An optimization procedure for the pultrusion process based on a finite element formulation

Abstract

CEP: 21 949-900-C.P: 68542-Rio de Janeuo, RJ, Brazil Composite materials are manufactured by different processes. In all, the process variables have to be analyzed in order to obtain a part with uniform mechanical properties. In the pultrusion process, two variables are the most important: the pulling speed of resin-impregnated fibers and the temperature profile (boundary condition) imposed on the mold wall. Mathematical modeling of this process results in partial differential equations that are solved here by a detailed procedure based on the Galerkin weighted residual finite element method. The combination of the Picard and Newton-Raphson methods with an analytical Jacobian calculation proves to be robust, and a mesh adaptation procedure is presented in order to avoid integration errors during the process optimization. The two earlier-mentioned variables are optimized by the Simulated Annealing method with some constraints, such as a minimum degree of cure at the end of the process, and the resin degradation (the part temperature cannot be higher than the resin degradation temperature at any time during the whole process). Herein, the proposed objective function is an economic criterion instead of the pulling speed of resin-impregnated fibers, used in the majority of papers.

Optimization of a Pultrusion Process Using Finite Difference and Particle Swarm Algorithms

“…Equation (2) describes the energy balance. As seen, the energy has a convective term in the z direction and a diffusive term in the radial direction; according to the literature (Coelho andCalado, 2002, Santos et al, 2012), the conductive heat transfer along the zdirection can be neglected.…”

“…In this section, the theoretical background of pultrusion is described (Coelho and Calado, 2002;Santos et al, 2012). Heat transfer in the pultrusion process, with a cylindrical die, can be modeled using the mass and energy balance equations described by Equations (1) and (2), respectively.…”

“…In order to optimize the pultrusion process, an objective function similar to that proposed by Coelho and Calado (2002), which represents the energy rate, was used:…”

“…The results were used to determine preferred process conditions and/or heating configurations for the pultrusion of the composite I beams. Coelho and Calado (2002) proposed an economical objective-function in order to find the optimal temperature profile. These authors used the simulated annealing optimization strategy and a finite element method to solve the algebraic-differential equations that represent the pultrusion model.…”

Polymer Composite Manufacturing Using a Pultrusion Process: A Review

“…Among these variables, the curing temperature is the most significant factor that affects the pultruded profile during pultrusion process (Coelho and Calado, 2002). The matrix curing behaviour became the most critical factor in pultrusion process and it included the resin bonding behaviour, type and size of the die and the heater capacity.…”