1、1700单词，8400英文字符，2900汉字 52 附 录 Numerical Filling Simulation of Injection Molding Using Three Dimensional Model Abstract： Most injection molded parts are three-dimensional, with complex geometrical configurations and thick thin wall sections A 3D simulation model will p
2、redict more accurately the filling process than 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 successfully The relation between velocity and pressure is obtained from the discretized
3、 momentum equations in order to derive the pressure equation A 3D control volume scheme is employed to track the flow front The validity of the model has been tested through the an analysis of the flow in cavity Key words： three dimension； equal-order interpolation； simulation； injection
4、 molding 1 Introduction During injection molding， the theological response of polymer melts is generally non-Newtonian and no isothermal with the position of the moving flow front Because of these inherent factors， it is difficult to analyze the filling process Therefore，
5、simplifications usually are used For example， in middle-plane technique and dual domain technique1, because 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
6、velocity and pressure in the gapwise (thickness) dimension are neglected So these two techniques are both 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 direction However, because of the us e of the Hele-Shaw
7、 approximation， the information that 2.5D models can generate is limited and incomplete The variation in the gapwise (thickness) dimension of the physical quantities with the exception of the temperature， which is solved by finite difference method， is neglected With the development of molding techn
8、iques， molded 华东交通大学理工学院毕业设计（论文） 53 parts will have more and more complex geometry and the difference in the thickness will be more and more notable， so the change in the gapwise (thickness) dimension of the physical quantities can not be neglected In addition， the flow simulated looks unreal
9、istic 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 cavity 3D simulation model has been a research direction and hot spot in the scope of simulation for plastic injection molding In 3D simulation mod
10、el， 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 part geometry After calculating， complete data are obtained(not only surface data but also internal data are obtained) The
11、refore, 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 parts than the one obtained when using a 2.5D model(based on the Hele-Shaw approximation) On the other hand， a 3D model wil
12、l predict more accurately the characteristics of molded parts having thick walled sections such as encountered in gas assisted injection molding Several flow behaviors at the flow front such as “fountain flow” which 2.5D model cannot predict, can be predicted by 3D mode1. Meanwhile, the flow simulat
13、ion looks more realistic inasmuch as the overall an analysis result is directly displayed in 3D part geometry or transparent mould cavity This Paper presents a 3 D finite element model to deal with the threedimensional flow, which employs an equa1-order velocity-pressure formulation method 3,4
14、 The relation between velocity and pressure is obtained from the discretized momentum equations, then substituted into the continuity equation to derive pressure equation A 3D control volume scheme is employed to track the flow front The validity of the model has been tested through the analysis of
15、the flow in cavity 2 Governing Equations The 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 incompressible Inertia and gravitation are neglected as compared to the viscous force &nb
16、sp;With the above approximation， the governing equations， expressed in cartesian coordinates，are as following： 54 Momentum equations Continuity equation Energy equation where, x， y， z are three dimensional coordinates and u, v， w are the velocity component in the x,
17、y, z directions P， T， and denote pressure， temperature, density and viscosty respectively Cross viscosity model has been used for the simulations： where， n,， r are non-Newtonian exponent， she
18、ar rate and material constant respectively Because there is no notable 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 Method 3.1 Velocity-Pressure Relation In a 3D model， since the change of the physical quantities are not neglected in the gapwise (thickness) dimension， the momentum equations are much more complex than those in a 2.5D mode1 It is impossible to obtain the velocitypressure relation by integrating the momentum
