Optimized Design Method for Profile Extrusion Die Based on NURBS Modeling

Abstract

For optimization design of polymer extrusion dies, dimensional accuracy is critical to product quality of the extrudate. The extrusion dies used to be a regular geometrical profile, which is mostly composed by a straight line. Traditional optimization methods for extrusion die design used to have poor controllability when dealing with a curved profile. In this paper, the response surface optimization method is used to find out an optimal solution of the design of the extrusion die. Firstly, the Latin Hypercube Sampling method is used to generate the experiment samples for the design of experiments. Secondly, ANSYS Polyflow software is adopted to execute the computational fluid dynamics analysis. Thirdly, the Kriging method is used to generate the response surface. Finally, nonlinear programming by using Quadratic-Lagrangian algorithm is applied to find out the optimal solution. It is worth noting that Non-uniform Rational B-Splines (NURBS) modeling is used to optimize flow channel of an extrusion die in order to obtain a qualified extrudate. Thus, design variables for the optimization involve control points of the NURBS curve of the inlet cross-section. Meanwhile, two new objective functions, including minimization of point displacement and minimization of dimensional tolerance are proposed in the optimization process. Compared with existing objective functions of flow balancing and homogeneous die swell, the new objective functions of minimization of point displacement and minimization of dimensional tolerance have significant advantages of strong adaptability, more precise shape of the extrudate and fast convergence, which significantly improve efficiency of the optimization design and thus lower manufacturing costs of the extrusion die.

Optimization of Polymer Processing: A Review (Part I—Extrusion)

“…The optimization results were assessed experimentally [ 152 , 153 ]. Zhang et al [ 154 ] applied a gradient method based on a sensitivity analysis of a response surface obtained from 3D numerical modelling relating the objective function with the design variables, to optimize an L-shape profile die. The design variables were the parameters of spline curves based on eight control points, and the objective function was the weighted sum of maximization of flow balance and extrudate-swell homogeneity and minimization of points displacement and dimensional tolerance.…”

Optimization of Polymer Processing: A Review (Part I- Extrusion)

“…The optimization results were assessed experimentally [152,153]. Zhang et al [154] applied a gradient method based on a sensitivity analysis of a response surface obtained from 3D numerical modelling relating the objective function with the design variables, to optimize an L-shape profile die. The design variables were the parameters of spline curves based on 8 control points, the objective function was the weighted sum of maximization of flow balance and extrudate-swell homogeneity, and minimization of points displacement and dimensional tolerance.…”

Optimization of catheter placement for convection-enhanced delivery to brain tumors

“…Zhang et al used RSO to determine the optimal extrusion die design, which resulted in a more accurate extrudate shape and lower extrusion die production costs 11 . Using a response surface methodology Sultana et al predicted that jute fiber can improve compressive and tensile concrete strength 12 .…”