外文翻译三维注射成型流动模拟的研究

1、附 录numerical filling simulation of injection moldingusing threedimensional modelabstract： most injection molded parts are three-dimensional, with complex geometrical configurations and thickthin wall sectionsa 3d simulation model will predict more accurately the filling process than a 2.5d mode1.thi

2、s paper gives a mathematical model and numeric method based on 3d model，in which an equal-order velocity-pressure interpolation method is employed successfullythe relation between velocity and pressure is obtained from the discretized momentum equations in order to derive the pressure equationa 3d c

3、ontrol volume scheme is employed to track the flow frontthe validity of the model has been tested through the an analysis of the flow in cavitykey words： three dimension；equal-order interpolation；simulation；injection molding 1 introductionduring injection molding，the theological response of polymer

4、melts is generally non-newtonian and no isothermal with the position of the moving flow frontbecause of these inherent factors，it is difficult to analyze the filling processtherefore，simplifications usually are usedfor example，in middle-plane technique and dual domain technique1, because the most in

5、jection molded parts have the characteristic of being thin but generally of complex shape，the hele-shaw approximation 2 is used while an analyzing the flow, i.e.the variations of velocity and pressure in the gapwise (thickness) dimension are neglectedso these two techniques are both 2.5d mold fillin

6、g models，in which the filling of a mold cavity becomes a 2d problem in flow direction and a 1d problem in thickness directionhowever, because of the us e of the hele-shaw approximation，the information that 2.5d models can generate is limited and incompletethe variation in the gapwise (thickness) dim

7、ension of the physical quantities with the exception of the temperature，which is solved by finite difference method，is neglectedwith the development of molding techniques，molded parts will have more and more complex geometry and the difference in the thickness will be more and more notable，so the ch

8、ange in the gapwise (thickness) dimension of the physical quantities can not be neglectedin addition，the flow simulated looks unrealistic in as much as the melt polymer flows only on surfaces of cavity, which appears more obvious when the flow simulation is displayed in a mould cavity3d simulation m

9、odel has been a research direction and hot spot in the scope of simulation for plastic injection moldingin 3d simulation model，velocity in the gapwise (thickness) dimension is not neglected and the pressure varies in the direction of part thickness，and 3 d finite elements are used to discretize the

10、part geometryafter calculating，complete data are obtained(not only surface data but also internal data are obtained)therefore, a 3d simulation model should be able to generate complementary and more detailed information related to the flow characteristics and stress distributions in thin molded part

11、s than the one obtained when using a 2.5d model(based on the hele-shaw approximation)on the other hand，a 3d model will predict more accurately the characteristics of molded parts having thick walled sections such as encountered in gas assisted injection moldingseveral flow behaviors at the flow fron

12、tsuch as “fountain flow”which 2.5d model cannot predict, can be predicted by 3d mode1. meanwhile, the flow simulation looks more realistic inasmuch as the overall an analysis result is directly displayed in 3d part geometry or transparent mould cavitythis paper presents a 3 d finite element model to

13、 deal with the threedimensional flow, which employs an equa1-order velocity-pressure formulation method 3,4the relation between velocity and pressure is obtained from the discretized momentum equations, then substituted into the continuity equation to derive pressure equationa 3d control volume sche

14、me is employed to track the flow frontthe validity of the model has been tested through the analysis of the flow in cavity2 governing equationsthe pressure of melt is not very big during filling the cavity, in addition，reasonable mold structure can avoid over big pressure，so the melt is considered i

15、ncompressibleinertia and gravitation are neglected as compared to the viscous forcewith the above approximation，the governing equations，expressed in cartesian coordinates，are as following：momentum equations continuity equationenergy equationwhere, x，y，z are three dimensional coordinates and u, v，w a

16、re the velocity component in the x, y, z directionsp，t，and denote pressure， temperature, density and viscosty respectivelycross viscosity model has been used for the simulations： where，n,，r are non-newtonian exponent，shear rate and material constant respectivelybecause there is no notable change in

17、the scope of temperature of the melt polymer during filling，anhenius model5 for 0 is employed as following：where b，tb， are material constants.3 numerical simulation method3.1 velocity-pressure relation in a 3d model，since the change of the physical quantities are not neglected in the gapwise (thickn

18、ess) dimension，the momentum equations are much more complex than those in a 2.5d mode1it is impossible to obtain the velocitypressure relation by integrating the momentum equations in the gapwise dimension，which is done in a 2.5d model. the momentum equations must be first discretized，and then the r

19、elation between velocity and pressure is derived from it. in this paper, the momentum equations are discretized using galerkins method with bilinear velocity-pressure formulationthe element equations are assembled in the conventional manner to form the discretized global momentum equations and the v

20、elocity may be expressed as following where the nodal pressure coefficients are defined aswhere represent global velocity coefficient matrices in the direction of x, y, z coordinate respectively. denote the nodal pressure coefficients the direction of x, y, z coordinate respectively. the nodal value

21、s for are obtained by assembling the element-by-element contributions in the conventional manner. n，is element interpolation and i means global node number and j , is for a node, the amount of the nodes around it.3.2 pressure equationsubstitution of the velocity expressions (2) into discretized cont

22、inuity equation, which is discretized using galerkin method，yields element equation for pressure:the element pressure equations are assembled the conventional manner to form the global pressure equations 3.3 boundary conditions in cavity wall, the no- slip boundary conditions are employed, e.g.on an

23、 inlet boundary, 3.4 velocity update after the pressure field has been obtained，the velocity values are updated using new pressure field because the velocity field obtained by solving momentum equations does not satisfy continuity equationthe velocities are updated using the following relationsthe o

24、verall procedure for fluid flow calculations is relaxation iterative，as shown in fig.l and the calculation is stable without pressure oscillation3.5 the tracing of the flow fronts the flow of fluid in the cavity is unsteady and the position of the flow fronts values with timelike in 2.5d model, in t

25、his paper, the control volume method is employed to trace the position of the flow fronts after the fan(flow analysis network)6. but 3d control volume is a special volume and more complex than the 2d control volumeit is required that 3d control volumes of all nodes fill the part cavity without gap a

26、nd hollow space. two 3d control volumes are shown in fig24 results and discussionthe test cavity and dimensions are shown in fig.3(a)the selected material is abs780 from kumbo. the parametric constants corresponding to then, ,b, tb and of the five-constant cross-type viscosity model are 02638, 4514

27、×le4 pa, 1.3198043×le-7 pa *s, 112236 ×1e4k，0000 pa-1injection temperature is 45，mould temperature is 250, injection flow rate is 4482 cu. cms. the meshed 3d model of cavity is shown in fig. 3(b).“fountain flow” is a typical flow phenomenon during fillingwhen the fluid is injected int

28、o a relatively colder mould，solid layer is formed in the cavity walls because of the diffusion cooling，so the shear near the walls takes place and is zero in the middle of cavity, and the fluid near the walls deflects to move toward the wallsthe fluid near the center moves faster than the average ac

29、ross the thickness an d catches up with the front so the shape of the flow front is round like the fountainthe round shape of the flow front of the example in several filling times predicted by present 3d model and shown in fig4(a)，conforms to the theory and experimentscontrarily, the shape of the f

30、low front predicted by 2.5d model and shown in fig4(b) do not reveal the“fountain flow” the flow front comparison at the filling stage is illustrated in fig5it shows that the predicted results based on present 3d model agree well with that based on moldflow 3d mode1the gate pressure is illustrated i

31、n fig6，compared with the prediction of moldflow 3d modelit shows that the predicted gate pressure of present 3d model is mainly in agreement with that based on moldflow 3d mode1the major reason for this deviation is difference in dealing with the model an d material parameters5 conclusionsa theoreti

32、cal model and numerical scheme to simulate the filling stage based on a 3d finite element model are presenteda cavity has been employed as example to test the validity. 3d numeral simulation of the filling stage in injection moulding is a development direction in the scope of simulation for plastic

33、injection molding in the futurethe long time cost is at present a problem for 3d filling simulation，but with the development of computer hardware and improvement in simulation technique，the 3d technique will be applied widely三维注射成型流动模拟的研究 摘要:大多数注射成型制品都是具有复杂的几何轮廓和厚壁或薄壁的制品。这种三维仿真模型将比两维半模型具有更精确的填充过程。本文

34、介绍了一种基于三维模型的注射成型流动模拟的数学模型和数值实现，把速度和压力同次插值方法成功地应用到三维注塑模拟的计算中，从离散的动量方程中找出压力和速度的关系，然后迭代到连续性方程中得到压力方程。用三维控制体积法追踪流动前沿，并通过算例分析来说明三维模型的有效性。关键词：三维模型 ； 等序插值法； 模拟； 注塑成型1引言在注塑成型的过程中，聚合物熔化的流变反应随着流动前沿的方向大多是非牛顿流体和非等温的。由于这些内在的因素，分析它的填充过程是很困难的，因此通常进行简易处理。例如在中面流和双面流技术中，由于大多数注塑成型的零件都是薄壁却有复杂的形状的特征，当分析流动性而厚度方向的速度和压力变化被

35、忽略时，通常使用heleshaw流动简化。因此这两种技术都是两维的填充模型，用这种方法填充一个模型的型腔就变成了流动方向的二维问题和厚度方向的一维分析。 但由于采用了简化假设，它产生的信息是有限的、不完整的。除了用有限差分法求解温度在壁厚方向的差异外，基本上没有考虑物理量在厚度方向上的变化 。随着塑料成型技术的发展，注塑成型零件将具有越来越复杂的形状，其壁的厚度的多样性将变得越来越显著，因此在厚度方向变化的物理量就不能被忽视。此外，熔体在型腔的表面流动模拟看起来不真实，仅当这些流动模拟出现在成型型腔时它的真实性才更加明显。三维流动模型已经是研究方向而且在塑料注塑成型模拟方面将是个热点。在三维流

36、动模型中，熔体在厚度方向的速度分量不再被忽略，熔体的压力沿厚度方向变化，并且在分解三维实体制品方面通常使用有限元分析。通过有限元计算，可以获得完整的数据（不仅获得实体制品表面的流动数据，还获得实体内部完整的流动数据。）。因此，对于薄壁制品，三维流动模拟能够产生更加详细的关于流动特征的信息和应力分布；对于如在气体辅助成型中遇到的有厚壁区域的制品，三维流动模拟能更加准确地预测其充填行为。许多在二维模型中不能预测的充模过程中的流动行为，如熔体前沿的流动形态和推进方式，即“喷泉”效应在三维流动模拟技术中都可以得到很好的体现。本文提出了一种三维有限元模型来预测模拟塑料熔体的充模流动，把速度和压力同次插值

37、方法成功地应用到三维注塑模拟的计算中，从离散的动量方程中找出压力和速度的关系，然后代到连续性方程得到压力方程。用三维控制体积法追踪流动前沿，并通过算例来说明该三维模型的有效性。2 控制方程 充模过程中熔体压力不是很高，且合理的模具结构可以避免过压现象，因此设熔体为未压缩流体。由于熔体粘性较大，相对于粘度剪切应力而言 ，惯性力和质量力都很小，可忽略不计。 经过简化和假设，控制方程的直角分量形式分别为： 动量方程：连续性方程：能量方程：式中：x, y, z三维坐标；u, v, w分别表示x, y, z方向的速度；熔体密度； p压力；t温度；熔体粘度粘度模型采用 cross模型 式中：n非牛顿指数；

38、剪切速率；材料常数；0零剪切粘度由于在充模过程中，熔体的温度变化范围不大，因此0采用 arrhenius型表达式： 式中：b，tb, 材料常数。3 数值模拟方法3.1 压力 速度关系 三维有限元模型由于没作 hele-shaw流动简化，其数值处理方法和二维模型有很大不同。在三维模型中，用三维立体单元离散制品空间，采用速度和压力同次插值和迦辽金法来离散控制方程 ，用三维控制体积法追踪流动前沿。由于三维模型考虑了厚度方向物理量的变化，其动量方程比二维模型复杂得多，不可能像二维模型那样直接通过在厚度方向上的积分得到速度和压力的关系，需要首先对动量方程进行离散，从中找出压力和速度的关系。本文采用压力、

39、速度双线形插值，用 galerkin法对动量方程离散，经逐个单元组装后得到节点速度和压力的关系如下：其中，虚拟速度定义为：节点上的压力系数定义为： (3)式中分别表示在 x，y，z 方向的总体速度系数矩阵分别表示节点在 x，y, z 方向的压力系数，其值利用式(3)在整个计算域内积分，由各单元的贡献值组装而得到 ni单元插值函数；i总体节点号；j每个节点所有领接节点的数量3.2 压力方程 把连续方程式(1d)用 galerkin法离散后，把速度方程式(2)代入，整理后得到离散的单元压力方程： 把单元刚度矩阵用常规的方法在整个计算域内组装就得到整体压力方程。3.3 边界条件在模壁上采用无滑移边界条件： 在浇口处：u=v=w=给定；3.4 速度修正 求解压力方程，得到压力场。但从动量方程求解得到的速度场并不满足连续性条件，因此，要按下式用所求得的压力场去修正当前得到的速度场。 上述压力、速度方程采用松弛迭代求解。整个求解过程如图