shown in Table 2 e mechanical properties ofthe material are measured by an uniaxial tensile test Figure 9is the stress-strain curve of the specimen obtained from thetest results Since ABAQUS requires the values of true stressand strain when inputting data the following formulas areused to calculate the required values [16]

ε ln 1 + εn0m1113872 1113873 (3)

σ σn0m 1 + εn0m1113872 1113873 (4)

where ε and σ are real stress and real strain and σn0m and εn0m

are nominal stress and nominal strain respectively

4 Finite Element Model

41 Modeling In this paper ABAQUSExplicit analysismethod is used to model and analyze the roll-formingprocess [12] For the convenience of research the rolls are setas an analytical rigid body e sheet is formed at a roomtemperature and a low speed and is set as a deformable bodyduring the simulation In order to be the same as the actualproduction process the diameter of upper roll is set as150mm the diameter of lower roll is set as 100mm and thediameter of vertical roll is set as 100mm e distancebetween the rolls is set as 350mm and the length of thesheets is set as 900mm

e roll group consists of 14 passes and is divided intothree parts e first group is the guide rolls the secondgroup is the forming rolls and the third group is the shapingrolls In the last three passes of the forming rolls and theshaping rolls the vertical rolls are used to assist the shapinge flower patterns designed with COPRA are used to createa plan drawing of the rolls and then the plan drawing isimported into the ABAQUS software to create three-di-mensional rolls

350

50

25

R5

50

Internal welding line

Figure 6 Section size of b-shaped tube

Figure 7 e diagram of roll-forming production line

Figure 8 e b-shaped tube flower pattern

4 Advances in Materials Science and Engineering

42 Contacts and Boundary Conditions ere are manychoices for the feeding method of the sheet In this paper aconstant speed is set at the front end of the sheet and theangular velocity is applied by the driving rolls is methodhas a long calculation time and the calculation results areaccurate Considering the actual forming process the cal-culation time is too long for the selection of the feedingspeed of the sheet metal if the simulation is based on theforming speed of the actual product e excessive speedsetting will lead to slippage between the sheet metal and rollswhich will lead to inaccurate calculation results In thesimulation experiment the line speed V of the sheet metal inthis paper is selected as 50ndash300mms and the angular ve-locity of the lower roll is obtained by the formula v ωr Inorder to simulate the actual production process as much aspossible the rolls retain only their degrees of freedom in thedirection of rotation and the remaining degrees of freedomare controlled e general contact between the sheet metaland rolls is adopted and the friction coefficient is set to 02[17] Figure 10 is the assembly drawing of the roll bendingmodel of the b-shaped tube

43 Element Type and Meshing In the process of finite el-ement analysis of roll forming the commonly used elementsare SC4R SC8R C3D8R and so on [13] In this numerical

simulation analysis the edge buckling analysis of theb-shaped tubersquos vertical edge is performed While savingcalculation time and improving calculation accuracy SC4Rshell element [8] is selected in this paper In the direction ofsheet width the mesh refinement element size at bend angleis set to 3mm the element size at flange and web is set to10mm the element size in length direction is set to 15mmand the element size in thickness direction is set to 9 integralpoints e meshing situation is shown in Figure 11

44 Comparison of Simulation Results with ExperimentalResults In order to verify the validity of the simulationresults this paper takes the sheet flange height of 70mm thethickness of 25mm and the forming speed of 150mms asan example e upper part of the side is selected for lon-gitudinal strain analysis e results show that the simula-tion results are basically consistent with the experimentalresults as shown in Figure 12

5 Results and Discussion

51 Analysis of Simulation Results According to the processdescribed in the previous sections it can be concluded fromthe postprocessing of the model that along the roll-formingdirection the edge of the sheet has a longitudinal strain andthe shear strain is formed along the sheet forming directionof the roll bending as well as the transverse strain along thetransverse direction of the sheet Taking the sheet metalflange height of 70mm thickness of 25mm and formingspeed of 150mms as an example Figure 13(a) isMises stressdiagram of ldquobrdquo tube It can be seen that the stress distributionof the whole tube is not uniform but the overall trend is thatthe closer to the bend the greater the stress of the tubewhich can be illustrated by the transverse stress distributionof the sheet in Figure 13(b) Figure 13(c) is the equivalentplastic strain diagram of the b-shaped tube It is shown thatthe strain of the tube mainly occurs at the bend corner asshown in the transverse strain distribution diagram of thesheet in Figure 13(d) And the cause of edge buckling atflange is closely related to stress and strain

52MechanismAnalysis of Buckling Defect at Vertical Edge ofb-Shaped Tube From the simulation results it can be seenthat the front flange of the tube tends to move inward asshown in Figure 14 is is due to the complex deformationforce when the sheet metal is bitten by the rolls in the processof roll forming erefore in order to ensure the accuracy ofthe simulation results the strain at the flange is measured at100ndash800mm along the length direction of the sheet metalAs shown in Figure 15 the longitudinal strain distributionsof the top middle and bottom nodes of the flange can beseen as follows the top of the flangegt the middle of theflangegt the bottom of the flange It can be seen from Fig-ure 15 that the curve of the top nodes of the flange is morefluctuating than the curve of the middle and bottom nodesindicating that the longitudinal strain distribution at the topof the flange is the most uneven and the longitudinal straindistribution at the bottom of the flange is the most uniform

Table 1 Orthogonal experimental table of 3 factors and 3 levels

Levels Flange heighth (mm)

Sheet thicknesst (mm)

Formingspeed v (mmmiddotsminus 1)

Level 1 60 20 50Level 2 70 25 100Level 3 80 30 150

Table 2 Material elastic phase properties

MaterialYoungrsquomodulusE (GPa)

Density(kgmiddotmminus 3)

Poissonrsquosratio v

B700L 216 7830 021998

000 005 010 015 0200

200

400

600

800

1000

Stre

ss (M

Pa)

Strain

Figure 9 Stress-strain curve of beam high-strength steel B700L

Advances in Materials Science and Engineering 5

erefore edge buckling is very easy to occur at the top ofthe flange

Comparing the longitudinal strain curves of flange it canbe concluded that when the longitudinal strain is greater

than 0 the sheet extends longitudinally and when thelongitudinal strain is less than 0 the sheet is compressedlongitudinally Because of the combined effect of stress andstrain edge buckling occurs at the flange of the sheet metal

53 Analysis of Orthogonal Experiments of Vertical EdgeBuckling of b-Shaped Tube In this paper B700L high-strength beam steel is used for simulation experiments andthree representative factors are selected which are flangeheight sheet thickness and forming speed A three-factorthree-level orthogonal experiment is designed with a total ofnine experiments e experimental results and resultanalysis are shown in Table 3

From the analysis of the experimental results in Table 3it can be seen that in nine experiments of orthogonal designfor roll forming of b-shaped tube the standard deviation oflongitudinal strain at the top of flange of Exp 6 is the largestwhich is 692times10minus 4 the standard deviation of Exp 1 is thesmallest which is 162times10minus 4 In order to make the exper-imental results more intuitive this paper selects the in-termediate values of two longitudinal strain standarddeviations Exp 2 and Exp 3 and compares with Exp 1 andExp 6 as shown in Figure 16 By comparing the charac-teristics of each curve it can be concluded that themaximumlongitudinal strain fluctuation at the top of the flange is Exp6 and its flange edge buckling is the most serious the resultof the Exp 1 is the smallest longitudinal strain fluctuationamplitude and the minimum edge buckling erefore themagnitude of the longitudinal strain fluctuation at the flangeis closely related to the severity of edge buckling

Table 4 shows the results of the Δε values of the results ofthe respective experiments e experimental values Δεcorresponding to each factor at different levels are summedup and then the average value is obtained and the rangeanalysis is made It can be seen from the data in the table thatthe effect degree of each factor on the side wave is the sheetthicknessgt flange heightgt forming speed erefore for thematerial properties of a certain high-strength beam steelB700L sheet the sheet thickness and flange height have agreater impact on the edge buckling of the flange of theb-shaped tube whereas the effect of the forming speed issmaller In order to further explore the effect of sheetthickness and flange height on edge buckling a comparativeexperiment is designed in this paper

Upper rolls

Lower rolls

Vertical rolls

Roll-forming direction

350mm

Sheet metal

xz

y

Figure 10 Assembly drawing of finite element model for roll forming of b-shaped tube

Web

Bending zone

Flange

Figure 11 Meshing of b-shaped tube sheet

0 100 200 300 400 500 600 700 800 900

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

Long

itudi

nal s

trai

n

Longitudinal distance

FEAEXP

Figure 12 Experimental and simulation comparison of flange topjoints

6 Advances in Materials Science and Engineering

S misesSNEG (fraction = ndash10)(avg 75)

+9180e + 02+8471e + 02+7762e + 02+7053e + 02+6343e + 02+5634e + 02+4925e + 02+4216e + 02+3507e + 02+2798e + 02+2088e + 02+1379e + 02+6701e + 01

Middle

Bottom

Top

yz

x

(a)

0100

Tran

sver

se st

ress

200300400500600700800900

1000

50 100Transverse distance

150 200

(b)

PEEQSNEG (fraction = ndash10)(avg 75)

+5613e ndash 01+5146e ndash 01+4678e ndash 01+4210e ndash 01+3742e ndash 01+3274e ndash 01+2807e ndash 01+2339e ndash 01+1871e ndash 01+1403e ndash 01+9356e ndash 02+4678e ndash 02+0000e + 00 y

zx

(c)

000

005

010

015

020

025

030

035

Equi

vale

nt st

rain

0 50 100Transverse strain

150 200

(d)

Figure 13 (a) Mises stress distribution diagram of b-shaped tube (b) Transverse stress of the sheet metal (c) Equivalent strain distributiondiagram of b-shaped tube (d) Transverse strain of the sheet metal

ndash30 ndash20 ndash10 0 10 20 30

0

10

20

30

40

50

60

70

80

X (m

m)

Y (mm)

FEAEXP

Figure 14 Front shape of b-tube

0 100 200 300 400 500 600 700 800 900Longitudinal distance

The top nodes of the flangeThe middle nodes of the flangeThe bottom nodes of the flange

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

20 times 10ndash3

Long

itudi

nal s

trai

n

Figure 15 Curves of longitudinal strain of flange nodes varyingwith longitudinal distance

Advances in Materials Science and Engineering 7

54 Additional Experimental Results and Analysis In orderto further explore the effect of sheet metal thickness andflange height on the flange edge buckling of ldquobrdquo tube twosets of comparative simulation experiments are designed inthis paper Based on the simulation results of the or-thogonal experiment the first experimental design iscarried out under the condition of flange height h 60 andforming speed v 100mms e variables are sheet metalthickness which is set as 2 25 3 and 35mm respectivelye second experimental design is carried out under thecondition of sheet thickness t 25mm and forming speedv 100mms and the variables are flange height which are65 70 75 and 80mm respectively e experimental re-sults are shown in Figure 15 Figure 17(a) shows that thelongitudinal strain at the flange increases with the increaseof flange height Figure 17(b) shows that as the thickness ofthe sheet increases the longitudinal strain at the flange isalso getting smaller and smaller It can be seen that the edge

buckling at the flange increases with the increase of flangeheight and decreases with the increase of plate thickness

6 Conclusion

In this paper COPRA is used for pass design ABAQUS isused for finite element modeling and analysis and or-thogonal experiments and comparative experiments aredesigned to study the roll-forming law of the b-shaped tubewhich provides theoretical basis for the production of ldquo日rdquoshape tube e conclusions are as follows

(1) Compared with the traditional roll-forming methodthe application of new roll-forming technology inthis paper not only improves the material utilizationrate and production efficiency but also ensures themechanical properties of the products such as tensilestrength bending strength and impact toughness

Table 3 Orthogonal experiment results and result analysis

Simulation number Flange height h (mm) Sheet thickness t (mm) Forming speed v (mmmiddotsminus 1) Δε1 60 (h1) 20 (t1) 50 (v1) 162times10minus 4

2 60 (h1) 25 (t2) 100 (v2) 280times10minus 4

3 60 (h1) 30 (t3) 150 (v3) 501times 10minus 4

4 70 (h2) 20 (t1) 100 (v2) 255times10minus 4

5 70 (h2) 25 (t2) 150 (v3) 367times10minus 4

6 70 (h2) 30 (t3) 50 (v2) 692times10minus 4

7 80 (h3) 20 (t1) 150 (v3) 235times10minus 4

8 80 (h3) 25 (t2) 50 (v1) 425times10minus 4

9 80 (h3) 30 (t3) 100 (v2) 513times10minus 4

0 100 200 300 400 500 600 700 800 900 Longitudinal distance

FEA1FEA2

FEA3FEA6

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

20 times 10ndash3

Long

itudi

nal s

trai

n

Figure 16 Longitudinal strain curves of the sheet metal along longitudinal position in Exp 1 2 3 and 6

Table 4 Range analysis of orthogonal experimental results

Δε Flange height (h) Sheet thickness (t) Forming speed (v)k1 314times10minus 4 217times10minus 4 427times10minus 4

k2 437times10minus 4 357times10minus 4 350times10minus 4

k3 400times10minus 4 560times10minus 4 367times10minus 4

Range R 123times10minus 4 343times10minus 4 077times10minus 4

8 Advances in Materials Science and Engineering

(2) For high-strength beam steel B700L sheet flangeheight sheet thickness and forming speed all effectthe generation of edge buckling in the roll-formingprocess When the standard deviation Δε of longi-tudinal strain is taken as the evaluation criterion theeffect degree of each factor on the formation of edgebuckling is sheet thicknessgt flange heightgt formingspeed

(3) e comparative experimental results show that theedge buckling of the vertical edge of the b-shapedtube decreases with the increase of the thickness ofthe sheet metal and increases with the increase of theflange height e effect of forming speed on edgebuckling of the sheet metal is small

Data Availability

is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricteduse distribution and reproduction in any medium pro-vided the original work is properly cited

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] B Abeyrathna B Rolfe P Hodgson and M Weiss ldquoLocaldeformation in roll formingrdquo e International Journal ofAdvanced Manufacturing Technology vol 88 no 9ndash12pp 2405ndash2415 2017

[2] X L Liu J G Cao X T Chai et al ldquoExperimental andnumerical prediction of the local thickness reduction defect ofcomplex cross-sectional steel in cold roll formingrdquo e In-ternational Journal of Advanced Manufacturing Technologyvol 95 no 5ndash8 pp 1837ndash1848 2017

[3] P Mahajan A Abrass and P Groche ldquoFE simulation of rollforming of a complex profile with the aid of steady statepropertiesrdquo Steel Research International vol 89 no 5Article ID 1700350 2018

[4] G T Halmos Roll Forming Handbook CRC New York NYUSA 2006

[5] B Shirani H M Naeini and R A Tafti ldquoExperimental andnumerical study of required torque in the cold roll forming ofsymmetrical channel sectionsrdquo Journal of ManufacturingProcesses vol 27 pp 63ndash75 2017

[6] F Heislitz H Livatyali M A Ahmetoglu et al ldquoSimulation ofroll forming process with the 3-D FEM code PAM-STAMPrdquoJournal of Materials Processing Technology vol 59 no 1-2pp 59ndash67 1996

[7] N Duggal M A Ahmetoglu G L Kinzel et al ldquoComputeraided simulation of cold roll formingmdasha computer programfor simple section profilesrdquo Journal of Materials ProcessingTechnology vol 59 no 1-2 pp 41ndash48 1996

[8] C K McClure and H Li ldquoRoll forming simulation using finiteelement analysisrdquo Manufacturing Review vol 8 no 2pp 114ndash122 1995

[9] D Bhattacharya and P D Smith ldquoe Development ofLongitudinal Strain in Cold Roll Forming and its Influence onProduct Straightnessrdquo in Proceedings of the First InternationalConference on Technology of Plasticity pp 422ndash427 TokyoJapan June 1984

[10] M S Tehrani H M Naeini P Hartley et al ldquoLocalized edgebuckling in cold roll-forming of circular tube sectionrdquo Journalof Materials Processing Technology vol 177 no 1ndash3pp 617ndash620 2006

[11] M S Tehrani P Hartley and H Khademizadeh ldquoLocalisededge buckling in cold roll-forming of symmetric channelsectionrdquo in-Walled Structures vol 44 no 2 pp 184ndash1962006

[12] N Kim S B Kang and S Lee ldquoPrediction and design of edgeshape of initial strip for thick tube roll forming using finiteelement methodrdquo Journal of Materials Processing Technologyvol 142 no 2 pp 479ndash486 2003

64 66 68 70 72 74 76 78 80 82

30 times 10ndash4

35 times 10ndash4

40 times 10ndash4

45 times 10ndash4

50 times 10ndash4

55 times 10ndash4St

anda

rd d

evia

tion

of lo

ngitu

dina

l str

ain

Longitudinal distance

FEAEXP

(a)

18 20 22 24 26 28 30 32 34 3630E ndash 04

35E ndash 04

40E ndash 04

45E ndash 04

50E ndash 04

55E ndash 04

60E ndash 04

65E ndash 04

Stan

dard

dev

iatio

n of

long

itudi

nal s

trai

n

Sheet thickness (mm)

FEAEXP

(b)

Figure 17 (a) Effect of flange height on longitudinal strain (b) Effect of sheet thickness on longitudinal strain

Advances in Materials Science and Engineering 9

[13] T Wang and H Fei ldquoPrediction of wrinkling in flexible rollforming based on finite element simulationrdquo Forging ampStamping Technology vol 38 no 6 pp 67ndash72 2013

[14] Data M Software GmbH ldquoCOPRAreg roll formingrdquo 2001httpwwwroll-designcom

[15] X Luo Z Guo S Li et al ldquoFinite element analysis of the effectof material properties on wavy flange in high strength steel rollformingrdquo Journal of Shanghai Jiaotong University vol 42no 5 pp 744ndash747 2008

[16] D Hibbitt B Karlsson and P Sorensen Getting started withABAQUSExplicitmdashinteractive version Hibbitt Karlsson ampSorensen Inc Providence RI USA 2002

[17] Q V Bui and J P Ponthot ldquoNumerical simulation of coldroll-forming processesrdquo Journal of Materials ProcessingTechnology vol 202 no 1ndash3 pp 275ndash282 2008

10 Advances in Materials Science and Engineering

(a) (b) (c) (d)

Figure 2 Cross section of the roll forming of the traditional commercial vehicle anticollision beam

Figure 3 Schematic diagram of the ldquo日rdquo cross section

Figure 4 Processing sequence diagram of ldquo日rdquo shape cross-section products

Welding spot

(a)

Welding spot

(b)

Internal welding line External welding line

(c) (d)

Figure 5 (a) ldquo日rdquo shape tube traditional forming method I (b) ldquo日rdquo shape tube traditional forming method II (c) New roll-formingmethod (d) Product photo

Advances in Materials Science and Engineering 3

23 Design of Orthogonal Experiment In the longitudinaldirection of the sheet the strain occurring in the formingzone is different which is easy to produce the defect of edgebuckling e standard deviation Δε of longitudinal strain ofeach node on the edge of channel steel is usually taken as acriterion to measure the magnitude of edge buckling ebigger the standard deviation the more serious the edgebuckling at the edge of the forming part the smaller thestandard deviation the smaller the edge buckling (1) is theformula for calculating the standard deviation Δε [15]

Δε

1n

1113944

n

i1εi minus ε( 1113857

2

11139741113972

(1)

ε ε1 + ε2 + ε3 + middot middot middot + εn

n (2)

where n is the number of vertical nodes of the measurementposition εi is the longitudinal strain of each node and ε isthe average value of the longitudinal strain

ere are many factors that affect the buckling defects ofthe edge of b-shaped tube roll-forming process amongwhich the factors such as flange height sheet thickness andforming speed have a great effect on the forming defects ofthe sheet metal is paper mainly investigates the effect of

various factors on the edge buckling of the b-shaped tube ofthe high-strength beam steel B700L material during the roll-forming process In order to ensure the rationality of theexperiment three factors and three levels are selected for theorthogonal experimental design e flange height of thematerial is 60 70 and 80mm the thickness of the sheetmetal is 2 25 and 3mm and the forming speed is 50 100and 150mms e orthogonal table of the three factors andthree levels that affect the edge buckling during the b-shapedtube roll forming process is shown in Table 1

3 Material Properties

Some material parameters of beam high-strength steelB700L are shown in Table 2 e mechanical properties ofthe material are measured by an uniaxial tensile test Figure 9is the stress-strain curve of the specimen obtained from thetest results Since ABAQUS requires the values of true stressand strain when inputting data the following formulas areused to calculate the required values [16]

ε ln 1 + εn0m1113872 1113873 (3)

σ σn0m 1 + εn0m1113872 1113873 (4)

where ε and σ are real stress and real strain and σn0m and εn0m

are nominal stress and nominal strain respectively

4 Finite Element Model

41 Modeling In this paper ABAQUSExplicit analysismethod is used to model and analyze the roll-formingprocess [12] For the convenience of research the rolls are setas an analytical rigid body e sheet is formed at a roomtemperature and a low speed and is set as a deformable bodyduring the simulation In order to be the same as the actualproduction process the diameter of upper roll is set as150mm the diameter of lower roll is set as 100mm and thediameter of vertical roll is set as 100mm e distancebetween the rolls is set as 350mm and the length of thesheets is set as 900mm

e roll group consists of 14 passes and is divided intothree parts e first group is the guide rolls the secondgroup is the forming rolls and the third group is the shapingrolls In the last three passes of the forming rolls and theshaping rolls the vertical rolls are used to assist the shapinge flower patterns designed with COPRA are used to createa plan drawing of the rolls and then the plan drawing isimported into the ABAQUS software to create three-di-mensional rolls

350

50

25

R5

50

Internal welding line

Figure 6 Section size of b-shaped tube

Figure 7 e diagram of roll-forming production line

Figure 8 e b-shaped tube flower pattern

4 Advances in Materials Science and Engineering

42 Contacts and Boundary Conditions ere are manychoices for the feeding method of the sheet In this paper aconstant speed is set at the front end of the sheet and theangular velocity is applied by the driving rolls is methodhas a long calculation time and the calculation results areaccurate Considering the actual forming process the cal-culation time is too long for the selection of the feedingspeed of the sheet metal if the simulation is based on theforming speed of the actual product e excessive speedsetting will lead to slippage between the sheet metal and rollswhich will lead to inaccurate calculation results In thesimulation experiment the line speed V of the sheet metal inthis paper is selected as 50ndash300mms and the angular ve-locity of the lower roll is obtained by the formula v ωr Inorder to simulate the actual production process as much aspossible the rolls retain only their degrees of freedom in thedirection of rotation and the remaining degrees of freedomare controlled e general contact between the sheet metaland rolls is adopted and the friction coefficient is set to 02[17] Figure 10 is the assembly drawing of the roll bendingmodel of the b-shaped tube

43 Element Type and Meshing In the process of finite el-ement analysis of roll forming the commonly used elementsare SC4R SC8R C3D8R and so on [13] In this numerical

simulation analysis the edge buckling analysis of theb-shaped tubersquos vertical edge is performed While savingcalculation time and improving calculation accuracy SC4Rshell element [8] is selected in this paper In the direction ofsheet width the mesh refinement element size at bend angleis set to 3mm the element size at flange and web is set to10mm the element size in length direction is set to 15mmand the element size in thickness direction is set to 9 integralpoints e meshing situation is shown in Figure 11

44 Comparison of Simulation Results with ExperimentalResults In order to verify the validity of the simulationresults this paper takes the sheet flange height of 70mm thethickness of 25mm and the forming speed of 150mms asan example e upper part of the side is selected for lon-gitudinal strain analysis e results show that the simula-tion results are basically consistent with the experimentalresults as shown in Figure 12

5 Results and Discussion

51 Analysis of Simulation Results According to the processdescribed in the previous sections it can be concluded fromthe postprocessing of the model that along the roll-formingdirection the edge of the sheet has a longitudinal strain andthe shear strain is formed along the sheet forming directionof the roll bending as well as the transverse strain along thetransverse direction of the sheet Taking the sheet metalflange height of 70mm thickness of 25mm and formingspeed of 150mms as an example Figure 13(a) isMises stressdiagram of ldquobrdquo tube It can be seen that the stress distributionof the whole tube is not uniform but the overall trend is thatthe closer to the bend the greater the stress of the tubewhich can be illustrated by the transverse stress distributionof the sheet in Figure 13(b) Figure 13(c) is the equivalentplastic strain diagram of the b-shaped tube It is shown thatthe strain of the tube mainly occurs at the bend corner asshown in the transverse strain distribution diagram of thesheet in Figure 13(d) And the cause of edge buckling atflange is closely related to stress and strain

52MechanismAnalysis of Buckling Defect at Vertical Edge ofb-Shaped Tube From the simulation results it can be seenthat the front flange of the tube tends to move inward asshown in Figure 14 is is due to the complex deformationforce when the sheet metal is bitten by the rolls in the processof roll forming erefore in order to ensure the accuracy ofthe simulation results the strain at the flange is measured at100ndash800mm along the length direction of the sheet metalAs shown in Figure 15 the longitudinal strain distributionsof the top middle and bottom nodes of the flange can beseen as follows the top of the flangegt the middle of theflangegt the bottom of the flange It can be seen from Fig-ure 15 that the curve of the top nodes of the flange is morefluctuating than the curve of the middle and bottom nodesindicating that the longitudinal strain distribution at the topof the flange is the most uneven and the longitudinal straindistribution at the bottom of the flange is the most uniform

Table 1 Orthogonal experimental table of 3 factors and 3 levels

Levels Flange heighth (mm)

Sheet thicknesst (mm)

Formingspeed v (mmmiddotsminus 1)

Level 1 60 20 50Level 2 70 25 100Level 3 80 30 150

Table 2 Material elastic phase properties

MaterialYoungrsquomodulusE (GPa)

Density(kgmiddotmminus 3)

Poissonrsquosratio v

B700L 216 7830 021998

000 005 010 015 0200

200

400

600

800

1000

Stre

ss (M

Pa)

Strain

Figure 9 Stress-strain curve of beam high-strength steel B700L

Advances in Materials Science and Engineering 5

erefore edge buckling is very easy to occur at the top ofthe flange

Comparing the longitudinal strain curves of flange it canbe concluded that when the longitudinal strain is greater

than 0 the sheet extends longitudinally and when thelongitudinal strain is less than 0 the sheet is compressedlongitudinally Because of the combined effect of stress andstrain edge buckling occurs at the flange of the sheet metal

53 Analysis of Orthogonal Experiments of Vertical EdgeBuckling of b-Shaped Tube In this paper B700L high-strength beam steel is used for simulation experiments andthree representative factors are selected which are flangeheight sheet thickness and forming speed A three-factorthree-level orthogonal experiment is designed with a total ofnine experiments e experimental results and resultanalysis are shown in Table 3

From the analysis of the experimental results in Table 3it can be seen that in nine experiments of orthogonal designfor roll forming of b-shaped tube the standard deviation oflongitudinal strain at the top of flange of Exp 6 is the largestwhich is 692times10minus 4 the standard deviation of Exp 1 is thesmallest which is 162times10minus 4 In order to make the exper-imental results more intuitive this paper selects the in-termediate values of two longitudinal strain standarddeviations Exp 2 and Exp 3 and compares with Exp 1 andExp 6 as shown in Figure 16 By comparing the charac-teristics of each curve it can be concluded that themaximumlongitudinal strain fluctuation at the top of the flange is Exp6 and its flange edge buckling is the most serious the resultof the Exp 1 is the smallest longitudinal strain fluctuationamplitude and the minimum edge buckling erefore themagnitude of the longitudinal strain fluctuation at the flangeis closely related to the severity of edge buckling

Table 4 shows the results of the Δε values of the results ofthe respective experiments e experimental values Δεcorresponding to each factor at different levels are summedup and then the average value is obtained and the rangeanalysis is made It can be seen from the data in the table thatthe effect degree of each factor on the side wave is the sheetthicknessgt flange heightgt forming speed erefore for thematerial properties of a certain high-strength beam steelB700L sheet the sheet thickness and flange height have agreater impact on the edge buckling of the flange of theb-shaped tube whereas the effect of the forming speed issmaller In order to further explore the effect of sheetthickness and flange height on edge buckling a comparativeexperiment is designed in this paper

Upper rolls

Lower rolls

Vertical rolls

Roll-forming direction

350mm

Sheet metal

xz

y

Figure 10 Assembly drawing of finite element model for roll forming of b-shaped tube

Web

Bending zone

Flange

Figure 11 Meshing of b-shaped tube sheet

0 100 200 300 400 500 600 700 800 900

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

Long

itudi

nal s

trai

n

Longitudinal distance

FEAEXP

Figure 12 Experimental and simulation comparison of flange topjoints

6 Advances in Materials Science and Engineering

S misesSNEG (fraction = ndash10)(avg 75)

+9180e + 02+8471e + 02+7762e + 02+7053e + 02+6343e + 02+5634e + 02+4925e + 02+4216e + 02+3507e + 02+2798e + 02+2088e + 02+1379e + 02+6701e + 01

Middle

Bottom

Top

yz

x

(a)

0100

Tran

sver

se st

ress

200300400500600700800900

1000

50 100Transverse distance

150 200

(b)

PEEQSNEG (fraction = ndash10)(avg 75)

+5613e ndash 01+5146e ndash 01+4678e ndash 01+4210e ndash 01+3742e ndash 01+3274e ndash 01+2807e ndash 01+2339e ndash 01+1871e ndash 01+1403e ndash 01+9356e ndash 02+4678e ndash 02+0000e + 00 y

zx

(c)

000

005

010

015

020

025

030

035

Equi

vale

nt st

rain

0 50 100Transverse strain

150 200

(d)

Figure 13 (a) Mises stress distribution diagram of b-shaped tube (b) Transverse stress of the sheet metal (c) Equivalent strain distributiondiagram of b-shaped tube (d) Transverse strain of the sheet metal

ndash30 ndash20 ndash10 0 10 20 30

0

10

20

30

40

50

60

70

80

X (m

m)

Y (mm)

FEAEXP

Figure 14 Front shape of b-tube

0 100 200 300 400 500 600 700 800 900Longitudinal distance

The top nodes of the flangeThe middle nodes of the flangeThe bottom nodes of the flange

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

20 times 10ndash3

Long

itudi

nal s

trai

n

Figure 15 Curves of longitudinal strain of flange nodes varyingwith longitudinal distance

Advances in Materials Science and Engineering 7

54 Additional Experimental Results and Analysis In orderto further explore the effect of sheet metal thickness andflange height on the flange edge buckling of ldquobrdquo tube twosets of comparative simulation experiments are designed inthis paper Based on the simulation results of the or-thogonal experiment the first experimental design iscarried out under the condition of flange height h 60 andforming speed v 100mms e variables are sheet metalthickness which is set as 2 25 3 and 35mm respectivelye second experimental design is carried out under thecondition of sheet thickness t 25mm and forming speedv 100mms and the variables are flange height which are65 70 75 and 80mm respectively e experimental re-sults are shown in Figure 15 Figure 17(a) shows that thelongitudinal strain at the flange increases with the increaseof flange height Figure 17(b) shows that as the thickness ofthe sheet increases the longitudinal strain at the flange isalso getting smaller and smaller It can be seen that the edge

buckling at the flange increases with the increase of flangeheight and decreases with the increase of plate thickness

6 Conclusion

In this paper COPRA is used for pass design ABAQUS isused for finite element modeling and analysis and or-thogonal experiments and comparative experiments aredesigned to study the roll-forming law of the b-shaped tubewhich provides theoretical basis for the production of ldquo日rdquoshape tube e conclusions are as follows

(1) Compared with the traditional roll-forming methodthe application of new roll-forming technology inthis paper not only improves the material utilizationrate and production efficiency but also ensures themechanical properties of the products such as tensilestrength bending strength and impact toughness

Table 3 Orthogonal experiment results and result analysis

Simulation number Flange height h (mm) Sheet thickness t (mm) Forming speed v (mmmiddotsminus 1) Δε1 60 (h1) 20 (t1) 50 (v1) 162times10minus 4

2 60 (h1) 25 (t2) 100 (v2) 280times10minus 4

3 60 (h1) 30 (t3) 150 (v3) 501times 10minus 4

4 70 (h2) 20 (t1) 100 (v2) 255times10minus 4

5 70 (h2) 25 (t2) 150 (v3) 367times10minus 4

6 70 (h2) 30 (t3) 50 (v2) 692times10minus 4

7 80 (h3) 20 (t1) 150 (v3) 235times10minus 4

8 80 (h3) 25 (t2) 50 (v1) 425times10minus 4

9 80 (h3) 30 (t3) 100 (v2) 513times10minus 4

0 100 200 300 400 500 600 700 800 900 Longitudinal distance

FEA1FEA2

FEA3FEA6

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

20 times 10ndash3

Long

itudi

nal s

trai

n

Figure 16 Longitudinal strain curves of the sheet metal along longitudinal position in Exp 1 2 3 and 6

Table 4 Range analysis of orthogonal experimental results

Δε Flange height (h) Sheet thickness (t) Forming speed (v)k1 314times10minus 4 217times10minus 4 427times10minus 4

k2 437times10minus 4 357times10minus 4 350times10minus 4

k3 400times10minus 4 560times10minus 4 367times10minus 4

Range R 123times10minus 4 343times10minus 4 077times10minus 4

8 Advances in Materials Science and Engineering

(2) For high-strength beam steel B700L sheet flangeheight sheet thickness and forming speed all effectthe generation of edge buckling in the roll-formingprocess When the standard deviation Δε of longi-tudinal strain is taken as the evaluation criterion theeffect degree of each factor on the formation of edgebuckling is sheet thicknessgt flange heightgt formingspeed

(3) e comparative experimental results show that theedge buckling of the vertical edge of the b-shapedtube decreases with the increase of the thickness ofthe sheet metal and increases with the increase of theflange height e effect of forming speed on edgebuckling of the sheet metal is small

Data Availability

is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricteduse distribution and reproduction in any medium pro-vided the original work is properly cited

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] B Abeyrathna B Rolfe P Hodgson and M Weiss ldquoLocaldeformation in roll formingrdquo e International Journal ofAdvanced Manufacturing Technology vol 88 no 9ndash12pp 2405ndash2415 2017

[2] X L Liu J G Cao X T Chai et al ldquoExperimental andnumerical prediction of the local thickness reduction defect ofcomplex cross-sectional steel in cold roll formingrdquo e In-ternational Journal of Advanced Manufacturing Technologyvol 95 no 5ndash8 pp 1837ndash1848 2017

[3] P Mahajan A Abrass and P Groche ldquoFE simulation of rollforming of a complex profile with the aid of steady statepropertiesrdquo Steel Research International vol 89 no 5Article ID 1700350 2018

[4] G T Halmos Roll Forming Handbook CRC New York NYUSA 2006

[5] B Shirani H M Naeini and R A Tafti ldquoExperimental andnumerical study of required torque in the cold roll forming ofsymmetrical channel sectionsrdquo Journal of ManufacturingProcesses vol 27 pp 63ndash75 2017

[6] F Heislitz H Livatyali M A Ahmetoglu et al ldquoSimulation ofroll forming process with the 3-D FEM code PAM-STAMPrdquoJournal of Materials Processing Technology vol 59 no 1-2pp 59ndash67 1996

[7] N Duggal M A Ahmetoglu G L Kinzel et al ldquoComputeraided simulation of cold roll formingmdasha computer programfor simple section profilesrdquo Journal of Materials ProcessingTechnology vol 59 no 1-2 pp 41ndash48 1996

[8] C K McClure and H Li ldquoRoll forming simulation using finiteelement analysisrdquo Manufacturing Review vol 8 no 2pp 114ndash122 1995

[9] D Bhattacharya and P D Smith ldquoe Development ofLongitudinal Strain in Cold Roll Forming and its Influence onProduct Straightnessrdquo in Proceedings of the First InternationalConference on Technology of Plasticity pp 422ndash427 TokyoJapan June 1984

[10] M S Tehrani H M Naeini P Hartley et al ldquoLocalized edgebuckling in cold roll-forming of circular tube sectionrdquo Journalof Materials Processing Technology vol 177 no 1ndash3pp 617ndash620 2006

[11] M S Tehrani P Hartley and H Khademizadeh ldquoLocalisededge buckling in cold roll-forming of symmetric channelsectionrdquo in-Walled Structures vol 44 no 2 pp 184ndash1962006

[12] N Kim S B Kang and S Lee ldquoPrediction and design of edgeshape of initial strip for thick tube roll forming using finiteelement methodrdquo Journal of Materials Processing Technologyvol 142 no 2 pp 479ndash486 2003

64 66 68 70 72 74 76 78 80 82

30 times 10ndash4

35 times 10ndash4

40 times 10ndash4

45 times 10ndash4

50 times 10ndash4

55 times 10ndash4St

anda

rd d

evia

tion

of lo

ngitu

dina

l str

ain

Longitudinal distance

FEAEXP

(a)

18 20 22 24 26 28 30 32 34 3630E ndash 04

35E ndash 04

40E ndash 04

45E ndash 04

50E ndash 04

55E ndash 04

60E ndash 04

65E ndash 04

Stan

dard

dev

iatio

n of

long

itudi

nal s

trai

n

Sheet thickness (mm)

FEAEXP

(b)

Figure 17 (a) Effect of flange height on longitudinal strain (b) Effect of sheet thickness on longitudinal strain

Advances in Materials Science and Engineering 9

[13] T Wang and H Fei ldquoPrediction of wrinkling in flexible rollforming based on finite element simulationrdquo Forging ampStamping Technology vol 38 no 6 pp 67ndash72 2013

[14] Data M Software GmbH ldquoCOPRAreg roll formingrdquo 2001httpwwwroll-designcom

[15] X Luo Z Guo S Li et al ldquoFinite element analysis of the effectof material properties on wavy flange in high strength steel rollformingrdquo Journal of Shanghai Jiaotong University vol 42no 5 pp 744ndash747 2008

[16] D Hibbitt B Karlsson and P Sorensen Getting started withABAQUSExplicitmdashinteractive version Hibbitt Karlsson ampSorensen Inc Providence RI USA 2002

[17] Q V Bui and J P Ponthot ldquoNumerical simulation of coldroll-forming processesrdquo Journal of Materials ProcessingTechnology vol 202 no 1ndash3 pp 275ndash282 2008

10 Advances in Materials Science and Engineering

23 Design of Orthogonal Experiment In the longitudinaldirection of the sheet the strain occurring in the formingzone is different which is easy to produce the defect of edgebuckling e standard deviation Δε of longitudinal strain ofeach node on the edge of channel steel is usually taken as acriterion to measure the magnitude of edge buckling ebigger the standard deviation the more serious the edgebuckling at the edge of the forming part the smaller thestandard deviation the smaller the edge buckling (1) is theformula for calculating the standard deviation Δε [15]

Δε

1n

1113944

n

i1εi minus ε( 1113857

2

11139741113972

(1)

ε ε1 + ε2 + ε3 + middot middot middot + εn

n (2)

where n is the number of vertical nodes of the measurementposition εi is the longitudinal strain of each node and ε isthe average value of the longitudinal strain

ere are many factors that affect the buckling defects ofthe edge of b-shaped tube roll-forming process amongwhich the factors such as flange height sheet thickness andforming speed have a great effect on the forming defects ofthe sheet metal is paper mainly investigates the effect of

various factors on the edge buckling of the b-shaped tube ofthe high-strength beam steel B700L material during the roll-forming process In order to ensure the rationality of theexperiment three factors and three levels are selected for theorthogonal experimental design e flange height of thematerial is 60 70 and 80mm the thickness of the sheetmetal is 2 25 and 3mm and the forming speed is 50 100and 150mms e orthogonal table of the three factors andthree levels that affect the edge buckling during the b-shapedtube roll forming process is shown in Table 1

3 Material Properties

Some material parameters of beam high-strength steelB700L are shown in Table 2 e mechanical properties ofthe material are measured by an uniaxial tensile test Figure 9is the stress-strain curve of the specimen obtained from thetest results Since ABAQUS requires the values of true stressand strain when inputting data the following formulas areused to calculate the required values [16]

ε ln 1 + εn0m1113872 1113873 (3)

σ σn0m 1 + εn0m1113872 1113873 (4)

where ε and σ are real stress and real strain and σn0m and εn0m

are nominal stress and nominal strain respectively

4 Finite Element Model

41 Modeling In this paper ABAQUSExplicit analysismethod is used to model and analyze the roll-formingprocess [12] For the convenience of research the rolls are setas an analytical rigid body e sheet is formed at a roomtemperature and a low speed and is set as a deformable bodyduring the simulation In order to be the same as the actualproduction process the diameter of upper roll is set as150mm the diameter of lower roll is set as 100mm and thediameter of vertical roll is set as 100mm e distancebetween the rolls is set as 350mm and the length of thesheets is set as 900mm

e roll group consists of 14 passes and is divided intothree parts e first group is the guide rolls the secondgroup is the forming rolls and the third group is the shapingrolls In the last three passes of the forming rolls and theshaping rolls the vertical rolls are used to assist the shapinge flower patterns designed with COPRA are used to createa plan drawing of the rolls and then the plan drawing isimported into the ABAQUS software to create three-di-mensional rolls

350

50

25

R5

50

Internal welding line

Figure 6 Section size of b-shaped tube

Figure 7 e diagram of roll-forming production line

Figure 8 e b-shaped tube flower pattern

4 Advances in Materials Science and Engineering

42 Contacts and Boundary Conditions ere are manychoices for the feeding method of the sheet In this paper aconstant speed is set at the front end of the sheet and theangular velocity is applied by the driving rolls is methodhas a long calculation time and the calculation results areaccurate Considering the actual forming process the cal-culation time is too long for the selection of the feedingspeed of the sheet metal if the simulation is based on theforming speed of the actual product e excessive speedsetting will lead to slippage between the sheet metal and rollswhich will lead to inaccurate calculation results In thesimulation experiment the line speed V of the sheet metal inthis paper is selected as 50ndash300mms and the angular ve-locity of the lower roll is obtained by the formula v ωr Inorder to simulate the actual production process as much aspossible the rolls retain only their degrees of freedom in thedirection of rotation and the remaining degrees of freedomare controlled e general contact between the sheet metaland rolls is adopted and the friction coefficient is set to 02[17] Figure 10 is the assembly drawing of the roll bendingmodel of the b-shaped tube

43 Element Type and Meshing In the process of finite el-ement analysis of roll forming the commonly used elementsare SC4R SC8R C3D8R and so on [13] In this numerical

simulation analysis the edge buckling analysis of theb-shaped tubersquos vertical edge is performed While savingcalculation time and improving calculation accuracy SC4Rshell element [8] is selected in this paper In the direction ofsheet width the mesh refinement element size at bend angleis set to 3mm the element size at flange and web is set to10mm the element size in length direction is set to 15mmand the element size in thickness direction is set to 9 integralpoints e meshing situation is shown in Figure 11

44 Comparison of Simulation Results with ExperimentalResults In order to verify the validity of the simulationresults this paper takes the sheet flange height of 70mm thethickness of 25mm and the forming speed of 150mms asan example e upper part of the side is selected for lon-gitudinal strain analysis e results show that the simula-tion results are basically consistent with the experimentalresults as shown in Figure 12

5 Results and Discussion

51 Analysis of Simulation Results According to the processdescribed in the previous sections it can be concluded fromthe postprocessing of the model that along the roll-formingdirection the edge of the sheet has a longitudinal strain andthe shear strain is formed along the sheet forming directionof the roll bending as well as the transverse strain along thetransverse direction of the sheet Taking the sheet metalflange height of 70mm thickness of 25mm and formingspeed of 150mms as an example Figure 13(a) isMises stressdiagram of ldquobrdquo tube It can be seen that the stress distributionof the whole tube is not uniform but the overall trend is thatthe closer to the bend the greater the stress of the tubewhich can be illustrated by the transverse stress distributionof the sheet in Figure 13(b) Figure 13(c) is the equivalentplastic strain diagram of the b-shaped tube It is shown thatthe strain of the tube mainly occurs at the bend corner asshown in the transverse strain distribution diagram of thesheet in Figure 13(d) And the cause of edge buckling atflange is closely related to stress and strain

52MechanismAnalysis of Buckling Defect at Vertical Edge ofb-Shaped Tube From the simulation results it can be seenthat the front flange of the tube tends to move inward asshown in Figure 14 is is due to the complex deformationforce when the sheet metal is bitten by the rolls in the processof roll forming erefore in order to ensure the accuracy ofthe simulation results the strain at the flange is measured at100ndash800mm along the length direction of the sheet metalAs shown in Figure 15 the longitudinal strain distributionsof the top middle and bottom nodes of the flange can beseen as follows the top of the flangegt the middle of theflangegt the bottom of the flange It can be seen from Fig-ure 15 that the curve of the top nodes of the flange is morefluctuating than the curve of the middle and bottom nodesindicating that the longitudinal strain distribution at the topof the flange is the most uneven and the longitudinal straindistribution at the bottom of the flange is the most uniform

Table 1 Orthogonal experimental table of 3 factors and 3 levels

Levels Flange heighth (mm)

Sheet thicknesst (mm)

Formingspeed v (mmmiddotsminus 1)

Level 1 60 20 50Level 2 70 25 100Level 3 80 30 150

Table 2 Material elastic phase properties

MaterialYoungrsquomodulusE (GPa)

Density(kgmiddotmminus 3)

Poissonrsquosratio v

B700L 216 7830 021998

000 005 010 015 0200

200

400

600

800

1000

Stre

ss (M

Pa)

Strain

Figure 9 Stress-strain curve of beam high-strength steel B700L

Advances in Materials Science and Engineering 5

erefore edge buckling is very easy to occur at the top ofthe flange

Comparing the longitudinal strain curves of flange it canbe concluded that when the longitudinal strain is greater

than 0 the sheet extends longitudinally and when thelongitudinal strain is less than 0 the sheet is compressedlongitudinally Because of the combined effect of stress andstrain edge buckling occurs at the flange of the sheet metal

53 Analysis of Orthogonal Experiments of Vertical EdgeBuckling of b-Shaped Tube In this paper B700L high-strength beam steel is used for simulation experiments andthree representative factors are selected which are flangeheight sheet thickness and forming speed A three-factorthree-level orthogonal experiment is designed with a total ofnine experiments e experimental results and resultanalysis are shown in Table 3

From the analysis of the experimental results in Table 3it can be seen that in nine experiments of orthogonal designfor roll forming of b-shaped tube the standard deviation oflongitudinal strain at the top of flange of Exp 6 is the largestwhich is 692times10minus 4 the standard deviation of Exp 1 is thesmallest which is 162times10minus 4 In order to make the exper-imental results more intuitive this paper selects the in-termediate values of two longitudinal strain standarddeviations Exp 2 and Exp 3 and compares with Exp 1 andExp 6 as shown in Figure 16 By comparing the charac-teristics of each curve it can be concluded that themaximumlongitudinal strain fluctuation at the top of the flange is Exp6 and its flange edge buckling is the most serious the resultof the Exp 1 is the smallest longitudinal strain fluctuationamplitude and the minimum edge buckling erefore themagnitude of the longitudinal strain fluctuation at the flangeis closely related to the severity of edge buckling

Table 4 shows the results of the Δε values of the results ofthe respective experiments e experimental values Δεcorresponding to each factor at different levels are summedup and then the average value is obtained and the rangeanalysis is made It can be seen from the data in the table thatthe effect degree of each factor on the side wave is the sheetthicknessgt flange heightgt forming speed erefore for thematerial properties of a certain high-strength beam steelB700L sheet the sheet thickness and flange height have agreater impact on the edge buckling of the flange of theb-shaped tube whereas the effect of the forming speed issmaller In order to further explore the effect of sheetthickness and flange height on edge buckling a comparativeexperiment is designed in this paper

Upper rolls

Lower rolls

Vertical rolls

Roll-forming direction

350mm

Sheet metal

xz

y

Figure 10 Assembly drawing of finite element model for roll forming of b-shaped tube

Web

Bending zone

Flange

Figure 11 Meshing of b-shaped tube sheet

0 100 200 300 400 500 600 700 800 900

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

Long

itudi

nal s

trai

n

Longitudinal distance

FEAEXP

Figure 12 Experimental and simulation comparison of flange topjoints

6 Advances in Materials Science and Engineering

S misesSNEG (fraction = ndash10)(avg 75)

+9180e + 02+8471e + 02+7762e + 02+7053e + 02+6343e + 02+5634e + 02+4925e + 02+4216e + 02+3507e + 02+2798e + 02+2088e + 02+1379e + 02+6701e + 01

Middle

Bottom

Top

yz

x

(a)

0100

Tran

sver

se st

ress

200300400500600700800900

1000

50 100Transverse distance

150 200

(b)

PEEQSNEG (fraction = ndash10)(avg 75)

+5613e ndash 01+5146e ndash 01+4678e ndash 01+4210e ndash 01+3742e ndash 01+3274e ndash 01+2807e ndash 01+2339e ndash 01+1871e ndash 01+1403e ndash 01+9356e ndash 02+4678e ndash 02+0000e + 00 y

zx

(c)

000

005

010

015

020

025

030

035

Equi

vale

nt st

rain

0 50 100Transverse strain

150 200

(d)

Figure 13 (a) Mises stress distribution diagram of b-shaped tube (b) Transverse stress of the sheet metal (c) Equivalent strain distributiondiagram of b-shaped tube (d) Transverse strain of the sheet metal

ndash30 ndash20 ndash10 0 10 20 30

0

10

20

30

40

50

60

70

80

X (m

m)

Y (mm)

FEAEXP

Figure 14 Front shape of b-tube

0 100 200 300 400 500 600 700 800 900Longitudinal distance

The top nodes of the flangeThe middle nodes of the flangeThe bottom nodes of the flange

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

20 times 10ndash3

Long

itudi

nal s

trai

n

Figure 15 Curves of longitudinal strain of flange nodes varyingwith longitudinal distance

Advances in Materials Science and Engineering 7

54 Additional Experimental Results and Analysis In orderto further explore the effect of sheet metal thickness andflange height on the flange edge buckling of ldquobrdquo tube twosets of comparative simulation experiments are designed inthis paper Based on the simulation results of the or-thogonal experiment the first experimental design iscarried out under the condition of flange height h 60 andforming speed v 100mms e variables are sheet metalthickness which is set as 2 25 3 and 35mm respectivelye second experimental design is carried out under thecondition of sheet thickness t 25mm and forming speedv 100mms and the variables are flange height which are65 70 75 and 80mm respectively e experimental re-sults are shown in Figure 15 Figure 17(a) shows that thelongitudinal strain at the flange increases with the increaseof flange height Figure 17(b) shows that as the thickness ofthe sheet increases the longitudinal strain at the flange isalso getting smaller and smaller It can be seen that the edge

buckling at the flange increases with the increase of flangeheight and decreases with the increase of plate thickness

6 Conclusion

In this paper COPRA is used for pass design ABAQUS isused for finite element modeling and analysis and or-thogonal experiments and comparative experiments aredesigned to study the roll-forming law of the b-shaped tubewhich provides theoretical basis for the production of ldquo日rdquoshape tube e conclusions are as follows

(1) Compared with the traditional roll-forming methodthe application of new roll-forming technology inthis paper not only improves the material utilizationrate and production efficiency but also ensures themechanical properties of the products such as tensilestrength bending strength and impact toughness

Table 3 Orthogonal experiment results and result analysis

Simulation number Flange height h (mm) Sheet thickness t (mm) Forming speed v (mmmiddotsminus 1) Δε1 60 (h1) 20 (t1) 50 (v1) 162times10minus 4

2 60 (h1) 25 (t2) 100 (v2) 280times10minus 4

3 60 (h1) 30 (t3) 150 (v3) 501times 10minus 4

4 70 (h2) 20 (t1) 100 (v2) 255times10minus 4

5 70 (h2) 25 (t2) 150 (v3) 367times10minus 4

6 70 (h2) 30 (t3) 50 (v2) 692times10minus 4

7 80 (h3) 20 (t1) 150 (v3) 235times10minus 4

8 80 (h3) 25 (t2) 50 (v1) 425times10minus 4

9 80 (h3) 30 (t3) 100 (v2) 513times10minus 4

0 100 200 300 400 500 600 700 800 900 Longitudinal distance

FEA1FEA2

FEA3FEA6

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

20 times 10ndash3

Long

itudi

nal s

trai

n

Figure 16 Longitudinal strain curves of the sheet metal along longitudinal position in Exp 1 2 3 and 6

Table 4 Range analysis of orthogonal experimental results

Δε Flange height (h) Sheet thickness (t) Forming speed (v)k1 314times10minus 4 217times10minus 4 427times10minus 4

k2 437times10minus 4 357times10minus 4 350times10minus 4

k3 400times10minus 4 560times10minus 4 367times10minus 4

Range R 123times10minus 4 343times10minus 4 077times10minus 4

8 Advances in Materials Science and Engineering

(2) For high-strength beam steel B700L sheet flangeheight sheet thickness and forming speed all effectthe generation of edge buckling in the roll-formingprocess When the standard deviation Δε of longi-tudinal strain is taken as the evaluation criterion theeffect degree of each factor on the formation of edgebuckling is sheet thicknessgt flange heightgt formingspeed

(3) e comparative experimental results show that theedge buckling of the vertical edge of the b-shapedtube decreases with the increase of the thickness ofthe sheet metal and increases with the increase of theflange height e effect of forming speed on edgebuckling of the sheet metal is small

Data Availability

is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricteduse distribution and reproduction in any medium pro-vided the original work is properly cited

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] B Abeyrathna B Rolfe P Hodgson and M Weiss ldquoLocaldeformation in roll formingrdquo e International Journal ofAdvanced Manufacturing Technology vol 88 no 9ndash12pp 2405ndash2415 2017

[2] X L Liu J G Cao X T Chai et al ldquoExperimental andnumerical prediction of the local thickness reduction defect ofcomplex cross-sectional steel in cold roll formingrdquo e In-ternational Journal of Advanced Manufacturing Technologyvol 95 no 5ndash8 pp 1837ndash1848 2017

[3] P Mahajan A Abrass and P Groche ldquoFE simulation of rollforming of a complex profile with the aid of steady statepropertiesrdquo Steel Research International vol 89 no 5Article ID 1700350 2018

[4] G T Halmos Roll Forming Handbook CRC New York NYUSA 2006

[5] B Shirani H M Naeini and R A Tafti ldquoExperimental andnumerical study of required torque in the cold roll forming ofsymmetrical channel sectionsrdquo Journal of ManufacturingProcesses vol 27 pp 63ndash75 2017

[6] F Heislitz H Livatyali M A Ahmetoglu et al ldquoSimulation ofroll forming process with the 3-D FEM code PAM-STAMPrdquoJournal of Materials Processing Technology vol 59 no 1-2pp 59ndash67 1996

[7] N Duggal M A Ahmetoglu G L Kinzel et al ldquoComputeraided simulation of cold roll formingmdasha computer programfor simple section profilesrdquo Journal of Materials ProcessingTechnology vol 59 no 1-2 pp 41ndash48 1996

[8] C K McClure and H Li ldquoRoll forming simulation using finiteelement analysisrdquo Manufacturing Review vol 8 no 2pp 114ndash122 1995

[9] D Bhattacharya and P D Smith ldquoe Development ofLongitudinal Strain in Cold Roll Forming and its Influence onProduct Straightnessrdquo in Proceedings of the First InternationalConference on Technology of Plasticity pp 422ndash427 TokyoJapan June 1984

[10] M S Tehrani H M Naeini P Hartley et al ldquoLocalized edgebuckling in cold roll-forming of circular tube sectionrdquo Journalof Materials Processing Technology vol 177 no 1ndash3pp 617ndash620 2006

[11] M S Tehrani P Hartley and H Khademizadeh ldquoLocalisededge buckling in cold roll-forming of symmetric channelsectionrdquo in-Walled Structures vol 44 no 2 pp 184ndash1962006

[12] N Kim S B Kang and S Lee ldquoPrediction and design of edgeshape of initial strip for thick tube roll forming using finiteelement methodrdquo Journal of Materials Processing Technologyvol 142 no 2 pp 479ndash486 2003

64 66 68 70 72 74 76 78 80 82

30 times 10ndash4

35 times 10ndash4

40 times 10ndash4

45 times 10ndash4

50 times 10ndash4

55 times 10ndash4St

anda

rd d

evia

tion

of lo

ngitu

dina

l str

ain

Longitudinal distance

FEAEXP

(a)

18 20 22 24 26 28 30 32 34 3630E ndash 04

35E ndash 04

40E ndash 04

45E ndash 04

50E ndash 04

55E ndash 04

60E ndash 04

65E ndash 04

Stan

dard

dev

iatio

n of

long

itudi

nal s

trai

n

Sheet thickness (mm)

FEAEXP

(b)

Figure 17 (a) Effect of flange height on longitudinal strain (b) Effect of sheet thickness on longitudinal strain

Advances in Materials Science and Engineering 9

[13] T Wang and H Fei ldquoPrediction of wrinkling in flexible rollforming based on finite element simulationrdquo Forging ampStamping Technology vol 38 no 6 pp 67ndash72 2013

[14] Data M Software GmbH ldquoCOPRAreg roll formingrdquo 2001httpwwwroll-designcom

[15] X Luo Z Guo S Li et al ldquoFinite element analysis of the effectof material properties on wavy flange in high strength steel rollformingrdquo Journal of Shanghai Jiaotong University vol 42no 5 pp 744ndash747 2008

[16] D Hibbitt B Karlsson and P Sorensen Getting started withABAQUSExplicitmdashinteractive version Hibbitt Karlsson ampSorensen Inc Providence RI USA 2002

[17] Q V Bui and J P Ponthot ldquoNumerical simulation of coldroll-forming processesrdquo Journal of Materials ProcessingTechnology vol 202 no 1ndash3 pp 275ndash282 2008

10 Advances in Materials Science and Engineering

42 Contacts and Boundary Conditions ere are manychoices for the feeding method of the sheet In this paper aconstant speed is set at the front end of the sheet and theangular velocity is applied by the driving rolls is methodhas a long calculation time and the calculation results areaccurate Considering the actual forming process the cal-culation time is too long for the selection of the feedingspeed of the sheet metal if the simulation is based on theforming speed of the actual product e excessive speedsetting will lead to slippage between the sheet metal and rollswhich will lead to inaccurate calculation results In thesimulation experiment the line speed V of the sheet metal inthis paper is selected as 50ndash300mms and the angular ve-locity of the lower roll is obtained by the formula v ωr Inorder to simulate the actual production process as much aspossible the rolls retain only their degrees of freedom in thedirection of rotation and the remaining degrees of freedomare controlled e general contact between the sheet metaland rolls is adopted and the friction coefficient is set to 02[17] Figure 10 is the assembly drawing of the roll bendingmodel of the b-shaped tube

43 Element Type and Meshing In the process of finite el-ement analysis of roll forming the commonly used elementsare SC4R SC8R C3D8R and so on [13] In this numerical

simulation analysis the edge buckling analysis of theb-shaped tubersquos vertical edge is performed While savingcalculation time and improving calculation accuracy SC4Rshell element [8] is selected in this paper In the direction ofsheet width the mesh refinement element size at bend angleis set to 3mm the element size at flange and web is set to10mm the element size in length direction is set to 15mmand the element size in thickness direction is set to 9 integralpoints e meshing situation is shown in Figure 11

44 Comparison of Simulation Results with ExperimentalResults In order to verify the validity of the simulationresults this paper takes the sheet flange height of 70mm thethickness of 25mm and the forming speed of 150mms asan example e upper part of the side is selected for lon-gitudinal strain analysis e results show that the simula-tion results are basically consistent with the experimentalresults as shown in Figure 12

5 Results and Discussion

51 Analysis of Simulation Results According to the processdescribed in the previous sections it can be concluded fromthe postprocessing of the model that along the roll-formingdirection the edge of the sheet has a longitudinal strain andthe shear strain is formed along the sheet forming directionof the roll bending as well as the transverse strain along thetransverse direction of the sheet Taking the sheet metalflange height of 70mm thickness of 25mm and formingspeed of 150mms as an example Figure 13(a) isMises stressdiagram of ldquobrdquo tube It can be seen that the stress distributionof the whole tube is not uniform but the overall trend is thatthe closer to the bend the greater the stress of the tubewhich can be illustrated by the transverse stress distributionof the sheet in Figure 13(b) Figure 13(c) is the equivalentplastic strain diagram of the b-shaped tube It is shown thatthe strain of the tube mainly occurs at the bend corner asshown in the transverse strain distribution diagram of thesheet in Figure 13(d) And the cause of edge buckling atflange is closely related to stress and strain

52MechanismAnalysis of Buckling Defect at Vertical Edge ofb-Shaped Tube From the simulation results it can be seenthat the front flange of the tube tends to move inward asshown in Figure 14 is is due to the complex deformationforce when the sheet metal is bitten by the rolls in the processof roll forming erefore in order to ensure the accuracy ofthe simulation results the strain at the flange is measured at100ndash800mm along the length direction of the sheet metalAs shown in Figure 15 the longitudinal strain distributionsof the top middle and bottom nodes of the flange can beseen as follows the top of the flangegt the middle of theflangegt the bottom of the flange It can be seen from Fig-ure 15 that the curve of the top nodes of the flange is morefluctuating than the curve of the middle and bottom nodesindicating that the longitudinal strain distribution at the topof the flange is the most uneven and the longitudinal straindistribution at the bottom of the flange is the most uniform

Table 1 Orthogonal experimental table of 3 factors and 3 levels

Levels Flange heighth (mm)

Sheet thicknesst (mm)

Formingspeed v (mmmiddotsminus 1)

Level 1 60 20 50Level 2 70 25 100Level 3 80 30 150

Table 2 Material elastic phase properties

MaterialYoungrsquomodulusE (GPa)

Density(kgmiddotmminus 3)

Poissonrsquosratio v

B700L 216 7830 021998

000 005 010 015 0200

200

400

600

800

1000

Stre

ss (M

Pa)

Strain

Figure 9 Stress-strain curve of beam high-strength steel B700L

Advances in Materials Science and Engineering 5

erefore edge buckling is very easy to occur at the top ofthe flange

Comparing the longitudinal strain curves of flange it canbe concluded that when the longitudinal strain is greater

than 0 the sheet extends longitudinally and when thelongitudinal strain is less than 0 the sheet is compressedlongitudinally Because of the combined effect of stress andstrain edge buckling occurs at the flange of the sheet metal

53 Analysis of Orthogonal Experiments of Vertical EdgeBuckling of b-Shaped Tube In this paper B700L high-strength beam steel is used for simulation experiments andthree representative factors are selected which are flangeheight sheet thickness and forming speed A three-factorthree-level orthogonal experiment is designed with a total ofnine experiments e experimental results and resultanalysis are shown in Table 3

From the analysis of the experimental results in Table 3it can be seen that in nine experiments of orthogonal designfor roll forming of b-shaped tube the standard deviation oflongitudinal strain at the top of flange of Exp 6 is the largestwhich is 692times10minus 4 the standard deviation of Exp 1 is thesmallest which is 162times10minus 4 In order to make the exper-imental results more intuitive this paper selects the in-termediate values of two longitudinal strain standarddeviations Exp 2 and Exp 3 and compares with Exp 1 andExp 6 as shown in Figure 16 By comparing the charac-teristics of each curve it can be concluded that themaximumlongitudinal strain fluctuation at the top of the flange is Exp6 and its flange edge buckling is the most serious the resultof the Exp 1 is the smallest longitudinal strain fluctuationamplitude and the minimum edge buckling erefore themagnitude of the longitudinal strain fluctuation at the flangeis closely related to the severity of edge buckling

Table 4 shows the results of the Δε values of the results ofthe respective experiments e experimental values Δεcorresponding to each factor at different levels are summedup and then the average value is obtained and the rangeanalysis is made It can be seen from the data in the table thatthe effect degree of each factor on the side wave is the sheetthicknessgt flange heightgt forming speed erefore for thematerial properties of a certain high-strength beam steelB700L sheet the sheet thickness and flange height have agreater impact on the edge buckling of the flange of theb-shaped tube whereas the effect of the forming speed issmaller In order to further explore the effect of sheetthickness and flange height on edge buckling a comparativeexperiment is designed in this paper

Upper rolls

Lower rolls

Vertical rolls

Roll-forming direction

350mm

Sheet metal

xz

y

Figure 10 Assembly drawing of finite element model for roll forming of b-shaped tube

Web

Bending zone

Flange

Figure 11 Meshing of b-shaped tube sheet

0 100 200 300 400 500 600 700 800 900

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

Long

itudi

nal s

trai

n

Longitudinal distance

FEAEXP

Figure 12 Experimental and simulation comparison of flange topjoints

6 Advances in Materials Science and Engineering

S misesSNEG (fraction = ndash10)(avg 75)

+9180e + 02+8471e + 02+7762e + 02+7053e + 02+6343e + 02+5634e + 02+4925e + 02+4216e + 02+3507e + 02+2798e + 02+2088e + 02+1379e + 02+6701e + 01

Middle

Bottom

Top

yz

x

(a)

0100

Tran

sver

se st

ress

200300400500600700800900

1000

50 100Transverse distance

150 200

(b)

PEEQSNEG (fraction = ndash10)(avg 75)

+5613e ndash 01+5146e ndash 01+4678e ndash 01+4210e ndash 01+3742e ndash 01+3274e ndash 01+2807e ndash 01+2339e ndash 01+1871e ndash 01+1403e ndash 01+9356e ndash 02+4678e ndash 02+0000e + 00 y

zx

(c)

000

005

010

015

020

025

030

035

Equi

vale

nt st

rain

0 50 100Transverse strain

150 200

(d)

Figure 13 (a) Mises stress distribution diagram of b-shaped tube (b) Transverse stress of the sheet metal (c) Equivalent strain distributiondiagram of b-shaped tube (d) Transverse strain of the sheet metal

ndash30 ndash20 ndash10 0 10 20 30

0

10

20

30

40

50

60

70

80

X (m

m)

Y (mm)

FEAEXP

Figure 14 Front shape of b-tube

0 100 200 300 400 500 600 700 800 900Longitudinal distance

The top nodes of the flangeThe middle nodes of the flangeThe bottom nodes of the flange

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

20 times 10ndash3

Long

itudi

nal s

trai

n

Figure 15 Curves of longitudinal strain of flange nodes varyingwith longitudinal distance

Advances in Materials Science and Engineering 7

54 Additional Experimental Results and Analysis In orderto further explore the effect of sheet metal thickness andflange height on the flange edge buckling of ldquobrdquo tube twosets of comparative simulation experiments are designed inthis paper Based on the simulation results of the or-thogonal experiment the first experimental design iscarried out under the condition of flange height h 60 andforming speed v 100mms e variables are sheet metalthickness which is set as 2 25 3 and 35mm respectivelye second experimental design is carried out under thecondition of sheet thickness t 25mm and forming speedv 100mms and the variables are flange height which are65 70 75 and 80mm respectively e experimental re-sults are shown in Figure 15 Figure 17(a) shows that thelongitudinal strain at the flange increases with the increaseof flange height Figure 17(b) shows that as the thickness ofthe sheet increases the longitudinal strain at the flange isalso getting smaller and smaller It can be seen that the edge

buckling at the flange increases with the increase of flangeheight and decreases with the increase of plate thickness

6 Conclusion

In this paper COPRA is used for pass design ABAQUS isused for finite element modeling and analysis and or-thogonal experiments and comparative experiments aredesigned to study the roll-forming law of the b-shaped tubewhich provides theoretical basis for the production of ldquo日rdquoshape tube e conclusions are as follows

(1) Compared with the traditional roll-forming methodthe application of new roll-forming technology inthis paper not only improves the material utilizationrate and production efficiency but also ensures themechanical properties of the products such as tensilestrength bending strength and impact toughness

Table 3 Orthogonal experiment results and result analysis

Simulation number Flange height h (mm) Sheet thickness t (mm) Forming speed v (mmmiddotsminus 1) Δε1 60 (h1) 20 (t1) 50 (v1) 162times10minus 4

2 60 (h1) 25 (t2) 100 (v2) 280times10minus 4

3 60 (h1) 30 (t3) 150 (v3) 501times 10minus 4

4 70 (h2) 20 (t1) 100 (v2) 255times10minus 4

5 70 (h2) 25 (t2) 150 (v3) 367times10minus 4

6 70 (h2) 30 (t3) 50 (v2) 692times10minus 4

7 80 (h3) 20 (t1) 150 (v3) 235times10minus 4

8 80 (h3) 25 (t2) 50 (v1) 425times10minus 4

9 80 (h3) 30 (t3) 100 (v2) 513times10minus 4

0 100 200 300 400 500 600 700 800 900 Longitudinal distance

FEA1FEA2

FEA3FEA6

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

20 times 10ndash3

Long

itudi

nal s

trai

n

Figure 16 Longitudinal strain curves of the sheet metal along longitudinal position in Exp 1 2 3 and 6

Table 4 Range analysis of orthogonal experimental results

Δε Flange height (h) Sheet thickness (t) Forming speed (v)k1 314times10minus 4 217times10minus 4 427times10minus 4

k2 437times10minus 4 357times10minus 4 350times10minus 4

k3 400times10minus 4 560times10minus 4 367times10minus 4

Range R 123times10minus 4 343times10minus 4 077times10minus 4

8 Advances in Materials Science and Engineering

(2) For high-strength beam steel B700L sheet flangeheight sheet thickness and forming speed all effectthe generation of edge buckling in the roll-formingprocess When the standard deviation Δε of longi-tudinal strain is taken as the evaluation criterion theeffect degree of each factor on the formation of edgebuckling is sheet thicknessgt flange heightgt formingspeed

(3) e comparative experimental results show that theedge buckling of the vertical edge of the b-shapedtube decreases with the increase of the thickness ofthe sheet metal and increases with the increase of theflange height e effect of forming speed on edgebuckling of the sheet metal is small

Data Availability

is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricteduse distribution and reproduction in any medium pro-vided the original work is properly cited

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] B Abeyrathna B Rolfe P Hodgson and M Weiss ldquoLocaldeformation in roll formingrdquo e International Journal ofAdvanced Manufacturing Technology vol 88 no 9ndash12pp 2405ndash2415 2017

[2] X L Liu J G Cao X T Chai et al ldquoExperimental andnumerical prediction of the local thickness reduction defect ofcomplex cross-sectional steel in cold roll formingrdquo e In-ternational Journal of Advanced Manufacturing Technologyvol 95 no 5ndash8 pp 1837ndash1848 2017

[3] P Mahajan A Abrass and P Groche ldquoFE simulation of rollforming of a complex profile with the aid of steady statepropertiesrdquo Steel Research International vol 89 no 5Article ID 1700350 2018

[4] G T Halmos Roll Forming Handbook CRC New York NYUSA 2006

[5] B Shirani H M Naeini and R A Tafti ldquoExperimental andnumerical study of required torque in the cold roll forming ofsymmetrical channel sectionsrdquo Journal of ManufacturingProcesses vol 27 pp 63ndash75 2017

[6] F Heislitz H Livatyali M A Ahmetoglu et al ldquoSimulation ofroll forming process with the 3-D FEM code PAM-STAMPrdquoJournal of Materials Processing Technology vol 59 no 1-2pp 59ndash67 1996

[7] N Duggal M A Ahmetoglu G L Kinzel et al ldquoComputeraided simulation of cold roll formingmdasha computer programfor simple section profilesrdquo Journal of Materials ProcessingTechnology vol 59 no 1-2 pp 41ndash48 1996

[8] C K McClure and H Li ldquoRoll forming simulation using finiteelement analysisrdquo Manufacturing Review vol 8 no 2pp 114ndash122 1995

[9] D Bhattacharya and P D Smith ldquoe Development ofLongitudinal Strain in Cold Roll Forming and its Influence onProduct Straightnessrdquo in Proceedings of the First InternationalConference on Technology of Plasticity pp 422ndash427 TokyoJapan June 1984

[10] M S Tehrani H M Naeini P Hartley et al ldquoLocalized edgebuckling in cold roll-forming of circular tube sectionrdquo Journalof Materials Processing Technology vol 177 no 1ndash3pp 617ndash620 2006

[11] M S Tehrani P Hartley and H Khademizadeh ldquoLocalisededge buckling in cold roll-forming of symmetric channelsectionrdquo in-Walled Structures vol 44 no 2 pp 184ndash1962006

[12] N Kim S B Kang and S Lee ldquoPrediction and design of edgeshape of initial strip for thick tube roll forming using finiteelement methodrdquo Journal of Materials Processing Technologyvol 142 no 2 pp 479ndash486 2003

64 66 68 70 72 74 76 78 80 82

30 times 10ndash4

35 times 10ndash4

40 times 10ndash4

45 times 10ndash4

50 times 10ndash4

55 times 10ndash4St

anda

rd d

evia

tion

of lo

ngitu

dina

l str

ain

Longitudinal distance

FEAEXP

(a)

18 20 22 24 26 28 30 32 34 3630E ndash 04

35E ndash 04

40E ndash 04

45E ndash 04

50E ndash 04

55E ndash 04

60E ndash 04

65E ndash 04

Stan

dard

dev

iatio

n of

long

itudi

nal s

trai

n

Sheet thickness (mm)

FEAEXP

(b)

Figure 17 (a) Effect of flange height on longitudinal strain (b) Effect of sheet thickness on longitudinal strain

Advances in Materials Science and Engineering 9

[13] T Wang and H Fei ldquoPrediction of wrinkling in flexible rollforming based on finite element simulationrdquo Forging ampStamping Technology vol 38 no 6 pp 67ndash72 2013

[14] Data M Software GmbH ldquoCOPRAreg roll formingrdquo 2001httpwwwroll-designcom

[15] X Luo Z Guo S Li et al ldquoFinite element analysis of the effectof material properties on wavy flange in high strength steel rollformingrdquo Journal of Shanghai Jiaotong University vol 42no 5 pp 744ndash747 2008

[16] D Hibbitt B Karlsson and P Sorensen Getting started withABAQUSExplicitmdashinteractive version Hibbitt Karlsson ampSorensen Inc Providence RI USA 2002

[17] Q V Bui and J P Ponthot ldquoNumerical simulation of coldroll-forming processesrdquo Journal of Materials ProcessingTechnology vol 202 no 1ndash3 pp 275ndash282 2008

10 Advances in Materials Science and Engineering

erefore edge buckling is very easy to occur at the top ofthe flange

Comparing the longitudinal strain curves of flange it canbe concluded that when the longitudinal strain is greater

than 0 the sheet extends longitudinally and when thelongitudinal strain is less than 0 the sheet is compressedlongitudinally Because of the combined effect of stress andstrain edge buckling occurs at the flange of the sheet metal

53 Analysis of Orthogonal Experiments of Vertical EdgeBuckling of b-Shaped Tube In this paper B700L high-strength beam steel is used for simulation experiments andthree representative factors are selected which are flangeheight sheet thickness and forming speed A three-factorthree-level orthogonal experiment is designed with a total ofnine experiments e experimental results and resultanalysis are shown in Table 3

From the analysis of the experimental results in Table 3it can be seen that in nine experiments of orthogonal designfor roll forming of b-shaped tube the standard deviation oflongitudinal strain at the top of flange of Exp 6 is the largestwhich is 692times10minus 4 the standard deviation of Exp 1 is thesmallest which is 162times10minus 4 In order to make the exper-imental results more intuitive this paper selects the in-termediate values of two longitudinal strain standarddeviations Exp 2 and Exp 3 and compares with Exp 1 andExp 6 as shown in Figure 16 By comparing the charac-teristics of each curve it can be concluded that themaximumlongitudinal strain fluctuation at the top of the flange is Exp6 and its flange edge buckling is the most serious the resultof the Exp 1 is the smallest longitudinal strain fluctuationamplitude and the minimum edge buckling erefore themagnitude of the longitudinal strain fluctuation at the flangeis closely related to the severity of edge buckling

Table 4 shows the results of the Δε values of the results ofthe respective experiments e experimental values Δεcorresponding to each factor at different levels are summedup and then the average value is obtained and the rangeanalysis is made It can be seen from the data in the table thatthe effect degree of each factor on the side wave is the sheetthicknessgt flange heightgt forming speed erefore for thematerial properties of a certain high-strength beam steelB700L sheet the sheet thickness and flange height have agreater impact on the edge buckling of the flange of theb-shaped tube whereas the effect of the forming speed issmaller In order to further explore the effect of sheetthickness and flange height on edge buckling a comparativeexperiment is designed in this paper

Upper rolls

Lower rolls

Vertical rolls

Roll-forming direction

350mm

Sheet metal

xz

y

Figure 10 Assembly drawing of finite element model for roll forming of b-shaped tube

Web

Bending zone

Flange

Figure 11 Meshing of b-shaped tube sheet

0 100 200 300 400 500 600 700 800 900

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

Long

itudi

nal s

trai

n

Longitudinal distance

FEAEXP

Figure 12 Experimental and simulation comparison of flange topjoints

6 Advances in Materials Science and Engineering

S misesSNEG (fraction = ndash10)(avg 75)

+9180e + 02+8471e + 02+7762e + 02+7053e + 02+6343e + 02+5634e + 02+4925e + 02+4216e + 02+3507e + 02+2798e + 02+2088e + 02+1379e + 02+6701e + 01

Middle

Bottom

Top

yz

x

(a)

0100

Tran

sver

se st

ress

200300400500600700800900

1000

50 100Transverse distance

150 200

(b)

PEEQSNEG (fraction = ndash10)(avg 75)

+5613e ndash 01+5146e ndash 01+4678e ndash 01+4210e ndash 01+3742e ndash 01+3274e ndash 01+2807e ndash 01+2339e ndash 01+1871e ndash 01+1403e ndash 01+9356e ndash 02+4678e ndash 02+0000e + 00 y

zx

(c)

000

005

010

015

020

025

030

035

Equi

vale

nt st

rain

0 50 100Transverse strain

150 200

(d)

Figure 13 (a) Mises stress distribution diagram of b-shaped tube (b) Transverse stress of the sheet metal (c) Equivalent strain distributiondiagram of b-shaped tube (d) Transverse strain of the sheet metal

ndash30 ndash20 ndash10 0 10 20 30

0

10

20

30

40

50

60

70

80

X (m

m)

Y (mm)

FEAEXP

Figure 14 Front shape of b-tube

0 100 200 300 400 500 600 700 800 900Longitudinal distance

The top nodes of the flangeThe middle nodes of the flangeThe bottom nodes of the flange

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

20 times 10ndash3

Long

itudi

nal s

trai

n

Figure 15 Curves of longitudinal strain of flange nodes varyingwith longitudinal distance

Advances in Materials Science and Engineering 7

54 Additional Experimental Results and Analysis In orderto further explore the effect of sheet metal thickness andflange height on the flange edge buckling of ldquobrdquo tube twosets of comparative simulation experiments are designed inthis paper Based on the simulation results of the or-thogonal experiment the first experimental design iscarried out under the condition of flange height h 60 andforming speed v 100mms e variables are sheet metalthickness which is set as 2 25 3 and 35mm respectivelye second experimental design is carried out under thecondition of sheet thickness t 25mm and forming speedv 100mms and the variables are flange height which are65 70 75 and 80mm respectively e experimental re-sults are shown in Figure 15 Figure 17(a) shows that thelongitudinal strain at the flange increases with the increaseof flange height Figure 17(b) shows that as the thickness ofthe sheet increases the longitudinal strain at the flange isalso getting smaller and smaller It can be seen that the edge

buckling at the flange increases with the increase of flangeheight and decreases with the increase of plate thickness

6 Conclusion

In this paper COPRA is used for pass design ABAQUS isused for finite element modeling and analysis and or-thogonal experiments and comparative experiments aredesigned to study the roll-forming law of the b-shaped tubewhich provides theoretical basis for the production of ldquo日rdquoshape tube e conclusions are as follows

(1) Compared with the traditional roll-forming methodthe application of new roll-forming technology inthis paper not only improves the material utilizationrate and production efficiency but also ensures themechanical properties of the products such as tensilestrength bending strength and impact toughness

Table 3 Orthogonal experiment results and result analysis

Simulation number Flange height h (mm) Sheet thickness t (mm) Forming speed v (mmmiddotsminus 1) Δε1 60 (h1) 20 (t1) 50 (v1) 162times10minus 4

2 60 (h1) 25 (t2) 100 (v2) 280times10minus 4

3 60 (h1) 30 (t3) 150 (v3) 501times 10minus 4

4 70 (h2) 20 (t1) 100 (v2) 255times10minus 4

5 70 (h2) 25 (t2) 150 (v3) 367times10minus 4

6 70 (h2) 30 (t3) 50 (v2) 692times10minus 4

7 80 (h3) 20 (t1) 150 (v3) 235times10minus 4

8 80 (h3) 25 (t2) 50 (v1) 425times10minus 4

9 80 (h3) 30 (t3) 100 (v2) 513times10minus 4

0 100 200 300 400 500 600 700 800 900 Longitudinal distance

FEA1FEA2

FEA3FEA6

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

20 times 10ndash3

Long

itudi

nal s

trai

n

Figure 16 Longitudinal strain curves of the sheet metal along longitudinal position in Exp 1 2 3 and 6

Table 4 Range analysis of orthogonal experimental results

Δε Flange height (h) Sheet thickness (t) Forming speed (v)k1 314times10minus 4 217times10minus 4 427times10minus 4

k2 437times10minus 4 357times10minus 4 350times10minus 4

k3 400times10minus 4 560times10minus 4 367times10minus 4

Range R 123times10minus 4 343times10minus 4 077times10minus 4

8 Advances in Materials Science and Engineering

(2) For high-strength beam steel B700L sheet flangeheight sheet thickness and forming speed all effectthe generation of edge buckling in the roll-formingprocess When the standard deviation Δε of longi-tudinal strain is taken as the evaluation criterion theeffect degree of each factor on the formation of edgebuckling is sheet thicknessgt flange heightgt formingspeed

(3) e comparative experimental results show that theedge buckling of the vertical edge of the b-shapedtube decreases with the increase of the thickness ofthe sheet metal and increases with the increase of theflange height e effect of forming speed on edgebuckling of the sheet metal is small

Data Availability

is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricteduse distribution and reproduction in any medium pro-vided the original work is properly cited

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] B Abeyrathna B Rolfe P Hodgson and M Weiss ldquoLocaldeformation in roll formingrdquo e International Journal ofAdvanced Manufacturing Technology vol 88 no 9ndash12pp 2405ndash2415 2017

[2] X L Liu J G Cao X T Chai et al ldquoExperimental andnumerical prediction of the local thickness reduction defect ofcomplex cross-sectional steel in cold roll formingrdquo e In-ternational Journal of Advanced Manufacturing Technologyvol 95 no 5ndash8 pp 1837ndash1848 2017

[3] P Mahajan A Abrass and P Groche ldquoFE simulation of rollforming of a complex profile with the aid of steady statepropertiesrdquo Steel Research International vol 89 no 5Article ID 1700350 2018

[4] G T Halmos Roll Forming Handbook CRC New York NYUSA 2006

[5] B Shirani H M Naeini and R A Tafti ldquoExperimental andnumerical study of required torque in the cold roll forming ofsymmetrical channel sectionsrdquo Journal of ManufacturingProcesses vol 27 pp 63ndash75 2017

[6] F Heislitz H Livatyali M A Ahmetoglu et al ldquoSimulation ofroll forming process with the 3-D FEM code PAM-STAMPrdquoJournal of Materials Processing Technology vol 59 no 1-2pp 59ndash67 1996

[7] N Duggal M A Ahmetoglu G L Kinzel et al ldquoComputeraided simulation of cold roll formingmdasha computer programfor simple section profilesrdquo Journal of Materials ProcessingTechnology vol 59 no 1-2 pp 41ndash48 1996

[8] C K McClure and H Li ldquoRoll forming simulation using finiteelement analysisrdquo Manufacturing Review vol 8 no 2pp 114ndash122 1995

[9] D Bhattacharya and P D Smith ldquoe Development ofLongitudinal Strain in Cold Roll Forming and its Influence onProduct Straightnessrdquo in Proceedings of the First InternationalConference on Technology of Plasticity pp 422ndash427 TokyoJapan June 1984

[10] M S Tehrani H M Naeini P Hartley et al ldquoLocalized edgebuckling in cold roll-forming of circular tube sectionrdquo Journalof Materials Processing Technology vol 177 no 1ndash3pp 617ndash620 2006

[11] M S Tehrani P Hartley and H Khademizadeh ldquoLocalisededge buckling in cold roll-forming of symmetric channelsectionrdquo in-Walled Structures vol 44 no 2 pp 184ndash1962006

[12] N Kim S B Kang and S Lee ldquoPrediction and design of edgeshape of initial strip for thick tube roll forming using finiteelement methodrdquo Journal of Materials Processing Technologyvol 142 no 2 pp 479ndash486 2003

64 66 68 70 72 74 76 78 80 82

30 times 10ndash4

35 times 10ndash4

40 times 10ndash4

45 times 10ndash4

50 times 10ndash4

55 times 10ndash4St

anda

rd d

evia

tion

of lo

ngitu

dina

l str

ain

Longitudinal distance

FEAEXP

(a)

18 20 22 24 26 28 30 32 34 3630E ndash 04

35E ndash 04

40E ndash 04

45E ndash 04

50E ndash 04

55E ndash 04

60E ndash 04

65E ndash 04

Stan

dard

dev

iatio

n of

long

itudi

nal s

trai

n

Sheet thickness (mm)

FEAEXP

(b)

Figure 17 (a) Effect of flange height on longitudinal strain (b) Effect of sheet thickness on longitudinal strain

Advances in Materials Science and Engineering 9

[13] T Wang and H Fei ldquoPrediction of wrinkling in flexible rollforming based on finite element simulationrdquo Forging ampStamping Technology vol 38 no 6 pp 67ndash72 2013

[14] Data M Software GmbH ldquoCOPRAreg roll formingrdquo 2001httpwwwroll-designcom

[15] X Luo Z Guo S Li et al ldquoFinite element analysis of the effectof material properties on wavy flange in high strength steel rollformingrdquo Journal of Shanghai Jiaotong University vol 42no 5 pp 744ndash747 2008

[16] D Hibbitt B Karlsson and P Sorensen Getting started withABAQUSExplicitmdashinteractive version Hibbitt Karlsson ampSorensen Inc Providence RI USA 2002

[17] Q V Bui and J P Ponthot ldquoNumerical simulation of coldroll-forming processesrdquo Journal of Materials ProcessingTechnology vol 202 no 1ndash3 pp 275ndash282 2008

10 Advances in Materials Science and Engineering

S misesSNEG (fraction = ndash10)(avg 75)

+9180e + 02+8471e + 02+7762e + 02+7053e + 02+6343e + 02+5634e + 02+4925e + 02+4216e + 02+3507e + 02+2798e + 02+2088e + 02+1379e + 02+6701e + 01

Middle

Bottom

Top

yz

x

(a)

0100

Tran

sver

se st

ress

200300400500600700800900

1000

50 100Transverse distance

150 200

(b)

PEEQSNEG (fraction = ndash10)(avg 75)

+5613e ndash 01+5146e ndash 01+4678e ndash 01+4210e ndash 01+3742e ndash 01+3274e ndash 01+2807e ndash 01+2339e ndash 01+1871e ndash 01+1403e ndash 01+9356e ndash 02+4678e ndash 02+0000e + 00 y

zx

(c)

000

005

010

015

020

025

030

035

Equi

vale

nt st

rain

0 50 100Transverse strain

150 200

(d)

Figure 13 (a) Mises stress distribution diagram of b-shaped tube (b) Transverse stress of the sheet metal (c) Equivalent strain distributiondiagram of b-shaped tube (d) Transverse strain of the sheet metal

ndash30 ndash20 ndash10 0 10 20 30

0

10

20

30

40

50

60

70

80

X (m

m)

Y (mm)

FEAEXP

Figure 14 Front shape of b-tube

0 100 200 300 400 500 600 700 800 900Longitudinal distance

The top nodes of the flangeThe middle nodes of the flangeThe bottom nodes of the flange

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

20 times 10ndash3

Long

itudi

nal s

trai

n

Figure 15 Curves of longitudinal strain of flange nodes varyingwith longitudinal distance

Advances in Materials Science and Engineering 7

54 Additional Experimental Results and Analysis In orderto further explore the effect of sheet metal thickness andflange height on the flange edge buckling of ldquobrdquo tube twosets of comparative simulation experiments are designed inthis paper Based on the simulation results of the or-thogonal experiment the first experimental design iscarried out under the condition of flange height h 60 andforming speed v 100mms e variables are sheet metalthickness which is set as 2 25 3 and 35mm respectivelye second experimental design is carried out under thecondition of sheet thickness t 25mm and forming speedv 100mms and the variables are flange height which are65 70 75 and 80mm respectively e experimental re-sults are shown in Figure 15 Figure 17(a) shows that thelongitudinal strain at the flange increases with the increaseof flange height Figure 17(b) shows that as the thickness ofthe sheet increases the longitudinal strain at the flange isalso getting smaller and smaller It can be seen that the edge

buckling at the flange increases with the increase of flangeheight and decreases with the increase of plate thickness

6 Conclusion

In this paper COPRA is used for pass design ABAQUS isused for finite element modeling and analysis and or-thogonal experiments and comparative experiments aredesigned to study the roll-forming law of the b-shaped tubewhich provides theoretical basis for the production of ldquo日rdquoshape tube e conclusions are as follows

(1) Compared with the traditional roll-forming methodthe application of new roll-forming technology inthis paper not only improves the material utilizationrate and production efficiency but also ensures themechanical properties of the products such as tensilestrength bending strength and impact toughness

Table 3 Orthogonal experiment results and result analysis

Simulation number Flange height h (mm) Sheet thickness t (mm) Forming speed v (mmmiddotsminus 1) Δε1 60 (h1) 20 (t1) 50 (v1) 162times10minus 4

2 60 (h1) 25 (t2) 100 (v2) 280times10minus 4

3 60 (h1) 30 (t3) 150 (v3) 501times 10minus 4

4 70 (h2) 20 (t1) 100 (v2) 255times10minus 4

5 70 (h2) 25 (t2) 150 (v3) 367times10minus 4

6 70 (h2) 30 (t3) 50 (v2) 692times10minus 4

7 80 (h3) 20 (t1) 150 (v3) 235times10minus 4

8 80 (h3) 25 (t2) 50 (v1) 425times10minus 4

9 80 (h3) 30 (t3) 100 (v2) 513times10minus 4

0 100 200 300 400 500 600 700 800 900 Longitudinal distance

FEA1FEA2

FEA3FEA6

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

20 times 10ndash3

Long

itudi

nal s

trai

n

Figure 16 Longitudinal strain curves of the sheet metal along longitudinal position in Exp 1 2 3 and 6

Table 4 Range analysis of orthogonal experimental results

Δε Flange height (h) Sheet thickness (t) Forming speed (v)k1 314times10minus 4 217times10minus 4 427times10minus 4

k2 437times10minus 4 357times10minus 4 350times10minus 4

k3 400times10minus 4 560times10minus 4 367times10minus 4

Range R 123times10minus 4 343times10minus 4 077times10minus 4

8 Advances in Materials Science and Engineering

(2) For high-strength beam steel B700L sheet flangeheight sheet thickness and forming speed all effectthe generation of edge buckling in the roll-formingprocess When the standard deviation Δε of longi-tudinal strain is taken as the evaluation criterion theeffect degree of each factor on the formation of edgebuckling is sheet thicknessgt flange heightgt formingspeed

(3) e comparative experimental results show that theedge buckling of the vertical edge of the b-shapedtube decreases with the increase of the thickness ofthe sheet metal and increases with the increase of theflange height e effect of forming speed on edgebuckling of the sheet metal is small

Data Availability

is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricteduse distribution and reproduction in any medium pro-vided the original work is properly cited

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] B Abeyrathna B Rolfe P Hodgson and M Weiss ldquoLocaldeformation in roll formingrdquo e International Journal ofAdvanced Manufacturing Technology vol 88 no 9ndash12pp 2405ndash2415 2017

[2] X L Liu J G Cao X T Chai et al ldquoExperimental andnumerical prediction of the local thickness reduction defect ofcomplex cross-sectional steel in cold roll formingrdquo e In-ternational Journal of Advanced Manufacturing Technologyvol 95 no 5ndash8 pp 1837ndash1848 2017

[3] P Mahajan A Abrass and P Groche ldquoFE simulation of rollforming of a complex profile with the aid of steady statepropertiesrdquo Steel Research International vol 89 no 5Article ID 1700350 2018

[4] G T Halmos Roll Forming Handbook CRC New York NYUSA 2006

[5] B Shirani H M Naeini and R A Tafti ldquoExperimental andnumerical study of required torque in the cold roll forming ofsymmetrical channel sectionsrdquo Journal of ManufacturingProcesses vol 27 pp 63ndash75 2017

[6] F Heislitz H Livatyali M A Ahmetoglu et al ldquoSimulation ofroll forming process with the 3-D FEM code PAM-STAMPrdquoJournal of Materials Processing Technology vol 59 no 1-2pp 59ndash67 1996

[7] N Duggal M A Ahmetoglu G L Kinzel et al ldquoComputeraided simulation of cold roll formingmdasha computer programfor simple section profilesrdquo Journal of Materials ProcessingTechnology vol 59 no 1-2 pp 41ndash48 1996

[8] C K McClure and H Li ldquoRoll forming simulation using finiteelement analysisrdquo Manufacturing Review vol 8 no 2pp 114ndash122 1995

[9] D Bhattacharya and P D Smith ldquoe Development ofLongitudinal Strain in Cold Roll Forming and its Influence onProduct Straightnessrdquo in Proceedings of the First InternationalConference on Technology of Plasticity pp 422ndash427 TokyoJapan June 1984

[10] M S Tehrani H M Naeini P Hartley et al ldquoLocalized edgebuckling in cold roll-forming of circular tube sectionrdquo Journalof Materials Processing Technology vol 177 no 1ndash3pp 617ndash620 2006

[11] M S Tehrani P Hartley and H Khademizadeh ldquoLocalisededge buckling in cold roll-forming of symmetric channelsectionrdquo in-Walled Structures vol 44 no 2 pp 184ndash1962006

[12] N Kim S B Kang and S Lee ldquoPrediction and design of edgeshape of initial strip for thick tube roll forming using finiteelement methodrdquo Journal of Materials Processing Technologyvol 142 no 2 pp 479ndash486 2003

64 66 68 70 72 74 76 78 80 82

30 times 10ndash4

35 times 10ndash4

40 times 10ndash4

45 times 10ndash4

50 times 10ndash4

55 times 10ndash4St

anda

rd d

evia

tion

of lo

ngitu

dina

l str

ain

Longitudinal distance

FEAEXP

(a)

18 20 22 24 26 28 30 32 34 3630E ndash 04

35E ndash 04

40E ndash 04

45E ndash 04

50E ndash 04

55E ndash 04

60E ndash 04

65E ndash 04

Stan

dard

dev

iatio

n of

long

itudi

nal s

trai

n

Sheet thickness (mm)

FEAEXP

(b)

Figure 17 (a) Effect of flange height on longitudinal strain (b) Effect of sheet thickness on longitudinal strain

Advances in Materials Science and Engineering 9

[13] T Wang and H Fei ldquoPrediction of wrinkling in flexible rollforming based on finite element simulationrdquo Forging ampStamping Technology vol 38 no 6 pp 67ndash72 2013

[14] Data M Software GmbH ldquoCOPRAreg roll formingrdquo 2001httpwwwroll-designcom

[15] X Luo Z Guo S Li et al ldquoFinite element analysis of the effectof material properties on wavy flange in high strength steel rollformingrdquo Journal of Shanghai Jiaotong University vol 42no 5 pp 744ndash747 2008

[16] D Hibbitt B Karlsson and P Sorensen Getting started withABAQUSExplicitmdashinteractive version Hibbitt Karlsson ampSorensen Inc Providence RI USA 2002

[17] Q V Bui and J P Ponthot ldquoNumerical simulation of coldroll-forming processesrdquo Journal of Materials ProcessingTechnology vol 202 no 1ndash3 pp 275ndash282 2008

10 Advances in Materials Science and Engineering

54 Additional Experimental Results and Analysis In orderto further explore the effect of sheet metal thickness andflange height on the flange edge buckling of ldquobrdquo tube twosets of comparative simulation experiments are designed inthis paper Based on the simulation results of the or-thogonal experiment the first experimental design iscarried out under the condition of flange height h 60 andforming speed v 100mms e variables are sheet metalthickness which is set as 2 25 3 and 35mm respectivelye second experimental design is carried out under thecondition of sheet thickness t 25mm and forming speedv 100mms and the variables are flange height which are65 70 75 and 80mm respectively e experimental re-sults are shown in Figure 15 Figure 17(a) shows that thelongitudinal strain at the flange increases with the increaseof flange height Figure 17(b) shows that as the thickness ofthe sheet increases the longitudinal strain at the flange isalso getting smaller and smaller It can be seen that the edge

buckling at the flange increases with the increase of flangeheight and decreases with the increase of plate thickness

6 Conclusion

In this paper COPRA is used for pass design ABAQUS isused for finite element modeling and analysis and or-thogonal experiments and comparative experiments aredesigned to study the roll-forming law of the b-shaped tubewhich provides theoretical basis for the production of ldquo日rdquoshape tube e conclusions are as follows

(1) Compared with the traditional roll-forming methodthe application of new roll-forming technology inthis paper not only improves the material utilizationrate and production efficiency but also ensures themechanical properties of the products such as tensilestrength bending strength and impact toughness

Table 3 Orthogonal experiment results and result analysis

Simulation number Flange height h (mm) Sheet thickness t (mm) Forming speed v (mmmiddotsminus 1) Δε1 60 (h1) 20 (t1) 50 (v1) 162times10minus 4

2 60 (h1) 25 (t2) 100 (v2) 280times10minus 4

3 60 (h1) 30 (t3) 150 (v3) 501times 10minus 4

4 70 (h2) 20 (t1) 100 (v2) 255times10minus 4

5 70 (h2) 25 (t2) 150 (v3) 367times10minus 4

6 70 (h2) 30 (t3) 50 (v2) 692times10minus 4

7 80 (h3) 20 (t1) 150 (v3) 235times10minus 4

8 80 (h3) 25 (t2) 50 (v1) 425times10minus 4

9 80 (h3) 30 (t3) 100 (v2) 513times10minus 4

0 100 200 300 400 500 600 700 800 900 Longitudinal distance

FEA1FEA2

FEA3FEA6

ndash50 times 10ndash4

00

50 times 10ndash4

10 times 10ndash3

15 times 10ndash3

20 times 10ndash3

Long

itudi

nal s

trai

n

Figure 16 Longitudinal strain curves of the sheet metal along longitudinal position in Exp 1 2 3 and 6

Table 4 Range analysis of orthogonal experimental results

Δε Flange height (h) Sheet thickness (t) Forming speed (v)k1 314times10minus 4 217times10minus 4 427times10minus 4

k2 437times10minus 4 357times10minus 4 350times10minus 4

k3 400times10minus 4 560times10minus 4 367times10minus 4

Range R 123times10minus 4 343times10minus 4 077times10minus 4

8 Advances in Materials Science and Engineering

(2) For high-strength beam steel B700L sheet flangeheight sheet thickness and forming speed all effectthe generation of edge buckling in the roll-formingprocess When the standard deviation Δε of longi-tudinal strain is taken as the evaluation criterion theeffect degree of each factor on the formation of edgebuckling is sheet thicknessgt flange heightgt formingspeed

(3) e comparative experimental results show that theedge buckling of the vertical edge of the b-shapedtube decreases with the increase of the thickness ofthe sheet metal and increases with the increase of theflange height e effect of forming speed on edgebuckling of the sheet metal is small

Data Availability

is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricteduse distribution and reproduction in any medium pro-vided the original work is properly cited

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] B Abeyrathna B Rolfe P Hodgson and M Weiss ldquoLocaldeformation in roll formingrdquo e International Journal ofAdvanced Manufacturing Technology vol 88 no 9ndash12pp 2405ndash2415 2017

[2] X L Liu J G Cao X T Chai et al ldquoExperimental andnumerical prediction of the local thickness reduction defect ofcomplex cross-sectional steel in cold roll formingrdquo e In-ternational Journal of Advanced Manufacturing Technologyvol 95 no 5ndash8 pp 1837ndash1848 2017

[3] P Mahajan A Abrass and P Groche ldquoFE simulation of rollforming of a complex profile with the aid of steady statepropertiesrdquo Steel Research International vol 89 no 5Article ID 1700350 2018

[4] G T Halmos Roll Forming Handbook CRC New York NYUSA 2006

[5] B Shirani H M Naeini and R A Tafti ldquoExperimental andnumerical study of required torque in the cold roll forming ofsymmetrical channel sectionsrdquo Journal of ManufacturingProcesses vol 27 pp 63ndash75 2017

[6] F Heislitz H Livatyali M A Ahmetoglu et al ldquoSimulation ofroll forming process with the 3-D FEM code PAM-STAMPrdquoJournal of Materials Processing Technology vol 59 no 1-2pp 59ndash67 1996

[7] N Duggal M A Ahmetoglu G L Kinzel et al ldquoComputeraided simulation of cold roll formingmdasha computer programfor simple section profilesrdquo Journal of Materials ProcessingTechnology vol 59 no 1-2 pp 41ndash48 1996

[8] C K McClure and H Li ldquoRoll forming simulation using finiteelement analysisrdquo Manufacturing Review vol 8 no 2pp 114ndash122 1995

[9] D Bhattacharya and P D Smith ldquoe Development ofLongitudinal Strain in Cold Roll Forming and its Influence onProduct Straightnessrdquo in Proceedings of the First InternationalConference on Technology of Plasticity pp 422ndash427 TokyoJapan June 1984

[10] M S Tehrani H M Naeini P Hartley et al ldquoLocalized edgebuckling in cold roll-forming of circular tube sectionrdquo Journalof Materials Processing Technology vol 177 no 1ndash3pp 617ndash620 2006

[11] M S Tehrani P Hartley and H Khademizadeh ldquoLocalisededge buckling in cold roll-forming of symmetric channelsectionrdquo in-Walled Structures vol 44 no 2 pp 184ndash1962006

[12] N Kim S B Kang and S Lee ldquoPrediction and design of edgeshape of initial strip for thick tube roll forming using finiteelement methodrdquo Journal of Materials Processing Technologyvol 142 no 2 pp 479ndash486 2003

64 66 68 70 72 74 76 78 80 82

30 times 10ndash4

35 times 10ndash4

40 times 10ndash4

45 times 10ndash4

50 times 10ndash4

55 times 10ndash4St

anda

rd d

evia

tion

of lo

ngitu

dina

l str

ain

Longitudinal distance

FEAEXP

(a)

18 20 22 24 26 28 30 32 34 3630E ndash 04

35E ndash 04

40E ndash 04

45E ndash 04

50E ndash 04

55E ndash 04

60E ndash 04

65E ndash 04

Stan

dard

dev

iatio

n of

long

itudi

nal s

trai

n

Sheet thickness (mm)

FEAEXP

(b)

Figure 17 (a) Effect of flange height on longitudinal strain (b) Effect of sheet thickness on longitudinal strain

Advances in Materials Science and Engineering 9

[13] T Wang and H Fei ldquoPrediction of wrinkling in flexible rollforming based on finite element simulationrdquo Forging ampStamping Technology vol 38 no 6 pp 67ndash72 2013

[14] Data M Software GmbH ldquoCOPRAreg roll formingrdquo 2001httpwwwroll-designcom

[15] X Luo Z Guo S Li et al ldquoFinite element analysis of the effectof material properties on wavy flange in high strength steel rollformingrdquo Journal of Shanghai Jiaotong University vol 42no 5 pp 744ndash747 2008

[16] D Hibbitt B Karlsson and P Sorensen Getting started withABAQUSExplicitmdashinteractive version Hibbitt Karlsson ampSorensen Inc Providence RI USA 2002

[17] Q V Bui and J P Ponthot ldquoNumerical simulation of coldroll-forming processesrdquo Journal of Materials ProcessingTechnology vol 202 no 1ndash3 pp 275ndash282 2008

10 Advances in Materials Science and Engineering

(2) For high-strength beam steel B700L sheet flangeheight sheet thickness and forming speed all effectthe generation of edge buckling in the roll-formingprocess When the standard deviation Δε of longi-tudinal strain is taken as the evaluation criterion theeffect degree of each factor on the formation of edgebuckling is sheet thicknessgt flange heightgt formingspeed

(3) e comparative experimental results show that theedge buckling of the vertical edge of the b-shapedtube decreases with the increase of the thickness ofthe sheet metal and increases with the increase of theflange height e effect of forming speed on edgebuckling of the sheet metal is small

Data Availability

is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricteduse distribution and reproduction in any medium pro-vided the original work is properly cited

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] B Abeyrathna B Rolfe P Hodgson and M Weiss ldquoLocaldeformation in roll formingrdquo e International Journal ofAdvanced Manufacturing Technology vol 88 no 9ndash12pp 2405ndash2415 2017

[2] X L Liu J G Cao X T Chai et al ldquoExperimental andnumerical prediction of the local thickness reduction defect ofcomplex cross-sectional steel in cold roll formingrdquo e In-ternational Journal of Advanced Manufacturing Technologyvol 95 no 5ndash8 pp 1837ndash1848 2017

[3] P Mahajan A Abrass and P Groche ldquoFE simulation of rollforming of a complex profile with the aid of steady statepropertiesrdquo Steel Research International vol 89 no 5Article ID 1700350 2018

[4] G T Halmos Roll Forming Handbook CRC New York NYUSA 2006

[5] B Shirani H M Naeini and R A Tafti ldquoExperimental andnumerical study of required torque in the cold roll forming ofsymmetrical channel sectionsrdquo Journal of ManufacturingProcesses vol 27 pp 63ndash75 2017

[6] F Heislitz H Livatyali M A Ahmetoglu et al ldquoSimulation ofroll forming process with the 3-D FEM code PAM-STAMPrdquoJournal of Materials Processing Technology vol 59 no 1-2pp 59ndash67 1996

[7] N Duggal M A Ahmetoglu G L Kinzel et al ldquoComputeraided simulation of cold roll formingmdasha computer programfor simple section profilesrdquo Journal of Materials ProcessingTechnology vol 59 no 1-2 pp 41ndash48 1996

[8] C K McClure and H Li ldquoRoll forming simulation using finiteelement analysisrdquo Manufacturing Review vol 8 no 2pp 114ndash122 1995

[9] D Bhattacharya and P D Smith ldquoe Development ofLongitudinal Strain in Cold Roll Forming and its Influence onProduct Straightnessrdquo in Proceedings of the First InternationalConference on Technology of Plasticity pp 422ndash427 TokyoJapan June 1984

[10] M S Tehrani H M Naeini P Hartley et al ldquoLocalized edgebuckling in cold roll-forming of circular tube sectionrdquo Journalof Materials Processing Technology vol 177 no 1ndash3pp 617ndash620 2006

[11] M S Tehrani P Hartley and H Khademizadeh ldquoLocalisededge buckling in cold roll-forming of symmetric channelsectionrdquo in-Walled Structures vol 44 no 2 pp 184ndash1962006

[12] N Kim S B Kang and S Lee ldquoPrediction and design of edgeshape of initial strip for thick tube roll forming using finiteelement methodrdquo Journal of Materials Processing Technologyvol 142 no 2 pp 479ndash486 2003

64 66 68 70 72 74 76 78 80 82

30 times 10ndash4

35 times 10ndash4

40 times 10ndash4

45 times 10ndash4

50 times 10ndash4

55 times 10ndash4St

anda

rd d

evia

tion

of lo

ngitu

dina

l str

ain

Longitudinal distance

FEAEXP

(a)

18 20 22 24 26 28 30 32 34 3630E ndash 04

35E ndash 04

40E ndash 04

45E ndash 04

50E ndash 04

55E ndash 04

60E ndash 04

65E ndash 04

Stan

dard

dev

iatio

n of

long

itudi

nal s

trai

n

Sheet thickness (mm)

FEAEXP

(b)

Figure 17 (a) Effect of flange height on longitudinal strain (b) Effect of sheet thickness on longitudinal strain

Advances in Materials Science and Engineering 9

[13] T Wang and H Fei ldquoPrediction of wrinkling in flexible rollforming based on finite element simulationrdquo Forging ampStamping Technology vol 38 no 6 pp 67ndash72 2013

[14] Data M Software GmbH ldquoCOPRAreg roll formingrdquo 2001httpwwwroll-designcom

[15] X Luo Z Guo S Li et al ldquoFinite element analysis of the effectof material properties on wavy flange in high strength steel rollformingrdquo Journal of Shanghai Jiaotong University vol 42no 5 pp 744ndash747 2008

[16] D Hibbitt B Karlsson and P Sorensen Getting started withABAQUSExplicitmdashinteractive version Hibbitt Karlsson ampSorensen Inc Providence RI USA 2002

[17] Q V Bui and J P Ponthot ldquoNumerical simulation of coldroll-forming processesrdquo Journal of Materials ProcessingTechnology vol 202 no 1ndash3 pp 275ndash282 2008

10 Advances in Materials Science and Engineering

[13] T Wang and H Fei ldquoPrediction of wrinkling in flexible rollforming based on finite element simulationrdquo Forging ampStamping Technology vol 38 no 6 pp 67ndash72 2013

[14] Data M Software GmbH ldquoCOPRAreg roll formingrdquo 2001httpwwwroll-designcom

[15] X Luo Z Guo S Li et al ldquoFinite element analysis of the effectof material properties on wavy flange in high strength steel rollformingrdquo Journal of Shanghai Jiaotong University vol 42no 5 pp 744ndash747 2008

[16] D Hibbitt B Karlsson and P Sorensen Getting started withABAQUSExplicitmdashinteractive version Hibbitt Karlsson ampSorensen Inc Providence RI USA 2002

[17] Q V Bui and J P Ponthot ldquoNumerical simulation of coldroll-forming processesrdquo Journal of Materials ProcessingTechnology vol 202 no 1ndash3 pp 275ndash282 2008

10 Advances in Materials Science and Engineering

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