Numerical simulation of blow molding—Viscoelastic flow analysis of parison formation

The simulation of the parison formation process in blow molding has been studied. The flow field was divided into two regions, namely, the extrudate swell region near the die lip and the parison formation region after the exit swell. In the swell region, we predicted the swelling ratio and residual stress distribution for high Weissenberg numbers for steady planar well using the 1-mode Giesekus model. In the parison formation region, the flow is assumed to be an unsteady unaxial elongational flow including drawdown and recoverable swell and is modeled using the 10-mode Giesekus model. We calculated the time course of parison length and thickness distribution, and compare the calculation results of parison length with experimental data. It was found that the predicted values agreed rather well with the experimental values. The calculation results could especially predict the shrink-back, which is the phenomenon where the parison length becomes shorter after the cessation of extrusion, and it was found tat this was caused by the recoverable swell of the parison, which depends on the tensile stress generation in the die. Various flow rates and die geometries were studied and confirmed the reliability and usefulness of the method.     

Effect of die gap width on annular extrudates by the annular extrudate swell simulation in steady-states

We calculated the steady-state annular extrudate swell of polymer melts through flow geometries encountered in processes used to control parison thickness. A streamline-upwinding finite element method with an under-relaxation for the rate of deformation tensor was used. The Giesekus model was employed as the constitutive equation. An operation that widens the die gap is appropriate for the control of parison thickness corresponding to the change of die gap width. However, a control process that decreases the die gap width is not useful, because the parison thickness does not correspond to the die gap width. Furthermore, thickness swells change strikingly with the Weissenberg number. It is difficult to control the parison outer diameter in the case of a converging die, because the change of the outer diameter swell becomes large with increasing Weissenberg number. In the case of a diverging die, the changing value of the outer diameter swell is smaller than that in the case of a converging die.     

Modeling parison formation in extrusion blow molding by neural networks

A series of experiments were carried out on the parison formation stage in extrusion blow molding of high‐density polyethylene (HDPE) under different die temperature, extrusion flow rate, and parison length. The drop time of parison when it reached a given length and its swells, including the diameter, thickness, and area swells, were determined by analyzing its video images. Two back‐propagation (BP) artificial neural network models, one for predicting the length evolution of parison with its drop time, the other predicting the swells along the parison, were constructed based on the experimental data. Some modifications to the original BP algorithm were carried out to speed it up. The comparison of the predicted parison swells using the trained BP network models with the experimentally determined ones showed quite a good agreement between the two. The sum of squared error for the predictions is within 0.001. The prediction of the parison diameter and thickness distributions can be made online at any parison length or any parison drop time within a given range using the trained models. The predicted parison swells were analyzed. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 2230–2239, 2005     

Fast online acquisition and analysis for parison swell and sag in blow molding

It is critical to quantitatively and reliably characterize the effects of swell and sag phenomena on the final parison dimensions in extrusion blow molding. To achieve this goal, an online image acquisition and analysis technique was developed. The successive images of parison were automatically taken using the online acquisition apparatus. These images were then analyzed by the combined use of the conventional digital image processing method and the new one developed by the authors. So the development of parison diameter and thickness swells with the extrusion time could be determined online. On the basis of the online obtained actual swell values, the pure swell and sag components were quantitatively determined. The developed technique was tested through a series of experiments using several resins under different processing parameters and die types. Shown in the present article were the results for a converging die under three different die gaps and a high‐density polyethylene. Some new phenomena were observed using the proposed technique. The results showed that the technique yields fast and accurate determination of the evolution of diameter, thickness, and length of parison during its extrusion. The technique can be employed as a part of the closed loop control for blow molded part thickness. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 2399–2406, 2006     

An experimental investigation of capillary extrudate swell in relation to parison swell behavior in blow molding

An experimental study was carried out to study and characterize the capillary extrudate swell and parison swell behavior in extrusion blow molding of two commercial blow molding grade high density polyethylene resins. The capillary extrudate swell behavior of these resins were determined employing a capillary rheometer and a special thermostatting chamber. Parison swell behavior was determined using an Impco A13-R12 reciprocating screw blow molding machine in conjunction with cinematography and pinch-off. The experimental conditions under which capillary extrudate and parison swell data can be related are elucidated. Excellent agreement is found between the area swell values determined on the basis of capillary and parison swell experiments.     

The dynamics of parison development in blow molding

An experimental program was carried out to study the dynamics of parison swell and development in extrusion-blow molding. Two commercial blow molding grade polyethylene resins were employed in conjunction with an Impco, Model A13-R12 reciprocating screw blow molding machine equipped with a cylindrical bottle mold. Parison weight swell was measured with the aid of a parison pinch-off mold. In order to obtain more reliable and useful information regarding diameter and thickness swell of the parison and the dynamics of parison formation and development, high speed cinematography was employed. Data obtained by this technique are more reliable than results obtained with the pinch-off mold alone. They also give further insight into the phenomena of swell, sag, and parison spring back or recovery.     

Measurement and calculation of parison dimensions and bottle thickness distribution during blow molding

Experimental data are reported regarding the dynamics of the blow molding process, including parison formation, growth, and inflation. These data have been obtained with the aid of high speed cinematography and pinch mold experiments, in conjunction with two commercial blow molding polyethylene resins. It is shown that pinch mold experiments alone do not yield accurate data regarding thickness and diameter swell. Furthermore, the inflation process involves decreasing rates of inflation with time, as a result of the rise in viscosity due to the cooling of the parison during inflation. Mathematical procedures are proposed for a first-order estimation of parison length and swell as a function of time and the inflation behavior after clamping. In the absence of more dependable basic procedures, the proposed treatment is employed to estimate the effective transient swell functions for the parison using experimental data obtained under the specified conditions. The mathematical treatment is extended to determine the thickness distribution of the bottle. Good agreement is obtained between experimental and calculated results.     

Modeling of complex parison formation in extrusion blow molding: Effect of medium to large die heads and fuel tank geometry

This work presents the effect of die geometry and die gap opening on the extrudate swell phenomenon, in complex parison formation using the vertical wall distribution system (VWDS) and partial wall distribution system (PWDS). The BlowParison^© software from IMI is used to predict the parison formation for a combined VWDS/PWDS system, accounting for swell, sag, and nonisothermal effects. This software couples a fluid mechanics approach to represent the die flow, with a solid mechanics approach to represent the parison behavior outside the die, and a mathematical swell model to account for the pronounced elongational and shear stresses at high Weissenberg numbers. The emphasis is placed on experimental validation of the predicted parison dimensions using four diverging die geometries and different sets of VWDS/PWDS profiles. The experimental and predicted weight profiles for a dissected fuel tank are also presented. Both experimental and simulation results suggest a strong dependence of extrudate swell to the die geometry in the die land zone. The results also demonstrate the validity of the numerical predictions for part design purposes given the multitude of experimental validations presented in this work. POLYM. ENG. SCI., 2009. Published by the Society of Plastics Engineers     

Isothermal swell of extrudate from annular dies; effects of die geometry,flow rate,and resin characteristics

An experimental study was made of the effects of die geometry and extrusion velocity on parison swell for three high-density-polyethylene blowmolding resins. Four annular dies were used: a straight, a diverging, and two converging dies. Diameter and thickness swells were measured as functions of time under isothermal conditions and in the absence of drawdown. This was accomplished by extruding into an oil having the same density and temperature as the extrudate. It was observed that 60 to 80 percent of the swell occurs in the first few seconds and that equilibrium swell is attained only after 5 to 8 minutes have elapsed. The diameter and thickness swells appear to be independent phenomena, as the relationship between them depends strongly on die design. The ranking of the resins in terms of the magnitude of the swell was found to be the same for all die geometries and extrusion rates used.     

Variables affecting parison diameter swell and their correlation with rheological parameters

An important factor in the selection of blow molding resins for producing handled bottles is the effective diameter swell of the parison. Ideally, the diameter swell is directly related to the weight swell and would require no separate consideration. In actual practice, the existence of gravity, the finite parison drop time and the anisotropic aspects of the blow molding operation prevent reliable prediction of the parison diameter swell directly from the weight swell. The parison diameter swell is a complex function of the weight swell, the rate of swell and the melt strength. Elements of this function are presented which show the effect of extrusion rate, parison drop time and parison weight. A technique is presented which allows the estimation of local weight and diameter swell ratios. Their direct relationship is confirmed by data obtained on several blow molding resins. The relationship between weight swell and diameter swell is definitely anisotropic. A mathematical model for swell is proposed which incorporates experimentally determined rate constants and swell coefficients. Correlations are given which suggest fundamental relationships between these derived coefficients and basic variables such as resin properties or process conditions. The model's predictive capability is demonstrated by using it to back calculate parison dimensions.     

Swell of extrudate from an annular die

Diameter and thickness swells have been measured as functions of time and wall shear rate for three high density polyethylenes at 170°C and one polypropylene at 190°C. By extruding into an oil having the same temperature and density as the extrudate, it was possible to measure isothermal swell in the absence of drawdown. Seventy to 80 percent of the swell occurs in the first one or two seconds, while several minutes are required to reach an equilibrium state. Relationships between various swell parameters, including parison weight swell and capillary extrudate swell, are examined. Important differences between the behavior of the polyethylenes and that of the polypropylene are noted.     

Noncontact measurement of parison thickness profiles affected by swell and sag in continuous extrusion blow molding

Optimization of final part thickness distributions is crucial in the extrusion blow molding process in order to minimize resin usage. Prediction of part thickness distributions from basic process and material parameters would be ideal. However, attempts to do so have been unsuccessful, largely because of the inability to predict parison thickness profiles. One must therefore resort to measurement of the parison thickness profile and estimation of the final part thickness distribution by computational methods. This paper describes a new technique for the noncontact estimation of parison thickness profiles in continuous extrusion blow molding. The method accounts for sag and requires no previous knowledge of rheological data. It can be employed on-line for the purposes of process monitoring and control. The approach is based on the measurement of the parison length evolution with time during extrusion, the parison diameter profile, the flow rate, and the melt temperature gradient along the length of the parison. These parameters are utilized in conjunction with a theoretical approach that describes the extrusion of a parison under the effects of swell, sag, and extrusion into ambient conditions. Results are presented for three resins of various molecular weight distributions. The degree of sag is minimal at the top and bottom of the parison, and reaches a maximum near the center of the parison. Results are also presented to demonstrate the versatility of the method under other process conditions, such as varying flow rate, die temperature, and die gap.     

Overall numerical simulation of extrusion blow molding process

This paper focuses on the overall numerical simulation of the parison formation and inflation process of extrusion blow molding. The competing effects due to swell and drawdown in the parison formation process were analyzed by a Lagrangian Eulerian (LE) finite element method (FEM) using an automatic remeshing technique. The parison extruded through an annular die was modeled as an axisymmetric unsteady nonisothermal flow with free surfaces and its viscoelastic properties were described by a K‐BKZ integral constitutive equation. An unsteady die‐swell simulation was performed to predict the time course of the extrudate parison shape under the influence of gravity and the parison controller. In addition, an unsteady large deformation analysis of the parison inflation process was also carried out using a three‐dimensional membrane FEM for viscoelastic material. The inflation sequence for the parison molded into a complex‐shaped mold cavity was analyzed. The numerical results were verified using experimental data from each of the sub‐processes. The greatest advantage of the overall simulation is that the variation in the parison dimension caused by the swell and drawdown effect can be incorporated into the inflation analysis, and consequently, the accuracy of the numerical prediction can be enhanced. The overall simulation technique provides a rational means to assist the mold design and the determination of the optimal process conditions.     

A comprehensive experimental study and numerical modeling of parison formation in extrusion blow molding

Parison dimensions in extrusion blow molding are affected by two phenomena, swell due to stress relaxation and sag drawdown due to gravity. It is well established that the parison swell and sag are strongly dependent on the die geometry and the operating conditions. The availability of a modeling technique ensures a more accurate prediction of the entire blow molding process, as the proper prediction of the parison formation is the input for the remaining process phases. This study considers both the simulated and the experimental effects of the die geometry, the operating conditions, and the resin properties on the parison dimensions using high density polyethylene. Parison programming with a moving mandrel and the flow rate evolution in intermittent extrusion are also considered. The parison dimensions are measured experimentally by using the pinch-off mold technique on two industrial scale machines. The finite element software BlowParison® developed at IMI is used to predict the parison formation, taking into account the swell, sag, and nonisothermal effects. The comparison between the predicted parison/part dimensions and the corresponding experimental data demonstrates the efficiency of numerical tools in the prediction of the final part thickness and weight distributions. POLYM. ENG. SCI., 47:1–13, 2007. © 2006 Society of Plastics Engineers     

New Strategies for Predicting Parison Dimensions in Extrusion Blow Molding

In this work, two new strategies were proposed for predicting the parison thickness and diameter distributions in extrusion blow molding. The first one was a finite-element-based numerical simulation for the parison extruded from a varying die gap. The comparison of simulated and experimental parison thickness distributions indicates that the new method has certain accuracy in predicting the parison thickness from a varying die gap. The second one was an artificial neural network (ANN) approach, the characteristics of which are in sufficient patterns that can be obtained without doing too many experiments. The diameter and thickness swells of the parisons extruded under different flow rates were obtained by a well-designed experiment. The obtained data were then used to train and test the ANN model. The dimension of one location on the parison can provide one pattern to train the ANN model. Trained and tested ANN model can be used to predict the dimensions at any location on the parison within a given range. The proposed two strategies can help search the processing conditions to obtain optimal parison thickness distributions.     

Three‐dimensional simulation on multilayer parison shape at pinch‐off stage in extrusion blow molding

We tried to predict the multilayer parison shape at pinch‐off stage in extrusion blow molding by nonisothermal and purely viscous non‐Newtonian flow simulation using the finite element method (FEM). We assumed the parison deformation as a flow problem. The Carreau model was used as the constitutive equation and FEM was used for calculation method. Multilayer parison used in this simulation was composed of high‐density polyethylene (HDPE) as inner and outer layers and low‐density polyethylene (LDPE) of which viscosity is five times lower than HDPE as a middle layer. We discussed multilayer parison shape in pinch‐off region. The results obtained are as follows; the parison shape of each layer was clearly visible in the pinch‐off during the mold closing. In addition, the distribution of parison thickness ratios for each layer was located for a large deformation near the pinch‐off region. The melt viscosity for each layer has an influence on the melt flow in the pinch‐off region. In a comparison with an experimental data of parison thickness ratios, the simulation results are larger than the experimental data. These simulation results obtained are in good agreement with the experimental data in consideration of the standard deviations. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers     

A modeling approach to the effect of resin characteristics on parison formation in extrusion blow molding

The most critical stage in the extrusion blow‐molding process is the parison formation, as the dimensions of the blow‐molded part are directly related to the parison dimensions. The swelling due to stress relaxation and sagging due to gravity are strongly influenced by the resin characteristics, die geometry, and operating conditions. These factors significantly affect the parison dimensions. This could lead to a considerable amount of time and cost through trial and error experiments to get the desired parison dimensions based upon variations in the resin characteristics, die geometry, and operating conditions. The availability of a modeling technique ensures a more accurate prediction of the entire blow‐molding process, as the proper prediction of the parison formation is the input for the remaining process phases. This study considers both the simulated and the experimental effects of various high‐density polyethylene resin grades on parison dimensions. The resins were tested using three different sets of die geometries and operating conditions. The target parison length was achieved by adjusting the extrusion time for a preset die gap opening. The finite element software BlowParison® was used to predict the parison formation, taking into account the swell and sag. Good agreements were found between the predicted parison dimensions and the experimental data. POLYM. ENG. SCI., 2009. Published by Society of Plastics Engineers     

On-Line measurement of parison geometry during blow molding: Parison swelling for three high-density polyethylenes with different molecular weights and molecular weight distributions

An image analysis technique has been developed to measure diameter and thickness distribution of a parison during the extrusion stage in blow molding. The system operates on-line during extrusion on any commercial blow-molding machine. The system has been developed to help development of new blow-molding resins by increasing our understanding of the connection between polymer structure and parison shape. The system can also be used for die design during optimization of a production process. The combined use of experimental design and multivariate projection techniques makes this an efficient tool for the practical processing engineer. Experiments done on three high-density polyethylene blow-molding resins show the importance of measuring the time dependence of the diameter and thickness distribution under different extrusion conditions for a given polymer. Our results show that many of the swell and sag related properties we see cannot be directly inferred from standard laboratory swell-experiments.     

Studies on melt-spinning process of hollow fibers

Profile development and dimensional change in the melt-spinning process of hollow fibers were studied using a finite element method, and a numerical simulation was compared with experimental results. The numerical simulation of a hollow-fiber spinning process was carried out by considering the changes in inner and outer boundaries. Initial dimensions of inner and outer radii were obtained by measuring the dimensions of extrudate at the extrudate swell point using a capturing device. Extrudate swell plays an important role in determining the initial dimensions of the inner and outer radii, but has less effect on the hollow portion at the die swell point. The effects of spinning variables on the hollow portion show that spinning temperature is the most critical variable in controlling the hollow portion, followed by mass throughput rate. Take-up velocity has relatively less effect. As the mass throughput rate and take-up velocity increase and the spinning temperature decreases, the hollow portion of as-spun fiber increases. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 68: 1209–1217, 1998     

Integrated numerical modeling of the blow molding process

The numerical modeling of the extrusion blow molding of a fuel tank is considered in this work. The integrated process phases are consecutively simulated, namely, parison formation, clamping, and inflation, as well as part solidification, part deformation (warpage), and the buildup of residual stresses. The parison formation is modeled with an integral type viscoelastic constitutive equation for the sag behavior and a semi-empirical equation for the swell behavior. A nonisothermal viscoelastic formulation is employed for the clamping and inflation simulation, since parison cooling during extrusion strongly affects the inflation behavior. Once the parison is inflated, it solidifies while in the mold and after part ejection. Warpage and residual stress development of the part are modeled with a linear viscoelastic solid model. Numerical predictions are compared with experimental results obtained on an industrial scale blow molding machine. Good agreement is observed. A process optimization based on a desired objective function, such as uniform part thickness distribution and/or minimal part weight, is performed. The integrated clamping, inflation, and cooling stages of the process are considered. The optimization is done by the systematic manipulation of the parison thickness distribution. Iterations are performed employing a gradient based updating scheme for the parison thickness programming, until the desired objective of uniform part thickness is obtained.