Presented for the North American Die Casting Association 1999 Die Casting Modeling and Simulation Session,
on November 1-4,1999 in Cleveland, Ohio

by:
Shawn Mahaney, Project Engineer
EKK, Inc.

November 1, 1999

It has been found desirable to use a finite element method (FEM) formulation in the simulation of die casting processes involving complex shapes.

FEM Mesh generation has in the past involved many hours of labor to get good meshes of multi-component dies. Sometimes geometry was compromised to save human time or mesh quality was not maintained - increasing computation time without decreasing human time.

Accurately representing different die components and their interfaces can be critical for accurate cyclic thermal modeling.

Great strides have been made in automating the generation of complex, multi-component FEM meshes. These efforts take advantage of both increases in computer speed and the more common creation of detailed 3-D solid models of die components.

A case study is presented demonstrating the application of several meshing techniques, from a semi-automatic layered approach to an almost fully automated system. Various simplifications are imposed and their consequences shown. In this study, a new fully automatic FEM mesh generation technique has been applied to a thin-walled high pressure die casting. The flow results on this mesh are compared to the traditional, labor-intensive, FEM mesh, a hybrid FEM-FDM mesh, an orthogonal (FDM) mesh, and the experimental result.
 

INTRODUCTION

Foundry process simulation technology has become an essential tool for the metal casting industry. This is especially true in diecasting where the tooling costs are high. As a result, the use of computer process simulations for diecastings has been increased recently. There are, however, still bottle-necks inhibiting wider spread use of this technology.

Recent computer hardware technology has increased the computer performance and decreased its price drastically. Current PC based systems can handle the simulation problems for which you might have required an expensive engineering workstation a few years ago. Thus, the computer hardware is not a significant problem anymore to practical process simulation.

Advantages of using the Finite Element Method (FEM) for diecasting processes have been discussed (1). The geometric flexibility of FEM is essential to model the thin-walled complex diecastings. With FEM, the numerical algorithm that is well suited to diecasting's filling and thermal analysis process simulation has been established.

One of the most significant bottle-necks (time-consuming efforts) in applications of FEM to any computer simulation is, ironically, the use of its geometric flexibility, namely mesh generation. Therefore three-dimensional (3-D) automatic mesh generation is recognized as essential to use FEM today and it becomes an active research area for the FEM community. Most commercially available automatic mesh generators create the tetrahedral elements based on the algorithm of a 3-D version of Delaunay tesselation (2) or advancing front method (3). They require a well shaped 3-D triangle surface mesh before starting to create the 3-D mesh. This also is not a trivial task. In addition, many analysts prefer to use hexahedral elements, noting their superior performance. Thus, we have developed new mesh generators for casting simulation.

In this paper, we describe two new mesh generation techniques particularly suited to metal casting process simulation. One is a fully automatic FEM mesh generator and the other is a unique hybrid FEM-FDM mesh generation.
 

AUTOMATIC MESHING

Contrary to FEM, automatic Finite Difference Method (FDM) mesh generation is in principle straightforward. First, the orthogonal block mesh is covered over the region that you want to analyze. Then, each element is examined for whether it is inside of the domain or not. To find if an element is inside, an arbitrary line is drawn through the element center and then the number of times this line cuts through the boundary surface is counted. An even number means that this element is outside and an odd number means the element is inside. There is no node or element modification at the boundary. Thus, a smooth curved surface can not be represented. Instead, it would be replaced by the zigzag element surfaces (see Figure 5). If the engineers could accept this poor reproduction of the geometry, the FDM mesh generator is very efficient and easy to use. This, however, could lead poor analysis results as well.

To reduce the inaccuracy of the FDM mesh without losing its efficiency and ease of use, only boundary elements have been modified to smooth the boundary. Six-noded wedge and tetrahedral elements have been introduced at the boundary over the orthogonal FDM mesh. This alters the integer index element numbering and the orthogonality of the conventional FDM mesh but improves the smoothness (accuracy) of the mesh. Since no nodes have been moved or modified, this meshing posseses the efficiency and ease of use of the traditional FDM mesh. This meshing scheme can even be used on an existing FDM mesh for improvements. This type of mesh is called hybrid FEM-FDM mesh.

Although the hybrid FEM-FDM mesh could give improvement over the FDM mesh, it is still limited. Thus, nodes near the boundary should move to the boundary without destroying the element. This leads us to a fully automatic voxel based 3-D FEM mesh generation (4)(5). This type of mesh generation scheme particularly suits casting process modeling, because the casting and the mold are created at the same time. One of the most common problems for this type of meshing is a poor element quality at the boundary. Thus, robust analysis software are needed to use this type of meshing scheme.
 

Case Study

We were approached with a simulation problem by MIRDC in Taiwan. A client of theirs was having difficulty with this thin-walled high-pressure die cast part. The part was not filling cleanly, showing heavy knit lines (figure 1). MIRDC was having trouble matching the flow patterns using a commercial FDM foundry software simulation package.

(fig1)

Initially, only a filling simulation was requested using our manual meshing system and FEM solver. From the defects in the castings, we suspected some influence of thermal conditions on the flow pattern and insisted on doing a cyclic thermal/solidification simulation in order to establish mold temperatures for a coupled flow/heat transfer solution. CAD data was only available for the casting, so the die components and cooling system were added to the FEM mesh from 2-D sketches (figure 2) and text descriptions.

We also invited MIRDC to participate in this study, initially with just their FDM result, our hand-built FEM result, and our hybrid mesh result. Later we would add results for an FDM mesh in our solver, as well as a new automatically generated FEM mesh. In each case, a half-symmetry model is used.
 
 

Mesh Generation

Hand-built FEM Mesh

Having had many years experience in solving real-world problems with manually generated meshes, we expected that the result on the hand-built mesh would closely match the real castings. Good correlation with the actual casting was indeed observed. The manual meshing method, as developed specifically for casting process simulation, provides good element quality and density control, but this mesh took about a week to create from the provided data. Even with a week into it, there are some clear approximations in the shape of the gating and overflows, and some subtle ones in the part itself.

FDM Mesh

It is relatively straightforward to generate a FDM mesh on a set of closed surface files. Even with some user guidance of the mesh density, this mesh can be made in less than an hour. Some care must be taken to ensure that thin walls are meshed with multiple elements across their thickness. The FDM mesh and the following hybrid and automatic FEM meshes were all generated with essentially equal element density.

Hybrid Mesh

This method was established recognizing the difficulties in building an automatic finite element mesh of sufficient quality for HPDC flow simulation, especially for complex multi-region dies. The hybrid meshing system begins at the same point as the fully automatic system, but stops short of actually moving nodes to smooth the mesh to the surface. The hybrid method does however take advantage of the finite element method by cutting the previously established hexahedral elements into appropriate "subordinate" shapes so as to cut the mesh as close to the real surface boundaries as possible. This method requires just as many elements as the fully automatic mesh generator, while still not getting the same geometric quality, but it can be applied to complex shapes very quickly. It also permits manual editing of the element assignment on the different layers, such as when adding a cooling loop. This method is also considered to be at a great advantage over a pure FDM mesh while still being almost as quick for the computer to generate.

Automatic FEM Mesh

Finally a fully smoothed version of the mesh was generated. Generation of this mesh relies on the same first steps as in generation of the FDM and hybrid meshes. It takes full advantage of the geometric flexibility inherent in the finite element method to fit the initially orthogonal grid smoothly to the casting surface. The reader is reminded that there are also numerous mold components around this cavity mesh which are also smoothly meshed at the various interfaces.

Results

The flow results for the hand-built and automatic meshes are compared in figures 8-13. All analyses were performed using a commercially available finite element solver Generally we were encouraged by the overall similarity of the results, and that the flow solver was stable and still relatively fast with the somewhat "bumpy" hybrid and FDM meshes.

Some of the die surface temperatures are shown. These temperatures were used in the flow simulation as the die temperatures during fill. Since the majority of the casting surface is in-plane with one of the FDM mesh axes, the temperatures are very similar in the FEM and FDM simulations. If there were longer curved sections in the casting surface, the surface area exposed to the mold would be incorrect for the FDM case and significant error would be expected in the heat transfer rate.

Independently, the flow patterns are each fairly convincing. That is, they look realistic. Comparing between them, however, the impact of the approximations in the geometry for the FDM and hybrid meshes becomes clear. In the FDM case the flow over the curving walls of the cavity is impeded by the "stair steps" in the wall. The flow front is artificially diffused, and also agitated, by this effect and the liquid metal appears to advance across the part uniformly, not showing any tendency toward the defects seen in the real castings. The results on the hybrid mesh are closer to the smooth mesh results. Metal advances faster on the outside of the flat part of the cavity. Still the faster stream in the center of the casting is not seen.

The smooth automatically generated finite element mesh reveals a more detailed flow pattern. This flow is much closer to the result on the hand built mesh. The metal temperatures are still more varied than from the hand built mesh. We suspect that this may be related simply to the greater element density in the automatically generated mesh.

Run times are reported for each simulation. Two desktop machines are used, one running at 200 MHz, the other at 450 MHz. Results of other benchmark tests show that these machines can be compared almost exactly by CPU

speed (i.e. the faster machine is 2.25 times faster on the same problem).
 

Conclusions

New automatic meshing techniques have been successfully applied to reduce human labor involved in casting process simulation. Capturing complete geometric detail, especially smooth interfaces, has been shown to be important for high pressure die casting flow modeling.

While this automatic meshing technique will save human labor costs, it should be noted that simulations will take longer. Computational costs increase in both time and hardware. Most importantly, this meshing technique is much more reliant on external CAD work. Any significant changes in the cavity design necessitate a new CAD model and a fresh start for the mesh generator.
 
 

References

1. S. Mahaney and C.-W. Kim, 'Modeling of the Die Casting Process - A Finite Element Method Approach', Die Casting Engineer, November, 1996
2. T. Taniguchi and C. Ohta, 'Grid generation for complex 3D body and its surface', Computer Mechanics (ed. by Y. K. Cheung, J. H. Lee and Y. T. Leung), Balkema, pp. 1283-1288 (1991)
3. O. Hassan, K. Morgan, E. J. Probert and J. Peraire, 'Unstructured Tetrahedral Mesh Generation For Three-Dimensional Viscous Flows', Int. J. Numer. Methods Eng., 39, 549-567(1996).
4. S. H. Lo, 'Volume Discretization Into Tetrahedra-II. 3D Triangulation by Advancing Front Approach', Comput. Struct., Vol.39, No. 5, 501-511(1991).
5. S. H. Lo, 'Automatic Mesh Generation Over Intersecting Surfaces', Int. J. Numer. Methods Eng., 38, 943-954(1995).
6. P. Frey, B. Sarter and M. Gautherie, 'Fully Automatic Mesh Generation For 3-D Domains Based Upon Voxel Sets', Int. J. Numer. Methods Eng., 37, 2735-2753(1994).
7. C. Yeker And I. Zeid, 'Automatic Three-Dimensional Finite Element Mesh Generation Via Modified Ray Casting', Int. J. Numer. Methods Eng., 38, 2573-2601(1995).

	Hand-built Mesh	FDM Mesh	Hybrid Mesh	Auto Mesh
(fig 8 a,b,c,d) Ejector side surface temperature before filling. (° C)
(fig 9 a,b,c,d) Fluid iso-contours 0.095 seconds into filling.
(fig 10 a,b,c,d) Fluid surface temperature contours 0.095 seconds into filling. (° C)
(fig 11 a,b,c,d) Fluid iso-contours 0.105 seconds into filling.
(fig 12 a,b,c,d) Fluid surface temperatures 0.105 seconds into filling. (° C)
(fig 13 a,b,c,d) Fluid velocity vectors 0.105 seconds into filling. (cm/sec)
Model size	Thermal: 472,000 nodes, 477,000 elements. Fluid: 50,600 nodes, 38,100 elements, 300,000 solid nodes & elements for heat transfer only.	Thermal: 2,620,000 nodes, 2,680,000 elements. Fluid: 142,000 nodes and 106,000 elements, 55,000 solid elements for heat transfer only.	Thermal: 2,720,000 nodes, 2,680,000 elements. Fluid: 149,000 nodes and 162,000 elements, 62,000 solid elements for heat transfer only.	Thermal: 2,260,000 nodes, 2,260,000 elements. Fluid: 139,000 nodes and 139,000 elements, 59,000 solid elements for heat transfer only.
Runtime and Hardware	Cyclic thermal: 16+ die casting cycles in 24.5 hours; Pentium Pro 200 MHz under Linux 2.2 using 70 MB RAM Fluid: 4.9 hours; Pentium II 450 MHz under Linux 2.2 using 130 MB RAM.	Cyclic thermal: 16+ die casting cycles in 140 hours; Pentium II 450 MHz under Linux 2.2 using 420 MB RAM Fluid: 14.6 hours, Pentium II 450 MHz under Linux 2.2 using 210 MB RAM	Cyclic thermal: 16+ die casting cycles in 110 hours; Pentium II 450 MHz under Linux 2.2 using 425 MB RAM Fluid: 34 hours, Pentium Pro 200 MHz under Linux 2.2 using 215 MB RAM	Cyclic thermal: 16+ die casting cycles in 70 hours; Pentium II 450 MHz under Linux 2.2 using 380 MB RAM Fluid: 39 hours, Pentium Pro 200 MHz under Linux 2.2 using 190 MB RAM