外文翻译三维注射成型流动模拟的研究.docx

1、外文翻译三维注射成型流动模拟的研究附 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

2、 a 2.5D mode1.This 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 pressu

3、re equationA 3D control 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 res

4、ponse of polymer 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, be

5、cause the most injection 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

6、 2.5D mold filling 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 gapwis

7、e (thickness) dimension 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

8、notable，so the change 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 cavi

9、ty3D simulation model 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 t

10、o discretize the 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

11、 thin molded parts 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

12、 at the flow frontsuch 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

13、 element model to 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 co

14、ntrol volume scheme 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 mel

15、t is considered incompressibleInertia 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 coordin

16、ates and u, v，w are 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 n

17、otable change in 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 th

18、e gapwise (thickness) 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 discretiz

19、ed，and then the relation 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 eq

20、uations and the velocity 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

21、. The nodal values 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

22、 discretized continuity 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 em

23、ployed, e.g.On an 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 followi

24、ng relationsThe overall 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

25、 2.5D model, in this 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 cav

26、ity without gap and 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

27、 are 02638, 4514 le4 Pa, 1.3198043le-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 into

28、 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 acr

29、oss 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 fl

30、ow 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 in

31、 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 theoretic

32、al 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 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 simul