# One-Time Roll-Forming Technology for High-Strength Steel Profiles with “日” Section

Authors: Jicai Liang; Chuandong Chen; Ce Liang; Yi Li; Guangyi Chen; Xiaoming Li; Aicheng Wang
Journal: Advances in Materials Science and Engineering
 (2019)

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## Abstract

Roll forming is an important processing method for the production of commercial vehicle anticollision beams, and edge buckling is one of the common defects in roll-forming process. In this paper, the “日” shape section of roll forming is studied, and first the b-shaped section is formed by roll forming, and the internal weld line is automatically welded while forming; then the long side of the b-shaped section is bent into the “U” shape, and the external weld line is welded while forming. The profile is cut off and then bent at both ends to form a commercial vehicle anticollision beam. The ABAQUS finite element software is used to model and analyze the factors affecting the “edge buckling” defect of roll-formed products. This paper uses three factors and three levels of orthogonal simulation experiments to study the problem. The results show that the effect of the factors of flange height, sheet thickness, and forming speed on the formation of edge buckling is in the order of sheet thickness > flange height > forming speed. The edge buckling size of the vertical edge of b-shaped tube decreases with the increase of sheet thickness and increases with the increase of flange height.


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## Body

## 1. Introduction

Roll forming is a plastic processing method for gradually forming a metal strip into a desired product section through multi-pass rolls [1], and its schematic diagram is shown in Figure 1.Figure 1
Schematic diagram of roll forming.Roll forming has many advantages such as high production efficiency, good forming effect, and saving forming material [2]. This processing method is widely used in automobile parts, track bus brackets, oil and gas pipelines, building components, and other aspects [3]. The sheet metal is constantly subjected to complex bending and shearing forces during the forming process, which makes the forming mechanism particularly complicated, and the forming law is extremely difficult to grasp. The main defects of the formed parts are distortion, warpage, fracture, edge buckling, springback, and so on [4].By using ABAQUS finite element software for numerical simulation, it is convenient and efficient to study the forming law of roll-forming process, master the technological conditions affecting its forming effect, avoid the waste caused by “trial and error method,” effectively improve the product forming quality, and create greater production value [5]. Domestic and foreign scholars have carried out a lot of research work on this and have achieved many achievements in the aspects of roll-forming mechanism, process parameter control, and finite element simulation: Heislitz and Duggal et al. [6, 7] began to simulate the simple U-shaped channel steel by finite element method to predict the stress-strain distribution and geometric shape after forming. McClure and Li [8] used ABAQUS’s implicit algorithm to simulate the roll forming of the channel section. They compared the calculated longitudinal strain with the experimental results of Bhattacharyya and Smith [9] to demonstrate the validity of the finite element simulation. Tehrani et al. [10, 11] conducted a finite element simulation study on the phenomenon of edge buckling in the roll-forming process and found that if the bending angle of the sheet metal in the first forming process exceeded a specific limit, it would appear edge buckling in the subsequent second roll-forming process. Kim et al. [12] studied the shape of the edge of the sheet before welding. In order to ensure the weld quality of the ERW pipeline, an optimized edge shape was obtained by preprocessing the edge to ensure a good welding effect. Wang and Fei [13] studied the effect of sheet thickness, arc radius, side leg height, and bending arc length on side leg wrinkling through orthogonal simulation experiments, which provided a basis for the formulation of roll-forming process and finite element model.As an important component product of automobile, the common anticollision beam is commonly used in the shape of rectangle, U-shape, and complex section as shown in Figure2.Figure 2
Cross section of the roll forming of the traditional commercial vehicle anticollision beam.
(a)
(b)
(c)
(d)The research content of this paper is to study the roll-forming process of anticollision beam with complex “日” closed section because the section needs to be further welded after forming, the forming effect of its edge will seriously affect the next step of production, so its profile welding edge-forming accuracy is particularly important. Edge buckling is one of the common forming defects in the roll-forming process, which cannot be eliminated but can be minimized by process optimization design. In this paper, COPRA, a professional roll-forming software of German Data M Company, is used to carry out inverse modeling and analysis of roll-forming parts and their forming methods [14]. The accuracy of the simulation model is verified by simulation and experiment comparison. The section nodes of tube after forming are compared with the section of test results, so as to master the forming law of closed section. The effects of different process conditions on the edge buckling of roll forming are studied to determine the process conditions for reducing the longitudinal strain and optimize the forming scheme, so as to provide guarantee for improving the product quality.


## 2. Experimental Design

### 2.1. Experimental Method

The “日” shape section is one of the typical product shapes of automobile anticollision beam, and its section shape is shown in Figure3.Figure 3
Schematic diagram of the “日” cross section.Due to the complexity of the roll-forming process, the design of the roll flower is cumbersome and difficult to process and the processing pass is more than that of the general shape. The processing sequence is shown in Figure4.Figure 4
Processing sequence diagram of “日” shape cross-section products.The traditional “日” shape tube processing method is divided into two types: The first type is carried out in three steps: (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 baffle as shown in Figure5(a). The second is done in two steps: (1) a rectangular tube and a U-shaped tube are manufactured by roll-forming equipment and (2) the rectangular tube and the U-shaped tube are weld as shown in Figure 5(b). The welding process of the above two methods is very complex, requiring repeated welding to achieve the forming effect, which not only increases the workload of workers but also has low production efficiency and poor product quality. The mechanical properties of the products are difficult to guarantee. In this paper, one-time roll forming is used to form the anticollision beam of commercial vehicle, which is a challenging forming method, as shown in Figure 5(c). First of all, the b-shaped tube is rolled out by the roll-forming equipment and the side position is automatically welded to complete the internal weld line; then, the b-shaped tube is rolled again to make the vertical edge roll into a U-shaped tube to obtain the “日” shape tube; finally, the curved edge position is welded to complete the external weld line, as shown in Figure 5(d). This not only reduces the manufacturing process and improves the material utilization and production efficiency but also ensures the mechanical properties of the product, such as tensile strength, flexural strength, and impact toughness, because it is the roll forming-internal welding-roll forming-external welding continuous roll forming.Figure 5
(a) “日” shape tube traditional forming method I. (b) “日” shape tube traditional forming method II. (c) New roll-forming method. (d) Product photo.
(a)
(b)
(c)
(d)In this paper, the vertical edge buckling of b-shaped tube is studied. The section size of the b-shaped tube is shown in Figure6. The forming material of the b-shaped tube is the beam high strength steel B700L, which is commonly used in the automobile field. The forming angle of each pass cannot be too large, and the b-shaped tube needs to be welded automatically in time after forming. Therefore, the requirements for the accuracy of the roll-forming section, especially the “edge buckling” control accuracy, should be ensured. The product is produced on the self-invented roll-forming production line, as shown in Figure 7. The distance between rolls is 350 mm. In the roll-forming process, the lower rolls are used as the driving rolls and the upper rolls are used as the passive rolls.Figure 6
Section size of b-shaped tube.Figure 7
The diagram of roll-forming production line.


### 2.2. The Flower Pattern for b-Shaped Tube Section

Flower pattern is a cross-sectional diagram describing the roll-forming process of the sheet metal. The forming sequence of the b-shaped tube is designed by COPRA’s roll design module. As shown in Figure8, the outer side angle is first formed to 75° for 6 passes. Then, the inner corners are formed, and the inner corners are finally formed to 90 degrees for 6 passes. Finally, the remaining unformed outer corners are formed, forming 7.5° per pass for 2 passes.Figure 8
The b-shaped tube flower pattern.


### 2.3. Design of Orthogonal Experiment

In the longitudinal direction of the sheet, the strain occurring in the forming zone is different, which is easy to produce the defect of edge buckling. The standard deviationΔε of longitudinal strain of each node on the edge of channel steel is usually taken as a criterion to measure the magnitude of edge buckling. The bigger the standard deviation, the more serious the edge buckling at the edge of the forming part; the smaller the standard deviation, the smaller the edge buckling. (1) is the formula for calculating the standard deviation Δε [15].(1)Δε=1n∑i=1nεi−ε¯2,(2)ε¯=ε1+ε2+ε3+⋯+εnn,where n is the number of vertical nodes of the measurement position, εi is the longitudinal strain of each node, and ε¯ is the average value of the longitudinal strain.There are many factors that affect the buckling defects of the edge of b-shaped tube roll-forming process, among which the factors such as flange height, sheet thickness, and forming speed have a great effect on the forming defects of the sheet metal. This paper mainly investigates the effect of various factors on the edge buckling of the b-shaped tube of the high-strength beam steel B700L material during the roll-forming process. In order to ensure the rationality of the experiment, three factors and three levels are selected for the orthogonal experimental design. The flange height of the material is 60, 70, and 80 mm, the thickness of the sheet metal is 2, 2.5, and 3 mm, and the forming speed is 50, 100, and 150 mm/s. The orthogonal table of the three factors and three levels that affect the edge buckling during the b-shaped tube roll forming process is shown in Table1.Table 1
Orthogonal experimental table of 3 factors and 3 levels.
Levels
Flange heighth (mm)
Sheet thicknesst (mm)
Forming speedv (mm·s−1)
Level 1
60
2.0
50
Level 2
70
2.5
100
Level 3
80
3.0
150


## 2.1. Experimental Method

The “日” shape section is one of the typical product shapes of automobile anticollision beam, and its section shape is shown in Figure3.Figure 3
Schematic diagram of the “日” cross section.Due to the complexity of the roll-forming process, the design of the roll flower is cumbersome and difficult to process and the processing pass is more than that of the general shape. The processing sequence is shown in Figure4.Figure 4
Processing sequence diagram of “日” shape cross-section products.The traditional “日” shape tube processing method is divided into two types: The first type is carried out in three steps: (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 baffle as shown in Figure5(a). The second is done in two steps: (1) a rectangular tube and a U-shaped tube are manufactured by roll-forming equipment and (2) the rectangular tube and the U-shaped tube are weld as shown in Figure 5(b). The welding process of the above two methods is very complex, requiring repeated welding to achieve the forming effect, which not only increases the workload of workers but also has low production efficiency and poor product quality. The mechanical properties of the products are difficult to guarantee. In this paper, one-time roll forming is used to form the anticollision beam of commercial vehicle, which is a challenging forming method, as shown in Figure 5(c). First of all, the b-shaped tube is rolled out by the roll-forming equipment and the side position is automatically welded to complete the internal weld line; then, the b-shaped tube is rolled again to make the vertical edge roll into a U-shaped tube to obtain the “日” shape tube; finally, the curved edge position is welded to complete the external weld line, as shown in Figure 5(d). This not only reduces the manufacturing process and improves the material utilization and production efficiency but also ensures the mechanical properties of the product, such as tensile strength, flexural strength, and impact toughness, because it is the roll forming-internal welding-roll forming-external welding continuous roll forming.Figure 5
(a) “日” shape tube traditional forming method I. (b) “日” shape tube traditional forming method II. (c) New roll-forming method. (d) Product photo.
(a)
(b)
(c)
(d)In this paper, the vertical edge buckling of b-shaped tube is studied. The section size of the b-shaped tube is shown in Figure6. The forming material of the b-shaped tube is the beam high strength steel B700L, which is commonly used in the automobile field. The forming angle of each pass cannot be too large, and the b-shaped tube needs to be welded automatically in time after forming. Therefore, the requirements for the accuracy of the roll-forming section, especially the “edge buckling” control accuracy, should be ensured. The product is produced on the self-invented roll-forming production line, as shown in Figure 7. The distance between rolls is 350 mm. In the roll-forming process, the lower rolls are used as the driving rolls and the upper rolls are used as the passive rolls.Figure 6
Section size of b-shaped tube.Figure 7
The diagram of roll-forming production line.


## 2.2. The Flower Pattern for b-Shaped Tube Section

Flower pattern is a cross-sectional diagram describing the roll-forming process of the sheet metal. The forming sequence of the b-shaped tube is designed by COPRA’s roll design module. As shown in Figure8, the outer side angle is first formed to 75° for 6 passes. Then, the inner corners are formed, and the inner corners are finally formed to 90 degrees for 6 passes. Finally, the remaining unformed outer corners are formed, forming 7.5° per pass for 2 passes.Figure 8
The b-shaped tube flower pattern.


## 2.3. Design of Orthogonal Experiment

In the longitudinal direction of the sheet, the strain occurring in the forming zone is different, which is easy to produce the defect of edge buckling. The standard deviationΔε of longitudinal strain of each node on the edge of channel steel is usually taken as a criterion to measure the magnitude of edge buckling. The bigger the standard deviation, the more serious the edge buckling at the edge of the forming part; the smaller the standard deviation, the smaller the edge buckling. (1) is the formula for calculating the standard deviation Δε [15].(1)Δε=1n∑i=1nεi−ε¯2,(2)ε¯=ε1+ε2+ε3+⋯+εnn,where n is the number of vertical nodes of the measurement position, εi is the longitudinal strain of each node, and ε¯ is the average value of the longitudinal strain.There are many factors that affect the buckling defects of the edge of b-shaped tube roll-forming process, among which the factors such as flange height, sheet thickness, and forming speed have a great effect on the forming defects of the sheet metal. This paper mainly investigates the effect of various factors on the edge buckling of the b-shaped tube of the high-strength beam steel B700L material during the roll-forming process. In order to ensure the rationality of the experiment, three factors and three levels are selected for the orthogonal experimental design. The flange height of the material is 60, 70, and 80 mm, the thickness of the sheet metal is 2, 2.5, and 3 mm, and the forming speed is 50, 100, and 150 mm/s. The orthogonal table of the three factors and three levels that affect the edge buckling during the b-shaped tube roll forming process is shown in Table1.Table 1
Orthogonal experimental table of 3 factors and 3 levels.
Levels
Flange heighth (mm)
Sheet thicknesst (mm)
Forming speedv (mm·s−1)
Level 1
60
2.0
50
Level 2
70
2.5
100
Level 3
80
3.0
150


## 3. Material Properties

Some material parameters of beam high-strength steel B700L are shown in Table2. The mechanical properties of the material are measured by an uniaxial tensile test. Figure 9 is the stress-strain curve of the specimen obtained from the test results. Since ABAQUS requires the values of true stress and strain when inputting data, the following formulas are used to calculate the required values [16]:(3)ε=ln1+εn0m,(4)σ=σn0m1+εn0m,where ε and σ are real stress and real strain and σn0m and εn0m are nominal stress and nominal strain, respectively.Table 2
Material elastic phase properties.
Material
Young’ modulusE (GPa)
Density (kg·m−3)
Poisson’s ratiov
B700L
216
7830
0.21998Figure 9
Stress-strain curve of beam high-strength steel B700L.


## 4. Finite Element Model

### 4.1. Modeling

In this paper, ABAQUS/Explicit analysis method is used to model and analyze the roll-forming process [12]. For the convenience of research, the rolls are set as an analytical rigid body. The sheet is formed at a room temperature and a low speed and is set as a deformable body during the simulation. In order to be the same as the actual production process, the diameter of upper roll is set as 150 mm, the diameter of lower roll is set as 100 mm, and the diameter of vertical roll is set as 100 mm. The distance between the rolls is set as 350 mm, and the length of the sheets is set as 900 mm.The roll group consists of 14 passes and is divided into three parts. The first group is the guide rolls, the second group is the forming rolls, and the third group is the shaping rolls. In the last three passes of the forming rolls and the shaping rolls, the vertical rolls are used to assist the shaping. The flower patterns designed with COPRA are used to create a plan drawing of the rolls, and then the plan drawing is imported into the ABAQUS software to create three-dimensional rolls.


### 4.2. Contacts and Boundary Conditions

There are many choices for the feeding method of the sheet. In this paper, a constant speed is set at the front end of the sheet, and the angular velocity is applied by the driving rolls. This method has a long calculation time and the calculation results are accurate. Considering the actual forming process, the calculation time is too long for the selection of the feeding speed of the sheet metal, if the simulation is based on the forming speed of the actual product. The excessive speed setting will lead to slippage between the sheet metal and rolls, which will lead to inaccurate calculation results. In the simulation experiment, the line speed V of the sheet metal in this paper is selected as 50–300 mm/s, and the angular velocity of the lower roll is obtained by the formulav=ωr. In order to simulate the actual production process as much as possible, the rolls retain only their degrees of freedom in the direction of rotation, and the remaining degrees of freedom are controlled. The general contact between the sheet metal and rolls is adopted, and the friction coefficient is set to 0.2 [17]. Figure 10 is the assembly drawing of the roll bending model of the b-shaped tube.Figure 10
Assembly drawing of finite element model for roll forming of b-shaped tube.


### 4.3. Element Type and Meshing

In the process of finite element analysis of roll forming, the commonly used elements are SC4R, SC8R, C3D8R, and so on [13]. In this numerical simulation analysis, the edge buckling analysis of the b-shaped tube’s vertical edge is performed. While saving calculation time and improving calculation accuracy, SC4R shell element [8] is selected in this paper. In the direction of sheet width, the mesh refinement element size at bend angle is set to 3 mm, the element size at flange and web is set to 10 mm, the element size in length direction is set to 15 mm, and the element size in thickness direction is set to 9 integral points. The meshing situation is shown in Figure 11.Figure 11
Meshing of b-shaped tube sheet.


### 4.4. Comparison of Simulation Results with Experimental Results

In order to verify the validity of the simulation results, this paper takes the sheet flange height of 70 mm, the thickness of 2.5 mm, and the forming speed of 150 mm/s as an example. The upper part of the side is selected for longitudinal strain analysis. The results show that the simulation results are basically consistent with the experimental results, as shown in Figure12.Figure 12
Experimental and simulation comparison of flange top joints.


## 4.1. Modeling

In this paper, ABAQUS/Explicit analysis method is used to model and analyze the roll-forming process [12]. For the convenience of research, the rolls are set as an analytical rigid body. The sheet is formed at a room temperature and a low speed and is set as a deformable body during the simulation. In order to be the same as the actual production process, the diameter of upper roll is set as 150 mm, the diameter of lower roll is set as 100 mm, and the diameter of vertical roll is set as 100 mm. The distance between the rolls is set as 350 mm, and the length of the sheets is set as 900 mm.The roll group consists of 14 passes and is divided into three parts. The first group is the guide rolls, the second group is the forming rolls, and the third group is the shaping rolls. In the last three passes of the forming rolls and the shaping rolls, the vertical rolls are used to assist the shaping. The flower patterns designed with COPRA are used to create a plan drawing of the rolls, and then the plan drawing is imported into the ABAQUS software to create three-dimensional rolls.


## 4.2. Contacts and Boundary Conditions

There are many choices for the feeding method of the sheet. In this paper, a constant speed is set at the front end of the sheet, and the angular velocity is applied by the driving rolls. This method has a long calculation time and the calculation results are accurate. Considering the actual forming process, the calculation time is too long for the selection of the feeding speed of the sheet metal, if the simulation is based on the forming speed of the actual product. The excessive speed setting will lead to slippage between the sheet metal and rolls, which will lead to inaccurate calculation results. In the simulation experiment, the line speed V of the sheet metal in this paper is selected as 50–300 mm/s, and the angular velocity of the lower roll is obtained by the formulav=ωr. In order to simulate the actual production process as much as possible, the rolls retain only their degrees of freedom in the direction of rotation, and the remaining degrees of freedom are controlled. The general contact between the sheet metal and rolls is adopted, and the friction coefficient is set to 0.2 [17]. Figure 10 is the assembly drawing of the roll bending model of the b-shaped tube.Figure 10
Assembly drawing of finite element model for roll forming of b-shaped tube.


## 4.3. Element Type and Meshing

In the process of finite element analysis of roll forming, the commonly used elements are SC4R, SC8R, C3D8R, and so on [13]. In this numerical simulation analysis, the edge buckling analysis of the b-shaped tube’s vertical edge is performed. While saving calculation time and improving calculation accuracy, SC4R shell element [8] is selected in this paper. In the direction of sheet width, the mesh refinement element size at bend angle is set to 3 mm, the element size at flange and web is set to 10 mm, the element size in length direction is set to 15 mm, and the element size in thickness direction is set to 9 integral points. The meshing situation is shown in Figure 11.Figure 11
Meshing of b-shaped tube sheet.


## 4.4. Comparison of Simulation Results with Experimental Results

In order to verify the validity of the simulation results, this paper takes the sheet flange height of 70 mm, the thickness of 2.5 mm, and the forming speed of 150 mm/s as an example. The upper part of the side is selected for longitudinal strain analysis. The results show that the simulation results are basically consistent with the experimental results, as shown in Figure12.Figure 12
Experimental and simulation comparison of flange top joints.


## 5. Results and Discussion

### 5.1. Analysis of Simulation Results

According to the process described in the previous sections, it can be concluded from the postprocessing of the model that along the roll-forming direction, the edge of the sheet has a longitudinal strain and the shear strain is formed along the sheet forming direction of the roll bending, as well as the transverse strain along the transverse direction of the sheet. Taking the sheet metal flange height of 70 mm, thickness of 2.5 mm, and forming speed of 150 mm/s as an example, Figure13(a) is Mises stress diagram of “b” tube. It can be seen that the stress distribution of the whole tube is not uniform, but the overall trend is that the closer to the bend, the greater the stress of the tube, which can be illustrated by the transverse stress distribution of the sheet in Figure 13(b). Figure 13(c) is the equivalent plastic strain diagram of the b-shaped tube. It is shown that the strain of the tube mainly occurs at the bend corner as shown in the transverse strain distribution diagram of the sheet in Figure 13(d). And the cause of edge buckling at flange is closely related to stress and strain.Figure 13
(a) Mises stress distribution diagram of b-shaped tube. (b) Transverse stress of the sheet metal. (c) Equivalent strain distribution diagram of b-shaped tube. (d) Transverse strain of the sheet metal.
(a)
(b)
(c)
(d)


### 5.2. Mechanism Analysis of Buckling Defect at Vertical Edge of b-Shaped Tube

From the simulation results, it can be seen that the front flange of the tube tends to move inward, as shown in Figure14. This is due to the complex deformation force when the sheet metal is bitten by the rolls in the process of roll forming. Therefore, in order to ensure the accuracy of the simulation results, the strain at the flange is measured at 100–800 mm along the length direction of the sheet metal. As shown in Figure 15, the longitudinal strain distributions of the top, middle, and bottom nodes of the flange can be seen as follows: the top of the flange > the middle of the flange > the bottom of the flange. It can be seen from Figure 15 that the curve of the top nodes of the flange is more fluctuating than the curve of the middle and bottom nodes, indicating that the longitudinal strain distribution at the top of the flange is the most uneven and the longitudinal strain distribution at the bottom of the flange is the most uniform. Therefore, edge buckling is very easy to occur at the top of the flange.Figure 14
Front shape of b-tube.Figure 15
Curves of longitudinal strain of flange nodes varying with longitudinal distance.Comparing the longitudinal strain curves of flange, it can be concluded that when the longitudinal strain is greater than 0, the sheet extends longitudinally, and when the longitudinal strain is less than 0, the sheet is compressed longitudinally. Because of the combined effect of stress and strain, edge buckling occurs at the flange of the sheet metal.


### 5.3. Analysis of Orthogonal Experiments of Vertical Edge Buckling of b-Shaped Tube

In this paper, B700L high-strength beam steel is used for simulation experiments, and three representative factors are selected, which are flange height, sheet thickness, and forming speed. A three-factor, three-level orthogonal experiment is designed with a total of nine experiments. The experimental results and result analysis are shown in Table3.Table 3
Orthogonal experiment results and result analysis.
Simulation number
Flange heighth (mm)
Sheet thicknesst (mm)
Forming speedv (mm·s−1)
Δ
ε
1
60 (h1)
2.0 (t1)
50 (v1)
1.62 × 10−4
2
60 (h1)
2.5 (t2)
100 (v2)
2.80 × 10−4
3
60 (h1)
3.0 (t3)
150 (v3)
5.01 × 10−4
4
70 (h2)
2.0 (t1)
100 (v2)
2.55 × 10−4
5
70 (h2)
2.5 (t2)
150 (v3)
3.67 × 10−4
6
70 (h2)
3.0 (t3)
50 (v2)
6.92 × 10−4
7
80 (h3)
2.0 (t1)
150 (v3)
2.35 × 10−4
8
80 (h3)
2.5 (t2)
50 (v1)
4.25 × 10−4
9
80 (h3)
3.0 (t3)
100 (v2)
5.13 × 10−4From the analysis of the experimental results in Table3, it can be seen that in nine experiments of orthogonal design for roll forming of b-shaped tube, the standard deviation of longitudinal strain at the top of flange of Exp. 6 is the largest, which is 6.92 × 10−4; the standard deviation of Exp. 1 is the smallest, which is 1.62 × 10−4. In order to make the experimental results more intuitive, this paper selects the intermediate values of two longitudinal strain standard deviations, Exp. 2 and Exp. 3, and compares with Exp. 1 and Exp. 6, as shown in Figure 16. By comparing the characteristics of each curve, it can be concluded that the maximum longitudinal strain fluctuation at the top of the flange is Exp. 6 and its flange edge buckling is the most serious; the result of the Exp. 1 is the smallest longitudinal strain fluctuation amplitude and the minimum edge buckling. Therefore, the magnitude of the longitudinal strain fluctuation at the flange is closely related to the severity of edge buckling.Figure 16
Longitudinal strain curves of the sheet metal along longitudinal position in Exp. 1, 2, 3, and 6.Table4 shows the results of the Δε values of the results of the respective experiments. The experimental values Δε corresponding to each factor at different levels are summed up, and then the average value is obtained and the range analysis is made. It can be seen from the data in the table that the effect degree of each factor on the side wave is the sheet thickness > flange height > forming speed. Therefore, for the material properties of a certain high-strength beam steel B700L sheet, the sheet thickness and flange height have a greater impact on the edge buckling of the flange of the b-shaped tube, whereas the effect of the forming speed is smaller. In order to further explore the effect of sheet thickness and flange height on edge buckling, a comparative experiment is designed in this paper.Table 4
Range analysis of orthogonal experimental results.
Δ
ε
Flange height (h)
Sheet thickness (t)
Forming speed (v)
k
1
3.14 × 10−4
2.17 × 10−4
4.27 × 10−4
k
2
4.37 × 10−4
3.57 × 10−4
3.50 × 10−4
k
3
4.00 × 10−4
5.60 × 10−4
3.67 × 10−4
RangeR
1.23 × 10−4
3.43 × 10−4
0.77 × 10−4


### 5.4. Additional Experimental Results and Analysis

In order to further explore the effect of sheet metal thickness and flange height on the flange edge buckling of “b” tube, two sets of comparative simulation experiments are designed in this paper. Based on the simulation results of the orthogonal experiment, the first experimental design is carried out under the condition of flange heighth = 60 and forming speed v = 100 mm/s. The variables are sheet metal thickness, which is set as 2, 2.5, 3, and 3.5 mm, respectively. The second experimental design is carried out under the condition of sheet thickness t = 2.5 mm and forming speed v = 100 mm/s, and the variables are flange height, which are 65, 70, 75, and 80 mm, respectively. The experimental results are shown in Figure 15. Figure 17(a) shows that the longitudinal strain at the flange increases with the increase of flange height. Figure 17(b) shows that as the thickness of the sheet increases, the longitudinal strain at the flange is also getting smaller and smaller. It can be seen that the edge buckling at the flange increases with the increase of flange height and decreases with the increase of plate thickness.Figure 17
(a) Effect of flange height on longitudinal strain. (b) Effect of sheet thickness on longitudinal strain.
(a)
(b)


## 5.1. Analysis of Simulation Results

According to the process described in the previous sections, it can be concluded from the postprocessing of the model that along the roll-forming direction, the edge of the sheet has a longitudinal strain and the shear strain is formed along the sheet forming direction of the roll bending, as well as the transverse strain along the transverse direction of the sheet. Taking the sheet metal flange height of 70 mm, thickness of 2.5 mm, and forming speed of 150 mm/s as an example, Figure13(a) is Mises stress diagram of “b” tube. It can be seen that the stress distribution of the whole tube is not uniform, but the overall trend is that the closer to the bend, the greater the stress of the tube, which can be illustrated by the transverse stress distribution of the sheet in Figure 13(b). Figure 13(c) is the equivalent plastic strain diagram of the b-shaped tube. It is shown that the strain of the tube mainly occurs at the bend corner as shown in the transverse strain distribution diagram of the sheet in Figure 13(d). And the cause of edge buckling at flange is closely related to stress and strain.Figure 13
(a) Mises stress distribution diagram of b-shaped tube. (b) Transverse stress of the sheet metal. (c) Equivalent strain distribution diagram of b-shaped tube. (d) Transverse strain of the sheet metal.
(a)
(b)
(c)
(d)


## 5.2. Mechanism Analysis of Buckling Defect at Vertical Edge of b-Shaped Tube

From the simulation results, it can be seen that the front flange of the tube tends to move inward, as shown in Figure14. This is due to the complex deformation force when the sheet metal is bitten by the rolls in the process of roll forming. Therefore, in order to ensure the accuracy of the simulation results, the strain at the flange is measured at 100–800 mm along the length direction of the sheet metal. As shown in Figure 15, the longitudinal strain distributions of the top, middle, and bottom nodes of the flange can be seen as follows: the top of the flange > the middle of the flange > the bottom of the flange. It can be seen from Figure 15 that the curve of the top nodes of the flange is more fluctuating than the curve of the middle and bottom nodes, indicating that the longitudinal strain distribution at the top of the flange is the most uneven and the longitudinal strain distribution at the bottom of the flange is the most uniform. Therefore, edge buckling is very easy to occur at the top of the flange.Figure 14
Front shape of b-tube.Figure 15
Curves of longitudinal strain of flange nodes varying with longitudinal distance.Comparing the longitudinal strain curves of flange, it can be concluded that when the longitudinal strain is greater than 0, the sheet extends longitudinally, and when the longitudinal strain is less than 0, the sheet is compressed longitudinally. Because of the combined effect of stress and strain, edge buckling occurs at the flange of the sheet metal.


## 5.3. Analysis of Orthogonal Experiments of Vertical Edge Buckling of b-Shaped Tube

In this paper, B700L high-strength beam steel is used for simulation experiments, and three representative factors are selected, which are flange height, sheet thickness, and forming speed. A three-factor, three-level orthogonal experiment is designed with a total of nine experiments. The experimental results and result analysis are shown in Table3.Table 3
Orthogonal experiment results and result analysis.
Simulation number
Flange heighth (mm)
Sheet thicknesst (mm)
Forming speedv (mm·s−1)
Δ
ε
1
60 (h1)
2.0 (t1)
50 (v1)
1.62 × 10−4
2
60 (h1)
2.5 (t2)
100 (v2)
2.80 × 10−4
3
60 (h1)
3.0 (t3)
150 (v3)
5.01 × 10−4
4
70 (h2)
2.0 (t1)
100 (v2)
2.55 × 10−4
5
70 (h2)
2.5 (t2)
150 (v3)
3.67 × 10−4
6
70 (h2)
3.0 (t3)
50 (v2)
6.92 × 10−4
7
80 (h3)
2.0 (t1)
150 (v3)
2.35 × 10−4
8
80 (h3)
2.5 (t2)
50 (v1)
4.25 × 10−4
9
80 (h3)
3.0 (t3)
100 (v2)
5.13 × 10−4From the analysis of the experimental results in Table3, it can be seen that in nine experiments of orthogonal design for roll forming of b-shaped tube, the standard deviation of longitudinal strain at the top of flange of Exp. 6 is the largest, which is 6.92 × 10−4; the standard deviation of Exp. 1 is the smallest, which is 1.62 × 10−4. In order to make the experimental results more intuitive, this paper selects the intermediate values of two longitudinal strain standard deviations, Exp. 2 and Exp. 3, and compares with Exp. 1 and Exp. 6, as shown in Figure 16. By comparing the characteristics of each curve, it can be concluded that the maximum longitudinal strain fluctuation at the top of the flange is Exp. 6 and its flange edge buckling is the most serious; the result of the Exp. 1 is the smallest longitudinal strain fluctuation amplitude and the minimum edge buckling. Therefore, the magnitude of the longitudinal strain fluctuation at the flange is closely related to the severity of edge buckling.Figure 16
Longitudinal strain curves of the sheet metal along longitudinal position in Exp. 1, 2, 3, and 6.Table4 shows the results of the Δε values of the results of the respective experiments. The experimental values Δε corresponding to each factor at different levels are summed up, and then the average value is obtained and the range analysis is made. It can be seen from the data in the table that the effect degree of each factor on the side wave is the sheet thickness > flange height > forming speed. Therefore, for the material properties of a certain high-strength beam steel B700L sheet, the sheet thickness and flange height have a greater impact on the edge buckling of the flange of the b-shaped tube, whereas the effect of the forming speed is smaller. In order to further explore the effect of sheet thickness and flange height on edge buckling, a comparative experiment is designed in this paper.Table 4
Range analysis of orthogonal experimental results.
Δ
ε
Flange height (h)
Sheet thickness (t)
Forming speed (v)
k
1
3.14 × 10−4
2.17 × 10−4
4.27 × 10−4
k
2
4.37 × 10−4
3.57 × 10−4
3.50 × 10−4
k
3
4.00 × 10−4
5.60 × 10−4
3.67 × 10−4
RangeR
1.23 × 10−4
3.43 × 10−4
0.77 × 10−4


## 5.4. Additional Experimental Results and Analysis

In order to further explore the effect of sheet metal thickness and flange height on the flange edge buckling of “b” tube, two sets of comparative simulation experiments are designed in this paper. Based on the simulation results of the orthogonal experiment, the first experimental design is carried out under the condition of flange heighth = 60 and forming speed v = 100 mm/s. The variables are sheet metal thickness, which is set as 2, 2.5, 3, and 3.5 mm, respectively. The second experimental design is carried out under the condition of sheet thickness t = 2.5 mm and forming speed v = 100 mm/s, and the variables are flange height, which are 65, 70, 75, and 80 mm, respectively. The experimental results are shown in Figure 15. Figure 17(a) shows that the longitudinal strain at the flange increases with the increase of flange height. Figure 17(b) shows that as the thickness of the sheet increases, the longitudinal strain at the flange is also getting smaller and smaller. It can be seen that the edge buckling at the flange increases with the increase of flange height and decreases with the increase of plate thickness.Figure 17
(a) Effect of flange height on longitudinal strain. (b) Effect of sheet thickness on longitudinal strain.
(a)
(b)


## 6. Conclusion

In this paper, COPRA is used for pass design, ABAQUS is used for finite element modeling and analysis, and orthogonal experiments and comparative experiments are designed to study the roll-forming law of the b-shaped tube, which provides theoretical basis for the production of “日” shape tube. The conclusions are as follows:(1)
Compared with the traditional roll-forming method, the application of new roll-forming technology in this paper not only improves the material utilization rate and production efficiency but also ensures the mechanical properties of the products, such as tensile strength, bending strength, and impact toughness.(2)
For high-strength beam steel B700L sheet, flange height, sheet thickness, and forming speed all effect the generation of edge buckling in the roll-forming process. When the standard deviationΔε of longitudinal strain is taken as the evaluation criterion, the effect degree of each factor on the formation of edge buckling is sheet thickness > flange height > forming speed.(3)
The comparative experimental results show that the edge buckling of the vertical edge of the b-shaped tube decreases with the increase of the thickness of the sheet metal and increases with the increase of the flange height. The effect of forming speed on edge buckling of the sheet metal is small.



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*Source: 6505914-2019-09-22.xml*