Numerical simulation and experimental verification of the filling stage in injection molding

The linear low‐density polyethylene melt is described by the modified Cross model, the dependence of melt viscosity on temperature incorporated with the Arrhenius equation, and the Moldflow second‐order model in this investigation. The mass, momentum conservation, and constitutive equations are discretized and solved by using the iterative stabilized fractional step algorithm along with the Crank–Nicolson implicit difference scheme. The energy conservation equation is discretized with the characteristic Galerkin approach. The free surface of molten polymer flow front is tracked by the arbitrary Lagrangian–Eulerian (ALE) method. It is demonstrated that good agreement of the numerical predictions given by the proposed ALE method with the results obtained by the injection short‐shot experiments is achieved in the locations and shape of the melt front. Furthermore, when the melt front completely reaches the wall of the mold cavity, the horizontal velocity distribution of counterflow at the section near the finally filling wall is exhibited in the present simulation. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

注塑成型熔接线截面熔接过程数值模拟

在多浇口和带嵌件注塑制品的成型过程中必然存在熔体的熔接过程,从而形成熔接线。熔接线沿厚度方向的熔接过程是影响该区域的力学强度以及纤维取向等制品性能的重要因素。本文采用有限元法针对注塑制品的典型截面建立数学模型,采用T6P3单元(速度二次插值,压力线性插值),数值模拟了注塑制品熔接线的截面熔接过程。通过等厚度截面和非等厚度截面两个算例,给出了两股熔体熔接过程中的截面速度场和压力场分布。讨论了熔接线区域的壁厚均匀程度对熔接过程的影响。该计算结果可以为制品力学性能以及纤维取向等数值模拟提供数据支持。     

Numerical simulation of reactive injection molding in a radial flow geometry

The radial flow of a chemically reactive fluid between two parallel circular disks during the process of Reactive Injection Molding (RIM) has been simulated in a decelerative, non-isothermal, transient flow environment. The effects of key operating and system parameters (feed temperature, volumetric flow rate, reaction rate, and cavity thickness) on velocity, conversion, and temperature profiles which occur in this decelerative flow environment were determined. A catalyzed, unfilled polyurethane RIM system was modeled by a linear step polymerization scheme using average literature values for the reaction rate, and thermodynamic and constitutive parameters. The numerical solution was achieved using the method of lines and upwind approximations of the spatial derivatives. The geometry studied (two parallel, center gated circular disks) models flow patterns in commercial RIM processes more realistically than the rectangular flow between two parallel surfaces (studied by previous workers) in which the average velocity is constant along the length of the mold. This simulation predicts the accumulation of high polymer near the entrance to the mold and near the outer edge of the cavity in fast reactive systems. The accumulation of material near the gate results in viscous heat generation and a maximum in temperature in the region immediately downstream from the restriction.     

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。     

Numerical simulation of mold filling in reaction injection molding

A two dimensional finite element model for the simulation of the advancing front in reaction injection molding (RIM) is presented. The model is based on the solution of the full Navier-Stokes equation for the computation of the velocity and pressure. The arbitrary Lagrange-Euler method is used for the moving front. The method of characteristics is used for the solution of the mass-and energy equations. An automatic remeshing algorithm is used to prevent element distortion and to optimize element size and number. Numerical results are presented for flow into a complex domain in order to illustrate the versatility of the method.     

注射微泡成型熔体固化过程数值模拟

通过研究微孔塑料注射成型熔体固化过程,基于合理的假设并进行必要的简化,建立了熔体固化过程的数学模型。采用有限元/有限差分耦合法对模型进行求解,预测固化过程型腔内的压力分布,以帮助注射成型加工人员确定工艺参数,提高第一次试模成功率。     

气辅成型过程中可压缩空气流动数值模拟

气辅成型技术能够有效地改善产品力学性能、提高产品的质量,因此在注射成型生产中应用广泛,与之相应的气辅成型CAE技术也得到了快速发展。当前的气辅成型CAE技术中假定空气为不可压缩流体,忽略了空气的可压缩性,因此研究气辅成型过程中可压缩空气的流动行为具有一定的实际意义。针对气辅成型过程中可压缩空气流动的复杂行为,基于假设将复杂的三维(3D)流动问题转化为二维(2D)。采用 CBS方法建立2D瞬态可压缩空气流动的有限元分析模型,求解算法采用预共轭梯度法,并用VC++完成了算法编制,实现了可压缩空气流动过程的数值模拟,其压力结果可作为充填流动分析的基础数据。     

Numerical simulation of thermoplastic wheat starch injection molding process

A numerical study is carried out on the thermoplastic wheat starch injection molding process. The simulation is performed using currently available molding software to determine optimal molding parameters. The molding of a standardized sample for tensile test is considered. It is shown that the conventional continuum mechanics equations can be used for modeling the injection molding of thermoplastic starch. These equations are solved using the finite element method. Comparisons with some experimental results are presented, indicating good agreement. Data on the processing of thermoplastic starch and several other basic aspects are also provided.     

Numerical simulation of fiber orientation in injection molding of short-fiber-reinforced thermoplastics

The present study develops a numerical simulation program to predict the transient behavior of fiber orientations together with a mold filling simulation for short-fiber-reinforced thermoplastics in arbitrary three-dimensional injection mold cavities. The Dinh-Armstrong model including an additional stress due to the existence of fibers is incorporated into the Hele-Shaw equation to result in a new pressure equation governing the filling process. The mold filling simulation is performed by solving the new pressure equation and energy equation via a finite element/finite difference method as well as evolution equations for the second-order orientation tensor via the fourth-order Runge-Kutta method. The fiber orientation tensor is determined at every layer of each element across the thickness of molded parts with appropriate tensor transformations for arbitrary three-dimensional cavity space.     

Analysis of the packing stage in injection molding

An unconditionally stable explicit finite difference numerical scheme is used to determine the pressure distribution during the packing stage of a rectangular mold cavity. Different initial conditions arising from both an isothermal and nonisothermal mold filling analysis are considered in relation to subsequent packing behavior. The packing stage is of short duration, may be assumed to be isothermal, and gives rise to a more uniform pressure distribution within the mold cavity.     

3D finite element method for the simulation of the filling stage in injection molding

During the molding of industrial parts using injection molding, the molten polymer flow through converging and diverging sections as well as in areas presenting thickness and flow direction changes. A good understanding of the flow behavior and thermal history is important in order to optimize the part design and molding conditions. This is particularly true in the case of automotive and electronic applications where the coupled phenomena of fluid flow and heat transfer determine to a large extent the final properties of the part. This paper presents a 3D finite element model capable of predicting the velocity, pressure, and temperature fields, as well as the position of the flow fronts. The velocity and pressure fields are governed by the generalized Stokes equations. The fluid behavior is predicted through the Carreau Law and Arrhenius constitutive models. These equations are solved using a Galerkin formulation. A mixed formulation is used to satisfy the continuity equation. The tracking of the flow front is modeled by using a pseudo-concentration method and the model equations are solved using a Petrov-Galerkin formulation. The validity of the method has been tested through the analysis of the flow in simple geometries. Its practical relevance has been proven through the analysis of an industrial part.     

Computer simulation of injection molding

The injection-molding process consists of three consecutive stages: filling, packing, and cooling. In order to obtain some insight into the phenomena involved in the process, and particularly in order to evaluate the moldability of certain resins and to predict the microstructure and properties of products molded therefrom, a number of workers have employed a variety of techniques based on mathematical simulation of the process. Mathematical simulation involves writing the relevant continuity, momentum, and energy equations governing the system, with appropriate boundary and initial conditions representing the prevailing conditions in the cavity and delivery channels. In order to obtain meaningful solutions to the above equations, detailed information is required regarding the thermodynamic, thermal, and rheological properties of the resin. Moreover, the prediction of the microstructure and ultimate properties of the molded article requires a knowledge of the morphological, crystallization, and orientation phenomena that take place under the influence of the thermo-mechanical history experienced by the resin. The complexity of the equations involved results in the utilization of a number of simplifying assumptions and the resort to computer simulation and numerical solutions of these equations. A variety of numerical schemes based on finite difference and finite element methods has been employed by various researchers.     

注塑成型模拟技术在注塑工艺中的应用

注塑成型工艺已经发展成为塑料工业最重要的加工手段,注射模塑过程中需要选择和控制的压力包括塑化压力、注射压力和保压压力,它们直接影响塑料的塑化和塑件质量。通过对注塑过程中所涉及的工艺条件如何影响塑料制品的质量作了探讨,借助注塑工程分析软件对塑料制品的成型过程进行模拟,合理确定这些工艺参数,并分析了一个应用CAE技术优化工艺参数的实例,提出了比较切合实际并容易提高产品质量的注塑工艺方案。     

充模过程的Level Set两相流模拟

采用Level Set两相流方法模拟了熔体充模过程,避免了处理复杂的边界以及用Ghost方法将熔体内的速度值外推到熔体外的情况。分别对型腔水平中面与垂直中面的充模过程进行了模拟。讨论了不同注射速度、不同注射口数量以及不同Reynolds数对充模过程的影响,得出了不同时刻各种情况下熔体界面的位置与充模过程刚结束时型腔内的压力分布,分析了熔体在型腔内运动的不同阶段的特点及形成不同阶段的原因。结果表明,在注射口宽度与型腔宽度相差不大的情况下,如果采用中低速充模,则整个充模运动过程以比较平稳的扩展性运动为主,充模较完全,熔体不发生破裂,制件效果较好。充模速度越大,熔体达到平稳流动的时间越短,充模过程越短。数值模拟结果与实验结果一致,同时表明Level Set两相流方法在求解拓扑性质发生较大变化问题时具有很大的优势。     

Modeling the packing stage in injection molding of thermoplastics

A model, for the packing stage In injection molding of thermoplastics is proposed. It allows one to calculate the time evolution of pressure and temperature fields and mass variations in simple geometries. The model holds for amorphous as well as for crystalline polymers if the kinetics of crystallization are known for temperatures far from the melting point, It applies after filling stage; initial temperature and pressure conditions are available from filling-simulating software. The principles rest on finite difference schemes computing simultaneously temperature and velocity of compressible non-Newtonian fluid in a filled cavity. The pressure field is determined from an equation of state at any time, owing to a mass balance in each gridmesh. The meaningful results of the simulation are local shrinkage and a good approximation of final weights of finished products. The algorithm is essentially checked for the influence of physical, thermal, and processing parameters on the cavity pressure for the injection of a polystyrene (Gedex 1541) into a rectangular mold cavity.     

Pressure losses in the packing stage of injection molding

The pressure loss between the mold and the nozzle in the injection molding of bar and box moldings has been monitored. The pressure drop observed during filling of the mold is reduced during the packing stage but remains finite. This has been attributed in the literature to solidification of polymer across the cavity transducer and to melt relaxation phenomena. Experiments have been carried out with hot molds to prolong the packing stage at the expense of the ‘cooling’ stage. Under these circumstances the pressure drop is reduced but not eliminated. The observed pressure drop may be related to the viscosity of the melt and its dependence on pressure and temperature although strain-induced crystallization and the pressure dependence of the melting point can confer effects similar to the cooling stage.     

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.     

气辅注射成型运动界面的Level Set方法数值模拟

给出气液两相流数学模型,选取Cross-WLF模型作为熔体的黏度模型,采用Level Set/SIMPLEC方法模拟了气体辅助注射成型中气体穿透过程,追踪到了不同时刻的运动界面(气熔界面和熔体前沿界面),描述了运动过程中不同时刻速度和温度等重要物理量的分布情况,分析了熔体温度、气体延迟时间和注射压力对气体穿透时间和穿透长度的影响。数值结果表明,Level Set/SIMPLEC方法可以准确追踪气体穿透过程中的两个运动界面;熔体温度、延迟时间和气体注射压力对气体穿透长度有显著影响。