Resin transfer molding: Mathematical models for process control

Resin Transfer Molding (RTM) is a composite manufacturing technique with a variety of applications. Resin cure is one of the two critical steps in RTM where the injected resin polymerizes/crosslinks and yields the solid polymer matrix. During cure the combination of exothermic reaction and low thermal conductivity of the medium results in high temperature for the inner portion of the part and non-uniform cure rates. This may result in residual stresses and the produced part will be of inferior quality. Real-time process control that has an objective to maintain spatial uniformity of processing conditions can solve this problem. However, computationally tractable models in convenient form are required for controller design. Detailed models for the cure can be obtained based on modeling of heat and mass transfer in porous media using volume averaging methods and in this work these coupled partial differential equations (PDE's) are solved using finite element approximation.; In this work, models of the cure process that are suitable for controller design are developed. These models are obtained based on Proper Orthogonal Decomposition which yields optimal, low dimensional subspaces which describe most of the system energy, followed by Galerkin projection of the PDE's on these subspaces. The final result is an ODE (finite dimensional) approximate process model which describes the evolution of the spatial distribution of field variables such as temperature and extent of cure (reaction coordinate). The model is in a standard state-space form. In our case the control variable is the temperature of the recirculating fluid which heats the mold. It is established that these finite dimensional models maintain their predictive capabilities under parameter variation in the open and the closed loop sense.