Modelling the pressure die casting process using a hybrid finite-boundary element model

In this paper an efficient three-dimensional hybrid thermal model for the pressure die casting process is described. The Finite Element Method (FEM) is used for modelling heat transfer in the casting, and the Boundary Element Method (BEM) for the die. The FEM can efficiently account for the non-linearity introduced by the release of latent heat on solidification, whereas the BEM is ideally suited for modelling linear heat conduction in the die, as surface temperatures are of principal importance. The FE formulation for the casting is based on the modified effective capacitance method, which provides high accuracy and unconditional stability. This is essential for accurate modelling of the pressure die casting process and efficient coupling to the BEM. The BE model caters for surface phenomena such as boiling in the cooling channels, which is important, as this effectively controls the manner in which energy is extracted. The die temperature is decomposed into two components, one a steady-state part and the other a time-dependent perturbation. This approach enables the transient die temperatures to be calculated in an efficient way, since only die surfaces close to the die cavity are considered in the perturbation analysis. A multiplicative Schwarz method for non-overlapping domains is used to couple the individual die blocks and casting. The method adopted makes use of the weak coupling between the domains, which is a result of the relatively high interfacial thermal resistance that is present. Numerical experiments are performed to demonstrate the computational effectiveness of the approach. Predicted die and casting temperatures are compared with thermocouple measurements and good agreement is indicated.