The Injection Molding Three-dimensional Flow Simulation

The molten polymer flow behavior directly influences the final properties of the part. Numerical simulation of the filling stage in injection molding is the tool which is used to predict the scale, distribution and variation laws of physical variables such as velocity, pressure and temperature etc. It can also be used to study the effects of process conditions and material properties on the quality of injection molding products as well as to determine whether the design of parts and downsprue are reasonable. So we can find the feasible or the most optimal design to avoid the waste caused by trial and error after the manufacture of the mold.In this thesis, we study the mid-plane approach for flow analysis of injection molding and analyze this model's drawbacks in simulation. A three-dimensional (3D) simulation model is established according to the classical hydrodynamics theory. The variational formulations are induced and their numerical solutions are obtained. A iterative procedure is present to solve the coupled nature of pressure and velocity fields in order to avoid the simultaneous determination of them. The main results are shown as below:(1) According to the characteristics of the injection molding process, the three dimensional flow analysis governing equations, boundary conditions and outset conditions are established based on the viscous hydrodynamics conservation laws of momentum, mass and energy. We discrete the variational equation with Galerkin method, analyze the characteristics of interpolation functions employed for discreting pressure and velocity fields and established the finite element solution of algebraic equations.(2) The coefficient matrix of the discreted equations is symmetric but not definite positive. A preconditioned conjugate minimal residual method is used to solve this system. But it's hard to determine the initial values and difficult to get the convergent solution by this method. This dissertation deduces a Poisson-like equation about pressure by modifying the variational formulation and solves the components independently at any given time step. The iterative procedure is employed for mass and momentum equations. It is also employed for velocity-viscosity solutions toobtain final pressure and velocity fields. The approach used in this paper can enhance the stability of numerical scheme and reduce memory needs in simulation.(3) Traditional Galerkin method may brings oscillations of temperature solution when directly applied to energy equation. A mixed implicit and 'up-wind' approach is proposed to discrete the energy equation. The positions of the flow fronts are tracked by the 'Volume Of Fluid(VOF)' type of method. The filling factor of each control volume is solved using a Petrov-Galerkin formulation.