Industrial applications DOI 10.1007/s00158-004-0440-x Struct Multidisc Optim 28, 180–194 (2004) Parameterization and optimization strategies for the automated design of uPVC profile extrusion dies H.J. Ettinger, J. Sienz, J.F.T. Pittman and A. Polynkin Abstract Optimization strategies for use within an automated optimization framework for PVC profile ex- trusion dies are presented. The methods are designed to work in an industrial environment and must there- fore account for the specific design and manufacturing techniques for these profile dies. The complex three- dimensional die geometry will be represented through a series of two-dimensional so-called ‘die-slices’. The pur- pose of the presented optimization cycle is to find the optimal shape of the die cross-section of the die-slices. Each die-slice geometry is optimized by a computerized optimization loop using a finite element (FE) analysis of the polymer flow through the die. Simple data rep- resentation of the complex die geometry allows an effi- cient parameterization. Several optimization strategies are compared regarding the achieved quality of the op- timization, the computational costs, the required user interaction and the robustness in industrial applications. The strategies are (i) a global scheme in which all design variables (DVs) are dealt with simultaneously, (ii) a se- quential optimization in which DVs are addressed one after each other, (iii) employing a height approximation type method in which the new values for the DVs are found using assumptions of the flow between two paral- lel plates, and (iv) a global scheme in which the DVs are decoupled taking advantage of the particular FE analysis applied. Key words extrusion die design, parameterization, shape optimization Received: 21 January 2004 Revised manuscript received: 23 March 2004 Published online: 8 July 2004  Springer-Verlag 2004 H.J. Ettinger, J. Sienz ✉ , J.F.T. Pittman and A. Polynkin ADOPT Research Group, Civil and Computational Engin- eering Centre, School of Engineering, University of Wales, Swansea, Singleton Park SA2 8PP, UK e-mail: J.Sienz@swansea.ac.uk 1 Introduction In the extrusion manufacturing process the material is shaped by forcing it through an appropriately designed die. The extrusion of unplasticized polyvinyl chloride (uPVC) is commonly used to produce profiles such as window or door frames for the building industry. Consid- ering the intricate cross-sections, the tight dimensional tolerances and the complexity of the physical phenomena (e.g. nonlinear material behaviour, viscoelasticity, wall- slip) involved in extrusion, the design of the required ex- trusion dies is a demanding exercise. Traditional methods rely heavily on the designer’s experience with repeated cycles of extrusion trials and die modifications. Compu- tational fluid dynamics (CFD) has already been estab- lished as a tool to shorten these trial-and-error cycles and various authors have addressed the problem of poly- mer extrusion, see for example Kim et al. (2001). Despite its undoubted value to the die designer by giving infor- mation of the polymer flow through the – not yet nec- essarily manufactured – die, it still lacks the possibility of directly indicating how to modify the die geometry. Furthermore it is only one automated part within an optimization loop, which is still mainly manual. These drawbacks can be bypassed by introducing computerized optimization. Starting from an initial die design, an opti- mization loop is cycled until a satisfying die geometry has been achieved. In essence this consists of defining the objective func- tion(s) as one or more scalar measures of the die perform- ance. Various objective functions have been suggested in the literature, each being suitable for certain applications and aiming at the optimization of different process and product properties as outlined in Szarvasy et al. (2000). Often used, e.g. Koziey et al. (1996), is flow balancing, in which the objective function gives an indication of the uniformity of the mass flow distribution. Depending on the CFD analysis used, other aspects such as melt frac- ture, see Carneiro et al. (2001), can be addressed, which in this case can be controlled via the critical extensional stress. The definition of the objective function purely in