Optimal design and analysis for polymer extrusion and molding

A manufacturing process design methodology is presented which can be used to improve the production of polymer components manufactured via the extrusion, injection molding, and compression molding processes. The design methodology employs polymer process modeling, design sensitivity analysis, and numerical optimization. It is applicable to systems with creeping flow of purely viscous non-Newtonian fluids through thin cavities where the lubrication approximation can be applied. The Newton-Raphson iteration is used to solve the nonlinear equations for the pressure field which are formed via the Hele-Shaw flow analysis and Galerkin finite element method. The pressure induced velocity field is then used to derive a hyperbolic differential equation which evaluates the material residence time in the polymer melt. This hyperbolic equation lacks natural diffusion, therefore, we employ the streamline upwind Petrov-Galerkin (SUPG) finite element method to compute a spatially stable residence time field. To compute the fill time and filling pattern in polymer injection and compression molding, a moving boundary analysis is developed based on the volume-of-fluid (VOF) method.; To solve the design problem, design sensitivities are used with numerical optimization. A general framework is developed to obtain analytical design sensitivities for steady-state, weakly-coupled nonlinear systems. The sensitivities are evaluated with respect to sizing, shape, and some topology design variables, and special emphasis ie given to design variables that parameterize essential boundary conditions. Design sensitivities are derived for a general response functional using both the direct and adjoint methods. The resulting adjoint and direct sensitivities are compared to show that the two sensitivity analysis methods yield identical expressions. Sensitivities for the generalized Hele-Shaw system are obtained using variational formulations which are discretized for finite element analysis. Design sensitivities are also derived for the VOF moving boundary analysis and for the residence time analysis where special emphasis is given to the design dependent SUPG weighting function.; Sheet extrusion dies and mold designs for injection molding are optimized to exemplify the polymer processing design methodology. Sheeting dies are designed to minimize pressure drop, reduce die length, and generate a uniform exit velocity and a uniform exit residence time. The injection molding process is designed to minimize mold fill time and to satisfy constraints on injection flow rate and mold clamp force.