A study on the springback in the sheet metal flange drawing

Journal of Materials Processing Technology 187–188 (2007) 89–93

A study on the springback in the sheet metal flange drawing Sang-Wook Lee a,∗ , Yoon-Tae Kim b a

Department of Mechanical Engineering, Soonchunhyang University, Asan, Chungnam 336-745, South Korea b Kyungshin Industrial Co. Ltd., 994-13 Dongchun 2, Yeonsu, Incheon 406-130, South Korea

Abstract The flange drawing process is used to make flanges from the sheet metal blank using the die, punch and blank holder optionally with the supporter. This process is being applied in many sheet metal industries. One of concerns of this process is that the flanged section formed is mostly not parallel with the original blank due to the springback occurrence, which could affect the quality of the formed part. This study has focused on the evaluation of springback occurring in the sheet metal flange drawing process by controlling some process factors like the punch corner radius (PR) and die corner radius (DR), the blank-holding-force (BHF), the supporting-force (SF), the lubrication and so on. The springback phenomenon in the flange drawing process has been studied first using the finite element method (FEM) in order to understand what the main causes of springback are. The distribution pattern of local x-component of stress along the longitudinal direction of the blank has been revealed to be very important in predicting the final shape of the flange. This fact has been backed up by the experimental results carried out with the developed test dies. The Taguchi table L18 has been used to determine which of the process factors of the flange drawing is the most influencing to make the flanged section parallel with the original blank in spite of springback occurrence. The results show that the punch corner radius (PR) is the most important factor of the process. © 2006 Elsevier B.V. All rights reserved. Keywords: Flange drawing; Springback; Taguchi method

1. Introduction The flange drawing process is used widely to make flanges from the sheet metal blank using the die, punch and blank holder optionally with the supporter. As shown in Fig. 1, while the blank is firmly gripped with the blank holder and the die, the punch moves down to make flange. The supporter could be used to keep the flange section as flat as possible during the process to obtain a flange with higher flatness. When the die set is removed the formed blank experiences springback to result in the change of angle of the flange section, which is considered as a representative indicator showing the effect of the residual stress in the blank because springback phenomenon occurs due to the redistribution of internal stress of the blank. Various process factors of the flange drawing can affect the springback. It is very important to find out the most influencing process factor on springback to design a successful die set for the flange drawing.

∗

Corresponding author. Tel.: +82 41 530 1356; fax: +82 41 530 1550. E-mail address: [email protected] (S.-W. Lee).

0924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.11.079

In this work, several process factors have been first chosen by carrying out some finite element analyses with related experiments. Secondly, these factors have been assessed comprehensively by the Taguchi method.

2. Finite element modeling Fig. 2 shows a finite element model for the flange drawing process. The commercial code LS-DYNA3D was used for the simulation. It is assumed that the blank is under the plane strain condition because of relatively very large width compared with the thickness of the blank. The blank was modeled with Belytschko-Tsay shell elements while the die set was modeled with rigid elements. Seven integration points are allocated along the thickness direction of the blank to take up bending deformation effectively. The blank-holding-force (BHF) and the supporting-force (SF) are applied to the model in the form of concentrated forces on nodes. Three types of corner radii, 3, 6 and 9 mm, are used to describe the die corner (DR) and the punch corner (PR) for the purpose of comparison. The number of elements used to depict the corner radii was determined from the guidelines of Ref. [1]. The material for the blank is

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S.-W. Lee, Y.-T. Kim / Journal of Materials Processing Technology 187–188 (2007) 89–93

Fig. 1. A schematic drawing showing the configuration of the flange drawing process. Fig. 3. Illustrative drawing of the expected path of the local x-component of stress of the blank element during the forming stage.

Fig. 2. Finite element model for the flange drawing process.

SUS316L. Table 1 shows the material properties of SUS316L and the process parameters used in the simulation. An expected path of the local x-component of stress for an element of the blank during the forming stage is shown in Fig. 3 [2]. A light-stretching mode occurs at the interval of A to B as the blank starts to deform. When the element of the blank enters into the die corner zone, bending deformation takes place. The

stress on its upper surface rises up to the point C during bending. Unbending follows just after the bending mode finishes at about the halfway point along the die corner to cause the sign reversal of the local stress (from C to D). The stress relaxation caused by stress waves coming out from the bending and unbending events at the die corner takes place at the interval of D to E [3]. The stress distribution over the entire elements of the blank at a specific process time can be obtained from the information of the elements’ position in the die set since the local stresses of all the elements in the blank move along the stress path as shown in Fig. 3. Thus, the stress distribution just after the forming stage is considered the most important because the shape by springback depends only on the internal stress state. 3. Representative cases of springback 3.1. Case 1: PR = DR and BHF = SF A schematic drawing showing the expected deformed configuration and the sign of stress at the outer surface of the blank

Table 1 Process parameters and material properties used in the finite element simulation Process parameters

Value/condition

Max. Punch stroke

30 mm

Punch velocity

1000 mm/s (in analysis) 0.25 mm/s (in experiment)

Blank-holding-force and supporting-force per unit width

50 N (total: 1.75 kN) 100 N (total: 3.5 kN) 200 N (total: 7.0 kN)

Initial blank size Initial blank thickness

35.0 mm × 173 mm 0.6 mm

Material: SUS316L Young’s modulus (E) Poisson’s ratio (ν) Lankford value (R) Yield stress (σ y ) Stress–strain curve

185.232 GPa 0.3 1.81 230.157 MPa σ = K(εo + εp )n : εo = 0.022638, K = 1257.614 MPa, n = 0.4483

S.-W. Lee, Y.-T. Kim / Journal of Materials Processing Technology 187–188 (2007) 89–93

Fig. 4. A schematic diagram showing the expected deformed configuration and the signs of stress at the outer surface of the blank just after the forming stage when PR = DR and BHF = SF.

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Fig. 7. A schematic diagram showing the expected deformed configuration and the signs of stress at the outer surface of the blank just after the forming stage when PR < DR and BHF = SF.

be inferred. Fig. 6 shows the deformed shape before and after springback by computation with the experimental result. The computed shape of after springback is seen very well coincident with that of the experiment. It is notable that the two flat sections of the blank keep almost parallel with each other regardless of springback, meanwhile the wall region undergoes geometric change to become z-shaped configuration due to springback. 3.2. Case 2: PR = DR and BHF = SF

Fig. 5. The distribution of the local x-component of stress over the entire elements of the blank before and after springback when PR = DR and BHF = SF.

is represented in Fig. 4 in which PR equals to DR and BHF equals to SF. The amount of draw-in at both ends of the blank is expected to be the same because of the balanced boundary condition. The expected sign of the local stress at the outer surface (upper or lower surface) of the blank is deduced from Fig. 3. A computed result of stress distribution is shown in Fig. 5. As expected from Fig. 4, the left half side of stress distribution is point-symmetric against the right one. The sign reversal of the stress during the springback stage can be seen. This means that the regions having the positive sign of stress just after the forming stage tend to bend inward during the springback stage and vice versa. Therefore, with the information about the sign of stress of the outer surface in hand, springback shape could

Fig. 6. The deformed shape before and after springback by computation with the experimental result when PR = DR and BHF = SF.

Fig. 7 shows a schematic drawing of the expected configuration when DR is greater than PR under the condition of BHF and SF being equal. The amount of draw-in at the side with a larger corner radius is expected to be much more than that at the other side because the material flow tends to be much easier as the corner radius becomes larger. Therefore, most of the deformation occurs at the side with the larger corner radius as shown in Fig. 8. Notice that the unbending and relaxation region in Fig. 8 is wider when compared with Fig. 5. The sign reversal of the local stress during springback can be also seen. The computed result after springback is seen well coincident with the experimental result as represented in Fig. 9. It is noticeable that when the double dotted line is drawn extending the flat flange section as shown in Fig. 9, the springback occurs actually at the left side having the larger corner radius.

Fig. 8. The distribution of the local x-component of stress over the entire elements of the blank before and after springback when PR < DR and BHF = SF.

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Fig. 9. The deformed shape before and after springback by computation with the experimental result when PR < DR and BHF = SF.

Fig. 12. The deformed shape before and after springback by computation with the experimental result when PR = DR and BHF > SF.

Fig. 13. The Taguchi method is used to estimate which process factor is the most influencing one on the springback angle. The orthogonal array L18 is chosen for use since it is one of the most recommended table to investigate the main effects of the factors [4]. Based on the results mentioned in the previous section, the following five process factors and their levels are selected.

Fig. 10. A schematic diagram showing the expected deformed configuration and the signs of stress at the outer surface of the blank just after the forming stage when PR = DR and BHF > SF.

Fig. 11. The distribution of the local x-component of stress over the entire elements of the blank before and after springback when PR = DR and BHF > SF.

3.3. Case 3: PR = DR and BHF = SF A schematic diagram for the case when PR equals to DR but BHF is greater than SF is shown in Fig. 10. It is expected that the amount of draw-in at the side with a smaller force is larger than that at the other side. Thus, most of the deformation by the forming operation is concentrated on the side of the larger draw-in, which is presented in Fig. 11. Springback also occurs at the side of large draw-in as shown in Fig. 12.

Lubrication (Lub) Grease Punch corner radius (PR) 3 mm Die corner radius (DR) 3 mm Blank-holding-force per unit width (BHF) 50 N Supporting-force per unit width (SF) 50 N

none 6 mm

9 mm

6 mm

9 mm

100 N

200 N

100 N

200 N

Table 2 represents the computational results of springback angle of all the eighteen cases. The analysis of variance (ANOVA) of θ is carried out in order to measure the degree of the effects of the factors on springback quantitatively. The result of ANOVA is represented in Table 3. The model is shown to have contribution explaining about 80 % of the total variation. The F-test on the model shows that the model is significant for explaining the springback result at the significance level of 0.1. This means that the five factors, the components of the model, are selected well. The order of strong factors influencing springback is as follows: PR > DR > BHF > SF > Lub Only PR and DR are the factors within the significance level of 0.1. It is noticeable that the effect of the PR factor is absolutely dominant whereas the effect by lubrication is considered negligible. The average response curves for the five process factors are shown in Fig. 14. It is again confirmed that the variation by PR is the largest among the five factors.

4. Estimation of the process factors using Taguchi method The amount of springback in the flange drawing process is defined as the angle θ between the two flat sections shown in

Fig. 13. Definition of the springback angle in the flange drawing process.

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Table 2 Experimental layout of Taguchi table L18 and the obtained data Case

Lub

PR (mm)

DR (mm)

BHF (N)

SF (N)

θ (deg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Grease Grease Grease Grease Grease Grease Grease Grease Grease None None None None None None None None None

3 3 3 6 6 6 9 9 9 3 3 3 6 6 6 9 9 9

3 6 9 3 6 9 3 6 9 3 6 9 3 6 9 3 6 9

50 100 200 50 100 200 100 200 50 200 50 100 100 200 50 200 50 100

50 100 200 100 200 50 50 100 200 200 50 100 200 50 100 100 200 50

0.48 11.46 8.65 10.02 16.76 17.39 11.51 12.05 12.38 0.46 12.00 7.17 20.09 16.46 12.13 10.75 16.68 12.05

Table 3 Result of analysis of variance (ANOVA) Source of variation

Sum of squares

DOF

Model Lub PR DR BHF SF

362.347 2.793 239.598 85.886 23.126 10.945

(78.36%) (0.60%) (51.82%) (18.57%) (5.00%) (2.37%)

Error Total

100.085 462.433

(21.64%) (100%)

Mean square

F0

Pr > F0

9 1 2 2 2 2

40.261 2.793 119.799 42.943 11.563 5.472

3.218 0.223 9.576 3.433 0.924 0.437

0.057 0.649 0.008 0.084 0.435 0.660

8 17

12.511

tion of the local x-component of stress just after the flange forming operation. (ii) Springback tends to occur more strongly on the side where the amount of draw-in is large. Therefore, the larger the corner radius of die set and the smaller the clamping force is, the more strongly the springback takes place. (iii) The order of strong factors influencing springback has been shown as PR > DR > BHF > SF > Lub. Particularly PR turned out to be the most dominant factor among them. Fig. 14. Average response curves of the five process factors of the flange drawing.

5. Conclusions From the computational and experimental results with the process factor estimation using the Taguchi method, the following conclusions can be drawn: (i) It has been shown that the information about the place where springback will occur inward or outward and how strongly it will happen can be obtained from the distribu-

References [1] S.W. Lee, D.Y. Yang, An assessment of numerical parameters influencing springback in explicit finite element analysis of sheet metal forming process, J. Mater. Process. Technol. 80–81 (1998) 60–67. [2] S.W. Lee, Elastoplastic Explicit Finite Element Formulation and its Applications to Sheet Metal Working with Springback, Ph. D. Thesis, KAIST, Daejeon, Korea, 1998. [3] K. Mattiasson, P. Thilderkvist, A. Strange, A. Samuelsson, Simulation of springback in sheet metal forming, in: S. Shen, P.R. Dawson (Eds.), Proceedings of NUMIFORM’95, Balkema, Rotterdam, The Netherlands, 1995, pp. 115–124. [4] G. Taguchi, S. Konishi, Orthogonal Arrays and Linear Graphs, ASI Press, Michigan, 1987.