Study on the Influence of Bending Angle of Multipoint Stretch-Bending of Profiles on Section Distortion of Parts

(e ABAQUS finite element simulation software was used to simulate the flexible 3Dmultipoint stretch-bending (MPSB) forming process of aluminum profiles. (e influence of bending angle on the section distortion was investigated. (e results show that the type of rectangular section distortion during horizontal bending and vertical bending is different. (e bulging rate and the depression rate increase with the increase in horizontal bending angles; when the vertical bending angle is less than 15°, the depression rate of the horizontally curved section is effectively reduced. When α is equal to 30°, β is less than 15° which can effectively reduce the depression rate caused by horizontal bending to the profile. When α is less than 30°, the depression rate which is caused by horizontal bending can be reduced through the vertical bending angle, with 5° than 15°; the vertical bending process changes the distortion pattern of the profile; the depression rate and the bulging rate increase with the increase of the vertical bending angle. (rough the support vector regression and selecting the parameter group c� 1.5, g � 0.05, the distortion rate of different angles in the common range is further expanded, and the quality control curve is drawn by combining the test results and prediction results which determine the depression rate as 2%, 2.5%, and 3% processing boundary. Using this curve to predict the distortion rate of the profile is instructive in the actual processing.


Introduction
Due to the rapid development of the automobile and highspeed rail industry in recent years, people pay more and more attention to the lightweight design of the structure.
is is because reducing the weight of cars and high-speed trains can not only reduce energy consumption and alleviate the growing energy crisis but also reduce waste emissions [1][2][3]. Aluminum has a wide range of properties such as low density, high strength, and easy recycling, so it is widely used in aerospace, rail vehicle, and automotive manufacturing. e rapid development of the manufacturing industry has made the demand for parts more diversified. e traditional processing methods are limited to two-dimensional bending and forming, or the three-dimensional deformation is realized by manual torsion after two-dimensional bending of the profile. is method is time-consuming and laborious, and the scrap rate is high. Clausen et al. used the finite element method to simulate the bending and forming process of the car bumper and conducted in-depth research on the section distortion and springback phenomenon [4]. Vaze and Corona used experimental methods to study the wrinkle line of the rectangular profile bending process [5]; Corona proposed an effective method for predicting crosssection distortion of thin-walled profiles [6]. In order to reduce the production cost and shorten the production cycle time, combined with the technical characteristics of threedimensional flexible bending, a team under Liang Jicai professor from Jilin University developed a new three-dimensional flexible multipoint stretch-bending technology has been developed, which can realize the complex forming of three-dimensional parts. e mold profile of this processing method is reconfigurable [7][8][9]. Teng et al. explored the prediction of the amount of springback in the threedimensional stretch-bending process of the profile [10], and Liang et al. explored the forming of the profile in threedimensional stretch-bending [11]. Yu et al. explored the extent to which processing parameters affect the distortion of profiles [12].
In the process of three-dimensional stretch-bending, the profile is a light high-strength aluminum alloy with large deformation resistance and good plasticity. Distortion is a significant defect in the forming process. Because the technology is at the forefront, engineers lack experience in multipoint stretch-bending [13]. ey are unable to predict whether a profile will be distorted. erefore, a large amount of waste parts may be processed, resulting in an increase in cost [14][15][16]. So, exploring the variation law of cross-section distortion of aluminum profiles during three-dimensional stretch-bending has certain guiding significance for actual production [17][18][19]. is paper investigates the influence of the bending angle of the profile on the cross-section distortion and the variation law.

Description of the 3D Stretch-Bending
Process. e basic principle of multipoint flexible forming of profiles is to bend the profiles in horizontal and vertical directions, respectively. Since the contact between the profile and multipoint dies is not continuous, the multipoint dies can be moved and rotated in both horizontal and vertical planes. erefore, there is greater flexibility and diversity for forming a target envelope surface in space. e steps of three-dimensional multipoint stretch-bending processing are shown in Figure 1. M h and M v represent the bending moments in the horizontal and vertical planes, respectively. T 1 and T 2 represent the axial tensile forces in the horizontal and vertical planes, respectively.
(1) Profile in the y-z plane: adjust the position parameters of each flexible unit of the multipoint dies to form the desired horizontal envelope surface (2) Prestretching: under the tensile action of the axial force of the clamp, the profile is stretched to the plastic state, and the purpose of the pre-stretching is to effectively reduce the springback defect of the three-dimensional of profiles, and the prestretching amount is generally 0.5%-1% (3) Horizontal bending deformation in the y-z plane: the profile is pulled by the clamp in the horizontal y-z plane, so that the profile gradually abuts the horizontal envelope surface formed by the multi-point dies (Figure 1(a)) (4) Vertical bending deformation in the x-z plane: after the horizontal bending in the y-z plane is completed, the profile is pulled along the x-axis under the traction of the clamp (Figure 1(b)) (5) Post-Stretching: after the horizontal and vertical bending processes are completed, the deformed profile is further stretched under the traction of the clamp, so that the spring back defect of the formed part can be more effectively reduced, and the amount of poststretching is generally 0.5%-0.8%

Material
Model. Aluminum alloy materials are widely used in the railway industry and automotive fields due to their good mechanical properties and low density. In the finite element model, the material used was a 6005A aluminum alloy. In order to accurately describe the change of cross-sectional area during large deformation, it is necessary to use true strain (ε true ) and true stress (σ true ). eir conversion formula between nominal strain and nominal stress is as follows: e rectangular profile with a length of 3600 mm has a cross-section dimension of 40 × 30 mm and a wall thickness of 2 mm. e length of the curved portion is 2840 mm, and isotropic is assumed for the profile material. e stress-strain relationship of the material constitutive is expressed as e mechanical properties of the material follow the Mises yield criterion and the Prandtl-Ruess flow rule. Yield strength (σ y ) is 260 Mpa, elastic modulus (E) is 70 Gpa, Poisson's ratio (]) is 0.3, density (ρ) is 2.71 g cm − 3 , and friction coefficient is 0.15. Intensity factor (K) is 398.87 MPa, and strain enhancement index (n) is 0.154.

Establishment of the Finite Element Model.
e numerical simulation of 3D stretch-bending is performed using ABAQUS/Explicit. Because the geometry of the profile and the operation of the forming process are symmetrical, the 1/2 model is used for analysis. e total model consists of profiles, clamps, multipoint dies, and limit screws. e clamps are used to apply tension and bending moments. Limit screws control the displacement of the profile by limiting the displacement of the clamp [15,16]. e threedimensional stretch-bending of aluminum profiles during the simulation process is a three-dimensional simulation problem, which will cause grid distortion. According to the principle of solid element selection, the solid element C3D8R can be selected for the aluminum profile. C3D8R is a hexahedral linearly reduced integral solid element with 8 nodes for large strain and deformation. Multipoint dies, limit screws, and clamps are modeled using the rigid unit R3D4, since the rigid unit is mainly used to simulate very strong components that can be either fixed or moving. Since the rigid body unit does not calculate the unit hierarchy in the simulation calculation, the calculation time can be significantly shortened. e classical Coulomb model is chosen to represent the interface friction condition σ f � μ|σ n |, in which σ f is the friction stress and μ is the friction coefficient and the σ n is the positive pressure. e assembled 3D flexible stretch-bending model is shown in Figures 2(a) and 2(b) is the result after the profile completed three-dimensional stretch-bending. A schematic diagram of horizontal and vertical bending is shown in Figure 3. Figure 3(a) shows a horizontal bending process and α represents an angle of horizontal bending. Figure 3(b) shows a vertical bending process, and β represents a vertical bending angle. e trajectory of the clamp is as follows: Horizontal bending: Vertical bending: Poststretching: x � δ po sin β, Here, L is the length of the profile, δ pre is the value of prestretching, R is the horizontal bending radius, R1 is the vertical bending radius, α is the horizontal bending angle, r is the vertical bending radius, β is the vertical bending angle, L2 represents the length of the profile projected in the vertical plane, L1 is the projection length of the contact part between the profile and the multipoint dies in the vertical plane, and δ po is the value of poststretching.

Study on the Section Distortion of Rectangular Profiles during Horizontal and Vertical Bending.
e section is distorted during the bending of rectangular section profile, and the distortion of rectangular section is usually the depression of outer web and bulging of the side wall. e distortion of rectangular section profile can be represented by the depression rate and bulging rate of the rectangular section.
e schematic diagram is shown in Figure 4. In Figure 4, B 0 represents the length of the rectangular section before deformation, B represents the length of the rectangular section after deformation, H 0 represents the height of the rectangular section before deformation, and H represents the height of the rectangular section after deformation. (B − B 0 )/B indicates the bulging rate, and (H − H 0 )/H indicates the depression rate [17,18]. e variation of depression rate and bulging rate with the bending angle and the type of bulging rate has been studied [19]. When the horizontal bending is completed, the distortion of cross section is shown in Figure 4(a). When the vertical bending is completed, the cross section of the rectangular profile is distorted as shown in Figure 4(b). And Figure 5(a) shows the numerical simulation results which show the aluminum profile that completed three groups of numerical simulations which are α � 20°β � 0°, α � 25°β � 0°, and α � 30°β � 0°. Figure 5(b) shows the results of numerical simulation which show the aluminum profile that completed three groups of numerical simulations which are α � 30°β � 20°, α � 20°β � 30°, and α � 25°β � 25°. e variation of the distortion rate of the rectangular profile completed the horizontal bending of 10°, 15°, 20°, 25°, and 30°as shown in Figure 6. With the increase in horizontal bending angle, the depression rate and bulging rate of the rectangular section gradually increase.

Distortion Rate Change of Rectangular Section after 3D
Stretch-Bending. Numerical simulation of α and β was carried out at different angles. e depression rate of rectangular profile after horizontal and vertical bending is shown in Table 1, and the bulging rate is shown in Table 2.
e depression rate after the rectangular profile completed poststretching is shown in Table 3, and the bulging rate is shown in Table 4. e results show that when the horizontal bending is completed, the depression rate and bulging rate of section have increased with the bending angle; when the vertical bending angle is less than 15°, the depression rate has a certain degree recovery. e vertical bending causes the form of distortion to change; the depression rate and bulging rate both increase with the increase in vertical bending angle. e depression rate and bulging rate increase slightly during the poststretching stage.
e processing device of 3D multipoint stretch-bending is shown in Figure 7. In this paper, the profile used in the front frame of high-speed rail train is chosen as the experimental part, and the experimental study is carried out. e depression rate of the section when the vertical bending is completed is shown in Table 5, and the bulging rate of the section when the vertical bending is completed is shown in Table 6. e depression rate of the rectangular cross section at the time of completion of poststretching is as shown in Table 7, and the bulging rate is as shown in Table 8.
e comparison between the experimental data and the numerical simulation data is shown in Figure 8. e deviation between the simulated data and the experimental data is not large. Also, the numerical simulation data is close to the actual situation of the actual processing and has certain credibility.   Mathematical Problems in Engineering

Machine Learning Determines the Range of Horizontal and Vertical Bending Angles that Match Different Forming
Accuracies. e machine learning method is a method of using probabilistic statistical means to learn the probability distribution or classification of the data from known smallscale samples and then predict the unknown sample points. SVM (Support Vector Machine) is a machine learning method based on the minimization of statistical theory and structural risk, which can effectively solve some defects of neural networks. SVM can solve the regression problem, classification problem, and clustering problem. It is a regression problem to predict the boundary of different machining precisions of aluminum profiles in the threedimensional bending process. e support vector machine used for regression prediction is called SVR (Support Vector Regression). SVR can obtain good statistical laws and generalization ability when the sample data are small. It has been widely used in the field of regression prediction.
For the linear indivisible problem of the distortion rate data of the rectangular profile, that is, the positive and negative samples cannot be separated by a straight line, and the SVR is solved by using a kernel function. e common kernel functions include a linear kernel and an RBF core, as shown in Table 9.
e results of finite element numerical simulation show that the variation of the depression rate is more obvious and the range of bulging rate is not obvious. erefore, the depression rate is used as the main index of machine learning. Different kernel functions contain different parameters. In this paper, the RBF kernel function, that is, Gaussian kernel, is selected, and its parameter "g" (g∈[0.005, 0.2]) and penalty parameter "c" (c∈[0.1, 10]) are grid search analysis. e six comparison graphs show the difference between the prediction results of the different parameters on the training set and the training set as shown in Table 10, wherein the green curve is the result of the profile depression rate normalized to [− 1, 1] which is the finite element analysis model above that finished different angles horizontal bending and vertical bending, and the red curve is the prediction of the distortion rate of the SVR according to different bending angles, and the horizontal and vertical angles correspond to the green curve one by one. Although most of them can basically restore the general trend, the parameter group c � 1.5 and g � 0.05 can better show the details of the change, and the correlation coefficient is the highest. erefore, SVR, with the parameter group Gaussian kernel, is selected to expand the MPSB finite element numerical simulation data.
Bulgi ng rate α β Simulated data Experimental data (d) Figure 8: Comparison between the experimental data and the numerical simulation data.
Tanh is a hyperbolic tangent function, β > 0, θ < 0  Mathematical Problems in Engineering is paper uses the LIBSVM software package to implement SVM regression prediction. It not only provides executable files under the compiled Windows series system but also provides source code for easy modification and improvement.
In the actual processing process, the parts will choose different processing precision according to the use. Drawing the quality control curve will help the workers to judge the quality of the processed profiles. Using the finite element simulation results to plot the allowable range of horizontal bending and vertical bending angles under different forming precisions will be of great significance for guiding production. e reasonable data extended by machine learning determine the boundary of the depression rate less than 2%, 2.5%, and 3%, as shown in Figure 9, and the workers can process according to the range in the figure during actual production. (1) In this paper, the distortion rate of rectangular section profiles is studied in the flexible three-dimensional multipoint bending process. e numerical simulation is used to obtain the variation law of the distortion rate of the rectangular profile during  the horizontal and vertical bending processes and the variation of the distortion: the depression rate and the bulging rate of the rectangular section increase with the increase of the bending angle during the horizontal bending process; when the vertical bending angle is small, the depression rate can be reduced to a certain extent, and the depression rate and the bulging rate of the rectangular section after vertical bending also increase with the increase of the vertical bending angle (2) Extend the limited data by machine learning, and find the range of horizontal and vertical bending angles corresponding to the distortion rate less than 2%, greater than 2%, less than 2.5%, greater than 2.5%, less than 3%, and greater than 3% in the plane. Make a quality control curve that is instructive for production.

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