Analysis of the filling capability to the microstructures in micro-injection molding

Micro-injection molding is an important fabrication process for polymer plastics with micro-features. In micro-injection molding of products with microstructures, the ability for the polymer melt to flow into the microstructures is a crucial factor for successful molding. An analytical model in micro-injection molding is constructed in this research. It has been reported that most of the filling in microstructure is done during the packing pressure. In this analytical model, the temperature of the polymer melt near the entrance of the microstructure at the end of mold filling is estimated first. With the temperature, we can calculate the injection distance into the microstructures of the mold insert during the packing stage. The model is compared with experimental results, and shows the feasibility. The experiment uses the LIGA-like lithography process to define the micro-feature and a micro-electroforming method to form the mold insert with the replicated micro-feature. The injection distance into the microstructures predicted by this analytical model shows reasonable result as compared to the experimental measurement.     

Modeling and simulation of injection molding process of polymer melt by a robust SPH method

In the present study, the injection molding process of polymer melt based on the generalized Newtonian fluid model is investigated by a robust smoothed particle hydrodynamics (SPH) method. The numerical method is proposed by introducing a Rusanov flux into the continuity equation to improve the prediction of the pressure distribution and employing a corrected kernel gradient to improve the computational accuracy. In addition, a robust treatment of solid boundary is presented and verified by the spin-down problem. The merits of the robust SPH method are firstly illustrated by 2D dam breaking flow. Then the numerical method is extended to deal with the flow phenomena related to injection molding process of polymer melt. A number of numerical examples including 2D injection moldings of a thin plate mold, a circular disc with core, a ring-shaped channel, and a S-shaped cavity, and 3D injection moldings of a Z-shaped cavity and a four-legged fork are conducted. The numerical results are in agreement with the experiments, which demonstrate that the SPH method proposed here is capable of handling with injection molding process of polymer melt in a robust manner. Moreover, the robust SPH method allows to recover the fluctuations-free pressure and velocity fields which in most cases cannot be easily obtained by the traditional SPH method.     

Comparative estimate of the molding capacities of injection molding machines with plunger and screw plastication

An analysis of the mold filling process, based on the equation of nonisothermal flow of an amorphous polymer melt, shows that for thin moldings the molding capacity of the machine, estimated as the maximum shot length, has a limit that does not depend on the pressure at the mold inlet and is determined by the flow rate of the polymer in the mold. As shown by an analysis of the process of compaction of the polymer in the system preceding the mold, this flow rate is many times less for plunger plastication, which is responsible for the reduced molding capacity of plunger machines. The effect can be eliminated by compressing the polymer before injecting it into the mold.Moscow Institute of Chemical Machine Building. Translated from Mekhanika Polimerov, No. 2, pp. 367–372, March–April, 1970.     

Transport equation with boundary conditions for free surface localization

Summary. During the filling stage of an injection moulding process, which consists in casting a melt polymer in order to manufacture plastic pieces, the free interface between polymer and air has to be precisely described. We set this interface as a zero level set of an unknown function. This function satisfies a transport equation with boundary conditions, where the velocity field has few regularity properties. In a first part, we obtain existence and uniqueness result for these equations, under weaker regularity assumptions than C. Bardos [Bar70], and C. Bardos, Y. Leroux and J.C. Nedelec [BLN79] in previous articles, but stronger assumptions than R.J. DiPerna and P.L. Lions [DL89b] who studied the case without boundary condition. We also study some regularity properties of the interface. A second part is devoted to an application to injection molding of melt polymer. We give a numerical experiment which shows that our method leads to an accurate localization of interface, which is robust, since it easily handles changes of topology of the free interface, as bubble formation or fusion of two fronts of melt polymer. Received November 1, 1997 / Revised version received December 9, 1998 / Published online September 24, 1999     

Optimization of the injection molding process for short-fiber-reinforced composites

A fast and effective methodology integrating the finite-element and Taguchi methods is presented to determine the optimal design conditions of the injection molding process for short-fiber-reinforced polycarbonate composites. The finite-element-based flow simulation software, M-flow, was employed to simulate the molding process to obtain the fiber orientation distributions required. The Taguchi optimization technique was used to identify the optimal settings of injection molding parameters to maximize the shear layer thickness. The effects of four main parameters — the filling time, melt temperature, mold temperature, and injection speed — on the fiber orientation or the shear layer thickness were investigated and discussed. It is found that the dominant parameter is the filling time. The best levels of the four parameters to acquire the thickest shear layer are also identified.     

Pressure distribution in molding GRP parts of complex shape

This paper presents the results of an experimental study of the pressure distribution in the mold in molding parts consisting of cylindrical and conical components. The effect of the weight of molding compound introduced into the mold and the loading conditions on the pressure distribution is investigated. It is shown that the hypothesis of hydrostatic pressure transmission to the walls of the mold is incorrect in relation to the manufacture of glass-reinforced plastic (GRP) parts of complex shape.Mekhanika Polimerov, Vol. 1, No. 4, pp. 130–135, 1965     

Ⅰ型拉伸试样金属注射成形多相流动的三维数值模拟

将粉末注射成形充模过程视为粘结剂、粉末和空气的三相流动过程,基于多相流理论给出金属注射成形的多相流动控制方程。根据金属注射成形的工艺特点确定多相流动控制方程的初边界条件,用多相流数值分析软件CFX对Ⅰ型拉伸试样的铁粉注射成形充模流动过程实现了三维数值模拟,分析了模腔中不同位置处粘结剂一粉末流动的速度曲线。数值模拟结果表明在Ⅰ型拉伸试样金属注射成形充模流动过程中发生过两相分离的现象,数值模拟的瞬态信息可用于金属注射成形产品缺陷的分析与控制。     

CFD-based predictive control of melt temperature in plastic injection molding

A unique method of coupling computational fluid dynamics (CFD) to model predictive control (MPC) for controlling melt temperature in plastic injection molding is presented. The methodology is based on using CFD to generate, via open-loop testing, a temperature and input dependent system model for multi-variable control of a three-heater barrel on an injection molding machine. Results clearly show the benefit of temperature and input dependent system models for MPC control, and that CFD can be used to dramatically reduce the time associated with open-loop testing through physical experiments.     

Numerical simulation of gas-assisted injection molding using CLSVOF method

It is a typical gas-liquid two phase flow phenomenon that gas penetrates the polymer melt in gas-assisted injection molding (GAIM) process. Numerical simulation is now playing an important role in GAIM, in which the accurate simulation of moving interface is of great importance. The level set (LS) method is a popular interface tracking method, but it does not ensure naturally mass-conservation. In order to improve the mass-conservation of LS method, a coupled level-set and volume-of-fluid (CLSVOF) method with mass-correction is presented for the numerical simulations of interfacial flows in GAIM. The performance of this CLSVOF method is demonstrated by two numerical tests including the three-dimensional deformation field test and the dam break problems. Finally the CLSVOF method is employed to simulate the 3D moving interfaces in GAIM, including gas-melt interface and the melt-front interface. The influences of melt temperature and gas delay time are also analyzed detailedly. As a case study, the processes that gas penetrates the polymer melt in complex cavities are also simulated using this method, and the simulation results are in agreement with those obtained by other researchers.     

Studying the longitudinal flow of polymers with periodic deformation

Conclusions 1. At low rates of elongation the state of a polymer melt depends neither on the strain nor on the strain rate. The frequency dependence of the components of the complex longitudinal modulus, measured by superposition of a periodic deformation on a steady longitudinal flow, resemble, at low elongation rates, the frequency characteristics of the components of the complex shear modulus.2. Relaxation processes due to steady longitudinal flow affect the components of the complex longitudinal modulus measured by periodic deformation.3. A melt of a polydisperse polymer under conditions of longitudinal flow begins, at some definite strain rate, to respond to periodic deformation as a rubber-like body and continues to do so as the amount of elongation increases, which is manifested by the trend of the frequency dependence of the modulus component E', this trend becoming similar to that for a solid body.4. As the strain increases during elongation, the upper boundary of the flow range, which is determined by the periodic deformation, shifts toward low frequencies.5. The viscoelasticity characteristics of a material subject to elongation can be accurately enough described by nonlinear equations with the aid of the linear shear-relaxation spectrum.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 507–513, May–June, 1978.     

Boundary element and finite element analysis for the efficient simulation of fluid-structure interaction and its application to mold filling processes

Metal casting and polymer molding are widely used for the economical shape processing of complex geometries. In these manufacturing processes, a liquid melt (metal, mineral or synthetic) is filled into a mold with a cavity of the desired shape. Cooling and solidification of the melt results in a product with almost the same shape as the cavity. Numerical simulations can be employed to increase the accuracy of the process. To this end, boundary element method for Stokes flow and a finite element formulation for liquid membranes are investigated in this work. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Control-oriented modeling of servo-pump driven injection molding machines in the filling and packing phase

Servo-valves or variable displacement pumps are typically used to control conventional hydraulic injection molding machines (IMMs). Recent developments in electrical drive technology allow to utilize servo-motor driven pumps instead, which is beneficial due to their higher energy efficiency. Their dynamic behavior, however, is significantly different compared to the conventional setup. Thus, currently used mathematical models and control concepts cannot be directly applied. This paper presents a computationally efficient and scalable mathematical model of the injection process for these servo-pump driven IMMs. A first-principles model of the injection machine is combined with a phenomenological model describing the injection process, i.e. the compression of the melt and the polymer flow into the mold. The proposed model is tailored to real-time applications and serves as an ideal basis for the design of model-based control strategies. The feasibility of the proposed model is demonstrated by a number of different experiments. They confirm a high model accuracy over the whole operating range for different mold geometries.     

Numerical simulation of the filling behavior of a Non-Newtonian Fluid

A numerical model for free surface flows of non-newtonian liquids which are injected into a cavity is presented. These flows are regarded as a basic model of injection molding. Model experiments of the injection process are performed with a water-based gel. The flow equations are integrated according to the finite-volume-method. The volume of fluid method (VoF) is employed in order to describe the free surface flow of two incompressible phases, the phase interface is resolved by the method of geometric reconstruction. The Herschel-Bulkley model is used in order to describe shear-thinning behavior of the molding material and the effects of a yielding point. Different patterns of the filling flow depending on the injection parameters are evident in the experiment and the simulation. They are characterized and arranged with respect to the similarity parameters of the flow. Again, the results of the simulation are found to agree well with the experimental observations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of processing conditions on the supramolecular structure and strength properties of polycaprolactam

The formation of supramolecular structures in block polycaprolactam is considered. It is shown that technological factors have a considerable effect on the nature of the supramolecular structure. Two of these factors are the temperature gradient of the polymer melt and the nature of its motion in the cylinder of the injection molding machine up to the moment of injection into the mold. It is shown that the nonuniformity of deformation and the considerable number of defects associated with large supraspherulitic formations lead to a deterioration in the strength and deformation properties of polymers.Mekhanika Polimerov, Vol. 2, No. 5, pp. 659–663, 1966     

Polymer flow in cylindrical channels

The author examines the problem of flow of a polymer melt in a cylindrical channel of arbitrary cross section. It is assumed that the polymer is an isotropic viscoelastic medium. All the coefficients of the equation of state obtained for the flow in question are functions of the second invariant of the strain rate tensor only and can be determined experimentally in simple types of flow. A perturbation method is proposed for the solution of specific problems, the Dirichlet problem for Poisson's equation being solved in each perturbation step.Mekhanika Polimerov, Vol. 2, No. 3, pp. 421–428, 1966     

On the Voitkunskii Amfilokhiev Pavlovskii Model of Motion of Aqueous Polymer Solutions

We study the mathematical properties of the model of motion of aqueous polymer solutions (Voitkunskii, Amfilokhiev, Pavlovskii, 1970) and its modifications in the limiting case of small relaxation times (Pavlovskii, 1971). In both cases, we examine plane unsteady laminar flows. In the first case, the properties of the flows are similar to those of the flow of an ordinary viscous fluid. In the second case, there may exist weak discontinuities that are preserved during the motion. We also address the steady flow problem for a dilute aqueous polymer solution moving in a cylindrical tube under a longitudinal pressure gradient. In this case, a flow with rectilinear trajectories (an analog of the classical Poiseuille flow) is possible. However, in contrast to the latter, the pressure in this flow depends on all three spatial variables.     

Effect of process parameters on injection compression molding of pickup lens

The residual stresses and shrinkages of pickup lens in injection compression molding are investigated in this study. It was realized that the behavior of residual stresses in injection compression molding parts was affected by different process conditions such as melt temperature, mold temperature, compression pressure and time. Moldings under different conditions were numerically investigated to study the effects of the process conditions on the residual stresses and shrinkage of a pickup lens with large thickness variations. The mold temperature and compression were found to be the most important factors that affect the shrinkage of lens in the thickness direction, resulting in surface profile deviation. The effect of heat transfer coefficient of the mold wall used in the molding simulation was also discussed.     

Some problems for a non-Newtonian liquid and their application to the study of polycarbonate flow

Approximate solutions are obtained for problems of polymer flow in certain cylindrical channels. The polymer is regarded as an isotropic viscoelastic medium. Solutions are constructed by the method of perturbations from the corresponding solutions for a Newtonian liquid. The velocity distribution is calculated for a polycarbonate melt flowing in circular, elliptical and square channels.Mekhanika Polimerov, Vol. 2, No. 4, pp. 603–610, 1966     

Numerical Simulation of Injection Molding using OpenFOAM

We show how to use and extend OpenFOAM's incompressible two-phase flow solvers for the simulation of injection molding with short fiber reinforced thermoplastics in a laminar flow regime. Second order fiber orientation tensors are computed using the Folgar-Tucker equation (FTE) with quadratic closure. The FTE is coupled to the viscosity-term of the Navier-Stokes equations for the non-Newtonian flow in a segregated manner. Phase dependent boundary conditions are implemented to simulate wall heat transfer, stickiness of the melt to the wall and to prevent air-traps close to the wall. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)