Primary and secondary gas penetration during gas‐assisted injection molding. Part II: Simulation and experiment

Simulation and experimental studies have been carried out on the transient gas‐liquid interface development and gas penetration behavior during the cavity filling and gas packing stage in the gas‐assisted injection molding of a spiral tube cavity. The evolution of the gas/melt interface and the distribution of the residual wall thickness of skin melt along with the advancement of gas/melt front were investigated. Numerical simulations were implemented on a fixed mesh covering the entire cavity. The residual thickness of a polymer layer and the length of gas penetration in the moldings were calculated using both the simulation and model developed in Part I of this study and commercial software (C‐Mold). Extensive molding experiments were performed on polystyrene at different processing conditions. The obtained results on the gas bubble dynamics and penetration behaviors were compared with those predicted by the present simulation and C‐Mold, indicating the good predictive capability of the proposed model. Polym. Eng. Sci. 44:992–1002, 2004. © 2004 Society of Plastics Engineers.     

Computer simulation of the filling process in gas‐assisted injection molding based on gas‐penetration modeling

Gas‐assisted injection molding can effectively produce parts free of sink marks in thick sections and free of warpage in long plates. This article concerns the numerical simulation of melt flow and gas penetration during the filling stage in gas‐assisted injection molding. By taking the influence of gas penetration on the melt flow as boundary conditions of the melt‐filling region, a hybrid finite‐element/finite‐difference method similar to conventional‐injection molding simulation was used in the gas‐assisted injection molding‐filling simulation. For gas penetration within the gas channel, an analytical formulation of the gas‐penetration thickness ratio was deduced based on the matching asymptotic expansion method. Finally, an experiment was employed to verify this proposed simulation scheme and gas‐penetration model, by comparing the results of the experiment with the simulation. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 2377–2384, 2003     

Dynamic modeling of a gas pressure control system for a gas‐assisted injection molding process

This study presents the development of dynamic models for gas injection pressure that may be implemented in the design of control systems for gas‐injection units. A nonlinear dynamic model was first derived and then verified by experimental measurements. This was done by using a laboratory‐built, gas‐assisted injection unit. The agreement between the prediction and measurement indicates that the present nonlinear dynamic model adequately predicts the dynamic behavior of gas injection pressure during the process. Although the resulting model is useful for understanding the behavior of the process and the effects of different process variables, its complexity may cause difficulties in a real control application. Therefore, a second‐order model based on the basic characteristics of the nonlinear model was proposed to approximate the gas injection pressure. In order to determine the model parameters, the algorithm of recursive least‐square system identification was employed. A comparison of simulated results of an identified model with experimental data showed that the model accurately predicted the transient behavior of gas injection pressure. Consequently, this low‐order model can be easily implemented into the control system design of a gas‐injection unit.     

Three‐dimensional simulation of primary and secondary penetration in a clip‐shaped square tube during a gas‐assisted injection molding process

This article proposes a generalized Newtonian model to predict the three‐dimensional gas penetration phenomenon in the GAIM process, where the gas and melt compressibility are both taken into account and hence the primary and secondary penetrations in GAIM processes are able to be quantitatively predicted. Additionally, an incompressible model requiring no outflow boundary is also presented to emphasis the influence of gas compressibility on the primary penetration. Based on a finite volume discretization, the proposed numerical model solves the complete momentum equation with two front transport equations, which are employed to track the gas/melt and air/melt interfaces. The modified Cross‐WLF model is adopted to describe the melt rheological behavior. The two‐domain modified Tait equation is exploited to represent the melt compressibility, while a polytropic model is employed to express the gas compressibility. The proposed schemes are quantitatively validated by the gas penetration characteristics in a clip‐shaped square tube, where good prediction accuracy is obtained. The influences of five major molding parameters, such as the injection pressure, mold temperature, melt temperature, delay time, and melt material on the gas penetration characteristics in the same clip‐shaped square tube via the proposed numerical approach are extensively presented and discussed. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Three‐dimensional simulation of multi‐material injection molding: Application to gas‐assisted and co‐injection molding

This paper presents an overview of the results obtained at the Industrial Materials Institute (IMI) on the numerical simulation of the gas‐assisted injection molding and co‐injection molding. For this work, the IMI's three‐dimensional (3D) finite element flow analysis code was used. Non‐Newtonian, non‐isothermal flow solutions are obtained by solving the momentum, mass and energy equations. Two additional transport equations are solved to track polymer/air and skin/core materials interfaces. Solutions are shown for different thin parts and then for thick three‐dimensional geometries. Different operating conditions are considered and the influence of various processing parameters is analyzed.     

Buildup and relaxation of molecular orientation in injection molding. Part I: Formulation

A numerical simulation model for the analysis of the buildup and, the relaxation of molecular orientation in injection-molded products has been developed. The constitutive equations of the material are described using an extended version of the viscoelastic material model developed by Leonov. The volumetric responses are described using two different equations of state, the Tait equation and an equation developed by Spencer and Gilmore. A WLF-type of equation is used for the temperature and pressure dependence. Stresses calculated with the model are coupled to birefringence by means of the stress-optical rule. Birefringence, in turn, is used to characterize the molecular orientation. The model is used to investigate the influence of the processing conditions, the mold elasticity, and the pressure dependence of the material functions on the pressure and birefringence profiles. The material data used are for polystyrene, PS 678E, and are determined experimentally.     

Interface evolution and penetration behavior during two‐component transfer molding. Part I: Modeling and formulation

A theoretical study of pressure‐controlled sequential sandwich transfer molding of rubber compounds under isothermal conditions has been carried out to obtain a two‐layered sandwich structure. A physical model, numerical simulation procedure, and a numerical algorithm have been formulated based on the Hele‐Shaw approximation along with the kinematics and dynamics of interface evolution. Based on the developed numerical simulation code, the effect of various processing conditions on the material distribution and interface shape can be evaluated and predicted. Comparison with experiments is carried out in Part II of this study. Polym. Eng. Sci. 44:687–696, 2004. © 2004 Society of Plastics Engineers.     

A 3‐D finite element model for gas‐assisted injection molding: Simulations and experiments

To gain a better understanding of the gas‐assisted injection molding process, we have developed a computational model for the gas assisted injection molding (GAIM) process. This model has been set up to deal with (non‐isothermal) three‐dimensional flow, in order to correctly predict the gas distribution in GAIM products. It employs a pseudo‐concentration method, in which the governing equations are solved on a fixed grid that covers the entire mold. Both the air downstream of the polymer front and the gas are represented by a fictitious fluid that does not contributeto the pressure drop in the mold. The model has been validated against both isothermal and non‐isothermal gas injected experiments. In contrast to other models that have been reported in the literature, our model yields the gas penetration from the actual process physics (not from a presupposed gas distribution). Consequently, it is able to deal with the 3‐D character of the process, as well as with primary (end of gas filling) and secondary (end of packing) gas penetration, including temperature effects and generalized Newtonian viscosity behavior.     

A simple method for forecast of cooling time of high‐density polyethylene during gas‐assisted injection molding

Gas‐assisted injection molding (GAIM) is an innovative plastic processing technology, which was developed from the conventional injection molding, and has currently found wide industrial applications. About 70% of the whole gas‐assisted injection molding cycle is actually occupied by the cooling stage. The quality and production efficiency of molded parts are considerably affected by the cooling stage. Hence, it is necessary to study the solidification behaviors during the cooling stage. In this work, a simple experimental method was designed to simulate the solidification behaviors of high‐density polyethylene during cooling stage of GAIM. The enthalpy transformation approach, coupled with the control‐volume/finite difference techniques, was adopted to deal with the transient heat transfer problems with phase change effects. In situ measurements of the temperature decreases in the cavity were also carried out. Reasonable agreements between the experimental values and the simulated results such as cooling time, cooling rates, and temperature curves were obtained, which proved that this simple experimental method was effective. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Study on the packing effects of external gas‐assisted injection molding on part shrinkage in comparison with conventional injection molding

Applying gas pressure on the reverse side of the part that called external gas‐assisted injection molding (EGAIM) has the potential to solve shrinkage‐related molding problems. We investigate the packing effects of EGAIM on part shrinkage and sink mark under various rib design and compare it to that of conventional injection molding (CIM). It was found that EGAIM has uniformly distributed packing pressure within the entire mold cavity. To achieve equivalent part shrinkage, CIM requires 100 MPa packing pressure from the molding machine, whereas EGAIM requires only 9 MPa. EGAIM can further reduce part shrinkage if the gas pressure and gas packing time are both increased. EGAIM can also eliminate sink marks for rib designs of an aspect ratio (rib width /part thickness) up to 1.2, whereas CIM can achieve the same sink mark level only at an aspect ratio of less than 0.5. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers     

Crystallization behavior and molecular orientation of high density polyethylene parts prepared by gas‐assisted injection molding

The dependence of hierarchy in crystalline structures and molecular orientations of high density polyethylene parts with different molecular weights molded by gas‐assisted injection molding (GAIM) was intensively examined by scanning electron microscopy, two‐dimensional wide‐angle X‐ray scattering as well as dynamic rheological measurements. The non‐isothermal crystallization kinetics of the samples were also analyzed with a differential scanning calorimeter at various scanning rates. It was found that oriented lamellar structure, shish‐kebab and common spherulites were formed in different regions of the GAIM samples. The scanning electron microscope observations were consistent with the two‐dimensional wide‐angle X‐ray scattering results and showed that the molecular chains near the mold wall had strong orientation behavior, revealing the distribution of the shear rate of the GAIM process. The differences in crystal morphologies can be attributed to molecular weight differences as well as their responses to the external fields during the GAIM process. The formation mechanism of the shish‐kebab structure under the flow field of GAIM was also explored. Copyright © 2012 Society of Chemical Industry     

A unified simulation of the filling and postfilling stages in injection molding. Part I: Formulation

This study employs a unified theoretical model to simulate the filling and postfilling stages of the injection-molding process. Implementation of such a model is based on a hybrid finite-element/finite-difference numerical solution of the generalized Hele-Shaw flow of a compressible viscous fluid under nonisothermal conditions. The shear viscosity of the polymeric material is represented by a Cross model for the shear-rate dependence and a WLF-type functional form for the temperature and pressure dependence, whereas the specific volume is modeled in terms of a double-domain Tait equation. The analysis also handles variable specific heat and thermal conductivity of the polymer as a function of temperature. Complex thin parts of variable thickness can be modeled and discretized by flat, triangular finite elements which may have arbitrary orientation in three-dimensional space, whereas runners and possible round pins or bosses in the part are represented as one-dimensional circular-tube elements. A control-volume scheme is employed that leads to automatic melt-front advancement during the cavity-filling stage.     

Ultrasonic measurement of residual wall thickness during gas assisted injection molding

Ultrasonic technology provides a powerful and noninvasive method of in‐process measurement during injection molding and extrusion. Changes in the velocity, attenuation and reflection coefficients of high frequency sound waves can be related to the state and conditions of the materials through which they propagate. The velocity of an ultrasonic wave changes with density and elastic moduli; this allows information on solidification and material properties to be collected during the molding cycle. The time of flight of the wave is a function of velocity and path length. This paper shows that it can be correlated with the residual wall thickness of polymer in the mold during gas assisted injection molding. POLYM. ENG. SCI., 47:1730–1739, 2007. © 2007 Society of Plastics Engineers     

Three-dimensional modeling of reaction injection molding. I

In this research a model to simulate both the filling the curing stages of a reaction injection molding (RIM) process in complex three-dimensional molds is developed. This model can be used to predict not only the temperature and conversion changes with time but also the front position during filling. Using given physical and chemical properties of the RIM system, moldability can be determined in advance. The numerical techniques used in this research include adaptation of the SIMPLE algorithm developed by Patankar for a moving-front, two-phase system with non-negligible inertial effects, and exothermic chemical reaction. The model predictions of temperature and conversion compare favorably with available data on simple two-dimensional molds. The ability of the model to predict the dynamics of filling in more complicated molds was verified by comparison to mold filling experiments with water and a polyurethane foam.     

The influence of gas‐assisted injection molding parameters on the structure and thermomechanical properties of hollow parts

The purpose of the work was to estimate an influence of gas‐assisted injection conditions (the temperature of plastic material, switch time‐delay time, gas injection time) of shape, position and dimension of gas channel, and structure of injection molded parts. The change in the value of the dynamic Young modulus and the mechanical loss tangent in function of temperature and oscillation frequency by the dynamic mechanical thermal analysis (DMTA) method was determined. It was found that injection molding parameters: injection molding temperature, switching time and gas injection time influenced significantly mass, wall thickness, and thermomechanical properties of parts. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers     

Birefringence in gas‐assisted tubular injection moldings: Simulation and experiment

The influence of the processing variables on the birefringence and polymer/gas interface distribution is analyzed for polystyrene moldings obtained by gas‐assisted injection molding (GAIM) under various processing conditions. The processing variables studied were: melt and mold temperatures, shot size, gas pressure, injection speed, and gas‐delay time. Measurements and viscoelastic simulations of the radial distribution of birefringence components, Δn and n_rr ? n_θθ, the variation of the average birefringence, 〈n_zz ? n_θθ〉, along the molding and polymer/gas interface along the length of spiral‐shaped tubular moldings are presented. The polymer/gas interface distribution and flow stresses were simulated using a numerical scheme based on a hybrid finite element/finite difference/control volume method. The birefringence was calculated from the flow‐induced stresses using the stress‐optical rule. Simulations qualitatively agreed with measurements and correctly described theeffect of the processing variables on the birefringence andthe polymer/gas interface distribution in GAIM moldings. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Simulation of phase‐change heat transfer during cooling stage of gas‐assisted injection molding of high‐density polyethylene via enthalpy transformation approach

Gas‐assisted injection molding (GAIM) is one of the significant fabricating technologies of plastics in modern industry, mainly owing to the light weight of products, good structural rigidity and dimensional stability, as well as shorter molding cycles. The objective of this article is to explore the temperature profiles during the cooling stage of gas‐assisted injection molded high‐density polyethylene (HDPE) parts using a transient heat transfer model of the enthalpy transformation method, which could always be utilized for the numerical studies of the phase‐change heat transfer issues. The simulated results were validated by the in situ measurement of temperature decay, and good agreement has been observed. The comparison between GAIM and conventional injection molding (CIM) reveals that it is the rapid cooling rate (because of thin wall‐thickness) and the inner gas cooling effects that together lead to the shortening of molding cycles. As cooling rate plays a part in the stabilization of the crystalline structure during the GAIM process according to our previous studies, this work is of significance for the operational designs in GAIM industrial applications and further investigation on the detailed mechanisms of various crystalline structures in GAIM parts. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Interface evolution and penetration behavior during two‐component transfer molding. Part II: Simulation and experiment

Simulation and experimental study of the pressure‐controlled sequential sandwich transfer molding of two SBR rubber compounds under isothermal condition have been carried out to obtain a two‐layered sandwich structure. One SBR compound, which is intended for the skin material, is first laid up in the cavity. Then, another SBR compound, intended for the core material, is transferred to penetrate into the skin material and to push the lay‐up to fully fill the cavity, resulting in an encapsulated skin/core sandwich structure. Two cases involving different material combinations with different viscosity ratios have been studied. The rheological interaction of the skin/core components and its effect on the penetration behavior and interface shape have been investigated. The influence of processing conditions, such as the volume fraction transferred and pressure, is discussed. The penetration and encapsulation behavior, and the interface development are found to be significantly affected by the rheological properties of the compounds and the volume fraction transferred. However, at a constant volume fraction transferred, the pressure imposed during transfer molding is found to have a little effect on the interface development. These experimental findings are in good agreement with the present predictions based on the model and simulation proposed in Part I of this study. Polym. Eng. Sci. 44:697–713, 2004. © 2004 Society of Plastics Engineers.     

Multizone circulating reactor modeling for gas‐phase polymerization. I. Reactor modeling

A new gas‐phase technology for polyolefin production is being developed to be commercially available for large‐scale production between 2004 and 2005. This new technology uses a multilane circulating reactor, which consists of two interrelated zones where two distinct and different fluodynamic regimes are realized, between which the polymer particles are kept in continuous circulation. This article presents a mathematical model for the multilane circulating reactor presenting the typical behavior of the reactor operation and a parameter sensibility analysis. Simulations were conducted for polyethylene production. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 1042–1052, 2004