springbackstudyonprofileflexible3dstretch-bending...

Research ArticleSpringback Study on Profile Flexible 3D Stretch-BendingProcess Using the Neural Network

Yi Li 12 Ce Liang 12 Xiangfeng Lin 13 Jicai Liang 13 Zhongyi Cai13 and Fei Teng4

1Key Laboratory of Automobile Materials (Jilin University) Ministry of Education Changchun 130025 Jilin China2College of Materials Science and Engineering Jilin University Changchun 130025 Jilin China3Roll Forging Institute Jilin University Changchun 130025 Jilin China4College of Mechanical and Automotive Engineering Changchun University Changchun 130025 Jilin China

Correspondence should be addressed to Ce Liang liangcejlueducn

Received 15 June 2019 Accepted 23 September 2019 Published 15 October 2019

Academic Editor Jose Antonio Fonseca de Oliveira Correia

Copyright copy 2019 Yi Li et al +is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

+e springback is one of the main defects in the flexible 3D stretch-bending process In this paper according to the orthogonaldesign of experiments the numerical simulation analysis of the springback for the 3D stretch-bending aluminum profile is carriedout by the ABAQUS finite element software And to investigate the effect of material properties on the springback the rangeanalysis of the orthogonal experiment is performed +e results show that these material properties of the aluminum profile(elastic modulus E yield strength σy and tangentmodulus E1) might have the biggest influence on the springback of the aluminumprofile and the optimized forming parameters are founded as follows the horizontal bending degree is 14deg the vertical bendingdegree is 14deg the number of multipoint stretch-bending dies is 10 the friction coefficient is 015 and aluminum alloy grade is 6063Moreover the model of the BP neural network for the prediction of the springback is established and trained based on theorthogonal experiment and the results with the BP neural network model are in good agreement with experimental results So it isobvious that the BP neural network could predict effectively the springback of 3D multipoint stretch-bending parts

1 Introduction

In recent years lightweight requirements have grown moredemanding for reduction of energy consumption and en-vironmental pollution caused by exhaust emissions [1ndash3]especially the design of the lightweight part plays a moreand more important role in economic and ecological aspects[4] Aluminum alloy is widely used in aerospace rail vehiclemanufacturing and automobile manufacturing as a light-weight material because of its low density high strength andease of recycling [5ndash7]

Aluminum profile can meet many diversified re-quirements but the formation of the aluminum profilebrings many new problems in the part design andmanufacturing process Because the elastic modulus of thealuminum alloy is only one-third that of the steel sheet thespringback of the aluminum alloy is much bigger than thesame data of the steel sheet and the springback becomes one

of the main defects for the aluminum profile stretch-bendingpart [8] If not to make reasonable estimation for thespringback of the aluminum profile stretch-bending part itwill have serious influence on the forming quality ofcomponents and furthermore service life

+ere are many influence factors on the springbacksuch as profile characteristics processing parameters anddie structure During the flexible 3D multipoint stretch-bending process of the aluminum profile the springbackanalysis is very complicated with geometric nonlinearitymaterial nonlinearity and contact nonlinearity so it is hardto find out an accurate mathematical model [9] +e ar-tificial neural network is widely used in the propertyprediction of the metal material for high ability of non-linear mapping and prediction of the output targetaccording to the finite training sample [10ndash12] Kazan et alinvestigated the springback of the metal sheet in thebending process and developed the prediction model for

HindawiAdvances in Materials Science and EngineeringVolume 2019 Article ID 6465196 9 pageshttpsdoiorg10115520196465196

the springback by using the artificial neural network [13]Jamli et al built the springback prediction model for metalsheet stretch bending and L-shaped bending respectivelybased on finite element simulation and artificial neuralnetwork [14 15] Nasrollahi and Arezoo investigated thespringback prediction for a bending area of the metal sheetwith hole by the experiment finite element simulation andartificial neural network [16] Babu et al developed anartificial neural network system to predict the behavior ofdeep drawing for welding blank made by steel and alu-minum alloy [17] However the neural network model isnot used for the springback prediction of three-di-mensional stretched profiles

Based on the orthogonal experiments the numericalsimulation of the springback in 3D multipoint stretchbending of the aluminum profile is investigated by theABAQUS finite element software the training samples of theBP neural network are achieved and the mapping abilitybetween stretch-bending parameters and output value of thespringback is built by using the powerful function mappingability of the BP neural network +e results show that it cansave a lot of simulation time and provide important refer-ence data for the forming precision and springback com-pensation of the aluminum profile-forming part

2 Concept and Finite Element Model ofMultipoint Stretch Bending (MPSB)

21 Principle of the Multipoint Stretch-Bending Process+e multipoint stretch bending (MPSB) is improved on thebasis of the traditional stretch bending +e stretch-bendingdie in the traditional stretch bending is discretized It cansolve the 3D stretch bending of the profiles through themultipoint technology combined with the traditional stretchbending +erefore the MPSB process is more diversifiedthan conventional bending process because of the additionalvertical bending stage of the profile

As shown in Figure 1 when the profile is three-di-mensionally stretched and formed the bending machine canmove the die units back forth up and down So the rotationangle of the profile can be adjusted on two planes therebydecomposing the 3D stretch bending into the horizontalbending and the vertical bending

22 Material Model Because the aluminum alloys havelightweight and good mechanical properties they are usedwidely for structural parts of the railway vehicle In thisstudy five aluminum alloy grades are used which are asfollows 6063 6005A 5052 5083 and 6082 the profilelength is 3200mm and the profile weight is about 33 kg It isassumed that the aluminummaterial is isotropic the elastic-plastic constitutive behavior is isotropic hardening andrelevant mechanical properties are as shown in Table 1

23 Setup of Finite Element Model In the finite elementsimulation of 3D stretch bending the reasonable simplificationof the finite element model can reduce the calculation timeavoid other problems caused by the complexity of the model

and affect the accuracy of the results +erefore it is necessaryto rationally simplify the finite element model As shown inFigure 2 the die is simplified on the stretch-bending machineusing only the die units in contact with the profile and the limitscrew that limits the displacement of the die units in the verticaldirection of the x-z plane is simplified as a planar flap which is50mm in length with the die units Meanwhile the clamp issimplified to the same shape as the profile and is bound to theprofile the length of which is 100mm So only different diesections and clamps need to be replaced when forming dif-ferent geometric profiles

When selecting the appropriate element type for thefinite element model not only the accuracy of the simulationresult but also the operation time should be considered It isnecessary to obtain the most accurate simulation result inthe shortest possible calculation time +e finite elementmodel consists of the aluminum profile clamp die unitsand limit screw +e unit types and unit and node numberinformation of each component are shown in Table 2

3 Orthogonal Experiment for the Springback ofAluminum Profile

31 Selecting the Level of Various Factors +e orthogonalexperiment is a kind of design method which has a goodeffect to study and deal with multifactor problems and it isbased on the orthogonality of the data to design the schemeIt has the advantage of being able to obtain reliable andrepresentative test results in as few test times as possible+rough the analysis and integration of the test results thebest test conditions can be selected as the optimal levelcombination of each factor

In the MPSB process many factors influence the spring-back of the aluminum profile such as yield strength elasticmodulus tangent modulus bending angle in horizontal andvertical directions die structure die clearance prestretchingvalue and friction force According to the stretch-bendingprocess and orthogonal experiment seven important impactfactors are as follows elastic modulus (E) yield strength (σy)tangent modulus (E1) horizontal bending angle (α) verticalbending angle (β) die number (N) and friction coefficient (μ)Five aluminum alloy grades used in the orthogonal experimentare 6063 6005A 5052 5083 and 6082 +e values of eachfactor level are as shown in Table 3

32 Orthogonal Design +e table of the orthogonal exper-iment is usually expressed as La(S1 times S2 times S3 times middot middot middot times Sb)where L is the orthogonal table a is the test number b is themaximum value of impact factors and S1－Sb are the valueof the impact factor level from column 1 to column 9 +eorthogonal experiment can effectively reduce the number ofexperiments In this study the design of the L25(55) or-thogonal table is selected and seven impact factors (E σy E1α β N and μ) all select five levels

+e design of the orthogonal experiment and thespringback of the aluminum profile are shown in Table 4 Andthe springback of the aluminum profile is simulated using theABAQUS software based on the parameters in the orthogonal

2 Advances in Materials Science and Engineering

ProfileMultipoint dies

T1T1

MhMh

z

y x

(a)


T2

T2

Mv

Mv

z

y x

(b)

Figure 1 Schematic diagram of the flexible 3D multipoint stretch-bending equipment (a) Bending forming in the horizontal direction(b) Bending forming in the vertical direction

Table 1 Aluminum alloy grade and mechanical properties

Aluminum alloygrade

Treatmentstate

Elastic modulus E(MPa)

Tangent modulus E1(MPa)

Tensile strengthσb (MPa)

Yield strengthσs (MPa)

Poissonrsquosratio υ

Density ρ(gcm3)

6063 T5 68300 341667 186 145 033 2696005A T5 69000 210 262 241 033 275052 H32 69300 291667 230 195 033 2685083 H112 70300 6875 303 193 033 2666082 T6 71000 66667 290 250 033 27

Multipoint dies

Limit screw

Aluminum profile

Clamp

Figure 2 Finite element model for the flexible 3D stretch-bending process

Advances in Materials Science and Engineering 3

table In the MPSB process the aluminum profile is formedalong the space curve which has more complex deformationthan the traditional stretch-bending process So the springbackof the 3D stretch-bending process can be divided into twoparts as shown in Figure 3 one part is horizontal springbackalong the horizontal direction in the x-y plane and the otherpart is vertical springback along the vertical direction in the x-zplane δy is the value of horizontal springback in the x-y planeδz is the value of vertical springback in the x-z plane and δ isthe value of total springback for the aluminum profile

33 Range Analysis in Orthogonal Experimental Data+e range analysis table of the orthogonal experiment isshown in Figure 4

According to Figure 4 the main factors affecting thehorizontal springback along the x-y plane in order of im-portance are elastic modulus (E) yield strength (σy) tangentmodulus (E1) friction coefficient (μ) die number (N)horizontal bending angle (α) and vertical bending angle (β)And the main factors affecting the vertical springback alongthe x-z plane in order of importance are elastic modulus (E)yield strength (σy) tangent modulus (E1) horizontalbending angle (α) die number (N) vertical bending angle(β) and friction coefficient (μ) +e main factors affectingthe total springback in order of importance are elasticmodulus (E) yield strength (σy) tangent modulus (E1)horizontal bending angle (α) die number (N) friction co-efficient (μ) and vertical bending angle (β)

34 Optimized Parameters and Verification +e optimizedparameter combination means that the combination oflevels can make test results reach the optimum state in therange of all factors +e optimized parameter combination isfounded by the experiment index +e larger the experimentindex is the better the level corresponding to the maximumvalue of the index selected is In contrast the smaller the testindex is the better the level corresponding to the minimumvalue of the index selected is

In this study the experiment index is the value of springbackclearance According to data in Table 5 the best combination forhorizontal springback along the x-y plane is A4B1C5D1E3 andthe best combination for vertical springback along the x-z planeand the best combination for total springback are A1B1C1D4E3+ese two combinations have little deviation for horizontalspringback along the x-y plane but the deviation is big forvertical springback along the x-z plane and total springback Sothe optimized parameter combination selected in the orthog-onal experiment is A1B1C1D4E3 and the corresponding pa-rameters are as follows the aluminum alloy material is 6063horizontal bending angle is 14deg vertical bending angle is 14degmultipoint die number is 10 and friction coefficient is 015

+e optimized parameter combination A1B1C1D4E3 isvalidated by using the ABAQUS software simulation andthe simulated results are shown in Table 5

Compared to data in Tables 4 and 5 it is found that thebest values of vertical springback and total springback areachieved by using the optimized parameter combinationA1B1C1D4E3 and the deviation is little for horizontalspringback +e stress-strain chart of 3D stretch bendingunder the combination A1B1C1D4E3 is shown in Figure 5

As can be seen from Figure 5 the stress and equivalentstrain are evenly distributed and the forming part has nodefects It shows that the forming effect is very good

4 Prediction of the Springback Based on BPNeural Network

41 Setup of BP Neural Network Model +e BP neural net-work is a kind ofmultilayer forward feeding neural network Itsmain feature is that the signals feed forward and the errorspropagate backward +e output error is used to predict theerror of the direct leading layer for the output layer +en theerror of the direct leading layer is used to predict the error ofthe further layer and the errors of others layers are gained fromlayer-by-layer backpropagation [18 19]

+e model of the BP neural network is composed of theinput layer hidden layer and output layer +e input layerand output layer are usually determined based on thepractice problem the neuron number in the input layer isequal to the dimension of input sample data and the neuronnumber in the output layer is equal to the dimension of theresult sample +e neuron number in the hidden layer isusually calculated by the following empirical equation [20]

lltm + n

radic+ p (1)

where m is the neuron number in the input layer n is theneuron number in the output layer p is the constant and1ltplt 10 and l is the neuron number in the hidden layer

Table 2 Unit types and number of units and nodes for finite element components

Finite element components Unit types Number of units Number of nodesAluminum profile C3D8R 9858 13912Die units R3D4 216 250Clamp R3D4 500 550Limit screw R3D4 80 99

Table 3 Levels and impact factors of the orthogonal experiment

LevelImpact factor

A B C D EAlloy grade α (deg) β (deg) N μ

1 6063 14 14 4 0052 6005A 18 18 6 013 5052 22 22 8 0154 5083 26 26 10 025 6082 30 30 12 025


In this study the neuron number in the input layer is 7and the neuron number in the output layer is 3 +e neuronnumber in the hidden layer is 10 based on the training timeand accuracy of the BP neural network +e 7-10-3 three-layer frame of the BP neural network is set up as shown inFigure 6

+e mathematical model of neural network functionwhich has 10 hidden layers is as follows

yk 111394410

j1wjk times sig 1113944

7

i1wij times xi + bj

⎛⎝ ⎞⎠ + bk (k 1 2 3)

(2)

where wij is the weight of the input layer to the hidden layerwjk is the weight of the hidden layer to the output layer bj isthe offset weight of the hidden layer bk is the offset weight ofthe output layer sig is the sigmoid activation function xi isthe input value of the neural network and yk is the outputvalue of the neural network

42 Training and Testing of BP Neural Network +e dataare normalized before training the BP neural network inorder to avoid large difference order of magnitude of theinput-output data result in big error of prediction and the

Table 4 Design and results of the orthogonal experiment

Number A B C D E Horizontal springback valueδy (mm)

Vertical springback valueδz (mm)

Total springback valueδ (mm)

1 6063 14 14 4 005 2401 4673 55662 6063 18 18 6 01 3185 4711 59333 6063 22 22 8 015 2777 4953 58804 6063 26 26 10 02 3529 5289 64385 6063 30 30 12 025 3493 5918 69056 6005A 14 18 8 02 4133 6793 88407 6005A 18 22 10 025 5310 7807 99558 6005A 22 26 12 005 5112 7345 94339 6005A 26 30 4 01 3166 9064 996810 6005A 30 14 6 015 5144 8727 104111 5052 14 22 12 01 3228 5704 703312 5052 18 26 4 015 1896 6395 711813 5052 22 30 6 02 4471 7328 862614 5052 26 14 8 025 3958 5657 721115 5052 30 18 10 005 2773 5824 681816 5083 14 26 6 025 4097 6420 786417 5083 18 30 8 005 3259 7597 832418 5083 22 14 10 01 2924 5318 671819 5083 26 18 12 015 2539 6731 762820 5083 30 22 4 02 1471 6735 779121 6082 14 30 10 015 4401 6086 750022 6082 18 14 12 02 7764 7705 109423 6082 22 18 4 025 8251 9178 123024 6082 26 22 6 005 7289 9630 120925 6082 30 26 8 01 9359 9835 1370

δy

δz

δ

Figure 3 +e front and back spatial positions of the end face contours


maximum-minimum method is applied on the normali-zation of data

xkprime 2 times

xk minus xmin

xmax minus xminminus 1 (3)

where xkprime is the value after the normalization of the data

sequence xmax is the maximum value of the data sequenceand xmin is the minimum value of the data sequence

+e training parameters are as follows the maximumtraining time is 10000 the expected training error is 1eminus 6the learning rate is 002 and the momentum factor is065 A total of 41 pairs of data in which 15 pairs of

simulated data are from ABAQUS software are used fortraining and testing the BP neural network Among thesedata under the optimized parameter combinationA4B1C5D1E3 orthogonal experiment sample nos 7 1319 and 25 are used for sample testing and the others areused for training the BP neural network +e comparisonof finite element simulation and prediction results of theBP neural network after MATLAB training is shown inFigure 7

As seen from Figure 7 it is shown that there is littledifference between the prediction results of the BP neuralnetwork and the simulation results the training accuracy ishigh so the BP neural network method can replace the finiteelement simulation to predict the springback of the 3Dstretch-bending process reduce the simulation runtime andincrease the simulation efficiency

43 Test Verification To validate the finite element simu-lation and BP neural network on the springback of the 3D

A1A2A3A4A5 B1B2B3B4B5 C1C2C3C4C5 D1D2D3D4D5 E1E2E3E4E5

Factors

2

3

4

5

6

7

8In

dex

(a)


Factors

4

5

6

7

8

9

10

Inde

x

(b)


Factors

5

6

7

8

9

10

11

12

Inde

x

(c)

Figure 4 Relationship between experimental factors and springback index (a) horizontal springback (b) vertical springback (c) totalspringback

Table 5 Springback value of the optimized parametercombination

Optimized parameter combination δy (mm) δz (mm) δ (mm)A1B1C1D4E3 2354 4098 5204


+1904e + 00+1542e + 01+2895e + 01+4247e + 01+5599e + 01+6951e + 01+8303e + 01+9655e + 01+1101e + 02+1236e + 02+1371e + 02+1526e + 02+1642e + 02

S Mises(Avg 75)

(a)

+0000e + 00+7156e ndash 03+1431e ndash 02+2147e ndash 02+2862e ndash 02+3578e ndash 02+4294e ndash 02+5009e ndash 02+5725e ndash 02+6440e ndash 02+7156e ndash 02+7872e ndash 02+8587e ndash 02

PEEQ(Avg 75)

(b)

Figure 5 Stress-strain chart of 3D stretch bending (combination A1B1C1D4E3)

Initial valueNeural network prediction

2

3

4

5

6

7

8

9

10

δ y (m

m)

2 3 4 51Training sample number

(a)


δ z (m

m)


2

3

4

5

6

7

8

9

10

11

(b)

Figure 7 Continued

Hidden layer Output layerInput layer

E σb σs

α

β

N

μ

δy

δz

δ

wij wjk

xi

yk

Oj

Figure 6 Frame chart of the BP neural network


stretch-bending process the comparison of experimentalresults simulation results and prediction results is in-vestigated +e experimental results are founded based onthe optimized parameter combination A1B1C1D4E3 whoseforming parameters are as follows the aluminum alloymaterial is 6063 horizontal bending angle is 14deg verticalbending angle is 14deg multipoint die unit number is 10 andfriction coefficient is 015 +e detection setup and theforming part through the MPSB process are shown inFigure 8

+e detection setup is used to detect the value of thespringback after stretch bending of the aluminum profile asshown in Figure 8 and the detected values are shown inTable 6

As seen from Table 6 the results with the BP neuralnetworkmodel and simulation results are in good agreement

with experimental results +erefore it is obvious that a newprediction method of the springback in the flexible 3Dstretch-bending process is provided by using the BP neuralnetwork

5 Conclusion

(1) According to the range analysis of the orthogonalexperiment the main factors affecting the springbackin the 3D stretch-bending process in order of im-portance are elastic modulus (E) yield strength (σy)and tangent modulus (E1) and it is shown that thematerial properties of the aluminum profile should beconsidered firstly then the forming parameters of the3D stretch-bending process are investigated

(2) Based on the orthogonal experiment and the influ-ence on the springback the optimized parametercombination is as follows the aluminum alloy ma-terial is 6063 horizontal bending angle is 14deg verticalbending angle is 14deg multipoint die number is 10and friction coefficient is 015



4

5

6

7

8

9

10

11

12

13

14δ

(mm

)

(c)

δxδyδ

0

1

2

3

4

5

6

7

8

9

10

Erro

r (

)


(d)


Figure 8 +e detection setup and the forming part through theMPSB process

Table 6 Comparison of experimental results simulation resultsand BP neural network-predicted results

Horizontalspringback

value δy (mm)

Verticalspringback

value δz (mm)

Totalspringbackvalue δ (mm)

Experimentalresults 279 455 573

Simulationresults 253 410 520

BP neuralnetwork-predictedresults

270 450 567


(3) Compared to orthogonal experimental data theresults of BP neural network simulation show that itis an effective way to predict the springback by usingthe BP neural network and provide a newmethod forpractice production

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+is work was supported by the National Natural ScienceFoundation of China (51675225)

References

[1] D-S Shim G-Y Baek G-Y Shin H-S Yoon K-Y Lee andK-H Kim ldquoInvestigation of tension force in stretch formingof doubly curved aluminum alloy (Al5083) sheetrdquo In-ternational Journal of Precision Engineering andManufacturing vol 17 no 4 pp 433ndash444 2016

[2] T Liu Y Wang J Wu et al ldquoSpringback analysis of Z ampT-section 2196-T8511 and 2099-T83 Al-Li alloys extrusions indisplacement controlled cold stretch bendingrdquo Journal ofMaterials Processing Technology vol 225 pp 295ndash309 2015

[3] J Liang S Gao F Teng P-Z Yu and X-J Song ldquoFlexible 3Dstretch-bending technology for aluminum profilerdquo e In-ternational Journal of Advanced Manufacturing Technologyvol 71 no 9ndash12 pp 1939ndash1947 2014

[4] Y Zhou P Li M Li and L Wang ldquoApplication and cor-rection of L-shaped thin-wall aluminum in flexible-bendingprocessingrdquo e International Journal of AdvancedManufacturing Technology vol 92 no 1ndash4 pp 981ndash988 2017

[5] S Chatti M Hermes A E Tekkaya andM Kleiner ldquo+e newTSS bending process 3D bending of profiles with arbitrarycross-sectionsrdquo CIRP Annals vol 59 no 1 pp 315ndash318 2010

[6] H Zhu and K A Stelson ldquoModeling and closed-loop controlof stretch bending of aluminum rectangular tubesrdquo Journal ofManufacturing Science and Engineering vol 125 no 1pp 113ndash119 2003

[7] C-L Yu and X-Q Li ldquo+eoretical analysis on springback ofL-section extrusion in rotary stretch bending processrdquoTransactions of Nonferrous Metals Society of China vol 21no 12 pp 2705ndash2710 2011

[8] R Lu X Liu Z Xu X Hu Y Shao and L Liu ldquoSimulation ofspringback variation in the U-bending of tailor rolled blanksrdquoJournal of the Brazilian Society of Mechanical Sciences andEngineering vol 39 no 11 pp 4633ndash4647 2017

[9] X Lin Y Li Z Cai et al ldquoEffect of flexible 3D multipointstretch bending dies on the shape accuracy and the optimaldesignrdquo Advances in Materials Science and Engineeringvol 2018 Article ID 1095398 9 pages 2018

[10] F Han J-H Mo H-W Qi R-F Long X-H Cui andZ-W Li ldquoSpringback prediction for incremental sheetforming based on FEM-PSONN technologyrdquo Transactions of

Nonferrous Metals Society of China vol 23 no 4 pp 1061ndash1071 2013

[11] Y Song and Z Yu ldquoSpringback prediction in T-section beambending process using neural networks and finite elementmethodrdquo Archives of Civil and Mechanical Engineeringvol 13 no 2 pp 229ndash241 2013

[12] H Aguir H BelHadjSalah and R Hambli ldquoParameteridentification of an elasto-plastic behaviour using artificialneural networks-genetic algorithm methodrdquo Materials ampDesign vol 32 no 1 pp 48ndash53 2011

[13] R Kazan M Fırat and A E Tiryaki ldquoPrediction ofspringback in wipe-bending process of sheet metal usingneural networkrdquo Materials amp Design vol 30 no 2pp 418ndash423 2009

[14] M R Jamli A K Ariffin and D A Wahab ldquoIntegration offeedforward neural network and finite element in the draw-bend springback predictionrdquo Expert Systems with Applica-tions vol 41 no 8 pp 3662ndash3670 2014

[15] M R Jamli A K Ariffin and D A Wahab ldquoIncorporatingfeedforward neural network within finite element analysis forL-bending springback predictionrdquo Expert Systems with Ap-plications vol 42 no 5 pp 2604ndash2614 2015

[16] V Nasrollahi and B Arezoo ldquoPrediction of springback insheet metal components with holes on the bending area usingexperiments finite element and neural networksrdquo Materialsamp Design (1980ndash2015) vol 36 pp 331ndash336 2012

[17] K V Babu R G Narayanan and G S Kumar ldquoAn expertsystem for predicting the deep drawing behavior of tailorwelded blanksrdquo Expert Systems with Applications vol 37no 12 pp 7802ndash7812 2010

[18] H-Y Li and X-C Lu ldquoSpringback and tensile strength of2A97 aluminum alloy during age formingrdquo Transactions ofNonferrous Metals Society of China vol 25 no 4 pp 1043ndash1049 2015

[19] Z Fu and J Mo ldquoSpringback prediction of high-strength sheetmetal under air bending forming and tool design based onGAndashBPNNrdquo e International Journal of AdvancedManufacturing Technology vol 53 no 5ndash8 pp 473ndash4832011

[20] X Wang and F Shi Analysis of 43 Cases of MATLAB NeuralNetwork Beihang University Press Beijing China 2013


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Submit your manuscripts atwwwhindawicom

the springback by using the artificial neural network [13]Jamli et al built the springback prediction model for metalsheet stretch bending and L-shaped bending respectivelybased on finite element simulation and artificial neuralnetwork [14 15] Nasrollahi and Arezoo investigated thespringback prediction for a bending area of the metal sheetwith hole by the experiment finite element simulation andartificial neural network [16] Babu et al developed anartificial neural network system to predict the behavior ofdeep drawing for welding blank made by steel and alu-minum alloy [17] However the neural network model isnot used for the springback prediction of three-di-mensional stretched profiles

Based on the orthogonal experiments the numericalsimulation of the springback in 3D multipoint stretchbending of the aluminum profile is investigated by theABAQUS finite element software the training samples of theBP neural network are achieved and the mapping abilitybetween stretch-bending parameters and output value of thespringback is built by using the powerful function mappingability of the BP neural network +e results show that it cansave a lot of simulation time and provide important refer-ence data for the forming precision and springback com-pensation of the aluminum profile-forming part

2 Concept and Finite Element Model ofMultipoint Stretch Bending (MPSB)

21 Principle of the Multipoint Stretch-Bending Process+e multipoint stretch bending (MPSB) is improved on thebasis of the traditional stretch bending +e stretch-bendingdie in the traditional stretch bending is discretized It cansolve the 3D stretch bending of the profiles through themultipoint technology combined with the traditional stretchbending +erefore the MPSB process is more diversifiedthan conventional bending process because of the additionalvertical bending stage of the profile

As shown in Figure 1 when the profile is three-di-mensionally stretched and formed the bending machine canmove the die units back forth up and down So the rotationangle of the profile can be adjusted on two planes therebydecomposing the 3D stretch bending into the horizontalbending and the vertical bending

22 Material Model Because the aluminum alloys havelightweight and good mechanical properties they are usedwidely for structural parts of the railway vehicle In thisstudy five aluminum alloy grades are used which are asfollows 6063 6005A 5052 5083 and 6082 the profilelength is 3200mm and the profile weight is about 33 kg It isassumed that the aluminummaterial is isotropic the elastic-plastic constitutive behavior is isotropic hardening andrelevant mechanical properties are as shown in Table 1

23 Setup of Finite Element Model In the finite elementsimulation of 3D stretch bending the reasonable simplificationof the finite element model can reduce the calculation timeavoid other problems caused by the complexity of the model

and affect the accuracy of the results +erefore it is necessaryto rationally simplify the finite element model As shown inFigure 2 the die is simplified on the stretch-bending machineusing only the die units in contact with the profile and the limitscrew that limits the displacement of the die units in the verticaldirection of the x-z plane is simplified as a planar flap which is50mm in length with the die units Meanwhile the clamp issimplified to the same shape as the profile and is bound to theprofile the length of which is 100mm So only different diesections and clamps need to be replaced when forming dif-ferent geometric profiles

When selecting the appropriate element type for thefinite element model not only the accuracy of the simulationresult but also the operation time should be considered It isnecessary to obtain the most accurate simulation result inthe shortest possible calculation time +e finite elementmodel consists of the aluminum profile clamp die unitsand limit screw +e unit types and unit and node numberinformation of each component are shown in Table 2

3 Orthogonal Experiment for the Springback ofAluminum Profile

31 Selecting the Level of Various Factors +e orthogonalexperiment is a kind of design method which has a goodeffect to study and deal with multifactor problems and it isbased on the orthogonality of the data to design the schemeIt has the advantage of being able to obtain reliable andrepresentative test results in as few test times as possible+rough the analysis and integration of the test results thebest test conditions can be selected as the optimal levelcombination of each factor

In the MPSB process many factors influence the spring-back of the aluminum profile such as yield strength elasticmodulus tangent modulus bending angle in horizontal andvertical directions die structure die clearance prestretchingvalue and friction force According to the stretch-bendingprocess and orthogonal experiment seven important impactfactors are as follows elastic modulus (E) yield strength (σy)tangent modulus (E1) horizontal bending angle (α) verticalbending angle (β) die number (N) and friction coefficient (μ)Five aluminum alloy grades used in the orthogonal experimentare 6063 6005A 5052 5083 and 6082 +e values of eachfactor level are as shown in Table 3

32 Orthogonal Design +e table of the orthogonal exper-iment is usually expressed as La(S1 times S2 times S3 times middot middot middot times Sb)where L is the orthogonal table a is the test number b is themaximum value of impact factors and S1－Sb are the valueof the impact factor level from column 1 to column 9 +eorthogonal experiment can effectively reduce the number ofexperiments In this study the design of the L25(55) or-thogonal table is selected and seven impact factors (E σy E1α β N and μ) all select five levels

+e design of the orthogonal experiment and thespringback of the aluminum profile are shown in Table 4 Andthe springback of the aluminum profile is simulated using theABAQUS software based on the parameters in the orthogonal



T1T1

MhMh

z

y x

(a)


T2

T2

Mv

Mv

z

y x

(b)



Aluminum alloygrade

Treatmentstate






Density ρ(gcm3)

6063 T5 68300 341667 186 145 033 2696005A T5 69000 210 262 241 033 275052 H32 69300 291667 230 195 033 2685083 H112 70300 6875 303 193 033 2666082 T6 71000 66667 290 250 033 27

Multipoint dies

Limit screw

Aluminum profile

Clamp














lltm + n

radic+ p (1)





LevelImpact factor


1 6063 14 14 4 0052 6005A 18 18 6 013 5052 22 22 8 0154 5083 26 26 10 025 6082 30 30 12 025




yk 111394410


7

i1wij times xi + bj

⎛⎝ ⎞⎠ + bk (k 1 2 3)

(2)







1 6063 14 14 4 005 2401 4673 55662 6063 18 18 6 01 3185 4711 59333 6063 22 22 8 015 2777 4953 58804 6063 26 26 10 02 3529 5289 64385 6063 30 30 12 025 3493 5918 69056 6005A 14 18 8 02 4133 6793 88407 6005A 18 22 10 025 5310 7807 99558 6005A 22 26 12 005 5112 7345 94339 6005A 26 30 4 01 3166 9064 996810 6005A 30 14 6 015 5144 8727 104111 5052 14 22 12 01 3228 5704 703312 5052 18 26 4 015 1896 6395 711813 5052 22 30 6 02 4471 7328 862614 5052 26 14 8 025 3958 5657 721115 5052 30 18 10 005 2773 5824 681816 5083 14 26 6 025 4097 6420 786417 5083 18 30 8 005 3259 7597 832418 5083 22 14 10 01 2924 5318 671819 5083 26 18 12 015 2539 6731 762820 5083 30 22 4 02 1471 6735 779121 6082 14 30 10 015 4401 6086 750022 6082 18 14 12 02 7764 7705 109423 6082 22 18 4 025 8251 9178 123024 6082 26 22 6 005 7289 9630 120925 6082 30 26 8 01 9359 9835 1370

δy

δz

δ




xkprime 2 times

xk minus xmin









Factors

2

3

4

5

6

7

8In

dex

(a)


Factors

4

5

6

7

8

9

10

Inde

x

(b)


Factors

5

6

7

8

9

10

11

12

Inde

x

(c)





+1904e + 00+1542e + 01+2895e + 01+4247e + 01+5599e + 01+6951e + 01+8303e + 01+9655e + 01+1101e + 02+1236e + 02+1371e + 02+1526e + 02+1642e + 02

S Mises(Avg 75)

(a)


PEEQ(Avg 75)

(b)



2

3

4

5

6

7

8

9

10

δ y (m

m)


(a)


δ z (m

m)


2

3

4

5

6

7

8

9

10

11

(b)

Figure 7 Continued


E σb σs

α

β

N

μ

δy

δz

δ

wij wjk

xi

yk

Oj







5 Conclusion





4

5

6

7

8

9

10

11

12

13

14δ

(mm

)

(c)

δxδyδ

0

1

2

3

4

5

6

7

8

9

10

Erro

r (

)


(d)





value δy (mm)

Verticalspringback

value δz (mm)





270 450 567



Data Availability




Acknowledgments


References

























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





T1T1

MhMh

z

y x

(a)


T2

T2

Mv

Mv

z

y x

(b)



Aluminum alloygrade

Treatmentstate






Density ρ(gcm3)

6063 T5 68300 341667 186 145 033 2696005A T5 69000 210 262 241 033 275052 H32 69300 291667 230 195 033 2685083 H112 70300 6875 303 193 033 2666082 T6 71000 66667 290 250 033 27

Multipoint dies

Limit screw

Aluminum profile

Clamp














lltm + n

radic+ p (1)





LevelImpact factor


1 6063 14 14 4 0052 6005A 18 18 6 013 5052 22 22 8 0154 5083 26 26 10 025 6082 30 30 12 025




yk 111394410


7

i1wij times xi + bj

⎛⎝ ⎞⎠ + bk (k 1 2 3)

(2)







1 6063 14 14 4 005 2401 4673 55662 6063 18 18 6 01 3185 4711 59333 6063 22 22 8 015 2777 4953 58804 6063 26 26 10 02 3529 5289 64385 6063 30 30 12 025 3493 5918 69056 6005A 14 18 8 02 4133 6793 88407 6005A 18 22 10 025 5310 7807 99558 6005A 22 26 12 005 5112 7345 94339 6005A 26 30 4 01 3166 9064 996810 6005A 30 14 6 015 5144 8727 104111 5052 14 22 12 01 3228 5704 703312 5052 18 26 4 015 1896 6395 711813 5052 22 30 6 02 4471 7328 862614 5052 26 14 8 025 3958 5657 721115 5052 30 18 10 005 2773 5824 681816 5083 14 26 6 025 4097 6420 786417 5083 18 30 8 005 3259 7597 832418 5083 22 14 10 01 2924 5318 671819 5083 26 18 12 015 2539 6731 762820 5083 30 22 4 02 1471 6735 779121 6082 14 30 10 015 4401 6086 750022 6082 18 14 12 02 7764 7705 109423 6082 22 18 4 025 8251 9178 123024 6082 26 22 6 005 7289 9630 120925 6082 30 26 8 01 9359 9835 1370

δy

δz

δ




xkprime 2 times

xk minus xmin









Factors

2

3

4

5

6

7

8In

dex

(a)


Factors

4

5

6

7

8

9

10

Inde

x

(b)


Factors

5

6

7

8

9

10

11

12

Inde

x

(c)





+1904e + 00+1542e + 01+2895e + 01+4247e + 01+5599e + 01+6951e + 01+8303e + 01+9655e + 01+1101e + 02+1236e + 02+1371e + 02+1526e + 02+1642e + 02

S Mises(Avg 75)

(a)


PEEQ(Avg 75)

(b)



2

3

4

5

6

7

8

9

10

δ y (m

m)


(a)


δ z (m

m)


2

3

4

5

6

7

8

9

10

11

(b)

Figure 7 Continued


E σb σs

α

β

N

μ

δy

δz

δ

wij wjk

xi

yk

Oj







5 Conclusion





4

5

6

7

8

9

10

11

12

13

14δ

(mm

)

(c)

δxδyδ

0

1

2

3

4

5

6

7

8

9

10

Erro

r (

)


(d)





value δy (mm)

Verticalspringback

value δz (mm)





270 450 567



Data Availability




Acknowledgments


References

























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls















lltm + n

radic+ p (1)





LevelImpact factor


1 6063 14 14 4 0052 6005A 18 18 6 013 5052 22 22 8 0154 5083 26 26 10 025 6082 30 30 12 025




yk 111394410


7

i1wij times xi + bj

⎛⎝ ⎞⎠ + bk (k 1 2 3)

(2)







1 6063 14 14 4 005 2401 4673 55662 6063 18 18 6 01 3185 4711 59333 6063 22 22 8 015 2777 4953 58804 6063 26 26 10 02 3529 5289 64385 6063 30 30 12 025 3493 5918 69056 6005A 14 18 8 02 4133 6793 88407 6005A 18 22 10 025 5310 7807 99558 6005A 22 26 12 005 5112 7345 94339 6005A 26 30 4 01 3166 9064 996810 6005A 30 14 6 015 5144 8727 104111 5052 14 22 12 01 3228 5704 703312 5052 18 26 4 015 1896 6395 711813 5052 22 30 6 02 4471 7328 862614 5052 26 14 8 025 3958 5657 721115 5052 30 18 10 005 2773 5824 681816 5083 14 26 6 025 4097 6420 786417 5083 18 30 8 005 3259 7597 832418 5083 22 14 10 01 2924 5318 671819 5083 26 18 12 015 2539 6731 762820 5083 30 22 4 02 1471 6735 779121 6082 14 30 10 015 4401 6086 750022 6082 18 14 12 02 7764 7705 109423 6082 22 18 4 025 8251 9178 123024 6082 26 22 6 005 7289 9630 120925 6082 30 26 8 01 9359 9835 1370

δy

δz

δ




xkprime 2 times

xk minus xmin









Factors

2

3

4

5

6

7

8In

dex

(a)


Factors

4

5

6

7

8

9

10

Inde

x

(b)


Factors

5

6

7

8

9

10

11

12

Inde

x

(c)





+1904e + 00+1542e + 01+2895e + 01+4247e + 01+5599e + 01+6951e + 01+8303e + 01+9655e + 01+1101e + 02+1236e + 02+1371e + 02+1526e + 02+1642e + 02

S Mises(Avg 75)

(a)


PEEQ(Avg 75)

(b)



2

3

4

5

6

7

8

9

10

δ y (m

m)


(a)


δ z (m

m)


2

3

4

5

6

7

8

9

10

11

(b)

Figure 7 Continued


E σb σs

α

β

N

μ

δy

δz

δ

wij wjk

xi

yk

Oj







5 Conclusion





4

5

6

7

8

9

10

11

12

13

14δ

(mm

)

(c)

δxδyδ

0

1

2

3

4

5

6

7

8

9

10

Erro

r (

)


(d)





value δy (mm)

Verticalspringback

value δz (mm)





270 450 567



Data Availability




Acknowledgments


References

























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






yk 111394410


7

i1wij times xi + bj

⎛⎝ ⎞⎠ + bk (k 1 2 3)

(2)







1 6063 14 14 4 005 2401 4673 55662 6063 18 18 6 01 3185 4711 59333 6063 22 22 8 015 2777 4953 58804 6063 26 26 10 02 3529 5289 64385 6063 30 30 12 025 3493 5918 69056 6005A 14 18 8 02 4133 6793 88407 6005A 18 22 10 025 5310 7807 99558 6005A 22 26 12 005 5112 7345 94339 6005A 26 30 4 01 3166 9064 996810 6005A 30 14 6 015 5144 8727 104111 5052 14 22 12 01 3228 5704 703312 5052 18 26 4 015 1896 6395 711813 5052 22 30 6 02 4471 7328 862614 5052 26 14 8 025 3958 5657 721115 5052 30 18 10 005 2773 5824 681816 5083 14 26 6 025 4097 6420 786417 5083 18 30 8 005 3259 7597 832418 5083 22 14 10 01 2924 5318 671819 5083 26 18 12 015 2539 6731 762820 5083 30 22 4 02 1471 6735 779121 6082 14 30 10 015 4401 6086 750022 6082 18 14 12 02 7764 7705 109423 6082 22 18 4 025 8251 9178 123024 6082 26 22 6 005 7289 9630 120925 6082 30 26 8 01 9359 9835 1370

δy

δz

δ




xkprime 2 times

xk minus xmin









Factors

2

3

4

5

6

7

8In

dex

(a)


Factors

4

5

6

7

8

9

10

Inde

x

(b)


Factors

5

6

7

8

9

10

11

12

Inde

x

(c)





+1904e + 00+1542e + 01+2895e + 01+4247e + 01+5599e + 01+6951e + 01+8303e + 01+9655e + 01+1101e + 02+1236e + 02+1371e + 02+1526e + 02+1642e + 02

S Mises(Avg 75)

(a)


PEEQ(Avg 75)

(b)



2

3

4

5

6

7

8

9

10

δ y (m

m)


(a)


δ z (m

m)


2

3

4

5

6

7

8

9

10

11

(b)

Figure 7 Continued


E σb σs

α

β

N

μ

δy

δz

δ

wij wjk

xi

yk

Oj







5 Conclusion





4

5

6

7

8

9

10

11

12

13

14δ

(mm

)

(c)

δxδyδ

0

1

2

3

4

5

6

7

8

9

10

Erro

r (

)


(d)





value δy (mm)

Verticalspringback

value δz (mm)





270 450 567



Data Availability




Acknowledgments


References

























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





xkprime 2 times

xk minus xmin









Factors

2

3

4

5

6

7

8In

dex

(a)


Factors

4

5

6

7

8

9

10

Inde

x

(b)


Factors

5

6

7

8

9

10

11

12

Inde

x

(c)





+1904e + 00+1542e + 01+2895e + 01+4247e + 01+5599e + 01+6951e + 01+8303e + 01+9655e + 01+1101e + 02+1236e + 02+1371e + 02+1526e + 02+1642e + 02

S Mises(Avg 75)

(a)


PEEQ(Avg 75)

(b)



2

3

4

5

6

7

8

9

10

δ y (m

m)


(a)


δ z (m

m)


2

3

4

5

6

7

8

9

10

11

(b)

Figure 7 Continued


E σb σs

α

β

N

μ

δy

δz

δ

wij wjk

xi

yk

Oj







5 Conclusion





4

5

6

7

8

9

10

11

12

13

14δ

(mm

)

(c)

δxδyδ

0

1

2

3

4

5

6

7

8

9

10

Erro

r (

)


(d)





value δy (mm)

Verticalspringback

value δz (mm)





270 450 567



Data Availability




Acknowledgments


References

























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




+1904e + 00+1542e + 01+2895e + 01+4247e + 01+5599e + 01+6951e + 01+8303e + 01+9655e + 01+1101e + 02+1236e + 02+1371e + 02+1526e + 02+1642e + 02

S Mises(Avg 75)

(a)


PEEQ(Avg 75)

(b)



2

3

4

5

6

7

8

9

10

δ y (m

m)


(a)


δ z (m

m)


2

3

4

5

6

7

8

9

10

11

(b)

Figure 7 Continued


E σb σs

α

β

N

μ

δy

δz

δ

wij wjk

xi

yk

Oj







5 Conclusion





4

5

6

7

8

9

10

11

12

13

14δ

(mm

)

(c)

δxδyδ

0

1

2

3

4

5

6

7

8

9

10

Erro

r (

)


(d)





value δy (mm)

Verticalspringback

value δz (mm)





270 450 567



Data Availability




Acknowledgments


References

























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








5 Conclusion





4

5

6

7

8

9

10

11

12

13

14δ

(mm

)

(c)

δxδyδ

0

1

2

3

4

5

6

7

8

9

10

Erro

r (

)


(d)





value δy (mm)

Verticalspringback

value δz (mm)





270 450 567



Data Availability




Acknowledgments


References

























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





Data Availability




Acknowledgments


References

























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




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