Numerical simulation of incremental forming of sheet metal

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Abstract

Applicability of numerical technique to incremental forming of sheet metal is examined. A dynamic explicit finite element code DYNA3D is used. Assumed product shape is quadrangular pyramid and there are two variations in its height. The traveling pattern of the tool is basically square loop in accordance with the final shape. The tool head is hemispherical. The tool forces the sheet to deform plastically around the contact area. Effect of traveling speed of the tool and the density of the sheet material are pre-examined to determine the computational condition for the practical use of the code, and the computational condition is optimized for shortening the computing time without inertial effect of the material on deformation behavior. Effect of the tool path on the deformation behavior is also examined with respect to several tool paths. Calculated deformation shapes are compared among tool paths and the distribution of thickness strain is also discussed. Furthermore, the force acting on the traveling tool is also evaluated. It is concluded that the numerical simulation might be exploited for optimization of the incremental forming process of sheet metal.

Introduction

Sheet metal forming process is very common in industry. It usually requires a set of specified dies and the high capacity press machine. Cost in realizing such process is rather high. This conventional process yields a fair return on investment for the large scale production but not for small scale production.

Recently, considerable attention has been paid for the many kinds of flexible production processes. Most concerned one is the incremental forming process, which does not require any high capacity press machine and a set of dies with specified shape for the product. Incremental forming apparatus requires a traveling tool with simple shape and a holder which holds the sheet stationary at its periphery. The former consecutively forces the sheet to deform locally. A cylindrical stylus with hemispherical head is usually used as the traveling tool in contact with the formed sheet, by which the sheet is plastically deformed only around the contact area and then the whole product shape is incrementally formed with tool travel tracing the prescribed path. Of course, the properly selected tool path is very important for the successful operation, which affects markedly the accuracy of the product shape.

Many papers have been published on the incremental forming process of sheet metal, most of which are concerned with the experimental work (Iseki et al., 1996, Mori et al., 1996, Dai et al., 2000, Iseki, 2001a, Iseki and Naganawa, 2002, Kim and Park, 2002). Numerical simulation of incremental forming of sheet metal has been also carried out in some papers (Iseki, 2001b, Shim and Park, 2001), in which however the tool path is relatively simple. Effect of tool path on the deformation behavior has not been discussed. Since there is no article to which can be referred for the practical use of the numerical simulation for this process, the authors think that it is of great worth to check its applicability from the view point of making the production process more efficient.

In the present paper, deformation behavior of sheet metal in an incremental forming process is numerically simulated using a dynamic explicit finite element code DYNA3D (Halliquist, 1989). Because this is a dynamic code, mass of the material and the deformation speed affect the deformation behavior. For the general use of this code, it is pre-examined to find the basic numerical condition that the effect of mass and the deformation speed are almost suppressed within the acceptable level.

Furthermore, the effect of tool path on the deformation behavior is also studied. Assumed product shape is the quadrangular pyramid with two variations of top height. Four types of the tool path are tested to examine its effect on the formability.

Section snippets

Code used for computation

A dynamic explicit finite element code of DYNA3D (Halliquist, 1989) is used. It enables us to solve the dynamic problems regarding elastic–plastic large deformation in three-dimension. The dynamic code is useful also for the analysis of practical quasi-static deformation, keeping the deformation speed low enough for suppression of the material inertia effect on the deformation behavior within an allowable level and eliminating any hour-glass mode of deforming elements with a slight loss of

Various tool paths adopted

Path of the traveling tool is most crucial for the successful product by the incremental forming process. Fig. 3 depicts various tool paths adopted which consist of repetition of the prescribed square loops. The traveling tool moves tracing clockwise loops and the working area shifts gradually from edge portion of the sheet to the center. Thus the size of square loop decreases. Four kinds of tool paths up to the goal shape are implemented as follows:

  • Tool path I: starting position is the corner

Determination of basic computational conditions

In recent years, the dynamic explicit FEM code has been widely used for the analysis of sheet metal forming processes such as deep-drawing, stretching and bending. One of the main objectives of this study is to check the applicability of dynamic explicit finite element analysis to the incremental forming process as stated above. Inertial effect inevitably arises in the simulated results due to this code. Hence, in order to investigate exclusively the effect of tool path on deformation pattern,

Deformed shape and thickness strain distribution of product

Examples of deformation patterns obtained for the tool paths I and III are shown in Fig. 5(a) and (b), respectively, where the product apex height is 5 mm. Deformed finite element mesh is also depicted for the final shape. On the other hand, those for the product of 10 mm high due to the tool path I are shown in Fig. 5(c). The interval in vertical direction step between neighboring square loops is the same for both products, while in the horizontal direction for a higher product it is smaller

Conclusions

Deformation behavior of sheet metal in an incremental forming process is numerically investigated using a dynamic explicit finite element code DYNA3D. Assumed product shape is a quadrangular pyramid. Applicability of the numerical simulation to the process is mainly inspected. Furthermore, several types of tool paths are tested in order to find the effect of the tool path on the deformation behavior. Thickness strain distribution in the formed product and the force acting on the traveling tool

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