[ Modélisation par éléments finis et optimisation de l’étape de chauffage infrarouge pour le traitement thermique de préformes en PET à l’aide de la commande Linéaire Quadratique (LQR) : Application au four infrarouge de la souffleuse industrielle FG-8 de l’usine de production d’eau minérale VALVITA ]
Volume 39, Issue 2, April 2023, Pages 1000–1049
KONGOLO MONGA Epaphrodite1, Moïse MUKEPE KAHILU2, and Jacques KADIMA KAZAKU3
1 Département d’Électromécanique, Faculté Polytechnique, Université de Lubumbashi, RD Congo
2 Département d’Électromécanique, Faculté Polytechnique, Université de Lubumbashi, RD Congo
3 Département d’Électromécanique, Faculté Polytechnique, Université de Lubumbashi, RD Congo
Original language: French
Copyright © 2023 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Our study focuses on the modeling of infrared radiation heating and the optimal control of the heating process of preforms used in the manufacturing process of PET bottles. In the manufacture of a bottle by injection blow molding, the heat treatment of the preform plays an essential role. In this work, we have set up an approach which goes from the phenomenological modeling of heat exchanges (conduction, radiation, convection) and which lead to partial differential equations until the numerical integration of these equations. The approach used is that based on finite elements, since the partial differential equations make it difficult to understand the behavior of the physical system. This choice is due to the fact that it allows to solve numerically the systems with complex geometry. The term source of radiation integrated into the heat equation was calculated with a Beer-Lambert law applied to each ray emitted by halogen lamps. The objective is to calculate, under a single digital simulation platform, the complete thermal mapping of the preform as it leaves the oven. It is therefore, using numerical simulation in Matlab, to be able to first predict the longitudinal temperature mapping of the preform, as well as a state representation of the system simulating the temporal temperature profile during of the heating phase. Secondly, it is about the optimal control of the heating process. This optimization consists of limiting the optimization variables included in the interval (90°C
Author Keywords: Heating, radiation, infrared, finite elements, preforms, PET preforms.
Volume 39, Issue 2, April 2023, Pages 1000–1049
KONGOLO MONGA Epaphrodite1, Moïse MUKEPE KAHILU2, and Jacques KADIMA KAZAKU3
1 Département d’Électromécanique, Faculté Polytechnique, Université de Lubumbashi, RD Congo
2 Département d’Électromécanique, Faculté Polytechnique, Université de Lubumbashi, RD Congo
3 Département d’Électromécanique, Faculté Polytechnique, Université de Lubumbashi, RD Congo
Original language: French
Copyright © 2023 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Our study focuses on the modeling of infrared radiation heating and the optimal control of the heating process of preforms used in the manufacturing process of PET bottles. In the manufacture of a bottle by injection blow molding, the heat treatment of the preform plays an essential role. In this work, we have set up an approach which goes from the phenomenological modeling of heat exchanges (conduction, radiation, convection) and which lead to partial differential equations until the numerical integration of these equations. The approach used is that based on finite elements, since the partial differential equations make it difficult to understand the behavior of the physical system. This choice is due to the fact that it allows to solve numerically the systems with complex geometry. The term source of radiation integrated into the heat equation was calculated with a Beer-Lambert law applied to each ray emitted by halogen lamps. The objective is to calculate, under a single digital simulation platform, the complete thermal mapping of the preform as it leaves the oven. It is therefore, using numerical simulation in Matlab, to be able to first predict the longitudinal temperature mapping of the preform, as well as a state representation of the system simulating the temporal temperature profile during of the heating phase. Secondly, it is about the optimal control of the heating process. This optimization consists of limiting the optimization variables included in the interval (90°C
Author Keywords: Heating, radiation, infrared, finite elements, preforms, PET preforms.
Abstract: (french)
Notre étude porte sur la modélisation du chauffage par rayonnement infrarouge et la commande optimale du processus de chauffage des préformes utilisées dans le procédé de fabrication des bouteilles en PET. Lors de la fabrication d’une bouteille par injection-soufflage, le traitement thermique de la préforme joue un rôle essentiel. Dans ce travail, nous avons mis sur pied une démarche qui va de la modélisation phénoménologique d’échanges thermiques (conduction, rayonnement, convection) et qui conduisent à des équations aux dérivées partielles jusqu’à l’intégration numérique de ces équations. L’approche utilisée est celle basée sur des éléments finis, étant donné que les équations aux dérivées partielles rendent difficile l’appréhension du comportement du système physique. Ce choix est dû au fait qu’elle permet de résoudre numériquement les systèmes à géométrie complexe. Le terme source de rayonnement intégré dans l’équation de la chaleur a été calculé avec une loi de Beer-Lambert appliquée à chaque rayon émis par les lampes halogènes. L’objectif est de calculer sous une unique plateforme de simulation numérique, la cartographie thermique complète de la préforme en sortie du four. Il s’agit donc, à l’aide de la simulation numérique sous Matlab, de pouvoir prédire dans un premier temps la cartographie longitudinale en température de la préforme, ainsi qu’une représentation d’état du système simulant le profil temporel de température lors de la phase de chauffage. Dans un second temps, il s’agit de la commande optimale du processus de chauffage. Cette optimisation consiste à borner les variables d’optimisation comprises dans l’intervalle (90°C
Author Keywords: Chauffage, rayonnement, infrarouge, éléments finis, préformes, préformes en P.E.T..
How to Cite this Article
KONGOLO MONGA Epaphrodite, Moïse MUKEPE KAHILU, and Jacques KADIMA KAZAKU, “Finite element modeling and optimization of the infrared heating step for the heat treatment of PET preforms using the Linear Quadratic (LQR) control: Application to the infrared oven of the FG-8 industrial blower of the factory of VALVITA mineral water production,” International Journal of Innovation and Applied Studies, vol. 39, no. 2, pp. 1000–1049, April 2023.
