Patent Application
20220284153
Computer systems can be used to create, use, and manage data for products and other items. Examples of computer systems include computer-aided design (CAD) systems (which may include computer-aided engineering (CAE) systems), computer-aided manufacturing (CAM) systems, visualization systems, product data management (PDM) systems, product lifecycle management (PLM) systems, and more. These systems may include components that facilitate the design and simulated testing of product structures and product manufacture.
Certain examples are described in the following detailed description and in reference to the drawings.
Additive manufacturing (sometimes referred to as 3-dimensional or 3D printing) may be performed through use of 3D printers that can construct objects on a layer-by-layer basis. With increasing capability and use of additive manufacturing technologies today, manufacture of arbitrary and complex product designs has become increasing possible. Within a given design space, previous manufacturing limitations can be overcome through additive manufacturing, and product designers now have increasing design freedoms that support optimization of manufactured objects. Moreover, additive manufacturing processes can enable the manufacturing of parts with unique physical properties through design or control of the part's geometric structure, including the design of micro-structures that form an internal geometry of the object design (e.g., lattices, internal geometric patterns, etc.).
With the increasing capability and prevalence of additive manufacturing technologies, topology optimization has become an increasingly popular design technique to generate product structures. Topology optimization may include technologies that modify material or structural layouts of an object to achieve a particular goal. Topology optimization may be used in aerospace, mechanical, bio-chemical, automotive, and many other fields to, for example, improve the performance of parts or reduce a required weight of raw materials.
While topology optimization technologies can produce part structures with increased design efficiencies, the output of topology optimization processes may require reconstruction into a geometric form suitable for 3D printing. Moreover, due to design space discretization requirements for finite element analyses (FEA) in topology optimizations, density maps or other topology optimized outputs may yield coarse, rigid, or non-smooth geometries. This may especially be the case as topology optimization discretization to high-resolution granularities may not be computationally feasible because topology optimization and FEA computations at such fine granularities may result in increased processing latencies or required computational resources that are not practical with current computing CAD, CAE, CAM, and other CAx systems.
The disclosure herein may provide systems, methods, devices, and logic for processing topology optimized geometries. In particular, the various topology optimized processing features may include smoothing of topology optimized geometries, conforming topology optimized geometries to preserve original geometry characteristics, and converting topology optimized geometries into CAD-editable models for subsequent design. Each of these various technologies are described in greater detail herein, and the disclosed processing technologies may include various technical features to increase the efficiency, feasibility, and capability of using topology optimization results to further design and manufacture 3D parts.
These and other features and technical benefits are described in greater detail herein.
As an example implementation to support any combination of the features described herein, the computing system 100 shown in
Note that the example implementation of the computing system 100 shown in
In operation, geometry access engine 108 may access geometries associated with a topology optimization process. In particular, the geometry access engine 108 may access an original geometry that represents a design space upon which the topology optimization process applies to as well as a topology optimized geometry that represents an output of the topology optimization process performed for the original geometry. In operation, the geometry processing engine 110 may generate a final geometry from the topology optimized geometry, including by conforming the topology optimized geometry to the original geometry at portions of the topology optimized geometry that correspond to fixed regions of the original geometry as well as smoothing the topology optimized geometry at portions that correspond to non-fixed regions of the original geometry. In operation, the geometry conversion engine 112 may convert the final geometry into a CAD-editable topology, including by extracting a triangle mesh from the final geometry, converting the triangle mesh into subdivision surfaces, and initializing a control cage for the subdivision surfaces
In that regard, the geometry access engine 108, geometry processing engine 110, and geometry conversion engine 112 may support post-processing of topology optimized geometries. These and other topology optimized geometry processing features are described in greater detail next.
The geometry access engine 108 may access various geometries in support of post-processing topology optimization results. As seen in
The original geometry 210 may be any geometry that represents a 3D part or object. As examples, the original geometry 210 may be a CAD model designed using CAD-based shapes and design primitives (e.g., planes, curves, lines, cylinders, cubes, 3D faces, and other solid bodies and CAD design primitives). As such, the original geometry 210 may be comprised of smooth parametrized geometries, e.g., using non-uniform rational B-Splines (NURBS) or in other forms. In some instances, the original geometry 210 may be in a form referred to as a cut model.
As another characteristic, the original geometry 210 may represent a design space upon which a topology optimization process applies to (e.g., is performed upon). Such a design space may be user-identified as an input to a topology optimization process (for which the output is the topology optimized geometry 220). In some instances, the original geometry may include fixed regions designated to remain unchanged by the topology optimization process. As such, fixed regions may represent a portion of the original geometry 210 that is fixed in design (e.g., should not change). In some cases, such fixed regions may be referred to as “keep in” or “keep out” regions for density-based topology optimizations, and may thus specify design constraints that should be adhered to in a topology optimization process.
The topology optimized geometry 220 may represent an output of the topology optimization process performed for the original geometry 210. While some of the examples are described herein in the context of density-based topology optimizations (e.g., Solid Isotrophic Material with Penalization (SIMP)-based topology optimizations), any type of topology optimization is contemplated herein. Topology optimization results may be represented in the form of a density map, as one example. As another example, density-based topology optimization results may be converted to a level-set representation, which may refer to a scalar function that encodes or otherwise represents a given geometry. As a continuing example used herein, the topology optimized geometry 220 is described as geometry encoded with a zero level set, in which a boundary of a geometry is the zero value of the level set function ϕ and the interior of the geometry is represented by negative values of the level set function ϕ. However, the topology optimized geometry processing features described herein may be consistently implemented for various other geometry representations as well.
As topology optimization may require discretization of a design space for FEA and other topology optimization computations, the topology optimized geometry 220 may likewise be represented or constructed from discretized data (e.g., a density map at a discretization granularity used for the topology optimization). To control computation latencies and required processing power, topology optimizations may be performed at a coarser discretization granularity than geometry resolutions typically used to additively manufacture objects. Consequently, reconstructing a faceted or parametric geometry for 3D printing directly from the topology optimized geometry 220 may result in a non-smooth and rough shape. This may be the case as the resolution of a topology optimization process (e.g., a discretization granularity of voxels for FEA of the original geometry 210) is coarser than the printing resolution of 3D printers, resulting in boxy or unrefined 3D printed parts.
The topology optimized geometry processing features described herein may provide post-topology optimization processing capabilities to support manufacture of topology optimized 3D parts with increased effectiveness. In some instances, such features may result in smoothed geometry representations that can be extracted into parametric representations and 3D printed to produce 3D parts with improved aesthetics or mechanical stability. In processing topology optimized geometries, the features described herein may increase the accuracy of 3D part designs by conforming fixed design regions to original geometry designs, smoothing topology optimization results at finer resolutions to improve part structures, converting topology optimization results into CAD-editable forms to support subsequent design adjustments, or any combination thereof.
In order to post-process topology optimization results, the geometry processing engine 110 may represent various geometries at a finer granularity (also referred to herein as a finer resolution) than the discretization resolution used to perform a topology optimization for a part design. As used herein, the “finer granularity” may refer to mesh or geometry resolution used to post-process topology optimized results that is finer or higher in resolution/granularity than that used by a topology optimization process to generate the topology optimization results. In the example shown in
In some cases, the geometry processing engine 110 refines the resolution by a factor of 2, but the degree to which the geometry processing engine 110 enhances resolution may be configurable (e.g., 4×, 8×, 16×, etc.) and dependent upon computational latency requirement, available computing resources, etc. Resolution enhancement by the geometry processing engine 110 may be performed, for example, by equally subdividing voxels (or other discrete elements) of the topology optimized geometry 220 into the finer resolution. In
The overall geometry 230 and the fixed geometry 240 may be represented from the original geometry 210, e.g., by discretizing the original geometry 210 (or portions thereof) at the finer granularity and representing the discretized original geometry as level set representations (or any other geometric form). The overall geometry 230 may set boundary limits of the design space of the original geometry 210 upon which a topology optimization process applies to (e.g., an initial input geometry, with bounding boxes or other design spaces to optimize as well as fixed regions in the initial input geometry). The fixed geometry 240 may include a portion of the design space of the original geometry 210 that is designated not to change from the topology optimization process (e.g., the fixed regions of the original geometry 210). As subsequently described, the geometry processing engine 110 may use the overall geometry 230 and the fixed geometry 240 to conform topology optimized geometries to correspond to fixed regions of the original geometry 210.
The geometry processing engine 110 may represent the topology optimized geometry 250 by discretizing the topology optimized geometry 220 at the finer granularity (e.g., enhancing the mesh resolution by a factor of 2, 4, 8, 16, etc.). In that regard, the geometry (e.g., represented shape) of the topology optimized geometry 250 may be identical to that of the topology optimized geometry 220, but discretized at a finer granularity to support conforming and smoothing operations as described herein.
In some implementations (and as a continuing example herein), the geometry processing engine 110 may represent the overall geometry 230, fixed geometry 240, and the topology optimized geometry 250 as level-set representations, which may be referred to herein respectively as ϕOG (for the overall geometry 230), ϕFG (for the fixed geometry 240), and ϕTO (for the topology optimized geometry 250). Moreover, some the examples described herein depict level set representations on a full rectangular grid, but the geometry processing engine 110 may support level set representations according to narrow band methods to provide increased processing efficiency.
To conform portions of the topology optimized geometry 250 to the original geometry 210, the geometry processing engine 110 may enrich the topology optimized geometry 250 with the fixed geometry 240, restrict the topology optimized geometry 250 with the overall geometry 240, or a combination of both. Examples of such features are described next in connection with
In performing the enrichment operation, the geometry processing engine 110 may add, into the topology optimized geometry 250, any fixed portions of the original geometry 210 (as represented by the fixed geometry 240) that were removed by a topology optimization process used to generate the topology optimized geometry 220 (and now represented as the topology optimized geometry 250). Such enriching may be performed by overlaying the fixed geometry 240 on the topology optimized geometry 250 (or vice versa) and ensuring any “keep-in”, solid, or interior portions of the fixed geometry 240 are likewise represented as solid and interior portions of the topology optimized geometry 250.
In
In examples in which the fixed geometry 240 and topology optimized geometry 250 are represented as zero level sets with interior geometries represented by negative values of a level set function ϕ, the geometry processing engine 110 may perform the enrichment operation as a minimum function. As such, the geometry processing engine 110 may generate the enriched TO geometry 320 (with a level set function of ϕeTO) as ϕeTO=min(ϕTO, ϕFG).
Accordingly, the geometry processing engine 110 may enrich a topology optimized geometry to include fixed portions of an original geometry that were removed from a design by topology optimization.
In performing the restriction operation, the geometry processing engine 110 may remove, from a topology optimized geometry (such as the enriched TO geometry 320) any additional portions, added by the topology optimization process used to generate the topology optimized geometry 220, that extend beyond a boundary of the design space of the original geometry 210. Such restricting may be performed by overlaying the overall geometry 230 on the enriched TO geometry 320 (or vice versa) and ensuring that (i) any “keep-out” portions of the fixed geometry 240 are likewise represented as empty or exterior shape portions of a topology optimized geometry (e.g., the enriched TO geometry 250) as well as (ii) solid portions of the topology optimized geometry (e.g., the enriched TO geometry 320) do not extend beyond the external boundaries of the overall geometry 230.
In
As described herein, the geometry processing engine 110 may restrict a topology optimized geometry (e.g., the enriched TO geometry 320) to exclude portions of the topology optimized geometry that extend beyond the overall geometry 230, exclude portions of the topology optimized geometry that are designated as fixed empty regions in the original geometry 210, or a combination of both. The geometry processing engine 110 may do so at the finer granularity. An example output of a restriction operation by the geometry processing engine 110 is shown in
In examples in which the fixed geometry 240 and enriched TO geometry 320 are represented as zero level sets with interior geometries represented by negative values of a level set function ϕ, the geometry processing engine 110 may perform the restriction operation as a maximum function. As such, the geometry processing engine 110 may generate the restricted TO geometry 420 (with a level set function of ϕrTO) as ϕrTO=max(ϕeTO, ϕOG).
Note that in the example shown in
While the ordering of
In that regard, the geometry processing engine 110 may enrich and restrict a topology optimized geometry (in various orders) to conform the topology optimized geometry to fixed regions an original geometry. The restricted TO geometry 420 shown in
In
In particular, the geometry processing engine 110 may identify portions of a topology optimized geometry that correspond to correlated portions of an original geometry 210 and replace such portions of the topology optimized geometry directly with the geometry of the original geometry. Using the original geometry 210 described in
That is, the geometry processing engine 110 may reconstruct portions of the original geometry 210 directly into a topology optimized geometry. Additionally or alternatively, the geometry processing engine 110 may input, align, or otherwise insert the boundary geometry of fixed regions of the original geometry 210 into topology optimized geometry, which may directly preserve the original design intent of a part design. In doing so, the geometry processing engine 110 may restrict or enrich portions of the topology optimized geometry directly with the boundary geometry itself of the original geometry 210 (e.g., corresponding portions thereof to form the exterior boundary of the topology optimized geometry). Explained in yet another way, the geometry processing engine 110 may adapt, insert, or configure geometry boundaries of the topology optimized geometry directly with geometry boundaries (or portions thereof) of fixed regions of the original geometry 210 (but need not enforce or insert internal boundaries of fixed regions that do not affect or form a geometry boundary of the topology optimized geometry). By doing so, the geometry processing engine 110 may support tighter integration of topology optimized geometries with the original geometry 210 from which a topology optimized geometry is generated from.
The reconstructed portions may be inserted into a topology optimized geometry as boundary geometries, cut models, CAD design primitives, or in any other CAD-editable form. In that regard, a conformed geometry generated in such a way by the geometry processing engine 110 may include multiple types of geometric representations in the same design. As an example shown in
As noted herein, to generate the convergent model 510, the geometry processing engine 110 may identify portions of a topology optimized geometry 250 that correspond to the fixed regions, and replace those identified directly with the fixed regions of the original geometry 210 (e.g., directly with CAD design primitives). Through insertion of portions of an original geometry into a topology optimized geometry, such features may preserve design intent and associativity and provide for downstream processing of such regions (e.g., for CAM simulations) with increased efficiency.
In
The geometry processing engine 110 may smooth the unsmoothed geometry 610 through geometric flows. For instance, the geometry processing engine 110 may solve the following evolution equation, described using a conformed topology optimized geometry level set function ϕcTO as an example:
In this example, the geometry processing engine 110 may set V equal to zero (0) at fixed regions of the unsmoothed geometry 610 to ensure the fixed (e.g., conformed) regions of the unsmoothed geometry 610 do not change from the smoothing, thereby preserving the fixed regions of the original geometry 220 conformed into the unsmoothed geometry 610. In the remaining portions of the domain, e.g., the non-fixed portions of the unsmoothed geometry 610, the geometry processing engine 110 may smooth the curves via geometry flows, such as mean curvature flow or Willmore Flow as two examples.
By applying such smoothing processes, the geometry processing engine 110 may generate the final geometry 620. Since non-fixed portions of the unsmoothed geometry 610 may be represented at finer granularity than a discretization granularity applied for topology optimization, the smoothing operations may result in increased smoothness of curves in the final geometry 620 as compared to the topology optimized geometry 220.
From the final geometry, the geometry processing engine 110 may extract a tessellated or triangular-faceted geometry, e.g., via Marching Cubes or dual contouring, which may then be provided to a 3D printing system for additive manufacture. In some implementations, the geometry processing may further conform a tessellated or triangular-faceted geometry extracted from the final geometry 620. As one example, the geometry processing engine 110 may perform a Boolean operation between a mesh representation of the final geometry 620 and the original geometry 220 to remove distortions to the final geometry 520 that extend beyond boundaries of the original geometry 220. As another example, the geometry processing engine 110 may perform triangle smoothing on an extracted representation to smooth a design prior to additive manufacture.
In some implementations, further processing may be performed on the final geometry 620 or a faceted geometry extracted from the final geometry 620. Such processing may include conversion into a parametric geometry to support CAD editing which may be performed by a geometry conversion engine 112 as described in greater detail subsequently herein.
In implementing the logic 700, the geometry access engine 108 may access geometries associated with a topology optimization process (702). Accessed geometries may include an original geometry that represents a design space upon which the topology optimization process applies to and a topology optimized geometry that represents an output of the topology optimization process performed for the original geometry. In implementing the logic 700, the geometry processing engine 110 may generate a final geometry from the topology optimized geometry (704), and generation of the final geometry may include performing conforming and smoothing operations on various portions of the topology optimized geometry.
For instance, the geometry processing engine 110 may conform the topology optimized geometry to the original geometry at portions of the topology optimized geometry that correspond to fixed regions of the original geometry (706). In doing so, the geometry processing engine 110 may generate a conformed geometry, whether by enrichment and restriction operations as described herein or by direct insertion of fixed regions of the original geometry into the topology optimized geometry, as also described herein. The geometry processing engine 110 may smooth topology optimized geometry at portions that correspond to non-fixed regions of the original geometry (708), e.g., by smoothing a conformed geometry via geometric flows.
The logic 700 shown in
In implementing the logic 800 and in operation, the geometry conversion engine 112 may convert a topology optimized geometry into a CAD-editable geometry (802). For instance, the geometry conversion engine 112 may convert the final geometry 620 described in
To convert a topology optimized geometry, the geometry conversion engine 112 may extract a triangle mesh from the topology optimized geometry (804). Isosurface extraction or other triangular meshing techniques may be used, e.g., to convert density maps generated by topology optimization processes into a triangular mesh. For geometries represented as level set functions (e.g., as described herein), the geometry conversion engine 112 may apply any number or tessellation or triangularization processes. In some instances, the geometry conversion engine 112 may further smooth the surface and remove jagged edges or other noisy artifacts as well, e.g., via standard surface mesh processing techniques.
The geometry conversion engine 112 may convert the triangle mesh into subdivision surfaces (806), doing so in various ways. In some examples, the geometry conversion engine 112 may decimate or otherwise simplify the triangle mesh using edge collapse operations. Then, the geometry conversion engine 112 may convert the decimated triangle mesh into a quadrilateral mesh, the quadrilaterals in the quadrilateral mesh may form a control cage through which subdivision surfaces can be generated via a subdivision process. As such, the geometry processing engine 110 may initialize a control cage with the quadrilateral mesh. As another example, the geometry conversion engine 112 may convert the triangle mesh into a quadrilateral mesh and then coarsen the quadrilateral mesh, in which the coarsened quadrilateral mesh may form the subdivision surfaces through the subdivision process. In this example, the geometry processing engine 110 may initialize a control cage from the coarsened quadrilateral mesh. Subdivision surfaces may be form from initialized control cages. Through subdivision processes of the control cage, a limit surface in a geometric shape that matches the topology optimized geometry may be formed to support editing via CAD processes.
In some instances, the geometry conversion engine 112 may initialize a control cage for the subdivision surfaces, doing so from the quadrilateral mesh formed from the triangle mesh. A control cage may be any CAD functionality that surrounds CAD faces that support manipulate underlying limit surfaces (e.g., faces formed by subdivision surfaces and the subdivision process). Control cages may be supported by various CAD systems, and the subdivision surfaces (e.g., limit surfaces) converted from the topology optimized geometry may provide references or anchors for the control cage, allowing subsequent CAD-based editing and modifications to a topology optimized geometry.
In some instances, the geometry conversion engine 112 may further adapt parameters of the control cage, e.g., by performing surface fitting to fit a triangular surface of the subdivision surfaces, adjusting weights of cage edges to create creases in the control cage, or combinations of both.
The logic 800 shown in
The computing system 900 may execute instructions stored on the machine-readable medium 920 through the processor 910. Executing the instructions (e.g., the geometry access instructions 922, the geometry processing instructions 924, and/or the geometry conversion instructions 926) may cause the computing system 900 to perform any of the features described herein, including according to any of the features with respect to the geometry access engine 108, the geometry processing engine 110, the geometry conversion engine 112, or any combinations thereof.
For example, execution of the geometry access instructions 922 by the processor 910 may cause the computing system 900 to access geometries associated with a topology optimization process. The accessed geometries may include an original geometry that represents a design space upon which the topology optimization process applies to and a topology optimized geometry that represents an output of the topology optimization process performed for the original geometry.
Execution of the geometry processing instructions 924 by the processor 910 may cause the computing system 900 to generate a final geometry from the topology optimized geometry, including by conforming the topology optimized geometry to the original geometry at portions of the topology optimized geometry that correspond to fixed regions of the original geometry as well as smoothing the topology optimized geometry at portions that correspond to non-fixed regions of the original geometry.
Execution of the geometry conversion instructions 926 by the processor 910 may cause the computing system 900 to convert the final geometry into a CAD-editable topology, including by extracting a triangle mesh from the final geometry, converting the triangle mesh into subdivision surfaces, and initializing a control cage for the subdivision surfaces.
Any additional or alternative features as described herein may be implemented via the geometry access instructions 922, geometry processing instructions 924, geometry conversion instructions 926, or any combinations thereof.
The systems, methods, devices, and logic described above, including the geometry access engine 108, the geometry processing engine 110, and the geometry conversion engine 112, may be implemented in many different ways in many different combinations of hardware, logic, circuitry, and executable instructions stored on a machine-readable medium. For example, the geometry access engine 108, the geometry processing engine 110, the geometry conversion engine 112, or combinations thereof, may include circuitry in a controller, a microprocessor, or an application specific integrated circuit (ASIC), or may be implemented with discrete logic or components, or a combination of other types of analog or digital circuitry, combined on a single integrated circuit or distributed among multiple integrated circuits. A product, such as a computer program product, may include a storage medium and machine-readable instructions stored on the medium, which when executed in an endpoint, computer system, or other device, cause the device to perform operations according to any of the description above, including according to any features of the geometry access engine 108, the geometry processing engine 110, the geometry conversion engine 112, or combinations thereof.
The processing capability of the systems, devices, and engines described herein, including the geometry access engine 108, the geometry processing engine 110, and the geometry conversion engine 112, may be distributed among multiple system components, such as among multiple processors and memories, optionally including multiple distributed processing systems or cloud/network elements. Parameters, databases, and other data structures may be separately stored and managed, may be incorporated into a single memory or database, may be logically and physically organized in many different ways, and may be implemented in many ways, including data structures such as linked lists, hash tables, or implicit storage mechanisms. Programs may be parts (e.g., subroutines) of a single program, separate programs, distributed across several memories and processors, or implemented in many different ways, such as in a library (e.g., a shared library).
While various examples have been described above, many more implementations are possible.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/US2019/048575 | 8/28/2019 | WO |
