Optimal Switching Time Control of UV Induced Cationic Curing Process

Abstract

This paper first describes a curing process model comprised of the coupled cure-kinetics and thermal evolution in a cationic polymerization of a single layer of material and then extends it to multi-mode curing of multiple layers. The model is characterized as a switching multi-mode dynamic system that switches when the UV source is turned off and when a new layer is added to the existing layer. These two switching conditions are explicitly defined. The model is then used to determine the optimal mode switching times and the final process time which are considered as manipulated control variables. This is done by explicitly deriving the necessary conditions of optimality for the multi-mode switching system. The results are first illustrated for a two-layer composite laminate and then the results of five-layer curing are briefly discussed to show the versatility of the proposed approach. The optimal switching times and final time result in minimal cure level deviation across the thick composite material.

On the Inter-Laminar Shear Strength of Composites Manufactured via a Stepped-Concurrent UV Curing and Layering Process

“…The computational framework for solving the optimization problem involves the derivation of the necessary conditions of optimality using traditional optimal control approaches, where the system/process model in equation (5) serves as constraints to the objective function in equation (6). The necessary conditions for optimality are derived and outlined in our previous work, 24 and similar derivations for acrylate-based composites can be found in Yebi and Ayalew. 9,13,14 For brevity, we skip those derivations here and discuss some typical outcomes from the model-based optimal control.…”

“…Previously, we experimentally verified the optimal switching times from our simulation that were most effective in curing a 2-mm thick epoxy. 24,33 Based upon those results, 2-mm thick material was used as the single layer in the present study. Figure 9 shows a schematic representation of the in-situ compaction or consolidation process investigated here.…”

“…The details of equation (5) can be found in our previous work. 13,24 In the next section, we demonstrate the SCC and layering process for making a two-layer part. As mentioned earlier, we use model-based optimal control to determine the optimal processing time sequence (comprised of layering time, UV switch OFF time, and final times), which gives uniform cure distribution across both layers.…”

“…The attenuation of the UV intensity along the depth is modeled by the Beer-Lambert's Law. 18,19 Bringing all of these together, the curing process model is summarized as follows 13,24 c @Tðt, yÞ @t…”