EXAMINATION OF SPRINGBACK IN SHEET METAL FORMING BY FINITE ... · examination of springback in sheet metal forming by finite element method metin kahraman1, * - lubomir dimitrov1

machine design, Vol.5(2013) No.4, ISSN 1821-1259 pp. 163-170

*Correspondence Author’s Address: Technical University of Sofia, Faculty of Mechanical Engineering, prof. Lubomir Dimitrov, Sofia 1000, Bulgaria, [email protected]

Original scientific paper

EXAMINATION OF SPRINGBACK IN SHEET METAL FORMING BY FINITE ELEMENT METHOD Metin KAHRAMAN1, * - Lubomir DIMITROV1 1 Technical University of Sofia, Faculty of Mechanical Engineering, Sofia, Bulgaria Received (28.07.2013); Revised (03.11.2013); Accepted (10.11.2013) Abstract: Sheet metal deformation is widely used in automotive industry. Nowadays the automakers try to reduce the weight of the cars by using high strength steel. The disadvantage of the high strength steel is its significant springback effect. One of the aims of this study is to utilize the springback compensation algorithm of the commercial software during the drawing simulation process. In this paper, we discuss how the sheet metal deformation was simulated by using DYNAFORM V5.5 software. The results of the simulations were compared with producers’ experience. The geometrical data of the simulated parts were provided in “.iges” file format by producers of machine components. The model prepared for the simulation was developed as a system of die, punch, addendum, binder, and blank. After sheet plastic forming analysis was done, springback was performed. LS-DYNA software was used as a solver in the simulations. Key words: FEA, plastic forming analysis, springback analysis, limit diagram 1. INTRODUCTION

The design of sheet materials in the automotive industry is one of the most important stages in this industry. Many manufacturing methods have been developed for sheet metal forming stage [1,2,3,4,5,6]. These methods generally are based on the specified thickness of sheet or plate material used to obtain the required form by using more rigid elements (die tool elements). Die parts may be produced from a hardened steel, pressured water, compressed gas, and some special composite material. The most commonly process is to place the sheet metal material between complementing each other "punch" and "female die" and the sheet metal is formed by pressing.

1.1. Die design

Die are designed according to process of sheet metal forming [1,6]. These operations are not usually completed simultaneously. The procedure sometimes includes several dies. The draw die is the first die for forming. The drawing process of the sheet metal requires unfolding external lines cutting in order to define the shape needed and the perimeter of cutting die. The drawing die performs the first and biggest forming of the sheet metal. At this stage, the importance of drawing die appears as clear as terms of achieving appropriate shape in the form sheet metal. Although it is possible to form certain surfaces of sheet metal, the amount of forming at this stage is limited. The large amount of deformation in the sheet metal forming process may cause large distortion, cracking, tearing or wrinkling. Shortly, a well-designed drawing die is very important to successfully manufacture sheet metal.

1.2. Springback

In order to reduce the weight of vehicles, many automotive companies use high-strength alloy steels for car panels. Those steels have good elasticity and when subjected to cold-pressing forming, upon release of the forming force, the material has a tendency to partially return to its original shape because of the elastic recovery of the material. This is called springback. All car panels make springback after plastic forming. Many companies rely on their experience when design against springback. If such experience is not available, we need to simulate it. The idea is to predict the possible springback and change the die design correspondingly.

1.3. Aim of the work

In this work finite element analysis (FEA) are used for simulation of sheet metal forming process. The simulation is made in DYNAFORM V5.5 [7,8]. All parameters of plastic forming analysis were performed by entering values close to real objects. The springback analysis is made after the sheet metal forming analysis. The aim is to calculate the compensations needed in dies in order to eliminate the springback process. Springback compensations are used to prevent errors that may occur in the pre-production sheet metal forming process.

2. SHEET METAL FORMING SIMULATION IN INDUSTRY

2.1. Sheet metal forming process steps

There are five major process steps in the simulation of sheet metal forming in automotive industry. They are: holding, drawing, cutting, bending and springback 1,5.

Metin Kahraman, Lubomir Dimitrov: Examination of Springback in Sheet Metal Forming by Finite Element Method; Machine Design, Vol.5(2013) No.4, ISSN 1821-1259; pp. 163-170

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Fig.1. Representation of the main die tools.

2.2. Modeling of sheet metal and die surfaces

During the holding and drawing simulations, corner radiuses of mold surfaces are not usually very small. The ratio r/t (t is sheet thickness) is greater than 3 1. Small flange bending radiuses are provided for preventing errors in calculation and three-dimensional modeling.

2.3. Existing sheet metal forming simulation algorithms

The existing sheet metal forming simulation algorithms (based on FEA) are shown in Table 1. Generally they defer depending on the method that they use: Rigid Plastic and Elastic Plastic

Static Closed Method Static Open Method Dynamic Open Method DYNAFORM software uses dynamic open method.

2.4. Dynamic open method

The Elasto-Plastic-Dynamic Time-History method is a nonlinear method. The dynamic equation and the equations for each nodal point resolved to the whole time steps are shown in 9. The main advantage of this method is that the stiffness matrix is not required. It allows a direct solution for each step if needed. This method is much faster than closed methods. A dynamic stable solution can be obtained for any incremental time, which is the critical time step in the point of view of the input waveform and must be limited. In general, this time is synchronized to the time step of 10E-6 seconds. DYNAFORM software originates from USA [7] and it uses dynamic open method. The analysis of the sheet metal plastic forming done in DYNAFORM makes the calculation explicit. On the other hand, it makes the implicit as a plate springback calculation. By the help of DYNAFORM various types of simulations can be performed for many elements and structures, such as: the shell, membrane, and some others. Die Face Engineering contained in this program (DFE) can be done by a module without the need of any other CAD package 9.

Table 1. Existing Commercial and Academic Software

Software Name Country Classification

SHEET-3 U.S.A.

Rigid- Visco-Plastic

MFP2D Spain

MFP3D Spain

FORMSYS-SHEET Korea

CASHE Korea

MİLFRM U.S.A.

Elasto-Plastic Static-Closed

Method

Dieka Netherlands

LAGAMINE Belgium

CAEMBOUR France

ABAQUS U.S.A.

FLECHE France

NIKE 3D U.S.A.

AUTOFORM Swiss

BENDI U.S.A.

INDEED Germany

PROFIL France

MARC U.S.A.

ROBUST Japan Elasto-Plastic Static-Open

Method ITAS-3D Japan

ITAS-2D Japan

LS-DYNA/DYNAFORM U.S.A.

Elasto-Plastic Dynamic-Open (Time-history)

Method

PAM-STAMP France

RADIOSS France

ABAQUS /Explicit U.S.A.

OPTRIS France

CES-3D Spain

3. Plastic forming and springback analysis

3.1. Analysis of the real panel

This project is applied to a real panel. Fig.2 shows a commercial vehicle front inner fender panel which is a part of the chassis. This panel has already been manufactured by “BEYÇELİK GESTAMP KALIP VE OTO YAN SANAYİ PAZARLAMA VE TİCARET A.Ş” [10,11]. Computer analysis was made of this fender and actual drawing of the die was taken in order to compare it with the real product. AutoForm software was carried out by the use of this vehicle chassis part in BEYÇELİK GESTAMP A.Ş. [10]. This panel has roughly the following dimensions: 592x464x85 mm. The sheet thickness is 2.5 mm. This thickness of a sheet metal part needs a quite large force for holding and drawing operations. The chosen material from library materials in DYNAFORM V5.5 is DC04 (Table 2). This is a low carbon steel with the following properties: modulus of elasticity 207 GPa; density 2850 kg/m; Poisson's ratio 0,28.


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Fig.2. Inner fender on chassis sheet metal part in vehicle. The amount of the total elongation is between 36% and 49%. This material in other countries corresponds to the materials shown in Table 2.

Fig.3. DC04 used in the simulation of drawing material properties of inner fender on chassis sheet metal part.

Table 2. Correspondence of chosen material to the materials in other countries.

For the simulations in DYNAFORM V5.5 we assume: the binder stroke speed to be 1000 mm/s for the drawing process; the sheet metal holding force to be 25 tons (2.5e+ 005N). The blank and binder together goes down with a speed of 2000 mm/s of the punch. The punch is set to a

fixed to the bottom tray. Draw Beads locks together with blank. 100 mm is the distance between the female die and the punch. 85 mm is the distance between the blank and the punch. 70 mm is the distance between the binder and the punch. The blank must be considered to be positioned between the die and the binder. The position of the elements before drawing is shown in Fig.4. In this way, a variety of numeric expressions on the blank sheet is shown in various colors where the line described of draw bead.

Fig.4. Positioning the drawing die inner fender on chassis sheet metal part.

The inner fender of the chassis sheet form is analyzed by DYNAFORM software and the results are shown in Fig.5. The figure illustrates the amount of thinning that occurs after the pressing process simulations. One can see that there are places with thickness of 1.4 mm.

Fig.5. The amount of thinning is shown on the inner fender on chassis sheet metal part that occurred as a

result of simulation.

DYNAFORM V5.5 uses many parameters for the evaluation and analysis. The results finally are combined into a single image that provides a graphical image of the forming. Fig. 6 shows the forming limit diagram. The deformed area is described in five main deformation models and the lines separating the zones are as follows [12]:

Biaxial Stretch (line of O-A): The sheet metal elongates in an equal amount in the same direction. The deformation and stresses are as follow:

minmaj , 0t (3.1)

t is strain in the direction of thickness,

min 0maj , 0t (3.2)


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Plane Strain (line of O – C): The sheet metal has been strained in one direction only.

Fig.6. General description of the forming limit diagrams. The deformations and stresses for isotropic materials are:

maj t , min 0 (3.3)

min 0maj , 0t (3.4)

Uniaxial Strain (line of O – B): The sheet metal is elongated in one direction while it has been reduced in the other direction. The deformations and stresses for isotropic materials are as follows:

2maj , min 2 t , (3.5)

0maj , min 0 , 0t (3.6)

Pure Shear (line of O – D): The deformation of one direction is balanced by an equal amount of compressive strain in the other direction:

min min , 0t (3.7)

0maj , min 0 , 0t (3.8)

Uniaxial compression (line of O – E): The sheet metal is subjected to compression in one direction while it has been elongated in the other direction.

min

2t maj

(3.9)

0maj , min 0 and min maj ,

0t (3.10)

The top on the sheet metal has an elliptical shape before the plastic forming. The longest axis of the ellipse is called major strain elongation and the shortest axis of the ellipse is called the minor strain elongation. The major elongations will be expressed in y direction and the minor elongations will be expressed in x direction. This is illustrated in the forming limit diagram. Sheet metal begins to tear from a certain point depending on the metal characteristics.These points create a specific line on the graph. This line is called boundary line of forming. The region to the left of the vertical axis on the diagram in Fig.6 is negative. The DYNAFORM analysis and the above mentioned rules applied to the inner fender of chassis sheet metal part are shown in Fig.7. At the same figure, the forming limit diagram in colors is given as well. The red regions on forming limit diagram represent the stresses above the limit line. The red regions indicate where cracks in terms of major and minor strain will occur. The yellow colored areas on the sheet material indicate the areas with high risk of cracking. The green colored areas on the sheet

material indicate regions formed by providing a safe yield. The blue-colored regions on the sheet material show the regions of wrinkles. The pink colored areas on the sheet material illustrate the consisting wrinkle areas. The purple colored regions on the sheet material show areas with severe wrinkles. The gray colored regions on the sheet indicate insufficient stretching locations.

Fig.7. Inner fender plastic forming analysis and forming limit diagram.

3.2. Springback analysis of inner fender on chassis sheet metal part

The results of analysis of sheet metal forming parts are imposed in the main program with file extension “dynain”. Then we start the springback analysis. For the analysis of springback, the "Process" section of the program is selected. For the analysis of springback, fixing points have to be marked. As shown in Fig.8, numbers "123" show coordinates in x, y, and z directions. Numbers "23" show coordinates in x and y directions and "3" shows z coordinates at the panel. The springback analysis results in z direction are given in Fig.9. As mentioned above, for the analysis the European standard material DC04 (FePO4) is selected. Its properties are: 207 GPa modulus of elasticity, density 2700 kg/m; Poisson's ratio is 0.28. The amount of the total elongation is between 36% and 49%. The maximum amount of springback in z direction is 1.084 mm in the positive direction and -0,0304 mm in the negative direction

3.3. Comparison of the inner fender on chassis sheet metal part three dimensional real measurement results and springback computer simulations

The inner fender is produced by BEYÇELİK GESTAMP KALIP VE OTO YAN SANAYİ PAZARLAMA VE


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TİCARET A.Ş. company [10,11]. Three-dimensional real measurement was made by the company and the reference points are shown in Fig.10.

Fig.8. Given fixing points for the springback analysis of the inner fender of chassis sheet metal part.

Fig.9. Result of analysis of the springback in Z direction.

Fig.10. BEYÇELİK GESTAMP company produced panel with reference points.

The three-dimensional measurements were made in a specific line direction. Fig.11 shows the measurement locations with a line of dark red. This measurement was made to determine the amount of deviation from the nominal geometry.

Fig. 11. The panel will determine the position of three-dimensional cross-section for the actual measurement of

the company.

In our work, the amount of deviation from the nominal geometry 3D measurement was compared to the results obtained by DYNAFORM springback analysis. As a result of the DYNAFORM analysis of the Z1915 cross-section of the panel, the amount of deviation from the z direction is shown in Fig. 12.This view was taken from the postprocess module of DYNAFORM V5.5.

Fig.12. Results of springback analysis of the inner fender on chassis sheet metal part taken from DYNAFORM that

is shown in Z1915 and Z1915A cross-sections 10.

Fig.13. Results of springback analysis of the inner fender on chassis sheet metal part taken from DYNAFORM.

Z1915 and Z1915A cross-section show the location of the measurement for the determination of the amount of

deviation from the desired geometry 10.


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Figure 14. Results of springback analysis of the inner fender on chassis sheet metal part taken from

DYNAFORM which is Z1915 and Z1915 A cross-section shows values for the amount of deviation from the desired

geometry.

Fig.15. The panel is manufactured by BEYÇELİK GESTAMP company. Z1915 and Z1915 A cross-sections

show the locations of the 3D measurement 10.

Fig.16. Three-dimensional measurement distances in Z=1915 and Z=1915A cross-sections 10.]

Z1915 cross-section and the displacement values of the determined locations and distances in the same cross-section above are listed in table 3. This graphically is illustrated in Fig.17. The hole is shown on the figure as a red rectangular. The panel springback compensation was further made. First of all, plastic forming and springback

analysis were made to obtain data indicating the amount of springback panel.

Fig.17. Graphical comparison of the results obtained by actual measurements and DYNAFORM simulations for

Z1915 - Z1915A cross-section This data is used in the program "Springback Compensation" module and the following analysis was made. Springback compensation data was obtained as a result of this analysis. Punch, female die, and binder surfaces were re-designed using the springback compensation data. Table 3. Comparison of the results obtained by real measurement and results of DYNAFORM simulations. Z-1915 and Z-1915A cross-section is shown on the displacement values and their distances on the geometry of the panel.


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Fig.18. The panel shown in three different situations.

Fig.18 shows the panel in three different situations. The first situation shows the springback of the compensated surface. The second situation shows the plastic forming and following springback analysis (before springback compensation). The third situation shows the actual female die surface. The die surfaces were changed by using the result of springback compensation data. In order to check the accuracy of the modified surfaces of die components, analyzes have been made. Plastic forming and springback analysis were applied to the panel. The springback values are shown in Fig.19. The result of the springback analysis was determined as 0.0478 mm in the positive direction and -0.0578 in the negative direction.

Fig.19. Various analyses were performed in order to verify the springback compensation. Plastic forming and

springback analyzes were performed in order to verify the panel geometry.

The displacement at the same cross-section (Z1915 - Z1915A) obtained by DYNAFORM V5.6 program is shown in Fig.20. Table 4 reveals comparison of all data obtained: the first column shows Z1915-Z1915A cross-section displacement rate (3-D measurement results on the panel); the second column shows not tolerated springback on the die surfaces in the same cross-section; the third column shows the tolerated springback on the die surfaces. With these results the plastic forming and springback have to be made.

Fig.20. Springback of the Inner fender die surfaces with the displacement in z direction.

Table 4. The 3-D measurement results; the springback on the die surfaces in the same cross-section (not tolerated); and the tolerated springback on the die surfaces.

4. CONCLUSIONS Tolerances for chassis sheet metal parts usually are given by the ordering company. The analyses show that too small margins of errors (less than 1 mm) in the calculation of the actual panels springback is required to be the same


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as the desired geometry tolerances. The springback value depends on several parameters: the method of simulation, software performance, the panel and the die geometry. Another reason relates to the compliance of the simulation parameters and the actual drawing process parameters. This fact concerns the margin errors as well. The causes of these errors can be listed as follows. A few millimeters reduction of the binder’s height can be adjusted by the sheet metal amount of flow with the die elements. If during the drawing process on the top of sheet metal surface some lubricant is presented – this causes error.

Fig.21. Comparisons of three deviations in Z1915 - Z1915A cross-section.

The mold surface roughness can also influence the final quality. If a raw sheet metal with a small shift is put on the mold, this also may cause an error. The linear assumption in the software causes errors too. Errors even occur during the actual measuring. In order to solve these problems, Springback compensations to the molds were calculated. This was done by the use of DYNAFORM. The analysis and computer simulation of the sheet metal forming reduce the error rate and reduce manufacturing problems in serial production. The compensation helps to avoid costly mistakes in design and manufacturing. The design can be made as faultless and appropriate to the material forming (drawing) process. This helps to avoid creases, wrinkles, cracks and tears.

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draw die surfaces using finite element method, İstanbul Technical University, ISBN 030194960019, pp. 01-14, İstanbul, Turkey.

[2] Makinouchi, A. (1996). Sheet metal forming simulation in industry, Journal of materials processing technology, Elsevier, Vol. 60. (19-26), ISSN: 0924-0136.

[3] Tang, S.C. (2000). Trends on Simulation of Sheet Metal Forming Process, SAE Papers, SAE Paper No.2000-01-1108

[4] Fırat, M. (2006). Computer Aided Analysis and design of sheet metal forming process: Part II: Deformation Response Modeling, Elsevier –Materials and Design Technical report, ISSN: 0264-1275, Adapazarı, Turkey

[5] Fırat, M. (2006). Computer Aided Analysis and design of sheet metal forming process: Part I: The Finite Element modeling concepts, Elsevier – Materials and Design Technical report, ISSN: 0264-1275, Adapazarı, Turkey

[6] Fırat, M. (2006). Computer Aided Analysis and design of sheet metal forming process: Part III: Stamping Die – Face Design. Elsevier – Materials and Design Technical report, ISSN: 0264-1275, Adapazarı, Turkey

[7] Eta/DYNAFORM. (2006). Eta/Dynaform User’s. Manual Version 5.5. Livermore Software Technology Corporation, California, USA

[8] Eta/DYNAFORM. (1999). Dynaform-Pc Application Manual, An LS-DYNA Based Sheet Metal Forming Simulation Solution Package, Approved by Morse B., Livermore Software Technology Corporation, pp. 1-27, California, USA

[9] Aslantaş,K. (2007). Üretim Yöntemleri 1 - Plastik şekil verme 1, Teknolojik Araştırmalar Elektronik Dergileri.

[10] BAŞARAN, T. (2008). Personal interview, BEYÇELİK GESTAMP Kalıp ve Oto Yan Sanayi Pazarlama ve Ticaret A.Ş.

[11] Mutlu, Z. (2008). Personal interview, BEYÇELİK GESTAMP Kalıp ve Oto Yan Sanayi Pazarlama ve Ticaret A.Ş.

[12] Lubarda, A. (2002). Elastoplasticity Theory, CRC Press, ISBN 0-8493-1138-1, 406-414, Florida, USA.

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EXAMINATION OF SPRINGBACK IN SHEET METAL FORMING BY FINITE ... · examination of springback in sheet metal forming by finite element method metin kahraman1, * - lubomir dimitrov1