System and method for assessing ability to remove loose powder from additively manufacturable article

Abstract

Systems and methods are provided for assessing the ability to remove loose powder from an additively manufacturable article, the method comprising the steps of: for each of a plurality of discrete starting points (322) distributed within a sampling volume (320), performing the following: calculating starting point directed trajectory lengths for a plurality of trajectories (328) of a particle (216), respectively, the particles start from a starting point (322) and move in initial directions (324) respectively along a plurality of combinations of polar and azimuth angles [phi] and [theta] of a spherical coordinate system (326) centered on the starting point (322), and for the starting point (322), an average of starting point orientation trajectory lengths is calculated to give a starting point average trajectory length. The method further includes calculating, for the article (200), an average of the starting point average trajectory lengths for the plurality of starting points (322), respectively, to give a global average trajectory length.

Description

Technical Field

[0001] The present disclosure relates generally to additive manufacturing, and more particularly, to systems and methods for assessing the ability to remove loose powder from an additively manufacturable article. Background Art

[0002] Additive manufacturing is the process of manufacturing an object via the sequential application and solidification of layers of material on top of each other. For example, powder bed fusion is a type of additive manufacturing in which metal powders are fused in a layer-by-layer manner to build an object, such as a sandwich panel. A sandwich panel is a structure having a pair of face sheets interconnected by an infill geometry. The infill geometry may consist of a repeating pattern of unit cells, resulting in a lightweight panel with relatively high bending stiffness.

[0003] The filler geometry of an AM article may present challenges in terms of removing loose powder upon completion of the AM build process. For example, the unit cell of the filler geometry that makes up a sandwich panel may have a unit cell geometry that entraps loose powder or inhibits its removal. Loose powder remaining inside an AM article may be problematic for economic and / or environmental reasons. For example, the inability to recover and recycle unused powder from an AM article may increase the cost of the production process.

[0004] When designing an additively manufacturable article, the ability to remove powder is an important factor in choosing which unit cell geometry to use for the infill geometry. Unfortunately, part designers currently have limited means to evaluate and compare different unit cell geometries for powder removability.

[0005] As can be seen, there is a need in the art for a system and method for assessing the ability to remove loose powder from an additively manufactured article upon completion of a build process. Summary of the invention

[0006] The present disclosure addresses the above needs associated with assessing the ability to remove loose powder from an additively manufactured article, and provides a method for assessing the powder removability of an article. The method includes the following steps: for each of a plurality of discrete starting points distributed within a sampling volume, performing the following items: respectively calculating a plurality of starting point oriented trajectory lengths of a plurality of trajectories of a particle, the particle starting from the starting point and moving along an initial direction, the initial direction being respectively along a plurality of combinations of polar angles φ and azimuthal angles θ of a spherical coordinate system centered at the starting point, and each of the starting point oriented trajectory lengths ends at a place where the particle leaves a boundary surface of an enclosing volume, and the trajectory includes reflections of the particle on one or more geometric surfaces defined by the geometry of the article within the enclosing volume. The method further includes the following steps: for each of the starting points, performing the following items: for the starting point, calculating an average of the starting point oriented trajectory lengths to give an average starting point trajectory length. The method also includes the following steps: for the article, respectively calculating an average of the starting point average trajectory lengths of the plurality of starting points to give a global average trajectory length.

[0007] A method for assessing the ability to remove powder from a filler geometry of an additively manufacturable article is also disclosed. The method comprises the following steps: for each of a plurality of discrete starting points distributed within a unit cell of a plurality of interconnected unit cells forming the filler geometry of the article, performing the following: respectively calculating a plurality of starting point oriented trajectory lengths of a plurality of trajectories of a particle starting from the starting point and moving along an initial direction, the initial direction being respectively along a plurality of combinations of polar angles φ and azimuthal angles θ of a spherical coordinate system centered at the starting point, and each of the starting point oriented trajectory lengths ends at a point where the particle leaves a sphere within the filler geometry. The sphere encompasses the unit cell containing the plurality of starting points and has a radius equal to the length of the body diagonal of the cube. The trajectory comprises reflections of the particle on one or more geometric surfaces defined by the filler geometry. The method further comprises the following steps: for each of the starting points, performing the following: for the starting point, calculating the average of the starting point directional trajectory lengths, and for the starting point, dividing the average by the body diagonal to give a point average particle mobility ratio. The method further comprises the following steps: for the filler geometry, respectively calculating the average of the point average particle mobility ratios of the plurality of starting points to give a global average particle mobility ratio.

[0008] In addition, a processor-based system for assessing the ability to remove powder from an additively manufacturable article is disclosed. The processor-based system includes a memory device configured to store an article geometry of an article, the article being composed of a plurality of interconnected unit cells, each unit cell fully fitting within a cube and having a common unit cell geometry. The processor-based system also includes a particle migration distance calculator configured to, for each of a plurality of discrete starting points distributed within a sampling volume, perform the following: respectively calculate a plurality of starting point oriented trajectory lengths of a plurality of trajectories of a particle, the particle starting from the starting point and moving along an initial direction, the initial direction being respectively along a plurality of combinations of polar angles φ and azimuthal angles θ of a spherical coordinate system centered at the starting point, and for the starting point, calculate an average of the starting point oriented trajectory lengths to give a starting point average trajectory length. The particle migration distance calculator is further configured to, for the article, respectively calculate an average of the starting point average trajectory lengths of the plurality of starting points to give a global average trajectory length.

[0009] The features, functions, and advantages that have been discussed can be achieved independently in various forms of the present disclosure or may be combined in other forms, and further details of these features, functions, and advantages can be seen with reference to the following description and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] The present disclosure may be better understood by referring to the following detailed description in conjunction with the accompanying drawings, which illustrate preferred and exemplary forms, but which are not necessarily drawn to scale. The drawings are examples and are not intended to be limiting of the description or claims.

[0011] Figure 1 is a flow chart of an example of a method for assessing the ability to remove powder from an additively manufacturable article;

[0012] Figure 2 is a perspective view of an example of an additively manufactured article configured as a sandwich panel having a pair of face sheets interconnected by an infill geometry (i.e., article geometry) consisting of a repeating pattern of a unit cell;

[0013] Figure 3 yes Figure 2 a cross-sectional view of a sandwich panel with one of the face sheets omitted to illustrate the repeating unit lattice constituting the infill geometry;

[0014] Figure 4 yes Figure 2 A side cross-sectional view of a sandwich panel illustrating loose powder after removal from the filler geometry;

[0015] Figure 5 yes Figure 2 5 and illustrates an example of a unit cell configured as a connectable cuboid in a multilayer arrangement;

[0016] Figure 6 is a perspective view of an example of a connectable cuboid configuration of a unit cell;

[0017] Figure 7 yes Figure 2 an end view of a sandwich panel illustrating a sampling volume defined by an inner surface of a face sheet and outside of a bounding box of an infill geometry of the sandwich panel;

[0018] Figure 8 yes Figure 7 an enlarged view of a portion of a sandwich panel of , wherein the face plate is omitted and a plurality of discrete starting points of dimensionless and weightless particles are illustrated, and wherein the starting points are uniformly distributed within the sampling volume;

[0019] Fig. 9 yes Figure 7 an end view of a portion of a sandwich panel of , illustrating a plurality of different trajectories of a particle starting from one of the starting points and reflecting off one or more geometric surfaces before the particle leaves the enclosed volume;

[0020] Fig.10 Shows Fig. 9 a trajectory in a trajectory of, the trajectory consisting of a plurality of trajectory segments resulting from a particle reflecting off a surface of a geometry of a packing geometry after starting from a starting point and moving along an initial direction along a combination of a polar angle and an azimuthal angle of a spherical coordinate system centered at the starting point;

[0021] Fig.11 Shown by Figures 7 and 8 an example of a portion of a domain defined by the set of all starting points contained within a sampling volume of a sandwich panel minus the set of all starting points contained within the geometry of the article, and illustrating the domain after discretization into tetrahedral elements;

[0022] Fig.11A yes Fig.11 An enlarged view of a portion of the domain identified by reference numeral 11A of FIG. 1 and illustrating one of the tetrahedral elements;

[0023] Fig.12 is a stereogram of a connectable cuboid configuration of a unit cell having a cell side length and which is exactly contained within a cube having a cube side length equal to the cell side length;

[0024] Fig.13 shows a cube configured to subtract Fig.12 An example of a sampling volume of the volume occupied by a unit cell of , and the sampling volume is shown to contain a plurality of uniformly distributed starting points;

[0025] Fig.14 An infinitely repeating pattern of a unit cell is shown, and further an enclosed volume as a sphere is illustrated, and a plurality of different trajectories of a particle starting from one of the starting points within the sampling volume of a cube are also illustrated;

[0026] Fig.15 Shows Fig.14 a trajectory among trajectories of , the trajectory consisting of a plurality of trajectory segments resulting from the particle reflecting off the surface of the geometric shape after starting from a starting point and moving along an initial direction along a polar angle and an azimuthal angle of a spherical coordinate system centered at the starting point;

[0027] Fig.16 is a perspective view of a connectable cuboid configuration of a unit cell, and further illustrates in a crosshatching fashion the values ​​of the point average particle mobility corresponding to the starting points. Fig.13 Some of the starting points;

[0028] Fig.17 It is for Fig.16 The corresponding cross-hatching of the starting points in and the corresponding point average particle mobility legend;

[0029] Fig.18 Contours of equal point-averaged particle mobility over a slice of a sample volume are shown, superimposed on a cross-sectional view of a Schwarz-P configuration of a unit cell;

[0030] Fig.19 Examples of histogram curves showing histograms of point averaged particle mobilities for different unit cell geometries;

[0031] Fig. 20 Shown in Fig.19 An example of a cubic framework unit cell lattice with point-averaged particle mobility is shown in the histogram of ;

[0032] Fig.21 Shown in Fig.19 An example of a connectable cuboid unit cell of point-averaged particle mobility is shown in the histogram of ;

[0033] Fig. 22 Shown in Fig.19 An example of a Schwarz-P unit cell of point-averaged particle mobility is shown in the histogram of ;

[0034] Fig.23 Shows Fig.19 An example of a gyroid unit cell of point-averaged particle mobility is shown in the histogram of ;

[0035] Fig.24 Shows Fig.19 An example of a body-centered-cubic unit cell of point-averaged particle mobility is shown in the histogram of ;

[0036] Fig.25 is a block diagram of a processor-based system for implementing a method for assessing the ability to remove powder from an additively manufacturable article;

[0037] Fig.26 Shown for Fig.25 An example of a user interface for a processor-based system.

[0038] The figures shown in this disclosure represent various aspects of the presented versions, and only the differences will be discussed in detail. DETAILED DESCRIPTION

[0039] Hereinafter, the disclosed configurations are described more fully with reference to the accompanying drawings, which show some, but not all, examples of the disclosed configurations. In fact, several different examples or configurations may be provided and should not be construed as being limited to the examples set forth herein. Rather, these examples are provided to make the disclosure thorough and to fully convey the scope of the disclosure to those skilled in the art.

[0040] This specification includes references to "some examples," "one example," or "an example." Instances of the phrase "some examples," "one example," or "an example" do not necessarily refer to the same example. The particular features, structures, or characteristics may be combined in any suitable manner consistent with the present disclosure.

[0041] As used herein, "comprising" is an open term and as used in the claims, the term does not exclude additional structures or steps.

[0042] As used herein, "configured to" means that various parts or components may be described or claimed as being "configured to" perform one or more tasks. In such contexts, "configured to" is used to imply structure by indicating that a part or component includes structure to perform that task or tasks during operation. Thus, a part or component may be said to be configured to perform a task even when the specified part or component is not currently included.

[0043] As used herein, an element or step recited in the singular and beginning with the singular should be understood as not necessarily excluding plural of said elements or steps.

[0044] As used herein, the phrase "at least one of" when used with a list of items means that different combinations of one or more of the listed items may be used, and only one of each item in the list may be required. In other words, "at least one of" means any combination of the items, and the number of items may be used according to the list, but not all of the items in the list are required. The item may be a particular object, thing, or category.

[0045] Now, referring to the accompanying drawings, Figure 1 200 ( Figure 4 ) to remove powder 214( Figure 4 ) capability. As mentioned above, upon completion of the additive manufacturing build process, the loose powder 214 will continue to remain on the object geometry 202 ( Figure 4 ). The item geometry 202 includes the filler geometry 210 ( Figure 4 ) of the unit cell 250( Figure 4 The method 100 of the present disclosure provides a method for evaluating the geometry of an article 202 to allow the powder 214 particles 216 ( Figure 4 ) means for the relative ease with which the article 200 passes through the unit cell 250 and leaves the article 200 when the article 200 is subjected to random agitation or vibration (such as via a shaker (not shown) or other device configured to shake or vibrate the article 200 to remove loose powder 214).

[0046] Reference Figures 2 to 6 , the method 100 is described in the context of a planar, constant thickness sandwich panel 206. The article geometry 202 of the sandwich panel 206 includes a pair of face sheets 208, and a filler geometry 210 interconnecting the face sheets 208, such as Figure 2 As shown. The sandwich panel 206 can be produced using any suitable additive manufacturing technology, wherein the powder 214 is an additive material. For example, the sandwich panel 206 can be produced using the powder bed fusion process mentioned above, which involves using a laser beam or an electron beam to fuse metal particles 216 layer by layer. However, the method 100 is applicable to assessing the removability of the powder 214 in the article 200 produced using the powder as a feedstock.

[0047] exist Figures 2 to 6 In FIG. 2 , the filler geometry 210 consists of a repeating pattern of unit cells 250 . Figure 3is a cross-sectional view of sandwich panel 206 with one of face sheets 208 omitted to illustrate the repeating pattern of unit cells 250 making up infill geometry 210 . Figure 4 2 is a side cross-sectional view of sandwich panel 206 illustrating loose powder 214 at the base of sandwich panel 206 after removal from filler geometry 210. Figure 6 ) is configured to connect the cuboid 254 ( Figure 6 ). Figure 5 Shows Figure 4 206, illustrating a repeating pattern of connectable cuboids 254 that sample a multi-layer arrangement. In the example shown, the infill geometry 210 is composed of three layers 272 of connectable cuboids 254 stacked on top of each other. A pair of panels 208 are located on opposite sides of the multi-layer arrangement of connectable cuboids 254.

[0048] Figure 6 An example of a single connectable cuboid 254 is shown. The connectable cuboid 254 includes a hollow three-dimensional center portion 256 and eight corner portions 258. The center portion 256 is closed except for eight openings 260. The eight corner portions 258 are connected to the center portion 256 at the eight openings 260, respectively. Each corner portion has a circular shape and a concave side away from the center portion 256. The connectable cuboid 254 has symmetry (e.g., is three-fold periodic) so that the corner portions 258 can be interconnected to the corner portions 258 of adjacent connectable cuboids 254.

[0049] Even though it is Figures 2 to 6 206, but the method 100 of the present disclosure is applicable to three-dimensional objects of any shape, size, or configuration, and is not limited to the sandwich panel 206. For example, the method 100 is applicable to any of a variety of sandwich panel configurations not shown, including non-planar sandwich panels, variable thickness sandwich panels, sandwich panels having a single layer of unit lattices 250 or two or more layers of unit lattices 250, or to a three-dimensional object having a single panel 208, or a three-dimensional object without a panel 208. As mentioned above, the method 100 of the present disclosure provides a means for evaluating and comparing the powder removability of different unit lattice geometries 252. The method 100 also provides a means for comparing the powder removability of the connectable cuboid 254 unit lattice geometry 252 with alternative unit lattice geometries 252 (such as in Figure 20 to Figure 24 This is described in the context of comparing the powder removability of the unit cell geometry (exemplified in FIG. 4 and described below).

[0050] Reference Figure 1 and see also Figures 7 to 10, step 102 of method 100 includes: performing step 102A and step 102B for each starting point in a plurality of discrete starting points 322 uniformly distributed within sampling volume 320. For example, Figures 7 and 8 A plurality of starting points 322 are shown evenly distributed within a sampling volume 320, the sampling volume being formed by sandwich plate 206 ( Figure 7 ) of the two panels 208( Figure 7 ) and Figure 3 and Figure 7 The sandwich panel 206 is shown as being closed on four sides (ie, the outer faces 213 of the bounding box 212).

[0051] Step 102A includes: calculating the particles 216 ( Figures 9 and 10 ) of multiple trajectories 328 ( Figures 9 and 10 ) of multiple starting point directional trajectory lengths, the particle starts from the starting point 322 ( Figures 9 and 10 ) and along the initial direction 324( Fig.10 ) moves, and the initial directions are respectively along the spherical coordinate system ( Fig.10 ) of the particle 216. The particle 216 is massless and dimensionless. The movement of the particle 216 from each starting point 322 is similar to the tracing of a ray starting from the starting point 322. In this regard, the method 100 includes the following steps: simulating a trajectory 328 of the particle 216, the particle starting from a plurality of different starting points 322, and moving along the initial trajectory 328 at different combinations of polar angles φ and azimuth angles θ from each starting point 322. Fig.10 As shown, azimuthal angle θ is measured relative to the x-axis and in the xy plane of spherical coordinate system 326. Polar angle φ is measured relative to the z-axis of spherical coordinate system 326. The orientation of spherical coordinate system 326 is irrelevant as long as it is consistently defined.

[0052] Fig. 9 Particle 216 is shown Figure 8 At least some of the trajectories 328 include reflections of the particles 216 on one or more geometric surfaces 204 defined by the article geometry 202 (i.e., at reflection points 332) within the closed volume 334. For example, Fig. 9 Particle 216 is shown reflecting (ie, at reflection point 332 - Fig. 9 and Fig.10)) exits the lattice wall of the unit cell 250 that constitutes the filler geometry 210 of the sandwich panel 206. Although not shown, the particles 216 may also reflect off the face sheet 208 of the sandwich panel 206. Each of the starting point directional track lengths ends where the particle 216 exits the boundary surface 336 of the enclosed volume 334. For example, at Fig. 9 , the end of each start point directional trajectory length is the location where the particle 216 leaves the filler geometry 210 outside 213 (e.g., side) of the bounding box 212, which is superimposed on the sandwich panel 206. At this point, Figures 7 to 9 An example of method 100 is illustrated in which the sample volume 320 and the closed volume 334 are the same area, which is the area bounded by the exterior 213 (eg, side) of the article 200 (eg, the sandwich panel 206). Figure 2 , Figure 4 as well as Figure 5 As shown, outer faces 213 (eg, sides) of the sandwich panel 206 are open.

[0053] exist Figures 9 and 10 In the example of , each starting point directional trajectory length includes a plurality of trajectory segments 330. All trajectory segments 330 are linear, and, except for the initial trajectory segment 330, the other trajectory segments are generated by the particle 216 reflecting off the geometric surface 204 (e.g., the lattice wall) of the unit cell 250 of the filler geometry 210. Although not shown in this example, it is possible that at least one trajectory 328 of the particle 216 from at least one starting point 322 will not reflect off the article geometry 202, but instead will travel directly out of the closed volume 334 from the starting point 322, which will result in the starting point directional trajectory length containing exactly one trajectory segment 330. Regardless of the number of trajectory segments 330 in each starting point directional trajectory length, the step 102A of respectively calculating the starting point directional trajectory lengths of the plurality of trajectories 328 of the particle 216 starting from each starting point 322 includes respectively summing the lengths of the plurality of trajectory segments 330 of the trajectory 328 from the starting point 322.

[0054] It should be noted that a geometric scenario in which the start point directional trajectory length is infinite may be encountered, in which case step 102A includes: delimiting the start point directional trajectory length to prevent infinite loops. This can be achieved, for example, by imposing an upper bound on the start point directional trajectory length, which is considered to be the start point directional trajectory length in instances where the start point directional trajectory length is exceeded. Alternatively, a maximum number of reflections can be specified. Examples of geometric scenarios in which the start point directional trajectory length is infinite include: (1) the item geometry 202 has a closed area (not shown) from which the powder 214 will never escape, and (2) the item geometry 202 results in a trajectory (not shown) that periodically returns to the position and direction of a previous start point 322 of the trajectory segment 330 without intersecting the boundary surface 336 of the closed volume 334 (i.e., a periodic orbit in the sense of a dynamic system).

[0055] For each starting point 322 within the sample volume 320, step 102B of method 100 includes: for the starting point 322, calculating the average of the starting point directional trajectory lengths to give the starting point average trajectory length. A variety of different techniques can be used to calculate the starting point average trajectory length. For example, the starting point average trajectory length can be calculated by analytically evaluating the definite integral of the multiple starting point directional trajectory lengths across a space defined by all possible combinations of polar angles φ (e.g., from 0 to 180 degrees) and azimuth angles θ (e.g., from 0 to 360 degrees). In another example, the starting point average trajectory length can be calculated by using a numerical integration technique on a space defined by all possible combinations of polar angles φ and azimuth angles θ to estimate the value of the definite integral of the multiple starting point directional trajectory lengths across the space. The numerical integration technique may include: calculating a Riemann sum, performing a Gaussian point integral, using a trapezoidal rule, using a Simpson rule, or using any other suitable numerical integration technique. In a further example, the starting point average trajectory length may be calculated by estimating the value of the definite integral of the plurality of starting point directional trajectory lengths across a space defined by all possible combinations of polar angles φ and azimuth angles θ using a Monte Carlo technique.

[0056] After calculating the starting point average trajectory length for each starting point 322 within the sampling volume 320, the method 100 includes step 104, which includes: for the sampling volume 320, respectively calculating the average of the starting point average trajectory lengths of the plurality of starting points 322 to give a global average trajectory length. The global average trajectory length may be calculated using any of a variety of techniques. In one example, the global average trajectory length may be calculated by analytically evaluating a definite integral across a domain defined by the set of all starting points 322 contained within the sampling volume 320 minus the set of all starting points 322 contained within the item geometry 202. In another example, the global average trajectory length may be calculated by using a Monte Carlo technique to estimate the value of a definite integral across a domain defined by the set of all starting points 322 contained within the sampling volume 320 minus the set of all starting points 322 contained within the item geometry 202. In yet another example, the global average trajectory length may be calculated by discretizing a domain defined by the set of all starting points 322 contained within the sampling volume 320 minus the set of all starting points 322 contained within the item geometry 202 into elements shaped as tetrahedrons (i.e., tetrahedron elements 274), and then integrating across the tetrahedron elements 274 to estimate the value of the definite integral across the domain. Fig.11 After discretization into tetrahedral elements 274 Figures 7 and 8 A portion of the above-mentioned domain of the sandwich panel 206. Fig.11A yes Fig.11 An enlarged view of a portion of the domain of , showing one of the tetrahedral elements 274 .

[0057] In one example of integrating across individual tetrahedral elements 274, method 100 involves the use of basis functions. As is known in the art, a basis function describes the value of a point of interest using a weighted combination of the values ​​at points surrounding the point of interest within a region. Fig.11 In the example of FIG. 2 , the point of interest within the tetrahedron element 274 is the starting point 322 (not shown). The points around the point of interest are the corner nodes (not shown) of the tetrahedron element 274. The method includes the following steps: calculating the volume coordinates (e.g., ζ 1 , 2 , 3 , 4 - not shown), the basis functions are then calculated at the starting point 322 using known techniques.

[0058] One example of an integration technique that can be used is Gaussian point integration (also known as Gaussian quadrature), which involves approximating the integral by calculating the value of a function integrated over a certain value and then multiplying that value by a certain weight. The weighted values ​​are then summed to obtain an approximation of the integral. A Gaussian point integration technique includes a variety of schemes with different weighting factors, including the 1-point rule, the 4-point rule, the 5-point rule, and the 11-point rule. To illustrate the use of the 5-point rule in Fig.11 An example of numerical integration over the domain in , where the following term is performed on each tetrahedral element 274:

[0059] Calculate the position ζ 1 =1 / 2, ζ 2 =1 / 6, ζ 3 =1 / 6 and ζ 4 = the value of the average trajectory length of the starting point at 1 / 6, and save it as the value V 1 .

[0060] Calculate the position ζ 1 =1 / 6, ζ 2 =1 / 2,ζ 3 =1 / 6 and ζ 4 = the value of the average trajectory length of the starting point at 1 / 6, and save it as the value V 2 .

[0061] Calculate the position ζ 1 =1 / 6, ζ 2 =1 / 6, ζ 3 = 1 / 2 and ζ 4 = the value of the average trajectory length of the starting point at 1 / 6, and save it as the value V 3 .

[0062] Calculate the position ζ 1 =1 / 6, ζ 2 =1 / 6, ζ 3 =1 / 6 and ζ 4 =1 / 2 of the average trajectory length of the starting point and save it as value V 4 .

[0063] Calculate the position ζ 1 =1 / 4, ζ 2 =1 / 4, ζ 3 = 1 / 4 and ζ 4 = the value of the average trajectory length of the starting point at 1 / 4 and save it as value V 5 .

[0064] Calculation 0.45(V 1 +V2 +V 3 +V 4 )-0.8V 5 .

[0065] The resulting value approximates the integral of the start point average trajectory length across one tetrahedral element 274 divided by the volume of the tetrahedral element 274. To obtain the integral itself, the value is multiplied by the volume of the tetrahedral element 274. However, because the start point average trajectory length is the integral divided by the volume, it is not necessary to multiply the value by the volume of the tetrahedral element 274.

[0066] Can be used in Figure 7 The global average track length is calculated for each of the plurality of different unit cell geometries 252 of the infill geometry 210 having the same size and shape, using the same number of starting points 322 uniformly distributed within the same sampling volume 320 enclosed by the face plate 208 and the outer surface 213 (e.g., the side) of the sandwich panel 206. For example, in addition to calculating the global average track length for the infill geometry 210 (i.e., the sampling volume 320) composed of the connectable cuboids 254, the global average track length can also be calculated for each of the plurality of different unit cell geometries 252 of the infill geometry 210 having the same size and shape. Figure 20 to Figure 24 The individual unit cell geometries 252 shown in FIG. 2 (such as the cubic frame 262 described below) Fig. 20 ) configuration, Schwarz-P 264( Fig. 22 ) configuration, pentagonal icosahedron 266 ( Fig.23 ) configuration, and body-centered cubic 268 ( Fig.24 ) configuration), to calculate the global average track length. The global average track lengths of different unit cell geometries 252 can be compared to each other to determine the relative ease with which the loose powder 214 can be removed from the infill geometry 210 of the sandwich panel 206 when the additive manufacturing build process is completed. This comparison can help the designer select which unit cell geometry 252 to use for the infill geometry 210.

[0067] In some examples, method 100 may include the step of normalizing the global average track length by a specified distance to give a global average particle mobility. In the example described below where article geometry 202 is a single unit cell 250, the global average track length may be divided by sphere 338 ( Fig.14 ), where the radius is equivalent to a cube 300 ( Fig.12 ) body diagonal 306( Fig.12 ),like Fig.12The global average particle mobility of different unit cell geometries 252 can be compared to each other to determine the relative ease with which each unit cell geometry 252 allows powder 214 to pass through the unit cell geometry 252 and exit the filler geometry 210 of the article 200 composed of the unit cell 250 .

[0068] As mentioned above, Fig.12 The unit cell 250 ( Figure 2 ) is used in the following description of an example of method 100, wherein article geometry 202 includes a single unit cell 250 having a periodic unit cell pattern for use in additively manufacturable article 200. Fig.12 In the example, a periodic unit cell lattice 250 is patterned to form Figures 2 to 4 The filler geometry 210 of the sandwich panel 206 (i.e., the additively manufacturable article) is shown. Fig.12 As shown, the connectable cuboid 254 unit cell 250 has a lattice side length 270 and is completely contained within a cube 300 having a cube side length 302 equal to the lattice side length 270 .

[0069] In the following example of method 100, sample volume 320 is Fig.13 300, which contains a plurality of uniformly distributed starting points 322. Moreover, in the following example of method 100, closed volume 334 is a sphere 338 (which is Fig.14 ), which encloses a portion of the infinitely repeating pattern of the unit cell lattice 252. The radius of the sphere 338 is equal to the square root of three times the lattice side length 270, which is the radius of the opposite cube corner 304 ( Fig.12 ) extending diagonally between the body diagonal line 306 ( Fig.12 ) length. The position of the sphere 338 is shifted for each starting point 322 so that the sphere 338 is centered on the starting point 322 when calculating the starting point oriented trajectory length associated with each starting point 322. The size of the sphere 338 is such that no matter which starting point 322 the sphere 338 is centered on, at least one complete unit cell 250 is contained within the sphere 338.

[0070] Figure 14 to Figure 15 The particles are shown as cube 300 ( Fig.13 ) of the sampling volume 320( Fig.13 ) in one of the starting points 322 in the plurality of trajectories 328. Fig. 9 In the above example, the trajectory 328, Figure 14 to Figure 15Trajectory 328 in φ includes reflections on the lattice walls of unit cell 250 of filler geometry 210 (ie, at reflection point 332 ). Fig.15 Shows Fig.14 A trajectory among the trajectories 328, wherein the initial direction 324 of the trajectory is defined according to the polar angle φ and the azimuth angle θ of the spherical coordinate system 326 centered at the starting point 322.

[0071] In targeting Fig.13 Step 102 of method 100 is performed at each of starting points 322 in a sampling volume 320 (i.e., cube 300), step 102A includes: respectively calculating a plurality of starting point oriented trajectory lengths of the plurality of trajectories 328 of the particle 216, the particle starting from the starting point 322 and moving along an initial direction 324, the initial direction being respectively along a plurality of combinations of polar angles φ and azimuthal angles θ of a spherical coordinate system 326 centered at the starting point 322, such as Figure 14 to Figure 15 As mentioned above, the trajectory 328 includes the reflection of the particle 216 on the geometric surface 204 defined by the filler geometry 210, and each of the starting point directional trajectory lengths ends at the point where the particle 216 leaves the sphere 338 within the filler geometry 210. In step 102A, the trajectory 328 used to calculate Figure 8 Any of the above techniques for calculating the average trajectory length of the starting points 322 in the sample volume 320 is used to calculate Fig.13 The starting point average trajectory length of the starting point 322 in the sampling volume 320.

[0072] Step 102A may optionally include normalizing the start point directional trajectory length for a given start point 322 by a specified distance to define a start point particle mobility. Figures 12 to 15 306, the prescribed distance to normalize all of the start point orientation track lengths is the radius of the sphere 338, which is equivalent to the length of the body diagonal 306 of the cube 300. In this regard, the process of normalizing the start point orientation track lengths includes, for each start point 322, dividing the start point orientation track length by the body diagonal 306 to give an orientation point mobility.

[0073] In targeting Fig.13 In terms of performing step 102B for each starting point 322 in the sampling volume 320 (i.e., the cube 300), the method 100 includes the following steps: for the starting point 322, calculating the average of the starting point directional trajectory lengths to give a starting point average trajectory length; and for the starting point 322, normalizing the starting point average trajectory length by a specified distance to define a point average particle mobility. Figures 12 to 15In the example of a single unit cell 250 of , the normalization process includes, for starting point 322, dividing the starting point average trajectory length by the radius of sphere 338 (ie, body diagonal 306) to give a point average particle mobility.

[0074] Reference Figure 16 to Figure 17 , some examples of method 100 may optionally include step 103 of generating and visualizing, by one or more means, a distribution of starting point average trajectory lengths for all starting points 322 within the sampling volume 320. For example, step 103 may include generating a two-dimensional or three-dimensional heat map or similar representation showing the relative point average particle mobility for different starting point 322 locations within the unit cell geometry 252. For example, step 103 may include displaying at least a subset of the plurality of starting points 322 in such a manner that each starting point 322 has a designation (e.g., color coding, cross-hatching, etc.) corresponding to a unique value of the point average particle mobility for that starting point 322, thereby illustrating the spatial variation of the point average particle mobility across the enclosed volume 334, or a subset thereof. Different values ​​of the point average particle mobility may be represented by color coding as mentioned above, or by other means (such as by using different cross-hatching patterns (e.g., Fig.17 ), by digital coding, or by other means).

[0075] For example, Fig.16 is an example Fig.13 A three-dimensional view of connectable cuboids 254 with some of starting points 322 . Fig.16 The starting point 322 in the graph is cross-hatched and / or shaded in a manner that represents the relative value of the point average particle mobility of the starting point 322. Fig.17 yes Fig.16 Legend for the cross-hatching and shading of the starting point 322 in FIG. Fig.17, the white shading on the left side of the legend specifies relatively low values ​​of point average particle mobility, the diagonal cross-hatching in the center of the legend specifies relatively intermediate values ​​of point average particle mobility, and the black shading on the right side of the legend specifies relatively high values ​​of point average particle mobility. Starting points 322 with white shading represent locations within the unit lattice geometry 252 at which loose powder 214 can be relatively easily or quickly removed from the additively manufactured article 200 when subjected to random agitation or vibration. In contrast, starting points 322 with black shading represent locations within the unit lattice geometry 252 at which loose powder 214 may be difficult or take longer to remove from the additively manufactured article 200 when subjected to agitation or vibration. Starting points 322 with diagonal cross-hatching represent locations at which the difficulty or average time required to remove loose powder 214 is somewhere between the difficulty or average time of starting points 322 represented by white shading and black shading. In this manner, Fig.16 A visual indication of the relative ease with which powder 214 can be removed from different locations of unit cell geometry 252 is provided.

[0076] Reference Fig.18 , showing a contour-based visualization of the point average particle mobility of the sample volume according to step 103. More specifically, contour lines 340 of equal point average particle mobility on a slice of the sample volume are shown, which are superimposed on a cross-sectional view of the Schwarz-P 264 configuration of the unit cell.

[0077] exist Figures 12 to 15 In the method 100, step 104 includes: for the filler geometry 210, respectively calculating the average of the point average particle mobility of the plurality of starting points 322 to provide a global average particle mobility. The method 100 may include: respectively calculating the global average particle mobility of a plurality of different unit cell geometries 252, and comparing the global average particle mobility as a measure of the ability to remove powder 214 from different unit cell geometries 252. The above step 103 of the method 100 may include: generating a histogram curve ( Fig.19 ), which histogram contains the distribution of point-averaged particle mobilities for each of the filling geometries having different unit cell geometries 252.

[0078] Fig.19 Shows Figure 20 to Figure 24 252. The histogram curve 400 includes: a cubic frame 262 ( Fig. 20 ) configuration histogram 462, connectable cuboid 254 ( Fig.21 ) configuration histogram 454, Schwarz-P 264 ( Fig. 22 ) configuration histogram 464, pentagonal icosahedron 266 ( Fig.23 ) configuration histogram 466, and body-centered cubic 268 ( Fig.24 ) configuration histogram 468. Each unit cell geometry 252 ( Figure 20 to Figure 24 ) plots the distribution of point average particle mobility, represented by the symbol λ, for different starting points 322 within the closed volume 334. The minimum possible value of the point average particle mobility λ is 1, as shown on the left side of the histogram curve 400, and it represents a free space without obstacles along the trajectory 328 of the powder 214 particle 216 from the starting point 322 until it leaves the closed volume 334. The maximum possible value of the point average particle mobility λ is infinity (not shown), which means that the powder 214 particle 216 is trapped and cannot be removed. It should be noted that since the starting point directional trajectory length is actually bounded, the upper limit will be dictated by this upper bound. Fig.19 , the values ​​of the point-averaged particle mobility increase from left to right.

[0079] exist Figure 20 to Figure 24 Among the different unit cell geometries 252 illustrated, the cubic framework 262 has the lowest point average particle mobility λ, which is consistent with the Figure 20 to Figure 24 The powder removability of the additively manufactured article 200 composed of the cubic framework 262 unit cell 250 is easier than that of the article 200 composed of one of the other unit cell geometries 252 in the pentagonal icosahedron 266 and the body-centered cubic 268. The relatively large number of starting points 322, which have relatively high point average particle mobility λ, indicates that the powder removability of the additively manufactured article 200 is easier than that of the article 200 composed of the cubic framework 262 unit cell 250. The pentagonal icosahedron 266 and the body-centered cubic 268 have relatively large number of starting points 322, which have relatively high point average particle mobility λ, which indicates that the powder removability of the additively manufactured article 200 is easier than that of the article 200 composed of the other unit cell geometries 252 in the pentagonal icosahedron 26 Figure 20 to Figure 24 Powder removability of articles 200 composed of these unit cells may be more difficult than articles 200 composed of one of the other unit cell geometries 252. As can be seen, histogram 400 provides a means for comparing the differences in powder removability between different unit cell geometries 252 under consideration for use in an article 200 to be additively manufactured, and thus can facilitate the selection of which unit cell geometry 252 to use for filler geometry 210. Although in Figure 20 to Figure 24 The histogram curve 400 is described in the context of the unit cell geometry 252 of FIG. 1 , but the histogram curve 400 can be implemented for any of a variety of alternative unit cell geometries 252. Moreover, the histogram curve 400 can be implemented for general feature geometries and is not limited to features achieved with fillers.

[0080] Now, refer to Fig.25, the above-described method 100 may be performed in whole or in part in a computer-implemented process, such as on a processor-based system 500 or other suitable computer system. The processor-based system 500 is configured to execute computer-readable program instructions 526. The computer-readable program instructions 526 are provided to or loaded onto the processor-based system 500 to implement any one or more of the above-described operations or steps of the method 100. In a non-limiting example, the processor-based system 500 and / or the computer-readable program instructions 526 facilitate the assessment of the ability to remove the powder 214 from the additively manufacturable article 200.

[0081] Fig.25 The block diagram of includes a data communication path 502 (e.g., a data link) to communicatively couple one or more components to facilitate data transfer between these components. The communication path 502 includes one or more data buses, or any other suitable communication path 502 that facilitates data transfer between components and devices of the processor-based system 500. In a non-limiting example, the components include one or more of the following: a processor 504, a memory device 506, a storage device 508, an input / output device 510, a communication device 512, a display device 514, and a particle migration distance calculator 516.

[0082] The memory device 506 is configured to store one or more item geometries 202. For example, the memory device 506 may store any of a variety of sandwich panel 206 configurations, including a planar sandwich panel 206 (e.g., Figures 2 to 6 ), or other sandwich panel 206 configurations, including non-planar sandwich panels 206s, variable thickness sandwich panels 206s, sandwich panels 206 having unit cells 250 of a single layer 272, and sandwich panels 206 having unit cells 250 of two or more layers 272. The memory device 506 may also store any of a variety of other three-dimensional objects of any shape, size, or configuration, including three-dimensional objects having a single panel 208, or three-dimensional objects without a panel 208. In addition to storing the item geometry 202, the memory device 506 is configured to store one or more unit cell geometries 252. For example, the memory device may store the cubic frame 262 ( Fig. 20 ), can connect rectangular parallelepiped 254 ( Fig.21 )、Schwarz-P 264( Fig. 22 ), pentagonal icosahedron 266 ( Fig.23 ), and body-centered cubic 268 ( Fig.24 )'s unit cell geometry 252.

[0083] Still refer to Fig.25, the processor-based system 500 includes a particle migration distance calculator 516 configured to perform the following operations for each of the plurality of discrete starting points 322 distributed within the sampling volume 320. For example, the particle migration distance calculator 516 calculates a plurality of starting point oriented trajectory lengths for each of the plurality of trajectories 328 of the particle 216 starting from the starting point 322 and moving along the initial direction 324, the initial direction being along a plurality of combinations of polar angles φ and azimuthal angles θ of the spherical coordinate system 326 centered at the starting point 322, as described above with respect to step 102A of the method 100. As mentioned above, each of the starting point oriented trajectory lengths ends where the particle 216 leaves the boundary surface 336 of the closed volume 334, and the trajectory 328 includes reflections of the particle 216 within the closed volume 334 on one or more geometric shape surfaces 204 defined by the article geometry 202. The particle migration distance calculator 516 also calculates the average of the starting point directional trajectory lengths for the starting point 322 to provide the starting point average trajectory length, as described above for step 102B of the method 100. The particle migration distance calculator 516 calculates the average of the starting point average trajectory lengths of the plurality of starting points 322 for the object 200 to provide the global average trajectory length.

[0084] The particle migration distance calculator 516 can calculate the average trajectory length of the starting point by analyzing and evaluating the definite integral of the directional trajectory lengths of the multiple starting points across a space defined by all possible combinations of polar angles φ and azimuth angles θ. Alternatively, the particle migration distance calculator 516 can calculate the average trajectory length of the starting point by using a numerical integration technique on a space defined by all possible combinations of polar angles φ and azimuth angles θ to estimate the value of the definite integral of the directional trajectory lengths of the multiple starting points across the space, wherein the numerical integration technique includes: calculating the Riemann sum, performing Gaussian point integration, using the trapezoidal rule, or using the Simpson rule. In another example, the particle migration distance calculator 516 can calculate the average trajectory length of the starting point by using a Monte Carlo technique to estimate the value of the definite integral of the directional trajectory lengths of the multiple starting points across a space defined by all possible combinations of polar angles φ and azimuth angles θ.

[0085] The particle migration distance calculator 516 may calculate the global average trajectory length using any of the techniques described above for the method 100. For example, the particle migration distance calculator 516 may calculate the global average trajectory length by analytically evaluating a definite integral across a domain defined by the set of all starting points 322 contained within the sampling volume 320 minus the set of all starting points 322 contained within the item geometry 202. Alternatively, the particle migration distance calculator 516 may calculate the global average trajectory length by discretizing the domain defined by the set of all starting points 322 contained within the sampling volume 320 minus the set of all starting points 322 contained within the item geometry 202 into elements shaped as tetrahedrons (i.e., tetrahedron elements 274), and then integrating across the tetrahedron using basis functions to estimate the value of the definite integral across the domain. In another example, the particle migration distance calculator 516 may calculate the global average trajectory length by estimating the value of a definite integral across a domain defined by the set of all starting points 322 contained within the sampling volume 320 minus the set of all starting points 322 contained within the item geometry 202 using Monte Carlo techniques.

[0086] Particle migration distance calculator 516 may use the above-described operations of method 100 to calculate a point average particle mobility for each of the plurality of item geometries 202. Particle migration distance calculator 516 may generate a histogram curve 400 of the point average particle mobility for each of the item geometries 202, similar to Fig.19 In addition, the particle migration distance calculator 516 can generate a visual representation of the unit cell geometry 252 and / or the article geometry 202, which shows the starting points 322 and the corresponding point average particle mobility associated with each starting point 322. Fig.16 , which shows starting points 322 encoded (e.g., shaded and cross-hatched) in a manner that represents relative values ​​of point average particle mobility, or similar Fig.18 , which shows contours of average particle mobility at equal points on a slice of the sample volume.

[0087] Fig.26 A non-limiting example of a user interface 528 of a processor-based system 500 is shown, illustrating the Figure 1The user interface 528 provides the ability to select a unit cell geometry 252 from among a plurality of different unit cell geometries 252 stored in memory. The user interface 528 also provides the ability to display the starting points 322 distributed within a volume or to display the starting points 322 distributed within a plane by selecting a radio button indicating the selection. The density of the starting points 322 in the x-direction (“X points”), the density in the y-direction (“Y points”), and if “points in volume” is selected, the density in the z-direction (“Z points”) may be input by the user. Furthermore, the user interface 528 provides the ability to select the “Number of Walks per Sample” and the “Maximum Segments per Walk”. The “Number of Walks per Sample” refers to the number of randomly selected angle pairs (i.e., polar angle φ and azimuthal angle θ) used to estimate the average trajectory length of the starting points. The starting point oriented trajectory lengths are summed and divided by the number of angle pairs selected in order to estimate the starting point average trajectory length. The "Maximum number of segments per walk" refers to the cutoff for the number of trajectory segments and is an upper bound in the case where particles are permanently bouncing between walls (e.g., walls of a packing geometry). Higher "number of walks per sample" results in a better approximation of the average. The "Maximum number of segments per walk" affects the situation where particles are trapped in an infinite loop, so that if the "Maximum number of segments per walk" is too high, the average result will become less accurate.

[0088] Optionally, the display device 514 is used to graphically display any one of the unit cell geometries 252 stored in the memory device 506. In addition, the display device 514 is configured to graphically display the unit cell geometry 252 and the point average particle mobility associated with each starting point 322, similar to the above-mentioned Fig.16 In addition, the display device 514 is configured to graphically display a histogram curve 400 of the point average particle mobility of each unit cell geometry in the unit cell geometry 252, similar to Fig.19 The display device 514 receives the above-mentioned data from one or more of the corresponding components of the processor-based system 500 via the communication path 502.

[0089] The processor-based system 500 includes a processor 504 for executing instructions of a computer-readable program instruction 526 installed in a memory device 506. Alternatively, the processor-based system 500 includes a multi-processor core having two or more integrated processor cores. In addition, the processor 504 may include a main processor and one or more auxiliary processors integrated on a chip. The processor 504 may also include a multi-processor system having multiple similarly configured processors.

[0090] Still refer to Fig.25 , the memory device 506 may include one or more volatile or non-volatile storage devices 508. However, the memory device 506 may include any hardware device for storing data. For example, the memory device 506 may include a random access memory or cache of a device interface and / or an integrated memory controller hub included in the communication path 502. The memory device 506 may store any of a variety of different types of data, computer readable code or program instructions, or any other type of information permanently and / or temporarily. The storage device 508 may be provided in a variety of configurations, including but not limited to, a flash memory device, a hard drive, an optical disk, a hard disk, a magnetic tape, or any other suitable example for long-term storage. In addition, the storage device 508 may include a removable device such as a removable hard drive.

[0091] In addition, the processor-based system 500 may include one or more of the input / output devices 510 to facilitate data transfer between components connected to the processor-based system 500. The input / output devices 510 may be directly and / or indirectly coupled to the processor-based system 500. The input / output devices 510 facilitate user input by means of peripheral devices such as a keyboard, a mouse, a joystick, a touch screen, and any other suitable means for inputting data to the processor-based system 500. The input / output devices 510 may also include output devices for transferring data representing the output of the processor-based system 500. For example, the input / output devices 510 may include a display device 514 configured as a computer monitor or a computer screen for displaying the results of data processed by the processor-based system 500. Alternatively, the input / output devices 510 may include a printer or a fax machine for printing a hard copy of the information processed by the processor-based system 500.

[0092] Still refer to Fig.25, the processor-based system 500 may include one or more communication devices 512 to facilitate the processor-based system 500 to communicate within a computer network and / or with other processor-based systems. The communication between the processor-based system 500 and the computer network or with other processor-based systems may be by wireless means and / or by hard-wired connection. For example, the communication device 512 may include a network interface controller to enable wireless or wired communication between the processor-based system 500 and the computer network. The communication device 512 may also include a modem and / or a network adapter, or any of a variety of alternative devices for sending and receiving data.

[0093] One or more of the operations of the above-described method 100 are performed by the processor 504 and / or by one or more of the particle migration distance calculators 516 using computer-readable program instructions 526. The computer-readable program instructions 526 may include program code, which may include computer-usable program code and computer-readable program code. The computer-readable program instructions 526 are read and executed by the processor 504. The computer-readable program instructions 526 enable the processor 504 to perform one or more operations of the above-described examples associated with assessing the ability to remove the powder 214 from the additively manufacturable article 200.

[0094] Still refer to Fig.25 , computer readable program instructions 526 include operating instructions for the processor-based system 500, and also include applications and programs. The computer readable program instructions 526 may be contained in and / or loaded onto one or more of the memory device 506 and / or storage device 508 for execution by the processor 504 and / or by the particle migration distance calculator 516. As shown above, the memory device 506 and / or storage device 508 may be communicatively coupled to the processor 504 via the communication path 502. Fig.24 One or more of the components illustrated in .

[0095] Computer readable program instructions 526 may be contained on a tangible or intangible, transitory or non-transitory computer readable medium 520 and may be loaded onto or transferred to the processor-based system 500 for execution by the processor 504. The computer readable program instructions 526 and the computer readable medium 520 comprise a computer program product 518. In an example, the computer readable medium 520 may include a computer readable storage medium 522 and / or a computer readable signal medium 524.

[0096] Computer readable storage medium 522 can include a variety of different examples, including but not limited to, optical disks and disks that can be loaded into a drive, flash memory device, or other storage device or hardware for transferring data to a storage device such as a hard drive. Computer readable storage medium 522 can be installed on a processor-based system 500 in an irremovable manner. Computer readable storage medium 522 can include any suitable storage medium, including but not limited to semiconductor systems or propagation media. In this regard, computer readable storage medium 522 can include: electronic media, magnetic media, optical media, electromagnetic media, and infrared media. For example, computer readable storage medium 522 can include: magnetic tape, computer disk, random access memory, and read-only memory. Non-limiting examples of optical disks include: read-only optical disks, read / write optical disks, and digital video disks (i.e., digital versatile disks).

[0097] Computer readable signal media 524 may contain computer readable program instructions 526 and may be provided in a variety of data signal configurations including, but not limited to, electromagnetic signals and optical signals. Such data signals may be transmitted via any suitable communication link, including by wireless or hard-wired means. For example, hard-wired means may include optical cables, coaxial cables, signal wires, and any other suitable means for transmitting data wirelessly or by physical means.

[0098] Still refer to Fig.25 The computer readable signal medium 524 can facilitate downloading of the computer readable program instructions 526 to a non-volatile storage device or other suitable storage device or memory device for use within the processor-based system 500. For example, the computer readable program instructions 526 contained in the computer readable storage medium 522 can be downloaded to the processor-based system 500 from a server or client computer of another system via a computer network.

[0099] Any of a variety of different examples of the processor-based system 500 may be implemented using any hardware device or system capable of executing computer-readable program instructions 526. For example, the processor 504 may include a hardware unit configured to perform one or more specific functions, wherein the computer-readable program instructions 526 for performing the functions are preloaded into the memory device 506.

[0100] In an example, the processor 504 may include: an application specific integrated circuit, a programmable logic device, or any other hardware device configured to perform one or more specific functions or operations. For example, the programmable logic device may be temporarily or permanently programmed to perform one or more operations related to the ability to assess the removal of powder 214 from the additively manufactured article 200. The programmable logic device may include, but is not limited to, a programmable logic array, a programmable array logic, a field programmable logic array, a field programmable gate array, and other suitable logic devices. In an example, the computer readable program instructions 526 may be operated by the processor 504 and / or by other devices including one or more hardware units communicating with the processor 504. Some parts of the computer readable program instructions 526 may be run by one or more hardware units.

[0101] The present disclosure includes example implementations according to the following clauses:

[0102] Clause 1. A method of assessing the ability to remove powder (214) from an additively manufacturable article (200), the method comprising the steps of:

[0103] For each of a plurality of discrete starting points (322) distributed within a sampling volume (320), the following is performed:

[0104] Respectively calculating a plurality of starting point oriented trajectory lengths of a plurality of trajectories (328) of a particle (216), the particle starting from the starting point (322) and moving along an initial direction (324), the initial direction being respectively along a plurality of combinations of polar angles φ and azimuthal angles θ of a spherical coordinate system (326) centered at the starting point (322), and each of the starting point oriented trajectory lengths ending at a location where the particle (216) leaves a boundary surface (336) of a closed volume (334), wherein the trajectory (328) includes reflections of the particle (216) on one or more geometric shape surfaces (204) defined by the object geometry (202) within the closed volume (334);

[0105] For the starting point (322), calculating the average of the starting point directional trajectory lengths to give a starting point average trajectory length; and

[0106] For the article (200), the average values ​​of the starting point average trajectory lengths of the multiple starting points (322) are calculated respectively to provide a global average trajectory length.

[0107] Clause 2. The method according to clause 1, wherein the sampling volume (320) and the closed volume (334) are the same area, which is an area bounded by the exterior (213) of the object (200).

[0108] Clause 3. A method according to any one of clauses 1 to 2, wherein:

[0109] At least one of the start-point directional trajectory lengths is comprised of a plurality of trajectory segments (330) resulting from reflection of the particle (216) off of the one or more geometrically shaped surfaces (204); and

[0110] The step of calculating the length of each starting point orientation trajectory for a given starting point (322), polar angle and azimuth angle comprises: summing the lengths of the plurality of trajectory segments (33).

[0111] Clause 4. The method according to any one of clauses 1 to 3, wherein the step of calculating the average trajectory length of the starting point comprises one of the following:

[0112] Analytically evaluating the definite integral of the lengths of the orientation trajectories of the plurality of starting points across a space defined by all possible combinations of the polar angle φ and the azimuth angle θ;

[0113] Using a numerical integration technique on the space defined by all possible combinations of the polar angle φ and the azimuth angle θ to estimate the value of the definite integral of the lengths of the directional trajectories of the multiple starting points across the space, the numerical integration technique comprising one of: calculating a Riemann sum, performing a Gaussian point integral, using a trapezoidal rule, using a Simpson's rule; or

[0114] The value of the definite integral of the lengths of the orientation trajectories of the plurality of starting points is estimated across the space defined by all possible combinations of the polar angle φ and the azimuth angle θ using a Monte Carlo technique.

[0115] Clause 5. The method according to any one of clauses 1 to 4, wherein the step of calculating the global average trajectory length comprises one of the following:

[0116] analytically evaluating a definite integral across a domain defined by the set of all starting points (322) contained within the sampling volume (320) minus the set of all starting points (322) contained within the item geometry (202);

[0117] estimating the value of the definite integral across the domain by discretizing the domain defined by the set of all starting points (322) contained within the sampling volume (320) minus the set of all starting points (322) contained within the item geometry (202) into elements shaped as a tetrahedron and then integrating across the tetrahedron using basis functions; or

[0118] The value of the definite integral is estimated using Monte Carlo techniques across the domain defined by the set of all starting points (322) contained within the sample volume (320) minus the set of all starting points (322) contained within the item geometry (202).

[0119] Clause 6. A method according to any one of clauses 1 to 5, wherein:

[0120] The article geometry (202) includes a single unit cell (250) having a periodic unit cell pattern for use in an additively manufacturable article (200);

[0121] normalizing the start point orientation trajectory length for a given start point (322) by a specified distance to define an orientation point mobility;

[0122] normalizing the starting point average trajectory length by the specified distance to define a point average particle mobility; and

[0123] The global average trajectory length is normalized by the specified distance to define a global average particle mobility.

[0124] Clause 7. The method according to clause 6, wherein:

[0125] The unit cell (250) has a cell side length (270);

[0126] The sampling volume (320) is a cube (300) having a cube side length (302) equal to the lattice side length (270);

[0127] The closed volume (334) is a sphere (338) whose position is shifted for each starting point (322) so that when calculating the starting point oriented trajectory length associated with each starting point (322), the sphere (338) is centered on the starting point (322);

[0128] The sphere (338) has a radius equal to the square root of three times the length of a side (270) of the lattice; and

[0129] The prescribed distance to which all start point orientation trajectory lengths are normalized is the radius of the sphere (338).

[0130] Clause 8. The method according to any one of clauses 6 to 7, further comprising the following steps:

[0131] The global average particle mobility of a plurality of different periodic unit cell geometries (252) is respectively compared as a measure of the ability to remove powder (214) from the different periodic unit cell geometries (252).

[0132] Clause 9. The method according to any one of clauses 6 to 8, further comprising the following steps:

[0133] calculating the global average particle mobility for a plurality of different unit cell geometries (252); and

[0134] A histogram curve (400) is generated containing a histogram of the global average particle mobility for each of the unit cell geometries (252).

[0135] Clause 10. The method according to any one of clauses 6 to 9, further comprising the following steps:

[0136] At least a subset of the multiple starting points (322) are displayed in such a manner that each starting point (322) has a color corresponding to a unique value of the point average particle mobility of the starting point (322), thereby illustrating the spatial variation of the point average particle mobility, or a subset thereof, across the enclosed volume (334).

[0137] Clause 11. A method of assessing the ability to remove powder from a filler geometry of an additively manufacturable article, the method comprising the steps of:

[0138] The following is performed for each of a plurality of discrete starting points (322) distributed within a unit cell of a plurality of interconnected unit cells (250) forming the filler geometry (210) of the article (200) (the unit cells (250) having a common unit cell geometry (252) and each unit cell (250) fitting completely within a cube (300) having a body diagonal (306)):

[0139] Calculating a plurality of starting point oriented trajectory lengths for a plurality of trajectories (328) of a particle (216), the particle starting from the starting point (322) and moving along an initial direction (324), the initial direction being respectively along a plurality of combinations of polar angle φ and azimuthal angle θ of a spherical coordinate system (326) centered at the starting point (322), and each of the starting point oriented trajectory lengths terminating at a location where the particle (216) leaves a sphere (338) within the filler geometry (210), the sphere (338) enclosing the unit cell (250) containing the plurality of starting points (322) and having a radius equal to the length of the body diagonal (306), wherein the trajectory (328) includes reflections of the particle (216) on one or more geometric surfaces (204) defined by the filler geometry (210);

[0140] calculating, for the starting point (322), an average of the starting point directional trajectory lengths, and dividing the average by the body diagonal (306) for the starting point (322) to give a point average particle mobility; and

[0141] For the packing geometry (210), the average of the point average particle mobilities of the plurality of starting points (322) is calculated respectively to give a global average particle mobility.

[0142] Clause 12. The method according to clause 11, wherein:

[0143] At least one of the start-point directional trajectory lengths is comprised of a plurality of trajectory segments (330) resulting from reflection of the particle (216) off of the one or more geometrically shaped surfaces (204); and

[0144] The step of calculating the length of each starting point orientation trajectory for a given starting point (322), polar angle and azimuth angle comprises: summing the lengths of the plurality of trajectory segments (33).

[0145] Clause 13. The method according to any one of clauses 11 to 12, wherein the step of calculating the lengths of the directional trajectories of the plurality of starting points comprises one of the following:

[0146] Analytically evaluating the definite integral of the lengths of the orientation trajectories of the plurality of starting points across a space defined by all possible combinations of the polar angle φ and the azimuth angle θ;

[0147] Using a numerical integration technique on a space defined by all possible combinations of the polar angle φ and the azimuth angle θ to estimate the value of the definite integral of the lengths of the directional trajectories of the multiple starting points across the space, the numerical integration technique comprising one of: calculating a Riemann sum, performing a Gaussian point integral, using a trapezoidal rule, using a Simpson's rule; or

[0148] The value of the definite integral of the lengths of the orientation trajectories of the plurality of starting points is estimated across a space defined by all possible combinations of the polar angle φ and the azimuth angle θ using a Monte Carlo technique.

[0149] Clause 14. The method according to any one of clauses 11 to 13, wherein the step of calculating the global average particle mobility comprises:

[0150] For each packing geometry (210), a plurality of global average particle mobilities for a plurality of different packing geometries (210) are calculated respectively using one of the following techniques:

[0151] analytically evaluating the average of the point average particle mobilities across a domain defined by the set of all starting points (322) contained within the cube (300) minus the set of all starting points (322) contained within the packing geometry (210);

[0152] estimating a value of the mean of the point-averaged particle mobilities across the domain by discretizing the domain defined by the set of all starting points (322) contained within the cube (300) minus the set of all starting points (322) contained within the packing geometry (210) into elements shaped as tetrahedrons and then integrating across the tetrahedrons using basis functions; and

[0153] Using Monte Carlo techniques, the value of the mean value of the point average particle mobility is estimated across the domain defined by the set of all starting points (322) contained within the cube (300) minus the set of all starting points (322) contained within the packing geometry (210).

[0154] Clause 15. The method of any of clauses 11 to 14, wherein the unit cell geometry (252) has one of the following configurations: a connectable cuboid (254), a Schwarz-P (264), a pentagonal icosahedron (266), or a body-centered cubic (268).

[0155] Clause 16. A processor-based system for assessing the ability to remove powder from an additively manufacturable article, the processor-based system comprising:

[0156] a memory device (506) configured to store an object geometry (202) of the object (200), the object being composed of a plurality of interconnected unit cells (250), each unit cell fitting completely within a cube (300) and having a common unit cell geometry (252);

[0157] A particle migration distance calculator (516) configured to, for each of a plurality of discrete starting points (322) distributed within a sampling volume (320), perform the following:

[0158] Respectively calculating a plurality of starting point oriented trajectory lengths of a plurality of trajectories (328) of a particle (216), the particle starting from the starting point (322) and moving along an initial direction (324), the initial direction being respectively along a plurality of combinations of polar angles φ and azimuthal angles θ of a spherical coordinate system (326) centered at the starting point (322), and each of the starting point oriented trajectory lengths ends at a location where the particle (216) leaves a boundary surface (336) of a closed volume (334), wherein the trajectory (328) includes reflections of the particle (216) within the closed volume (334) on one or more geometric shape surfaces (204) defined by the object geometry (202);

[0159] For the starting point (322), calculating the average of the starting point directional trajectory lengths to give a starting point average trajectory length; and

[0160] The particle migration distance calculator (516) is configured to calculate, for the article (200), an average value of the starting point average trajectory lengths of the plurality of starting points (322) to provide a global average trajectory length.

[0161] Clause 17. The processor-based system of clause 16, wherein the particle migration distance calculator is configured to calculate the starting point average trajectory length by performing one of the following:

[0162] Analytically evaluating the definite integral of the lengths of the orientation trajectories of the plurality of starting points across a space defined by all possible combinations of the polar angle φ and the azimuth angle θ;

[0163] Using a numerical integration technique on the space defined by all possible combinations of the polar angle φ and the azimuth angle θ to estimate the value of the definite integral of the lengths of the directional trajectories of the multiple starting points across the space, the numerical integration technique comprising one of: calculating a Riemann sum, performing a Gaussian point integral, using a trapezoidal rule, using a Simpson's rule; or

[0164] The value of the definite integral of the lengths of the orientation trajectories of the plurality of starting points is estimated across the space defined by all possible combinations of the polar angle φ and the azimuth angle θ using a Monte Carlo technique.

[0165] Clause 18. The processor-based system of any of clauses 16 to 17, wherein the particle migration distance calculator is configured to calculate the global average trajectory length using one of:

[0166] analytically evaluating a definite integral across a domain defined by the set of all starting points (322) contained within the sample volume (320) minus the set of all starting points (322) contained within the item geometry (202);

[0167] estimating the value of the definite integral across the domain by discretizing the domain defined by the set of all starting points (322) contained within the sampling volume (320) minus the set of all starting points (322) contained within the item geometry (202) into elements shaped as a tetrahedron and then integrating across the tetrahedron using basis functions; or

[0168] The value of the definite integral is estimated using Monte Carlo techniques across the domain defined by the set of all starting points (322) contained within the sample volume (320) minus the set of all starting points (322) contained within the item geometry (202).

[0169] Clause 19. A processor-based system as described in any of Clauses 16 to 18, wherein:

[0170] The memory device (506) is configured to store a plurality of different unit cell geometries (252) for a corresponding plurality of different article geometries (202) of the article (200);

[0171] The particle migration distance calculator (516) is configured to:

[0172] calculating the global average particle mobility for each item geometry in the plurality of item geometries (202); and

[0173] A histogram is generated containing the global average particle mobility for each of the item geometries (202).

[0174] Clause 20. A processor-based system as described in any of Clauses 16 to 19, wherein:

[0175] The particle migration distance calculator (516) is configured to generate a visual representation of the item geometry (202) illustrating the plurality of starting points (322) and indicating the corresponding point average particle mobility associated with each starting point (322).

[0176] With the benefit of the teachings presented in the foregoing description and the associated drawings, those skilled in the art to which the present disclosure belongs will think of many modifications of the present disclosure as well as other forms and examples. The forms and examples described herein are intended to be illustrative and are not intended to be limiting or exclusive. Although specific terms are employed herein, they are used only in a general and descriptive sense and not for the purpose of limitation. According to the foregoing description, in addition to those methods and devices listed herein, functionally equivalent methods and devices within the scope of the present disclosure are possible. Such modifications and variations fall within the scope of the appended claims. The present disclosure is limited only by the appended claims together with the full range of equivalents protected by such claims.

Claims

1. A method of evaluating the ability to remove powder (214) from an additively manufacturable article (200), the method comprising the steps of: For each of a plurality of discrete starting points (322) distributed within a sampling volume (320), the following is performed: Respectively calculating a plurality of starting point oriented trajectory lengths of a plurality of trajectories (328) of a particle (216), the particle starting from the starting point (322) and moving along an initial direction (324), the initial direction (324) respectively being along a plurality of combinations of polar angle φ and azimuthal angle θ of a spherical coordinate system (326) centered at the starting point (322), and each of the starting point oriented trajectory lengths ending at a location where the particle (216) leaves a boundary surface (336) of a closed volume (334), wherein the trajectory (328) includes reflections of the particle (216) on one or more geometric shape surfaces (204) defined by the object geometry (202) within the closed volume (334); For the starting point (322), calculating the average of the starting point directional trajectory lengths to give a starting point average trajectory length; and For the article (200), the average values ​​of the starting point average trajectory lengths of the multiple starting points (322) are calculated respectively to provide a global average trajectory length.

2. The method according to claim 1, wherein: The sampling volume (320) and the enclosed volume (334) are the same area, which is the area bounded by the exterior (213) of the article (200).

3. The method according to claim 1, wherein: At least one of the start-point directional trajectory lengths is comprised of a plurality of trajectory segments (330) resulting from reflection of the particle (216) off of the one or more geometrically shaped surfaces (204); and The step of calculating the length of each starting point orientation trajectory for a given starting point (322), polar angle and azimuth angle comprises: summing the lengths of the plurality of trajectory segments (33).

4. The method according to claim 1, wherein: The step of calculating the average trajectory length of the starting point includes one of the following: Analytically evaluating the definite integral of the lengths of the orientation trajectories of the plurality of starting points across a space defined by all possible combinations of the polar angle φ and the azimuth angle θ; Using a numerical integration technique on the space defined by all possible combinations of the polar angle φ and the azimuth angle θ to estimate the value of the definite integral of the lengths of the directional trajectories of the plurality of starting points across the space, the numerical integration technique comprising one of: computing a Riemann sum, performing a Gaussian point integral, using a trapezoidal rule, using a Simpson's rule; or The value of the definite integral of the lengths of the orientation trajectories of the plurality of starting points is estimated across the space defined by all possible combinations of the polar angle φ and the azimuth angle θ using a Monte Carlo technique.

5. The method according to claim 1, wherein: The step of calculating the global average trajectory length comprises one of the following: analytically evaluating a definite integral across a domain defined by the set of all starting points (322) contained within the sampling volume (320) minus the set of all starting points (322) contained within the item geometry (202); estimating the value of the definite integral across the domain by discretizing the domain defined by the set of all starting points (322) contained within the sampling volume (320) minus the set of all starting points (322) contained within the item geometry (202) into elements shaped as a tetrahedron, and then integrating across the tetrahedron using basis functions; or The value of the definite integral is estimated using Monte Carlo techniques across the domain defined by the set of all starting points (322) contained within the sample volume (320) minus the set of all starting points (322) contained within the item geometry (202).

6. The method according to claim 1, wherein: The article geometry (202) includes a single unit cell (250) having a periodic unit cell pattern for use in an additively manufacturable article (200); normalizing the start point orientation trajectory length for a given start point (322) by a specified distance to define an orientation point mobility; normalizing the average trajectory length of the starting point according to the specified distance to define the point average particle mobility; as well as The global average trajectory length is normalized by the specified distance to define a global average particle mobility.

7. The method according to claim 6, wherein: The unit cell (250) has a cell side length (270); The sampling volume (320) is a cube (300) having a cube side length (302) equal to the lattice side length (270); The closed volume (334) is a sphere (338), the position of the sphere (338) being shifted for each starting point (322) so that when calculating the starting point oriented trajectory length associated with each starting point (322), the sphere (338) is centered on the starting point (322); The sphere (338) has a radius equal to the square root of three times the length of a side (270) of the lattice; as well as The prescribed distance to which all start point orientation trajectory lengths are normalized is the radius of the sphere (338).

8. The method according to claim 6, further comprising the steps of: The global average particle mobility of a plurality of different periodic unit cell geometries (252) is respectively compared as a measure of the ability to remove powder (214) from the different periodic unit cell geometries (252).

9. The method according to claim 6, further comprising the steps of: calculating the global average particle mobility for a plurality of different unit cell geometries (252); as well as A histogram curve (400) is generated containing a histogram of the global average particle mobility for each of the unit cell geometries (252).

10. The method according to claim 6, further comprising the steps of: At least a subset of the plurality of starting points (322) are displayed in such a manner that each starting point (322) has a color corresponding to a unique value of the point average particle mobility of the starting point (322), thereby illustrating the spatial variation of the point average particle mobility, or a subset thereof, across the enclosed volume (334).

11. A method of assessing the ability to remove powder (214) from a filler geometry (210) of an additively manufacturable article (200), the method comprising the steps of: The following is performed for each of a plurality of discrete starting points (322) distributed within a unit cell of a plurality of interconnected unit cells (250) forming a filler geometry (210) of the article (200), wherein the unit cells (250) have a common unit cell geometry (252) and each unit cell (250) fits entirely within a cube (300) having a body diagonal (306): calculating a plurality of start-point oriented trajectory lengths for a plurality of trajectories (328) of a particle (216), the particle starting from the start point (322) and moving along an initial direction (324), the initial direction (324) respectively being along a plurality of combinations of polar angle φ and azimuthal angle θ of a spherical coordinate system (326) centered at the start point (322), and each of the start-point oriented trajectory lengths terminating at a location where the particle (216) leaves a sphere (338) within the filler geometry (210), the sphere (338) enclosing the unit cell (250) containing the plurality of start points (322) and having a radius equal to the length of the body diagonal (306), wherein the trajectory (328) includes reflections of the particle (216) on one or more geometric surfaces (204) defined by the filler geometry (210); calculating, for the starting point (322), an average of the starting point directional trajectory lengths, and dividing the average by the body diagonal (306) for the starting point (322) to give a point average particle mobility; and For the packing geometry (210), the average of the point average particle mobilities of the plurality of starting points (322) is calculated respectively to give a global average particle mobility.

12. The method according to claim 11, wherein: At least one of the start-point directional trajectory lengths is comprised of a plurality of trajectory segments (330) resulting from reflection of the particle (216) off of the one or more geometrically shaped surfaces (204); and The step of calculating the length of each starting point orientation trajectory for a given starting point (322), polar angle and azimuth angle comprises: summing the lengths of the plurality of trajectory segments (33).

13. The method according to claim 11, wherein: The step of calculating the lengths of the plurality of starting point orientation trajectories comprises one of the following: Analytically evaluating the definite integral of the lengths of the orientation trajectories of the plurality of starting points across a space defined by all possible combinations of the polar angle φ and the azimuth angle θ; Using a numerical integration technique on a space defined by all possible combinations of the polar angle φ and the azimuth angle θ to estimate the value of the definite integral of the lengths of the directional trajectories of the plurality of starting points across the space, the numerical integration technique comprising one of: calculating a Riemann sum, performing a Gaussian point integral, using a trapezoidal rule, using a Simpson's rule; or The value of the definite integral of the lengths of the orientation trajectories of the plurality of starting points is estimated across a space defined by all possible combinations of the polar angle φ and the azimuth angle θ using a Monte Carlo technique.

14. The method according to claim 11, wherein: The step of calculating the global average particle mobility comprises: For each packing geometry (210), a plurality of global average particle mobilities for a plurality of different packing geometries (210) are calculated respectively using one of the following techniques: analytically evaluating an average of the point average particle mobility across a domain defined by the set of all starting points (322) contained within the cube (300) minus the set of all starting points (322) contained within the packing geometry (210); estimating a value of the mean of the point-averaged particle mobilities across the domain by discretizing the domain defined by the set of all starting points (322) contained within the cube (300) minus the set of all starting points (322) contained within the packing geometry (210) into elements shaped as tetrahedrons and then integrating across the tetrahedrons using basis functions; and Using Monte Carlo techniques, the value of the mean value of the point average particle mobility is estimated across the domain defined by the set of all starting points (322) contained within the cube (300) minus the set of all starting points (322) contained within the packing geometry (210).

15. The method according to claim 11, wherein: The unit cell geometry (252) has one of the following configurations: a connectable cuboid (254), a Schwarz-P (264), a pentagonal icosahedron (266), or a body-centered cubic (268).

16. A processor-based system (500) for assessing the ability to remove powder (214) from an additively manufacturable article (200), the processor-based system (500) comprising: a memory device (506) configured to store an article geometry (202) of the article (200), the article (200) being composed of a plurality of interconnected unit cells (250), each unit cell fitting completely within a cube (300) and having a common unit cell geometry (252); A particle migration distance calculator (516) configured to, for each of a plurality of discrete starting points (322) distributed within a sampling volume (320), perform the following: Respectively calculating a plurality of starting point oriented trajectory lengths of a plurality of trajectories (328) of a particle (216), the particle starting from the starting point (322) and moving along an initial direction (324), the initial direction (324) respectively being along a plurality of combinations of polar angle φ and azimuthal angle θ of a spherical coordinate system (326) centered at the starting point (322), and each of the starting point oriented trajectory lengths ending at a location where the particle (216) leaves a boundary surface (336) of a closed volume (334), wherein the trajectory (328) includes reflections of the particle (216) within the closed volume (334) on one or more geometric shape surfaces (204) defined by the object geometry (202); For the starting point (322), calculating the average of the starting point directional trajectory lengths to give a starting point average trajectory length; and The particle migration distance calculator (516) is configured to calculate, for the article (200), an average value of the starting point average trajectory lengths of the plurality of starting points (322) to provide a global average trajectory length.

17. The processor-based system (500) of claim 16, wherein: The particle migration distance calculator (516) is configured to calculate the starting point average trajectory length by performing one of the following: Analytically evaluating the definite integral of the lengths of the orientation trajectories of the plurality of starting points across a space defined by all possible combinations of the polar angle φ and the azimuth angle θ; Using a numerical integration technique on the space defined by all possible combinations of the polar angle φ and the azimuth angle θ to estimate the value of the definite integral of the lengths of the directional trajectories of the plurality of starting points across the space, the numerical integration technique comprising one of: computing a Riemann sum, performing a Gaussian point integral, using a trapezoidal rule, using a Simpson's rule; or The value of the definite integral of the lengths of the orientation trajectories of the plurality of starting points is estimated across the space defined by all possible combinations of the polar angle φ and the azimuth angle θ using a Monte Carlo technique.

18. The processor-based system (500) of claim 16, wherein: The particle migration distance calculator (516) is configured to calculate the global average trajectory length using one of the following: analytically evaluating a definite integral across a domain defined by the set of all starting points (322) contained within the sampling volume (320) minus the set of all starting points (322) contained within the item geometry (202); estimating the value of the definite integral across the domain by discretizing the domain defined by the set of all starting points (322) contained within the sampling volume (320) minus the set of all starting points (322) contained within the item geometry (202) into elements shaped as a tetrahedron, and then integrating across the tetrahedron using basis functions; or The value of the definite integral is estimated using Monte Carlo techniques across the domain defined by the set of all starting points (322) contained within the sample volume (320) minus the set of all starting points (322) contained within the item geometry (202).

19. The processor-based system (500) of claim 16, wherein: The memory device (506) is configured to store a plurality of different unit cell geometries (252) for a corresponding plurality of different article geometries (202) of the article (200); The particle migration distance calculator (516) is configured to: calculating a global average particle mobility for each of a plurality of item geometries (202); as well as A histogram is generated containing the global average particle mobility for each of the plurality of item geometries (202).

20. The processor-based system (500) of claim 16, wherein: The particle migration distance calculator (516) is configured to generate a visual representation of the item geometry (202) illustrating the plurality of starting points (322) and indicating a corresponding point average particle mobility associated with each starting point (322).

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