Hybrid manufacturing system and method for reducing inaccessible support structures

Abstract

To provide a hybrid manufacturing system and method that reduce inaccessible support structures.SOLUTION: A geometry model is defined of a part targeted for a manufacturing operation that includes an additive process followed by a subtractive process. Potential build orientations of the geometry model used in the additive process are defined, as are one or more removal tools of the subtractive process. For each of the potential build orientations, supports that are used by the additive process at the orientation are determined.EFFECT: One of the build orientations is selected that minimizes portions of one of the supports that are inaccessible via at least one of the removal tools.SELECTED DRAWING: Figure 15

Description

[Technical field]

[0001] STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT This invention was made with Government support under Contract No. G011.3809.00 awarded by the Defense Advanced Research Projects Agency (DARPA). The Government has certain rights in this invention. Summary of the Invention

[0002] The embodiments described herein include a hybrid manufacturing system that reduces inaccessible support structures. In one embodiment, a model of a part is defined, and the part is subjected to a manufacturing operation that includes an additive manufacturing process followed by a subtractive manufacturing process. A plurality of potential build orientations for the additive manufacturing process are defined, similar to how one or more removal tools for the subtractive manufacturing process are defined. For each orientation of the plurality of potential build orientations, a support structure to be used by the additive manufacturing process in that orientation is determined. A build orientation is selected from the plurality of potential build orientations in which the cost of inaccessible portions of the support structure is minimized by a set of subtractive tools. The selected build orientation is used to build the part using the additive manufacturing process and at least one tool in the set of tools for the subtractive manufacturing process.

[0003] In another embodiment, a manufacturing operation is defined that includes an additive manufacturing process followed by a subtractive manufacturing process. The subtractive manufacturing process uses a removal tool. A model of a part that is to be subjected to the manufacturing operation is determined. The manufacturing process is modeled for a plurality of potential build orientations of the additive manufacturing process. For each orientation of the plurality of potential build orientations, a support is determined that is used by the additive manufacturing process in that orientation. One of the plurality of potential build orientations that reduces a cost of inaccessible portions of the support structure is selected. The selected build orientation is used to build the part using the additive manufacturing process.

[0004] These and other features and aspects of various embodiments may be understood in view of the following detailed discussion and accompanying drawings. [Brief description of the drawings]

[0005] The following discussion will refer to the following figures, in which the same reference numbers may be used to identify similar / identical components in the various figures. The drawings are not necessarily drawn to scale.

[0006] [Figure 1] FIG. 1 illustrates aspects of hybrid manufacturing, according to an illustrative embodiment.

[0007] [Diagram 2] FIG. 1 is an illustration of a simplified part and removal tool used for accessibility analysis in accordance with an illustrative embodiment;

[0008] [Diagram 3] FIG. 3 illustrates a near net shape of the part shown in FIG. 2 with supports according to an exemplary embodiment.

[0009] [Figure 4] FIG. 4 illustrates a diagram illustrating the results of an inaccessibility analysis of the shapes shown in FIG. 3 in accordance with an illustrative embodiment. [Diagram 5] FIG. 4 illustrates a diagram illustrating the results of an inaccessibility analysis of the shapes shown in FIG. 3 in accordance with an illustrative embodiment.

[0010] [Figure 6] 3A-3C are diagrams illustrating accessible and inaccessible supports in different build orientations of the part shown in FIG. 2 in accordance with an illustrative embodiment. [Figure 7] 3A-3C are diagrams illustrating accessible and inaccessible supports in different build orientations of the part shown in FIG. 2 in accordance with an illustrative embodiment. [Figure 8] 3A-3C are diagrams illustrating accessible and inaccessible supports in different build orientations of the part shown in FIG. 2 in accordance with an illustrative embodiment. [Figure 9] 3A-3C are diagrams illustrating accessible and inaccessible supports in different build orientations of the part shown in FIG. 2 in accordance with an illustrative embodiment.

[0011] [Figure 10] 11 is a flowchart illustrating an automated design process in accordance with an illustrative embodiment.

[0012] [Figure 11] 11 is a graph illustrating support volume and inaccessible support volume for different build orientations for a 90 degree overhang angle, in accordance with an illustrative embodiment;

[0013] [Figure 12] FIG. 3 illustrates accessible and inaccessible supports of the part shown in FIG. 2 in an orientation that minimizes the inaccessible supports for a 90 degree overhang angle in accordance with an illustrative embodiment.

[0014] [Figure 13] 11 is a graph illustrating support volume and inaccessible support volume at different build orientations for a 45 degree overhang angle, in accordance with an illustrative embodiment;

[0015] [Figure 14] FIG. 3 illustrates accessible and inaccessible supports of the part shown in FIG. 2 in an orientation that minimizes the inaccessible supports for a 45 degree overhang angle in accordance with an illustrative embodiment.

[0016] [Figure 15] 1 is a flowchart illustrating a method, according to an example embodiment.

[0017] [Figure 16] 1 is a block diagram of a system and device according to an exemplary embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0018] The present disclosure relates to a method for planning a hybrid manufacturing process. Hybrid manufacturing refers to a manufacturing process that combines two different processing types that are usually performed on separate and different machines, such as additive manufacturing (AM), subtractive manufacturing (SM), welding, deformation / bending, etc. Additive manufacturing includes processing processes such as fused deposition modeling, stereolithography, selective laser sintering, etc., commonly referred to as 3D printing. Additive manufacturing can create complex structures with customized material gradations, such as complex and efficient filling structures. Subtractive manufacturing is useful for manufacturing high-precision mechanical parts. Although additive manufacturing offers a wide degree of freedom in customizing the internal structure of a part, subtractive manufacturing can achieve finer precision and higher surface quality specifications than currently possible with additive manufacturing. Such precision and quality specifications are necessary, for example, for functional interfaces that require high tolerance fit and assembly.

[0019] Historically, the production of parts from raw materials or materials has involved these two distinct, but combinable, manufacturing processes. Subtractively manufacturing a part involves the incremental removal or machining of material from a raw material until the part has the desired form within specified tolerances. The raw material is often removed by turning, drilling, or milling. Additively manufacturing a part involves the incremental addition or deposition of material, often successive layers, onto the part being produced until the part approximates the intended shape and size as used with three-dimensional (3D) printing by Fused Deposition Modeling (FDM).

[0020] For example, metal additive manufacturing is sometimes used instead of traditional metal processing methods such as casting, but it offers more freedom in creating complex forms and can produce near-net shapes that are close enough to the final part. However, the functional interface can still be completed using subtractive manufacturing to meet tolerance and surface quality specifications. Often, in layer-by-layer additive manufacturing processes such as fused deposition modeling (FDM), support material is printed on layers below the near-net shape to allow the upper layers to extend beyond the width of the lower layers without sagging due to gravity. In such cases, post-processing with subtractive manufacturing may be required to remove the support material.

[0021] The embodiments described herein include a method and system for automatically optimizing build orientation in additive manufacturing based on support structure accessibility. This is a systematic approach to automatically optimizing build orientation while ensuring the possibility of removing sacrificial support structures by subtractive machining processes (e.g., milling) in terms of "accessibility" to all points of the supports. The optimization is done without imposing any artificial constraints on the geometric complexity of the part, the geometry of the supports, the cutting tools, and the fixtures, given a "set" of cutting tool assemblies, fixture orientations, and substrate. The approach explores an efficient and effective design space, but allows for the near net shape (part + supports) to be fabricated using additive manufacturing methods, and finds an optimal build orientation such that it can be post-processed using well-established subtractive machining equipment.

[0022] As mentioned above, additive manufacturing techniques can produce parts with complex geometries by adding material layer by layer. There has been growing interest in additive manufacturing, and specifically metal additive manufacturing, due to its ability to exploit geometric complexity to engineer high performance, lightweight designs for applications such as aerospace, automotive, and medical. However, in most metal additive manufacturing techniques, such as powder bed fusion, sacrificial support structures are required in the overhanging areas to bleed off excess heat and ensure successful construction of the near net shape (part + supports). The overhanging area is often specified by the overhang angle, which is a measure of the maximum amount that one layer can extend beyond the layer on which it is deposited without requiring support. For example, if a deposition process extrudes material approximately 1 mm in diameter, an overhang angle of 45° would allow the extruded layer to extend approximately 1 mm beyond the layer below without requiring a support structure below. Because the support structures are typically removed using a subtractive machining process, such as milling, the supports need to be "accessible" by available cutting tools and fixtures.

[0023] A simplified diagram of an additively manufactured part with a support structure is shown in the diagram of FIG. 1. An additively manufactured part 100 is built on a fixture 102. A support 104 is built with the part 100 to ensure that the top flange 100a is built to the correct shape. After the additive manufacturing process is completed, a removal tool 106 is used to remove the support 104. The removal tool 106 may include any combination of tools that perform cutting, grinding, polishing, polishing, slicing, engraving, etc., and any reference herein to "cutting" or "cutting tool" may apply equally to any of these types of removal tools. It should also be noted that the terms "tool" and "tool assembly" may be used interchangeably herein, as the tool may include non-cutting components (e.g., chucks, bearings, etc.) that may limit the area in which the tool can be used. It should be noted that the removal tool 106 may be oriented differently than shown here in order to leave the bottom of the flange 100a smooth.

[0024] There is a large amount of published literature on build orientation optimization, which concerns overall support volume, build time, surface quality, volumetric error, and mechanical strength. However, to the best of our knowledge, there is no systematic approach to optimizing build orientation based on support accessibility for a common set of tool assemblies, fixtures, and support types.

[0025] Subtractive manufacturing techniques such as multi-axis machining have been widely used to produce high quality, reproducible parts across multiple industries, including aerospace and automotive. Subtractive manufacturing begins with a raw stock of material, which is gradually carved out until the desired shape appears. In hybrid models, additive manufacturing processes are first used to obtain a near net shape, but temporary supports may be added to obtain this shape. Subtractive manufacturing processes may be used to remove at least the supports and also to bring certain areas of the near net shape to final dimensional tolerances, for example, by precision machining of mounting interfaces.

[0026] Accessibility analysis can be used to impose constraints on support accessibility with multi-axis machining. For further details, see Amir M. Mirzendehdel, Morad Behandish, and Saigopal Nelaturi - "Topology optimization with accessibility constraint for multi-axis machining," Computer Aided Design, 122 (May, 2020), 102825. Assume that the tool assembly T can move with all six rigid body degrees of freedom available (three translations and three rotations), where T = (H ∪ K), H and K are the holder and cutter, respectively. Let Ω denote the part, F the substrate (and other fixtures), and S the support structure.

[0027] The configuration space of rigid body motion is mathematically given by

number

number

number

[0028] Note that point x∈N0, N0=Ω0∪S denotes the near-net shape produced from the design domain Ω0 and its corresponding support structure S, and obstacle O=Ω0∪F. In practice, there are two independent transformations: 1) the shift T→(Tk) in equation (1) is to try different ways of aligning the translation space with the design domain by changing the local coordinate system and moving different cusps to the origin, and 2) the rotation (Tk)→(RT-Rk) followed by the translation (RT-Rk)→(RT-Rk)+x brings the candidate cusp (new origin) to the query point x∈N0.

[0029] The same effect can be obtained by querying the convolution at t:=(x-Rk), so that the rigid transformation (R,t) predictably brings the cusp to the query point: (R,t)k=Rk+t=Rk+(x-Rk)=x. The IMF is then computed as follows:

number

[0030] In general, the IMF is a continuous spatial field that quantifies the extent to which different points in the design domain are inaccessible by a set of one or more tools for a subtractive machining process. Equation (1) can be further extended to consider multiple removal tools. This may include separate removal machines, or it may include a single machine with multiple interchangeable parts, e.g., cutting heads of different sizes / shapes. T ≧1, and the available tool assembly Ti =(H i ∪K i ) where 1≦i≦n T Then, the combined IMF is calculated by applying different minimization operations to different tools to identify the tool with the minimum volume interference at the available orientations and tips, as shown in the following equation (3). IMF (x;O,Ti,K i ) is calculated from equation (2).

number

[0031] For all query points in the design domain (f IMF A field indicating the magnitude of inaccessibility for the plurality of subtractive tools in (x;O) can be calculated as the minimum of the magnitude of inaccessibility for different configurations in which the query point can be removed by the subtractive tools of the subtractive tool assembly as defined in equation (3). The configurations for which the minimum is calculated include at least one of the displacements that would bring a tip on the subtractive tool into contact with the query point and the tool orientations available to the tool assembly. The magnitude of inaccessibility is defined by the amount of collision between the subtractive tool and the intermediate part design.

[0032] Optimizing support accessibility based on build orientation can be challenging. For example, minimizing the volume of support structures is not necessarily the same as minimizing the volume or cost of inaccessible supports. For example, the volume of inaccessible supports can be larger and reduced with the overall volume of supports. Also, calculating a large number of build orientations can be time and computationally intensive, so the analysis needs to be efficient and parallelizable. Another issue to consider when optimizing build orientation is that there are many types of support shapes (e.g., beam or tree-like structures) and overhang angles (e.g., 45° or more and 90° or less), depending on the additive manufacturing process. If the overhang angle is 90°, there can be no parts that extend beyond the layer below. Also, the shape of the cutter in the subtractive manufacturing process cannot be ignored. Therefore, translational optimization is difficult unless all possible contact configurations are considered and boundary points are treated differently from interior points.

number

[0033] When optimizing the build orientation, the geometry of the tool, substrate, and fixture cannot be ignored in a general setting. Also, the analysis is highly nonlinear; i.e., small changes in x∈N can dramatically change the accessibility at a far-away point y∈R. In FIG. 2, the diagram shows a simplified part 200 used for accessibility analysis according to an exemplary embodiment. The part is shown on a build substrate 202, and a removal (e.g., cutting tool) 204 is shown in four different exemplary orientations, namely, 0°, 90°, 180°, and 270°. However, the removal 204 may be rotated to any orientation angle within this range. In FIG. 3, the diagram shows a near-net part 300 produced by additive manufacturing with supports 300a at θ build =0°. The near net shape IMF of part 300 is shown in FIG.

[0034] The accessibility analysis of a near net part 300 produced by additive manufacturing is shown in Figures 4 and 5. Figure 4 is the IMF for the near net shape and Figure 5 is the IMF for the supports. The diagrams in Figures 6-9 show accessible supports (one-way diagonal hatching) and inaccessible supports (cross hatching) for build orientations of 0°, 30°, 135°, and 200°, all for an overhang angle of 45°. For a build orientation of 135° (Figure 8), there are no inaccessible supports. It should be noted that some of the process parameters other than the selected tool (e.g., maximum overhang angle, fixture, deposition rate, etc.) can affect the geometry of the supports and their accessibility.

[0035] These process parameters may be fixed for each build orientation or may vary with the build orientation and / or tool selection. For example, it may be possible to build using a range of overhang angles, but a larger overhang may affect some quality of the part, such as surface smoothness, which may be acceptable in some cases but not others. In such a scenario, the overhang angle may be a parameter that is relaxed or optimized, along with the accessibility of the supports. Another process parameter that may be varied is the selection of different available fixtures to secure the part during its manufacture. For example, a larger fixture may be preferred for reasons such as stability, while a smaller fixture may allow more areas of the part and supports to be accessed by the tools used in subtractive manufacturing. However, a smaller fixture may be less stable and result in a lower quality of the final part.

[0036] IMF can be used to set constraints on accessibility to support structures. Some frameworks, methods, and systems can enable automatically optimizing build orientations, where the resulting shapes are guaranteed to be manufacturable using additive manufacturing processes and post-processed using subtractive manufacturing processes. At a high level, the proposed automated design process is as shown in FIG. 10. The process iterates through a number of build angles, specifically build orientations Θ, as indicated by the loop limit 1000. build ⊆SO3. For each angle analyzed, a support structure is generated (block 1001), e.g., mathematically modeled using a format that matches the geometry of the part. This may involve repositioning the substrate / fixture relative to the part and generating support structures based on the maximum overhang angle and the type of support (e.g., beam, tread-like, etc.).

[0037] After the support structures are generated, an accessibility analysis 1002 is performed. This analysis 1002 may involve building a configuration space (C-space) of the part, substrate, and tool assembly, extracting tool rotations in C-space, and building a field indicating the magnitude of inaccessibility. After the accessibility analysis 1002, a target value is calculated (block 1003). This calculation 1003 may involve, for example, calculating the accessible support volume, and other objective cost functions, such as the overall support volume, build time, etc. After all angles have been analyzed, the process loops out of block 1000 via path 1004. An optimal build angle is then determined (block 1005) based on, for example, minimizing the cost of inaccessible supportive parts, accessibility to supportive parts, and other objectives. In some cases, the optimal build angle may not minimize the cost of inaccessible supportive parts, but the cost may be reduced compared to a non-optimized variant. For example, a build orientation may be possible that results in zero inaccessible supportive parts, but that orientation may have other disadvantages (e.g., total supportive volume, build quality). Thus, an orientation is selected that does not result in zero inaccessible parts, but still reduces them.

[0038] These five activities should not be performed in isolation, as they involve understanding the geometric, topological, material, and physical aspects of available manufacturing capabilities. Now consider part 200, shown in Figure 2. Part 200 has an overhang angle α=45° and a set of build orientations Θ build ⊆SO3,

number

[0039] A multi-axis cutting tool 204 is also shown in Figure 2. The set of tool orientations are:

number

[0040] The graph in FIG. 11 shows the volume of supports and the volume of inaccessible support for different build orientations and with a modest 90° overhang angle. In this example, the cost is assumed to be equivalent to the volume of inaccessible support, but this example can be modified and adapted to account for other cost measures, such as removal tool cost, removal time, etc. Also, there is no orientation that results in zero inaccessible support volume. The orientation that minimizes the volume of inaccessible support is the θ build = 305°. build The supports for θ = 305° are shown in the diagram of FIG. 12. The graph in FIG. 13 shows the support volume and inaccessible support volume for an overhang angle of 45° and various different build orientations. There is no inaccessible support volume at build angles of 45°, 135°, 225°, 295°, 305°, 310°, and 315°. However, the set of orientations with accessible supports can be further optimized based on other competing objectives, such as overall cost / total support volume. In this case, the Pareto optimal solution is θ build = 135°. build = 135° is shown in the diagram of FIG.

[0041] In FIG. 15, a flow diagram illustrates a method according to an example embodiment. The method includes defining a model of a part that is to be subjected to a manufacturing operation, including an additive manufacturing process followed by a subtractive manufacturing process (block 1500). The model may define the part geometry, tolerances, materials, etc. A plurality of potential build orientations of the additive manufacturing process are defined (block 1501). One or more tools of the subtractive manufacturing process are also defined (block 1502). Block 1503 represents iterating through each of the plurality of potential build orientations where a support structure is determined to be used by the additive manufacturing process in that orientation (block 1504).

[0042] One of a plurality of potential build orientations is selected (block 1505). The selected build orientation minimizes the cost of portions of the support structure that are inaccessible via one or more removal tools. Note that the term "minimal" in this context may not necessarily be an absolute or global minimum, but may be a local minimum, Pareto optimal, etc. Also, depending on the granularity of the analyzed build orientation, the local or global minimum cost may be an orientation that has not been analyzed, and perhaps it can be estimated that the selected orientation will have a minimum cost that is near the local or global minimum. The selected build orientation may also be selected by jointly minimizing other factors along with the cost of the inaccessible support portions, such as the cost of the selected removal tool and / or the total volume of the support structure. The selected build orientation is used to build the part using additive and subtractive machining processes (block 1506).

[0043] The above-mentioned methods and processes can be implemented on computer hardware, e.g., workstations, servers, as known in the art. In FIG. 16, a block diagram illustrates a system and computing device 1600 that can be used to implement the method according to an exemplary embodiment. The device 1600 includes one or more processors 1602, such as a central processing unit, co-processor, digital signal processor, etc. The processor 1602 is coupled to memory, which may include both random access memory 1604 and persistent storage 1606, via one or more input / output buses 1608. Other general-purpose or special-purpose hardware may be coupled to the bus 1608, such as a graphics processing unit (GPU) 1611 and a network interface 1612. It should be noted that the functionality of the device 1600 described below may be implemented across multiple devices, e.g., via a client-server configuration, clustered computing, cloud computing, etc.

[0044] The network interface 1612 facilitates communication with two or more manufacturing devices 1616 capable of performing additive and subtractive manufacturing operations over a network 1614 using wired or wireless media. Examples of manufacturing devices 1616 include 3D printers, selective laser metal sintering machines, computer numerically controlled (CNC) mills, CNC lathes, CNC laser cutters, CNC water cutters, etc. Data may also be transferred to the manufacturing devices 1616 using a non-network data transfer interface, for example, via portable data storage drives, point-to-point communications, etc.

[0045] The apparatus 1600 includes software 1620. The software 1620 includes, for example, an operating system 1622 and drivers 1624 that facilitate communication between user-level programs and the hardware. The software 1620 includes a process planner 1626 that facilitates optimizing the build orientation of a part under additive manufacturing to minimize inaccessible supports that are subsequently removed by subtractive manufacturing processing processes. Support inaccessibility may be the only optimization objective or may be optimized in conjunction with other objectives such as support volume and subtractive manufacturing implementation costs. The process planner 1626 interfaces with a geometry database 1634 that includes part geometry and other factors (e.g., build tolerances, materials, etc.). The process planner 1626 also interfaces with a manufacturing database 1634 that provides information such as tool geometry and cost, fixture geometry, and additive manufacturing parameters (e.g., allowable overhang angle). The resulting build orientation and subtractive manufacturing removal operations may be stored as a process plan, for example in plan database 1630. The plan may be communicated to one or more of the manufacturing tools 1616 to manufacture the part according to the plan.

[0046] The above-described systems and methods can automatically optimize build orientations based on support structure accessibility. This can be implemented within a process planner that can automatically find the best additive manufacturing process and support generation strategy based on support accessibility. For example, such a planner can automatically find a Pareto-optimal build orientation based on support structure accessibility and other competing objectives.

[0047] Unless otherwise indicated, all numbers expressing feature sizes, quantities, and physical properties used in the specification and claims are to be understood in all instances as modified by the term "about." Thus, unless otherwise indicated, the numerical parameters set forth in the foregoing specification and appended claims are approximations that may vary depending on the desired properties one of ordinary skill in the art would obtain utilizing the teachings disclosed herein. The use of numerical ranges by endpoints includes all numbers within that range (e.g., 1 to 5 includes 1, 1.5, 2, 2.75, 3, 3.80, 4, and 5), as well as any range within that range.

[0048] The various embodiments described above may be implemented using circuits, firmware, and / or software modules that interact to provide particular results. Those skilled in the art can readily implement the functionality described herein, either at a modular level or as a whole, using knowledge generally known in the art. For example, the flow charts and control diagrams illustrated herein may be used to create computer readable instructions / code for execution by a processor. Such instructions may be stored on a non-transitory computer readable medium and transferred to a processor for execution as known in the art. The structures and procedures described above are merely representative examples of embodiments that may be used to provide the functionality described above.

[0049] The foregoing description of exemplary embodiments is presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the embodiments to the precise form disclosed. Many modifications and variations are possible in light of the above teachings. Any or all features of the disclosed embodiments may be applied individually or in any combination and are not intended to be limiting but are purely exemplary. It is intended that the scope of the present invention be determined not by this Detailed Description, but rather by the Claims appended hereto.

Claims

1. Defining a model of a part to be manufactured by additive and then subtractive manufacturing processes; defining a plurality of potential build orientations for the additive manufacturing process, the plurality of potential build orientations for the additive manufacturing process being based on a plurality of build angles Θ build of a part relative to a build substrate or build fixture, where Θ build ⊂ SO3; defining a set of one or more tools for the subtractive machining process; determining a support structure for the additive manufacturing process for each of the plurality of potential build orientations; selecting at least one of the plurality of potential build orientations that minimizes cost of portions of the support structure that are inaccessible by the set of one or more tools; using the at least one selected build orientation to build the part using the additive manufacturing process and using at least one tool in the set of tools for the subtractive manufacturing process to remove the support structure; A method comprising:

2. The method of claim 1 , wherein the at least one selected build orientation minimizes the cost of the portion of the support structure and the cost of all support structures together.

3. The method of claim 2 , wherein the cost is based on a volume of the support structure.

4. The selected build orientation is a field indicating a magnitude of inaccessibility of the set of one or more tools for the subtractive machining process; The model of the part; and a model of the fixture used to secure the part and the supports during the subtractive machining process; and The method of claim 1, wherein the

5. 5. The method of claim 4, wherein the inaccessibility magnitude field comprises a continuous spatial field quantifying the extent to which different points within a design space are inaccessible by the set of one or more tools for the subtractive machining process.

6. the set of one or more tools comprises a plurality of tools; the inaccessibility magnitude field is calculated as a minimum of the inaccessibility magnitude fields for each tool of the plurality of tools; The method according to claim 5.

7. 7. The method of claim 6, wherein a field indicating the magnitude of inaccessibility for the multiple tools for every query point in the design space is calculated as a minimum of the magnitude of inaccessibility for different configurations that can remove a query point by each tool of the multiple tools.

8. The method of claim 7 , wherein the configurations for which the minimum is calculated include at least one of a displacement that brings a tip of each tool into contact with the query point and a tool orientation available for each tool.

9. 8. The method of claim 7, wherein the magnitude of inaccessibility is defined by an amount of collision between each tool and the model of the part and a model of a fixture used to secure the part and the supports during the subtractive machining process.

10. the set of one or more tools includes two or more tools; and determining, for each of the potential build orientations, a selected set of the two or more tools that affects a cost of the inaccessible portion of the support structure. The method of claim 1.

11. The selected build orientation is a cost associated with the set of tools for the subtractive machining process; and the cost of the inaccessible portion of the support structure; and 11. The method of claim 10, further selected based on jointly minimizing:

12. 2. The method of claim 1, further comprising: for each of the potential build orientations, determining a selected fixture from a plurality of available fixtures on which the part may be built, the selected fixture impacting a cost of the inaccessible portion of the support structure.

13. Defining a manufacturing operation for a part including an additive machining process followed by a subtractive machining process using a subtractive tool; modeling the manufacturing operation for a plurality of potential build orientations for the additive manufacturing process, the plurality of potential build orientations for the additive manufacturing process based on a plurality of build angles Θ build of a part relative to a build substrate or build fixture, where Θ build ⊂ SO3; for each of the plurality of potential build orientations, determining a support for the part to be used by the additive manufacturing process in that orientation; selecting one of the plurality of potential build orientations that reduces costs of inaccessible portions of the support; and using the selected build orientation and using the removal tool of the subtractive manufacturing process to build the part using the additive manufacturing process; A method comprising:

14. The selected build orientation is a field indicating the degree of inaccessibility of the removal tool; The model; a model of a fixture used during the subtractive machining process to secure the part and the supports; The method of claim 13, wherein the

15. 15. The method of claim 14, wherein the inaccessibility magnitude field comprises a continuous spatial field quantifying how inaccessible different points within a design space are by the removal tool for the subtractive machining process.

16. the removal tool comprises two or more removal tools; and determining, for each of the potential build orientations, a tool of the two or more removal tools that affects a size of the inaccessible portion of the support structure as a selected tool. The method of claim 13.

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