Patent ID: 12240182

DETAILED DESCRIPTION

Reference will now be made in detail to exemplary embodiments of the present teachings, examples of which are illustrated in the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same, similar, or like parts.

FIG.1depicts a schematic cross-sectional view of a 3D printing system100, according to an embodiment. The 3D printing system100may include an ejector (also referred to as a pump chamber)110. The ejector110may define an inner volume that is configured to receive a printing material120. The printing material120may be or include a metal, a polymer, or the like. For example, the printing material120may be or include aluminum (e.g., a spool of aluminum wire). In another embodiment, the printing material120may be or include copper.

The 3D printing system100may also include one or more heating elements130. The heating elements130are configured to melt the printing material120within the inner volume of the ejector110, thereby converting the printing material120from a solid material to a liquid material (e.g., liquid metal)122within the inner volume of the ejector110.

The 3D printing system100may also include a power source132and one or more metallic coils134. The metallic coils134are wrapped at least partially around the ejector110and/or the heating elements130. The power source132may be coupled to the coils134and configured to provide power thereto. In one embodiment, the power source132may be configured to provide a step function direct current (DC) voltage profile (e.g., voltage pulses) to the coils134, which may create an increasing magnetic field. The increasing magnetic field may cause an electromotive force within the ejector110, that in turn causes an induced electrical current in the liquid metal122. The magnetic field and the induced electrical current in the liquid metal122may create a radially inward force on the liquid metal122, known as a Lorentz force. The Lorentz force creates a pressure at an inlet of a nozzle114of the ejector110. The pressure causes the liquid metal122to be jetted through the nozzle114in the form of one or more drops124.

The 3D printing system100may also include a substrate (also referred to as a build plate)140that is positioned below the nozzle114. The drops124that are jetted through the nozzle114may land on the substrate140and cool and solidify to produce a near-net shape (NNS)126, which may also be referred to as a 3D object. As described in greater detail below, the NNS126may include a desired 3D part (also referred to as the net shape) and a support volume.

The substrate140may include a heater142therein that is configured to increase the temperate of the substrate140. The 3D printer100may also include a substrate control motor144that is configured to move the substrate140as the drops124are being jetted (i.e., during the printing process) to cause the NNS126to have the desired shape and size. The substrate control motor144may be configured to move the substrate140with up to six degrees of freedom (e.g., three translations and three rotations). In another embodiment, the ejector110and/or the nozzle114may be also or instead be configured to move with up to six degrees of freedom.

The 3D printing system100may also include one or more subtractive tool assemblies (one is shown160). The subtractive tool assembly160may include one or more holders (one is shown:162) and one or more cutters (one is shown:164). The holder162may be configured to mount and/or guide the cutter164to regions of interest on the NNS126. The cutter164may be configured to cut (e.g., mill, machine, etc.) the support volume away from the NNS126to yield the 3D part. The 3D printing system100may also include one or more fixturing devices (one is shown:166) that hold the NNS126as material is added and/or removed therefrom. For example, the fixturing device166may be configured to hold the NNS126, after the AM process, as material (e.g., the support volume) is/are removed therefrom by the subtractive tool assembly160.

In one embodiment, the 3D printing system100may also include an enclosure170. The enclosure170may be positioned at least partially around the ejector110, the nozzle114, the drops124, the NNS126, the heating elements130, the coils134, the substrate140, the subtractive tool assembly160, or a combination thereof. In one embodiment, the enclosure170may be hermetically sealed. In another embodiment, the enclosure170may not be hermetically sealed. In other words, the enclosure170may have one or more openings that may allow gas to flow therethrough. For example, the gas may flow out of the enclosure170through the openings.

In one embodiment, the 3D printing system100may also include one or more gas sources (one is shown:180). The gas source180may be positioned outside of the enclosure170and configured to introduce gas into the enclosure170. The gas source180may be configured to introduce a gas that flows (e.g., downward) around the ejector110, the nozzle114, the heating elements130, or a combination thereof. The gas may flow around and/or within the coils134. The gas may flow into the enclosure170and/or proximate to (e.g., around) the drops124, the NNS126, and/or the substrate140.

The 3D printing system100may also include a gas sensor182. The gas sensor182may be positioned within the enclosure170. The gas sensor182may also or instead be positioned proximate to the drops124, the NNS126, and/or the substrate140(e.g., in an embodiment where the enclosure170is omitted). The gas sensor182may be configured to measure a concentration of the gas, oxygen, or a combination thereof.

The 3D printing system100may also include a computing system190. The computing system190may be configured to control the introduction of the printing material120into the ejector110, the heating elements130, the power source132, the substrate control motor144, the subtractive tool assembly160, the fixturing device166, the gas source180, the gas sensor182, or a combination thereof. For example, the computing system190may be configured to automate generation of a design (e.g., of the NNS126) such that the design, when subsequently manufactured via AM, contains an accessible support volume that may be removed via SM to yield the 3D part.

Automated Design Generation for Additive Manufacturing with an Accessible Support Volume

The systems and methods described herein may provide automated design generation for additive manufacturing with an accessible support volume. This provides a systematic approach to automated design generation while also providing removability of the support volume through subtractive manufacturing (e.g., milling) in terms of accessibility of one or more points of the support volume given the substrate140, the subtractive tool assemblies160, and/or the fixturing devices166without imposing artificial constraints on geometric complexity of the 3D part, the support geometry, the subtractive tool assemblies160, the fixturing devices166, or a combination thereof. This also provides efficient and effective design space exploration by providing complex designs for which its NNS126(e.g., 3D part+support volume) can be fabricated using additive manufacturing and post-processed using subtractive manufacturing.

Different automated design techniques (e.g., topology optimization, machine learning, cellular automata, etc.) may consider the physical performance of a 3D part to provide organic shapes. The present disclosure solves the following optimization problem:

MinimizeΩ⊆Ω0φ⁡(Ω),(1⁢a)such⁢that[KΩ][uΩ]=[f],(1⁢b)VΩ≤Vtarget,(1⁢c)
Where φ(Ω)∈is the value of an objective function for a given design Ω⊆Ω0. The variables [f], [uΩ], and [KΩ] represent discretized external force, a displacement vector, and a stiffness matrix, respectively, for finite element analysis (FEA). The variable VΩ:=vol[Ω] represents the design volume, and Vtarget>0 is the volume budget

The present disclosure may provide a physics-based performance analysis by invoking physics solvers such as finite element analysis (FEA) to evaluate objectives and constraints. The present disclosure may also determine optimization decision variables such as gradients, sensitivity fields, etc. based at least partially upon the objectives and/or constraints. The present disclosure may also design manufacturing constraints (e.g., by augmenting/filtering decision variables based at least partially upon design and manufacturing considerations). The present disclosure may also update design variables based at least partially upon decision variables, and then generate an optimized design of the NSS126and/or 3D part.

The accessibility constraint may be augmented to the sensitivity field to allow the 3D part to be manufactured using SM. However, the automated design of AM parts with respect to accessibility of the support volume has not yet been explored.

Inaccessibility Access

The 3D printing system100(e.g., the nozzle114, the substrate140, the subtractive tool assembly160, or a combination thereof) can operate with up to six degrees of freedom (e.g., three translations and three rotations) available for a rigid body. For example, T=(H∪K), where T represents the subtractive tool assembly160for multi-axis machining, H represents the holder162, and K represents the cutter164. Mathematically, the configuration space (C-space) of rigid motions is represented as C=3×SO(3) where C represents the configuration space,3represents the Euclidian space, and SO(3) refers to the group of 3×3 orthogonal transformations that represent spatial rotations.

An inaccessibility measure field (IMF) may be defined over the 3D design domain fIMF:3→for each given tool assembly T as the pointwise minimum of shifted convolutions for different choices of sharp points and available orientations ΘT⊆SO(3). The IMF is described by the following equation:

fIMF(x;O,N,T,K):=minR∈ΘTmink∈Kvol[O⋂(R,x)⁢(T-k)](2)
where R∈Θ is a rotation matrix corresponding to an available tool orientation, and point x∈3with N=Ω∪S denoting the near-net shape fabricated of the workpiece and its corresponding support structures S. There are two independent transformations in effect. First, the shift T→(T−k) in Equation 2 may sample different ways to register the translation space with the design domain, by changing the local coordinate system to bring different sharp points to the origin. Second, the rotation (T−k)→(RT−Rk) followed by translation (RT−Rk)→(RT−Rk)+x may bring the candidate sharp point (new origin) to the query point x∈Ω0.

The same effect can be obtained by querying the convolution at t=(x−Rk) so that the rigid transformation (R, t) brings the sharp point in contact with the query point: (R, t)k=Rk+t=Rk+(x−Rk)=x, as expected. The IMF may thus be computed as follows:

fIMF(x;O,N,T,K)=minR∈ΘTmink∈K(1O*1~RT)⁢(x-Rk).(3)

Equation 2 can be further extended to consider multiple subtractive tool assemblies160. Given nT≥1, available subtractive tool assemblies160, Ti=(Hi∪Ki) for 1≤i≤nT, their combined IMF may be determined by applying another minimum operation over different subtractive tool assemblies to identify the subtractive tool assemblies with the smallest volumetric interference at available orientations and sharp points:

fIMF(x;N,O):=min1≤i≤nTfIMF(x;N,O,Ti,Ki)(4)
in which fIMP(x; N, O, Ti, Ki) may be determined using Equation 3.

There may be challenges in optimizing the build orientation based at least partially upon the accessibility of the support volume. As used herein, the term “build orientation” (also referred to as “build angle”) refers to a direction at which the NNS126is additively printed layer-by-layer. First, minimizing the volume of the support volume may not be the same as minimizing the volume of inaccessible support volume (i.e., the inaccessible support volume can decrease at a higher overall support volume). Second, a large number of build orientations can become time and computationally intensive. Third, there are numerous types of support geometries (e.g., beams or tree-like structures) and overhang angles (e.g., 45° or 90°) depending on the AM process. Fourth, the shapes of the subtractive tool assembly160may not be ignored. Hence, it may be difficult to assign a correspondence between the translations t∈3and the points x∈3within the near-net shape126unless one or more (e.g., all) possible contact configurations are analyzed, and the boundary points are treated differently from the interior points. Fifth, the shapes of the substrate140, the subtractive tool assembly160, and the fixture166may not be ignored. Sixth, the analysis may be highly non-linear, meaning a small change in x∈N can dramatically change the accessibility in a far-away point y∈3.

FIG.2depicts a schematic side view of an initial design and boundary condition200, according to an embodiment. The “initial design” and/or the “initial design domain” refers to an envelope within which the optimized design lies. The “boundary condition” refers to one or more physical forces and restraints applied to the design. As shown inFIG.2, the initial design and boundary condition200may have one or more fixed points (one is shown:210). The fixed point210may secure the initial design and boundary condition200in a predetermined build orientation (e.g., 0°) during the AM process. The initial design and boundary condition200may also experience one or more forces (five are shown:220A-220E). The forces may be vertical (e.g., downward) forces.

FIG.3depicts a schematic side view of the initial design and boundary condition200in a different build orientation (e.g., 45°), according to an embodiment. The build direction300is vertical (e.g., upward) from the substrate140. Referring toFIGS.2and3, the present disclosure may be able to determine the stiffest design at Vtarget=0.5. The build direction300and substrate140may be as shown inFIG.3.

FIG.4depicts a schematic side view of the NNS126, according to an embodiment.FIG.5depicts a schematic view of the subtractive tool assembly160, according to an embodiment. The NNS126includes a 3D part400and a support volume (also referred to as support structures). The support volume may include a first support volume410and a second support volume420. The first support volume410may be accessible by the subtractive tool assembly160, and thus may be removed. The second support volume420may be inaccessible by the subtractive tool assembly160, and thus may not be removed. The design inFIG.4is at a 0.5 volume fraction without considering support volume accessibility.

FIGS.4and5illustrate a predetermined (e.g., optimized) design Ω of the NSS126and/or 3D part400, the accessible support volume410, the inaccessible support volume420, and the subtractive tool assembly160. The set of approach directions are Θ=0°, 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°, 270°, 300°, and 330°. A fraction of the support volume may be inaccessible, and thus cannot be removed from the NNS126. As a result, the 3D part400may not be manufacturable.

FIG.6depicts an image of the IMF over the NNS126inFIG.4, andFIG.7depicts an image of the IMF over the inaccessible support volume420inFIG.4, according to an embodiment. The IMF images may be generated without considering the accessibility of the support volume410,420.

Accessibility Constraint on Support Volume Based on IMF

The system and method disclosed herein may automatically generate the design of the NNS126such that the resulting shape of the NNS126and/or 3D part400may be manufacturable using AM and then SM. The present disclosure may use a physics-based performance analysis that invokes physics solvers (e.g., FEA) to evaluate objectives and constraints. The present disclosure may also determine decision variables (e.g., gradients, sensitivity fields, etc.) based at least partially upon objectives and/or constraints. The present disclosure may also perform an accessibility analysis by constructing the configuration space (C-space) of the 3D part400and subtractive tool assembly160, sampling the tool rotations in C-space, and constructing the IMF field(s). The present disclosure may also enrich decision variables with accessibility information by filtering/augmenting the decision variables with/by the IMF field(s) such that only the accessible parts are subject to modification. The present disclosure may also update design variables based on the modified decision variables. A SM design may then be generated.

These activities may be based at least partially upon geometric, topological, material, and/or physical aspects of the available manufacturing capabilities. These activities may not be performed in isolation. For example, density-based TO may involve a continuous density function ρΩ:Ω→[0,1] to represent intermediate designs, rather than indicator functions. A threshold 0<τ1 (e.g., τ=0.5) may be used to define the indicator functions as 1Ω(x)=1 iff ρΩ(x)>τ for use in equation 3. However, in other embodiments, direct use of the density function may provide additional smoothing:

fIMF(x;ρO,T,K):=minR∈Θmink∈K(ρO⋆1˜R⁢T)⁢(x-Rk).(5)
The function ρO: O→[0,1] can be obtained as ρO(x):=ρΩ(x)+1F(x), in which ρΩ(x) may be obtained directly from TO. The combined IMF for the tool assemblies fIMF(x; ρO)fIMF(x; ρO) may be computed as:

fIMF(x;ρO):=min1≤i≤nTfIMF(x;ρO,Ti,Ki)(6)MinimizeΩ⊆Ω0⁢φ⁡(Ω),(7⁢a)such⁢that[KΩ][uΩ]=[f],(7⁢b)VΩ≤Vtarget,(7⁢c)VSsec=0,(7⁢d)
where Vssecis the volume of the inaccessible support volume420. To incorporate the accessibility constraints for multi-axis machining, the sensitivity field SΩmay be modified as follows.
Ω:=(1−wacc)φ+waccIMP,(8)
where 0≤wacc<1 is the filtering weight for accessibility, and can be either a constant or adaptively updated base on the secluded volume Vr(o). The variablerepresents the normalized sensitivity field with respect to the objective function. The volume constraint may be satisfied with the optimality criteria iteration. The variablerepresents the normalized accessibility field defined in terms of the normalized IMF as:

IMF(x):={0.01f_IMP(x;ρO)if⁢x∈Ω⋃Sacc,f_IMP(x;ρO)if⁢x∈Ssec,0otherwise.(9)

FIG.8depicts another schematic side view of the NNS126, according to an embodiment. The design inFIG.8is at a 0.5 volume fraction and considers support volume accessibility.FIG.9depicts an image of the IMF over the NNS126inFIG.8, according to an embodiment.

FIG.10depicts a flowchart of a method1000for generating a design, according to an embodiment. The design may be of the NNS126, the 3D part400, or both. The NNS126may then be manufactured via AM, and the NNS126may include an accessible support volume410that may subsequently be removed via SM to yield the 3D part400.

An illustrative order of the method1000is provided below; however, one or more steps of the method1000may be performed in a different order, combined, split into sub-steps, repeated, or omitted without departing from the scope of the disclosure. One or more steps of the method1000may be performed using the computing system190.

The method1000may include receiving a representation of the initial design domain200, as at1002. The representation may be received by (and/or provided to) the computing system190. The representation may also or instead include a build orientation for building the initial design domain200using the additive manufacturing process. The representation may also or instead include the subtractive tool assembly160.

The method1000may also include generating intermediate part designs within the initial design domain200, as at1004. The intermediate part designs may be generated by the computing system190. An intermediate part design refers to a design of the near-net shape126and/or the 3D part400that is generated after the initial design domain200and before the final part design (described below). The intermediate part designs may be generated iteratively by redistributing material within the initial design domain. Each intermediate part design may include the near-net shape126, the 3D part400, the support volume410,420, or a combination thereof. In at least one embodiment, the near-net shape126, the 3D part400, the support volume410,420, or a combination thereof may vary (e.g., slightly) from one intermediate part design to the subsequent intermediate part design.

The method1000may also include calculating a measure of inaccessibility of the support volume410,420of each intermediate part design, as at1006. The measure of inaccessibility may be calculated by the computing system190. The measure of inaccessibility refers to an inability of the subtractive cutting assembly160to access and/or remove one or more regions of the support volume410,420(e.g., in the initial design domain). The measure of inaccessibility may be quantitative. For example, the measure of inaccessibility may be in terms of a volumetric amount of the support volume410,420that is inaccessible, a percentage of the support volume410,420that is inaccessible, a ratio of the support volume410,420that is inaccessible, or the like.

As mentioned above, at least a portion of the method1000may be iterative. Thus, at least one (e.g., each) of the intermediate part designs may be generated based at least partially upon the measure of inaccessibility of a previous one of the intermediate part designs. This iterative process may continue until termination criteria are met. In one embodiment, the termination criteria may include the measure of inaccessibility dropping below a predetermined threshold. This may help to minimize the amount, percentage, and/or ratio of the inaccessible support volume420(e.g., with respect to the accessible support volume410).

The method1000may also include generating a final part design, as at1010. The final part design may be generated by the computing system190. The final part design may be generated within the initial design domain200. The final part design may be generated based at least partially upon the intermediate part design(s) and/or the measure(s) of inaccessibility.

The method1000may also include building the final part design with the 3D printing system100, as at1012. The method1000may also include removing the support volume410,420from the final part design with the 3D printing system100, as at1014. More particularly, this may include removing the accessible support volume410from the final part design using the subtractive tool assembly160. This may yield the 3D part400.

Path Planning

In one embodiment, the system and method may invoke path planners such as open motion planning library (OMPL) to test for sufficient accessibility conditions. The new field, coupled with IMF, can be used to generate designs that satisfy both conditions of existence of a connected path.

In one embodiment, the system and method may provide an automated approach to removing the support volume410,420where the IMF is computed over one or more (e.g., all) of the support volume410,420, and the conditions for existence of a plan is evaluated. In another embodiment, the system and method may automatically optimize a shape to meet multiple physical performance criteria while ensuring that the resulting shape has an accessible support volume410given the multiple subtractive tool assemblies160, tool orientations, and build direction(s). In another embodiment, the system and method may provide an automated approach to support volume removal planning where the IMF is computed over one or more (e.g., all) of the support volume410,420, and the support volume410,420is removed based upon a predetermined (e.g., optimized) path. For example, the accessible support volume410may be removed using path planners such as OMPL. In another embodiment, the system and method may automatically generate a shape to meet multiple physical performance criteria while ensuring that the resulting support volume410,420is removable from the NNS126with the given set of subtractive tool assemblies160, orientations, and fixturing devices166.

Physics-Aware Automatic Spatial Planning for Subtractive and Hybrid Manufacturing

As mentioned above, an additive manufacturing (AM) process may produce a near-net shape126, defined as a shape that closely conforms to the intended design to be manufactured (e.g., the 3D part400) along with additional support volume (also referred to as support structures and/or scaffolding)410,420added during the AM process. The support volume410,420may be subsequently removed so that the intended design (e.g., 3D part400) may be fabricated from the NNS126. The systems and methods disclosed herein may provide a spatial planning approach to automatically remove the support volume410,420using the multi-axis subtractive tool assembly160while ensuring that 1) the work-piece (e.g., NNS126) is held by the fixture166throughout the support removal process (i.e., it is not detached from the platform before some or all supports410,420are removed) and 2) the part400is not damaged in the removal process. The multi-disciplinary approach involves solving the corresponding physics problems, augmenting additional physics-based sensitivity fields such as topological sensitivity field (TSF) to the inaccessibility measure field (IMF), and producing an efficient support removal plan.

Producing the 3D part400using AM may include some post-processing operations, typically in the form of machining or other subtractive manufacturing (SM) processes. AM may therefore be understood as one of many processes that may be used to manufacture a part and not a stand-alone solution. A sequence of AM and SM processes (in no particular order) is defined as a hybrid manufacturing process. Hybrid machines may couple a LENS (Laser Engineered Net Shaping) AM process with a high-axis milling center to enable AM on curved surfaces.

In a hybrid manufacturing process, the interaction between SM and AM may be analyzed, for example, when planning the layout and removal of supporting/scaffolding material410,420generated by the AM process to create the NNS126. The AM process may generate the support volume410,420to sustain the manufactured part (e.g., NNS126) so that it does not collapse under its own weight as material is added during the AM process. The resulting NNS126(e.g., the 3D part400along with the support volume410,420) may then be manually post-processed to remove the support volume410,420and then finish the 3D part400. It is possible that with some AM process plans, the support volume410,420may be placed at locations that are inaccessible to the subtractive tool assemblies160used in the SM process. Furthermore, the geometry of the part400, the support volume410,420, and the subtractive tool assembly160may create a complex space of feasible (e.g., non-colliding) tool configurations (e.g., positions and orientations) that determine support volume removability. Therefore, the problem of removing AM support volume410,420in a SM process is a spatial planning problem involving the analysis of the tool's feasible configurations against a dynamic NNS126that is updated whenever a support volume410,420is removed. The following description focuses on SM operations that remove previously generated AM support volume410,420.

Inaccessibility Measure Field

The accessibility analysis for imposing support volume accessibility constraints through multi-axis machining is provided below. For the subtractive tool assembly160, T=(H∪K) can operate with up to six degrees of freedom (e.g., three translations and three rotations) available for a rigid body, where H and K represent the holder162and the cutter164, respectively, Ω represents the 3D part400, F represents the substrate140(and other fixtures), and S represents the support volume410,420.

Mathematically, the configuration space (C-space) of rigid motions may be represented as C=3×SO(3); SO(3) refers to the group of 3×3 orthogonal transformations that represent spatial rotations. The inaccessibility measure field (IMF) may be defined over the 3D design domain fIMF:3→for each given tool assembly T and orientation R∈Θ, where available orientations for the tool T is Θ⊂SO 3, as the pointwise minimum of shifted convolutions for different choices of sharp points (which depends on T):

fIMF⁢(x;O,T,K,R):=mink∈Kvol[O⋂(R,x)⁢(T-k)].(10)
where point x∈O, and obstacle O=Ω∪F. There are two independent transformations in effect. First, the shift T→(T−k) in Equation 10 may try different ways to register the translation space with the design domain, by changing the local coordinate system to bring different sharp points to the origin. Second, the rotation (T−k)→(RT−Rk) followed by translation (RT−Rk)→(RT−Rk)+x may bring the candidate sharp point (new origin) to the query point x∈Ω.

The same effect can be obtained by querying the convolution at t=(x−Rk) so that the rigid transformation (R, t) brings the sharp point in contact with the query point: (R, t)k=Rk+t=Rk+(x−Rk)=x, as expected. The IMF may thus be computed as follows:

fIMF⁢(x;O,T,K,R)=mink∈K(1O*1~RT)⁢(x-Rk).(11)
Physics-Based Sensitivity Field

For a given physical quantity of interest φ, a topological sensitivity field (TSF) defined at every point x of the design Ω may be determined to measure the change in φ if an infinitesimally small amount of material is removed from that point. TSF can be defined as:

TSF⁡(x;Ω):=limϵ→0+φ⁡(Ω-Bϵ(x))-φ⁡(Ω)vol[Ω⋂Bϵ(x)],(12)

B∈(x)⊂Ω is a small 3D ball of radius ∈→0+centered at a given query point x∈Ω. The numerator of the limit evaluates the (e.g., presumably infinitesimal) change in φ(Ω) when the candidate design is modified as Ω→(Ω−B∈(x)) (e.g., by puncturing an infinitesimal cavity at the query point). The denominator vol[Ω∩B∈(x)]=O (∈3) as ∈→0+measures the volume of the cavity.

TSF may be used in topology optimization where the material is removed from regions with lower TSF values. However, TSF has not previously been used in the context of spatial planning.

Physics-Aware Automatic Spatial Planning

One of the challenges in automated spatial planning for subtractive and hybrid manufacturing is considering the impact of the physical forces. Examples of these forces can be the contact forces of the subtractive tool assembly160with the NNS126at removal points or gravity when the sacrificial support volume410,420is connecting the 3D part400to the substrate140held by the fixture166. Given the two fields IMF and TSF, a physics-aware IMF (PIMF) may be defined to find accessible regions with the least negative impact on the work-piece, and subsequently generate automated manufacturing plans that are feasible and practical. Mathematically, PIMF can be written as:
PIMF(x;Ω):=w1IMF(x;Ω)+(1−w1)TSF(x;Ω),  (13)

Both IMF and TSF may be normalized, and w1may be from about 0.1 to about 0.9, from about 0.2 to about 0.8, from about 0.3 to about 0.7, or from about 0.4 to about 0.6 (e.g., about 0.5).

Physics-Aware Automatic Support Removal Planning for Hybrid Manufacturing

Automatic support volume removal planning is an example of spatial manufacturing planning, where given a set of tool assemblies160, tool orientations, and fixturing devices166, a greedy algorithm may be constructed to remove the support volume410,420while ensuring that the NNS126remains attached to the substrate140held by the fixturing device166until the last support volume410,420is removed. In other words, a sequence of support removal may be determined by selecting the most efficient tool160, orientation, and fixture166while ensuring that NNS126and/or 3D part400does not prematurely detach from the substrate140and fall under its weight. Subsequently, the TSF may be determined, which captures the change in the overall structural stiffness if material is (e.g., hypothetically) removed from each point in NNS126. To find the total accessible regions Siaccfor each tool Ti, i=1, . . . , nT, orientation Rij(jthorientation of the ithtool), and fixture166, the IMF with respect to non-sacrificial obstacle O=Ω∪F may be determined according to Equation 11. This is a condition to prevent a collision between the selected tool160in a particular orientation with the NNS126and fixturing devices166. The accessible support volume regions for each tool160and orientation can be written as:
iacc⊆={∀x∈: fIMF(x;Ω,F,Ti,Ki,Rij)≤τacc}.(5)  (14)

where τaccis a small threshold value given the numerical errors from discretization of models. To find the next step in removing the sacrificial support volume410,420, the near-net IMFs fIMF(x; Ω, S, F, Ti, Ki, Rij) may be determined for each tool160and its available orientations over the NNS126to find removable support volume Sito ensure no collision between the tool Tiunder orientation Rijand the remaining support volume410,420. Subsequently, the TSF may be augmented with these near-net IMFs, and the following PEW may be determined:
PIMFij:=w1fIMF(,F,Ti,Ki,Rij)+(1−w1)fTSF(,F,Ti,Ki,Rij),  (15)

Considering a maximum allowed removal volume and a threshold level-set value τrem, the removable support volume for the tool Timay be determined under orientation Riij:
remij⊆acci={∀x∈: PIMFij≤τrem}.  (16)

FIG.11depicts a portion of the 3D printing system100, according to an embodiment. More particularly,FIG.11shows a support volume removal setup with 3 different subtractive tool assemblies160A-160C and a plurality of (26) different subtractive tool orientations. In this example, the first subtractive tool assembly160A has 14 different orientations, the second subtractive tool assembly has 6 different orientations, and the third subtractive tool160C has 6 different orientations.FIG.11also shows another example of the 3D part1210, the substrate (i.e., build platform)140, the fixturing device166holding the substrate140.

FIG.12depicts another example of the NNS1200with the substrate140, according to an embodiment. The NSS1200includes the 3D part1210and the support volume1220.

FIGS.13A-13Edepict different fields that are computed for the first subtractive tool assembly160A (T1) and its first orientation R11, according to an embodiment. More particularly,FIG.13Ashows the IMF with obstacle O=Ω∪F for T1and R11.FIG.13Bshows the IMF with obstacle N=NÅF.FIG.13Cshows the deformation field on the NNS1200.FIG.13Dshows the TS field on the support volume1220.FIG.13Eshows the physics-aware IMF for T1and R11(PIMF11).

FIGS.14A-14Edepict progressive removal of the support volume1220from the NSS1200to yield the 3D part1210, according to an embodiment. In this particular example, the structure removal plan has/uses τacc=0.025 and τrem=0.1. InFIG.14A, the first subtractive tool assembly160A has removed 19.78% of the support volume1220. InFIG.14B, the first subtractive tool assembly160A has removed an additional 31.59% of the support volume1220. InFIG.14C, the second subtractive tool assembly160B has removed an additional 29.57% of the support volume1220. InFIG.14D, the third subtractive tool assembly160C has removed an additional 13.52% of the support volume1220. InFIG.14E, a fourth subtractive tool assembly160D has removed another 2.24% of the support volume1220. As a result, the 3D part1210remains. Other heuristics or quantities of interest such as the time or cost of each subtractive tool assembly160A-160D, reorientation, or different physics can also be added to the proposed framework to construct more informed manufacturing plans. Further, motion planning tools such as an OMPL can be used to increase the accuracy of generated plans.

FIG.15depicts a flowchart of a method1500for planning for removal of the support volume1220in hybrid manufacturing, according to an embodiment. An illustrative order of the method1500is provided below; however, one or more steps of the method1500may be performed in a different order, combined, split into sub-steps, repeated, or omitted without departing from the scope of the disclosure. One or more steps of the method1000may be performed using the computing system190.

The method1500may include receiving the near-net shape1200, as at1502. The representation may be received by (and/or provided to) the computing system190. The representation may also or instead include the 3D part1210and/or the support volume1220. The representation may also or instead include the subtractive tool assembly160.

The method1500may also include calculating a measure of inaccessibility of the support volume1220by the at least one subtractive tool assembly160, as at1504. The measure of inaccessibility may be calculated using the computing system190. The measure of inaccessibility is defined above.

The method1500may also include calculating a measure of change in a physical quantity of interest with respect to a change in the near-net shape, as at1506. The measure of change may be calculated by the computing system190. The physical quantity of interest may be or include deformation, strain energy, stress, strain, buckling, thermal conduction, thermal convection, etc. The change may be or include a hypothetical change. The change may be smaller than a predetermined size. For example, the change may be infinitesimal.

The method1500may also include constructing a physics-aware inaccessibility measure based at least partially upon the measure of inaccessibility, the measure of change, or both, as at1508. The physics-aware inaccessibility measure may be constructed using the computing system190. The physics-aware inaccessibility measure may be constructed by combining the measure of inaccessibility and the measure of change. The physics-aware inaccessibility measure indicates a removability (i.e., an ability to remove) of a region of the support volume1220from the near-net shape1200.

The method1500may also include creating a plan to remove a region of the support volume1220based at least partially upon the physics-aware inaccessibility measure, as at1510. The plan may be created using the computing system190. More particularly, this step may include creating a plan to remove the region of the support volume1220with the at least one subtractive tool assembly160.

The method1500may also include building the near-net shape1200with the 3D printing system100, as at1512. The near-net shape1200may be built based at least partially upon the plan.

The method1500may also include removing the support volume1220from the near-net shape1200with the 3D printing system100, as at1514. More particularly, this may include removing the accessible support volume1220from the near-net shape1200using the subtractive tool assembly160. This may yield the 3D part1210.

Notwithstanding that the numerical ranges and parameters setting forth the broad scope of the present teachings are approximations, the numerical values set forth in the specific examples are reported as precisely as possible. Any numerical value, however, inherently contains certain errors necessarily resulting from the standard deviation found in their respective testing measurements. Moreover, all ranges disclosed herein are to be understood to encompass any and all sub-ranges subsumed therein. For example, a range of “less than 10” may include any and all sub-ranges between (and including) the minimum value of zero and the maximum value of 10, that is, any and all sub-ranges having a minimum value of equal to or greater than zero and a maximum value of equal to or less than 10, e.g., 1 to 5.

While the present teachings have been illustrated with respect to one or more implementations, alterations and/or modifications may be made to the illustrated examples without departing from the spirit and scope of the appended claims. For example, it may be appreciated that while the process is described as a series of acts or events, the present teachings are not limited by the ordering of such acts or events. Some acts may occur in different orders and/or concurrently with other acts or events apart from those described herein. Also, not all process stages may be required to implement a methodology in accordance with one or more aspects or embodiments of the present teachings. It may be appreciated that structural objects and/or processing stages may be added, or existing structural objects and/or processing stages may be removed or modified. Further, one or more of the acts depicted herein may be carried out in one or more separate acts and/or phases. Furthermore, to the extent that the terms “including,” “includes,” “having,” “has,” “with,” or variants thereof are used in either the detailed description and the claims, such terms are intended to be inclusive in a manner similar to the term “comprising.” The term “at least one of” is used to mean one or more of the listed items may be selected. Further, in the discussion and claims herein, the term “on” used with respect to two materials, one “on” the other, means at least some contact between the materials, while “over” means the materials are in proximity, but possibly with one or more additional intervening materials such that contact is possible but not required. Neither “on” nor “over” implies any directionality as used herein. The term “conformal” describes a coating material in which angles of the underlying material are preserved by the conformal material. The term “about” indicates that the value listed may be somewhat altered, as long as the alteration does not result in nonconformance of the process or structure to the illustrated embodiment. The terms “couple,” “coupled,” “connect,” “connection,” “connected,” “in connection with,” and “connecting” refer to “in direct connection with” or “in connection with via one or more intermediate elements or members.” Finally, the terms “exemplary” or “illustrative” indicate the description is used as an example, rather than implying that it is an ideal. Other embodiments of the present teachings may be apparent to those skilled in the art from consideration of the specification and practice of the disclosure herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the present teachings being indicated by the following claims.