Development of an improved mathematical model of the heating phase of thermoforming process

This paper presents an improved mathematical model to represent a more accurate relationship among inputs and outputs of the heating phase of the thermoforming process. The proposed state-space model of the heating phase of thermoforming process can present and explain some incidents which are impossible to explain using the existing model. The main purpose of the paper is to improve the quality of predictions of the system´s output and state through more accurate evaluation of the inputs and system properties. First, the modeling is developed based on the heat transfer method and system´s behaviour. Then, a series of specialized experimental data were compared with the simulation data obtained from the developed model to validate it. All three kind of heat transfer methods (conduction, convection and radiation) are considered in the development of the model of a thermoforming machine. The proposed state space model is simulated using a Simulink model to compare with real time results. The input output relationship of the proposed model almost accurately follows the real time relationship of the inputs and outputs at different operating conditions. The proposed model gives the improved results compared to the existing model with the real time experimental data even there was some discrepancy of the existed model result with the real time data. The accuracy of the proposed model is evidenced by the results.