Methodological approach to efficient modeling and optimization of thermal processes taking place in a die: Application to pultrusion

Optimization of manufacturing processes involves the optimal choice of many process parameters. Usual strategies proceed by defining a trial choice of those parameters and then solving the resulting model. Then, an appropriate cost function is evaluated and its optimality checked. While the optimum is not reached, the process parameters should be updated by using an appropriate optimization procedure, and then the model must be solved again for the updated process parameters. Thus, a direct numerical solution is needed for each choice of the process parameters, with the subsequent impact on the computing time. In this work we propose a methodological approach to the efficient numerical modeling and optimization of thermal processes taking place in a die. This scenario is usually encountered in polymer and composites processing where material flows inside a die equipped with different heating devices. An example of such kind of processes concerns the pultrusion of composites. The main aim of this work is to described an original approach for modeling and then optimizing the thermal process by solving only once the thermal model, and then, optimizing the process without the necessity of performing new solutions of the thermal model. For this purpose we introduce the temperatures of the heaters as extra-coordinates in the thermal model. The solution of the resulting multi-dimensional heat equation gives the temperature field for any choice of the temperature prescribed in the heaters. The curse of dimensionality is circumvented by invoking the Proper Generalized Decomposition – PGD – introduced in our former works but never until now used in the framework of process optimization.