A comparison of finite element formulations for analysis of the converting process of packaging materials

Packaging industry supplies a variety of different carton packages to their customers in the food and beverage industries. Packaging industry also develops and produces packaging material. One key aspect of the production of the packaging material is the converting process, where the lamination of the core material, paperboard, takes place. To improve the quality of the produced packaging material it is important to understand the converting process. To deepen the knowledge about the converting process, simulation tools are used to investigate how the process affects the packaging material. The company is continuously working on improving its abilities on simulations. This thesis investigates new methods, apart from those used today, that can be used to simulate parts of the converting process. All performed simulations are based on the finite element method and created in the commercial software Abaqus. The first part of the converting process that is studied is a web motion problem where paperboard is transported over idle rollers. This is a key aspect of the converting process and the company has had some difficulties with their simulations of the web motion. Non-converging finite element analyses and failure to reach steady state in the paperboard flow are some displayed problems with the current model. The other part of the converting process that is studied is the nip in the lamination process. At the lamination nip, a steel roller and a roller consisting of a steel core and a rubber coating, are forced together. The industry wants to have a simple, thin model of the lamination nip, from where the contact pressure in the nip and the temperature distribution throughout the rubber are sought for. The model used today is somewhat complicated and demands a lot of manual labor why a more simple model is desired. For the web handling problem, two different methods are investigated. An Eulerian approach is studied where the element mesh is fixed in space and the paperboard is allowed to flow through the mesh. By using Eulerian inflow and outflow boundary conditions the paperboard may flow in and out of the mesh freely and thus the modeled paperboard may be shortened to reduce the model size. The other approach investigated is an Abaqus functionality called periodic media analysis. The paperboard is then divided into building blocks which are reused in the analysis, meaning that the model size may be reduced to improve calculation time. For the lamination nip, an Eulerian approach is once more considered. The rubber is then modeled using the Eulerian approach, allowing for a finer mesh at the nip and a more coarse mesh where only rotation of the roller occurs. It was shown that the Eulerian approach resulted in infeasible run times for the web handling problem wherefore further studies of this model are not recommended. The periodic media model on the other hand displays some potentially good qualities such as mesh reduction. However, uneven stresses in the paperboard and inaccurate contact pressure are obtained. Based on these findings, this method is recommended for analyses where the paperboard is not the main part of interest. Further studies on this approach are needed. Also the Eulerian approach for the lamination nip needs further investigations. The key factors for an good setup where identified but no such model was created.