Modifying additively manufactured part designs using topological analyses
Set differences between an as-designed and an as-manufactured model are computed. Discrepancies between the as-designed model and the as-manufactured model are determined based under-deposition and over-deposition features of the set differences. Based on the discrepancies, an input to a manufacturing instrument is changed to reduce topological differences between the as-manufactured model and the as-designed model.
1. A method, comprising:
computing set differences between an as-designed shape and an as-manufactured shape, the set differences comprising:
over deposition (OD) features that are within the as-manufactured shape and outside the as-designed shape;
OD cut boundaries that connect the OD features to a boundary of the as-manufactured shape;
under deposition (UD) features that are within the as-designed shape and outside the as-manufactured shape; and
UD cut boundaries that connect the UD features to the boundary of the as-manufactured shape;
determining a combination of Euler characteristics (EC) of: the OD features; the OD cut boundaries; the UD features; and the UD cut boundaries; the combination of the EC indicating topological discrepancies between the as-designed shape and the as-manufactured shape; and
changing an input to a manufacturing instrument based on the topological discrepancies to reduce topological differences between the as-manufactured shape and the as-designed shape.
2. The method of claim 1 , further comprising:
computing local topological properties of each of the UD features, the OD features, the UD cut boundaries, and the OD cut boundaries;
combining the local topological properties to obtain contributions to a global topological property of the shape; and
quantifying the discrepancies based on the local topological properties, such that changing the input to the manufacturing instrument introduces discrepancies to the local topological properties that are not seen in the global topological property.
3. The method of claim 2 , wherein the local topological properties comprise Betti numbers.
4. The method of claim 2 , wherein the set differences are based on a range of settings of the manufacturing instrument, the method further comprising representing persistence of topological features of the shape as a function of the range of settings.
5. The method of claim 1 , wherein changing the input to the manufacturing instrument comprises applying one of an OD or UD policy to a local region that is different than a global policy used by the manufacturing instrument.
6. The method of claim 1 , wherein the manufacturing instrument comprises an additive manufacturing instrument.
7. A system comprising a processor coupled to memory, the processor configured to perform the method of claim 1 .
8. The method of claim 1 , wherein reducing the topological differences between the as-manufactured shape and the as-designed shape comprises recovering an as-designed topological characteristic by sacrificing geometric accuracy.
9. The method of claim 1 , wherein changing the input to the manufacturing instrument comprises changing a design of the as-manufactured shape.
10. The method of claim 1 , wherein changing the input to the manufacturing instrument comprises changing manufacturing process parameters of the manufacturing instrument.
11. The method of claim 1 , wherein the input to the manufacturing instrument is further based on geometric discrepancies between the as-designed shape and the as-manufactured shape.
12. The method of claim 1 , wherein determining the combination of the EC comprises:
determining an OD contribution based on the EC for the OD features minus the EC for the OD cut boundaries;
determining a UD contribution based on the EC of the UD features minus the EC of the UD cut boundaries; and
determining a total change in EC of the shape based on the OD contribution minus the UD contribution.
13. A method, comprising:
computing differences between an as-designed shape and an as-manufactured shape;
computing topological persistence of the differences with the as-designed shape in response to changes in process parameters of a manufacturing instrument;
representing the topological persistence in a persistence diagram that shows birth and death of new topological features in the as-manufactured shape in response to a continuous change of the process parameters;
based on the persistence diagram, identifying values of the process parameters at which the as-manufactured shape experiences a change in topological properties that further deviate the topology of the as-manufacture shape from the as-designed shape;
determining a Pareto front along a representation of the changes in the topological properties over ranges of the process parameters, the Pareto front indicating a combination of the process parameters that result a tolerable bound on the further deviation of the topology; and
changing an input to the manufacturing instrument to use the combination of the process parameters to reduce topological differences between the as-manufactured shape and the as-designed shape.
14. The method of claim 13 , wherein computing the topological persistence comprising applying a persistent homological computation.
15. The method of claim 13 , wherein the topological persistence utilizes single-variate filtration in terms of under- or over-deposition allowance, keeping other parameters fixed.
16. The method of claim 13 , wherein the topological persistence uses multi-variate filtration as a combination of two or more manufacturing parameters.
17. The method of claim 13 , wherein changing the input to the manufacturing instrument comprises applying one of an over deposition (OD) or under deposition (UD) policy to a local region that is different than a global policy used by the manufacturing instrument.
18. A system comprising a processor coupled to memory, the processor configured to perform the method of claim 13 .
19. The method of claim 13 , wherein reducing the topological differences between the as-manufactured shape and the as-designed shape comprises recovering an as-designed topological characteristic by sacrificing geometric accuracy.
20. The method of claim 13 , wherein changing the input to the manufacturing instrument comprises changing a design of the as-manufactured shape.
21. The method of claim 13 , wherein changing the input to the manufacturing instrument comprises changing manufacturing process parameters of the manufacturing instrument.