Thermo-Chemical Modelling Strategies for the Pultrusion Process
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Thermo-Chemical Modelling Strategies for the Pultrusion Process Ismet Baran & Jesper H. Hattel & Cem C. Tutum
Received: 11 April 2013 / Accepted: 17 June 2013 # Springer Science+Business Media Dordrecht 2013
Abstract In the present study, three dimensional (3D) numerical modeling strategies of a thermosetting pultrusion process are investigated considering both transient and steady state approaches. For the transient solution, an unconditionally stable alternating direction implicit Douglas-Gunn (ADI-DG) scheme is implemented as a first contribution of its kind in this specific field of application. The corresponding results are compared with the results obtained from the transient fully implicit scheme, the straightforward extension of the 2D ADI and the steady state approach. The implementation of the proposed approach is described in detail. The calculated temperature and cure degree profiles at steady state are found to agree well with results obtained from similar analyses in the literature. Detailed case studies are carried out investigating the computational accuracy and the efficiency of the 3D ADI-DG solver. It is found that the steady state approach is much faster than the transient approach in terms of the computational time and the number of iteration loops to obtain converged results for reaching the steady state. Hence, it is highly suitable for automatic process optimization which often involves many design evaluations. On the other hand sometimes the transient regime may be of interest and here the proposed ADI-DG method shows to be considerably faster than the transient fully implicit method which is generally used by the general purpose commercial finite element solvers. Finally, using the proposed steady-state approach, a design of experiments is carried out for the curing characteristic of the product based on pulling speed and part thickness. Keywords Numerical modeling . ADI . Finite difference method . Pultrusion . Curing
1 Introduction Pultrusion is one of the most cost efficient manufacturing processes for producing continuous lengths of fiber reinforced composite shapes with a constant cross section. The process is basically the same although the pultrusion machines vary in their design. The fibers and mats are first pulled into a resin bath or resin injection chamber in which the reinforcements are saturated or wetted out. The wet out reinforcements then enter the heating or forming die in which an exothermic reaction I. Baran (*) : J. H. Hattel Department of Mechanical Engineering, Technical University of Denmark, Kgs. Lyngby, Denmark e-mail: [email protected] C. C. Tutum Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI, USA
Appl Compos Mater
takes place inside the thermosetting resin. This reaction generates an internal heat and the resin cures. The cured profile is advanced via a pulling system to the cut-off saw where it will be cut to its final length. A schematic view of a pultrusion process is shown in Fig. 1. In recent years, seve
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