Bingfeng Fan

An Analytical Non-Newtonian and Nonisothermal Viscous Flow Simulation

ABSTRACT Polymer process control is limited by a lack of observability of the distributed and transient polymer states. An analytical solution is presented for on-line simulation of non-Newtonian and nonisothermal viscous flow in real-time polymer processing. The modeling of the non-Newtonian viscous flow utilizes a modified Ellis model that expresses viscosity as a function of shear stress; the modeling of the heat transfer utilizes a Bessel series expansion to include effects of heat conduction, heat convection, and internal shear heating. The resulting simulation is suitable for inclusion in real-time process controllers requiring sub millisecond response. Numerical verification indicates that the flow rate predictions of the described analysis compare well with the results from a commercial molding simulation. However, empirical validation utilizing a design of experiments for an injection molding process indicates that the described analysis is qualitatively useful but does not possess sufficient accuracy for quantitative process and quality control.

Process-Driven Input Profiling for Plastics Processing

Most plastic processing set points are variables that need to be defined for each sample point of the cycle. However, in the absence of on-line measures of part quality, the set points cannot be defined by feedback and need to be prescribed a priori for the entire cycle. In conventional practice, the shape of each set-point profile is defined either heuristically, according to qualitative experience, or mechanistically, to enforce a predefined trajectory for a simulated internal process state that is used as a surrogate measure of part quality (e.g., the velocity profile defined to dictate a constant melt front velocity). The purpose of this study is twofold: (i) to evaluate the efficacy of using a single internal state as the surrogate of part quality, and (ii) to explore the feasibility of devising a multivariate profiling approach, where indices of multiple process states act as surrogates of part quality. For this study, an injection-compression molding process used for production of digital video disks was considered as the development domain, and a pseudo-optimal cycle of the process was found by reinforcement learning to provide a basis for evaluating the ideal behavior of the process states. Compared to conventional molding, the results indicate that the asymmetric process capability index, CPK, was increased by ∼50% with velocity profile optimization and to 120% with both velocity profile and pressure profile optimization. Two general conclusions result. First, velocity and pressure profiling provide important degrees of freedom for optimizing process control and maximizing part quality. Second, estimators for unobservable process states, in this case birefringence and warpage, can be used to develop different machine profiles to selectively trade off multiple quality attributes according to user preferences.

Polymer Flow in a Melt Pressure Regulator

A non-Newtonian, non-isothermal flow analysis has been developed to assist the design of a self-compensating polymer melt regulator, which is a device capable of regulating the melt pressure in polymer processing via an open loop control architecture. The governing mass and momentum equations for the two-dimensional, axisymmetric flow field are solved by a mixed finite element method, in which the velocity components are interpolated by quadratic functions, and the pressure is interpolated by a linear function. The temperature field is solved by the finite difference method. Results of the outlet pressure, valve pin position, bulk temperature rise, and flow rate as functions of the control force for Newtonian isothermal analyses and non-Newtonian non-isothermal analyses are provided. The simulation demonstrates the behavior of candidate regulator designs and provides the performance attributes such as outlet pressure, flow rate, temperature rise, etc., given the decision variables, such as valve parameters, process conditions, and polymer melt rheology. The results indicate that for a regulator design on the order of 20 mm diameter, the regulator operates in a mostly closed condition with an aperture opening varying between 0.1 and 1 mm. The results suggest that the bulk temperature increases with control force and flow rate and is largely attributable to the increases in viscous heating of the melt through the flow channels, rather than the pinch off between the valve pin and the valve body.

Simulation of Polymer Flow in a Dynamic Pressure Regulator

A non‐Newtonian, non‐isothermal flow analysis including acceleration effects has been developed to simulate the polymer flow in two‐dimensional, axisymmetric geometries. The governing mass and momentum equations are solved by a mixed finite element method, in which the velocity components and temperature are interpolated by quadratic functions, and the pressure is interpolated by a linear function. Modeling of the changing feed system geometry is implemented by dynamic meshing. The described analysis is applied to the design and control of a flow regulator. The results describe the behavior of non‐steady, viscous flows and are useful for machine design.