A Novel Approach to Automatically Balance Flow in Profile Extrusion Dies Through Computational Modeling

This work presents a novel fully automated computational framework for optimizing profile extrusion dies, aiming to achieve balanced flow at the die flow channel outlet while minimizing total pressure drop. The framework integrates non-isothermal, non-Newtonian flow modeling in OpenFOAM with a geometry parameterization routine in FreeCAD and a Bayesian optimization algorithm from Scikit-Optimize. A custom solver was developed to account for temperature-dependent viscosity using the Bird-Carreau-Arrhenius model, incorporating viscous dissipation and a novel boundary condition to replicate the thermal regulation used in the experimental process. For optimization, the die flow channel outlet cross-section is discretized into elemental sections, enabling localized flow analysis and establishing a convergence criterion based on the total objective function value. A case study on a tire tread die demonstrates the framework's ability to iteratively refine internal geometry by adjusting key design parameters, resulting in significant improvements in outlet velocity uniformity and reduced pressure drop. Within the searching space, the results showed an optimal objective function of 0.2001 for the best configuration, compared to 0.7333 for the worst configuration, representing an enhancement of 72.7%. The results validate the effectiveness of the proposed framework in navigating complex design spaces with minimal manual input, offering a robust and generalizable approach to extrusion die optimization. This methodology enhances process efficiency, reduces development time, and improves final product quality, particularly for complex and asymmetric die geometries commonly found in the automotive and tire manufacturing industries.