Modifying additively manufactured part designs using topological analyses
Set differences between an as-designed and an as-manufactured model are computed. Topological deviations 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:
determining a family of as-manufactured shapes based on an as-designed shape of a part, each member of the family comprising different overlap measure ratios between one and zero respectively corresponding to strict over-deposition and strict under-deposition policies of an additive manufacturing instrument;
determining under deposition (UD) regions and over deposition (OD) regions based on intersection regions between the as-designed shape and the as-manufactured shapes;
decomposing the UD regions and the OD regions into respective connected components;
computing contributions of the connected component to a total topological deviation between the as-designed shape and the as-manufactured shapes in terms of an additive topological property;
composing the connected components into smaller components;
characterizing the contributions of the smaller components to the respective connected component in terms of alternating sums of the additive topological property to identify a subset of the connected components that contribute nonzero values to a global topological property;
for each of the subset of connected components, providing localized remedies to reduce the contributions of the connected components to the global topological property; and
changing an input to the additive manufacturing instrument to include the localized remedies when building the as-manufactured shapes.
2 . The method of claim 1 , wherein decomposing the UD regions and the OD regions into the connected components defines cut boundaries of the connected components, the intersection regions sharing the cut boundaries with the as-designed shape and the as-manufactured shapes, and wherein the cut boundaries are used computing contributions of the connected components to the total topological deviation.
3 . The method of 1 , wherein determining the family of as-manufactured shapes comprises cross-correlations or convolutions of defining functions of a minimum manufacturable neighborhood (MMN) and the as-designed shape.
4 . The method of claim 1 , wherein determining the family of as-manufactured shapes comprises:
determining a first indicator function based on the as-designed shape;
determining a second indicator function based on a minimum manufacturable neighborhood (MMN) of the additive manufacturing instrument;
determining a cross-correlation of the first indicator function with the second indicator function, the cross-correlation providing a real-valued field corresponding to an overlap measure of the MMN with the as-designed shape; and
selecting a superlevel set of the real-valued field that defines the family of as-manufactured shapes.
5 . The method of claim 4 , wherein the first and second indicator functions are fields in the respective underlying spaces that map every point in the underlying spaces to 0 if points are outside the underlying spaces and to 1 if the points are inside the underlying spaces.
6 . The method of claim 1 , wherein composing the connected components into smaller components comprises composing:
OD features that are within the as-manufactured shapes and outside the as-designed shape;
OD cut boundaries that connect the OD features to a boundary of the as-manufactured shapes;
UD features that are within the as-designed shape and outside the as-manufactured shapes; and
UD cut boundaries that connect the UD features to the boundary of the as-manufactured shapes.
7 . The method of claim 6 , wherein the additive topological properties comprise Euler characteristics (EC) of: the OD features; the OD cut boundaries; the UD features; and the UD cut boundaries.
8 . The method of claim 1 , wherein the localized remedy comprises one or both of applying an OD policy to a UD feature and applying a UD policy to an OD feature, wherein the OD policy and UD policy are applied only to the vicinity of the respective UD and OD feature, and not to the entire as-manufactured shapes.
9 . A system comprising a processor configured via instructions to perform the method of claim 1 .
10 . A method comprising:
determining a family of as-manufactured shapes based on an as-designed shape of a part, each member of the family comprising different overlap measure ratios between one and zero respectively corresponding to strict over-deposition and strict under-deposition policies of an additive manufacturing instrument;
determining localized topological discrepancies for each of the as manufactured shapes as compared to the as-designed shape, the localized topological discrepancies contributing nonzero values to a global topological property;
performing topological persistence filtering over a continuous change of process parameters of the additive manufacturing instrument;
based the topological persistence filtering, determining a combination of the process parameters that result a predefined bound on the localized topological discrepancies;
changing an input to the additive manufacturing instrument to utilize the combination of the process parameters.
11 . The method of claim 10 , wherein the topological persistence filtering comprises changing the size of a minimum manufacturable neighborhood of the additive manufacturing instrument for a given deposition policy.
12 . The method of claim 10 , wherein the topological persistence filtering comprises changing deposition policies of the additive manufacturing instrument for a given minimum manufacturable neighborhood.
13 . The method of 10 , wherein determining the family of as-manufactured shapes comprises cross-correlations or convolutions of defining functions of a minimum manufacturable neighborhood (MMN) and the as-designed shape.
14 . The method of claim 13 , wherein determining the family of as-manufactured shapes comprises:
determining a first indicator function based on the as-designed shape;
determining a second indicator function based on a minimum manufacturable neighborhood (MMN) of the additive manufacturing instrument;
determining a cross-correlation of the first indicator function with the second indicator function, the cross-correlation providing a real-valued field corresponding to an overlap measure of the MMN with the as-designed shape; and
selecting a superlevel set of the real-valued field that defines the family of as-manufactured shapes.
15 . The method of claim 14 , wherein the first and second indicator functions are fields in the respective underlying spaces that map every point in the underlying spaces to 0 if points are outside the underlying spaces and to 1 if the points are inside the underlying spaces.
16 . A system comprising a processor configured via instructions to perform the method of claim 10 .