Springback Study on Profile Flexible 3D Stretch-Bending Process Using the Neural Network

Li, Yi; Liang, Ce; Lin, Xiangfeng; Liang, Jicai; Cai, Zhongyi; Teng, Fei

doi:https://doi.org/10.1155/2019/6465196

Advances in Materials Science and Engineering

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Abstract Introduction Conclusion Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2019 | Article ID 6465196 | https://doi.org/10.1155/2019/6465196

Springback Study on Profile Flexible 3D Stretch-Bending Process Using the Neural Network

Yi Li,^1,2Ce Liang ,^1,2Xiangfeng Lin,^1,3Jicai Liang,^1,3Zhongyi Cai,^1,3and Fei Teng⁴

Academic Editor: José António Fonseca de Oliveira Correia

Received15 Jun 2019

Accepted23 Sept 2019

Published15 Oct 2019

Abstract

The springback is one of the main defects in the flexible 3D stretch-bending process. In this paper, according to the orthogonal design of experiments, the numerical simulation analysis of the springback for the 3D stretch-bending aluminum profile is carried out by the ABAQUS finite element software. And to investigate the effect of material properties on the springback, the range analysis of the orthogonal experiment is performed. The results show that these material properties of the aluminum profile (elastic modulus E, yield strength σ_y, and tangent modulus E₁) might have the biggest influence on the springback of the aluminum profile, and the optimized forming parameters are founded as follows: the horizontal bending degree is 14°, the vertical bending degree is 14°, the number of multipoint stretch-bending dies is 10, the friction coefficient is 0.15, and aluminum alloy grade is 6063. Moreover, the model of the BP neural network for the prediction of the springback is established and trained based on the orthogonal experiment, and the results with the BP neural network model are in good agreement with experimental results. So it is obvious 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 more demanding for reduction of energy consumption and environmental pollution caused by exhaust emissions [1–3]; especially, the design of the lightweight part plays a more and more important role in economic and ecological aspects [4]. Aluminum alloy is widely used in aerospace, rail vehicle manufacturing, and automobile manufacturing as a lightweight material because of its low density, high strength, and ease of recycling [5–7].

Aluminum profile can meet many diversified requirements, but the formation of the aluminum profile brings many new problems in the part design and manufacturing process. Because the elastic modulus of the aluminum alloy is only one-third that of the steel sheet, the springback of the aluminum alloy is much bigger than the same data of the steel sheet, and the springback becomes one of the main defects for the aluminum profile stretch-bending part [8]. If not to make reasonable estimation for the springback of the aluminum profile stretch-bending part, it will have serious influence on the forming quality of components and furthermore service life.

There are many influence factors on the springback such as profile characteristics, processing parameters, and die structure. During the flexible 3D multipoint stretch-bending process of the aluminum profile, the springback analysis is very complicated with geometric nonlinearity, material nonlinearity, and contact nonlinearity, so it is hard to find out an accurate mathematical model [9]. The artificial neural network is widely used in the property prediction of the metal material for high ability of nonlinear mapping and prediction of the output target according to the finite training sample [10–12]. Kazan et al. investigated the springback of the metal sheet in the bending process and developed the prediction model for the springback by using the artificial neural network [13]. Jamli et al. built the springback prediction model for metal sheet stretch bending and L-shaped bending, respectively, based on finite element simulation and artificial neural network [14, 15]. Nasrollahi and Arezoo investigated the springback prediction for a bending area of the metal sheet with hole by the experiment, finite element simulation, and artificial neural network [16]. Babu et al. developed an artificial neural network system to predict the behavior of deep drawing for welding blank made by steel and aluminum alloy [17]. However, the neural network model is not used for the springback prediction of three-dimensional stretched profiles.

Based on the orthogonal experiments, the numerical simulation of the springback in 3D multipoint stretch bending of the aluminum profile is investigated by the ABAQUS finite element software, the training samples of the BP neural network are achieved, and the mapping ability between stretch-bending parameters and output value of the springback is built by using the powerful function mapping ability of the BP neural network. The results show that it can save a lot of simulation time and provide important reference data for the forming precision and springback compensation of the aluminum profile-forming part.

2. Concept and Finite Element Model of Multipoint Stretch Bending (MPSB)

2.1. Principle of the Multipoint Stretch-Bending Process

The multipoint stretch bending (MPSB) is improved on the basis of the traditional stretch bending. The stretch-bending die in the traditional stretch bending is discretized. It can solve the 3D stretch bending of the profiles through the multipoint technology combined with the traditional stretch bending. Therefore, the MPSB process is more diversified than conventional bending process because of the additional vertical bending stage of the profile.

As shown in Figure 1, when the profile is three-dimensionally stretched and formed, the bending machine can move the die units back, forth, up, and down. So the rotation angle of the profile can be adjusted on two planes, thereby decomposing the 3D stretch bending into the horizontal bending and the vertical bending.

(a)

(b)

2.2. Material Model

Because the aluminum alloys have lightweight and good mechanical properties, they are used widely for structural parts of the railway vehicle. In this study, five aluminum alloy grades are used which are as follows: 6063, 6005A, 5052, 5083, and 6082, the profile length is 3200 mm, and the profile weight is about 3.3 kg. It is assumed that the aluminum material is isotropic, the elastic-plastic constitutive behavior is isotropic hardening, and relevant mechanical properties are as shown in Table 1.

2.3. Setup of Finite Element Model

In the finite element simulation of 3D stretch bending, the reasonable simplification of the finite element model can reduce the calculation time, avoid other problems caused by the complexity of the model, and affect the accuracy of the results. Therefore, it is necessary to rationally simplify the finite element model. As shown in Figure 2, the die is simplified on the stretch-bending machine, using only the die units in contact with the profile, and the limit screw that limits the displacement of the die units in the vertical direction of the x-z plane is simplified as a planar flap, which is 50 mm in length with the die units. Meanwhile, the clamp is simplified to the same shape as the profile and is bound to the profile, the length of which is 100 mm. So only different die sections and clamps need to be replaced when forming different geometric profiles.

When selecting the appropriate element type for the finite element model, not only the accuracy of the simulation result but also the operation time should be considered. It is necessary to obtain the most accurate simulation result in the shortest possible calculation time. The finite element model consists of the aluminum profile, clamp, die units, and limit screw. The unit types and unit and node number information of each component are shown in Table 2.

3. Orthogonal Experiment for the Springback of Aluminum Profile

3.1. Selecting the Level of Various Factors

The orthogonal experiment is a kind of design method which has a good effect to study and deal with multifactor problems, and it is based on the orthogonality of the data to design the scheme. It has the advantage of being able to obtain reliable and representative test results in as few test times as possible. Through the analysis and integration of the test results, the best test conditions can be selected as the optimal level combination of each factor.

In the MPSB process, many factors influence the springback of the aluminum profile such as yield strength, elastic modulus, tangent modulus, bending angle in horizontal and vertical directions, die structure, die clearance, prestretching value, and friction force. According to the stretch-bending process and orthogonal experiment, seven important impact factors are as follows: elastic modulus (E), yield strength (), tangent modulus (E₁), horizontal bending angle (), vertical bending angle (), die number (N), and friction coefficient (). Five aluminum alloy grades used in the orthogonal experiment are 6063, 6005A, 5052, 5083, and 6082. The values of each factor level are as shown in Table 3.

3.2. Orthogonal Design

The table of the orthogonal experiment is usually expressed as , where L is the orthogonal table, a is the test number, b is the maximum value of impact factors, and S₁－S_b are the value of the impact factor level from column 1 to column 9. The orthogonal experiment can effectively reduce the number of experiments. In this study, the design of the L₂₅(5⁵) orthogonal table is selected, and seven impact factors (E, , E₁, , , N, and ) all select five levels.

The design of the orthogonal experiment and the springback of the aluminum profile are shown in Table 4. And the springback of the aluminum profile is simulated using the ABAQUS software, based on the parameters in the orthogonal table. In the MPSB process, the aluminum profile is formed along the space curve, which has more complex deformation than the traditional stretch-bending process. So the springback of the 3D stretch-bending process can be divided into two parts, as shown in Figure 3; one part is horizontal springback along the horizontal direction in the x-y plane, and the other part is vertical springback along the vertical direction in the x-z plane. δ_y is the value of horizontal springback in the x-y plane, δ_z is the value of vertical springback in the x-z plane, and δ is the value of total springback for the aluminum profile.

3.3. Range Analysis in Orthogonal Experimental Data

The range analysis table of the orthogonal experiment is shown in Figure 4.

(a)

(b)

(c)

According to Figure 4, the main factors affecting the horizontal springback along the x-y plane in order of importance are elastic modulus (E), yield strength (), tangent modulus (E₁), friction coefficient (), die number (N), horizontal bending angle (), and vertical bending angle (). And the main factors affecting the vertical springback along the x-z plane in order of importance are elastic modulus (E), yield strength (), tangent modulus (E₁), horizontal bending angle (), die number (N), vertical bending angle (), and friction coefficient (). The main factors affecting the total springback in order of importance are elastic modulus (E), yield strength (), tangent modulus (E₁), horizontal bending angle (), die number (N), friction coefficient (), and vertical bending angle ().

3.4. Optimized Parameters and Verification

The optimized parameter combination means that the combination of levels can make test results reach the optimum state in the range of all factors. The optimized parameter combination is founded by the experiment index. The larger the experiment index is, the better the level corresponding to the maximum value of the index selected is. In contrast, the smaller the test index is, the better the level corresponding to the minimum value of the index selected is.

In this study, the experiment index is the value of springback clearance. According to data in Table 5, the best combination for horizontal springback along the x-y plane is A₄B₁C₅D₁E₃, and the best combination for vertical springback along the x-z plane and the best combination for total springback are A₁B₁C₁D₄E₃. These two combinations have little deviation for horizontal springback along the x-y plane, but the deviation is big for vertical springback along the x-z plane and total springback. So the optimized parameter combination selected in the orthogonal experiment is A₁B₁C₁D₄E₃, and the corresponding parameters are as follows: the aluminum alloy material is 6063, horizontal bending angle is 14°, vertical bending angle is 14°, multipoint die number is 10, and friction coefficient is 0.15.

The optimized parameter combination A₁B₁C₁D₄E₃ is validated by using the ABAQUS software simulation, and the simulated results are shown in Table 5.

Compared to data in Tables 4 and 5, it is found that the best values of vertical springback and total springback are achieved by using the optimized parameter combination A₁B₁C₁D₄E₃, and the deviation is little for horizontal springback. The stress-strain chart of 3D stretch bending under the combination A₁B₁C₁D₄E₃ is shown in Figure 5.

(a)

(b)

As can be seen from Figure 5, the stress and equivalent strain are evenly distributed, and the forming part has no defects. It shows that the forming effect is very good.

4. Prediction of the Springback Based on BP Neural Network

4.1. Setup of BP Neural Network Model

The BP neural network is a kind of multilayer forward feeding neural network. Its main feature is that the signals feed forward and the errors propagate backward. The output error is used to predict the error of the direct leading layer for the output layer. Then, the error of the direct leading layer is used to predict the error of the further layer, and the errors of others layers are gained from layer-by-layer backpropagation [18, 19].

The model of the BP neural network is composed of the input layer, hidden layer, and output layer. The input layer and output layer are usually determined based on the practice problem, the neuron number in the input layer is equal to the dimension of input sample data, and the neuron number in the output layer is equal to the dimension of the result sample. The neuron number in the hidden layer is usually calculated by the following empirical equation [20]:where m is the neuron number in the input layer; n is the neuron number in the output layer; is the constant, and ; and l is the neuron number in the hidden layer.

In this study, the neuron number in the input layer is 7, and the neuron number in the output layer is 3. The neuron number in the hidden layer is 10 based on the training time and accuracy of the BP neural network. The 7-10-3 three-layer frame of the BP neural network is set up, as shown in Figure 6.

The mathematical model of neural network function which has 10 hidden layers is as follows:where is the weight of the input layer to the hidden layer, is the weight of the hidden layer to the output layer, b_j is the offset weight of the hidden layer, b_k is the offset weight of the output layer, sig is the sigmoid activation function, x_i is the input value of the neural network, and y_k is the output value of the neural network.

4.2. Training and Testing of BP Neural Network

The data are normalized before training the BP neural network in order to avoid large difference order of magnitude of the input-output data result in big error of prediction, and the maximum-minimum method is applied on the normalization of data:where is the value after the normalization of the data sequence, x_max is the maximum value of the data sequence, and x_min is the minimum value of the data sequence.

The training parameters are as follows: the maximum training time is 10000, the expected training error is 1e⁻⁶, the learning rate is 0.02, and the momentum factor is 0.65. A total of 41 pairs of data in which 15 pairs of simulated data are from ABAQUS software are used for training and testing the BP neural network. Among these data, under the optimized parameter combination A₄B₁C₅D₁E₃, orthogonal experiment sample nos. 7, 13, 19, and 25 are used for sample testing, and the others are used for training the BP neural network. The comparison of finite element simulation and prediction results of the BP neural network after MATLAB training is shown in Figure 7.

(a)

(b)

(c)

(d)

As seen from Figure 7, it is shown that there is little difference between the prediction results of the BP neural network and the simulation results, the training accuracy is high, so the BP neural network method can replace the finite element simulation to predict the springback of the 3D stretch-bending process, reduce the simulation runtime, and increase the simulation efficiency.

4.3. Test Verification

To validate the finite element simulation and BP neural network on the springback of the 3D stretch-bending process, the comparison of experimental results, simulation results, and prediction results is investigated. The experimental results are founded based on the optimized parameter combination A₁B₁C₁D₄E₃, whose forming parameters are as follows: the aluminum alloy material is 6063, horizontal bending angle is 14°, vertical bending angle is 14°, multipoint die unit number is 10, and friction coefficient is 0.15. The detection setup and the forming part through the MPSB process are shown in Figure 8.

The detection setup is used to detect the value of the springback after stretch bending of the aluminum profile, as shown in Figure 8, and the detected values are shown in Table 6.

As seen from Table 6, the results with the BP neural network model and simulation results are in good agreement with experimental results. Therefore, it is obvious that a new prediction method of the springback in the flexible 3D stretch-bending process is provided by using the BP neural network.

5. Conclusion

(1)According to the range analysis of the orthogonal experiment, the main factors affecting the springback in the 3D stretch-bending process in order of importance are elastic modulus (E), yield strength (), and tangent modulus (E₁), and it is shown that the material properties of the aluminum profile should be considered firstly; then, the forming parameters of the 3D stretch-bending process are investigated.(2)Based on the orthogonal experiment and the influence on the springback, the optimized parameter combination is as follows: the aluminum alloy material is 6063, horizontal bending angle is 14°, vertical bending angle is 14°, multipoint die number is 10, and friction coefficient is 0.15.(3)Compared to orthogonal experimental data, the results of BP neural network simulation show that it is an effective way to predict the springback by using the BP neural network and provide a new method for practice production.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (51675225).

References

D.-S. Shim, G.-Y. Baek, G.-Y. Shin, H.-S. Yoon, K.-Y. Lee, and K.-H. Kim, “Investigation of tension force in stretch forming of doubly curved aluminum alloy (Al5083) sheet,” International Journal of Precision Engineering and Manufacturing, vol. 17, no. 4, pp. 433–444, 2016.
View at: Publisher Site | Google Scholar
T. Liu, Y. Wang, J. Wu et al., “Springback analysis of Z & T-section 2196-T8511 and 2099-T83 Al-Li alloys extrusions in displacement controlled cold stretch bending,” Journal of Materials Processing Technology, vol. 225, pp. 295–309, 2015.
View at: Publisher Site | Google Scholar
J. Liang, S. Gao, F. Teng, P.-Z. Yu, and X.-J. Song, “Flexible 3D stretch-bending technology for aluminum profile,” The International Journal of Advanced Manufacturing Technology, vol. 71, no. 9–12, pp. 1939–1947, 2014.
View at: Publisher Site | Google Scholar
Y. Zhou, P. Li, M. Li, and L. Wang, “Application and correction of L-shaped thin-wall aluminum in flexible-bending processing,” The International Journal of Advanced Manufacturing Technology, vol. 92, no. 1–4, pp. 981–988, 2017.
View at: Publisher Site | Google Scholar
S. Chatti, M. Hermes, A. E. Tekkaya, and M. Kleiner, “The new TSS bending process: 3D bending of profiles with arbitrary cross-sections,” CIRP Annals, vol. 59, no. 1, pp. 315–318, 2010.
View at: Publisher Site | Google Scholar
H. Zhu and K. A. Stelson, “Modeling and closed-loop control of stretch bending of aluminum rectangular tubes,” Journal of Manufacturing Science and Engineering, vol. 125, no. 1, pp. 113–119, 2003.
View at: Publisher Site | Google Scholar
C.-L. Yu and X.-Q. Li, “Theoretical analysis on springback of L-section extrusion in rotary stretch bending process,” Transactions of Nonferrous Metals Society of China, vol. 21, no. 12, pp. 2705–2710, 2011.
View at: Publisher Site | Google Scholar
R. Lu, X. Liu, Z. Xu, X. Hu, Y. Shao, and L. Liu, “Simulation of springback variation in the U-bending of tailor rolled blanks,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 39, no. 11, pp. 4633–4647, 2017.
View at: Publisher Site | Google Scholar
X. Lin, Y. Li, Z. Cai et al., “Effect of flexible 3D multipoint stretch bending dies on the shape accuracy and the optimal design,” Advances in Materials Science and Engineering, vol. 2018, Article ID 1095398, 9 pages, 2018.
View at: Publisher Site | Google Scholar
F. Han, J.-H. Mo, H.-W. Qi, R.-F. Long, X.-H. Cui, and Z.-W. Li, “Springback prediction for incremental sheet forming based on FEM-PSONN technology,” Transactions of Nonferrous Metals Society of China, vol. 23, no. 4, pp. 1061–1071, 2013.
View at: Publisher Site | Google Scholar
Y. Song and Z. Yu, “Springback prediction in T-section beam bending process using neural networks and finite element method,” Archives of Civil and Mechanical Engineering, vol. 13, no. 2, pp. 229–241, 2013.
View at: Publisher Site | Google Scholar
H. Aguir, H. BelHadjSalah, and R. Hambli, “Parameter identification of an elasto-plastic behaviour using artificial neural networks-genetic algorithm method,” Materials & Design, vol. 32, no. 1, pp. 48–53, 2011.
View at: Publisher Site | Google Scholar
R. Kazan, M. Fırat, and A. E. Tiryaki, “Prediction of springback in wipe-bending process of sheet metal using neural network,” Materials & Design, vol. 30, no. 2, pp. 418–423, 2009.
View at: Publisher Site | Google Scholar
M. R. Jamli, A. K. Ariffin, and D. A. Wahab, “Integration of feedforward neural network and finite element in the draw-bend springback prediction,” Expert Systems with Applications, vol. 41, no. 8, pp. 3662–3670, 2014.
View at: Publisher Site | Google Scholar
M. R. Jamli, A. K. Ariffin, and D. A. Wahab, “Incorporating feedforward neural network within finite element analysis for L-bending springback prediction,” Expert Systems with Applications, vol. 42, no. 5, pp. 2604–2614, 2015.
View at: Publisher Site | Google Scholar
V. Nasrollahi and B. Arezoo, “Prediction of springback in sheet metal components with holes on the bending area, using experiments, finite element and neural networks,” Materials & Design (1980–2015), vol. 36, pp. 331–336, 2012.
View at: Publisher Site | Google Scholar
K. V. Babu, R. G. Narayanan, and G. S. Kumar, “An expert system for predicting the deep drawing behavior of tailor welded blanks,” Expert Systems with Applications, vol. 37, no. 12, pp. 7802–7812, 2010.
View at: Publisher Site | Google Scholar
H.-Y. Li and X.-C. Lu, “Springback and tensile strength of 2A97 aluminum alloy during age forming,” Transactions of Nonferrous Metals Society of China, vol. 25, no. 4, pp. 1043–1049, 2015.
View at: Publisher Site | Google Scholar
Z. Fu and J. Mo, “Springback prediction of high-strength sheet metal under air bending forming and tool design based on GA–BPNN,” The International Journal of Advanced Manufacturing Technology, vol. 53, no. 5–8, pp. 473–483, 2011.
View at: Publisher Site | Google Scholar
X. Wang and F. Shi, Analysis of 43 Cases of MATLAB Neural Network, Beihang University Press, Beijing, China, 2013.

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Copyright © 2019 Yi Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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