Thermal models for copper-alloyed dies in pressure die casting

Abstract

A recent innovation in pressure die casting is the use of copper-alloyed dies suitably protected with a thermally sprayed steel layer. The thermal response of copper-alloyed dies is dictated principally by the deposited layer, the cooling arrangement and the casting geometry. This paper is concerned with the development of efficient numerical models for the prediction of both steady-state and transient thermal behaviour of the new die designs. Die temperatures are cyclic but useful information is obtained from a steady-state model, which provides for time-averaged temperatures and energy fluxes. The modelling strategy presented in the paper involves the indirect determination of transient temperatures. A perturbation approach is adopted, where a model for the difference between transient and steady-state temperature is developed. It is shown that this approach can be utilised to determine transient temperature efficiently once steady-state information is available with the transient perturbation model only involving surfaces where a significant variation in temperature occurs. The die-thermal models are founded on the boundary element method as die surface temperatures are of primary importance in pressure die casting. The finite element method is used to model casting solidification, where the formulation adopted provides for accurate energy transport. The dies form a multi-domain environment for thermal predictions making it necessary to utilise a suitably constructed coarse preconditioner to enhance numerical stability and provide for efficient computation. A multiplicative Schwarz method is presented that enables a parameter matrix accelerated GMRES method to be applied on each domain. Numerical experiments are performed to demonstrate the computational effectiveness of the approach. Predicted temperatures are compared with thermocouple readings obtained from a copper–steel die on a commercial die casting machine.