Optimum design of pultrusion process via evolutionary multi-objective optimization

Abstract

Pultrusion is one of the most cost-effective manufacturing techniques for producing fiber-reinforced composites with constant cross-sectional profiles. This obviously makes it more attractive for both researchers and practitioners to investigate the optimum process parameters, i.e., pulling speed, power, and dimensions of the heating platens, length and width of the heating die, design of the resin injection chamber, etc., to provide better understanding of the process, consequently to improve the efficiency of the process as well as the product quality. Using validated computer simulations is "cheap" and therefore is an attractive and efficient tool for autonomous (numerical) optimization. Optimization problems in engineering in general comprise multiple objectives often having conflict with each other. Evolutionary multi-objective optimization (EMO) algorithms provide an ideal way of solving this type of problems without any biased treatment of objectives such as weighting constants serving as pre-assumed user preferences. In this paper, first, a thermochemical simulation of the pultrusion process has been presented considering the steady-state conditions. Following that, it is integrated with a well-known EMO algorithm, i.e., nondominated sorting genetic algorithm (NSGA-II), to simultaneously maximize the pulling speed and minimize "total energy consumption" (TEC) which is defined as a measure of total heating area(s) and associated temperature(s). Finally, the results of the evolutionary computation step is used as starting guesses for a serial application of a of gradient-based classical algorithm to improve the convergence. As a result, a set of optimal solutions are obtained for different trade-offs between the conflicting objectives. The trade-off solution, thus obtained, would remain as a valuable source for a multi-criterion decision-making task for eventually choosing a single preferred solution for the pultrusion process.

Thermoplastic Pultrusion: A Review

“…Thermoplastic pultrusion cannot boast significant progress in mathematical modeling as opposed to the thermoset pultrusion, where it widely applied, first, to model complex shaped profiles (L- and I-shaped sections [ 274 ], wind turbine blades [ 299 , 300 ], etc.) with complex reinforcement lay-ups, and, second, to develop algorithm for their optimization [ 301 , 302 , 303 , 304 , 305 , 306 , 307 , 308 , 309 , 310 , 311 , 312 , 313 , 314 , 315 , 316 , 317 ]. In recent years, a significant interest to optimization has been observed in the scientific and engineering community.…”

Numerical optimisation of thermoset composites manufacturing processes: A review

“…Although, it is possible by applying constraints, to contain the outcomes of objectives not specifically addressed by the optimisation, SO objective optimisation does not address the challenges of the manufacturing process as a whole and its outcomes are not optimal trade-offs between them which is the reason why recent research efforts focus on MO optimisation and SO optimisation is being abandoned. A MO variant of the problem aiming to identify the optimal number of heaters, their dimensions and the temperature profile along the die in order to maximise pulling speed and minimise energy consumption subject to maximum temperature and minimum final degree of cure constraints has led to 70% reduction in energy consumption and 100% increase in pulling speed [86,87]. The MO problem of maximising pulling speed and degree of cure by optimising first and second heater temperature profiles and initial resin temperature has been tackled.…”

“…The procedure is able to update on-line the local permeability via inversion of measurements/observations achieving optimal control of the process [127]. 2007-Heating profile optimisation to maximise cure degree uniformity [81] 2004-2006 -Cure cycles optimisation under uncertainty to minimise process time [76,77] 2009 -Optimal curing profiles to minimise energy consumption [74] 2013-2017 -MO optimisation with quality/cost objectives [86][87][88][89] 2010-2012 -Optimal temperature profile and pulling speed to minimise cure degree variation [83,84] 2013 -Optimal number of heaters and pulling speed to minimise energy consumption [85] 2002 -Pulling speed/die heaters optimisation to minimise cure degree gradient [73,78] 2003 -Simultaneous optimisation of pulling speed and die-heating to minimise cure degree gradient [79] 2003 -pre-heating and die-cooler additional optimisation parameters considered [80] 2018 -Heating profile optimisation to maximise cure degree uniformity [82] 2015 -Optimal curing profiles to minimise energy consumption [75] 1994-1997 -Optimal cure cycle to minimise cure time [90][91][92] 1998-2000 -Graphical methods to minimise residual stresses [103,104] 2001 -Optimal cure cycles for thick laminates to minimise cure time [95,96] 2012-2019 -MO optimisation quality/cost objectives [116][117][118][119][120][121][122] 2017 -Optimal cure cycles to minimise cure time/final curvature (Weighted fitness function) [113] 1993-1995 -Optimal cure cycle to minimise residual stresses [100] and maximum material properties…”

Multiphysics modelling of manufacturing processes: A review

“…In addition, the process conditions were optimized in several studies for the pultrusion process. [197][198][199][200] Modelling process-induced strains and stresses in a thick laminate plate…”