Development of a Computationally Efficient Model of the Heating Phase in Thermoforming Process Based on the Experimental Radiation Pattern of Heaters

In this study, an accurate and computationally efficient model for the heating process of thin thermoplastic sheets during thermoforming is developed. This model opens the door to efficient training of model-free control approaches in thermoforming applications, which often require extensive training data that would be significantly costly and time-consuming to generate using physical setups. This model takes into account heat transfer via radiation between heaters and the sheet, heat transfer via conduction through the sheet, and heat transfer via convection between the sheet and the ambient. In this paper, rather than using an analytical relationship for the view factor, an experiment is designed to determine the exact radiation pattern of the heater on the sheet and the fraction of infrared emission absorbed by the sheet. Comparing the output temperature profile on the sheet from the designed model to IR images from a laboratory-scale heating system indicates that the mean square error is reduced by around four times when compared to traditional models with analytical view factors. Moreover, a comparison of the computation time with COMSOL software for a scenario with the same configuration of computation hardware reveals that the designed model is almost ten times faster.