Modeling and simulation for varying die gap fluid extrusion

Abstract

The analysis and the simulation of fluid extruded out of a die opening are of great importance in different industrial applications. Mathematical modeling and experimental studies of extrusion out of a constant die gap has been the subject of numerous publications in the literature. Extrusion Blow Molding is a polymer forming technique used to manufacture a wide range of large hollow parts such as fuel tanks used in the automotive industry. The die gap is varied during extrusion to adjust the manufactured product's final thickness and to compensate for uneven stretching during molding. In this work, mathematical modeling of varying die gap extrusion is introduced. Two models using different approaches are presented to model the time dependent effects of varying the die gap on the extrudate.In the first approach, physics based partial differential equations are used to simulate extrusion. The Navier Stokes equations are used as governing equations to simulate molten polymers. The governing equations are solved using Arbitrary Lagrangian Eulerian based Finite Element Method. A novel numerical method for defining the free surface of the extrudate is proposed. In addition, the effects of varying the die gap on the material velocity, pressure and extrudate shape are reported.In the second approach, a parameter identification scheme is used to obtain the parameters of a novel model with a predefined structure. The purpose of the proposed model is to replicate time dependent extrudate thickness of the physics based model. The parameters of the model are identified by minimizing the response error between the two models due to step inputs. The parameter identification based model provides a computationally low cost alternative to the physics based model. Moreover, the parameter identification based model has a transport Partial Differential Equation/Ordinary Differential Equation cascade structure that is suitable for designing feedback controllers for Extrusion Blow Molding.First, I would like to express sincere gratitude and appreciation to my supervisor Prof. Benoit Boulet for his great guidance and the intellectual freedom I was granted throughout this research. This work would not have been possible without his great dedication, constructive criticism and support. A special thanks to my co-supervisor Prof. Roni Khazaka for his mentorship and guidance. I also gratefully acknowledge Prof. Savvas Hatzikiriakos and Mr. Haile Atsbha for sharing with me their profound knowledge and expertise. I gratefully acknowledge the Natural Sciences and Engineering Research Council of Canada (Automotive Partnership Canada) for the financial support and giving me the opportunity to pursue my passion in science and engineering.Finally, I would like to thank my loving friends and family for their encouragement and support along my journey over the past five years. viii