Thermal Modelling In Pressure Die Casting

Abstract

The pressure die casting process is cyclic and the temperature levels in the die are principally dictated by the total energy received from the casting. It is thus extremely important that any solidification model for the casting is able to predict energy extraction rates to a high degree of accuracy. 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, coupled to a boundary element (BE) model 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 a control volume capacitance method, which is shown to provide high accuracy and stability. This method is similar to the apparent and effective heat capacitance methods, which are popular approaches used where conduction predominates over other heat transfer mechanisms. These methods involve the specification of element or nodal capacitances to accommodate for the release of latent heat. Unfortunately they suffer from a major drawback in that energy is not correctly transported through elements and so providing a source of inaccuracy. The control volume capacitance method allows for the transport of mass arising from volumetric shrinkage and ensures that energy is correctly transported. 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. The governing equations across domains are coupled by means of a multiplicative‐Schwarz method for non‐overlapping domains as focus is on the use of serial processing. A coarse preconditioner is utilised and obtained from a crude representation of the global system of equations. 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.