# Simulation of micro casting

The simulation of micro casting requires multiscale and multiphysics models. A combination of particle methods, the finite element method and model order reduction is proposed.

### Coupling of smoothed particle hydrodynamics and reduced order heat transfer model for casting simulation

Microcasting is a metal forming process based on lost-wax lost-mold investment casting. It is used to create small structures in the micrometer range by using a metal melt which is cast into a microstructured mold. Fields of application are, e.g., instruments for minimal invasive surgery, dental devices and instruments for biotechnology, allowing for very complicated parts even with undercuts.

The process parameters have a large influence on the casting results. Especially in the micro range, solidification may occur before the mold is filled completely, and long structures with small diameters could clog. The reason is that since the melt may be cooled below its liquidus temperature too early due to the contact with the colder mold. It is thus imperative to preheat the mold, yet temperatures should remain as low as possible to save processing time and energy. Further, the cooling curve determines the size of grains in the microstructure.

Simulation is used to estimate the cooling curves and to optimize process parameters. Further, the microstructure of the metal, with grain sizes which can come close to the lenght scale of the device's features, are interesting for the designer. Simulation can help to optimize the process parameters, predict the filling of the mold and provide cooling curves for the determination of the grain structure with the microstructure simulator MICRESS.

Figure 1 shows an example of a coupled simulation of the micro casting process using the finite element method with model order reduction for the heat transfer and smoothed particle hydrodynamics for the flow.

### General simulation concept

Casting simulation for microscale components requires multiscale modelling of the heat exchange between the melt and the macroscopic mould, the results allowing for detection of early solidification and the calculation of cooling curves. This challenge can be handled by a combination of the finite element method (FEM) with model order reduction (MOR) [1,2] of the resulting system of ordinary differential equations (ODEs) and smoothed particle hydrodynamics (SPH) in an integrated model.

The melt model, discretized with SPH, is coupled to an order reduced FEM system representing the mould. In this way, the advantages of the Lagrangian discretization of the fluid can be combined with the potential of a spatially refined FEM grid while keeping the requirements on computational ressources low.

Figure 2 illustrates the general concept of coupling the different simulation methods.

### Coupling with master/slave particles

Coupling is performed through a set of fixed ("wall") particles placed outside of the cavity's boundary, inside the FE mesh (see figure 3). They serve as the slaves in a master/slave coupling setup [3]. To each of those, a small patch on the boundary is assigned, the patches being chosen based on the expected fluid flow and required spatial resolution and serving as thermal input of the reduced ODE system.

#### References

[1] Lienemann, J., Rudnyi, E. B., and Korvink, J. G.: MST MEMS model order reduction: Requirements and benchmarks. Linear Algebra and its Applications, 415: 469498, 2006.

[2] Antoulas, A. C.: Approximation of Large-Scale Dynamical Systems, Advances in Design and Control 6. SIAM, 2005.

[3] Rabczuk, T., Xiao, S. P. and Sauer, M.: Coupling of mesh-free methods with finite elements: basic concepts and test results. Commun. Numer. Meth. Engng, 22:10311065, 2006.

### Relevant publications

- Jan Lienemann, Iva Cenova, David Kauzlaric, Andreas Greiner, Jan G.Korvink, Coupling of Smoothed Particle Hydrodynamics and Reduced Order Heat Transfer Model for Casting Simulation, Proceedings MATHMOD 09, Vienna, February 11-13: 1287-1292, 2009
- J. Lienemann, I.Cenova, D. Kauzlarić, A.Greiner, J. G. Korvink, Kopplung der Smoothed Particle Hydrodynamics-Methode mit einem Wärmetransportmodell reduzierter Ordnung für die schnelle Simulation des Mikrogussprozesses, Proccedings of the 4. Kolloquium Mikroproduktion, Eds.: F. Vollertsen, S. Büttgenbach, O. Kraft, W. Michaeli, Bremen: 99-104, 2009
- D. Kauzlarić, J. Lienemann, L. Pastewka, A. Greiner, J. G. Korvink, Integrated process simulation of primary shaping: multi scale approaches Microsystem Technologies: doi 10.1007/s00542-0, 2008

### Contact persons

Raghav Pasricha, Jan Lienemann

### Collaboration partners

Jürgen Haußelt, IMF3, Karlsruhe Institue of Technology (KIT)