A Springback Reduction Method for Sheet Metal Bending

Hu Kan1, 2

1. State Key Lab of Automobile Dynamic Simulation, Jilin University,

Changchun 130022, China 2. Engineering Training Center, Beihua University

Jilin 132021, China Hukan2010@gmail.com

Zhang Hailing Design Institute, PetroChina Northeast

Refining&Chemicals Engineering Company Limited Jilin, 132002, China

Zhhling@qq.com

Abstract —The springback is mainly an elastic deformation which occurs after sheet metal forming processes. This paper analyzed the mechanism of deep drawing springback of sheet metal forming, and the springback compensation was studied. Based on this, taking the stiffener parts of auto as an example, the paper analyzed the trend and distribution of springback and its distribution under different conditions after the forming, and compensation was adopted with a multi-step implicit algorithm. The results showed that springback compensation was valid and the precision forming was realized.

Keywords-springback, springback compensition, bending, stamping, material processing

I. INTRODUCTION

The spring back is mainly an elastic deformation which occurs after sheet metal forming processes, when the formed part is removed from the forming tools. The spring back changes the part’s geometry so it can cause difficulties during a subsequent assembly process, or cause the twisting in the assembled part. An accurate prediction of spring back of formed sheets is of vital importance for the design of tools in automotive and aircraft industries, so the analysis of spring back behavior

of thin high strength steel products represents a current

research topic. However, accurate calculation of spring back, especially for cases involving large curvatures, is

routinely still not feasible because that analysis of the

spring back phase is complicated since it involves material and geometric non-linearity.

In order to reduce the influence of the spring back

effect and, thus, to get a higher accuracy, Many researches have been performed for decreasing the amount of spring back by increasing sheet tension during forming process. Liu [1] has proposed a method to reduce spring back using different histories of restraining force during forming. In this approach, the in-process variation of binder force can provide tensile pre-loading or post loading on the formed part in order to significantly reduce spring back. However, a tight control during production is required, making this process sensitive to any variations in manufacturing conditions such as friction coefficient. Sunseri et al. [2] developed and implemented a closed-loop algorithm for binder force control to make the

forming process more robust and repeatable. In their strategy, a punch force trajectory is introduced as the target curve instead of using a binder force trajectory. The tooling shape is not required to be modified in these approaches but a control system for adjusting the binder force is needed. Also increasing the binder force can cause tearing of sheet in many cases. Therefore the applications of such approaches are limited and costly.

In another group of researches [3-7], the springback deformation is compensated by modifying the shape of the forming tools. It is very important to predict the spring back and correct it at the tool design stage, since the geometry correction on the finished tools is very expensive and time-consuming. In this group, iterative algorithms have been proposed for modifying the tooling shape to compensation springback error. For prediction of spring back in these researches, incremental finite element method is used. Some other approaches have been presented for modifying the tool shape to compensate the spring back error with the help of finite element method [8-12]. These approaches are applicable for a wide range of processes. However, an enormous amount of time and cost is needed for the process design by FEM. Analytical methods for process analysis are time-saving but can only be used for simple problems. Vin et al. represented an analytical model to evaluate the spring back and punch displacement in the air V-bending process [13]. They investigated the influence of changing Young’s modulus on the spring back. Zhang et al. developed a mathematical model for predicting the sheet spring back of U-bending. They investigated the effect of blank holding force and several material hardening models on the sheet spring back. Kim et al. proposed an analytical model to calculate the bend allowance and the spring back in the air V-bending process. They assumed plane-strain condition and used Swift’s material model to represent strain-hardening behavior. The shift of neutral axis is considered in their model.

II. BENDING WITH SPING BACK COMPENSATION

Die bending is a bending procedure between bending punch and bending die until the workpiece touches the die at its flanks. Depending on the process state, a differentiation has to be made between free bending (air bending) in the die and coining (die bending). In contrast to coining, in the case of which the workpiece is pressed into the tool with a large force until it comes to rest in the

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2011 International Conference on Mechatronic Science, Electric Engineering and ComputerAugust 19-22, 2011, Jilin, China

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die, the tools in air bending are used only for the transmission of forces and bending moments on the workpiece in such a way that the bending line develops freely in the forming zone. Both die and air bending are accompanied, when the punch load is removed at the end of the forming process, by the so-called springback effect a phenomenon in which the bend angle becomes smaller than the initial loaded angle after unloading. Die bending shows less springback compared to air bending which leads to a better workpiece accuracy.

A. Mechanism of bending springback In the role of external bending moment by the punch,

bending sheet metal is first into the elastic deformation stage, during this period the relative bending radius is large, sheet metal bending radius and punch radius do not overlap, sheet metal deformation is small. In the bending area, sheet metal bending inside (near the punch side) of the material is shortened by compression; the stress state is one-way compressive stress. Sheet metal bending lateral (near the die side) in tension and elongation, the stress state is one-way tension.

As the moment and the sheet bending increases, the inner and the outer surface of the metal reach its yield limit first, and then the deformation of sheet is from the elastic deformation turn to the plastic deformation. With the bending moment increase continuously, the plastic deformation zone extended from the surface inward, the middle of the elastic deformation of sheet area became smaller, and finally the entire section into the plastic state. During the time of sheet metal bending, the inner bearing the compressive stress and the outer bearing the tensile stress. When plastic bending, although two stress above are exceed yield stress , but in practice, the transition from tensile to compressive stress, there always have the middle section which is in elastic deformation zones where the local stress is less than the yield stress. Because of the presence of elastic zone, bending sheet inevitably produce a spring back after unloading it. In a relatively large bending radius, the ratio of elastic deformation region and a major, this spring back is particularly significant.

B. Calculation of Spingback in Bending For the onetime integral unload, it is the equivalent of

imposing a equal and opposite moment bending moment M ′ with the role of M (M is the final step informing the corresponding node access to torque). If it is

elastic unload, then /x x Eδσ δε ′= , and if it is plane strain, then 2(1 )E E v′ = − /x h Rδε δ δ= hδ and Rδ are changed with the thickness and radius of bending unit change, So u uR R Rδ ′= − , as fig.2 showed. Unload moment is:

/2 3 3

02 ( ) /12(1 )

h

u u uM w d WEh R R v R Rθ ησ η′ ′ ′= Δ = − −

where θσ is stress components, h is sheet thickness, W is width of sheet, R′ , uR are curvature radius of stress neutral layer pre and post unloading;

If the equivalent stress σ remains constant, the load moment is:

2 211 1( ) ( )( )

1 4 4(1 ) 21 2 1 2n nr Wh r Wh h

M Kn n Rcr r

σ ++ += =+ ++ +

Then 1 1( ) ln ( ) ( )21 2 1 2

n n no

c c

Rr r hK K

R Rr rσ + += ≈

+ +,

M MΔ = −2

11 1 1 3(1 )( ) ( )(1 ) 21 2

n n

c c c

r v hKR R hE n Rr

++ −− = × ×′ ++

Where r is normal anisotropy coefficient, n is hardening exponent, η is the thickness of the selected mesh. If we has c cR Rθ θ′ ′= , then resilience ratio is:

21 11 3(1( ) ( ) ( )

(1 ) 21 2n n

c

r v hKhE n Rr

θθ

+ −Δ + −= × ×++

,

where 1 1 1( )c c cR R R

θΔ = −′

.

III. SPINGBACK AFFECT FACTOR

A. The fit clearance Z The fit clearance between punch and the mould is

smaller; the springback angle will become smaller. But if the clearance is too small, it will scratch the surface of the workpiece or thinner it; and if Z < t, the workpiece may have a negative rebound

B. Radius of die Radius R of die is an important parameter in stamping

process. If R is too small, it may cause severe stress concentration which may lead to crack.

Figure.1 The procedure of compensation reduce

Figure2. Element analysis model of sheet

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C. Relative bending radius If relative bending radius increases, the elastic

deformation of the proportion of the total deformation would increases, the springback also increased.

D. Punch velocity Punch speed have greatly efficiency for finite element

simulation. In the actual calculation, we tend to use a virtual punch velocity, but if it goes beyond the limit, the result of simulation will be fuzzy badly.

E. Friction coefficient F The friction between the mold surface and sheet

surface affect the stress state of sheet metal. It is believed that the friction can increase tensile stress of the deformation zone and it can make the part shape close to the die shape, which reduces the springback of stamping.

F. Blank holder force(BHF) Increasing the BHF can reduce the springback of sheet

metal, but the increment of BHF premise of no other forming defects.

IV. THE CONFIRMATION OF SPRINGBACK COMPENSATION

A. Principle of Spring back Compensation in Bending In order to reduce the influence of the spring back

effect and, thus, to get a higher accuracy, several methods have been applied in research and practice. Some alternatives to classical die bending are the die bending with pliable die and the three point bending. In these procedures, the superposition of compressive stresses was

found to be an effective method for spring back compensation. In most cases, the procedure extension did not involve high technical efforts. However, the spring back compensation was not optimal due to procedure-related aspects. The aim is to develop a simple and flexible procedure with a high reproducibility and a considerable spring back reduction.

The stress superposition is carried out with stress values below the flow stress. Thus, unwanted part

deformations and hardening are avoided. Moreover, the

application of an additional external energy provokes a reduction of theas an effect of too high tensile stress is

also minimized. The superimposed compressive stresses influence the

accumulated elastic energy, leading to a springback reduction. Due to the energy stored during this process, the crash properties of the part are improved.

B. The Comfirmation of Springback Compensation Since the forming process of the workpiece to produce

the inevitable rebound, the shape of the workpiece to be qualified to the appropriate method must be adopted to eliminate the bias caused by the rebound. Springback control methods of sheet forming can be divided into two categories: The first is to form over the stamping by modifying the mold surface or mold structure that is use the springback law to get the similar shape after unload the sheet. The second method is to develop a reasonable forming process to change the stress status of the sheet forming, or make the full plastic deformation occurred to suppress the occurrence of springback.

In this paper, the stiffeners parts of auto beam(as picture showed) is selected, by use of virtual processing software environment to simulate the springback compensation in the software Dynaform to get a better

springback compensation in the panels forming stage for that the plates is generated in line with the design requirements after a subsequent series of trimming and punching process.

Figure.3 The stiffener parts of auto

Figure.4 The thickness of parts in stamping process

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Part material is B210P1 (the yield strength is 249 MPa, tensile strength is 413MPa, elongation is 38.23, n value is 0.208, R value is 1.64), thickness of part is 1.6 mm. For this part, if do the drawing simulated directly, calculated according to section line(as figure 6 showed), we know that the maximum springback is 3.2mm. In the conventional treatment, it’s usually to calculate the springback of part firstly, then do compensation in the drawing process and simulate calculation by it, so the cycle to continue until rebound is less than an allowed value. We do this process in Dynaform and use the overall compensation simulation method, re-count the results of the compensated part of the spring prior to the section line with the resilience to do comparison, it can be found the two cross sections fit the basic line, according to measurement, the maximum amount of error 0.5mm(as figure 7 showed), basically meet the processing requirements, as fig showed.

V. CONCLUSIONS

In the processing of bending, it’s very important to predict the springback of parts. This paper predicted the springback of the stiffener parts of auto, it’s found that springback mainly concentrated at the bending position, The more drawing depth, the more resilience value; we used multi-step implicit algorithm to calculate the springback compensation of parts in Dynaform software, and according to resilience value we made the workpiece

overbending, then, after the demould, rebounding parts is the shape required, so we achieve the purpose of forming precision parts ultimately.

REFERENCES

[1]. YC. Liu, “The effect of the restraining force on shape deviations in flanged channels”, Journal of Engineering Materials and Technology, 1988, 110, pp. 389-394.

[2]. M. Sunseri, J. Cao, A. P. Karafillis and M. C. Boyce, “Accommodation of Springback Error in Channel Forming Using Active Binder Force Control: Numerical Simulations and Results”, Journal of Engineering Materials And Technology, 1996, 118(3), pp. 426-35.

[3]. P. Karafillis and M. C. Boyce, “Tooling and binder design for sheet metal forming processes compensating springback error”. Int. J. Machine Tools & Manufacturing, 1996, 36, pp. 503-526.

[4]. E. L. Anagnostou, “Optimized tooling design algorithm for sheet metal forming over reconfigurable compliant tooling”. NUMIFORM 2004, 712, pp. 741-748.

[5]. W. Gan and R.H. Wagoner, “Die design method for sheet springback”. Int. J. Mech. Sci., 2004, 46, pp. 1097-1113.

[6]. W. Gan, R.H. Wagoner, K. Mao, S. Price and F. Rasouli, “Practical methods for the design of sheet formed components”. J. Eng. Mat. Tech., 2004, 126, pp. 360-367.

[7]. Rosochovski, “Die compensation procedure to negate die deflection and component springback”. J. Mat. Proc. Tech., 2001, 115, pp.187-191.

[8]. R. Lingbeek, J. Huetink, S. Ohnimus, M. Petzoldt and J. Weiher, “The development of a finit elements based springback compensationtool for sheet metal products”. J. Mat. Proc. Tech., 2005, 169, pp. 115-125.

[9]. H.S. Cheng, J. Cao and Z.C. Xia, “An accelerated springback compensation method”. Int. J. Mech. Sci., 2007, 49, pp.267-279.

[10]. T. Meindres, I.A. Burchitz, M.H.A. Bonte and R.A. Lingbeek, “Numerical product design: Springback prediction, compensation and optimization”. Int. J. Machine Tools & Manu., 2008, 48, pp.499-514.

[11]. Behrouzi, B. Mollaei and M. Shakeri, “A New Approach for Inverse Analysis of Springback in Sheet Bending Process”. Journal of Engineering Manufacture, 2008, 222, pp.163-1374.

[12]. L.J. Vin, A.H. Streppel, U.P. Singh, and H.J.J. Kals, “A process model for air bending”. J. Mat. Proc. Tech, 1996, 57, pp. 48-54.

[13]. Z. Dongjuan, C. Zhenshan, R. Xueyu and L.Yuqiang, “An analytical model for predicting springback and side wall curl of sheet after U-bending”. Computation Materials Sci., 2007, 38, pp. 707-715.

Figure.5 The cross section line

Figure.6 The section line of springback

Figure.7 The section line after springback compensation

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