Automated generation of lean models for injection molding simulation
The present invention is a method and system for simulating fluid flow in a cavity, having relevance to the modeling of viscous flows within thin cavities of complex shapes in which heat exchange with the cavity walls may be a governing factor, as in injection molding of plastic parts. Its automated discretization scheme, in which the model cavity is partitioned into macrocells, each macrocell having substantial contact areas with the model cavity walls, eliminates the need for time consuming and expensive manual model configuration required by some modeling methods. Because of the simplicity of the discretization, models based on the invention are less demanding on computer resources then conventional finite element methods, and execute more quickly. A key innovation of the method is a function characterizing the shape of a macrocell that appears in a coefficient in equations governing the flow. As a consequence of the improvements offered by the invention, molds for complex parts can be fabricated more rapidly, with the resulting parts having high quality.
1. A method for simulating fluid flow in a cavity of arbitrary shape, comprising:
a. receiving digital data describing walls of a 3D model cavity;
b. partitioning a portion of the model cavity into a plurality of 3D macrocells, each macrocell having at least one contact area with at least one proximate cavity wall, and at least one macrocell being neither a flat element nor a cylindrical element;
c. for each macrocell,
(i) computing, at each of a plurality of values of depth δ, values of a shape function representing the volume of a portion of the macrocell consisting of those points such that the minimum distance from each point to a respective nearest wall exceeds δ, and
(ii) assigning a plurality of discretized model equations, adapted to governing a simulated evolution of the fluid, including a model equation having at least one coefficient derived from the shape function; and
d. running a simulation using the discretized model equations to produce a plurality of model flow variables at a plurality of times within the simulation and storing a data structure representing a model flow variable in a digital storage device, wherein the step of running the simulation is performed using a digital computer.
2. The method of claim 1 , wherein the discretized model equations govern the simulated evolution of a molten material that is injected into the cavity, the model cavity specifying the geometry intended for a part to be molded.
3. The method of claim 2 , wherein the material is a polymer resin.
4. The method of claim 1 , wherein the discretized model equations include a temperature equation having a coefficient derived from the shape function.
5. The method of claim 1 , step c further comprising:
(iii) dividing the macrocell into non-overlapping layers, each layer including those points such that the minimum distance from each point to a respective nearest wall is between two values of depth, and
(iv) using a value of depth δ taken from within each layer in computing values of the shape function.
6. The method of claim 5 , wherein all the layers contain the same volume.
7. The method of claim 1 , further comprising:
e. selecting within the portion of the model cavity a set of sampling points with known density, and using the sampling points for representation of macrocells and evaluation of the shape functions of the macrocells.
8. The method of claim 1 , the step of partitioning a portion of the model cavity including:
(i) selecting a plurality of nodes at points located throughout the portion of the model cavity;
(ii) choosing a model metric that specifies how model distance will be computed between any pair of points within the model cavity; and
(iii) constructing macrocells by Voronoi partitioning, based on the nodes and the model metric.
9. The method of claim 8 , wherein internal distance between two sampling points is defined to be the length of the shortest polyline path between the two sampling points that is internal to the model cavity, and the model metric specifies that the distance between any two sampling points will be calculated by internal distance.
10. The method of claim 8 , wherein each node is substantially equidistant from opposing model cavity walls.
11. The method of claim 1 , wherein the portion of the model cavity contains at least one feature from the group consisting of
(i) an intersection of two substantially planar regions,
(ii) an intersection of two runners,
(iii) an intersection of a runner and a planar region,
(iv) a serrated region of wall,
(v) a corrugated region of wall, and
(vi) an indentation in a wall.
12. A method for use in the art of molding objects, comprising:
a. obtaining data, stored in tangible digital media, describing walls of a 3D model cavity;
b. partitioning a portion of the model cavity into a plurality of 3D macrocells, each macrocell having at least one contact area with at least one contact area with at least one proximate cavity wall, and at least one macrocell being neither a flat element nor a cylindrical element;
c. for each macrocell,
(i) computing, at each of a plurality of values of depth δ, values of a shape function representing the volume of a portion of the macrocell consisting of those points such that the minimum distance from each point to a respective nearest wall exceeds δ, and
(ii) assigning a plurality of discretized model equations, adapted to governing a simulated evolution of fluid flow through the cavity, including a discretized model equation having at least one coefficient derived from the shape function;
d. running a simulation using the discretized model equations on a digital electronic device, thereby producing a plurality of model variables characterizing the simulated evolution of the fluid flow; and
e. using at least one of the plurality of model variables characterizing the simulated evolution of the fluid flow, making a prediction of a quality factor that would result if an object were to be molded using a tangible mold that has a mold cavity represented by the 3D model cavity.
13. The method of claim 12 , wherein the quality factor is in the group consisting of
(i) whether fluid will fill the mold cavity before freezing;
(ii) whether the object will contain bubbles;
(iii) whether there will be regions of weakness in the object; and
(iv) whether the object will have burns or blemishes.
14. The method of claim 12 , further comprising:
f. based on the prediction, choosing whether to fabricate a tangible mold that has a mold cavity represented by the 3D model cavity.
15. The method of claim 14 , further comprising:
g. fabricating a tangible mold that has a mold cavity represented by the 3D model cavity.
16. The method of claim 15 , further comprising:
h. injecting molten material into the tangible mold.
17. The method of claim 12 , further comprising:
f. based on the prediction, redesigning a mold or a part, or terminating a project.
18. A method for molding an object, comprising:
a. obtaining data, stored in tangible digital media, describing walls of a 3D model cavity;
b. partitioning a portion of the model cavity into a plurality of 3D macrocells, each macrocell having at least one contact area with at least one contact area with at least one proximate cavity wall, and at least one macrocell being neither a flat element nor a cylindrical element;
c. for each macrocell,
(i) computing, at each of a plurality of values of depth δ, values of a shape function representing the volume of a portion of the macrocell consisting of those points such that the minimum distance from each point to a respective nearest wall exceeds δ, and
(ii) assigning a plurality of discretized model equations, adapted to governing a simulated evolution of fluid flow through the cavity, including a discretized model equation having at least one coefficient derived from the shape function;
d. running a simulation using the discretized model equations on a digital electronic device, thereby producing a plurality of model variables characterizing the simulated evolution of the fluid flow;
e. using at least one of the plurality of model variables characterizing the simulated evolution of the fluid flow, making a prediction of success of the model cavity for producing the molded object; and
f. if the prediction is favorable, injecting molten material into a tangible mold having walls substantially corresponding to the walls of the 3D model cavity.