Optimization of the heating system by electrical resistances in a rapid thermal response mold based on MSR-PSO-FEM

Abstract

The aim of this work to optimization of the heating system by electrical resistances for a rapid thermal response mold (MRTR), using the response surface methodology (MSR). Applying the design technique of the Box-Behnken experiments, a matrix of experiments with four factors and three levels was designed. The design variables that are used to describe the design and shape of the heating system are the heat flux per unit area of the electrical resistance, the distances from the center of the heaters to the surface of the cavity, the distance between the adjacent electrical resistors and the thickness of the heating plate. The heating time, the variation of the temperature in the cavity and the VonMises stress were considered as the variables of the model. Thermal and thermal-structural resistance analyzes of the model based on finite element method (FEM) are performed to acquire the objective variables. Mathematical response surface models are developed using the mixed regression model and the response surface model and the variance analysis method (ANOVA) is used to verify the accuracy of these mathematical models. With the obtained models, the position of the electric resistances is optimized and the ratio between mass and volume of the cavity insert is reduced to minimize the heating time within a reasonable temperature distribution and structural strength, coupling the surface models of response developed with the method of particle swarm optimization (PSO). The results obtained indicate that the required heating time on the surface of the cavity can be significantly reduced in the molding cycle, demonstrating with these the effectiveness of the heating system.