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Abstract. The rather unintuitive and non-linear behavior of plastics melts is a well-known obstacle in the design and manufacturing cycle of profile extrusion dies. This is reflected, for example, in the so-called running-in experiments, in which the already manufactured die is modified up to 15 times until the final product, shaped by the die, matches the quality requirements. Besides a homogeneous outflow velocity and thus homogeneous material distribution, an appropriate die swell is a second design objective which complicates the reworking of the manufactured die. We are conducting work to shorten the manual running-in process by the means of numerical shape optimization, making this process significantly less costly and more automatic. From a numerical point of view, the extrusion process is not as challenging as high-speed flows, since it can be described by steady Stokes equations without major loss of accuracy. The drawback, however, is the need for ac- curate modeling of the plastics behavior, which generally calls for shear-thinning or even viscoelastic models, as well as for 3D computations, leading to large computational grids. The intention of this paper is to investigate the application of specific geometry features in extrusion dies and their influence on objective functions in an optimization framework. However, representative objective functions concerning die swell and the incorporation of known geometry features, as used by experienced die designers, into the optimization framework still remain a challenge. Hence, the topics discussed are the influence of the mentioned geometry features on existing objective functions as well as an outlook on an algorithmic implementation into the optimization process with regard to representative objective functions.

The classical approach to extrusion die design relies heavily on the experience of the die designer; Especially the designer's ability to create an initial die design from a product design, the designer's constructional knowledge and performance during the running-in trials. Furthermore, the relative unpredictability of the running-in trials combined with the additional resource usage introduce uncertainties and delays in the time-to-market of a given product. To lower these delays and resource usage, extrusion die design can benefit greatly from numerical shape optimization.In this application, however, plastics melts pose a difficult obstacle, due to their rather unintuitive and nonlinear behavior. These properties complicate the numerical optimization process, which mimics running-in trials and relies on a minimal number of optimization iterations. As part of the Cluster of Excellence Integrative Production Technologies for High-Wage Countries at the RWTH Aachen University, an effort is made to shorten the manual running-in process by the means of numerical shape optimization.Using an in-house numerical shape optimization framework, a set of optimization algorithms, consisting of global, derivativefree and gradient-based optimizers, are evaluated with respect to the best die quality and a minimal number of optimization iterations. This evaluation is an important step on the way to include more computationally intensive material models into the optimization framework and identify the best possible optimization strategy for the numerical design of extrusion dies.

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