Comparing Optimization Algorithms for Shape Optimization of Extrusion Dies

Abstract

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.

Reduced Flow Model for Plastics Melt Inside an Extrusion Die

“…In particular, we assume that B and C can vary by ± 5 % about reference values B 0 and C 0 , respectively, and collect them in a parameter vector µ = [B, C]. To measure the homogeneity of the flow, a cost functional J as presented in [1] is used; it relates local velocity fluctuations to the overall average velocity. The relevant region, on which J will be evaluated, is the outlet of the extrusion die (see Fig.…”

Isogeometric shape optimization of nonlinear, curved 3D beams and beam structures

“…To solve the nonlinear, constrained optimization problem given by ( 24), two general types of algorithms can be distinguished, global derivative-free or local gradient-based methods [66][67][68]. While the advantages of the former are that they do not require implementation and evaluation of gradients and that they avoid local minima by searching the whole design space, the severe disadvantages in the context of nonlinear structural shape optimization are that convergence is slower, requiring many expensive function evaluations and, most importantly, that trial design vectors u may often lead to mechanically infeasible designs.…”

Optimized Design Method for Profile Extrusion Die Based on NURBS Modeling

“…Pauli et al [10] proposed the homogeneous die swell as objective function. Siegbert et al [11] demonstrated an optimization design method that profile shape was used as an objective function. Gifford [12] demonstrated a method of compensation for die swell in the design of profile extrusion die.…”