1. Introduction
Incremental Sheet Forming (ISF) has reached by now a high level of awareness in the industry as a forming technique for rapid prototyping or small batch production of sheet metal parts. Over the last decades, scientists and engineers from all over the world have investigated this process with the aim to achieve a flexible production of prototypes or small batches in the automotive industry, aerospace industry, and others. Thus, many relationships and influencing factors that affect the final geometrical accuracy of a part are already identified. However, for many components and applications, the required geometrical tolerances cannot be achieved. Deviations of the final geometry compared to the target geometry are too large and still hinder an industrial application of this technology. The resulting geometrical accuracy depends on many influencing factors that are interdepending and, in many cases, cannot be controlled independently. This makes the process layout a complex and iterative process. Knowledge about these influencing factors is limited to the fact that it is known which influencing factor increases or decreases an effect, but not to what extent. One example for this is the tool diameter: the formability in ISF increases with decreasing tool diameter [
1]. This statement cannot be formulated more specifically without knowledge about material, sheet thickness, wall angle, and several other influencing factors. There is still not enough process understanding to deal with all the possible interdependencies. While geometry correction algorithms sometimes achieve good results for some parts, they also might raise new questions, problems, and geometrical deviations for other parts [
2,
3]. With the experience from many manufactured parts for various industries, the authors found different forming results for the same parts depending on the dominating tool path direction. This makes it even more difficult to achieve the target geometry for new geometries. Therefore, this needs to be investigated further. After focusing on the sensitivity of the tool path direction, questions regarding other path parameters arose, in particular on the intrusion depth and how it influences the forming result.
This work is therefore structured as follows: First, a brief overview is given on the state of the art in incremental sheet forming with particular attention to the tool path. Then, finite element (FE) models and experiments are used to investigate and demonstrate the sensitivity of the tool path direction and the intrusion depth.
Incremental sheet forming is a flexible forming process for the production of small batches and prototypes. The process is characterized by incremental plastic deformations of the sheet metal, by a computerized numerical controlled (CNC) tool, which continuously moves along the contour of the target geometry according to a predefined tool path. A general distinction is made between single-point incremental forming (SPIF) and two-point incremental forming (TPIF), whereby in both cases the basic concept of local plastic deformation is retained. TPIF uses a partial or full die as a support tool, which increases the geometrical accuracy [
1]. SPIF does not use a support tool, which provides greater flexibility at the expense of geometrical accuracy. Among others, Hirt et al. [
4] and Bambach et al. [
5] were able to demonstrate a high reproducibility of incremental sheet forming parts and conclude that the geometrical accuracy can be increased by adapting or optimizing the tool path. The influence of the tool path on the resulting geometry is therefore a central issue of current research. There is already a certain amount of literature which deals with the relationships between different tool paths or path strategies and the effect on the part geometry.
Hirt et al. [
6], for example, stated that the achieved geometrical accuracy can be significantly increased by multi-stage forming strategies compared to single-stage forming strategies. A multi-stage forming strategy is a path strategy in which the final contour of the part is gradually approximated within several steps until the target geometry is reached in a final step, while the forming time is significantly increased. This confirms the underlying assumption that the tool path has a high influence on the part geometry. By a specific adjustment of the tool path, in this case by the application of a multi-stage forming strategy, geometrical properties of the sheet metal can be influenced in a systematical manner. These observations were confirmed by Duflou et al. [
7], among others. By using a multi-stage strategy in the production of a solar cooker, the achieved component accuracy was significantly increased. For “multi-pass forming strategies”, Malhotra et al. [
8] showed that the direction in which the tool moves over the sheet (inwards or outwards in multi-stage forming) also has a significant influence on the resulting part geometry. Thus, not only the tool path strategy itself could have an influence, but also the direction in which the sheet metal is formed. In addition, there are various approaches to generate specialized tool paths that try to take into account the above-mentioned relationships. For example, Wang et. al. [
9] could increase the formability and geometrical accuracy at the expense of surface quality by circular movements of the tool on the surface during the path. A modification of the standard paths created by most computer aided design (CAD)/computer aided manufacturing (CAM) applications, which is based on the knowledge of different influencing parameters, offers the ability to modify the geometrical accuracy.
To improve the forming results, correction algorithms are described in the literature that generate new paths or adapt existing paths. Bambach et al. [
10] presented a correction mechanism, in which the final geometry is scanned and a new tool path is generated based on the deviation from the target geometry. The actual geometry is mirrored in contrast to the target geometry and a new tool path is generated based on this overbent geometry. The intensity of overbending can be adjusted by a scaling factor. This correction mechanism, which is particularly suitable for SPIF, has in some cases increased the geometrical accuracy. However, the disadvantage of the overbending strategy is the development of bulges, which is based on an enlargement of the surface by creating a longer tool path than the actual part contour [
11]. Lu et al. [
12] worked on using a two-dimensional model predictive control (MPC) algorithm to control and optimize the tool path during the forming process. This resulted in increases of the achieved accuracy for the presented component geometries. Allwood et al. [
13] were able to show an on-line feedback control algorithm in their work. The reaction of the sheet metal to small deflections of the tool path in different directions is measured optically. Based on this reaction, the following part of the tool path can be adapted, which increases the geometrical accuracy. Lu et al. [
12] and Allwood et al. [
13] did not consider trimming of the parts in the presented investigations.
Another way to improve the geometrical accuracy is to combine incremental sheet forming with stretch forming. In stretch forming, a clamped sheet is formed over a lower die. The die has the shape of the target geometry. By combining these processes, the sheet can already be formed into an initial preform with stretch forming. This enables a reduced forming time compared to pure ISF because only the remaining complex areas like cavities have to be formed by incremental sheet forming. Besides the reduction of process time, Araghi et al. [
14,
15] were able to show that the superimposed tensile stresses lead to a more homogeneous strain distribution along the sheet thickness, which decreases springback.
In conclusion, the literature already describes investigations and proves the influence of the selected tool path strategy on the geometrical part accuracy. Based on this, a multitude of correction mechanisms for the targeted adaptation or generation of tool paths is described. Nevertheless, a fundamental understanding between the selected tool path strategy and the resulting geometrical accuracy is still not available. For this reason, one part of this paper focuses on the influence of the tool path direction in which the forming tool moves within a tool path strategy.
However, in conventional process planning for incremental sheet forming, the tool path direction as well as the intrusion depth are mostly not the main focus. The intrusion depth
i is defined as the distance by which the tool penetrates the sheet material and is shown schematically in
Figure 1b. This may happen in ISF as well as in the process combination for stretch forming and ISF. If sheet thinning is taken into account for process planning of the tool path (see
Figure 1a) (blue, sheet thickness
t1), then it is usually determined using simplified models such as the sine law. These models are subjected to certain limitations and assumptions. Therefore, they are not generally suitable for a precise prediction of sheet thickness distribution, especially in corners, radii, and edges [
16]. Thus, accepting these assumptions leads to cases where the forming tool intrudes the sheet material. By intruding the sheet material, which may happen due to several process inaccuracies such as the deformation of lower dies or incorrect tool path planning, the state of stress in the sheet might be changed leading to geometrical deviations. Consequently, the following investigations aim to answer the following questions:
Both the influence of tool path and intrusion depth have many interdependencies with other parameters and especially with the part geometry. Hence, this paper presents a simple test setup, trying to exclude the influence of the part geometry, using flat specimens in the first setup. These investigations aim to isolate the influence of tool path direction and intrusion depth as far as possible.
The presented results from experiments and FE simulations will demonstrate that the influence of the tool path direction and the intrusion depth on the resulting part geometry is very sensitive. Besides the tool path design, such as “z-level” or “multi-stage”, even the tool path direction influences the part geometry. To be able to control the geometrical accuracy in ISF at all in the future, the authors would like to raise the awareness for these effects and to motivate further investigations with this paper. The investigations are supported by an FE model, which reproduces the experimental findings qualitatively and therefore enables a deeper understanding of the influences on the geometrical accuracy in further work in the future.