Finite element analysis of springback in L-bending of sheet metal

doi:10.1016/j.jmatprotec.2005.02.236

Journal of Materials Processing Technology

Volume 168, Issue 2, 30 September 2005, Pages 296-302

https://doi.org/10.1016/j.jmatprotec.2005.02.236 Get rights and content

Abstract

In the metal stamping industry, one of the major problems is getting the sheet metal to conform exactly to the shape of the die. Due to the effects of springback, die designs are usually finalized only after the fabrication and testing of multiple prototypes. The design of a die for a given part may undergo many rounds of iterations in the debugging stage before a satisfactory geometry is obtained. In order to reduce time spent on such manual corrections of the die, a parametric study is conducted on how the inclusion of a step in the die may reduce springback. The results provide a better understanding of how die parameters like die clearance, die radius, step height and step distance affect springback.

Introduction

Sheet metal stamping plays a major role in many industries today. As part components get smaller and tolerances get tighter, the dimensional accuracy of a stamped part becomes a crucial factor in determining the overall quality of the part. In most, if not all, sheet metal forming processes, springback is the major problem faced. Springback often complicates the design of forming dies, and final die designs may only be accomplished after fabrication and testing of multiple prototypes. This poses significant problems to designers, who must accurately assess the amount of springback which occurs during a forming process so that a final desired part shape can be obtained. In this paper, L-bending with a step in the die is analyzed with finite element methods, and the amount of springback reduction that can be achieved with variations in die clearance, die radii, step height and step distance (Fig. 1) is studied. Recommendations on how these parameters can be used in combination to give the most springback reduction are also made.

Section snippets

Background

As early as 1958, Gardiner [1] derived a generalized mathematical analysis for springback corrections in the pure bending of metals such as aluminum, nickel, titanium, and ferrous alloys. In 1981, Johnson and Yu [2], [3] followed the work of Gardiner to give a theoretical analysis of springback in the bi-axial, elastic–plastic pure bending of a rectangular plate. Ayres [4] proposed a process called “shape-set” to reduce side-wall curl springback in high-strength steel rails. Wang et al. [5]

Finite element model

In the finite element model, the workpiece, the male die steel, the punch and the pressure pad form the main components. In the model definition in ABAQUS/standard, the die, punch, and pressure pad are defined by rigid surfaces, The workpiece is represented by a deformable mesh. The simulation begins with the pressure pad in contact with the workpiece. The die then moves up to contact the workpiece, followed by the lowering of the punch to bend the workpiece. After the bending operation, the

Simulation details

The simulations are carried out in five batches. In the first batch of simulations, the die step height and step distance set to zero so as to study the effects of changes in die clearances and die radii. Die clearances used are 0.75t, 0.80t, 0.85t, 0.90t, 0.95t, 0.98t, 1.00t, 1.03t, 1.05t and 1.10t. Die radii used are 0.5t, 1.0t, 2.0t, 3.0t and 4.5t. With 10 die clearance values and 5 die radii values, a total of 50 simulations are conducted in the first batch.

The second batch consists of

Effects of die clearance

Due to the large amount of data from the simulations, only selected results will be shown. The variation of springback with changes in die clearance is summarized in Fig. 3. It is noted that for simulations with die radii of 0.5t to 3.0t, the change in springback angle follows a similar trend. As the die clearance increases from 0.75t to 0.95t, the springback increases to a maximum in a non-linear manner. Between die clearances of 0.98t and 1t, there is a sudden drop in springback. As the die

Effects of die radius

The effect of die radius on springback is commonly expressed using the springback factor K: $K = \frac{A}{A_{1}} = \frac{R_{1} + t / 2}{R + t / 2}$ where A = bend angle of part after springback (°), A₁ = bend angle of part during bending (°), R = part radius, R₁ = die radius, and t = metal thickness.

Using the results from the first batch of simulations, another graph of springback factor against die radius is plotted, as shown in Fig. 7. Generally, for all die clearances, the springback factor decreases as die radius increase. It is also

Effects of step height and step distance

With the presence of a step, it is observed that the effects of changes in die clearance on springback still follow the trends shown in Fig. 3. The springback increases non-linearly to a maximum from clearance 0.75t to 0.95t, followed by a sudden decrease to clearance 1.00t, after which it increases again to clearance 1.10t. This trend is consistently seen in all simulations of die radii 2.0t and 3.0t. For die radius of 4.5t, the trend is also similar except for the absence of a decrease in

Die design recommendations

The results and observations made thus far clearly show that die radius, clearance, step height and step distance can be used to reduce springback. Of the four parameters, die radius and clearance have the more significant effects on springback compared to step height and step distance. If the die design allows for small radius, the recommendation is to use as small a die radius as possible to reduce springback. However, care must be taken to avoid using a die radius smaller than the minimum

Conclusion

The variation in springback with different die parameters for L-bending has been analyzed using finite element methods. From the results of numerous FE simulations, trends of how springback changes with die clearance, die radius, step height and step distance are studied, and die design recommendations are made on the use of these parameters to reduce springback.

The simulations were conducted only for one material type: AL2024-T4. There is a need to conduct the simulation for other material

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Finite element analysis of springback in L-bending of sheet metal

Abstract

Introduction

Section snippets

Background

Finite element model

Simulation details

Effects of die clearance

Effects of die radius

Effects of step height and step distance

Die design recommendations

Conclusion

Int. J. Mech. Sci.

Int. J. Mech. Sci.

J. Mater. Proc. Tech.

J. Mater. Proc. Tech.

J. Mater. Proc. Tech.

J. Mech. Sci.

Int. J. Mach. Tools Manuf.

Int. J. Mach. Tools Manuf.

J. Mater. Proc. Tech

The spring back of metals

Trans. ASME, J. Appl. Mech.