Multi-objective optimization for resin transfer molding process
Introduction
Recently, resin-transfer molding (RTM) has been greatly advanced to manufacture fiber-reinforced plastics (FRPs) in a transport system because of its high productivity. Since this procedure does not require large equipment, RTM is a highly efficiency, low-cost method compared with conventional autoclave molding. RTM productivity becomes even more efficient with multi-gate injection. Despite these advantages of RTM, it is difficult to reduce air voids that cause loss of the product’s properties [1], [2], [3], [4], [5], [6], [7], [8]. Specifically, for multi-gate injection in RTM, recent studies [9], [10] have reported that air-voids are frequently generated in weld lines, that is, in the resin contact area originating from a front collision between opposite resin flows [11]. Therefore, in order to increase the quality of the products, the area of the weld line must be reduced, not only for thermoplastic resin, but also for thermosetting resin.
Okabe et al. [12] demonstrated that air voids are generated between filaments. Leclerc et al. [13] experimentally demonstrated that material properties depend on void contents and are related to the saturation speed of the resin. This result suggests that productivity is closely related to the quality of the products. Therefore, it is necessary to improve the quality of the products (reducing air voids) without decreasing productivity.
Several researchers have already attempted to reduce the contents of void and improve manufacturing efficiency. One approach involves controlling resin injection [14], [15], [16], [17], [18]. By adjusting two or more injection pressures, the resin can be impregnated uniformly, thus reducing the number of voids formed during molding and reducing fill time. However, this method involves the additional cost of a pressure-control device and feedback equipment. Another approach involves optimizing the gate locations. RTM is complicated and consists of widely different objective functions and design variables. Studies have attempted to optimize the filling process and thus improve its efficiency. Kim et al. [19] optimized gate locations and minimized fill time using a genetic algorithm (GA). Hsiao et al. [20] optimized the flow distribution network and minimized an objective function, which was the sum of the dry spot volume and fill time multiplied by the weight functions. Henz et al. [21] used a GA to search for an optimal solution in the global domain. They then further refined the solution using a gradient-based search. Ratle et al. [22] treated two objective functions independently and obtained multiple optimal solutions, i.e., Pareto solutions. In practice, it is important to consider multiple objective functions for optimization. When treating more than two objective functions, it is usually difficult to understand the relationship and physical meaning of the obtained Pareto solutions. Thus, it is necessary to facilitate the extraction of design rules and knowledge from the Pareto solutions using visualization technique.
In this study, we explored multi-objective design for optimizing four gate locations to improve molding efficiency while maintaining the product’s material properties. Four objective functions (fill time, dry spot, weld line, and wasted resin) were used in this study. Multi-objective GAs were used to solve the multi-objective optimization problem to determine optimum gate locations. After optimization, the results were mapped using a self-organizing map [23]; we also created a scatter plot matrix. Finally, using these visualization techniques, we extracted the design rules and knowledge for multiple gate optimizations of RTM.
Section snippets
Modeling and optimization
In this section, we describe a simulation to represent RTM, a MOGA for searching the Pareto solution, and a SOM for data mining.
Flat-plate model
As a first target to optimize the filling process, a simple 150-mm square flat-plate model with a thickness of 1 mm was selected. The injection parameters were as follows: permeability in each direction [28] ; off-diagonal components are 0; viscosity Pa·s; and injection pressure = 97,992 Pa. A finite-element mesh was generated with 3380 nodes and 2500 elements, 625 elements in the xy plane by four elements in the thickness direction (
Experiment
In this section, we validated both the filling analysis and the optimization algorithm by comparing simulations and experiments. The filling process can be reproduced by the present FEM analysis. Moreover, in the result of the optimization presented in Section 3, we obtained diagonal and quadrangular distributions as Pareto solutions. These two solutions represent the existence of trade-off relations between the fill time and the weld line. In Section 4, we confirmed the trade-off relations
Conclusion
In this study, multi-objective optimization for multi-point injection of RTM for composite structures was performed to investigate optimal gate positions using FEM and MOGA. In addition, trade-offs among objective functions were visualized with the help of a scatter plot matrix and a SOM. By applying the present approach to RTM for flat-plate and rib models, we acquired the following design rules for the flat-plate model. There is a strong trade-off between fill time and weld line contents,
Acknowledgement
Authors acknowledge the support of the Cross-ministerial Strategic Innovation Promotion Program in Japan.
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