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.     

Mathematical modeling of the blow-molding process

A mathematical simulation of the blow-molding cycle has been developed by combining general conservation principles along with appropriate constitutive relations for the material. A model of the parison formation stage has been devised by considering the competing effects due to swell and drawdown. A more rigorous numerical analysis of parison formation is also discussed. A theoretical treatment of parison inflation is described for both inelastic and viscoelastic materials by assuming uniform radial growth, Comparisons are made with experimental data for all phases of the molding cycle. The mathematical model is in reasonable quantitative agreement with experimental results and is capable of elucidating the influence of material properties and process conditions on the dynamics and performance of the blow-molding process.     

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.     

Parison formation and inflation behavior of polyamide-6 during extrusion blow molding

Parison formation and inflation behavior of three polyamide 6 resins during extrusion blow molding were investigated using cinematography, a transparent mold, a pinch-off mold and a modified blow pin, which allowed the pressure inside the parison to be determined during inflation. The glass fiber filled polyamide exhibited negligible extrudate swell and significant drawdown, whereas polyolefin modified polyamide exhibited appreciable extrudate swell and relatively small drawdown effects. The inflation behavior of the polyolefin modified polyamide was similar to the behavior of conventional blow molding grade polyolefins, whereas the unmodified and glass filled polyamides exhibited different inflation characteristics. Their inflation behavior at different internal pressures was characterized by decreasing and increasing Hencky strain rates with inflation time at high and low internal blow pressures, respectively. The characterized parison formation and inflation behavior of the polyamides emphasize the importance of rigorous blow moldability experiments and the difficulties associated with linking various rheological material functions to the blow moldability of modified polyamides.     

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     

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.     

熔体挤出速度对共挤吹塑型坯离模膨胀影响的数值模拟

基于三维非等温黏弹性熔体多相分层流动有限元数值模拟技术,模拟研究了熔体挤出速度对多层共挤吹塑成型环坯离模膨胀和初始温度场的影响规律,揭示了型坯离模膨胀的产生机理。结果表明,多层共挤吹塑成型环坯离模膨胀是由熔体的二次流动诱发而产生,与熔体流出机头进入自由膨胀段的二次流动强度成正比,而其二次流动强度随着熔体挤出速度的增大而增强,因而导致环坯离模膨胀随着熔体挤出速度的增加而增大;多层共挤吹塑成型熔体的二次流动强度与其第二法向应力差成正比关联关系,这与Debbaut的试验研究结论完全吻合,表明二次流动是由第二法向应力差驱动而产生。     

Numerical simulation of blow molding—prediction of parison diameter and thickness distributions in the parison formation process

In our previous study, we calculated the time course of parison length in the parison formation stage, but it could predict only the parison area swell. The next target in our study is to calculate the parison diameter and thickness swell. Annular extrudate swell simulation is necessary for the understanding of various kinds of swelling ratios in blow molding. We have examined three kinds of swells (outer diameter, thickness, and area swells) obtained from simulation results of annular extrudate swell, using the Giesekus model, and have developed a method of predicting parison outer diameter and thickness swell values. The predicted values of parison outer diameters are discussed in comparison with experimental data, and reasonable results are obtained by the proposed method. This prediction method could also be applied to the parison formation process using a parison controller. As a result, it is possible to predict approximately the whole process of parison formation by numerical simulation.     

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.     

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     

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     

Experimental and theoretical investigation of the inflation of variable thickness parisons

In today's blow molding of complex parts, an optimal resin distribution is critical to a successful operation. These goals are mostly attained through a technique known as parison programming. The process involves varying the die gap during extrusion and therefore results in a parison having a variable thickness along its length. The subsequent inflation of a variable thickness parison is a complex phenomenon involving the interaction of many process variables. The final thickness distribution and inflation patterns were obtained for various programmed parisons. Constant, one step, two step, and sinusoidal thickness parisons were studied. The inflation patterns were monitored by employing a transparent mold in conjunction with a video camera. The experimental data indicated the presence of an oscillatory inflation pattern for some of the variable thickness parisons. The experimental final part thickness distribution for these cases was highly nonlinear. Theoretical predictions of the final thickness distribution were also obtained for some of the cases. The simulation is based on the inflation of a Mooney-Rivlin hyperelastic material. A wide range of deformation is accounted for by introducing an evolutionary Mooney constant, dependent on the level of deformation.     

异型材口模挤出三维流动计算机模拟系统

建立了异型材口模挤出三维流动计算机模拟系统的基本框架，介绍了其结构和功能，该系统主要包括前置处理，有限元分析和后置处理三大模块，有限元分析模块又包括对口模内幂律流动的分析模块，粘弹性PTT流体流动的分析模块以及粘弹性PTTI充体三维挤出胀大的分析模块，后置处理主要包括速度场和应力场的后置处理。该系统目前只是一个雏形，经过不断发展和完善，有望成为异型材口模挤出过程模拟的通用分析软件。     

塑料挤出吹塑的机理问题

采用不同的方法对挤出吹塑过程的型坯成型、型坯吹胀与制品冷却三阶段的机理问题进行了研究.采用人工神经网络方法预测了受模口温度和挤出流率影响的型坯成型阶段的膨胀.利用建立起来的神经网络模型预示的膨胀与实验结果很吻合,且可在一定范围内,预示不同工艺条件下型坯的直径膨胀和壁厚膨胀,为型坯的直径和壁厚的在线控制提供了理论依据.基于薄膜近似和neo-Hookean本构关系,建立了描述型坯自由吹胀的数学模型,并通过实验方法获得了型坯吹胀的瞬态图象.     

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     

聚合物异型材气辅口模挤出成型气辅滑移对异型材挤出胀大的影响

基于流变学和流体动力学理论，经合理假设，建立了描述异型材气辅口模挤出成型过程的三维等温黏弹性理论模型，并通过DEVSS／SUPG、最小元法Mini—Element和罚函数法等稳态有限元技术，建立了与该模型相适应的快速收敛的稳态有限元数值算法，并以此通过有限元数值模拟，系统研究了聚合物异型材气辅口模挤出成型过程的机理。研究结果表明：在异型材的挤出成型过程中，随着滑移系数的增大，离模膨胀也增大。聚合物异型材气辅挤出成型能基本消除挤出成型中的离模膨胀和翘曲变形。同时，解决了由于离模膨胀和翘曲变形引起的挤出口模难于设计的技术难题。     

马鞍型异型材挤出成型过程三维等温粘弹性的数值模拟

基于PTT粘弹性本构模型,通过马鞍型异型材挤出成型过程的全三维稳态等温有限元数值模拟,系统研究了聚合物粘弹性流变性能参数和成型工艺参数对异型材口模挤出成型过程的影响规律,并揭示了其影响机理.研究结果表明,聚合物异型材口模挤出离模膨胀是由口模出口处的二次流动引起,离模膨胀比随着口模出口处的二次流动强度增加而增大.聚合物异型材口模挤出离模膨胀随着进口流量和聚合物熔体松弛时间的增加而增加,而随着聚合物熔体材料常数和粘度比的增大而减小.     

Numerical simulation of suction blow molding process for producing curved ducts

During suction blow molding process, the extruded parison undergoes twisting deformation within the mold cavity, as the air drawing flow around the deforming parison exerts non‐uniform shear stresses on its surface. Such twisting deformation can compromise the specific radial and circumferential variations in parison thickness that are intentionally generated during extrusion. This research is devoted in developing a fluid–structure interaction model for predicting parison deformation during suction blow molding process, with a specific emphasis on the suction stage. A fluid flow model, based on Hele‐Shaw approximations, is formulated to simulate the air drag force exerted on the parison surface. The rheology of the material of the parison is assumed to obey the viscoelastic K‐BKZ model. As the suction process also involves the sliding of the parison within the mold cavity, a modified Coulomb's law of dry friction is used to simulate the frictional contact between parison and mold. The numerical results of this study allowed identifying a clear correlation between the twisting deformation undergone by the parison during the suction stage, also observed experimentally and the design parameters, namely, the air drawing speed, the geometry of the duct mold cavity, and the parison/mold eccentricity. POLYM. ENG. SCI., 59:418–434, 2019. © 2018 Her Majesty the Queen in Right of Canada     

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     

挤出吹塑中型坯成型的有限元模拟——型坯尺寸预测

建立了塑料挤出吹塑中平直型机头内非牛顿粘弹性熔体的流动模型，并利用POLYFLOW有限元软件进行求解，预测了不同型坯长度和不同流量时的型坯尺寸分布。