A level set based immersed boundary method for simulation of non-isothermal viscoelastic melt filling process

In this work, the polymer melt filling process is simulated by using a coupled finite volume and level-set based immersed boundary (LS-IB) method. Firstly, based on a shape level set (LS) function to represent the mold boundary, a LS-IB method is developed to model the complex mold walls. Then the non-isothermal melt filling process is simulated based on non-Newtonian viscoelastic equations with differ-ent Reynolds numbers in a circular cavity with a solid core, and the effects of Reynolds number on the flow patterns of polymer melt are presented and compared with each other. And then for a true polymer melt with a small Reynolds number that varies with melt viscosity, the moving interface, the temperature distributions and the molecular deformation are shown and analyzed in detail. At last, as a commonly used application case, a socket cavity with seven inserts is investigated. The corresponding physical quantities, such as the melt velocity, molecular deformation, normal stresses, first normal stress differ-ence, temperature distributions and frozen layer are analyzed and discussed. The results could provide some predictions and guidance for the polymer processing industry.     

Filling of a complex-shaped mold with a viscoelastic polymer. Part I: The mathematical model

A model for the filling stage of injection molding of viscoelastic thermoplastics in cavities of complex shape is presented. The model considers two-dimensional melt flow, with converging and diverging flow patterns induced by complex boundary shape and by the presence of an obstacle. The model is non-isothermal (with the melt loosing heat to the mold walls as it travels into the cavity) and handles a viscoelastic (following the White-Metzner model) material with properties that vary with temperature, shear rate, and pressure. The numerical method is based on finite differences, with boundary fitted curvilinear coordinates used in the mapping of the flow field (which has an arbitrary shape that evolves with time) into a time invariant rectangle. The numerical results reveal geometry-induced asymmetries in the flow and thermal fields as well as the effect of various process parameters on the pressure and temperature profiles in the cavity. The model admits variable cavity thickness, thus allowing for a treatment of the cavity thickness as a process parameter in the simulations.     

注塑模充填过程动态模拟

本文基于注塑模型腔内充填机理和流体力学基本方程，视聚合物熔体在型腔中的流动为平行板中的流动，在浇注系统中的流动为等效圆柱管内的流动，在此假定的基础上进行合理简化，建立了三维薄壁型腔的基于非弹性、非牛顿流体在非等温下的Ｈｅｌｅ－Ｓｈａｗ流动的数学模型及浇注系统的数学模型，并采用混合有限元／有限差分数值方法耦合求解压力方程和能量方程，采用控制体积法自动跟踪熔体前峰面，从而实现充填过程的动态模拟。模拟结     

A full 3D finite element analysis of the powder injection molding filling process including slip phenomena

A full 3D finite element analysis system has been developed to simulate a Powder Injection Molding (PIM) filling process for general three‐dimensional parts. The most important features of the analysis system developed in this study are i) to incorporate the slip phenomena, the most notable rheological characteristics of PIM feedstock, into the finite element formulation based on a nonlinear penalty‐like parameter and ii) to simulate the transient flow during the filling process with a predetermined finite element mesh with the help of a volume fill factor and a melt front smoothing scheme. The treatment of the nonlinear slip boundary condition was successfully validated via a steady state pipe flow. For the purpose of comparisons, not only the numerical simulations but also experimental short‐shot experiments were performed with two 3D mold geometries using two typical materials of slip and no‐slip cases. The good agreements between the numerical and experimental results indicate that the melt front tracking scheme successfully simulates the transient filling process.     

Conformal mapping analysis of infection mold filling

A conformal mapping analysis of the mold filling behavior in rectangular cavities is developed. The polymer melt is assumed to behave as a purely viscous Generalized Newtonian Fluid. The shape of the advancing flow front, the pressure distribution in the mold cavity, streamlines, constant temperature lines, and the required filling time may be readily determined using the techniques described. The theoretical results are in good agreement with experimental data previously reported in the literature.     

Some relationships between injection molding conditions and the characteristics of vitrified molded parts

The various mold filling phenomena influencing the characteristics of fabricated parts are surveyed. The phenomena leading to jetting in injection mold filling are considered. These are associated with the magnitude of swell by the melt as it exits the gate into the mold. Special attention is given to the influence of non-isothermal runner flow. A theory of extrudate swell of polymer melts with temperature profiles is developed using Tanner's unconstrained recovery theory. In the. absence of jetting, mold filling by a simple advancing front takes place. The hydrodynamics of the advancing front and the stress fields in the flowing melt are determined. Analysis and modeling are presented based on the use of hydrodynamic lubrication theory involving a solid layer along the mold wall and a hot isothermal melt core. This theory is compared with experimental measurements of pressure losses in mold filling. The development of birefringence in injection molding processes is analyzed. Birefringence distributions are due to frozen-in flow birefringence. A new experimental study is presented and its results compared with theoretical predictions. The problem of thermal stresses in injection molded parts is considered.     

聚丙烯微阵列结构制品熔体充填行为

根据微阵列结构制品熔体的充填特性,设计直径为500 μm的微圆柱阵列结构制品模型,并加工注射成型模具,对微圆柱结构制品熔体的充填规律进行实验和模拟研究。结果表明:微结构制品熔体的充填过程和流动前沿形态的实验结果与模拟分析虽然在趋势上比较一致,但在微圆柱成型过程中,流动前沿的形成过程和充填高度的模拟变化规律与实验结果有一定偏差;实验还发现,前期充填阶段对微圆柱成型的贡献较小,微圆柱内流动前沿的形成受到熔体流动速度、微圆柱模壁、熔体流动惯性影响较大,熔体流经微圆柱结构时产生向上的流动涡流,流动前沿形状呈偏心椭球冠状并逐渐发展成球冠状。     

Research on a Numerical Schemes for Capturing Free Front during Injection Molding

In order to capture the free front in injection molding filling precisely, the numerical method is studied for the H-J (Hamilton Jacobi) equations. The central WENO (Weighted Essentially Non-Oscillatory) scheme for the level set equations, the third-order central WENO scheme in space respectively and the third-order TVD R-K (Total Variation Diminishing Runge–Kutta) scheme in time, are used for capturing the melt flow front in injection molding filling. The numerical results show the high-order WENO scheme can capture discontinuity precisely and the melt flow front can be captured precisely using this kind of numerical method during the injection molding filling.     

注塑充模过程中温度场的全三维数值模拟

注塑充填过程中,聚合物温度的变化直接影响到成型过程的各个方面,因此,对注塑流动过程中温度场的准确预测具有重要意义.采用有限元方法对注塑充填过程中温度场的三维数值分析进行了研究.没有采用传统的Hele-Shaw薄壁假设,而是全面考虑了对流项在各个方向的影响,提出了一种全三维的温度场计算的数学模型和数值实现方法.采用Galerkin法对能量方程进行了三维有限元离散,同时,为保证数值计算过程的稳定性,采用上风法来处理对流项和黏性热项.模型可预测非牛顿非等温流体在任意厚度型腔内流动时的温度场.和二维模型相比,它具有更加广泛的适用范围,计算结果也更准确.数值算例证明了给出的模型和算法的可靠性.     

A method for determining the flow front velocity of a plastic melt in an injection molding process

During the filling phase of an injection molding process, the flow front velocity of the plastics melt has a decisive influence on the form part quality. It has been believed that a constant flow front velocity of the melt leads to distortion‐free and residual stress‐free form parts. A process control strategy based on a constant flow front velocity of the melt, however, requires the full understanding of the flow front position as a function of the screw position of the injection molding machine. With current methods, this can only be achieved by direct measurements using a number of sensors inside the mold, which leads to complicated structure, great efforts, and high cost for the tooling equipment. This article proposes, designs, and develops an innovative method for determining the flow front velocity of a plastic melt in an injection molding using only one pressure sensor at the front of the screw and based on the idea of mapping a simulated filling process to a real injection molding process. The mapping ensues that the characteristic event points are identified and matched for both the simulated and real filling process. The results of the simulation analysis and experimental evaluation show that the proposed method can be used to determine the flow front position and the resulting flow front velocity of the melt within the cavity of the mold and provide evidence that the new method offers great potential to process control strategies based on machine independent parameters. POLYM. ENG. SCI., 59:1132–1145 2019. © 2019 Society of Plastics Engineers     

Simulation of cottonseed cake melt flow in metering zone of a single screw extruder

Research on the extrusion of natural polymers (food, feed, etc.) is relatively new due to the complex physicochemical transformations of raw materials, although plastics melt conveying and transport have been well studied. The structure and composition, rheological behavior as well as extrusion processing of natural polymer are much more complicated. In this study, a quasi-three-dimensional (3D) fluid flow model for non-Newtonian, non-isothermal and undeveloped temperature was developed, the model prediction being in reasonably good agreement with the experiment. Results show that the influence of moisture content, among other process variables, is the most significant, followed by screw speed. Some interaction exists between these two variables and the screw speed effect becomes marginal at high moisture contents. In addition, viscosity change in the channel was studied.     

Modeling of mold filling process for powder injection molding

The mold filling process has been modeled for the injection molding of different polymer-based binders and powder-polymer mixtures. It is essentially a two dimensional non-Newtonian fluid flow analysis in a non-isothermal environment. A complete analysis is accomplished by combining a finite element method and control volume technique to describe an increment of flow front movement, whereas a finite difference method is used to solve the energy equation to characterize the temperature distribution. Numerical results are compared to exact solutions for a circular ring cavity using a power law fluid model under an isothermal condition. Comparison of computed results against published data for a simple circular disk shows good agreement between the two analysis methods. After making selected comparison studies, it is demonstrated that the filling process in Powder Injection Modeling with different combination of powder-polymer mixtures is markedly dependent on specific combinations of powder; and polymer based binders. Computed flow front results for a rectangular cavity also compared favorably against the data for a power law fluid model under non-isothermal conditions.     

矩形薄腔中聚合物熔体非等温注气充填的数值模拟

采用五参数Cross粘度模型,利用有限元和控制体积法对矩形薄腔中聚合物熔体非等温注气充填过程中不同时刻的气泡边界、熔体前沿、熔体压力场、温度场和速度场等进行了数值模拟,结果表明:气泡主体边界平行于模壁方向生长,其前沿总是先向中心线附近移动,再向中心线两边移动;熔体压力在气泡周围某一区域内保持不变且等于气压;对于充模时间很短的情况,除气泡附近外,温度在各处相差不大。     

注塑成型充填过程的可压缩流动分析

注塑成型过程中,熔体在型腔中的流动和传热对制品质量性能有重要的影响.为了预测注塑制品的收缩、翘曲和力学性能,精确预测充填过程的流动及传热历史是十分必要的.本文考虑熔体的可压缩性及相变的影响,将充填过程中熔体的流动视为非牛顿可压流体在非等温状态下的广义Hele-Shaw流动.采用有限元/有限差分混合方法求解压力场和温度场,采用控制体积法跟踪熔体流动前沿,并应用Visual C++实现了注塑充填过程的可压缩流动分析.为了保证能量方程各项在单元内边界的连续性,结点能量方程各项由单元形心处的离散值加权平均获得,因而,能量方程在计算区域内整体求解.对两个算例进行了分析,模拟结果与实验结果的对比,验证了本文数值算法及程序.     

水辅助注塑中高压水穿透过程的数值模拟

对水辅助注塑(WAIM)中高压水的穿透过程进行有限元模拟,研究熔体的充模行为,并分析其拉伸场和剪切场。结果显示,高压水推动熔体充模的过程可分为填充初期、快速填充期和填充末期3个阶段;较明显的拉伸应变速率仅出现在高压水前沿和熔体前沿区域;高压水前沿区域存在分布较宽且较为强烈的剪切速率,而高压水对已穿透区域的熔体几乎没有剪切作用。此外,模拟所得WAIM制品的穿透长度和掏空率与实验结果较吻合。     

Boundary conditions in the modeling of injection mold-filling of thin cavities

A governing equation for injection mold-filling of thin cavities with a power-law fluid is derived. The interaction between upstream delivery channel flow and cavity flow results in a continuously changing gate condition as the total viscous dissipation of the delivery channel-cavity assembly is minimized. Depending upon the relative magnitude of pressure drops or viscous dissipation across the channel and the cavity, the boundary conditions which determine the cavity filling process will lie between the following two limiting cases: a Cauchy type gate condition such that the location of the melt front is completely determined by the upstream flow; a Cauchy type melt front condition in which the gate condition is controlled by the downstream flow. For most injection molding cases this may be manifested as equilibration of dissipation density on the melt front. Experimentally observed melt front locations from isothermal, Newtonian filling of a constant gap rectangular cavity and of a bi-gap rectangular cavity are reported and the validity of the limiting cases are tested.     

3D Viscoelastic Simulation of Jetting in Injection Molding

A three‐dimensional model and algorithm were proposed to simulate the jetting phenomenon in injection molding. The Giesekus model was employed to describe the viscoelastic behavior of the incompressible, non‐isothermal polymer flow, and the volume of filling method was used to track the jetting free surface and advancing melt front. The governing and constitutive equations were discretized by finite volume method. To improve the precision and stability of the numerical method, a modified pressure implicit with splitting of operator algorithm was proposed to solve the pseudo Navier–Stokes problem, and an iterative scheme was constructed to determine the solution of the coupled nonlinear equations. Numerical results showed this method successfully predicted the snake‐like flow in thin‐wall cavities and buckling flow in thick‐wall cavities. The viscoelastic characteristics of polymer influenced the reptile swing frequency and amplitude. Finally, a suitable nonlinear parameter in the Giesekus model improved the precision of simulation. POLYM. ENG. SCI., 59:E397–E405, 2019. © 2019 Society of Plastics Engineers     

Simulation of injection–compression‐molding process. II. Influence of process characteristics on part shrinkage

A numerical algorithm is developed to simulate the injection–compression molding (ICM) process. A Hele–Shaw fluid‐flow model combined with a modified control‐volume/finite‐element method is implemented to predict the melt‐front advancement and the distributions of pressure, temperature, and flow velocity dynamically during the injection melt filling, compression melt filling, and postfilling stages of the entire process. Part volumetric shrinkage was then investigated by tracing the thermal–mechanical history of the polymer melt via a path display in the pressure–volume–temperature (PVT) diagram during the entire process. Influence of the process parameters including compression speed, switch time from injection to compression, compression stroke, and part thickness on part shrinkage were understood through simulations of a disk part. The simulated results were also compared with those required by conventional injection molding (CIM). It was found that ICM not only shows a significant effect on reducing part shrinkage but also provides much more uniform shrinkage within the whole part as compared with CIM. Although using a higher switch time, lower compression speed, and higher compression stroke may result in a lower molding pressure, however, they do not show an apparent effect on part shrinkage once the compression pressure is the same in the compression‐holding stage. However, using a lower switch time, higher compression speed, and lower compression stroke under the same compression pressure in the postfilling stage will result in an improvement in shrinkage reduction due to the melt‐temperature effect introduced in the end of the filling stage. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 75: 1640–1654, 2000     

Finite element analysis for wavelike flow marks in injection molding

Wavelike flow marks are a kind of surface defect that can arise during the filling stage of the injection molding process. In this study, we performed a numerical analysis using a finite element method to predict the conditions under which flow marks are generated. To simplify the analysis, a two dimensional flow through a channel between two parallel plates was considered. The viscosity of the polymer melt was modeled by the Cross‐WLF equation. For the finite element analysis, a velocity–pressure formulation was used to simultaneously solve the continuity and momentum equations. The calculation domain for the numerical analysis keeps changing with time due to the advancing melt front. To handle the free surface more accurately, a moving grid method was employed. A numerical mesh was generated at each time step using an automatic mesh generation scheme. An analytical model was developed to correlate the effects of process variables to the flow mark geometry. Results of the numerical analysis were compared with the available experimental data. The estimated geometry of the flow marks were in good qualitative agreement with experimental observations. Parametric studies have been performed to examine the effects of various processing conditions and the material properties on flow mark size. POLYM. ENG. SCI., 47:922–933, 2007. © 2007 Society of Plastics Engineers     

Preparation and properties of waterborne poly(urethane acrylate)/silica dispersions and hybrid composites

Abstract

Simulations of the isothermal and non-isothermal filling of a rectangular cavity were carried out for polystyrene using a Giesekus viscoelastic constitutive equation, whereby in the non-isothermal case the thermal resistance at the mould wall was modelled with different heat transfer coefficients to investigate the effect of the thermal resistance on the development of the molecular orientation. Results for stress development along the flow front and the cold wall were compared showing that the principal stress differences in the middle of the flow front are lower than those at the mould wall. In case of the non-isothermal filling, the latter one will increase further while the melt is gradually cooling down, which is especially true if the thermal resistance at the mould wall has been properly considered. Consequently, the high molecular orientation at the wall seems to be rather a result of the non-isothermal shear flow than of the extension at the advancing front as usually assumed.