1. Scope of the Study
In the modern engineering world, technological advancements drive the product design process. Increasingly powerful CAD programs make more complex product designs possible, which in turn boost the demand for more complex prototypes. At the same time, fast-moving competitive markets require frequent design changes, shorter lead times, and tighter budgets. In short, prototyping must be faster, better, and less expensive.
Within this context, rapid prototyping in sheet metal is highly desirable because the manufacturing of functional prototypes speeds up the time to market. While the market is well developed when it comes to rapid prototyping for plastic parts, the options for prototyping geometrically complicated sheet metal components are more limited and extremely expensive, because all the methods available require expensive tooling, machinery or manual labor.
Unlike many other sheet metal forming processes, incremental forming does not require any dedicated dies or punches to form a complex shape. Instead, the process uses a standard smooth-end tool, the diameter of which is far smaller than the part being made, mounted on a three-axis CNC milling machine.
The sheet metal blank is clamped around its edges using a blank-holder. During the forming process, the tool moves along a succession of contours, which follow the final geometry of the part, and deforms the sheet into its desired shape incrementally.
2. Context of the Research
The work presented in this thesis was started in October 2003 in the framework of the SeMPeR project (Sheet Metal oriented Prototyping and Rapid manufacturing). This was a four-year-long project, whose purpose was to develop a research platform that would support an in-depth analysis of the incremental forming and laser forming processes. This platform supported experimental, numerical, and analytical research activities, the interaction between which was expected to lead to the design of new and improved process variants and the identification of effective process planning and control strategies.
Four research partners from three different universities were involved in the project, covering the various academic disciplines required. As project leader, the PMA Department of the Catholic University of Leuven (KUL) provided extensive background knowledge in numerically controlled sheet metal forming processes, as well as long-term experience of experimental hardware development and process planning. This department was in charge of the experimental study of the processes. The MTM Department from the same university studied the processes in detail using accurate finite element models. The MEMC Department of the Free University of Brussels (VUB) provided expertise in in-process strain and displacement measurement, and material characterization by means of inverse method techniques. Finally, the ArGEnCo Department of the University of Liège (ULg), to which the present author is affiliated, undertook the task of developing a finite element code adapted to the incremental forming process.
Because of its promising outcome, the project held wide industrial interest: several companies assisted in ensuring the ultimate industrial relevance of the research and provided logistical support in terms of hardware, materials, and specific data.
3. Objective of the Thesis
Although the SeMPeR project aimed at studying two rapid prototyping processes, the present work focused only on one of those: incremental forming. The goal of the team at the University of Liège was to adapt a department-made finite element code, Lagamine, to the incremental forming process. In particular, the computation time had to be reduced as much as possible while maintaining a sufficient level of accuracy.
4. Outline of the Thesis
The body of the text is divided into three parts.
The first part contains two chapters. The first of these provides a literature review in the field of incremental forming. More specifically, it introduces the process, presents an overview of its practical implementation and experimental setup requirements, and shows its benefits and limitations. Then, the chapter focuses on the latest developments in terms of finite element modeling and analytical computations.
The second chapter presents the numerical tools used throughout this research. This consists mainly of the finite element code, the elements, and the constitutive laws. Then, this chapter gives an overview of the experimental setup and measuring devices used during the experimental tests performed in Leuven. The second part focuses on dynamic explicit simulations of incremental forming and contains four chapters. The first justifies the use of a dynamic explicit strategy. The second presents the new features added to the finite element code in order to be able to model incremental forming with such a strategy. The third explains the computation of the mass matrix of the shell element used throughout this part of the thesis and justifies this computation. Finally, the fourth chapter analyzes the overall performance of the dynamic explicit simulations both in terms of accuracy and computation time.
The third part of this thesis contains an in-depth analysis of the incremental forming process using more classic implicit finite element simulations. This analysis is performed in two steps. In a first chapter, the influence of using a partial mesh for the simulations is evaluated in terms of accuracy and computation time. Then, in a second and final chapter, a detailed analysis of the deformation mechanism occurring during this forming process is carried out.
Finally, this thesis ends with the major conclusions drawn from the research and perspectives on possible means of further improving the simulation tool.
5. Original Contributions
Through this research, several major contributions were achieved.
First, a comprehensive literature review of the incremental forming process was carried out. In particular, the review focused on original articles concerning the limitations of the process and possible ways of bypassing them; on the most recent explanations for the increased formability observed during the process; and on the state of the art in finite element simulations of incremental forming. Understanding the concepts and difficulties inherent in these publications was made possible particularly by the SeMPeR project thanks to the discussions held and the monthly follow-ups on research performed by its members.
Secondly, Lagamine's shell element was corrected and its mass matrix modified to enable its use with an explicit strategy. Following this, a new approach for modeling the contact between an element and the forming tool during simulations in a dynamic explicit strategy was developed and thoroughly tested. A detailed comparison of the influence of various finite element parameters on the simulations' results was performed, in particular regarding the choice between using the implicit and explicit strategies and the use of mass scaling to reduce the computation time.
In addition, many simulations were validated thanks to experimental results.
Moreover, the computation time required for simulations of the forming of parts with rotational symmetry was radically reduced by using a partial model with a new type of boundary conditions.
Finally, the material behavior occurring during incremental forming was analyzed.