Method and device for forming overhung structure by metal-drip discharging three-dimensional (3D) object printer
Patent Information
- Application Number
- JP2022002487
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2021-01-27
- Filing Date
- 2022-01-11
- Publication Date
- 2025-01-22
AI Technical Summary
Existing 3D metal printers struggle to form angled surfaces greater than 45° without the need for support structures, limiting the complexity and design possibilities of printed objects.
A method and system for a 3D metal object printer that identifies sloped edges and generates machine-compatible instructions to form beveled edges, allowing angled surfaces greater than 45° by adjusting the operation of the metal drop ejection device and platform movement.
Enables the creation of angled surfaces exceeding 45° without requiring support structures, enhancing the design flexibility and structural integrity of 3D metal objects.
Smart Images

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Abstract
Description
Technical Field
[0001] The present disclosure relates to a molten metal ejection device used in a three-dimensional (3D) object printer, and more particularly, to the formation of overhang structures in 3D objects manufactured by those systems.
Background Art
[0002] Three-dimensional printing, also known as additive manufacturing, is a process of creating three-dimensional solid objects from digital models of virtually any shape. Many three-dimensional printing techniques use an additive process in which an additive manufacturing device forms successive layers of a part on top of previously deposited layers. Some of these techniques use an ejection device that ejects an ultraviolet-curable material such as a photopolymer or an elastomer. The printer typically operates one or more extruders to form successive layers of a plastic material that form a three-dimensional object to be printed having various shapes and structures. After each layer of the three-dimensional object to be printed is formed, the plastic material is ultraviolet-cured and solidified, adhering the layer to the underlying layer of the three-dimensional object to be printed. This additive manufacturing method is distinguishable from conventional object formation techniques that mostly rely on the removal of material from a workpiece by a subtractive process such as cutting or drilling.
[0003] Recently, several 3D object printers have been developed that form 3D objects by ejecting droplets of molten metal from one or more ejection devices. These printers have a solid metal source, such as a roll of wire or pellets, which is fed into a heating chamber where solid metal is melted, and the molten metal flows into the chamber of the ejection device. Non-insulated wire is wound around the chamber. Current passes through a conductor, generating an electromagnetic field, which separates the meniscus of molten metal at the nozzle of the chamber from the molten metal in the chamber and propels it out of the nozzle. A platform opposite the nozzle of the ejection device is moved in an XY plane parallel to the plane of the platform by a controller-operated actuator, so that the ejected metal droplets form a metal layer of an object on the platform, and another actuator, operated by the controller, changes the position of the ejection device or platform in the vertical or Z direction, maintaining a constant distance between the ejection device and the top layer of the formed metal object. This type of metal droplet ejection printer is also known as a magnetohydrodynamic printer.
[0004] All 3D object printers must be capable of printing some portion of an unfinished object material, supported by previously printed object material, in order to form structures such as angled surfaces or overhangs. Some 3D printers using processes such as SLA or SLS use the previously printed material as a support when forming such structures. Other 3D object printers, such as object printers, construct support structures using a different material from the object material. These support structures are later removed after the object construction is complete. Extrusion 3D object printers can form overhangs and angled surfaces without requiring the construction of support structures. However, angled surfaces formed with these printers may deviate from the vertical by approximately 45° or less. It is beneficial to be able to form angled surfaces with angles greater than 45° without requiring the construction of support structures. [Overview of the Initiative]
[0005] A novel method for operating a 3D metal object printer can form angled surfaces greater than 45° without requiring the construction of a support structure. The method includes: identifying angled edges to be formed on each perimeter within a layer of the object being formed by a metal droplet ejector; generating machine-ready instructions that operate the metal droplet ejector to form the identified angled edges on each perimeter within a layer of the object being formed, using individual maximum step-out distances; and executing the generated machine-ready instructions to operate the metal droplet ejector to form angled edges on each perimeter within a layer of the object being formed.
[0006] The new 3D metal object printer can form angled surfaces greater than 45° without requiring the construction of a support structure. The 3D metal object printer includes a melting device configured to receive and melt bulk metal; an ejection head having a nozzle fluidly connected to the melting device to receive molten bulk metal from the melting device; a platform positioned opposite the ejection head; at least one actuator operably connected to the platform and at least one of the at least one ejection heads, configured to move the platform and at least one of the at least one ejection heads relative to each other; and a controller operably connected to the melting device, at least one ejection head, and at least one actuator. The controller is configured to identify angled edges to be formed around each portion of the periphery in a layer of the object being formed by the metal droplet ejector; generate machine-ready instructions to operate the metal droplet ejector to form the identified angled edges around each portion of the periphery in a layer of the object being formed, using individual maximum step-out distances; and execute the generated machine-ready instructions to operate the metal droplet ejector to form the angled edges around each portion of the periphery in a layer of the object being formed. [Brief explanation of the drawing]
[0007] The above-described aspects and other features of a method for operating a 3D metal object printer capable of forming angled surfaces greater than 45° without requiring the construction of a support structure are described below in conjunction with the attached drawings.
[0008] [Figure 1A] This graph compares empirically obtained data on the reciprocal of the droplet spacing, which is proportional to the mass of the metal droplet, with the step-out obtained by a metal droplet ejection printer.
[0009] [Figure 1B] This shows the step-out formed for the object layer.
[0010] [Figure 2] This is a flowchart illustrating a method for operating a 3D metal object printer capable of forming angled surfaces greater than 45° without requiring the construction of a support structure.
[0011] [Figure 3] This demonstrates prior art 3D metal object printers. [Modes for carrying out the invention]
[0012] To gain a general understanding of the 3D metal object printer and the environment for its operation disclosed herein, as well as the details of the printer and its operation, refer to the drawings. In the drawings, similar reference numbers represent similar elements.
[0013] Figure 3 shows one embodiment of a prior art molten metal 3D object printer 100, which may include a controller modified to produce angled surfaces that deviate by more than 45° from the vertical. In the printer of Figure 3, droplets of molten bulk metal are discharged from an ejector head 104 having a single nozzle, and the droplets from the nozzle form a swath of layers of object 108 on a platform 112. As used herein, the term “bulk metal” means conductive metal available in aggregate form, such as commonly available standard-sized wire or macro-sized pellets. A source of bulk metal 160, such as metal wire 130, is fed into the ejector head, melted, and provides molten metal to a chamber within the ejector head. An inert gas supply unit 164 provides a pressure-regulated inert gas source 168, such as argon, to the molten metal in the ejector head 104 through a gas supply pipe 144 to prevent the formation of aluminum oxide within the ejector head.
[0014] The discharge head 104 is movably mounted within the respective z-axis tracks 116A and 116B of a pair of vertically oriented members 120A and 120B. Members 120A and 120B are connected at one end to one side of the frame 124 and at the other end to each other by a horizontal member 128. An actuator 132 is mounted on the horizontal member 128 and movably connected to the discharge head 104 to move the discharge head along the z-axis tracks 116A and 166B. The actuator 132 is operated by a controller 136 to maintain the distance between the multiple nozzles (not shown in Figure 3) of the discharge head 104 and the uppermost surface of the object 108 on the platform 112.
[0015] A planar member 140 is attached to the frame 124, which may be formed of granite or other sturdy material to ensure that it provides solid support for the movement of the platform 112. Since the platform 112 is fixed to the X-axis tracks 144A and 144B, the platform 112 can move bidirectionally along the X-axis as shown in the figure. Since the X-axis tracks 144A and 144B are fixed to the stage 148, and the stage 148 is fixed to the Y-axis tracks 152A and 152B, the stage 148 can move bidirectionally along the Y-axis as shown in the figure. Actuator 122A is operably connected to the platform 112, and actuator 122B is operably connected to the stage 148. The controller 136 operates actuators 122A and 122B to move the platform along the X-axis and the stage 148 along the Y-axis, thereby moving the platform in the XY plane opposite to the discharge head 104. As droplets of molten metal 156 are ejected toward the platform 112, a swath of molten metal droplets is formed on the object 108 by performing this movement of the platform 112 in the XY plane. The controller 136 also operates the actuator 132 to adjust the vertical distance between the ejection head 104 and the layer most recently formed on the substrate, thereby facilitating the formation of other structures on the object. The molten metal 3D object printer 100 is shown in Figure 1 as operating vertically, but other alternative orientations may be used. Also, the embodiment shown in Figure 1 has a platform that moves in the XY plane and the ejection head moves along the Z axis, but other arrangements are possible. For example, the ejection head 104 may be configured for movement in the XY plane and along the Z axis.
[0016] The controller 136 may be implemented using one or more general-purpose or dedicated programmable processors that execute programmed instructions. Instructions and data required to perform programmed functions may be stored in memory associated with the processor or controller. The processors, their memories, and interface circuits constitute the controller to perform the operations described above and below. These components may be provided on a printed circuit card or as circuits in an application-specific integrated circuit (ASIC). Each circuit may be implemented on a separate processor, or multiple circuits may be implemented on the same processor. Alternatively, the circuits may be implemented as individual components or circuits provided in a very large-scale integrated (VLSI). Furthermore, the circuits described herein may be implemented in combination of processors, ASICs, individual components, or VLSI circuits. During the formation of the metallic object, image data of the resulting structure is transmitted to the processor or multiple processors for the controller 136 from a scanning system or either online or via a workstation connection for processing and generating ejector head control signals output to the ejector head 104.
[0017] The controller 136 of the molten metal 3D object printer 100 requires data from an external source to control the printer and manufacture metal objects. Generally, a three-dimensional model or other digital data model of the object to be formed is stored in memory operably connected to the controller 136. The controller may access a remote database where the digital data model is stored via a server or the like, or a computer-readable medium where the digital data model is stored may be selectively coupled to the controller 136 for access. This three-dimensional model or other digital data model is processed by a slicer implemented with the controller to generate machine-ready instructions for execution by the controller 136 in a known format, thereby operating the components of the printer 100 to form a metal object corresponding to the model. The generation of machine-ready instructions includes the generation of intermediate models, such as when a CAD model of a device is converted to an STL data model, or to other polygonal meshes or other intermediate representations. These intermediate models can be processed sequentially to generate machine instructions, such as g-code, for the printer to manufacture the device. As used herein, the term “machine-responsive instruction” means a computer language command executed by a computer, microprocessor, or controller to operate components of a 3D metal object additive manufacturing system to form a metal object on the platform 112. The controller 136 executes machine-responsive instructions to control the discharge of molten metal droplets from the discharge head 104, the positioning of the stage 148 and the platform 112, and the distance between the discharge head 102 and the uppermost layer of object 108 on the platform 112.
[0018] The graph shown in Figure 1A illustrates the comparison between the amount of step-out that can be obtained within a single layer of an object corresponding to a digital data model of the object, and the mass of droplets distributed across the formed step-out. The horizontal axis of the graph represents the amount of step-out in mm, and the vertical axis represents 1 / (droplet spacing) in mm, which is proportional to the mass of droplets distributed across the step-out distance. As used herein, the term “step-out” means the distance from a line perpendicular to the edge of a previously formed layer to the edge of the layer being formed. This is shown in Figure 1B. This step-out originates from the surface of a portion where its surface intersects the plane of the previous layer and the plane of the current layer. This is the average of the surface angles in the perpendicular direction between layers.
[0019] A metal droplet discharge head has a limit to the step-out distance that can be obtained along the periphery in a single pass of the discharge head. As used herein, the term “single pass” means a single crossing of the periphery while the discharge head is discharging metal droplets. The term “multiple passes” means crossing the periphery more than once while the discharge head is discharging metal droplets, and the height of multiple passes corresponds to the height of a single layer of the formed object. In one embodiment, the limit of the step-out distance is 0.25 mm, which means that the maximum step-out distance that can be obtained in a single pass is 0.25 mm. Thus, using the reciprocal of the corresponding droplet spacing distance identified from the graph in Figure 1A, a step-out distance of up to 0.25 mm can be achieved in a single pass by the reciprocal of the step-out distance. Thus, as the step-out distance in a single pass increases, the droplet spacing decreases. For example, a single step-out distance of 0.1 mm correlates to the reciprocal of the droplet spacing distance of approximately 3, so if 1 / (droplet spacing distance) is 3, the droplet spacing distance is 1 / 3 mm or 0.333 mm, while a single step-out distance of 0.2 mm corresponds to the reciprocal of the droplet distance of slightly more than 4, so the droplet spacing distance decreases to approximately 0.25 mm. Figure 1A shows that the reciprocal of the droplet spacing distance decreases as the step-out distance of a step-out formed in a single pass increases. As used herein, the term “droplet spacing distance” means the distance between the center of a droplet fully supported by a previously formed layer and the center of a droplet partially supported by a previously formed layer that forms a step-out. The reciprocal of the droplet spacing distance is proportional to the mass of droplets ejected to form a line; that is, as the droplet spacing distance decreases, the mass of material ejected for the step-out increases. As used herein, the term “fully supported droplet” means, as may also be referred to herein, a peripheral droplet within a layer, or a droplet at the edge of a filling region adjacent to the first (or only) droplet that forms a step-out edge.
[0020] In the embodiment used, for step-outs exceeding the maximum step-out distance of 0.25 mm, multiple passes must be performed. Thus, a 0.45 mm step-out requires a first pass with a 0.25 mm step-out followed by another pass with a 0.20 mm step-out to obtain a 0.45 mm step-out in that layer. Referring to the graph in Figure 1A, a 0.45 mm step-out distance correlates with the reciprocal of a droplet spacing of 8, which corresponds to a droplet spacing distance of 0.125 mm. Therefore, the mass of metal ejected to form a 0.45 mm step-out corresponds to a droplet spacing of 0.125 mm. Since two passes are required to form a 0.45 mm step-out, the droplet spacing for each pass is selected to be 2 × 0.125 mm, which equals 0.25 mm, because larger droplet spacings produce less mass for the line formed in the pass, but the combined mass of the two passes is similar to that of a line with a droplet spacing of 0.125 mm. Therefore, the slicer generates a machine-ready instruction which causes the printer to move the ejector head 204 along the tool path at a droplet spacing of 0.25 mm to create a 0.25 mm step-out on the previously formed layer edge, followed by moving the ejector head at a droplet spacing of 0.25 mm to form a 0.20 mm step-out from the first pass, achieving a 0.45 mm step-out for that layer. Alternatively, to form the step-out using equal step-out passes, the amount of the step-out distance can be divided by the number of passes required to form the step-out. In this embodiment, even an equal step-out of 0.225 mm can achieve a 0.45 mm step-out in two passes. The droplet spacing of these two passes is determined using the graph in Figure 1A.
[0021] As used herein, the term “tool path” means the relative movement between the nozzle of the discharge head and the platform on which the object is being manufactured while the discharge head is operating to form a structure within the object. This embodiment uses a mass distribution of 1 / N, where N is the droplet spacing distance used to distribute the metal mass discharged by the discharge head in each pass within the layer, but other proportional relationships can be used. For example, if the maximum step-out is 0.2 mm, a step-out of 0.45 mm can be obtained in three passes by a first pass with a step-out of 0.20 mm, a second pass with a step-out of 0.20 mm, and a third pass with a step-out of 0.05 mm. Alternatively, a step-out of 0.45 mm can also be obtained by forming an equal step-out of 0.15 mm using three passes. The objective is to cause the discharge head to distribute a portion of the metal mass required for the step-out corresponding to the step-out distance in the graph of Figure 1A over one or more passes without exceeding the maximum step-out distance that can be obtained in a single pass. The number of passes is calculated by dividing the step-out distance by the maximum step-out distance and rounding up to the nearest integer value.
[0022] One additional tweak to the algorithm is the placement of the inner perimeter relative to multiple perimeters. In the case of a single pass, the inner perimeter or fill is placed at a certain distance from the perimeter. However, in multiple passes, for larger step-out distances, the spacing between the innermost path and the inner perimeter may need to be adjusted. Multiple passes essentially generate a perimeter distributed across multiple step-outs, and the size of this perimeter is larger than the perimeter before the step-outs were formed. As a result, the inner perimeter or fill may need to overlap this area, sharing more than the innermost path and inner perimeter would need to overlap this same area to form a single-pass step-out. The larger the step-out distance, the greater the need for overlapping.
[0023] A process for operating a metal droplet ejection printer to obtain a step-out with an incline greater than 45° is shown in Figure 2. In the description of the process, when the process performs several tasks or functions, it means that the controller or general-purpose processor executes program instructions stored in a non-temporary computer-readable storage medium operably connected to the controller or processor in order to perform a task or function by operating data or by manipulating one or more components in the printer. The controller 136 described above may be such a controller or processor. Alternatively, the controller may be implemented with two or more processors and associated circuits and components, each configured to form one or more tasks or functions described herein. In addition, the steps of the method may be performed in any executable chronological order, regardless of the order shown in the figures or the order in which the processes are described.
[0024] FIG. 2 is a flow diagram of a process for operating a metal droplet ejection printer, such as printer 10, to form a step-out having an inclination greater than 45°. Process 200 begins with a slicer receiving a digital data model of an object to be produced (block 204). For any layer in which an inclined edge or a portion of an inclined edge is to be formed (block 208), the process identifies the step-out distance of the layer and compares it to the maximum of the individual step-out distances of the paths from the previous layer or pass (block 212). As used herein, the term "inclined edge" means a feature of a layer of an object that requires at least one step-out for its formation. Otherwise, the inclined surface treatment is skipped. If the identified step-out distance achieved in the layer exceeds the individual maximum pass limit, the process determines the number of passes required to form the inclined edge (block 216). Next, the droplet spacing for the identified step-out distance is determined using a graph of empirically obtained data, which can be implemented in a look-up table stored in the memory of the controller (block 220). This identified droplet spacing is distributed over a single pass if it does not exceed the maximum step-out distance, or over each pass within the determined number of multiple passes required for the layer (block 224). Next, the slicer operates the actuator and the ejection device head of the printer to generate machine-specific instructions for forming the inclined surface of the layer and stores them in a program for operating the printer (block 228). After the last layer of the object in the digital data model has been processed (block 232), the controller executes the machine-specific instructions to form the metal object (block 236).
[0025] It will be understood that the variations, or alternatives of the features and functions disclosed above, or others, may desirably be combined in many other different systems, applications, or methods. Various presently unforeseen or unanticipated alternatives, modifications, variations, or improvements, which are also intended to be encompassed by the following claims, may subsequently be made by those skilled in the art.
Claims
1. A metal droplet ejection device comprising: a melting device configured to receive and melt the bulk metal; at least one discharge head having a nozzle fluidly connected to the melter for receiving molten bulk metal from the melter; a platform positioned opposite the ejection head; at least one actuator operatively connected to at least one of the platform and the at least one ejection head, the at least one actuator configured to move the platform and the at least one ejection head relative to one another; a controller operatively connected to the melting device, the at least one discharge head, and the at least one actuator, the controller configured to, when executed by the controller, cause a first group of machine-enabled instructions stored on a non-transitory computer-readable medium to: identifying a beveled edge to be formed for each portion of a perimeter within a layer of an object formed by the metal drop ejector; generating additional machine-enabled instructions to operate the metal drop ejector to form the identified beveled edge at each portion of the perimeter within the layer of the object being formed using a respective maximum step-out distance; and executing the generated additional machine-enabled instructions to operate the metal drop ejector to form the beveled edge at each portion of the perimeter within the layer of the object being formed; The second group of machine-enabled instructions stored on the non-transitory computer-readable medium when executed by the controller causes the controller to: identifying a step-out distance for each identified beveled edge for each portion of the perimeter formed in the layer of the object; and identifying a number of passes for forming each identified beveled edge for each portion of the perimeter using the identified step-out distance and the respective maximum step-out distance for each identified beveled edge in each portion of the perimeter; The third group of machine-enabled instructions stored on the non-transitory computer-readable medium when executed by the controller causes the controller to: The metal drop ejector further configured to identify the number of passes for at least one identified beveled edge as being greater than one.
2. A fourth group of machine-enabled instructions stored on the non-transitory computer-readable medium when executed by the controller causes the fourth group of machine-enabled instructions to:
2. The apparatus of claim 1, further configured to distribute the identified step-out distance for each identified beveled edge for each portion of the perimeter formed in the layer of the object over the identified number of passes.
3. A fifth group of machine-enabled instructions stored on the non-transitory computer-readable medium when executed by the controller causes the fifth group of machine-enabled instructions to:
3. The apparatus of claim 2, further configured to identify the identified step-out distances for each pass within the identified number of passes for at least one of the portions of the perimeter for at least one of the identified beveled edges that are equal in amount.
4. A sixth group of machine-enabled instructions stored on the non-transitory computer-readable medium when executed by the controller causes the sixth group of machine-enabled instructions to: The apparatus of claim 3 , further configured to identify the identified step-out distance for each of the equal amounts of paths as being the respective maximum step-out distance.
5. A seventh group of machine-enabled instructions stored on the non-transitory computer-readable medium when executed by the controller causes the seventh group of machine-enabled instructions to:
3. The apparatus of claim 2, further configured to identify an amount of the identified step-out distance for at least one of the passes within the identified number of passes for at least one of the portions of the perimeter for at least one of the identified beveled edges as different from an amount of the identified step-out distance distributed to another one of the passes within the identified number of passes for at least another one of the portions of the perimeter for the at least one of the identified beveled edges.
6. an eighth group of machine-enabled instructions stored on the non-transitory computer-readable medium when executed by the controller, the eighth group of machine-enabled instructions causing the controller to: distributing the maximum step-out distance to each pass within the identified number of passes for forming at least one beveled edge for at least one portion of the perimeter within the layer, except for a last pass performed; and allocating the portion of the identified step-out distance to the last pass equal to the step-out distance less the sum of the maximum step-out distances allocated to the other passes within the identified number of passes.
7. A metal droplet discharge device, comprising: a melting device configured to receive and melt the bulk metal; at least one discharge head having a nozzle fluidly connected to the melter for receiving molten bulk metal from the melter; a platform positioned opposite the ejection head; at least one actuator operatively connected to at least one of the platform and the at least one ejection head, the at least one actuator configured to move the platform and the at least one ejection head relative to one another; a controller operatively connected to the melting device, the at least one discharge head, and the at least one actuator, the controller configured to, when executed by the controller, cause a first group of machine-enabled instructions stored on a non-transitory computer-readable medium to: identifying a beveled edge to be formed for each portion of a perimeter within a layer of an object formed by the metal drop ejector; generating additional machine-enabled instructions to operate the metal drop ejector to form the identified beveled edge at each portion of the perimeter within the layer of the object being formed using a respective maximum step-out distance; and executing the generated additional machine-enabled instructions to operate the metal drop ejector to form the beveled edge at each portion of the perimeter within the layer of the object being formed; The second group of machine-enabled instructions stored on the non-transitory computer-readable medium when executed by the controller causes the controller to: identifying a step-out distance for each identified beveled edge for each portion of the perimeter formed in the layer of the object; and identifying a number of passes for forming each identified beveled edge for each portion of the perimeter using the identified step-out distance and the respective maximum step-out distance for each identified beveled edge in each portion of the perimeter; The third group of machine-enabled instructions stored on the non-transitory computer-readable medium when executed by the controller causes the controller to: identifying the step-out distance for at least one identified beveled edge for at least one of the portions of the perimeter as being less than the respective maximum step-out distance; A fourth group of machine-enabled instructions stored on the non-transitory computer-readable medium when executed by the controller causes the fourth group of machine-enabled instructions to: identifying the number of passes of the at least one identified beveled edge relative to at least one of the portions of the perimeter as being one; A fifth group of machine-enabled instructions stored on the non-transitory computer-readable medium when executed by the controller causes the fifth group of machine-enabled instructions to: and identifying, during a single pass, a droplet spacing for forming the at least one identified beveled edge for the at least one of the portions of the perimeter, wherein the droplet spacing decreases as the identified step-out distance of the at least one identified beveled edge for the at least one portion of the perimeter approaches the respective maximum step-out distance.
8. A sixth group of machine-enabled instructions stored on the non-transitory computer-readable medium when executed by the controller causes the sixth group of machine-enabled instructions to:
8. The apparatus of claim 7, further configured to identify a drop spacing between a fully supported drop and a drop that forms the at least one identified beveled edge for the at least one of the portions of the perimeter in the layer.
9. A seventh group of machine-enabled instructions stored on the non-transitory computer-readable medium when executed by the controller causes the seventh group of machine-enabled instructions to:
10. The apparatus of claim 8, further configured to identify the step-out distance for at least one of the identified beveled edges for at least one of the portions of the perimeter as corresponding to an angle of greater than 45 degrees from a normal to a structure on which the layer of the object is formed.
10. A seventh group of machine-enabled instructions stored on the non-transitory computer-readable medium when executed by the controller causes the seventh group of machine-enabled instructions to:
10. The apparatus of claim 8, further configured to identify the step-out distance for at least one of the identified beveled edges for at least one of the portions of the perimeter as corresponding to an angle of at least 60 degrees from a normal to a structure on which the layer of the object is formed.