Method and apparatus for modeling injection of a fluid in a mold cavity

Abstract

The invention relates to a method and apparatus for analyzing fluid flow while considering heat transfer effects and, in particular, a phase change from a molten state to a solid state. In particular, the method and apparatus may be applied to the analysis of an injection molding process for producing a molded polymer component from a thermoplastic or a thermosetting polymer. In one embodiment, the method may be used to determine pressure required to fill a mold cavity and pressure gradients introduced during filling and packing of the cavity of an injection mold. The results of these analyses may be used to determine the number and location of gates, to determine the best material for the component, and to optimize the process conditions used in the molding process.

1 - 25 . (canceled)  
   
   
       26 . A method for modeling injection of a fluid into a mold defining a three dimensional cavity, the method comprising the steps of: 
 (a) providing a three dimensional computer model defining the cavity;    (b) discretizing a solution domain based on the model;    (c) specifying boundary conditions;    (d) solving for filling phase process variables over at least part of the solution domain to provide respective filling phase solutions therefor; and    (e) solving for packing phase process variables over at least part of the solution domain using respective states of the process variables at termination of filling; to provide respective packing phase solutions therefor,    wherein at least one of steps (d) and (e) comprises the substeps of: 
 using a first description of a distribution of a process variable about each of a plurality of nodes or elements within the solution domain; and  
 using a second description of the distribution of the process variable in at least part of the solution domain comprising the plurality of nodes or elements, the second description comprising conservation of mass, conservation of momentum, and conservation of energy equations.  
   
   
   
       27 . The method according to  claim 26 , wherein the filling phase process variables and packing phase process variables are selected from the group consisting of density, fluidity, mold cavity fill time, mold cavity packing time, pressure, deformation rate, shear stress, temperature, internal energy, velocity, velocity gradient, flow rate, viscosity, and volumetric shrinkage.  
   
   
       28 . The method according to  claim 26 , further comprising the steps of: 
 (f) determining whether at least one of the respective filling phase solutions and packing phase solutions are acceptable;    (g) modifying at least one of the discretized solution domain and the boundary conditions in the event at least one of the respective filling phase solutions and packing phase solutions is determined to be unacceptable; and    (h) repeating steps (d) through (g) until the respective filling phase solutions or packing phase solutions are determined to be acceptable.    
   
   
       29 . The method according to  claim 26 , further comprising the step of: 
 displaying in graphics format a filling phase solution selected from the group consisting of fill time, pressure, deformation rate, shear stress, temperature, velocity, and viscosity.    
   
   
       30 . The method according to  claim 26 , further comprising the step of: 
 displaying in graphics format a packing phase solution selected from the group consisting of density, packing time, pressure, deformation rate, temperature, velocity, viscosity, and volumetric shrinkage.    
   
   
       31 . A method for modeling injection of a fluid into a mold defining a three dimensional cavity, the method comprising the steps of: 
 (a) providing a three dimensional computer model defining the cavity;    (b) discretizing a solution domain based on the model;    (c) specifying boundary conditions; and    (d) solving for filling phase process variables over at least part of the solution domain to provide respective filling phase solutions therefor,    wherein step (d) comprises the substeps of: 
 using a first description of a distribution of a process variable about each of a plurality of nodes or elements within the solution domain; and  
 using a second description of the distribution of the process variable in at least part of the solution domain comprising the plurality of nodes or elements, the second description comprising conservation of mass, conservation of momentum, and conservation of energy equations.  
   
   
   
       32 . The method according to  claim 31 , wherein the discretizing step (b) comprises the substep of generating a finite element mesh based on the model by subdividing the model into a plurality of connected elements defined by a plurality of nodes.  
   
   
       33 . The method according to  claim 31 , wherein the boundary conditions are selected from the group consisting of fluid composition, fluid injection location, fluid injection temperature, fluid injection pressure, fluid injection volumetric flow rate, mold temperature, cavity dimensions, cavity configuration, and mold parting plane, and variations thereof.  
   
   
       34 . The method according to  claim 31 , wherein the solving step (d) utilizing the conservation of mass and conservation of momentum equations comprises the substeps of: 
 (i) solving for fluidity over at least part of the solution domain;    (ii) solving for pressure over at least part of the solution domain; and    (iii) calculating velocity over at least part of the solution domain.    
   
   
       35 . The method according to  claim 34 , wherein the solving step (d) utilizing the conservation of energy equation comprises the substep of calculating viscosity over at least part of the solution domain.  
   
   
       36 . The method according to  claim 35 , wherein the viscosity calculating substep is based on temperature.  
   
   
       37 . The method according to  claim 36 , wherein at least one of velocity and viscosity is calculated iteratively, until pressure converges.  
   
   
       38 . The method according to  claim 37 , wherein the solving step (d) comprises the substep of determining free surface evolution of the fluid in the cavity based on velocity.  
   
   
       39 . The method according to  claim 38 , wherein the solving step (d) comprises the substep of calculating temperature based on at least one of a convective heat transfer contribution, a conductive heat transfer contribution, and a viscous dissipation contribution.  
   
   
       40 . The method according to  claim 39 , wherein free surface evolution is determined iteratively, until the cavity is filled.  
   
   
       41 . The method according to  claim 31  further comprising the step of: 
 (e) solving for packing phase process variables using conservation of mass, conservation of momentum, and conservation of energy equations for at least a portion of the solution domain based in part on respective states of the process variables at termination of filling, to provide respective packing phase solutions therefor for at least some of the portion of the solution domain.    
   
   
       42 . The method according to  claim 41 , wherein the solving step (e) utilizing the conservation of mass and conservation of momentum equations comprises the substeps of: 
 (i) solving for fluidity over at least part of the solution domain;    (ii) solving for pressure over at least part of the solution domain; and    (iii) calculating velocity over at least part of the solution domain.    
   
   
       43 . The method according to  claim 41 , wherein the solving step (e) utilizing the conservation of energy equation comprises the substep of calculating viscosity over at least part of the solution domain.  
   
   
       44 . The method according to  claim 43 , wherein the viscosity calculating substep is based on temperature.  
   
   
       45 . The method according to  claim 44 , wherein at least one of velocity and viscosity is calculated iteratively, until pressure converges.  
   
   
       46 . The method according to  claim 45 , wherein the solving step (e) comprises the substep of calculating temperature based on at least one of a convective heat transfer contribution, a conductive heat transfer contribution, and a viscous dissipation contribution.  
   
   
       47 . The method according to  claim 46 , further comprising the step of: 
 (f) calculating mass properties of a component.    
   
   
       48 . The method according to  claim 47 , wherein the mass properties are selected from the group consisting of component density, volumetric shrinkage, component mass, and component volume.  
   
   
       49 . The method according to  claim 47 , wherein at least one of velocity, viscosity, and mass properties is calculated iteratively, until a predetermined pressure profile is completed.  
   
   
       50 . The method according to  claim 32 , wherein the mesh generating substep comprises generating an anisotropic mesh in thick and thin zones such that mesh refinement provides increased resolution in a thickness direction without increasing substantially mesh refinement in a longitudinal direction.  
   
   
       51 . The method according to  claim 26 , wherein at a given time step, the first description describes each of the plurality of nodes or elements independently of the others.  
   
   
       52 . The method according to  claim 26 , wherein the value of the process variable at a first point provided by the first description of the process variable about a first node or element is not necessarily equal to the value of the process variable at the first point provided by the first description of the process variable about a second node or element.  
   
   
       53 . The method according to  claim 26 , wherein the value of the process variable at a first point provided by the first description of the process variable about a node or element is used in the second description.  
   
   
       54 . The method according to  claim 26 , wherein the first description is a one dimensional analytic function or is a discrete function.  
   
   
       55 . The method according to  claim 26 , wherein the first description describes a distribution of temperature or internal energy about a node or element.  
   
   
       56 . The method according to  claim 55 , wherein the first description is or approximates a solution for one dimensional heat conduction in a solid.  
   
   
       57 . The method according to  claim 26 , wherein the first description comprises or is derived from an error function.  
   
   
       58 . The method according to  claim 26 , wherein the first description is a one dimensional description of temperature distribution about a node or element, the description comprising an error function.  
   
   
       59 . The method according to  claim 31 , further comprising the step of: 
 (e) determining whether the respective solutions are acceptable for injection of the fluid during filling of the mold cavity.    
   
   
       60 . The method according to  claim 31 , wherein at a given time step the first description describes each of the plurality of nodes or elements independently of the others.  
   
   
       61 . The method according to  claim 31 , wherein the value of the process variable at a first point provided by a first description of the process variable about a first node or element differs from the value of the process variable at the first point provided by a first description of the process variable about a second node or element.  
   
   
       62 . The method according to  claim 31 , wherein the value of the process variable at a first point provided by the first description of the process variable about a node or element is used in the second description.  
   
   
       63 . The method according to  claim 31 , wherein the first description is a one dimensional analytic function or is a discrete function.  
   
   
       64 . The method according to  claim 31 , wherein the first description describes a distribution of temperature or internal energy about a node or element.  
   
   
       65 . The method according to  claim 64 , wherein the first description is or approximates a solution for one dimensional heat conduction in a solid.  
   
   
       66 . The method according to  claim 31 , wherein the first description comprises or is derived from an error function.  
   
   
       67 . The method according to  claim 31 , wherein the first description is a one dimensional description of temperature distribution about a node or element comprising an error function.  
   
   
       68 . The method according to  claim 31 , wherein the solving step (d) utilizing the conservation of mass and conservation of momentum equations comprises the substeps of: 
 (i) solving for pressure over at least part of the solution domain; and    (ii) calculating velocity over at least part of the solution domain.    
   
   
       69 . The method according to  claim 31 , wherein the solving step (d) comprises the substep of calculating temperature based on a convective heat transfer contribution, a conductive heat transfer contribution, and a viscous dissipation contribution.  
   
   
       70 . The method according to  claim 41 , wherein the solving step (e) utilizing the conservation of mass and conservation of momentum equations comprises the substeps of: 
 (i) solving for pressure over at least part of the solution domain; and    (ii) calculating velocity over at least part of the solution domain.    
   
   
       71 . The method according to  claim 41 , wherein the solving step (e) comprises the substep of calculating temperature based on a convective heat transfer contribution, a conductive heat transfer contribution, and a viscous dissipation contribution.  
   
   
       72 . The method according to  claim 26 , wherein at least one of steps (d) and (e) comprises solving for fluidity over at least part of the solution domain.  
   
   
       73 . The method according to  claim 26 , wherein at least one of steps (d) and (e) comprises using a formulation derived from the conservation of mass and conservation of momentum equations.  
   
   
       74 . The method according to  claim 26 , wherein at least one of steps (d) and (e) comprises using at least one of a Nakano formulation, a Stokes formulation, and a Navier-Stokes formulation to solve for fluidity over at least part of the solution domain.  
   
   
       75 . The method according to  claim 31 , wherein step (d) comprises solving for fluidity over at least part of the solution domain.  
   
   
       76 . The method according to  claim 31 , wherein step (d) comprises using a formulation derived from the conservation of mass and conservation of momentum equations.  
   
   
       77 . The method according to  claim 31 , wherein step (d) comprises using at least one of a Nakano formulation, a Stokes formulation, and a Navier-Stokes formulation to solve for fluidity over at least part of the solution domain.  
   
   
       78 . An apparatus for modeling injection of a fluid into a mold defining a three dimensional cavity, the apparatus comprising: 
 a memory for storing code that defines a set of instructions; and    a processor for executing said set of instructions to:    (a) discretize a solution domain based on a three dimensional computer model defining a cavity;    (b) at least one of: 
 (i) solve for filling phase process variables over at least part of the solution domain to provide respective filling phase solutions therefore; and  
 (ii) solve for packing phase process variables over at least part of the solution domain using respective states of the process variables at termination of filling to provide respective packing phase solutions therefor,  
   wherein at least one of (i) and (ii) comprises: 
 using a first description of a distribution of a process variable about each of a plurality of nodes or elements within the solution domain; and  
 using a second description of the distribution of the process variable in at least part of the solution domain comprising the plurality of nodes or elements, the second description comprising conservation of mass, conservation of momentum, and conservation of energy equations.