Dynamic modeling of fluid-cooled tools in periodic thermal processes

Due to the cyclical nature of the high pressure casting process, there will be a thermal periodic steady state of the high pressure die casting dies (hpdc-dies) during operation. A continuous temperature pattern (as a function of time), that is recurring during each process step can be observed. The quality of the castings as well as the life span of the tools is highly dependent on these periodic temperature patterns. It would be state of the art to simulate the hpdc-process with highly-specialized process simulation software. However, because of the high initial costs and the necessary human and computational resources, their use during operation to adjust the parameters of the cooling management is generally not utilized. Instead, the input parameters of the cooling management are chosen by trial and error. This paper focuses on the development a simple linear thermal model to describe the temperature patterns within the die. This is helpful to control the cooling management more effectively during operation. Approaches of dynamic systems simulation are used to create a model of the energy transport phenomena within the hpdc-die. Here it is shown in general terms how to model fluid-cooled solids by the combination of n sub process steps in n state space models to depict the whole thermal cyclical process. The set up of sets of balance equations are shown with a simplified example, using formal matrix operations. The obtained results of the simulation are discussed and evaluated. The conclusions of measured data from the experimental hpdc-die are compared to the solution of the simulation using the thermal model approach described above.