Thermal marking of 3D printed objects

The method addresses the resolution and durability issues in marking 3D printed objects by using a thermally treated layer and a point energy source to achieve high-resolution, permanent color changes.

JP7782993B2Active Publication Date: 2025-12-09XEROX CORP
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Patent Information

Application Number
JP2021144461
Authority / Receiving Office
JP · JP
Patent Type
Patents
Current Assignee / Owner
Priority Date
2020-09-08
Filing Date
2021-09-06
Publication Date
2025-12-09
Estimated Expiration
2041-09-06

AI Technical Summary

Technical Problem

Existing methods for marking 3D printed objects using FDM/FFF printers lack sufficient resolution and durability, and painting often results in low-resolution and non-durable markings.

Method used

A method involving a thermally treated layer in the 3D printed object that is marked with a point energy source, such as a laser, to achieve high-resolution and durable color changes by altering the physical properties of additives at specific temperatures.

Benefits of technology

The method provides high-resolution, durable color markings on 3D printed objects by using thermally treated layers and a point energy source, ensuring precise and permanent color changes without deforming the object.

✦ Generated by Eureka AI based on patent content.

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Abstract

To provide a method, non-transitory computer readable media, and apparatus for marking a printed object.SOLUTION: A method for marking a printed object includes: printing a three dimensional (3D) object 110 via a fused filament fabrication (FFF) printer; receiving a color marking desired to be marked on a surface of the 3D object; and controlling a point energy source 104 to emit energy on a heat treatment layer of the 3D object according to the desired color marking.SELECTED DRAWING: Figure 1
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Description

[Technical Field]

[0001] The present disclosure relates generally to three-dimensional (3D) printed objects, and more particularly to methods for thermally marking 3D printed objects. [Background technology]

[0002] Three-dimensional printers can be used to print 3D objects. 3D printers can be used to print a variety of different types of objects using different types of materials. Different types of processes can be used for 3D printing, such as extrusion, powder fusion, and UV curing of inkjet printed materials. 3D printing represents an alternative additive approach to printing 3D objects layer by layer, as opposed to subtractive processes in which a block of material is machined / etched / chisel-removed to create the final object.

[0003] One type of additive 3D printing process can be fused deposition modeling (FDM), also known as fused filament fabrication (FFF). The FDM process can extrude partially melted material that is dispensed in layers onto a platform. The extruded material can be dispensed in a desired shape or pattern for each layer. This process can be repeated to print a three-dimensional object. Summary of the Invention [Problem to be solved by the invention]

[0004] According to aspects presented herein, a method, a non-transitory computer-readable medium, and an apparatus for marking a printed object are provided. One disclosed feature of an embodiment is a method for printing a three-dimensional (3D) object via a fused filament fabrication (FFF) printer, receiving a desired color marking to be marked on a surface of the 3D object, and controlling a point energy source to emit energy on a heat-treated layer of the 3D object according to the desired color marking.

[0005] Another disclosed feature of an embodiment is a non-transitory computer-readable medium storing a plurality of instructions, the plurality of instructions including instructions that, when executed by a processor, cause the processor to perform operations of printing a three-dimensional (3D) object via a fused filament fabrication (FFF) printer, receiving desired color markings to be marked on a surface of the 3D object, and controlling a point energy source to emit energy on a heat-treated layer of the 3D object in accordance with the desired markings.

[0006] Another disclosed feature of an embodiment is an apparatus comprising: a processor; and a computer-readable medium storing a plurality of instructions that, when executed by the processor, cause the processor to perform operations of printing a three-dimensional (3D) object via a fused filament fabrication (FFF) printer, receiving desired color markings to be marked on a surface of the 3D object, and controlling a point energy source to emit energy on a heat-treated layer of the 3D object in accordance with the desired color markings. [Brief explanation of the drawings]

[0007] The teachings of the present disclosure can be readily understood by considering the following detailed description in conjunction with the accompanying drawings, in which:

[0008] [Figure 1] FIG. 1 shows a block diagram of the system of the present disclosure.

[0009] [Figure 2]FIG. 2 shows a block diagram of different examples of how a thermally treatable layer can be included in a printed article of the present disclosure.

[0010] [Figure 3] FIG. 3 illustrates an example of marking a print object with multiple colors according to the present disclosure.

[0011] [Figure 4] FIG. 4 shows a flowchart of an example method for marking a print object of the present disclosure.

[0012] [Figure 5] FIG. 5 depicts a high-level block diagram of an example computer suitable for use in performing the functions described herein.

[0013] For ease of understanding, wherever possible, the same reference numbers have been used to designate identical elements that are common to the figures. DETAILED DESCRIPTION OF THE INVENTION

[0014] The present disclosure broadly discloses methods and apparatus for thermally marking three-dimensional (3D) printed objects. As discussed above, various types of 3D printers can be used to print 3D objects. In some cases, it may be desirable to add writing, images, or any other type of marking to the 3D object. Previous methods may not provide sufficient resolution or may use methods that may not be compatible with fused deposition modeling (FDM) or fused filament fabrication (FFF) 3D printing methods.

[0015] For example, using different colored filaments and designing 3D objects with different colored filaments can be complex, expensive, and time-consuming. In other examples, some methods may simply paint desired color markings onto the 3D printed object. However, paint may not be very durable and / or may have low resolution.

[0016] The present disclosure provides a method for adding text, images, or any other type of marking to a 3D object printed with an FDM or FFF printer. The method can use a thermally treated layer that can be thermally marked with an energy source. The energy source can be a point energy source that can provide high accuracy and high resolution when applied to the thermally treated layer to mark the printed object.

[0017] In one embodiment, the heat-treated layer may be an additive that is part of the extruded filament material. However, the additive may react at temperatures above the melting / extrusion temperature of the filament material. As a result, the additive may not change color during extrusion. Rather, the color of the additive may be selectively changed via a separate marking process with a point energy source.

[0018] The color change can be a chemical change to the physical properties of a portion of the heat-treated layer exposed to the energy emitted by the energy source. The change can be caused by the exposure to the energy. In this way, the color change can be more durable and permanent than painting a marking on the 3D object.

[0019] In one embodiment, the heat treatment layer can be added as a coating after the 3D object is printed. A point energy source can then be applied to the coating in a desired location or pattern to create markings. Thus, the present disclosure provides a process for providing high-resolution coloring of 3D printed objects via thermal marking.

[0020] 1 illustrates an example of a system 100 of the present disclosure. In one embodiment, the system 100 may include a 3D printer 102, a point energy source 104, and a processor 106. While the 3D printer 102, the point energy source 104, and the processor 106 are shown as separate components, it should be noted that the 3D printer 102, the point energy source 104, and the processor 106 may be part of a single device within a common housing.

[0021] In one embodiment, the processor 106 may be communicatively coupled to the 3D printer 102 and the point energy source 104. The processor 106 may control the operation of the 3D printer 102 and the point energy source 104.

[0022] In one embodiment, the system 100 may include a computing device 118. The computing device 118 may be a computer capable of creating a design for the 3D printed object 110 via a computer aided drawing (CAD) program. The computing device 118 may create the desired markings 120 via the CAD program.

[0023] In one embodiment, the desired markings 120 and object design 122 may be generated by the computing device 118 and transmitted to the processor 106. The object design 122 may be in a format that can be used by the 3D printer 102 (e.g., a .dxf file, a .stl file, etc.). The desired markings 120 may include images, text, a combination of images and text, etc. that can be marked on the object 110 being printed.

[0024] The processor 106 may control the 3D printer 102 to print the object 110 according to the object design 122. In one embodiment, the 3D printer 102 may be a fused deposition modeling (FDM) printer or a fused filament fabrication (FFF) printer. Note that the 3D printer 102 is simplified for ease of explanation and may include additional components not shown (e.g., a heat source for melting, a print head for dispensing the filament material 108, a movable platform, etc.).

[0025] The FFF printer may extrude the filament material 108 layer-by-layer onto a platform to print the object 110. The filament material 108 may be delivered to a print head, which heats the filament material 108, causing it to melt or nearly melt. The print head may then dispense the melted filament material 108 according to the object design 122.

[0026] After the object 110 is printed, the point energy source 104 may emit energy to a location 114 on the surface 112 of the object 110. The processor 106 may control the point energy source 104 to emit energy according to the desired marking 120.

[0027] In one embodiment, the point energy source 104 may be an energy source capable of emitting energy in a well-defined, narrow energy beam. For example, the point energy source 104 may be a laser. In one embodiment, the laser may be powered at a power level having an energy density sufficient to raise the temperature of the surface 112 of the object 110 sufficiently to create the desired marking 120. The power level may be a function of the scanning speed. For example, a slower scanning speed may allow for a lower energy level to be used. A faster scanning speed may allow for a higher energy level to be used. In one embodiment, the laser may be a carbon dioxide laser capable of emitting between 5 watts (W) and 50 W of energy.

[0028] Because the amount of energy emitted by the point energy source 104 generates a temperature greater than the extrusion temperature of the filament material 108, the point energy source 104 may emit energy in short bursts or for a short period of time (e.g., a few seconds) to mark the surface 112 of the object 110. The short bursts or short period of time may prevent the point energy source 104 from deforming, damaging, or melting the surface 112 of the object 110. In one embodiment, the point energy source 104 may use short bursts or short periods of time to pass over the location 114 on the surface 112 several times to thermally mark the location 114.

[0029] In one embodiment, the point energy source 104 may emit an energy source at a location 114 on the surface 112 of the object 110 immediately after the filament material 108 is deposited. For example, after a layer of filament material 108 is deposited, the filament material 108 may still be hot. As such, a lower power point energy source 104 may be used to apply color to the location 114 on the surface 112 of the object 110. In other words, some energy savings may be realized in using a lower power energy source immediately after depositing the filament material 108, rather than waiting until the entire object 110 is printed and cooled. In one example, the point energy source may have an energy of 1 W to 10 W if used immediately after each layer of filament material 108 is deposited.

[0030] In one embodiment, the point energy source 104 may emit different levels of energy. For example, the different energy levels may correspond to different temperatures that may be used to thermally mark the object 110. As discussed in more detail below, the object 110 may be thermally marked with different colors. The different colors may be created by applying different energy levels to alter or activate different additives on the surface 112 of the object 110.

[0031] In one embodiment, the object 110 may rotate and / or move to thermally mark different sides of the object 110. The point energy source 104 may then thermally mark the sides of the object 110 to create the image 116 on the object 110.

[0032] In one embodiment, the surface 112 of the object 110 may include a heat-treated layer. The heat-treated layer may include additives that can change color or respond to a specific temperature to produce a desired color. In other words, the point energy source 104 may apply a localized amount of energy to the location 114 to color a portion of the heat-treated layer through a physical change in the properties of the additives in the heat-treated layer.

[0033] In one embodiment, the heat-treated layer may include an additive that changes color at a specific temperature. The additive may include a leuco dye and an acid developer in a matrix. The leuco dye may include at least one of crystal violet lactone, triarylmethane, sulfur dye, vat dye, fluoran dye, etc. Examples of acid developers may include diphenols, salicylic acid derivatives, octadecylphosphonic acid, etc. The matrix may further include a metal salt activator and / or inhibitor. The metal salt activator may include a zinc salt of an aromatic carboxylic acid. The inhibitor may include 2-hydroxy-1-aminopropanol, butylamine, and mixtures thereof.

[0034] In another example, the additive may be an irreversible material. The irreversible material may include an irreversible inorganic thermochromic material. Examples of irreversible inorganic thermochromic materials may include copper(I) iodide, ammonium metavanadate, manganese violet (Mn(NH4)2P2O7), and the like.

[0035] In one embodiment, different leuco dyes may be mixed together in the thermally treated layer to produce different colors. For example, different leuco dyes may change color at different temperatures. The point energy source 104 may emit energy at a first wattage to heat the thermally treated layer to a first temperature, causing the first leuco dye to change to a first color. The point energy source 104 may then emit energy at a second wattage to heat the thermally treated layer to a second temperature, causing the second leuco dye to change to a second color. This process may be repeated for any number of different leuco dyes that may change at different temperatures in the thermally treated layer.

[0036] FIG. 2 shows block diagrams of different examples of how a heat-treated layer can be included in a printed object 110 of the present disclosure. Example 202 shows a solid fill. For example, the heat-treated layer can be mixed with the filament material 108. The combination of the heat-treated layer and the filament material 108 can be fed into the 3D printer 102 and formed into a roll that is extruded. The additives in the heat-treated layer can change color at temperatures higher than the extrusion temperature of the filament material 108. As a result, the additives may not react to change color when exposed to extrusion temperatures that melt the filament material 108 during extrusion. The 3D printed object 110 can then include the heat-treated layer mixed throughout the printed object 110.

[0037] Example 204 shows a printed shell 206. For example, the object 110 can be printed with the filament material 108. A second filament material having a heat-treated layer can then be extruded by the 3D printer 102 to form the printed shell 206 around the printed object 110. In one embodiment, the 3D printer 102 can switch between the filament material 108 and the filament material mixed with the heat-treated layer to print the outer shell 206 layer by layer, along with an inner portion.

[0038] Example 208 illustrates spray coating. For example, the heat-treated layer can be stored in a spray can 210 or dispenser. After the object 110 is printed by the 3D printer 102, the heat-treated layer can be spray-coated onto the object 110 with the spray can 210. The heat-treated layer can be coated onto a desired portion of the object 110 or over the entire exterior surface of the object 110.

[0039] The thermally treated layer can be dried on the object 110. After the thermally treated layer is dried, the point energy source 104 can thermally mark the thermally treated layer to mark the image 116 on the object 110.

[0040] Example 212 illustrates dip coating. For example, the heat-treated layer 216 can be stored in a container 214. After the object 110 is printed by the 3D printer 102, the object 110 can be immersed in the heat-treated layer 216. A desired portion of the object 110 can be immersed, or the entire object 110 can be submerged in the heat-treated layer 216 to coat the entire outer surface of the object 110.

[0041] The thermally treated layer 216 may be allowed to dry on the object 110. After the thermally treated layer 216 is dried, the point energy source 104 may thermally mark the thermally treated layer 216 to mark the image 116 on the object 110.

[0042] 3 illustrates an example of marking a print object 110 with multiple colors according to the present disclosure. Figure 3 illustrates an example with two different colors. As noted above, different additives with different color change temperatures can be used to mark the object 110 with different colors.

[0043] In one embodiment, object 110 may be marked with two different colors 302 and 304. For example, a heat-treated layer may include a first additive or leuco dye that changes color at a first temperature and a second additive or leuco dye that changes color at a second temperature. The first and second additives may be mixed together in the heat-treated layer or may be applied to different portions of object 110 as separate heat-treated layers.

[0044] The first additive may correspond to color 302 and the second additive may correspond to color 304. In one embodiment, the point energy source 104 may emit energy at a first energy level onto the surface of the object 110. The first energy level may heat the surface of the object 110 to a first temperature that causes the first additive to change to color 302.

[0045] After the desired portion of the surface of the object is marked with the first color 302, the point energy source 104 can emit energy at a second energy level onto the surface of the object 110. The second energy level can heat the surface of the object 110 to a second temperature that causes the second additive to change to the second color 304. For example, any two temperatures above the extrusion temperature of the filament material 108 (e.g., temperatures above 160 degrees Celsius (°C)) can be used. For example, a first temperature of 250°C can be used to change to the first color 302, and a temperature of 400°C can be used to change to the second color 304. Other example temperatures can also be used. For materials with higher melting points, higher temperatures can be used to change to colors 302 and 304.

[0046] 3, two different colors 302 and 304 are shown, however, it should be noted that any number of different colors may be produced. The number of different colors may correspond to the number of different additives having different non-overlapping temperatures to activate the color change of each additive contained in the heat-treated layer.

[0047] 4 shows a flowchart of an example method 400 for marking a printed object of the present disclosure. In one embodiment, one or more blocks of method 400 may be performed by system 100 or the computer / processor controlling the operation of system 100 shown in FIG. 5 and discussed below.

[0048] At block 402, the method 400 begins. At block 404, the method 400 prints a three-dimensional (3D) object via a fused filament fabrication (FFF) printer. For example, an FFF printer or an FDM printer may extrude filament material layer by layer to print the 3D object. The object may be printed according to an object design generated by a computing device in communication with the 3D printer.

[0049] At block 406, the method 400 receives a desired color marking to be marked on the surface of the 3D object. The color marking may be a design generated by a computing device. The desired color marking may be text, an image, a graphic, or a combination thereof.

[0050] At block 408, the method 400 controls a point energy source to emit energy on the heat-treated layer of the 3D object according to a desired color marking. In one embodiment, the heat-treated layer can be intermixed with the filament material being extruded. In this manner, the filament material can be formed with the heat-treated layer intermixed throughout.

[0051] In one embodiment, a 3D object can be printed with an outer shell that includes a heat-treated layer. For example, the 3D object can be printed using a filament material. The filament material mixed with the heat-treated layer can then be extruded to form the outer shell.

[0052] In one embodiment, the heat treatment layer can be spray-coated or dip-coated onto the object. For example, the 3D object can be printed. After the 3D object is printed, the heat treatment layer can be applied to the entire exterior surface of the 3D object or to a desired portion of the exterior surface of the 3D object.

[0053] In one embodiment, the heat-treated layer may include an additive capable of changing color when exposed to a specific temperature. The additive may include a leuco dye and an acid developer in a matrix. Examples of leuco dyes that may be used include crystal violet lactone, triarylmethane, sulfur dyes, vat dyes, fluoran dyes, etc.

[0054] In one embodiment, different additives can be mixed together to produce different colored markings on a 3D object. For example, different additives with different, non-overlapping color change temperatures can be used to produce different colored markings. A point energy source can apply a first energy level to heat the heat-treated layer to a first temperature. One of the additives can respond to the first temperature and change to a first color. The point energy source can apply a second energy level to heat the heat-treated layer to a second temperature. Another of the additives can respond to the second temperature and change to a second color.

[0055] In this manner, method 400 may provide an efficient, non-contact method for thermally marking 3D printed objects to create color markings on the surface of the 3D printed object. In this manner, embodiments of the present disclosure may avoid the use of direct coloring with inks or paints or additive materials. At block 410, method 400 ends.

[0056] Figure 5 depicts a high-level block diagram of a computer dedicated to performing the functions described herein. As depicted in Figure 5, the computer 500 includes one or more hardware processor elements 502 (e.g., a central processing unit (CPU), microprocessor, or multi-core processor), memory 504, such as random access memory (RAM) and / or read-only memory (ROM), a module for marking print objects 505, and various input / output devices 506 (e.g., storage devices including, but not limited to, tape drives, floppy drives, hard disk drives, or compact disk drives, receivers, transmitters, speakers, displays, voice synthesizers, output ports, input ports, and user input devices (keyboard, keypad, mouse, microphone, etc.)). It should be noted that while only one processor element is shown, multiple processor elements may be employed in a computer.

[0057] It should be noted that the present disclosure may be implemented in software and / or a combination of software and hardware, for example, using an application specific integrated circuit (ASIC), a programmable logic array (PLA) including a field-programmable gate array (FPGA), or a state machine deployed on a hardware device, a computer, or any other hardware equivalent, such as computer-readable instructions that may accompany and be used to configure a hardware processor to perform the steps, functions, and / or operations of the methods discussed above. In one embodiment, instructions and data (e.g., a software program including computer-executable instructions) for this module or process 505 for marking a print object may be loaded into memory 504 and executed by hardware processor element 502 to perform the steps, functions, or operations discussed above in conjunction with the example method 400. Also, when a hardware processor executes instructions to perform an "action," this may include the hardware processor performing the action directly and / or facilitating, directing, or cooperating with another hardware device or component (e.g., a coprocessor, etc.) to perform the action.

[0058] A processor that executes computer-readable instructions or software instructions related to the above methods may be known as a programmed processor or a specialized processor. As such, the present module 505 for marking print objects of the present disclosure (including corresponding data structures) may be stored in a tangible or physical (broadly defined, non-transitory) computer-readable storage device or medium, such as volatile memory, non-volatile memory, ROM memory, RAM memory, magnetic or optical drive, device, or diskette. More specifically, a computer-readable storage device may comprise any physical device that provides the capability to store information, such as data and / or instructions, that may be accessed by a processor or computing device, such as a computer or application server.

[0059] It will be appreciated that variations of the above-disclosed and other features and functions, or alternatives thereof, may be combined into many other different systems or applications. Various presently uncontemplated or unanticipated alternatives, modifications, variations, or improvements may subsequently occur to those skilled in the art, which are intended to be encompassed by the following claims.

Claims

1. 1. A method comprising: Depositing a three-dimensional (3D) object by a fused filament fabrication (FFF) printer with a filament material; receiving a desired color marking to be marked on a surface of the 3D object; and after forming the 3D object by depositing the filament material, controlling a point energy source to generate energy on a heat-treated layer on the surface of the 3D object according to the desired color marking, the heat-treated layer including a leuco dye and an acid developer in a matrix that changes color at a temperature higher than a temperature that melts the filament material extruded by the FFF printer, and controlling the point energy source to generate energy on the heat-treated layer by multiple passes generating bursts of energy over predetermined locations on the energy-receiving heat-treated layer.

2. 10. The method of claim 1, wherein the heat-treated layer of the 3D object is formed by an additive mixed with the filament material extruded by the FFF printer to form the 3D object.

3. The method of claim 2 , wherein the heat-treated layer is deposited as an outer shell of the 3D object.

4. 10. The method of claim 1, wherein the heat treatment layer is applied as a coating after the 3D object is formed.

5. The method of claim 4 , wherein the heat treatment layer is applied by a dipping process or a spray coating process.

6. 10. The method of claim 1, wherein the leuco dye comprises at least one of a crystal violet lactone, a triarylmethane, a sulfur dye, a vat dye, or a fluoran dye.

7. The method of claim 1 , wherein the desired color marking comprises multiple colors.

8. 8. The method of claim 7, wherein the heat-treated layer includes a plurality of different additives, each one of the plurality of different additives changing color at a different temperature than the other additives to produce the plurality of colors in the heat-treated layer.

9. The method of claim 1 , wherein the point energy source comprises a laser generating between 5 watts and 50 watts of energy.

10. The method of claim 1, wherein the matrix containing the acid developer further contains a metal salt activator and inhibitor.

11. The method of claim 10 , wherein the metal salt activator comprises a zinc salt of an aromatic carboxylic acid.

12. 11. The method of claim 10, wherein the inhibitor comprises one or more of 2-hydroxy-1-aminopropanol, or butylamine.

13. The method of claim 1 , wherein the acid developer contained in the matrix comprises at least one of a diphenol, a salicylic acid derivative, or octadecylphosphonic acid.

14. 1. A non-transitory computer-readable medium storing a plurality of instructions that, when executed by a processor, cause the processor to perform operations, the operations including: Depositing a three-dimensional (3D) object by a fused filament fabrication (FFF) printer with a filament material; receiving a desired color marking to be marked on a surface of the 3D object; a non-transitory computer-readable medium comprising: after forming the 3D object by depositing the filament material, controlling a point energy source to generate energy on a heat-treated layer of the 3D object according to the desired color marking, the heat-treated layer including a leuco dye and an acid developer in a matrix that changes color at a temperature higher than a temperature that melts the filament material extruded by the FFF printer; and controlling the point energy source to generate energy on the heat-treated layer by passing the point energy source multiple times generating bursts of energy over predetermined locations on the energy-receiving heat-treated layer.

15. 15. The non-transitory computer-readable medium of claim 14, wherein the heat-treated layer of the 3D object is formed by an additive mixed with the filament material extruded by the FFF printer to form the 3D object.

16. 15. The non-transitory computer-readable medium of claim 14, wherein the heat treatment layer is applied as a coating after the 3D object is formed.

17. 15. The non-transitory computer-readable medium of claim 14, wherein the leuco dye comprises at least one of a crystal violet lactone, a triarylmethane, a sulfur dye, a vat dye, or a fluoran dye.

18. The non-transitory computer-readable medium of claim 14 , wherein the desired color marking comprises multiple colors.

19. 15. The non-transitory computer-readable medium of claim 14, wherein the heat-treated layer includes a plurality of different additives, each one of the plurality of different additives changing color at a different temperature than the other additives to produce the plurality of colors in the heat-treated layer.

20. 1. A method comprising: building a three-dimensional (3D) object by layer-by-layer extrusion of a filament material through a fused filament fabrication (FFF) printer; receiving a desired color marking to be marked on a surface of the 3D object; coating the 3D object with a heat-treated layer including a leuco dye and an acid developer in a matrix, the heat-treated layer changing color at a temperature higher than a temperature that melts the filament material extruded by the FFF printer, wherein a predefined temperature is applied to portions of the heat-treated layer to induce a color change; drying the heat-treated layer; controlling a laser to generate energy on the heat-treated layer of the 3D object in accordance with the desired color marking, wherein the laser is controlled to pass the laser multiple times over predetermined locations on the heat-treated layer receiving the energy while generating bursts of energy.

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