EP2917012A2 - Systèmes et procédés pour fabriquer des objets tridimensionnels - Google Patents

Systèmes et procédés pour fabriquer des objets tridimensionnels

Info

Publication number
EP2917012A2
EP2917012A2 EP13853522.4A EP13853522A EP2917012A2 EP 2917012 A2 EP2917012 A2 EP 2917012A2 EP 13853522 A EP13853522 A EP 13853522A EP 2917012 A2 EP2917012 A2 EP 2917012A2
Authority
EP
European Patent Office
Prior art keywords
slice
lamp
illustrates
image
slicing
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Ceased
Application number
EP13853522.4A
Other languages
German (de)
English (en)
Other versions
EP2917012A4 (fr
Inventor
Dajun Yuan
Anirudh RUDRARAJU
Paul CILINO
Suman Das
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
DDM Systems Inc
Original Assignee
DDM Systems Inc
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by DDM Systems Inc filed Critical DDM Systems Inc
Priority to EP21179065.4A priority Critical patent/EP3925761A1/fr
Publication of EP2917012A2 publication Critical patent/EP2917012A2/fr
Publication of EP2917012A4 publication Critical patent/EP2917012A4/fr
Ceased legal-status Critical Current

Links

Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B33—ADDITIVE MANUFACTURING TECHNOLOGY
    • B33Y—ADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3-D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3-D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
    • B33Y30/00—Apparatus for additive manufacturing; Details thereof or accessories therefor
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
    • B29C64/10—Processes of additive manufacturing
    • B29C64/106—Processes of additive manufacturing using only liquids or viscous materials, e.g. depositing a continuous bead of viscous material
    • B29C64/124—Processes of additive manufacturing using only liquids or viscous materials, e.g. depositing a continuous bead of viscous material using layers of liquid which are selectively solidified
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
    • B29C64/10—Processes of additive manufacturing
    • B29C64/171—Processes of additive manufacturing specially adapted for manufacturing multiple 3D objects
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
    • B29C64/20—Apparatus for additive manufacturing; Details thereof or accessories therefor
    • B29C64/264—Arrangements for irradiation
    • B29C64/268—Arrangements for irradiation using laser beams; using electron beams [EB]
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
    • B29C64/20—Apparatus for additive manufacturing; Details thereof or accessories therefor
    • B29C64/264—Arrangements for irradiation
    • B29C64/277—Arrangements for irradiation using multiple radiation means, e.g. micromirrors or multiple light-emitting diodes [LED]
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
    • B29C64/40—Structures for supporting 3D objects during manufacture and intended to be sacrificed after completion thereof

Definitions

  • Rapid prototyping or solid free-form fabrication has become an increasingly important tool, and is a technology that has seen great advances since its initial application in the 1980s, evidenced in U.S. Patent No. 4,575,330, which is incorporated by reference herein as if fully set forth below.
  • rapid prototyping manufacturing makes use of a bath of curable liquid, wherein some movable point within the bath is subjected to stimulation by a prescribed curing source. As the source is moved with respect to the bath or as the bath is moved with respect to the source, the point that undergoes solidification or curing is constantly made to move. The result is the construction of a solidified mass of cured material contained within the otherwise liquid bath.
  • the region commonly solidified is positioned at or very near the surface of the bath in most practical applications. As the liquid is solidified, the solid structure is progressively lowered into the bath allowing the uncured liquid to flow over the surface, which is in turn subjected to the same process. By continuing to solidify these very thin layers, the solid object is built up into its final shape. Bonding of one layer to a previous layer is an inherent property of the process as is known in the art.
  • photolithography systems that direct light beams onto a photosensitive surface covered by a mask, etching a desired pattern on the substrate corresponding to the void areas of the mask, are known in the art.
  • the patterns generated are defined by physical masks placed in the path of light used for photo-activation.
  • Maskless photolithography systems are also known in the art and often use an off-axis light source coupled with a digital micromirror array to fabricate chips containing probes for genes or other solid phase combinatorial chemistry to be performed in high-density microarrays.
  • maskless photolithography systems address several of the problems associated with mask-based photolithography systems, such as distortion and uniformity of images, problems still arise. Notably, in environments requiring rapid prototyping and limited production quantities, the advantages of maskless systems as a result of efficiencies derived from quantities of scale are not realized. Further, while maskless photolithography systems are directed to semiconductor manufacturing, these prior art systems and methods notably lack reference to other applications lending themselves to maskless photolithography techniques.
  • a commonly-used curable medium includes photopolymers, which are polymerizable when exposed to light. Photopolymers may be applied to a substrate or objects in a liquid or semi-liquid form and then exposed to light, such as ultraviolet light, to polymerize the polymer and create solid coatings or castings.
  • conductive photopolymers are known that exhibit electrically conductive properties, allowing creation of electric circuits by polymerizing the polymers in circuit layout patterns.
  • Conventional methods of photopolymerization use physical masks to define areas of polymerization. This mask-based photopolymer process suffers from the disadvantages of mask-based photolithography methods, including the requisite need for many different masks, long lead time for mask creation, inability to modify masks, and the degradation of masks used in the manufacturing process.
  • the rapid prototyping process has the ability to drastically reduce the time between product conception and final design, and to create complex shapes. More traditional modeling or prototyping is obtained from an iterative generation of a series of drawings which are analyzed by the design team, manufacturing, the consumer, and perhaps others, until a tentative final design results which is considered viable. This agreed upon design is then created by casting and/or machining processes. If molds are needed, these must be fabricated as well, which may take considerable and valuable time. The finished prototype is then tested to determine whether it meets the criteria for which the part was designed. The design and review process is often tedious and tooling for the creation of the prototype is laborious and expensive. If the part is complex, then a number of interim components must first be assembled. The prototype itself is then constructed from the individual components.
  • CAD computer aided design
  • drawings are not required for fabrication.
  • the CAD system is used to generate a compatible output data file that contains information on the part's geometry. This file is typically converted into a "sliced" data file that contains information on the part's cross-section at predetermined layer depths.
  • the rapid prototype control system then regenerates each cross-section sequentially at the surface of the curable resin.
  • the fabricated part may be analyzed by the team or used for various form, fit, and functional tests.
  • Embodiments of the present invention relate to optical modeling methods and systems and, more particularly, to optical modeling methods and systems in which a three-dimensional object is created by a continuously moving optical imaging source using a plurality of light beams to illuminate portions of a photo-curable medium. Furthermore, embodiments of the present invention relate to systems and processes for large area maskless photopolymerization (LAMP) using spatial light modulators (SLMs).
  • LAMP large area maskless photopolymerization
  • SLMs spatial light modulators
  • a process/system of the present invention involves using SLMs that scan at least a portion of the surface of a photopolymer.
  • the SLMs In scanning a surface of the photopolymer, the SLMs project a two-dimensional image (e.g., from a CAD file) thereon.
  • the two-dimensional image comprises a cross-section of a three-dimensional object to be formed within the various layers of the photopolymer, once cured.
  • the process/system involves continuous movement of the SLMs, instead of so-called “step and expose” or “step and repeat” movements.
  • the two- dimensional image projected by the SLMs is a dynamic image. That is, rather than projecting a fixed, single image on a portion of the photopolymer surface, followed by movement of the SLMs to a new location, changing the SLMs to a new image that corresponds to the desired image over the new location, and projection of the new image on the portion of the photopolymer surface at the new location, embodiments of the present invention involve projecting an image that continuously changes as the SLMs scan over the surface of the photopolymer.
  • Embodiments of the present invention also provide optional features that may overcome some of the limitations of conventional systems and methods, such as polymerization shrinkage, liquid polymer movement prior to being cured, and the like. Further, a combination of increased resolution and speed of fabrication may be achieved. Examples of improvements in the LAMP systems that result in such properties may be found at least in the polymer container design, light modulation process, and light patterns.
  • composite materials e.g., those that contain a filler material for the polymer
  • a polymer-ceramic matrix may be used in the LAMP systems and processes, followed by removal of the polymeric component, thereby leaving behind a ceramic body that may be subjected to additional processing.
  • Fig. 1 is a flow chart of a conventional foundry for investment casting of three- dimensional objects.
  • Fig. 2 is a pie chart of a conventional perfectly yielded investment cast object.
  • Figs. 3A-3B are perspective views of a large area maskless photopolymerization (LAMP) system, in accordance with an exemplary embodiment of the present invention.
  • LAMP large area maskless photopolymerization
  • Fig. 4 is another perspective view of the LAMP system, in accordance with an exemplary embodiment of the present invention.
  • Fig. 5 is an exemplary computer aided design slice pattern, in accordance with an exemplary embodiment of the present invention.
  • Figs. 6-7 are perspective view of the LAMP system for fabricating the three-dimensional objects using a maskless optical imaging system, a material build platform, a material recoating system, and a control system, in accordance with an exemplary embodiment of the present invention.
  • Fig. 8 is a perspective view of an optical imaging system for the LAMP system, in accordance with an exemplary embodiment of the present invention.
  • Fig. 9 illustrates a plurality of cross-sectional views of a three-dimensional computer aided design drawing, in accordance with an exemplary embodiment of the present invention.
  • Fig. 10A illustrates a plurality of stacked cross-sectional views of the two dimensional computer aided design drawings, in accordance with an exemplary embodiment of the present invention.
  • Fig. 10B illustrates a perspective view of a three-dimensional object from the stacked cross-sectional views of the two-dimensional computer aided design drawings of Fig. 10A, in accordance with an exemplary embodiment of the present invention.
  • Fig. 11 illustrates one embodiment of a LAMP machine having a gantry-style scanning maskless optical imaging system in accordance with various aspects described herein.
  • Fig. 12 illustrates one embodiment of a scanning maskless optical imaging system in accordance with various aspects described herein.
  • Fig. 13 illustrates one embodiment of a scanning maskless optical imaging system in accordance with various aspects described herein.
  • Fig. 14 illustrates one embodiment of a material build platform (MBP) in accordance with various aspects described herein.
  • Fig. 15 illustrates one embodiment of a material recoating system (MRS) in accordance with various aspects described herein.
  • Fig. 16 illustrates another embodiment of a material recoating system (MRS) in accordance with various aspects described herein.
  • MRS material recoating system
  • Fig. 17 illustrates a loss of build precision using a material recoating system having a single-edge recoater.
  • Fig. 18 illustrates one embodiment of a material recoating system having a multiblade recoater in accordance with various aspects described herein.
  • Fig. 19 illustrates one embodiment of a screen printing-style inking window pane in accordance with various aspects described herein.
  • Fig. 20 illustrates a loss of build precision using a material recoating system.
  • Fig. 21 illustrates one embodiment of a method of constructing a conformal lattice in an inter-part space using break lines in accordance with various aspects as described herein.
  • Fig. 22 illustrates another embodiment of a method of constructing a conformal lattice in inter-part space using break lines in accordance with various aspects as described herein.
  • Fig. 23 illustrates one embodiment of a LAMP machine in accordance with various aspects as described herein.
  • Fig. 24 illustrates one embodiment of a method for correcting a gap error in accordance with various aspects described herein.
  • Fig. 25 illustrates another embodiment of a method for correcting a gap error in accordance with various aspects described herein.
  • Fig. 26 illustrates one embodiment of a method of automated part layout and scaffolding in accordance with various aspects described herein.
  • Fig. 27 illustrates one embodiment of a method of identifying a floating island in accordance with various aspects as described herein.
  • Fig. 28 illustrates one embodiment of a method of identifying a multifunctional support structure in accordance with various aspects as described herein.
  • Fig. 29 illustrates one embodiment of a method for screening for shrinkage relief and support structures in accordance with various aspects as described herein.
  • Fig. 30 illustrates another embodiment of a method for screening for shrinkage relief and support structures in accordance with various aspects as described herein.
  • Fig. 31 illustrates another embodiment of a method for screening for shrinkage relief and support structures in accordance with various aspects as described herein.
  • Fig. 32 provides a chart of screening-based grayscale working curves for one embodiment of a LAMP system.
  • Fig. 33 provides a chart of screening-based grayscale working curves for one embodiment of a LAMP system.
  • Fig. 34 provides a chart of screening-based grayscale working curves for one embodiment of a LAMP system.
  • Fig. 35 provides a chart of screening-based grayscale working curves for one embodiment of a LAMP system.
  • Fig. 36 provides a chart of screening-based grayscale working curves for one embodiment of a LAMP system.
  • Fig. 37 provides a chart of screening-based grayscale working curves for one embodiment of a LAMP system.
  • Fig. 38 illustrates one embodiment of a method of performing direct slicing in accordance with various aspects as described herein.
  • Fig. 39 illustrates one embodiment of a method of identifying the "interior” from the “exterior” in accordance with various aspects as described herein.
  • Fig. 40 is a slice image having rough edges due to floating point errors in counting a distance traveled.
  • Fig. 41 illustrates test parts used in much of the previously reported work in the direct slicing literature.
  • Fig. 42 shows a CAD model of a typical internally cooled HP turbine blade.
  • Fig. 43A provides a chart of the number of stray lines observed in each image from a stack of hundred consecutive slices produced at two different ACIS resolutions.
  • Fig. 43B provides a graph of the time to compute one slice scaling with DPI.
  • Fig. 44 shows the various elements of the BRep (Boundary Representation) data structure.
  • Fig. 45 illustrates a corner table data structure in accordance with various aspects described herein.
  • Fig. 46 shows a schematic of a cell structure used to identify redundant vertices in accordance with various aspects described herein.
  • Fig. 47 is a flow chart of a method used to fill V[c] in accordance with various aspects described herein.
  • Fig. 48 provides a trend of this scaling with respect to the number of facets.
  • Fig. 49 A illustrates a method for identifying the intersecting facets at an arbitrary Z- height in accordance with various aspects as described herein.
  • Fig. 49B illustrates a data structure used for direct slicing of STL files in accordance with various aspects as described herein.
  • Fig. 49C illustrates computational time scaling with respect to a number of facets.
  • FIG. 50 illustrates a data structure used to store these intersection points in accordance with various aspects as described herein.
  • Fig. 51 illustrates slicing time scaling with respect to mesh size.
  • Fig. 52 illustrates a particularly bad instance of stray line errors.
  • Fig. 53 illustrates a method of rectifying multi-pixel wide rows with stray lines in accordance with various aspects as described herein.
  • Fig. 54 illustrates a method of tiling in accordance with various aspects as described herein.
  • Fig. 55 illustrates the staircase effect while two created contours are same size in inner area.
  • Fig. 56 illustrates a cusp volume for a hemispherical part.
  • Fig. 57 illustrates each of these steps for calculating the volume deviation while slicing a sample CAD part in accordance with various aspects as described herein.
  • Fig. 58 is a sample CAD part adaptively sliced using the volume deviation approach.
  • Fig. 59 provides a chart of variation of layer thickness vs. height z for sample part.
  • Fig. 60 provides a chart of the percentage volume deviation vs. height for sample part.
  • Fig. 61 provides a chart of percentage total volumetric error vs. height for sample part.
  • Fig. 62 illustrates stair stepping caused on downward facing surfaces while using all white build images.
  • Fig. 63 illustrates a method for producing a gray scale image in accordance with various aspects described herein.
  • Fig. 64 illustrates gray scale exposure results.
  • Fig. 65 illustrates a sample exposure image with a known constant square length with ten different tiles.
  • Fig. 66 illustrates cured squares obtained by exposing the image in Fig. 65.
  • Fig. 67 shows the native orientation of the blade mold.
  • Fig. 68 illustrates a build orientation that reduces overhangs observed in the original orientation.
  • Fig. 69 illustrates a build orientation that reduces overhangs observed in the original orientation.
  • Fig. 70 illustrates a cross-section of the part as the base of the leading edge cavity is being built.
  • Fig. 71 illustrates 3D slices of successive layers at the location corresponding to the floating island shown in Fig. 70.
  • Fig. 72 illustrates various supports generated on the sample HP blade shown in Fig. 67 using this method.
  • Fig. 73 illustrates a temperature profile obtained on the internal wall of a leading edge with and without a support structure.
  • Fig. 74 illustrates velocity streamlines in internal cavities.
  • Fig. 75 illustrates a loss of build precision using a material recoating system having a single-edge recoater.
  • Fig. 76 illustrates one embodiment of a material recoating system having a multiblade recoater in accordance with various aspects described herein.
  • Fig. 77 illustrates one embodiment of a screen printing-style inking window pane in accordance with various aspects described herein.
  • Fig. 78 illustrates one embodiment of a LAMP machine in accordance with various aspects as described herein.
  • Fig. 79 illustrates one embodiment of a LAMP machine in accordance with various aspects described herein.
  • Fig. 80 illustrates one embodiment of a LAMP machine in accordance with various aspects described herein.
  • Fig. 81 illustrates one embodiment of a LAMP machine in accordance with various aspects described herein.
  • Fig. 82 illustrates one embodiment of a LAMP machine material build platform in accordance with various aspects described herein.
  • Fig. 83 illustrates one embodiment of a LAMP machine material build platform in accordance with various aspects described herein.
  • Fig. 84 illustrates one embodiment of a LAMP machine material build platform substrate and substrate mount in accordance with various aspects described herein.
  • Fig. 85 illustrates one embodiment of a LAMP machine material build platform substrate and substrate mount in accordance with various aspects described herein.
  • Fig. 86 illustrates one embodiment of a LAMP machine material build platform substrate and substrate mount in accordance with various aspects described herein.
  • Fig. 87 illustrates one embodiment of a LAMP machine material recoating system in accordance with various aspects described herein.
  • Fig. 88 illustrates one embodiment of a LAMP machine material build platform seal system and material recoating system in accordance with various aspects described herein.
  • Fig. 89 illustrates one embodiment of a LAMP machine material build platform seal system and material recoating system in accordance with various aspects described herein.
  • Fig. 90 illustrates one embodiment of a LAMP machine material build platform seal system and material recoating system in accordance with various aspects described herein.
  • Fig. 91 illustrates one embodiment of a LAMP machine material build platform seal system and material recoating system supply reservoir in accordance with various aspects described herein.
  • Fig. 92 illustrates one embodiment of a LAMP machine material recoating system supply reservoir and recoater in accordance with various aspects described herein.
  • Fig. 93 illustrates one embodiment of a LAMP machine material recoating system supply reservoir and recoater in accordance with various aspects described herein.
  • Fig. 94 illustrates one embodiment of a LAMP machine material build platform seal, material recoating system supply reservoir and recoater in accordance with various aspects described herein.
  • Figs. 95 (A), 95 (B) and 95 (C) illustrate an embodiment for employing a series of imaging heads that move concurrently across the surface of a resin in accordance with various aspects as described herein.
  • Fig. 96 illsutrates an embodiment of for employing a two dimensional array of imaging heads to simultaneously pattern the surface of the resin in accordance with various aspects as described herein.
  • Fig. 97 provides a graph of the emission spectrum of a light source used in an embodiment of LAMP.
  • Fig. 98 provides a comparison of the grayscale factor resulting from a screened grayscale image at different screening resolutions.
  • Fig. 99 illustrates intensity distributions and profiles for (a) 1 pixel, (b) 2 pixel, (c) 3 pixel, (d) 4 pixel, (e) 5 pixel, and (f) 10 pixel line projections from the SLM.
  • Fig. 100 illustrates a light intensity distribution resulting from an all white projection.
  • Fig. 101 provides a chart of cure depth measurements at a fixed exposure time and screening resolution as the grayscale was varied from 30% to 90% white.
  • Fig. 102 illustrates a schematic for cure depth measurements with the incorporation of neutral density filters to determine the curing characteristics at different light intensities.
  • Fig. 103 provides a chart of working curves of a PCMS with exposure to different light intensities.
  • Fig. 104 illustrates a summary of the dependence of the critical energy and resin sensitivity on light intensity.
  • Fig. 105 provides a chart of working curves for various grayscale values and screening resolutions.
  • Fig. 106 provides a summary of the critical energy and resin sensitivity for various grayscale values and screening resolutions.
  • Fig. 107 provides a graph summarizing the influence of light intensity on curing characteristics resulting from homogenous grayscale exposure.
  • Fig. 108 illustrates a checkerboard pattern that can be used to extract dimensional information.
  • Fig. 109 shows images of checkerboard exposure at 600ms with various square lengths to illustrate a homogenous transition.
  • Fig. 110 provides a chart illustrating homogenous transition of a PCMS resulting from a checkerboard exposure pattern.
  • Fig. I l l shows images of a checkerboard exposure at 170 ⁇ square length with various exposure times to illustrate the time dependence of the homogenous transition.
  • Fig. 112 provides a chart of exposure time working curves for selected screening resolutions.
  • Fig. 113 provides a chart summarizing the trends in the critical exposure time and resin sensitivity at screening resolutions within the homogenous transition.
  • Fig. 114 illustrates a schematic of material system resolution, where the projected pattern has features finer than the "pixel" of the material system, which can be defined by the scattering length.
  • Fig. 115 illustrates simulated light intensity distribution experienced by the PCMS for selected checkerboard screening resolutions.
  • Fig. 116 provides charts comparing experimental cure depth measurements with the scattering length pixel model for predicting the light intensity for grayscale and homogenous transition exposure.
  • Fig. 117 provides a chart showing the degree of conversion and rate of polymerization for the PCMS at selected grayscale intensities of 100%.
  • Fig. 118 provides a chart characterizing the influence of screening resolution on the degree of conversion.
  • Fig. 119 shows iteration steps in the development of grayscale support structures.
  • Fig. 120 shows the results of a trial of fabricating unsupported geometries using grayscale support structures with various grayscale values.
  • Fig. 121 shows images for a test of selective etching for a challenge component.
  • Fig. 122 shows images of fabrication of a test component using various grayscale values.
  • Fig. 123 shows images of results from print- through mediated alternating GSS.
  • Fig. 124 shows stereomicroscope images of an airfoil mold with "fissures.”
  • Fig. 125 provides a schematic of the shrinkage mechanisms occurring for one embodiment of a LAMP system.
  • Fig. 126 shows an image of curvature induced by UV illumination within a single layer exposure.
  • Fig. 127 provides a schematic of a hollow cylinder design used to investigate methods to reduce defects in LAMP components.
  • Fig. 128 shows the result from fabrication of a test cylinder with all white exposure for one embodiment of a LAMP system.
  • Fig. 129 shows the result from fabrication of a test cylinder with all white exposure after
  • Fig. 130 shows green body molds for cylinders fabricated with checkerboard exposure at selected square lengths for one embodiment of a LAMP system.
  • Fig. 131 shows the effects of BBO and sintering on the test cylinders fabricated using a staggered checkerboard exposure with square length after BBO and sintering for one embodiment of a LAMP system.
  • Fig. 132 shows test cylinders exhibiting vertical cracks for one embodiment of a LAMP system.
  • Embodiments of the present invention are not limited to use in the described systems. Rather, embodiments of the present invention may be used when a three-dimensional prototype object, e.g., a casting, is desired or necessary.
  • a three-dimensional prototype object e.g., a casting
  • the system described hereinafter as a continuously moving rapid prototyping system and method may also find utility as a system for many applications and for many sized objects.
  • Fig. 1 illustrates a conventional foundry flow chart for investment casting of three- dimensional objects.
  • the flow chart illustrated in Fig. 1 could be utilized to create turbine airfoils; turbine airfoils with extremely complex interior cooling passages are often produced by investment casting.
  • the exterior airfoil shape is defined by injection molded wax patterns that are removed or "lost” after shelling.
  • the interior passages of the airfoil are defined by injection molded ceramic cores that are removed or "lost” after casting.
  • the core and wax molding operations require sophisticated tooling, leading to excessive initial and maintenance costs, very slow fabrication cycles, and low casting yields.
  • the next step involves fabrication 12 of ceramic cores by injection molding. Molten wax may also be injection molded 14 to define the patterns for the object's shape. Several such wax patterns are then assembled 16 into a wax pattern assembly or tree. The pattern assembly is then subjected to multiple rounds of slurry coating 18 and stuccoing 20 to form the completed mold assembly. The mold assembly is then placed in an autoclave for dewaxing 22. The result is a hollow ceramic shell mold into which molten metal in poured to form the castings 24. Upon solidification, the ceramic mold is broken away and the individual metal castings are separated therefrom.
  • the castings are next finished 26, 28, 30 and inspected 32 prior to shipment 34.
  • conventional casting steps 10, 12, 14, 16, 18, 20, 22 are obsolete, resulting in the elimination of over 1,000 tools and five major process steps of three-dimensional item prototyping.
  • Turbine airfoils lay at the heart of gas turbine engines, operating at the highest temperatures - even in excess of their melting point. Because turbine airfoils are subjected to very high heat, there has been a continuing effort to identify improvements to the design, materials, and coatings for turbine airfoils to achieve even higher temperature capability and thus higher performance - typically at the sacrifice of affordability.
  • improvements of embodiments of the present invention may be made in casting yield and secondarily through a reduction in handling, which also impacts casting yield.
  • a third of the cost is comprised of manufacturing the integral core/shell "lost" mold (steps 10-22 of Fig. 1); a third of the cost is metal pouring; and a third of the cost is finishing, gauging, and inspecting the finished metal casting.
  • the cost of making integral core/shell molds dominates more of the overall costs, sometimes commanding up to half of the cost of an investment casting.
  • cost is evenly divided among manufacturing the mold, casting, and finishing, as illustrated in Fig. 2.
  • the cost of manufacturing the "lost" integral core/shell is a large part of the cost of an investment cast object because approximately 60-90% percent of the causes for low casting yield occur in fabrication and handling of the cores 12, wax injection 14 and dewaxing 22; whereas relatively less scrap is typically caused by metal pouring and finishing, steps 24, 26, 28, 30, 32, 34.
  • Causes are typically due to the enormous amount of handling and handling-induced variation and damage that occurs in the fabrication of cores, injection of wax around the cores, and subsequent high stresses placed on the cores during dewaxing.
  • Core fracture and breakage, hand finishing breakage, wax injection-induced core fracture, breakage and shift, and core shift and shell defects caused during dewaxing typically lead to downstream yield problems such as kiss-out, miss-run, recrystallized grains, surface defects, inclusions, and other defects detected after casting.
  • downstream yield problems such as kiss-out, miss-run, recrystallized grains, surface defects, inclusions, and other defects detected after casting.
  • early causes for low casting yield are not discovered until after the metal has been cast, the shell and core removed, and the metal component is inspected.
  • some incremental productivity improvements have been made, such as semi-automated finishing and handling, none have dramatically lowered the cost of investment casting turbine airfoils. Elimination of the "lost" processes and accompanying tooling and handling by directly digitally manufacturing the investment casting mold may dramatically increase production yields, reduce costs and lead-times.
  • Embodiments of the present invention relate to systems and methods that develop a disruptive manufacturing technology for the direct digital manufacturing (DDM) of three- dimensional items or objects, such as airfoils.
  • Embodiments of the present invention are based on large area maskless photopolymerization (LAMP) of photocurable materials (e.g., photopolymers alone, composites comprising a photopolymer, ceramic- or ceramic-precursor- filled photopolymers, metals, and the like).
  • LAMP large area maskless photopolymerization
  • LAMP may be used, in some embodiments, to produce integral ceramic cored molds ready for step 24, i.e., the casting step.
  • DDM of items using LAMP will replace and thus eliminate steps 10-22, amounting to the elimination of over 1,000 tools and five major processes with a single step corresponding to direct digital mold production.
  • LAMP will fundamentally eliminate at least approximately 95% percent or more of tooling and tooling costs, at least approximately 20-30% of the overall part cost, and at least approximately 60-90% of the causes for low casting yield.
  • LAMP may enable in situ casting of more sophisticated features, such as film cooling holes, that are otherwise difficult or physically impossible to cast with conventional investment casting processes, further improving casting yield and dramatically improving downstream machining yields and costs.
  • the system for fabricating a three-dimensional object includes an optical imaging system for providing a light source, a photosensitive medium that is adapted to change states, and a control system for continuously moving the optical imaging system above the medium.
  • the optical imaging system may use a spatial light modulator (SLM) to scan a portion of the surface of the medium housed in a container.
  • the medium is a photopolymer. As the optical imaging system scans the medium, when the light source illuminates a portion of the surface of the medium, the characteristics of the medium change, e.g., from a liquid or aqueous state to the solid state.
  • the optical imaging system or radiation system includes a light source, a reflector system, an optical lens system, a mirror, the SLM comprising a digital mirror device (DMD), and a projection lens.
  • the light source may illuminate an ultraviolet light source, e.g., having a particular, predetermined wavelength in the UV spectrum.
  • Various embodiments of the present invention may include light sources comprising any one of an ultraviolet light, violet light, blue light, green light, actinic light, and the like. The light emitting from the light source may be directed upon a portion of the reflector system, and thus reflects from the reflector system, which may comprise a concave-shaped reflector.
  • the reflector of the reflector system directs the light through a lens of the optical lens system before it reaches a mirror.
  • the mirror then reflects the light towards the digital mirror device (DMD).
  • the DMD is a microelectromechanical device comprising a plurality of tiny mirrored surfaces that each may be independently pivoted from a first to a second position.
  • the mirrors are formed into the surface of a semiconductor chip and through the application of an appropriate voltage to the circuitry built under each mirror, that mirror may be made to tilt to one side or another with respect to a plane normal to the semiconductor chip. With respect to some fixed frame of reference, pivoting in one direction causes the mirror to reflect light whereas pivoting in the opposite direction causes the light to be deflected from the fixed frame of reference.
  • the light from the DMD is next directed towards a projection lens. The light then is projected onto the surface of the medium in the container.
  • Other types of SLMs such as liquid crystal displays, grating light valves, and the like, may also be implemented.
  • one process/system involves using SLMs that scan at least a portion of the surface of a photopolymer.
  • the SLMs In scanning a surface of the photopolymer, the SLMs project a two- dimensional image (e.g., from a CAD file) thereon.
  • the two-dimensional image comprises a cross-section of a three-dimensional object to be formed within the various layers of the photopolymer, once cured.
  • the process/system involves continuous movement of the SLMs, instead of so-called “step and expose” or “step and repeat” movements.
  • the two- dimensional image projected by the SLMs is a dynamic image. That is, rather than projecting a fixed, single image on a portion of the photopolymer surface, followed by movement of the SLMs to a new location, changing the SLMs to a new image that corresponds to the desired image over the new location, and projection of the new image on the portion of the photopolymer surface at the new location, embodiments of the present invention involve projecting an image that continuously changes as the SLMs scan over the surface of the photopolymer.
  • the systems and processes above are not limited to use of photopolymers as the photosensitive medium alone.
  • composite materials e.g., those that contain a filler material for a photopolymer, or those that combine the photopolymer with another polymer
  • a polymer-ceramic matrix or a polymer-ceramic precursor matrix may be used in the LAMP systems and processes, followed by removal of the polymeric component, thereby leaving behind a ceramic green body that may be subjected to additional processing.
  • UV ultraviolet
  • the laser source is focused to the desired spot size on the surface of the polymer to be cross-linked or the ceramic suspension to be photo-formed in stereolithography, or on a substrate coated with a photosensitive material in the platesetting print industry, or on a substrate coated with photoresist in microelectronics manufacturing.
  • the focused spot may be modulated as the beam is raster scanned across the substrate.
  • the SLM is a two-dimensional array of approximately one million micro-pixels, each of which may be individually turned ON or OFF.
  • the SLM is controlled by the control system, which may include a computer.
  • the computer accesses CAD files containing the ON/OFF states for all of the pixels in an entire frame, e.g., a bitmap frame.
  • Computer-to-conventional plate (CtCP) lithography technology may utilize SLMs as programmable, massively parallel write-heads, as illustrated in Fig. 3.
  • the CtCP system may be manufactured by BasysPrint's UV Series 57F machine equipped with a single DMD-based scanning head, which was commercialized in the early 2000s. The success of this technology led to the 700 series UV platesetters with two DMD- based scanning heads working in tandem to achieve process throughput that was orders of magnitude higher than single laser beam writing techniques.
  • Figs. 3A-3B illustrate a perspective view of an optical imaging system providing a light source to a given surface, in accordance with an exemplary embodiment of the present invention.
  • the LAMP system 100 for fabricating a three-dimensional object includes the optical imaging system 200.
  • the optical imaging system 200 or radiation system includes a light source 205, a reflector system 210, an optical lens system 215, a mirror 220, at least one SLM 225, e.g., a DMD, and a projection lens 230.
  • the light source 205 may illuminate, and thus provide a light.
  • Various embodiments of the present invention may include light sources comprising any one of an ultraviolet light, violet light, blue light, green light, actinic light, and the like.
  • the light source has a particular, predetermined wavelength in the UV spectrum.
  • Embodiments of the present invention may be described herein as a UV light source, but embodiments of the present invention are not limited to such a light source, and other light sources, including the examples disclosed may be implemented.
  • the light emitting from the light source 205 may be projected upon a portion of the reflector system 210, and reflects from the reflector system 210, which may comprise a concave- shaped reflector 211.
  • the reflector 211 of the reflector system 210 directs the light through a lens 216 of the optical lens system 215 before it reaches the mirror 220.
  • the mirror 220 then reflects the light towards the DMD 225.
  • the light from the DMD 225 is next directed towards the projection lens 230.
  • the light from the projection lens 230 is then projected onto the surface 300 of the photosensitive medium.
  • the BasysPrint device may incorporate the optical imaging system.
  • BasysPrint' s massively parallel scanning device may include a single DMD-based SLM. If desired and/or necessary, the BasysPrint device may be extended to multiple DMDs working in parallel.
  • Fig. 4 illustrates a perspective view of an exemplary embodiment of the optical imaging system 200 emitting a light source onto a given surface 300 of the photosensitive medium.
  • Fig. 4 illustrates a schematic of an SLM-based CtCP scanning maskless imaging system.
  • the UV light source 205 may be a mercury vapor lamp, xenon lamp, violet laser diode, diode pumped solid state laser, frequency-tripled Nd:YAG laser, XeF excimer laser, or the like.
  • the UV light source 205 may illuminate an SLM or an array of SLMs, e.g., one by two, such that the beams reflected from the ON pixels of the SLM array are coupled into the projection lens while the beams from the OFF pixels are directed away from the lens.
  • the elements of the SLM e.g., a DMD, 225, nominally approximately 15 micrometers ( ⁇ ) square in size, are individually controllable by the CAD data from the computer, enabling rapid, programmable selection of a large number of sites for laser irradiation.
  • the DMD 225 may modulate the illumination by means of its bi-stable mirror configuration, which, in the ON state, directs reflected illumination toward a projection lens, and in the OFF state, directs illumination away from the lens.
  • the entire optical imaging system 200 may be mounted on an XY scanning stage with a large area of travel spanning several hundred millimeters.
  • the projection lens 230 As the optical imaging system 200 is scanned over different areas of the medium, e.g., the substrate 300, the projection lens 230, with the appropriate magnification or reduction, images the ON pixels of the SLM array directly onto the substrate 300.
  • the projection lens 230 reduction ratio may be between approximately 1 and approximately 50, which may result in a minimum feature size between approximately 15 microns and approximately 0.3 microns.
  • Each pixel in the array is digitally controlled to be either ON or OFF.
  • a desired pattern corresponding to an input bitmap image may be generated by the SLM by loading the array with bitmap data that configures each pixel.
  • a different bitmap data set may be loaded.
  • the SLM may be a rapidly programmable structured light pattern generator that may reproduce an entire bitmap image with high fidelity across a large area substrate. Comparing SLMs to serial exposure via laser direct-write techniques, SLMs enable massively parallel processing by exposing an entire image field in a single shot.
  • the digital signal processing electronics integrated into commercial SLMs may support a high frame rate (several kHz) allowing the exposure image data to be refreshed continuously such that large areas of a substrate (photosensitive medium) may be continuously scrolled and dynamically exposed by scanning at high speeds.
  • Fig. 5 illustrates exemplary computer aided design slice patterns of a turbine airfoil mold, in accordance with an exemplary embodiment of the present invention.
  • the seamless scanning configuration of a maskless imaging system for projecting CAD slice patterns of multiple airfoil molds on a large area is illustrated in Fig. 5.
  • the optical imaging system 200 may be mounted on an X-Y stage, and is scanned while the SLM sends a sequence of frames.
  • Each frame e.g., see exemplary frames in Fig. 5, represents a portion of a full pattern, mimicking a mask scanning synchronously with the substrate.
  • the SLM is illuminated by a pulsed UV light source 205 while the pulses are synchronized to the data stream that configures the SLM.
  • the data sent to the SLM is continuously and synchronously updated, line-by-line, and frame-by-frame, delivering the entire pattern information to the substrate 300 during its scanning motion.
  • the SLM operates such that the entire array is reconfigured for each pulse to properly form the correct image on the substrate.
  • the desired image on the substrate 200 may be digitized and fed to the SLM as a stream of data in a similar fashion as used in raster- writing systems.
  • the difference between the SLM -based imaging system and conventional raster-writing methods is that the massively parallel processing power of the SLM is utilized to increase the data throughput by many orders of magnitude.
  • Exemplary embodiments integrate layered manufacturing of complex three-dimensional objects by solid freeform fabrication (SFF) using photocurable resins with the fine-feature resolution and high throughput of direct digital computer-to-plate (CtP) lithography techniques from the printing industry. These techniques have recently advanced to dramatically increased throughput by using SLMs to pattern large-area photosensitive plates directly from computer- processed bitmap images for making print masters.
  • SFF solid freeform fabrication
  • CtP direct digital computer-to-plate
  • This integration of technologies achieves a disruptive breakthrough in part build speed, size, and feature definition over current SFF methods.
  • Exemplary embodiments may provide an ability to rapidly manufacture parts or objects that have macro-scale exterior dimensions (approximately a few centimeters) and micro- scale interior features (approximately microns to approximately tens of microns).
  • exemplary embodiments may be well-suited for mass production of state-of-the-art integral ceramic cored molds for casting turbine airfoils directly from digital information.
  • Fig. 4 it illustrates a perspective view of a system and method for fabricating three-dimensional objects, in accordance with an exemplary embodiment of the present invention. That is, a LAMP system 100 is illustrated in Fig. 4, and illustrates layer-by- layer simultaneous fabrication of several objects - in an exemplary embodiment airfoil mold structures - over a large area.
  • light from UV light sources 205 of the optical imaging system 200 is conditioned and conveyed through optics.
  • the UV light sources 205 are conditioned and conveyed through transmissive and reflective optics onto an array of SLMs 225.
  • the SLM array may receive a real-time video stream of CAD data-slice bitmap images from the control system 400.
  • a process control computer 405 of the control system 400 may turn the corresponding pixels in the array ON or OFF.
  • the light from the ON pixels may be reflected downwards and transmitted into the projection lens system 230.
  • the projection lens 230 may convey highly focused images at the rate of several kilohertz (kHz) corresponding to the ON pixels onto the surface 300 of a photosensitive medium in the material build platform 500.
  • the optical imaging system 200 including the light source 205, optics 215, SLM array 225, and projection lens 230, may be scanned along the X and Y axes at high speeds to continuously expose new areas of the resin 300 synchronously with images that are continuously refreshed on the SLM array.
  • the surface of material build platform 500 may be moved downward along the negative Z-axis by a slice layer thickness, and a new layer of photocurable material may be swept by a material recoating system 600.
  • the material recoating system 600 which for illustration purposes is shown as a wire- wound draw-down bar - sweeps uniform thickness layers of the photosensitive medium at high speeds across the interior of the material build platform 500, without disturbing the previously built layers.
  • focusing and alignment optics may ensure that the surface of the medium is at the focal plane of the projection lens, making fine adjustments in the Z-direction if necessary.
  • the LAMP process repeats the cycle of building the next layer and delivering new resin until the entire build is completed. As shown in Figs.
  • the system and method for fabricating the three-dimensional object includes a maskless optical imaging system 200, a container 500 for holding the medium, material recoating system 600, and the control system 400.
  • the LAMP system 100 may include: (1) a maskless optical imaging system (MOIS) for exposing the patterns into a photosensitive medium; (2) the material build platform (MBP) for layer-by-layer UV curing and freeform fabrication of a three-dimensional object; (3) the material recoating system (MRS) for rapidly coating approximately 25-100 ⁇ uniform thickness layers of the photosensitive medium onto the MBP; and (4) the control system comprising hardware and software interfaces with the MOIS, the MBP, the MRS, and with 3-D CAD data bitmap slices in order to enable a completely automated and synchronized LAMP system.
  • MOIS maskless optical imaging system
  • MBP material build platform
  • MRS material recoating system
  • MOIS 200 may comprise the UV light source, beam homogenization optics, mirrors, condenser optics, illumination optics, an array of SLMs, and the projection lens system.
  • the MOIS 200 may comprise a UV light source, transmission and condenser optics, array of spatial light modulators (SLMs) (e.g., DMDs), projection lens system, and high-precision XY scanning stage.
  • SLMs spatial light modulators
  • MOIS 200 may utilize scanning exposure with the SLM array having well in excess of a million modulator elements.
  • MOIS 200 exploits state-of-the-art SLM 225, such as DMD chips (e.g., from Texas Instruments) with 1024 x 768 pixels and with an approximate 10 kHz frame rate.
  • SLM 225 such as DMD chips (e.g., from Texas Instruments) with 1024 x 768 pixels and with an approximate 10 kHz frame rate.
  • MOIS 200 exploits extensive software algorithms to coordinate and synchronize the SLM data frames and the position information of the scanning optical imaging system over the MBP.
  • MOIS 200 may be mounted on an overhead gantry style precision XY motion stage with sub-micron position resolution for achieving a minimum in-plane feature resolution of at least approximately 15 ⁇ with an error of approximately +1.5 ⁇ .
  • the XY motion stage may scan over the entire MBP 500 at high speeds (e.g., approximately several hundred mm/s) to expose different areas of the top surface of the MBP 500 that has a new unexposed layer of the photosensitive medium.
  • the MBP 500 may comprise a container 505 that serves as the build volume 510.
  • the MBP 500 may incorporate a build substrate mounted on a high- accuracy z-translation stage for building an object in layers e.g., 25 micrometer (and larger) thicknesses using the photosensitive medium. Thinner layers of the photosensitive medium may be created when the dimensions of a feature of the three-dimensional object require so. Similarly, when the dimensions of a feature of the three-dimensional object are large, thicker layers of the photosensitive medium may be used.
  • the overall dimensions of the overall build volume 510 may be approximately 24 inches (X) by 24 inches (Y) by 16 inches (Z) (24" x 24" x 16").
  • a build surface 515 made of a precision machined plate 516 may be located within the build volume 510 (i.e., in the MBP's interior) and may be mounted on a precision linear motion stage for motion in the Z-direction. During the fabrication of a part, the build surface 515 may be moved incrementally downwards by a distance equal to the layer thickness with which the part is being built. The control system 400 may control this downward movement.
  • the MBP 500 may be constructed using a precision linear positioning system with sub-micron resolution for achieving a minimum build layer thickness of approximately 25 ⁇ with an error of approximately +2.5 ⁇ .
  • the build surface 515 may move down via its downwardly moving plate 516, and the MRS 600 may apply a new layer of the photocurable ceramic material.
  • the MRS 600 may comprise a coating device 605, which may be, without limitation, a wire- wound Mayer draw-down bar, a comma bar, or a knife edge or a slurry dispensing system.
  • the MRS 600 may incorporate a coating device capable of applying coatings as thin as approximately 2.5 microns with 0.25 micron variation.
  • the MRS 600 may be designed to successively deposit the layers of the photosensitive medium. During a part build, upon the completion of a layer exposure, the MRS 600 may quickly sweep the medium across the build area under computer 405 control.
  • the MRS 600 may implement principles from the web- coating industry, where extremely thin and uniform coatings (on the order of a few micrometers) of various particulate-loaded formulations are deposited on fixed, flat, or flexible substrates.
  • the photosensitive medium may comprise a concentrated dispersion of refractory ceramic particles in a photopolymerizable matrix.
  • the ceramic particles can, after firing, produce a high quality ceramic object.
  • the photopolymerizable matrix may be a mixture of camphor with an acrylic monomer, formulated so that it is solid at room temperature, but liquid when warm (above about 60°C). Camphene may be selected due to of its convenient melting point, and because solid camphene has a high vapor pressure, making it easy to remove by sublimation. Liquefied resin may be supplied warm to the recoating system, and applied on the material build platform as a thin liquid layer. It may quickly freeze, providing a smooth solid surface.
  • Exposure to the UV may cross-link the monomer, rendering the exposed areas infusible.
  • heating the block of build material above about 60°C may melt away the unexposed material, which drains as a liquid.
  • the solid camphene c removed from the green body by sublimation at or slightly above room temperature.
  • the LAMP-fabricated mold may be a dry body containing enough polyacrylate for high green strength, but not so much that special binder-burnout is required before firing.
  • the solid build material may further provide sharper curing profiles, and may improve resolution.
  • a solid build material may not require a liquid vat with associated issues of flow- related disturbance of the previously-exposed layers. Consequently, recoating may be done much faster and with thinner layers, because the higher shear forces from the recoating device may not disrupt underlying solid layers.
  • the solid build material that the support structures are inside may not be needed.
  • Support structures are endemic to 3-D free-forming from liquid materials.
  • a layer that has overhangs (such as a curved part) cannot float in space, so the build software produces a temporary scaffold to support it, i.e., a support structure.
  • the support structures need to be removed. But if the object is a metal casting mold, the cavity on the inside of the mold is the relevant surface, and an interior support structure cannot be simply removed. Careful consideration of the design is required to find optimal build directions where support structures are not needed.
  • Solid build materials do not require support structures, because the overhangs are supported by the solid (but uncured) material below.
  • Silica is an exemplary ceramic material, whereas the LAMP process may be applied to a wide range of ceramic materials.
  • Alumina- or yttria-containing photosensitive media may be produced, for example, to cast more reactive superalloys (for making turbine airfoils) that require alumina or yttria molds. Adjusting exposures for the alumina-based or yttria-based resin causes a different sensitivity for photopolymerization. Sensitivity in ceramic-containing resins is mostly limited by light scattering, which depends upon the refractive index of the ceramic and also on the particle size distribution and suspension structure affecting photon transport. The refractive index of silica is close to the monomer, so silica resins are very sensitive. Alumina and yttria have higher refractive indices and so they require a higher exposure dose.
  • a new photosensitive medium may be developed taking into account the rheological behavior of the medium material in the liquid state, the photocuring behavior of the medium, the clean draining of the uncured medium, cured polymer removal, firing, and the refractory properties of the final fired ceramic object.
  • a solid medium may adopt the successful terpenoid-based vehicles, such as camphor, which may be removed after forming by sublimation. This eliminates nearly all drying and binder burnout issues.
  • terpenoid-based vehicles such as camphor
  • the rheology of ceramic powders in warm liquid terpenoids is well understood, and effective colloidal dispersants are commercially available.
  • Detailed information is available on solidification of camphor and camphene at room temperature, as these have been a preferred model system for solidification research.
  • the solidification of concentrated ceramic suspensions is also well understood.
  • Preliminary results of the photopolymerization behavior of solid photosensitive medium based on terpenoid-acrylate monomers are encouraging. Solid polymers are routinely used in pre-press platesetting print industry, as well as in photolithography.
  • the photocuring characteristics of the ceramic-containing resins as a function of composition and properties may be tailored to develop an optimized PCMS composition.
  • Examples of ceramic-containing resins for use as the photosensitive medium and of their manipulability may be found in U.S. Patent No. 6,117,612, which is incorporated by reference herein as if fully set forth below.
  • the control system 400 may comprise the PCS 405 for the LAMP system 100.
  • the PCS 405 forms the brains of the LAMP system 400 and is the central processing unit of the system, responsible for automation functions.
  • the PCS 405 may include the software algorithms to conduct adaptive slicing of the integral cored mold CAD files for optimized layer thickness, part surface finish, avoidance of stairstepping, and minimum build time as a function of critical features and feature sizes present in the mold design.
  • the PCS 405 further may include the algorithms and signal communication logic for coordinating the motion of the MBP, the MRS, and the MOIS for automated layer-by-layer material delivery, scanning, and photoexposure to build 3D parts in the shortest possible time with the least possible idle time in the LAMP machine.
  • Software algorithms may process the CAD data slices into the stacks of images (e.g., see Fig. 10A) necessary to be flashed to the SLMs at the high rates necessary for seamless and maskless exposure of the photosensitive medium as the MOIS moves at high speeds over the MBP.
  • Software algorithms may also adaptively adjust the exposure dose in real- time as a function of slice layer thickness to achieve the necessary full cure depth through the layer thickness regardless of the layer thickness.
  • the overall PCS and user interface for the LAMP system may integrate the software algorithms and signal communication logic.
  • the PCS may include all the necessary CAD data interfaces, machine automation and control hardware and software interfaces, and fault detection and recovery in order for the LAMP machine to function as a fully automated, operator- free solid freeform fabrication (SFF) machine.
  • SFF solid freeform fabrication
  • Fig. 9 illustrates a plurality of cross-sectional views of a 3D CAD drawing
  • Fig. 10A illustrates a plurality of stacked cross-sectional views of the 3D image that results in the turbine airfoil mold 3D casting of Fig. 10B.
  • Figs. 6-7 illustrate an exemplary LAMP device illustrating the optical imaging system, the material recoating system, and the material build platform. In other words, Figs. 6-7 are conceptual schematics of the LAMP system showing the MOIS, the high -precision XY scanning stage, the MRS, and the MBP.
  • the MOIS 200 is shown in greater detail in Fig. 7.
  • the MOIS 200 may transform the non-uniform output from the UV light source 205 into a rectangular beam of uniform intensity that illuminates the SLM array after being redirected by two mirrors and after passing through condenser optics.
  • the SLM array or DMD 225 may be illuminated at an angle with respect to the normal of the pixel plane, because the ON mirrors tilt to direct the light into the projection lens.
  • the projection lens 230 magnifies or reduces the image with the appropriate ratio and projects the image onto the surface of the medium in the MBP 500, which is located at the focal plane of the projection lens.
  • the MOIS 200 is mounted overhead gantry style on an XY scanning stage and is traversed preferably over the MBP 500, while the SLM sends a sequence of frames. Each frame represents a portion of a full continuously scrolling pattern that covers the entire exposable area of the MBP 500.
  • the SLM may be illuminated by a pulsed UV light source that is synchronized to the SLM data stream. As the substrate moves, the data sent to the SLM is continuously updated, row-by-row, and frame-by-frame of the micromirror array, delivering the entire pattern information to the substrate during its scanning motion.
  • the massively parallel processing power of the SLM is utilized to increase the photopolymerization throughput by at least six orders of magnitude over that of a single point laser light source, as is the case in stereolithography.
  • Commercial high-speed scanning stages may move the optical imaging system at speeds of 400-600 mm/s, so 200 parts may be exposed in a 24 inches by 24 inches build area within approximately one second.
  • a time budget of one second for exposure means that recoating a layer should take no more than four seconds. This means that the recoating device may move at relatively high speeds, upwards of approximately 100 mm/s to traverse the 24 inch (610mm) length of the build platform in less than four seconds.
  • the recoating device may successfully coat a new layer of the photosensitive medium at speeds of approximately 300mm/s to approximately 1500 mm/s (approximately 1-5 ft/s). These types of coating speeds, commercially in use in the converting and web coating industry enables the system to meet the critical time budget per layer, while achieving the high throughout necessary to make LAMP a cost-effective process. Calculations further reveal that by implementing adaptive slicing to use thinner layers (e.g., approximately 25-75 micrometers) in regions of the part containing critical features and thicker layers (e.g., approximately 250 micrometers) elsewhere, the part build rate may be increased to at least approximately 90 parts per hour, resulting in a cost savings of approximately 25-30% per part.
  • thinner layers e.g., approximately 25-75 micrometers
  • thicker layers e.g., approximately 250 micrometers
  • Superalloy objects e.g., airfoils
  • the photosensitive medium for the integral cored molds to be produced through the LAMP process may be designed and developed based on a silica formulation.
  • a formulation may be modeled on the same composition used for conventional cores and shell molds.
  • Silica may be the refractory material because it is relatively easy to remove by leaching after casting.
  • at least two photocurable ceramic media or materials may be used: 1) a liquid ceramic resin, and 2) a solid ceramic resin.
  • the photocurable ceramic material may be a liquid ceramic resin, based on existing stereolithography resins.
  • Such resins contain approximately 50-60 vol suspensions of ceramic particles in a low viscosity fluid monomer (non-aqueous acrylate or aqueous methacrylate).
  • a low viscosity fluid monomer non-aqueous acrylate or aqueous methacrylate.
  • the liquid ceramic resin is locally solidified by photopolymerization where it is exposed to UV light. After the build is complete, the integral cored mold is a solid ceramic-filled photopolymer in a vat of liquid resin. The excess resin drains away after the mold is removed from the vat.
  • the as-cured mold must undergo a binder burnout process (approximately 200- 500°C) to remove the polymer without damaging the mold.
  • Liquid resins have many disadvantages, including: (1) they cure to a "green" build state that is composed of a ceramic in a polymer in the case of acrylate, requiring careful binder pyrolysis, or a wet ceramic in wet hydrogel (aqueous methacrylate) which requires careful drying. Both of these are controllable for the thin sections relevant for the molds, but place a constraint on the process; and (2) they require support structures to be built along with the part for some designs.
  • the photocurable ceramic material may be a solid ceramic resin including a solid, sublimable monomer solution.
  • This may include a build material that may be applied as a liquid, but one that freezes upon application to form a photopolymerizable solid.
  • a build material that may be applied as a liquid, but one that freezes upon application to form a photopolymerizable solid.
  • the solid solvent may be a low-melting vehicle that melts above about approximately 50°C (e.g., a camphor-camphene alloy). In the molten state, it is a fluid suspension of approximately 50-60 vol ceramic powder in a low viscosity monomer-vehicle solution.
  • a fresh layer of material may be applied as a warm liquid, which freezes after application creating a solid build material.
  • the frozen solid ceramic resin is locally cross-linked by photopolymerization where it is exposed to UV light.
  • the integral cored mold is a solid ceramic-filled cross- linked photopolymer in a block of frozen solid resin.
  • the block is simply heated above the melting point of the vehicle, so that the uncured excess resin drains away.
  • the remaining camphor in the as-cured mold is removed by sublimation after building (ambient temperature freeze drying). After sublimation, only a small amount of cured monomer remains, so binder burnout is much easier.
  • Camphene is a non-toxic material derived from pine trees (a terpenoid), and melts just above room temperature (50°C), but is a solid at room temperature.
  • Camphor is a similar material, with a higher melting point. These terpenoids may be used for freeze casting of ceramic suspensions.
  • the solid camphene (or camphor) is easily sublimed, so that after forming it may be removed by sublimation. This eliminates difficulties associated with binder polymer pyrolysis (as with polyacrylates) and liquid drying of hydrogels (as with aqueous methacrylates).
  • the sublimation is a gentle solid- vapor transformation that results in no dimensional change, and hence there is little or no warping or cracking.
  • the LAMP process may build "green" ceramic devices, including ceramic powder in a photopolymerized binder. Draining the devices of uncured ceramic resin may be necessary, and effective procedures for draining, flushing, and removal of all loose materials may further be necessary. After draining is complete, the as-built "green” ceramic devices may be successfully fired for polymer removal and sintering to create strong objects with the correct mineralogy and functionality.
  • the embodiments disclosed herein allow for the design and manufacture of components that would otherwise be difficult or impossible to manufacture conventionally.
  • ceramic-containing LAMP products With respect to ceramic-containing LAMP products, the disclosed embodiments may radically change how the casting of nearly any component that employs temporary cores and molds is done worldwide.
  • the various embodiments of the present invention are further illustrated by the following non-limiting example. LAMP was used to build complex 3D products by photo patterning many thin layers of a UV-curable resin.
  • An exemplary UV-curable resin contains approximately 76 weight percent silica powder prepared by grinding fused silica to an average particle size of 7 microns, 19.17 weight percent SR238 monomer (Sartomer, Warrington PA) and 2.34 weight percent SR494 monomer (Sartomer, Warrington PA), 1.58 weight percent Variquat CC55 dispersant (Degussa), and a photointiator, such as 0.86 weight percent Irgacure 819 (Ciba- Giegy). Other photoinitiators, absorbers, or dyes may be added to modify the UV-curing characteristics as desired.
  • a maskless optical imaging system scanned the UV-curable resin with a high resolution bitmap pattern to cure individual layers.
  • Refractory ceramic molds were produced using as the resin UV-curable suspensions of silica powders in acrylate monomers.
  • the system includes an optical imaging system, a photocurable medium, and a control system.
  • the optical imaging system provides a light source.
  • the photocurable medium changes states upon exposure to a portion of the light source from the optical imaging system.
  • the control system controls movement of the optical imaging system, wherein the optical imaging system moves continuously above the photocurable medium.
  • the optical imaging system comprises a reflector receiving a portion of the light source; an optical lens system comprising a lens that receives a portion of the reflected light source; a spatial light modulator for receiving the reflected light source from the optical lens system; and a projection lens for focusing the light source received from the spatial light modulator onto a surface of the photocurable medium.
  • the optical imaging system includes a maskless light system for providing the light source and comprising a spatial light modulator scanning a portion of the medium.
  • the light source continuously changes as the optical light system moves over the surface of the photocurable medium.
  • the photocurable medium may include a photopolymer.
  • the control system may receive a computer aided design drawing.
  • the optical imaging system projects a two-dimensional image comprising a cross-section of a three-dimensional object to be formed, the two-dimensional image received from the control system, onto a surface of the medium.
  • the projected two-dimensional image may be a dynamic image that continuously changes as the optical imaging system scans over the medium.
  • the system further comprises a container for housing the photocurable medium.
  • the container includes a lower platform that may move downwardly for lowering away from the optical imaging system, wherein the container includes an inlet for introducing more of the photocurable medium therein.
  • the system further comprises a recoating system for rapidly coating a uniform thickness of the photocurable medium.
  • an optical modeling method in which a photocurable medium is exposed with a light beam to form a three-dimensional model includes a number of steps.
  • the method comprises moving a maskless optical imaging system providing the light beam in a continuous sequence; presenting the light beam on a portion of the photocurable medium; lowering a plate upon which the photocurable medium resides; and applying a new layer of photocurable media.
  • the method may further include analyzing a plurality of two-dimensional computer aided designs; the light beam presented on the portion of the photocurable medium having the shape from one of the plurality of two-dimensional computer aided designs.
  • the method may further include projecting the light beam that continuously changes as the light beam scans a surface of the photocurable medium.
  • the method may include providing a material build platform for housing the photocurable medium and the plate upon which the photocurable medium resides.
  • the method may include directing the light beam to reflect off a reflector, through at least one lens system, and to a spatial light modulator.
  • the lowering of the plate upon which the photocurable medium resides occurs after the light beam is presented to the portion of the photocurable medium.
  • a method for fabricating a three-dimensional object comprises moving a maskless optical imaging system providing a light source in a continuous sequence; directing the light source to reflect off a reflector, through at least one lens system, and into a spatial light modulator; analyzing a plurality of two-dimensional computer aided designs; presenting the light source on a portion of a photocurable medium contained in a material build platform, the light source presented on the portion of the photocurable medium having a pattern corresponding to one of the plurality of two-dimensional computer aided designs; projecting the light source to continuously change as the light source scans a surface of the photocurable medium; lowering a plate disposed within the material build platform upon which the photocurable medium resides, the lowering of the plate upon which the photocurable medium resides occurring after the light source is presented to the portion of the photocurable medium; and applying a new layer of photocurable media to the material build platform.
  • LAMP Large Area Maskless Photopolymerization
  • LAMP technology may be used for the fabrication of integrally-cored ceramic molds, with complex internal geometries, such as in the investment casting of high-pressure turbine blades.
  • LAMP may be applied to produce functional ceramic components that may withstand the rigors of, for instance, high temperature processes involved in the single-crystal casting of turbine blades.
  • the complex internal geometries and the stringent requirements on the physical properties of the parts to be produced may pose multiple challenges.
  • STL files which are meshed approximations of the part geometry
  • AM additive manufacturing
  • an error-tolerant, direct slicing approach using ACIS kernel may be used to slice the native CAD geometry and may output high resolution (1500 dpi) bitmap images of the slice contour.
  • STL file slicing algorithms may be used with the LAMP technology.
  • a suite of post processing algorithms such as error-checking, part placement, tiling and the like that work on the slice image data may be used with the LAMP technology.
  • this disclosure also describes several computational schemes to further improve part quality using the LAMP technology, such as a volume deviation-based method for adaptively slicing CAD models to alleviate "stairstepping" effects on parts produced using the LAMP technology and other AM processes in general and a gray-scaling and dithering method applied to the slice images to alleviate the stair-stepping effect, which takes into account the effects of gray scale factor on the curing characteristics of the material system when computing gray scale intensities unlike previous approaches.
  • This disclosure also describes a method for supporting geometries that result in unsupported features or "floating islands” during part builds. This method may work on native CAD geometry. Moreover, prior approaches may not be applied to the LAMP technology due to, for instance, the inability to remove support structures after build completion.
  • Fig. 11 illustrates one embodiment of a LAMP machine 1100 having a gantry-style scanning maskless optical imaging system in accordance with various aspects described herein.
  • the LAMP machine 1100 may be configured as described by Fig. 11. Further, the LAMP machine 1100 may be configured to include a material recoating system 1101, an overhead gantry style maskless optical imaging system 1103, a high-precision XY scanning stage 1105, and a material build platform 1107.
  • Fig. 12 illustrates one embodiment of a scanning maskless optical imaging system 1200 in accordance with various aspects described herein.
  • the system 1200 may be configured as described by Fig. 12.
  • Fig. 13 illustrates one embodiment of a scanning maskless optical imaging system 1300 in accordance with various aspects described herein.
  • the scanning maskless optical imaging system 1300 may be configured as described in Fig. 13. Further, the scanning maskless optical imaging system 1300 may be configured to include a UV pixel array flashed from DMD 1301, a projection lens 1303, a DMD 1305, a condenser 1307, a first mirror 1309, a second mirror 1311, a UV light source 1313, and a domed reflector 1315.
  • Fig. 14 illustrates one embodiment of a material build platform (MBP) 1400 in accordance with various aspects described herein.
  • the material build platform 1400 may be configured as described in Fig. 14. Further, the material build platform 1400 may be configured to include a dynamic containment build tank 1401.
  • the dynamic containment build tank 1401 may be empty, as described by reference number 1411.
  • the dynamic containment build tank 1401 may have a part 1403 that is completed, as described by reference number 1412.
  • the build tank 1401 may incrementally grows as each layer is added to the part 1403, as described by reference numbers 1413 to 1420.
  • each side of the dynamic containment build tank may grow as each layer is added to the part 1403.
  • Fig. 15 illustrates one embodiment of a material recoating system (MRS) 1500 in accordance with various aspects described herein.
  • the system 1500 may be configured as described in Fig. 15.
  • the system 1500 may be configured to use dispense-on-demand to address, for instance, in-tank and intra-layer sedimentation.
  • Fig. 16 illustrates another embodiment of a material recoating system (MRS) 1600 in accordance with various aspects described herein.
  • the system 1600 may be configured as described in Fig. 16. Further, the system 1600 may be configured to use dispense-on-demand to address, for instance, in-tank and intra-layer sedimentation.
  • Fig. 17 illustrates a loss of build precision using a material recoating system having a single-edge recoater.
  • the material recoating system having a single-edge recoater may cause starvation or doming, which may result in loss of build precision.
  • a blade may have removed too much slurry and may form a crater shape in the slurry area around a mold.
  • a dome shape of slurry may be formed surrounding the mold parts. This doming problem may get worse as, for instance, more layers are added, which may cause a build of a part to fail.
  • Fig. 17 illustrates a loss of build precision using a material recoating system having a single-edge recoater.
  • the material recoating system having a single-edge recoater may cause starvation or doming, which may result in loss of build precision.
  • a blade may have removed too much slurry and may form a crater shape in the slurry area around a mold.
  • FIG. 18 illustrates one embodiment of a material recoating system 1800 having a multiblade recoater in accordance with various aspects described herein.
  • the system 1800 may be configured as described in Fig. 18. Further, the system 1800 may be configured to address the starvation and doming issues described in Fig. 17, which may increase build precision of a part.
  • Fig. 19 illustrates one embodiment of a screen printing-style inking window pane in accordance with various aspects described herein.
  • the screen printing-style inking window pane 1900 may be configured as described in Fig. 19.
  • Fig. 20 illustrates a loss of build precision using a material recoating system.
  • the material recoating system may cause erosion of a surface of a part due to, for instance, a large volume of uncured liquid. Further, as the material recoating system sweeps new layers at a high speed, a large trapped volume of uncured monomer may erode a surface of a part.
  • Fig. 21 illustrates one embodiment of a method 2100 of constructing a conformal lattice in an inter-part space using break lines in accordance with various aspects as described herein.
  • the method 2100 may include collectively building a build block including tank walls, a part, and a conformal lattice. Further, the method 2100 may include reducing a trapped volume of uncured monomer, reducing or eliminating part erosion, reducing starvation or doming, or the like, resulting in increased build precision of a part.
  • Fig. 22 illustrates another embodiment of a method 2200 of constructing a conformal lattice in inter-part space using break lines in accordance with various aspects as described herein.
  • the method 2200 may include collectively building a build block including tank walls, a part, and a conformal lattice.
  • the method 2100 may include performing a post-build part break-out, which may include deconstructing the tank walls or the conformal lattice from the build block along the break lines.
  • the method 2100 may include retrieving the part.
  • Fig. 23 illustrates one embodiment of a LAMP machine 2300 in accordance with various aspects as described herein.
  • the LAMP machine 2300 may be configured as described in Fig. 23.
  • Fig. 24 illustrates one embodiment of a method 2400 for correcting a gap error in accordance with various aspects described herein.
  • Fig. 25 illustrates another embodiment of a method 2500 for correcting a gap error in accordance with various aspects described herein.
  • Fig. 26 illustrates one embodiment of a method 2600 of automated part layout and scaffolding in accordance with various aspects described herein.
  • Fig. 27 illustrates one embodiment of a method 2700 of identifying a floating island in accordance with various aspects as described herein.
  • Fig. 28 illustrates one embodiment of a method 2800 of identifying a multifunctional support structure in accordance with various aspects as described herein.
  • Fig. 29 illustrates one embodiment of a method 2900 for screening for shrinkage relief and support structures in accordance with various aspects as described herein.
  • Fig. 30 illustrates another embodiment of a method 3000 for screening for shrinkage relief and support structures in accordance with various aspects as described herein.
  • Fig. 31 illustrates another embodiment of a method 3100 for screening for shrinkage relief and support structures in accordance with various aspects as described herein.
  • Fig. 32 provides a chart 3200 of screening-based grayscale working curves for one embodiment of a LAMP system.
  • Fig. 33 provides a chart 3300 of screening-based grayscale working curves for one embodiment of a LAMP system.
  • Fig. 34 provides a chart 3400 of screening-based grayscale working curves for one embodiment of a LAMP system.
  • Fig. 35 provides a chart 3500 of screening-based grayscale working curves for one embodiment of a LAMP system.
  • Fig. 36 provides a chart 3600 of screening-based grayscale working curves for one embodiment of a LAMP system.
  • Fig. 37 provides a chart 3700 of screening-based grayscale working curves for one embodiment of a LAMP system.
  • the LAMP process may be intended to fabricate high-precision internally cooled turbine blades and hence may not afford the coarse tessellated geometry approximation of STL files.
  • the native CAD geometry may need to be processed to output the slice data used for building these components.
  • a direct slicing algorithm for accomplishing this may be implemented using a geometric kernel such as ACIS.
  • Fig. 38 illustrates one embodiment of a method 3800 of performing direct slicing in accordance with various aspects as described herein.
  • the method 3800 may include loading an original CAD part into a program, as referenced at 3800a.
  • the method 3800 may include computing a bounding box, as referenced at 3800b.
  • the method 3800 may include creating a slice plane, as referenced at 3800c.
  • the method 3800 may include computing an intersection between the part and the slicing plane, as referenced at 3800d.
  • the method 3800 may include rasterizing an intersection wire to create a bitmap image, as referenced at 3800e.
  • the method 3800 may include obtaining or compressing slice bitmaps using, for instance, CCITT FAX4, as referenced at 3800f.
  • the ACIS kernel is a commercially available C++ CAD library marketed by Spatial Corp, a subsidiary of Dassault Systems. It offers robust APIs (Application Programming Interface) and function calls for most of the basic CAD operations. These APIs have been integrated into the slicing software to produce CAD slices. The resulting CAD slices are then rasterized to obtain the bitmaps used for exposure.
  • the original CAD mold that needs to be sliced may be first loaded into the algorithm using ACIS's load functions, as referenced at 3800a.
  • ACIS libraries may work with the SAT file format and hence CAD files in other formats may need to be converted first into the SAT format either by using commercial CAD software or by using ACIS's inbuilt file format translation functions. During the translation, numerical or topological inaccuracies may creep into the part. In severe cases, error checking and correction schemes may need to be implemented.
  • its bounding box may be computed to obtain an estimate of the size of the bitmaps that would be generated, as referenced at 3800b.
  • a slicing plane may then be created and intersected with the part using, for instance, ACIS's Boolean APIs to get an intersection wire, as referenced at 3800c.
  • the intersection wire Once the intersection wire is obtained, it may be rasterized to obtain the bitmaps, as referenced at 3800d. This may involve shooting rays for each row of pixels in the image and computing the intersection points with the intersection wire. Pixel values may then be filled with alternating white and black segments in between each of these intersection points, as referenced at 3800e.
  • the bitmap images obtained may then be compressed using CCITT fax4 lossless compression scheme that compresses the data by three orders of magnitude without any loss, as referenced at 3800f.
  • CCITT fax4 is an industry standard lossless compression scheme for efficiently compressing 1-bit TIFF images. These bitmaps may then be fed to the post processing algorithms.
  • Algorithm 1 In order to accomplish the tasks discussed in the basic algorithm outline shown in Fig. 38, several different steps may need to be completed. An example of these steps is shown in the pseudocode for direct slicing, referred to as Algorithm 1.
  • Image Width Ximx ⁇ X ⁇ in , Equation ( 1 ) .
  • Image Height Fmax ⁇ Y ⁇ in , Equation (2) .
  • an ASCII character array denoted by 'characterBuffer' may be created and dynamically allocated in order to store the necessary information for each slice.
  • each pixel may require 1- bit of memory. There may be no provision in C++ to access each bit of memory individually. So, sets of values ('O's and Ts; '0' denoting black and T denoting white) of eight pixels may be read at a time and the ASCII character corresponding to their decimal sum may be stored in the appropriate location of the 'characterBuffer' array.
  • the part may then be sliced at the corresponding 'Z' height location by calling the 'api_planar_slice' API to produce an intersection contour. Details of the various ACIS APIs may be found at their documentation portal, as described in ACIS Documentation Portal found at http://doc.spatial.com/index2.php. If the part file has multiple bodies, each of these bodies may be sliced as well and the resulting cross section contours may be stored in a list denoted by 'crossSectionList'. Having computed all of the planar intersections, all the edges from each of these contours may be extracted and stored in an 'edgeList'.
  • the 'edgeList' Once the 'edgeList' is populated, it may then be time for computing the necessary color information for creating the bitmap image.
  • the "exterior” of the part may be denoted by black whereas the “interior” of the part may be denoted by white.
  • a point's membership with respect to the interior may be established by originating a non "osculating" (touch without crossing) curve from the desired point and letting it propagate to infinity (with the assumption that a point infinitely far away is exterior to the part) while counting the number of times it intersects with the part. If the number of intersections is odd (even), then the point may be interior (exterior) to the part.
  • Fig. 39 illustrates one embodiment of a method of identifying the "interior” from the "exterior” in accordance with various aspects as described herein.
  • the ray originating from the exterior point makes an even number (four) of intersections while the ray originating from the interior point makes an odd number (five). It is fairly evident that the same logic applies if the ray were to start at infinity and terminate at a point whose membership is to be determined. More importantly, it may be observed that if a ray starting at infinity were to cut across a part, its membership toggles between interior and exterior of the part every time it intersects with the part boundary. For the purposes of making the slice image, this fact may be taken advantage of.
  • Rays starting at the left end of the bounding box may be created for each row of pixels in the image and their intersection points with each of the edges in 'edgeList' may be computed. As previously mentioned, these rays may have to be non-"osculating" for this method to work and hence the computed intersection points may be stored to the 'intersectionList' if the ray is non-tangential to the edge with which the intersection point is computed.
  • an 'integerBuffer' array may be created to store the pixel color data.
  • a boolean 'color' variable (a variable that may only take values of '0' and T) may be created and initiated to '0' to start with (as the start point of the ray may be external to the part).
  • the process of marching along the ray may be simulated by counting the pixels as we move from left to right in the row.
  • the value of the 'color' variable may be toggled every time the pixel number exceeds the 'X' coordinates of one of the points in 'intersectionList' . This progression along the ray may be counted in terms of pixels and may not be counted in the absolute floating-point distance traveled along the ray with respect to size of each pixel.
  • the size of each pixel may be a floating-point number such as 0.00066667 inches for a 1500dpi image and counting the distance traveled with respect to this size instead of the integer pixel numbers may lead to floating point errors and may result in rough edges in the slice image, as described in Fig. 40.
  • Fig. 40 is a slice image having rough edges due to floating point errors in counting a distance traveled. In Fig. 40, the inset shows the resulting rough edges. Such rough edges may diminish the surface quality of the part and hence may need to be avoided.
  • the 'integerBuffer' array may then be converted to the corresponding ASCII characters to fill the 'characterBuffer' array for the image.
  • the 'character-Buffer' array may get completely filled when this process of intersection and collecting the pixel color information is completed for all the rows of the image, at which point it may be used to make the compressed TIFF image.
  • Fig. 41 illustrates test parts used in much of the previously reported work in the direct slicing literature. As may be seen, most of the test parts are single volume solids with a few that have one or two voids in them.
  • Fig. 42 shows a CAD model of a typical internally cooled HP turbine blade. It is deliberately shown in the wire frame view to give a better appreciation of the geometric complexity involved. Every edge in the figure represents an interface where two or more NURBS surfaces meet. Upon comparing the test parts previously shown with the HP blade mold, the order of magnitude difference in the geometric complexities involved in LAMP parts is evident. There is so much scope for errors with parts of such high complexity.
  • Tiny gaps in the model due to CAD translations or non manifold geometry due to improperly defined surface intersections at the interfaces by the designer are very common.
  • the direct slicing algorithm described in the previous section may be implemented to be tolerant to these errors.
  • the first step is slicing which involves computation of the intersection between the slice plane and the CAD object. Due to the improperly defined geometry at complex regions of the mold, in some instances the slicing operation fails to produce a wireframe intersection curve (step (c) in Figure 10).
  • the second step that contributes to errors is rasterization (step (d) in Figure 10) which involves computing the intersections between rays and the wire frame intersection curve. Any gaps in the model manifest as gaps in the wire frame curve and these, in turn, manifest as stray lines in the rasterized image (refer to Figure 28(a) for an illustration of these stray lines).
  • Fig. 43A provides a chart 4300a of the number of stray lines observed in each image from a stack of hundred consecutive slices produced at two different ACIS resolutions. It may be seen that consistently more numbers of errors are produced in each slice layer at the lower resolution (lower ACIS tolerance to topology errors) value. Not only does the ACIS Resolution parameter influence the slice image errors in rasterization, but it was also observed to influence the errors produced in the slicing step. When the slicing operation fails, in some instances it was observed that by lowering the ACIS resolution (thus making the kernel more tolerant) and re- slicing, the wire frame intersection curves may still be computed.
  • this error checking algorithm may work on a stack of slice images irrespective of whether they are produced by the direct slicing algorithm or the several STL file slicing algorithms.
  • this second level of error tolerancing apart from making the direct slicing algorithm error tolerant, makes all the STL file slicing algorithms error tolerant as well.
  • the time complexity of the algorithm may be estimated as follows: Assuming there are N surfaces in the part, for every layer in the part:
  • N surface intersections need to be computed with the slicing plane. This amounts to N operations requiring roughly constant time. 2) Next, considering the worst case scenario, for each row of pixels in the image, N ray- edge intersections need to be computed. This amounts to another Image Height * N operations.
  • T(N) #Layers * (N + Image Height * (N + C * Image Width ⁇ ⁇ , Equation (3).
  • N denotes the number of surfaces in the part and C is a constant.
  • the computation time of the algorithm roughly scales linearly with the number of layers in the part ,which may be directly proportional to the height of the part and inversely proportional to the Layer thickness, and the number of surfaces in the part.
  • Equation 3 predicts the slicing time to scale quadratically with respect to the Image Height and Image Width, the number of operations are much more dependent on the image height than the width of the image. Therefore, the slicing time may roughly scaled linearly with respect to the image height and may be independent of the image width (linear in reality but with a very small slope) and therefore also scales linearly with respect to the output resolution (DPI, dots per inch) of the slice image.
  • DPI dots per inch
  • Fig. 43B provides a graph 4300b of the time to compute one slice scaling with DPI. For the full edged, internally cooled HP turbine blade mold shown in Fig. 42, it takes about two (2) minutes to compute each slice and about a day and a half to compute the entire stack of slice images along the length of the part.
  • STL files are just a random collection on triangular facets with no edge or vertex connectivity information embedded in it.
  • the basic structure of a sample STL file is shown below: solid cube_corner facet normal 0.0 -1.0 0.0 outer loop vertex 0.0 0.0 0.0 vertex 1.0 0.0 0.0 vertex 0.0 0.0 1.0 endloop endfacet facet normal 0.0 0.0 -1.0 outer loop vertex 0.0 0.0 0.0 vertex 0.0 1.0 0.0 vertex 1.0 0.0 vertex 1.0 0.0 0.0 endloop endfacet facet normal 0.0 0.0 -1.0 outer loop vertex 0.0 0.0 0.0 vertex 0.0 0.0 0.0 vertex 0.0 1.0 vertex 0.0 0.0 endloop endfacet facet normal 0.5770.5770.577 outer loop vertex 1.0 0.0 0.0 vertex 0.0 0.0 vertex 0.0 0.0 0.0 1.0 endloop endfacet endsolid
  • Fig. 44 shows the various elements of the BRep (Boundary Representation) data structure.
  • the BRep (Boundary Representation) data structure may need to be created and populated.
  • Each body in the BRep data structure may be divided into 'Lumps'. Lumps may or may not be disconnected and may be present for the reason of simplifying the geometry to make the CAD algorithms more efficient.
  • Each Lump may include a list of disconnected closed objects called 'Shells'.
  • Each shell may include a list of 'Faces' that bound the space defined by the shell.
  • Each 'Face' may include a series of 'Loops' .
  • a Loop may be a ring of end-to-end connected 'Co-edges' .
  • a Co-edge may be a topological entity associated with every 'Edge' in the model and may be used to store edge connectivity information in the part. If two faces meet at an edge, the corresponding co-edges from the loops of each of these faces may refer to the same edge and this may be how the modeling kernel identifies adjacency information between them.
  • edges may need to be created and corresponding co-edges from the adjacent faces may need to point to the same edge.
  • each shell may have a list of all the faces that are interconnected but do not touch or intersect with any of the faces of the other shells. 4) These shells may be arbitrarily grouped into lumps and the whole body may be created from the resulting list of lumps.
  • the Corner table data structure may store the topology and connectivity information in two integer arrays.
  • Fig. 45 illustrates a corner table data structure 4500 in accordance with various aspects described herein.
  • the corner table data structure 4500 may be configured to include nomenclature 4500a or integer arrays 4500c that hold topology and connectivity information.
  • the region around a vertex in a facet may be loosely referred to as a 'Corner'.
  • the vertex that corresponds to that corner may be referred to as 'v(c)'.
  • the corner opposite to the current corner 'c' may be referred to as 'o(c)' .
  • the left and the right corners may be respectively referred to as '1(c)' and 'r(c)' .
  • next and previous corners may be given by 'n(c)' and 'p(c)', respectively (assuming the vertices are listed in a counterclockwise manner).
  • the triangle to which the current corner belongs may be referred to as 't(c)'.
  • the two integer arrays that store the connectivity information may be the Vertex array 'V[c]' and the Opposite array O[c]', as shown in Fig. 45.
  • the corresponding vertex and opposite corner indices may be obtained from the Vertex array 'V[c]' and Opposite array O[c]', respectively. Once these two arrays are populated, the adjacency information may be available.
  • the left triangle may be accessed by querying t(o(p(c))), the right triangle by t(o(n(c))) and the opposite triangle by t(o(c)).
  • the edge connectivity information may also be required.
  • this data structure may be extended by also constructing an edge array 'E[c] ⁇ It may store the edge index of the edge opposite to a given corner 'c'. If these three arrays are computed, then all the topological information required to reconstruct the SAT file may be recovered.
  • Fig. 46 shows a schematic of a cell structure used to identify redundant vertices in accordance with various aspects described herein.
  • Fig. 47 is a flow chart of a method 4700 used to fill V[c] in accordance with various aspects described herein.
  • 'V[c]' may be constructed by implementing a cell structure where the space enclosed in the bounding box of the part may be divided into discrete cells.
  • each of their vertices may be first checked for redundancy before they are given an index or stored in V[c].
  • the vertex may be discarded or the index of the vertex closest to it may be stored in V[c]. If not, a new vertex index may be created or stored in V[c]. Continuing this process for the vertices of the facets in the STL file may result in V[c] being completed.
  • O[c]' may be constructed by first identifying all the corners associated with a vertex and revolving around each vertex, marking the opposite corners. This is done by first populating a temporary data structure called 'bins'. Each node in 'bins' corresponds to a unique vertex in the mesh. For each corner 'c' in the part, the minimum vertex index among the vertex indices corresponding to the next and previous corners of 'c' is identified. The triplet of (min ⁇ V [n(c), V lp(c)] ⁇ , max ⁇ V[n(c)], V [p(c)] ⁇ , c) is stored in the min ⁇ V[n(c), Vlpic)] ⁇ 01 node of 'bins' .
  • Algorithm 2 Constructing 0[c].
  • 'E[c]' may be easily constructed as follows. First an empty array ⁇ ' is created and initialized to null. For every corner 'c' in the mesh, check if either or both of 'p(c)' and O(p(c))' are not pointing to any edge. If one of them is not pointing to an edge, assign the edge index of the edge pointed by the other. If both of them are not pointing to any edge, then create a new index for the edge corresponding to the two vertices of 'c' and 'n(c)' and store this edge index in 'E[c]' for the two corners 'n(c)' and O(p(c))' . Doing this for every corner in the mesh, the 'E[c]' table may be fully populated. A pseudo-code for constructing 'E[c]' is given in Algorithm 3.
  • a simple function called 'swirl' may be implemented in order to identify the number of disjoint shells in the mesh.
  • an array called 'Shell' with a length equal to the number of facets in the mesh is initiated and set to null.
  • Each node in shell points to the shell number of a facet.
  • Swirl function is a recursive function which calls itself.
  • Algorithm 4 Identifying the number of disjoint shells in a mesh using Swirl' function.
  • the SAT file may be constructed by populating the BRep data structure as previously discussed.
  • An algorithm with these ideas has been implemented and STL files were successfully sliced with the ACIS kernel.
  • other operations like error checking, geometry modification, calculation of integral properties like center of gravity, volume etc. have also been successfully performed.
  • the approach of recovering the topological information has several advantages as outlined before, it does have its limitations.
  • One of the severe limitations crippling this method is the excessive size of the resulting SAT files. This is due to the fact that a number of excess entities like edges, coedges, vertices, faces etc need to be created to store the topological information in place of much fewer entities in the case of a native CAD representation. For example, if the STL file of a sphere consisting of N facets were to be reconstructed into a SAT file, it would now have N surface planar patches and several edges and vertices in place of just the one surface if it was represented in its native CAD format.
  • the SAT file size is several times larger than that for a native CAD file representing the same geometry, and this file size scales linearly with the number of faces.
  • Table 3 gives an estimate of the SAT file sizes generated for a few sample meshes.
  • Fig. 48 provides a trend of this scaling with respect to the number of facets.
  • Table 3 SAT file sizes produced for a few sample STL meshes. # Facets SAT File Size (KB)
  • Fig. 49A illustrates a method 4900a for identifying the intersecting facets at an arbitrary Z-height in accordance with various aspects as described herein.
  • An example of a triangular mesh and slicing plane is provided, as referenced at 4901a.
  • the slicing may be assumed to be along the z-direction without loss of generality.
  • In order to identify the intersecting facets first each facet' s maximum and minimum z-coordinates are computed and stored in memory. For a given slicing plane, the facets whose minimum z-coordinate is lesser than the slice plane height are selected, as referenced at 4903a.
  • Figure 24 shows a schematic of this data structure. It consists of a primary linked list sorted in the increasing order of z-values. Each node in this linked list consists of its specific z-value and a pointer to a secondary list that contains all facets with the same minimum z-coordinate value as the z-value of that node.
  • Equation 5 For each slice, once the facets in the intersection region are identified, a simple parametric intersection is computed between the facets and the slice plane to yield the various edges of the intersection wire. If each of the edges of a facet are represented as a straight line in parametric form as shown in Equation 4 (where subscripts 'i' & 'j' denote two different vertices of a facet), the parameter value at the intersection between the edge and the slice plane at height 'Z' may be computed as shown in Equation 5.
  • Each facet yields two intersection points when it intersects with the slice plane.
  • the other intersection point is also computed similarly and these two points together make an edge of the cross-section wire.
  • the wire edges are also computed in a random order. In conventional contour planning operations, these edges need to be sorted and the intersection loops need to be constructed.
  • Algorithm 5 Direct Slicing of STL files.
  • STL files may be of two types: ASCII and Binary.
  • ASCII STL files contain all the facet information listed in plain text and may be opened in any standard text editor.
  • Binary STL files store all the information in a binary format instead of plain text and hence may be much smaller in size. Since the typical STL meshes encountered in LAMP have very large facet counts (upwards of 5 million), the slicing algorithm has been implemented to specifically slice binary STL files.
  • Binary STL files begin with an 80 byte block of memory known as the header which contains any file specific information. Following the 80 byte block, there is a block of 4 bytes which contains the number of facets in an unsigned integer format. Following the first 84 bytes of memory in the file, each facet information is stored in blocks of 50 bytes. Every facet block of 50 bytes consists of 12 bytes to store the normal vector (4 each for the three direction cosines) and 36 bytes to store each of the three vertices. The rest of the 2 bytes of the 50 byte block for each facet is usually empty but may be used to store special attribute information like color in some applications.
  • the number of facets in the file is read from the 4 byte block of memory following the header and assigned to #facets. Starting from zero, for every i ⁇ #facets, the normal vector and vertex coordinate information of the corresponding facet is read using the function readFacet and stored in a temporary variable called bufferFacet.
  • the pseudo code for the function readFacet is shown in Algorithm 6.
  • Algorithm 6 Reading a facet from binary STL file.
  • This function may seek the file to the correct memory location corresponding to the i th facet and may read the corresponding bytes of information within each facet block of memory and may populate the temporary variable bufferFacet.
  • Each facet i begins at the (84 + 50 * i) th byte from the beginning of the file as there are eighty (80) bytes for the header, four (4) bytes for #facets and fifty (50) bytes for each of the i - 1 facets before the i th facet.
  • Fig. 49B illustrates a data structure used for direct slicing of STL files in accordance with various aspects as described herein. This is accomplished by passing each facet that is read from the file to the function addFacet.
  • Algorithm 7 Populating a facet in the Data Structure.
  • end function The given facet's minimum Z-coordinate value is identified and the zList is traversed to find a node whose Z value matches the minimum Z-coordinate of the facet. If such a node is found, the given facet is added to the list pointed by the node. In the event that such a node is not found, a new node variable denoted by toad is created with its Z value equal to the facet's minimum Z-coordinate and with its facet list pointing to the give facet. This new node is then added to the zList in the appropriate location so it stays sorted in the increasing order with respect to the Z values of the nodes.
  • Algorithm 8 Isolating facets in the intersection zone.
  • each node in zList is read. If the Z value corresponding to the node is less than the Z height of the slice plane, each of the facets in the facet list pointed by the node is parsed. If a facet with maximum Z value of greater than the slice plane height is found, it is added to facetsToSlice list. After each of the nodes whose Z values are less than the slice plane height have been parsed in this manner, the isolateFacets function returns back the facets collected in facetsToSlice. Having isolated the facets in the intersection zone of the slice plane, Algorithm 5 then computes the intersection of these facets with the slice plane using the function slice.
  • intersections are computed parametrically as described in the previous section. Having computed the intersection edges, which form the contour of the part cross-section, the next step is to generate an image from them. In order to accomplish this, rays are created for each row of the image and their intersection with the contour edges are computed. In order to compute these intersections efficiently, the edges are in turn populated in a data structure very similar to the one used for populating the facets. The edges are arranged into bins based on their minimum Y -coordinate instead of the Z-coordinate in case of the facets. This data structure for sorting edges is denoted by eList is Algorithm 5.
  • the function addEdge is used to populate the edges in this data structure and its implementation is very similar to addFacet function previously described.
  • eList is populated, the process of computing intersections between the rays and the edges is the same as the one used for computing intersections between the slice plane and facets.
  • the intersecting edges are isolated using isolateEdges whose implementation is similar to isolateFacets.
  • isolateEdges whose implementation is similar to isolateFacets.
  • the intersection points are computed parametrically.
  • the process of creating bitmap data is performed. First, a temporary inter gerBuffer array is populated and later converted to ASCII character array charBuffer which is then used to save the bitmap image.
  • N denotes the number of facets in an STL mesh
  • the following operations need to be completed for every facet read: 1) Scan through the each node in zList to identify a matching node and 2) Scan through to the end of the facet list pointed by the matching node to add the facet.
  • Each of these two operations take, in the worst case scenario, N time steps. Since these two operations need to be performed for every facet in the file, the time complexity for populating the data structure is 0(N3).
  • FIG. 50 illustrates a data structure 5000 used to store these intersection points in accordance with various aspects as described herein.
  • Each row in the data structure represents a Z height corresponding to each slice i in the part.
  • Each column represents a Y level corresponding to a row j of the slice image.
  • Each location (i; j) in the data structure contains all the intersection points corresponding to the jth row of the ith slice image.
  • Algorithm 9 The bounding box coordinates of the part are first created, either by doing a linear scan of the whole part or by directly inputing the information in the program from the CAD model.
  • the minimum and maximum vertices of the bounding box are denoted by (minx, minY, minZ) and (maxX, maxY, maxZ) respectively.
  • memory for the 2D array data structure denoted by zY Matrix is allocated and initiated to NULL.
  • minLayer and maxLayer denote the layer numbers of the lowermost and uppermost slices in this range.
  • the facet is sliced at the corresponding slice height and the resulting edge is stored in a variable denoted by e.
  • the range of image rows to which this edge contributes an intersection point are computed. The lowermost and uppermost rows of this range are denoted by minRow and maxRow respectively.
  • the intersection point of the edge e and the ray corresponding to the row j is computed and stored in a variable denoted by intPoint.
  • the intPoint thus computed is populated in the (i, j) th cell of the 2D array zYMatrix.
  • the slice images may be created.
  • the variables integerBujfer and characterBuffer are populated based on the intersection points retrieved from (i, j) th cell of zYMatrix.
  • the characterBuffer array is completely filled for all rows of the slice, it may be used to write the slice image to disk.
  • Algorithm 9 Improved direct slicing of STL files.
  • compute bounding box of the part (minX; minY; minZ) ⁇ — minimum extents of the part : (maxX; maxY; maxZ) ⁇ — maximum extents of the part : zYMatrix ⁇ - NULL : for each facet f in the file do : bufferFacet ⁇ — readFacet(f ) buJferFacet.minZ - minZ : minLayer ⁇ — floor ⁇ + 1
  • N denotes the number of facets in the file
  • Z denotes the slice range (maxLayer - minLayer)
  • Y denotes the row range (maxRow - minRow)
  • C denotes some independent constant.
  • Z and Y may both be equal to N and the time complexity reduces to 0(N ) just like the linked list STL slicing algorithm discussed in the previous section.
  • both Z and Y are much smaller than N.
  • the constant C is also very small since an array structure is used instead of a linked list. Hence, in most typical scenarios, the algorithm behaves like it is O(N) complexity with a very small constant value and hence is much faster than the linked list algorithm discussed in the previous section.
  • Table 5 An estimate of indexing times using this 2D Matrix approach to slice typical STL files with various facet counts and the corresponding times for the linked list algorithm discussed in the previous section are shown in Table 5.
  • Table 5 Slicing time for various mesh sizes.
  • Fig. 51 illustrates slicing time scaling with respect to mesh size.
  • the savings in slicing time are substantial using this approach. It takes just 30 minutes to slice a 5.5M facet STL file versus the 4 days it to slice the same file using the linked list approach. This leads to enormous time savings in preparing build ready images for each new part design. Although, this new approach reduces the computational time, it does have its limitations.
  • this new approach uses far more memory than the linked list approach since it stores all the intersection points of all the rays with each of the slices in the part whereas in the linked list approach, just the facets are stored in memory.
  • the new approach takes about 2.5 gigabytes of memory versus just 300 megabytes of memory using the linked list approach. Since memory is very cheap in recent times, this limitation is not a significant hurdle.
  • the approach in this section is the preferred method to slice extremely high resolution STL files for LAMP.
  • the slice images produced through STL slicing and Direct CAD Slicing require further post-processing before they are ready for use in a LAMP build.
  • the details of these various post-processing operations and algorithms are given in this section.
  • One of the mandatory post-processing operations that needs to be performed on the slice images is checking for errors and validity of the images. These errors are caused by gaps that creep into the model either due to errors in the CAD model or due to translation between different CAD formats.
  • rays are created for each row of the image to identify the correct pixel color values as previously described.
  • Fig. 52 illustrates a particularly bad instance of stray line errors. Such stray lines need to detected and corrected before the images may be used for part builds on the LAMP machine.
  • an error checking and correction algorithm has been implemented. The algorithm takes an erroneous slice like the one shown in Fig. 52 referenced at 5200a and outputs a corrected slice shown in Fig. 52 referenced at 5200b.
  • the algorithm scans through each row of the image and checks for pixels that are sandwiched by pixels of an opposite color, i.e, pixels that have a different color value than the ones present on the rows immediately above and below the current row that is being searched. Once it finds such pixels, it flips their values to match the color values of the top and bottom rows to correct the stray lines.
  • This approach works for correcting only stray lines that are 1 -pixel thick but may be extended to detect lines that multiple pixels wide. The details of the extended algorithm along with the pseudo code for detecting stray lines that are multiple pixels wide is given next.
  • the pseudo code for the error correction operation is shown in Algorithm 10.
  • the given stack of slice images that need to checked are first loaded into the program.
  • its pixel data is first converted from ASCII representation to integer representation for easy data manipulation and stored in an integer array integerBuffer. If an intersection point was missed in the slicing operation and a stray line caused, then the last pixel of the row containing the stray line will have a white pixel on a surrounding black backdrop. This fact is exploited in identifying erroneous rows that need to be corrected. This is accomplished by checking for pixels with a color value of 1 (i.e, white) in the last column of pixels in integerBuffer.
  • the next step is to determine the width this stray line. So, having identified the row at which a stray line originates, the color values of end pixels in the rows immediately following the identified row are checked. If consecutive rows are found to have white pixel values, then the width of the stray line is more than one. The number of consecutive rows are counted and the stored in the variable width. Having identified the beginning row number and the width of a stray line, this information is then passed to the function correctRow.
  • correctedlntegerBuffer ⁇ correctRow(integerBuffer, j - width, width)
  • the pseudo code for the function correctRow is shown in Algorithm 11. It is just an extended version of the logic described previously for correcting one pixel wide stray lines. Three counters i, j and k are used in the algorithm. Counter k keeps track of the row number in the image corresponding to each row in a multi-pixel wide stray line that is being corrected. Counter i keeps track of the number of rows above a particular row in the stray line that needs to be checked for color information. Similarly, counter j keeps track of the number of rows below a particular row in the stray line that needs to be checked for color information. For each pixel in each row of the stray line, the color of the corresponding pixel in the row that is i rows above and j rows below is checked. If it is the same but different from the color of the current pixel in the row that is being corrected, the pixel value is flipped.
  • All of these error checking operations are based on the assumption that the collective width of these consecutive stray lines is much less than the minimum feature size in the CAD part that is to be sliced.
  • For the blade designs that are currently being built by LAMP have minimum features sizes of about 500 microns, i.e, approximately 30 pixels in size at 1500 dpi.
  • the widest stray lines observed in the slices were five pixels wide which is much less than the minimum feature size of 30 pixels and hence may be corrected with reasonable accuracy.
  • Fig. 53 illustrates a method 5300 of rectifying multi-pixel wide rows with stray lines in accordance with various aspects as described herein. This phenomenon is shown in Fig. 53 referenced at 5300b for a sample stray line shown in Fig. 53 referenced at 5300a.
  • the stray lines are thin (less than 5 pixels wide) the inaccuracy caused is negligible but as they get wider, it needs to be corrected for.
  • This problem may be fixed by constructing a spline (a Hermite cubic spline with CI continuity for example) to close the contour in a continuous way and the color toggling points in each of the rows in the stray line may be computed from the so constructed spline.
  • a spline a Hermite cubic spline with CI continuity for example
  • This way smoothness of the edge contours may be maintained as shown in Fig. 53 referenced at 5300c while correcting stray lines that are arbitrarily wide.
  • it may correct a stray line of any arbitrary width, if the stray line is too wide (width of the stray line approaching minimum feature size in the part) then rather than passively correcting it in the image, the geometry of the original CAD part needs to be repaired for accurate slices.
  • the function correctRow may correct stray lines given the starting row number of the stray line in the slice image and its width.
  • the function correctRow may correct stray lines given the starting row number of the stray line in the slice image and its width.
  • FIG. 54 reference at 5400a shows a typical input image to the tiling code.
  • a mesh structure as shown in Fig. 54 reference at 5400b is used as the background on which this input slice is tiled.
  • the mesh structure has been optimized after considerable experimentation to prevent the uncured Suspension in the empty regions from sloshing around in the build tank during recoating of a fresh layer of Suspension by the blade.
  • the algorithm automatically computes the maximum extents of the slice image, determines the number of parts that may be built within the build area, lays them out at the correct coordinates and creates break lines along the mesh structure for easy removal of parts after the build is complete.
  • the final build-ready images produced by the code look like the one shown in Fig. 54 reference at 5400c.
  • the code runs through the entire stack of the slice images to produce a build- ready stack that is then fed to the LAMP machine.
  • Fig. 55 illustrates the staircase effect while two created contours are same size in inner area.
  • Fig. 55 if the CAD geometry were an inclined cylinder, there would still be a staircase effect in the layered part while having slice contours of exactly the same area. In such a situation, the area deviation approach would fail to identify the geometry deviation due to staircase effect and hence layer height adaptation will not be achieved.
  • Fig. 56 illustrates a cusp volume for a hemispherical part.
  • the geometric deviation of each 2.5D layer with the corresponding 3D layer of the part is labeled as the cusp volume.
  • the cusp volume is computed and used as a measure to determine the height of the next layer.
  • the cusp volume may dramatically change over the height of a part as it is a function of the perimeter of the cross- section, layer thickness and the angle made by the local surface tangent vector with the build direction.
  • the cusp volume is normalized by the volume of the 3D slice of the part to give an estimate of the percentage volumetric error within each layer of the additive manufactured part as compared to the original geometry as shown in Equation 24.
  • the %VolumetricError is placed and the layer thickness at each slice height is determined so as to satisfy this upper bound criterion.
  • the %VolumetricError is first estimated using the maximum possible layer thickness. If the computed error is less than the maximum bound, the maximum layer thickness is used. If not, the layer thickness is successively converged to a value that yields the specified maximum error using a 'bisection' scheme. If the resulting layer thickness is greater than the minimum layer thickness that may be built, then it is used as next layer height. Otherwise, the next layer height is set to the minimum layer thickness and the operation is repeated. Implementation details of this approach using ACIS kernel are given next.
  • the pseudo code for the adaptive slicing operation using volume deviation approach is shown in Algorithm 12.
  • the part of the given name is first loaded into the program and all the important ACIS parameters like resolution are set.
  • the bounding box of the part is computed next to identity its min and max extents. Slicing is started at a height just slightly above minZ. For each slice height minZ ⁇ z ⁇ maxZ, the slice contour is computed and slice image created.
  • the slice height of the next layer is determined by passing the part (wig) and the current slice height (z) to a function called layerThickness.
  • the pseudocode for this function is shown in Algorithm 13.
  • Algorithm 13 computing layer thickness.
  • the height trackers denoted by low, mid and high are used. For finding the layer thickness at height z, these three trackers are first set to z, 0 and MAXTHICKNESS (denotes the maximum layer thickness that may be built) respectively. First the % volume deviation of the part at height z is computed at the maximum allowable layer thickness. If this deviation is either non zero or greater than the maximum allowable volume deviation denoted by MAXDEVIATION, the height of the next layer is adjusted using a scheme similar to the bisection method in root finding (until the volume deviation is in the vicinity of the maximum allowable volume deviation). So, if at MAXLA YERTHICKNESS, the volume deviation is greater than the
  • the height marker mid is adjusted to its new value as shown in Equation 25: high + low
  • the 3D slice geometry is computed.
  • a rectangular cuboid of height equal to the given layer thickness (denoted by thickness) is created and stored in the variable named block.
  • the 3D slice geometry may then be computed by performing a solid intersection operation in ACIS between the given part wig and the cuboid denoted by block.
  • the 2.5D slice (the geometry of each printed layer assuming rectangular walls) geometry is computed by the following steps a) creating a slice plane at height z + thickness, b) computing the intersection of the plane with the given CAD part wig to get the 2D slice contour, c) sweeping the 2D slice contour vertically down by a distance equal to the current layer thickness.
  • the volume lost by the layered part (denoted by cuspV olumel) at the given height z and the given layer thickness thickness is determined by performing a subtraction operation in ACIS using the 3D slice as the 'blank' body and 2.5D slice as the 'tool' body and computing the volume of the resulting geometry.
  • the volume gained by the layered part is determined by swapping the blank and tool bodies from the previous step and computing the volume of the resulting geometry.
  • the % volume deviation may be computed as shown in the expression on Line 16 in Algorithm 14, where 3DVolume denotes the volume of the 3D slice.
  • Fig. 57 illustrates each of these steps for calculating the volume deviation while slicing a sample CAD part in accordance with various aspects as described herein.
  • Fig. 58 is a sample CAD part adaptively sliced using the volume deviation approach.
  • the minimum and maximum layer thicknesses used were 0.001 inch and 0.1 inches respectively.
  • a maximum volumetric deviation of 2% is used as the adaptive slicing criteria.
  • the layer thickness is varied gradually with thickness decreasing towards the top.
  • the layer thickness is varied continuously, with thickness increasing or decreasing depending on the local surface complexity.
  • Fig. 59 provides a chart 5900 of variation of layer thickness vs. height z for sample part.
  • Fig. 59 provides a plot of how the layer thickness varies along the height of the part to give a more clear illustration of the observations presented above. It may seen that the layer thickness ranges between the maximum and minimum thickness specified in the algorithm.
  • Fig. 60 provides a chart 6000 of the percentage volume deviation vs. height for sample part.
  • Fig. 60 gives a plot of % volume deviation present in each layer along the height of the part and how this varies for the adaptively slicing as compared to uniform slicing at the maximum layer thickness.
  • the adaptively sliced part has a volumetric deviation of at most 2% as specified by the maximum bound in the algorithm whereas, for the uniformly sliced part, the volumetric deviation fluctuates through a wide range from 0% to nearly 35% as a function of location in the build direction.
  • Fig. 61 provides a chart 6100 of percentage total volumetric error vs. height for sample part.
  • Fig. 61 gives a plot showing the variation of the total absolute volume in (in3) lost or gained in the part for both the adaptive slicing and uniform slicing.
  • the % volumetric deviation metric is a relative measure as compared to the cusp height metric (which is an absolute one).
  • this approach yields satisfactory outcomes and its evident simplicity (quicker computation time as a consequence) and scalability to handle generic BRep models with more complex geometry (as compared to only parametric surface splines handled by Kulkarni and Dutta) give it the advantage.
  • the relativeness of the volume deviation metric may be alleviated by having more designer knowledge of the parts being built (like the minimum feature sizes, maximum curvature regions etc.) while setting the parameters (minimum and maximum layer thickness ranges and the maximum volume deviation bound) in the slicing algorithm.
  • the other major approach pursued herein to address the issue of stair stepping is through gray scaling and dithering.
  • the basic idea behind using gray-scaling and dithering in LAMP is to effectively modulate the cure depth in a single exposure by using screened gray scale regions in the build images in place of using the original all white regions for the cured regions in the slice images.
  • the stair stepping effect observed in additively manufactured parts, as discussed previously, is a result of the fact that the cured layers have 2.5D geometry with a constant depth across the entire region of exposure. For surfaces that are facing downward (i.e surfaces whose normal vectors make an angle greater than 90o and less than 270o with respect to build direction), this means that the cured layer overshoots the part geometry at the edges. This effect is illustrated in Fig. 62.
  • Fig. 62 illustrates stair stepping caused on downward facing surfaces while using all white build images.
  • Energy dose (E) is a product of the light intensity (denoted by / and has units of W/m ) and exposure time (t) as shown below:
  • one method of locally modulating the exposure energy dose E involves manipulating exposure time t.
  • An alternate method for manipulating the exposure dose involves by manipulating the light intensity. Since LAMP and most other projection systems use a single light source with a fixed power output, locally manipulating the light intensity would is also very challenging.
  • gray- scaling followed by dithering is used to manipulate the effective light intensity incident upon the material. Details of the algorithm and the methodology followed for generating gray scale images in order to modulate the cure depth within each exposure to reduce the stairstepping effect on downward facing surfaces, are presented in this section.
  • the cure depth C d is a function of light intensity /, resin parameters sensitivity D p and critical energy E c and exposure time t. As previously discussed, the exposure time t is held constant in this approach. Through the experimental investigations presented in the previous sections, it was determined that rest of the parameters are in turn functions of the gray scale value G. This functional dependence on gray scale value G is shown in Equation 39.
  • the direct slicing algorithm may be extended to output gray scale slice images instead of the usual black and white images.
  • the pseudo code for accomplishing this is presented in this Algorithm 15.
  • Algorithm 15 Gray Scale slice image generation.
  • the given CAD model is first loaded into the program and assigned to the variable wig. For each slice height z along the height of the part, first a three dimensional slice, denoted by 3DSlice, is computed in order to identify the accurate geometry that needs to be cured. This is accomplished by creating a cuboid, denoted by block of thickness equal to the build layer thickness denoted by layerThickness and computing the intersection of it with the given part denoted by wig. Next, the 2D slice contour denoted by 2DSlice is computed at a height z + layerThickness by creating a slice plane at this height and computing its intersection with wig.
  • the gray scale factor G may be solved for by using any of the standard root finding techniques like Newton-Raphson or Bisection method.
  • the corresponding pixel value of the slice image is set to G _ 255 (For an 8-bit gray scale image, like the one being created in this case, a value of 255 corresponds to full white and a value of 0 corresponds to full black). In this manner, the gray scale values for each of the pixels in the slice image are determined and the slice image is created.
  • Fig. 63 illustrates a method 6300 for producing a gray scale image in accordance with various aspects described herein.
  • Fig. 63 referenced at 6300a shows the sample part used for computing gray scale slice images.
  • Fig. 63 referenced at 6300b shows the process of identifying the required cure depth corresponding to each pixel of the slice image. From the cured depth determined by this process of ray intersections with the 3D slice, the gray scale value required at each pixel value may in turn be computed from the cure depth model established in Equation 40.
  • the gray scale slice image obtained from this process is shown in Fig. 63 referenced at 6300c.
  • Fig. 63 referenced at 6300d shows a zoomed in view of the dithered gray scale region obtained by dithering the gray scale slice image.
  • Fig. 64 illustrates gray scale exposure results.
  • Fig. 64 referenced at 6400a shows the cured profile obtained with an all white exposure. As expected, the profile is more or less 2.5 D cross-sectional.
  • the cured profile of the same layer now exposed with the gray scale slice image obtained using the process discussed in the previous section is shown in Fig. 64 referenced at 6400a. As may be seen, the cured profile obtained with the gray scale exposure is very close to the actual 3D slice geometry of each layer for the sample part shown in Fig. 64 referenced at 6400a.
  • These single layer cured profiles serve as a proof of concept.
  • Discrete values for each of the parameters were identified and the cure width characteristics at each of these parameters are determined experimentally. Cure widths were determined by exposing squares of known length over a glass slide and by measuring the deviation of the cured square lengths obtained.
  • Fig. 65 illustrates a sample exposure image with a known constant square length with ten different tiles.
  • Fig. 66 illustrates cured squares obtained by exposing the image in Fig. 65.
  • Fig. 65 shows a sample image with known squares that is used for exposure and Fig. 66 shows an image of the corresponding cured layers obtained.
  • each tile in the exposure image in Fig. 65 is exposed at a different exposure dose and hence the resulting square lengths obtained in the cured square tiles shown in Fig. 66 are different.
  • the corresponding cure widths Cw at each of the exposure doses is computed as follows:
  • Equation (60) where lcured is the square length obtained after curing each tile, and lo is the nominal square length in the exposure Image.
  • lcured is the square length obtained after curing each tile
  • lo is the nominal square length in the exposure Image.
  • Critical energy dose and sensitivities for cure width Cw analogous to Ec and Dp for the case of cure depth Cd are introduced.
  • a different notation is used for identifying the critical energy doses and sensitivities corresponding to cure depth and cure width respectively.
  • the critical energy dose corresponding to cure depth Cd is denoted from here on by Ed c and the sensitivity for cure depth is denoted by Dd p.
  • a new parameter known as broadening depth Bd is introduced, which gives the maximum cure depth that may be achieved before the layers begin to cure in the width direction. It is determined by computing the cure depth obtained at an energy dose equal to the cure width critical energy dose Ew c at which lateral curing just begins to occur as shown in Equation 61.
  • composition should be optimized for maximum broadening depth in order to get deep cured parts with good layer- to-layer bonding and minimal excess side scattering.
  • Fig. 67 shows the native orientation of the blade mold. When built in this orientation, features that define the tip cap of the blade cause very large overhangs leading to a failure of the build. However, from previous experience, for the typical HP blade geometries, an orientation may be found which minimizes these overhangs thereby resulting in successful builds. Such an orientation is shown in Fig. 68, which enables the tip cap features which were previously causing build failure to grow more gradually from their root at the trailing edge. Fig. 68 illustrates a build orientation that reduces overhangs observed in the original orientation.
  • the re-coating blade travels a distance of 26 cm in 6 seconds and is at height of 200 _m above the build platform.
  • the shear stresses imparted on the part will be of the order of _100 Pa. Due to such high shear forces and the curling up effect of unsupported features due to shrinkage stresses, any unsupported features formed will be swept away by the re-coating arm causing the build to fail.
  • support structures are necessary for any geometries that produce floating islands during a build, in order to obtain successful parts.
  • all of the geometric features, supports or otherwise are enclosed within the outer shell of an integrally- cored mold and removing these supports post-build is impossible. This results in additional unintended features in the cast blades which might adversely impact the designed cooling performance of the molds. This issue of floating islands is probably the only limitation potentially preventing the LAMP process from building blade designs of any arbitrary complexity.
  • the given part is first loaded into the algorithm and its minimum and maximum extents are computed.
  • a cuboid denoted by blockl with a cross-sectional area equal to the cross-sectional area of the bounding box of the part and a thickness equal to layer thickness is created.
  • a solid body intersection is computed between the part denoted by wig and blockl to yield a three dimensional slice denoted by 3DSlicel at height Z of the part.
  • a three dimensional slice denoted by 3DSlice2 at height Z + layerThickness is computed.
  • the two slices computed using the previous steps are illustrated in Fig. 71.
  • 71 illustrates 3D slices of successive layers at the location corresponding to the floating island shown in Fig. 70.
  • slices separated by a few layers are shown and hence the apparent large overhangs.
  • the overhang will be very small but so is the floating feature generated and hence it will be difficult to perceive.
  • the slices look two dimensional because of very thin layer thickness (100 _m), they are in fact three dimensional because of the way they were created.
  • Each of the disconnected solid regions in these slices are stored as a lump in the ACIS data structure.
  • each of the lumps of this slice is checked for intersection with each of the lumps of the first slice. If there exists a lump in the second slice, which does not intersect with any of the lumps in the first slice, it is classified as a floating island and support structures need to be created.
  • curvature ⁇ local surface curvature at intersection point
  • the algorithm takes in four parameters as input as follows:
  • a list of possible candidate orientations along which a support may be built is created by discretizing the "cone" underneath origin with a vertex angle equal to maxTiltAngle. For each of these candidate orientations, rays originating from origin are generated and their intersections with the part geometry is computed. At each of these points of intersection, the smoothness of the surface is measured. If local surface curvature is high, there is a good possibility that it corresponds to a cooling feature and this orientation is abandoned. Likewise, if the intersection point is near to the boundary of two or more surfaces and the adjoining surfaces do not maintain continuity, this orientation is abandoned as well as it was observed from experience that shrinkage stresses accumulate at such corners and cause the supports or other slender structures to fail.
  • the rest of orientations are stored as potential directions for support propagation.
  • the lengths of the rays originating from origin in each of these potential directions are computed and the list of potential orientations is then sorted in the ascending order w.r.t their lengths.
  • cylindrical supports with radius r are created by sweeping a circular cross-section along the ray until it connects to the part.
  • Fig. 72 illustrates various supports generated on the sample HP blade shown in Fig. 67 using this method.
  • many of the orientations are discarded because they either intersect the surface at regions of high curvature or are very long.
  • the support structure highlighted in green is the one that is preferred as it is the shortest and also partitionects the part at a low curvature region.
  • Fig. 72 illustrates supports generated by the algorithm.
  • an additional parameter that indicates the maximum amount of overhang a particular support feature of a given size may support needs to be incorporated in to the algorithm. Based on this parameter, the area of the large floating island may be sub divided into smaller regions and the procedure may be applied for each of the smaller regions with an additional constraint to produce non intersecting supports.
  • Fig. 73 illustrates a temperature profile obtained on the internal wall of a leading edge with and without a support structure.
  • Fig. 74 illustrates velocity streamlines in an internal cavities. It may be seen that in the case without the support, the flow streams from the lower most impingement jets are unable to reach bottom most region of the leading edge cavity wall which is not the case for the supported geometry.
  • the support structure does not stymie the flow of the lower impingement may be clearly seen that, unlike what was expected, the temperature profile in the case of the support added is much lower than the case without a support. There is a hot spot at the lower region of the leading edge for the case without a support and the addition of a support reduces the peak temperature occurring on the leading edge wall significantly.
  • Fig. 74 shows the velocity streamlines of the flow to give a better understanding of temperature results obtained. It may be seen that in the case without the support, the flow streams from the lower most impingement jets are unable to reach bottom most region of the leading edge cavity wall which is not the case for the supported geometry. It may also be seen that, unlike what was intuitively expected, the support structure does not stymie the flow of the lower impingement jets and neither does it starve any of the upper impingement jets from cooling air.
  • LAMP Large Area Maskless Photopolymerization
  • Fig. 75 illustrates a loss of build precision using a material recoating system having a single-edge recoater.
  • the material recoating system having a single-edge recoater may cause starvation or doming, which may result in loss of build precision.
  • a blade may have removed too much slurry and may form a crator shape in the slurry area around a mold.
  • a dome shape of slurry may be formed surrounding the mold parts. This doming problem may get worse as, for instance, more layers are added, which may cause a build of a part to fail.
  • Fig. 76 illustrates one embodiment of a material recoating system 7600 having a multiblade recoater in accordance with various aspects described herein.
  • the system 7600 may be configured as described in Fig. 76. Further, the system 7600 may be configured to address the starvation and doming issues described in Fig. 75, which may increase build precision of a part.
  • Fig. 77 illustrates one embodiment of a screen printing-style inking window pane in accordance with various aspects described herein.
  • the screen printing-style inking window pane 7700 may be configured as described in Fig. 77.
  • Fig. 78 illustrates one embodiment of a LAMP machine in accordance with various aspects as described herein.
  • Fig. 79 illustrates one embodiment of a LAMP machine 7900 in accordance with various aspects described herein.
  • Fig. 80 illustrates one embodiment of a LAMP machine 8000 in accordance with various aspects described herein.
  • Fig. 81 illustrates one embodiment of a LAMP machine 8100 in accordance with various aspects described herein.
  • Fig. 82 illustrates one embodiment of a LAMP machine material build platform 8200 in accordance with various aspects described herein.
  • Fig. 83 illustrates one embodiment of a LAMP machine material build platform 8300 in accordance with various aspects described herein.
  • Fig. 84 illustrates one embodiment of a LAMP machine material build platform substrate and substrate mount 8400 in accordance with various aspects described herein.
  • Fig. 85 illustrates one embodiment of a LAMP machine material build platform substrate and substrate mount 8500 in accordance with various aspects described herein.
  • Fig. 86 illustrates one embodiment of a LAMP machine material build platform substrate and substrate mount 8600 in accordance with various aspects described herein.
  • Fig. 87 illustrates one embodiment of a LAMP machine material recoating system 8700 in accordance with various aspects described herein.
  • Fig. 88 illustrates one embodiment of a LAMP machine material build platform seal system and material recoating system 8800 in accordance with various aspects described herein.
  • Fig. 89 illustrates one embodiment of a LAMP machine material build platform seal system and material recoating system 8900 in accordance with various aspects described herein.
  • Fig. 90 illustrates one embodiment of a LAMP machine material build platform seal system and material recoating system 9000 in accordance with various aspects described herein.
  • Fig. 91 illustrates one embodiment of a LAMP machine material build platform seal system and material recoating system supply reservoir 9100 in accordance with various aspects described herein.
  • Fig. 92 illustrates one embodiment of a LAMP machine material recoating system supply reservoir and recoater 9200 in accordance with various aspects described herein.
  • Fig. 93 illustrates one embodiment of a LAMP machine material recoating system supply reservoir and recoater 9300 in accordance with various aspects described herein.
  • Fig. 94 illustrates one embodiment of a LAMP machine material build platform seal, material recoating system supply reservoir and recoater 9400 in accordance with various aspects described herein.
  • Figs. 95 A, 95B and 95C illustrate an embodiment for employing a series of imaging heads that move concurrently across the surface of a resin in accordance with various aspects as described herein.
  • ULTRA-LAMP employs a series of imaging heads as shown in Figs 95A-C that may image the surface of the photocurable resin by concurrently moving over the photocurable resin's surface while exposing and curing patterns in the resin.
  • Fig. 95A demonstrates the ULTRA-LAMP in two staggered rows of image projection units.
  • the projection units may sweep across the resin in opposite directions.
  • the entire surface of the resin may be thus patterned in a single pass, providing an increase in throughput of about 10X over current LAMP technology (which uses a serpentine scan of a single imaging head over the resin's surface.)
  • Fig. 96 illustrates an embodiment of for employing a two dimensional array of imaging heads to simultaneously pattern the surface of the resin in accordance with various aspects as described herein.
  • the technology may be applied in a FLASH-LAMP concept.
  • FLASH-LAMP is illustrated in Fig. 96.
  • FLASH-LAMP may use a two-dimensional array of projectors, all simultaneously projecting portions of a larger image but at high resolution. The entire area of the photocurable resin may be thus patterned in a single flash, or a few flashes with small indexing movements of the array between flashes to cover areas of the resin not exposed in the previous flash.
  • FLASH-LAMP may increase photoexposure throughput dramatically by up to 50X over current LAMP technology.
  • the light source used in LAMP may be a high pressure mercury vapor lamp.
  • the emission spectrum of the light source is shown in Fig. 97.
  • the G-line is the strongest spectral feature, followed by the H-line and I-line, respectively. It is important to note that the primary peak utilized for photopolymerization is the I-line, since the photoinitiator utilized exhibits negligible absorption for the longer wavelengths.
  • I gr is the averaged light intensity incident on the PCMS resulting from a half-toned grayscale exposure
  • I 0 is the light intensity resulting from a full exposure, where every pixel on the DMD is turned to the on position.
  • the grayscale factor could be assumed as being equal to the grayscale value of the image, i.e. the percentage of white pixels in the designed image, G, and independent of the pixel distribution. This assumption was tested and the results are shown in Fig. 98.
  • the grayscale factor was determined using a photodetector provided by the supplier of the optical scanning system. First, the current from a full projection was measured, which corresponds to the total light power delivered to the photodetector.
  • the exposure area was held constant throughout the experiment to give a direct relationship to the light intensity.
  • the current resulting from projected grayscale images at different screening resolutions and grayscale values was measured.
  • the screening process was accomplished using Harlequin RIP by Global Graphics, details may be found elsewhere.
  • the screening technique used was Harlequin Dispersive Screening (HDS), which is a proprietary screening technique. Screening resolutions were varied from HDS super fine to HDS super coarse; here HDS super fine has the highest screening resolution (lxl pixel half-tone cells) and HDS has the lowest screening resolution (4x4 half-tone cells).
  • the grayscale factor was determined by dividing the grayscale current by the full exposure current. The error associated with this measurement technique was determined to be +1%.
  • Fig. 99(a) shows the light intensity distribution at the focal plane resulting from one pixel of the DMD being projected.
  • the top panel shows the light intensity plotted in the x-y plane, which is parallel with the PCMS surface, where reds correspond to high light intensity and blues correspond to low light intensity. Previous reports have described the intensity distribution for a single pixel as Gaussian.
  • the bottom panel of Fig. 99(a) shows a plot of the cross-sectional profile of the projected pixel.
  • the curve fit shown in the profile was obtained through a two-dimensional Gaussian regression. From this regression, the Gaussian radius was determined to be ⁇ 8.3 ⁇ , which is consistent with a pixel resolution of 17 ⁇ .
  • the maximum measured value of intensity for a single pixel exposure was 3601counts/px-sec.
  • the statistical error from the measurement was determined to be +85 counts/px-sec and the horizontal error bars show the dimensions of the CCD for which the data points were averaged.
  • additional pixel patterns were investigated.
  • Fig. 100 shows the underlying complexity of the optical projection which is being neglected due to its negligible influence on the peak intensities.
  • a periodic distribution in the intensity of the valleys is observed, which has a period of ⁇ 220 ⁇ and may be a result of diffraction.
  • the material system could cure according to the local, averaged or an intermediate light intensity incident to the surface. Above, it was shown that the distribution of projected pixels does not significantly alter the maximum incident light intensity. Therefore, if the cure depth resulting from grayscale exposure is similar to the cure depth resulting from an all white exposure, then it may be concluded that the PCMS cures according to the local light intensity. However, if the cure depth resulting from grayscale exposure is lower than the cure depth of an all white exposure, then the curing behavior of the PCMS may be modeled as an effective light intensity reduction.
  • cure depth measurements were conducted at a fixed exposure time and screening resolution and the grayscale was varied from 30% to 90% white. The exposure time used was 600ms and the screening resolution was HDS super fine.
  • the resulting films were homogenously smooth with no evidence of the pixel distribution utilized in the grayscale exposure.
  • the cure depth measurements in Fig. 101 clearly show that in addition to the homogeneity of the films produced from grayscale exposure, the cure depth decreases with a decrease in grayscale. This indicates that the light intensity has been effectively smoothed and reduced. From the findings in Fig. 101, it may be hypothesized that grayscale exposure causes the PCMS to cure as though the light intensity was reduced in proportion to the grayscale value of the projected image. The validity and the limits of this hypothesis are the focus of the following discussion. Reports by Atencia et al. suggest that grayscale exposure with a sufficiently high screening resolution results in an effective reduction in intensity which corresponds to the grayscale of the projected image.
  • UV neutral density (ND) filters which act to uniformly attenuate light intensity over a specified range of wavelength.
  • UV-VIS ND filters of a nominal optical density (OD) of 0.3 and 0.5 were purchased from Edmund Optics to uniformly attenuate wavelengths from 200nm to 700nm.
  • the transmission of the filters was measured using a technique similar to that used for determining the grayscale factor. First, an all white image was projected onto the photodetector and the resulting current was measured.
  • the ND filters 10202 were placed between the light source and the photodetector, and the current from an attenuated all white projection was measured. The ratio of these two current measurements provides the transmission for each filter. The percent transmitted for the 0.3 and 0.5 OD filters measured were 56% and 32%, which corresponds to a light intensity of
  • the ND filter 10202 was placed on top of the glass slide 10203 as shown in Fig. 102.
  • Fig. 103 shows the resulting working curves.
  • the working curve resulting from an unfiltered light intensity of 1.6W/cm is also shown for comparison. It may be seen that the cure depth for a constant energy dose increases when the light intensity decreases. As a result, the cure depth from the highest source of light intensity resulted in the lowest cure depth. Consequently, the critical energy decreases with a decrease in light intensity. While at first counterintuitive, it should be noted that for a constant energy dose, the exposure time increase for a lower intensity, i.e. there is more time for photopolymerization to proceed. From Fig. 103, it may also be seen that the slopes resulting from each light intensity curve remain constant, which indicates that the resin sensitivity has little dependence on light intensity under these exposure conditions.
  • Fig. 104 shows a summary of the dependence of the critical energy and resin sensitivity on light intensity.
  • Grayscale images from about 20% to about 90% white were designed at five different screening resolutions: HDS super fine, fine, medium, coarse and super coarse.
  • Working curves for each of the grayscale values and screening resolutions were developed by measuring the cure depth at different exposure times. The range of energy dose investigated under the light intensity
  • Fig. 105 shows a sample of the working curves resulting from grayscales of 50%, 40%, and 20% white and with HDS super fine screening.
  • Fig. 106 Quantifies the trends observed in Fig. 105. It may be seen that a linear regression of the critical energy accurately describes the variation with grayscale, which is evidenced by the high R values. This indicates that the critical energy for grayscale exposure at different screening resolutions varies in a manner similar to its variation with uniform light intensity.
  • Fig. 107 The trends in curing parameters from homogenous grayscale exposure are shown in Fig. 107.
  • the image grayscale was converted to its effective intensity in order to compare the results with the critical energies obtained from a true reduction in light intensity.
  • Both the critical energies from grayscale exposure and true intensity measurements were plotted. From Fig. 107 it may be seen that the grayscale exposure critical energies are within the error of the critical energies obtained from true intensity measurements. This shows that the critical energy resulting from grayscale exposure behaves as a true reduction in light intensity.
  • the regression obtained for the influence of grayscale exposure on the critical energy was:
  • R was determined to be 0.94, which shows that the regression is an adequate representation of the influence of grayscale light intensity on the resin sensitivity.
  • the film contained regions of a larger cure depth connected by regions of partially cured resin with a lower cure depth. This corresponds to the homogenous transition, which corresponds to dimensions of exposed and unexposed regions for which the material system cannot create distinct regions of cured polymer separated by distinct regions of uncured monomer.
  • the cure depth must be predicted to ensure proper binding to the previous layer.
  • the investigation of the homogenous transition was accomplished through the selection of one grayscale value. Also, the screening technique was converted to a well-defined pattern in order to easily extract dimensional information. The pattern chosen was a "checkerboard," which is shown in Fig. 108.
  • the checkerboard pattern consists of alternating squares of exposed and unexposed regions. To investigate the influence of screening resolution, the length of the square primitive was successively increased. The range of square lengths investigated was from about 1 pixel to about 80 pixels, which corresponds to about 17 ⁇ to about 1360 ⁇ . Each checkerboard pattern has an image grayscale value of 50%. However, as the screening resolution decreases, the image visually appears less gray and more as a pattern of distinct black and white squares. Similarly, as the screening resolution decreases, the light intensity reduction assumption of grayscale exposure breaks down.
  • Fig. 109 show the homogenous transition for a 600ms exposure. It may be seen in Fig. 109(a) that a checkerboard exposure with a square length of 17 ⁇ results in a film with uniform thickness. However, when the square length reaches 85 ⁇ in Fig. 109(b), inhomogeneities in the film thickness are observed. This represents the onset of the homogenous transition.
  • Figs. 109(c) and (d) depict the continued deviation from homogeneity for square lengths of 170 ⁇ and 255 ⁇ . As the homogenous transition progresses, the cure depth of the exposed regions increases and that of the unexposed regions decreases.
  • the homogenous transition separates two regions of constant and homogenous cure depth.
  • the region with lower cure depth occurs when square length of the checkerboard exposure pattern is small, which corresponds to grayscale exposure.
  • the region with a higher constant cure depth is from an all white exposure.
  • - I l l - Fig. 110 is the shifting of the homogenous transition to the right with an increase in exposure time.
  • the center of the sigmoid regression increases with an increase in exposure time to larger square lengths.
  • the center of the 200ms exposure time was at a square length of about 172 ⁇ , while the center of the 900ms exposure was at a square length of about 330 ⁇ . From these cure depth measurements, it was observed that the average square length range of the homogenous transition was from about ⁇ to 450 ⁇ .
  • Fig. I l l shows a checkerboard exposure with a square length of about 170 ⁇ .
  • the side length was measured to be 156 ⁇ .
  • the side length increases to 173 ⁇ at 400ms, and 203 ⁇ at 800ms.
  • a homogenous film of uniform thickness is developed.
  • D p is equivalent to the resin sensitivity in the unmodified Jacobs equation
  • t is the exposure time
  • t c is the critical exposure time
  • I is the maximum effective light intensity.
  • This equation may be applicable to the light source used. However, it may accurately predict the cure depth, which allows the implementation of exposure patterns within the homogenous transition in LAMP.
  • the critical exposure time, t c may be determined by the same method use to determine E c . Exposure time working curves of selected checkerboard square lengths are shown in Fig. 112. From these results, it may be seen that as the square length of the checkerboard pattern increases, the slopes (resin sensitivity) first decrease, reach a minimum and then increase. A similar pattern is also demonstrated in the x-intercepts (critical exposure time). Both minimums in the resin sensitivity and the critical exposure time occur at a similar checkerboard pattern.
  • Fig. 113 a summary of the curing parameters obtained within the homogenous transition are provided.
  • the curing parameters are constant, indicating that grayscale light intensity assumptions may be made.
  • the square length is about 1360 ⁇ and greater, the curing parameters reach all white intensity values and a full intensity assumption may be made to accurately predict the cure depth. It may be seen that within the transition from grayscale exposure to all white exposure a minimum exists in both the critical exposure time and resin sensitivity at a square length of 425 ⁇ . It is interesting to note that at this screening resolution, curing will begin sooner than an all white exposure. However, due to the minimum in resin sensitivity, the cure depth growth rate is much slower than an all white exposure.
  • Equation 2.2 When the intensity of light incident on the PCMS is increased, the rate of initiation of primary radicals is directly affected, which is shown in Equation 2.2. If the light intensity is increased, more primary radicals are generated for polymerization. A higher rate of initiation will increase the rate of polymer chain propagation.
  • E C:DE is the "dose equivalent" critical energy, which corresponds to the range of light intensities where the critical energy is constant and independent of light intensity and E c ,excess(I) is the increase in critical energy resulting from exposure to light intensities greater than the dose equivalent intensity range.
  • the dose equivalent critical energy can be predicted by the inhibitor exhaustion model in Equation 2.12. Since HDDA is a fast reacting monomer, it was found that at low light intensities, the PCMS shows dose equivalence. This is expressed by Equation 5.3 and in Equation 5.4 an expression for a minimum light intensity was proposed.
  • I min k M]fkv 5.4
  • k p the propagation rate constant
  • [M] the monomer concentration
  • f a proportionality factor
  • h Planck's constant
  • v the frequency of the incident light. If the light intensity is lower than I min the system behaves independent of light intensity and if the light intensity is greater than Imin the system depends on the light intensity. The change in critical energy with light intensity was proposed to be described by Equation 5.5.
  • YINH and ⁇ ⁇ is the effectiveness of the inhibitors and absorbers
  • CINH and c A are the concentrations of inhibitors and absorbers
  • f is a proportionality factor. From this equation, it is predicted that the change in critical energy will be inversely proportional to photoinitiator concentration and directly proportional to inhibitor and absorber concentration. However, for a selected formulation, the change in critical energy is expected to be linear. The linear trends found for the critical energy with grayscale and uniform light intensity suggest that this model can be used to predict the dependence of critical energy on light intensity. However, it should be noted that the predicted values deviate from the measured values. Values for the change in critical energy with light intensity presented by Halloran et al. were between 0.08mJ/mW and O.
  • the prediction of the cure depth from grayscale exposure deviates from the common method for predicting the cure depth in stereolithography, which uses the peak intensity of the laser beam to predict the depth of cure.
  • grayscale exposure cures according to the grayscale value of the projected image, which corresponds to the average light intensity incident to the PCMS.
  • the PCMS begins to deviate from this averaging effect. This indicates that the PCMS has some critical dimension for which the light intensity is distributed or averaged.
  • the material system has its own "pixel,” where the power input to the "pixel” divided by its area is the resultant light intensity that causes curing in the PCMS.
  • the dimensions of the material system's pixel are determined by the scattering length. Due to ceramic particle loading, light may be scattered instead of being absorbed by the photoinitiator. As a result, the light intensity is spread laterally to unexposed regions.
  • the resin sensitivity equation can be considered, which is shown in Equation 2.11 and can be rearranged to solve for scattering length.
  • Fig. 114 shows a schematic for how the light intensity within the PCMS can be predicted by the "scattering length pixelation model.”
  • the PCMS resolution is defined as the scattering length, which translates into the radius of the PCMS "pixel.”
  • the light intensity input into this pixel is averaged over the pixel area to obtain an effective light intensity at the pixel's center.
  • the pixel's center is translated an incremental distance from the previous location and the intensity is averaged over the scattering length pixel area for the new center. This process is repeated over the entire exposure area and acts to smooth out the light intensity by increasing the light intensity in unexposed regions and decreasing the light intensity in exposed regions.
  • the correct resin sensitivity is be selected to determine the proper scattering length.
  • the resin sensitivity varies with the length of the square length in the checkerboard pattern. This variation may be described by the same mechanisms proposed to explain the decrease in resin sensitivity observed in grayscale exposure. As the separation between exposed regions increases from grayscale exposure, more absorption is permitted to occur laterally due to scattering, which results in a decrease in D p . However, as the pixel distribution approaches near all white exposure, lateral absorption is reduced, and the vertical absorption increases to the all white exposure resin sensitivity. Therefore, to predict the cure depth within homogenous transition exposure, the resin sensitivity values for each particular screening resolution are used.
  • Results from these simulations are shown for selected checkerboard screening resolutions of 17 ⁇ , 170 ⁇ , 340 ⁇ , and 510 ⁇ in Fig. 115.
  • the result is a uniform reduction in light intensity at the grayscale value of the projected image, which for the checkerboard exposure pattern is 50%.
  • the square length of the checkerboard pattern increases the light intensity increases in the exposed regions and decreases in the unexposed regions. Once the square length is sufficiently large the light intensity reaches the all white exposure intensity.
  • the cure depth will be determined by the maximum thickness of the cured sample, which will result from the maximum incident light intensity experienced by the PCMS. From the simulations in Fig. 115, the maximum light intensity was determined and the cure depth is predicted by Equation 5.7 as follows
  • D p>sr is the resin sensitivity for the selected screening resolution
  • E C (I) is the intensity dependent critical energy shown in Equation 4.2
  • ⁇ ⁇ is the maximum light intensity obtained from the simulations
  • t is the exposure time.
  • Results from these simulations are compared with the experimental working curves in Fig. 116. It can be seen that the scattering length pixel model accurately predicts the maximum light intensity.
  • the R values obtained from these simulations ranged from 0.89 to 0.99. Due to these high R values, this indicates that the scattering length pixelation model accurately simplifies the complex phenomena of light scattering in ceramic loaded suspensions.
  • this model introduces new length scales which can be used in LAMP to fabricate features within the homogenous transition.
  • a possible limitation of the model may be the need to determine the effective resin sensitivity for the target screening resolution.
  • This possible limitation may be overcome by the development of a method to approximate the resin sensitivity or scattering length within the homogenous transition.
  • the homogenous transition is dependent on exposure time. This can be attributed to cure width growth. While the light intensity distribution experienced by the PCMS can be assumed to be independent of exposure time, the cure width from regions of high light intensity will grow into regions of lower light intensity, which can be described by an adapted Jacobs' cure width equation, which is shown in Equation 5.8.
  • LAMP may be used to fabricate unsupported geometries and to reduce defects which arise during BBO due to internal stresses resulting from polymerization shrinkage stress. Discussed below are trends observed in the degree of conversion due to grayscale exposure, wherein the effect of grayscale exposure and screening resolution are presented and compared to an all white exposure. All discussed is a framework for utilizing grayscale exposure to fabricate unsupported features. The effectiveness of generating grayscale support structures (GSS) is also presented and the results are discussed. A framework for reducing defects in LAMP using grayscale exposure is discussed and the effectiveness of this framework is presented and the influence of grayscale on other types of defects is discussed.
  • GSS grayscale support structures
  • a cure depth model for the incorporation of grayscale exposure in LAMP. It may enable, for example, the prediction of exposure dose or exposure time to generate the desired cure depth to ensure adhesion to the previous layer.
  • the cure depth model provides no information on the degree of polymerization, which is useful for making decisions regarding which grayscales are appropriate to address the challenges facing LAMP.
  • FTIR measurements may provide information about the degree of monomer conversion, which is directly related to the degree of polymerization.
  • grayscale exposure may be applied to the surrounding regions in order to provide a GSS, where a particular degree of conversion will correspond to an appropriate support structure.
  • volumetric shrinkage and shrinkage stress information may be obtained from degree of conversion and rate of conversion measurements.
  • the degree of conversion may be calculated from the resulting FTIR spectra according to equation 2.13.
  • the grayscale values investigated were 20%, 40%, 60% and 80%.
  • the degree of conversion for an all white, 100% exposure was investigated to serve as a reference.
  • the degree of conversion was measured for each grayscale value at various exposure times so as to maintain a constant range of energy dose. Results of the degree of conversion measurements are shown in Fig. 117.
  • Photopolymerization may be described in three phases, which are initiation, propagation and termination. These stages are observed in Fig. 117. Initially, at low exposure times, the degree of conversion slowly increases, which is due primarily to the limited mobility of initiated radical species. After initiation, the monomer is rapidly converted to increase the molecular weight and form a cross-linked polymer network, which occurs during the propagation stage. The termination stage experiences autodeceleration, where chain propagation becomes diffusion controlled and the mobility of propagating radical chains is reduced. In the use on multifunctional acrylates such as HDDA, this prevents the final conversion from reaching 100%. As shown, the degree of conversion plateaus at approximately 82%. This indicates that residual monomer is retained in the PCMS.
  • grayscale exposure prolongs the initiation and propagation stages. This may be seen from a lower degree of conversion for a lower grayscale at a given exposure dose when the exposure time is lower than 2000ms.
  • grayscale exposure does not change the final conversion of the polymer; rather, grayscale primarily affects the rates of polymerization. This is shown in the bottom panel of Fig. 117, where the derivatives of the regressed models are plotted. As shown, as the grayscale value decreases, so does the
  • Fig. 118 In addition to considering grayscales within the homogenous region, it is also necessary to characterize the degree of conversion resulting from grayscale exposure within the homogenous transition, which is shown in Fig. 118. To characterize the effect of the homogenous transition on the degree of conversion, an exposure time of 600ms and a grayscale value of 50% white were examined. The checkerboard pattern was used as the screening technique and the square length of the primitives was varied from 17 ⁇ to 1360 ⁇ . It may be seen that there exists a minimum in the degree of conversion as the square lengths increase through the homogenous transition, which follows a similar trend to that seen in the resin sensitivity in Fig. 113.
  • results from the dependence of the degree of conversion on the screening resolution may be separated into three regions: (1) grayscale exposure, (2) homogenous transition exposure, and (3) all white exposure.
  • the degree of conversion is found to be constant.
  • a constant degree of conversion is obtained since any screening resolution with dimensions smaller than the scattering length acts to effectively reduce the light intensity to the grayscale of the projected image.
  • the degree of conversion drastically decreases. This is anomalous behavior, since the homogenous transition is a result of grayscale light intensity increasing to all white light intensity.
  • the degree of conversion would also increase with the transition from grayscale exposure to all white exposure.
  • the light intensity is increasing in the exposed regions of the checkerboard pattern, the light intensity is decreasing in the unexposed regions. Consequently, residual and partially polymerized monomer becomes trapped between the exposed regions within the film.
  • FTIR-ATR provides an averaged spectrum of the conditions of the investigated surface. Therefore, the average degree of conversion decreases upon entering the homogenous transition from the grayscale exposure region.
  • the actual state of the investigated layer consists of regions with high and low degree of conversion, which corresponds to the exposed and unexposed regions, respectively. As the square lengths increase and exit the homogenous transition the degree of conversion increases and exceeds the degree of conversion obtained from grayscale exposure.
  • This gradual increase in degree of conversion is related to the increased ability to remove residual monomer from the unexposed holes in the film. As the square length continues to increase, the degree of conversion eventually reaches a constant value. This region corresponds to the all white exposure region and the degree of conversion measured for this region is consistent with the degree of conversion measured for the 100% white exposure sample shown in Fig. 117.
  • the GSS is preferably strong enough to survive material recoating, (2) the GSS is preferably rigid enough to maintain the spatial location and geometry of the unsupported feature, and (3) the GSS should be easily removed by development with an appropriate solvent, for example, after completion of the build.
  • the degree of conversion As the degree of conversion increases, both the viscosity and hardness increase.
  • the degree of conversion is preferably sufficiently high - i.e., the viscosity and hardness should reach a predetermined value - to prevent the partially polymerized region from being removed or shifted from the intended location.
  • the degree of conversion should reach a predetermined value to ensure accuracy of the target feature.
  • the viscosity and hardness are preferably low enough to be easily removed after completion of the build to fabricate only the intended feature. The result of these two competing requirements is a target
  • a constant exposure time is used in LAMP for photopolymerizing individual layers throughout an entire build, which may be determined by calculating the exposure time required to produce a cure depth of approximately 135 ⁇ - 155 ⁇ (depending on the polymer used). A cure depth larger than the layer thickness may be used to ensure proper adhesion to the previous layer.
  • These exposure times typically range from approximately 120ms to 180ms, again based on the material formulation and age of the light source.
  • this provides an exposure time range for which the cure depth and degree of conversion from grayscale exposure may be considered.
  • Both the cure depth model and degree of conversion measurements may be used to determine the appropriate range of grayscale values to investigate for GSS fabrication. If the critical energy dose for a selected grayscale value is greater than the grayscale energy dose, then no curing will occur, which indicates that this grayscale is not appropriate for GSS. However, if grayscale exposure produces a suitable cure depth (e.g., ⁇ or greater), then the GSS may be not be easily removed after the build is complete. Based on this rationale, the appropriate grayscale range for GSS may be estimated. In some embodiments, the range may be between approximately 46% and 82% by incorporating equations 4.2 and 4.3 into Jacobs' e uation
  • the degree of conversion may also aid in the selection of an appropriate grayscale for GSS. From Fig. 117 it may be seen that at an exposure time of ⁇ 170ms, the degree of conversion is -14%. As a result, the grayscale used should preferably produce a degree of conversion lower than that of the all white exposure. Grayscale values near 80%, for example, produce a degree of conversion similar to that for an all white exposure, which tends to indicate that an 80% grayscale value will produce mechanical properties similar to an all white exposure during a build. Consequently, a grayscale value of 80% is likely not appropriate for GSS. From Fig.
  • grayscale values of 60% and below produce a degree of conversion notably lower (-5%) than an all white exposure.
  • range of grayscales appropriate for GSS fabrication in LAMP may be predicted. In some embodiments, the range may be between approximately 46% and 60%. It should be noted that a degree of conversion of 14% is below the gel point, which is defined as the degree of conversion where the maximum rate of polymerization is reached. 4 This indicates that when a layer is first exposed to UV light in LAMP, the viscosity and modulus are low compared to the completed airfoil mold. The maximum rate of polymerization for an all white exposure was shown to occur at -27% +2%, which is consistent with the literature.
  • a proper screening resolution may also be chosen, i.e. to determine if the exposure technique should be a grayscale exposure or within the homogenous transition.
  • the rationale behind fabricating GSS is to uniformly increase the viscosity of the region surrounding the unsupported feature. Therefore, it is appropriate to select a screening resolution within the grayscale exposure region, as the homogenous transition does not tend to produce uniform layers. Therefore, the screening
  • a challenge component was designed.
  • the side and front views of the challenge component are shown in Fig. 119a, where the build direction is from the bottom up and the white regions correspond to areas to be solidified by UV exposure.
  • the test component consists of a base, side wall, overhang and an unsupported square column. As the build progresses there will eventually be an unsupported feature for which the effectiveness of GSS may be assessed.
  • the unsupported feature was a square column which has a square side length of 1360 ⁇ and column height of 3mm. The column was separated from the base by a distance of 1mm, the side wall by 3.06mm and the unsupported structure connects to the part through an overhang.
  • Fig. 119b shows the first method employed for GSS. In this GSS, one grayscale level is selected for each layer and grayscale exposure surrounds the entire column. The grayscale exposure region connects to the base, side wall overhang, and unsupported feature.
  • results from the first trial are shown in Fig. 120.
  • the grayscale values investigated were 50%, 54%, 56%, 58% and 62% at a screening resolution of HDS super fine.
  • the build parameters, such as material recoating speed and exposure time were set to 30mm/s and 170ms, respectively. From these results, an "all or nothing" behavior was observed.
  • grayscale values of 50% and 54% were unable to fabricate any component of the unsupported column.
  • the grayscale value was increased to 56%, nearly all the grayscale region polymerized to a degree of conversion which could not be easily removed.
  • the GSS became an unsupported feature in the following layer and was accordingly removed during recoating. This indicates that the GSS must be successful for each layer.
  • grayscale values of 56% and greater were used, the GSS was strong enough to survive the material recoating process.
  • Each additional layer induced incremental polymerization in the previous layers due to print-through. Since, the degree of conversion from a single layer is below the gel point, the PCMS is within the autoacceleration stage of polymerization. This causes the degree of conversion to rapidly increase with minimal energy dose. As a result, the degree of conversion within the GSS approaches a value similar to an all white exposure. Reports by Xia and Fang demonstrate similar behavior in their investigation of GSS for projection microstereolithography.
  • the GSS was bonded to the test component.
  • the GSS was able to be removed through a piranha solution, which preferentially etched the partially polymerized support structure at a faster rate than the test component.
  • selective etching was investigated for the challenge component with a GSS of 56% to determine if this technique was suitable for LAMP.
  • Two solvents appropriate for LAMP were tested, which were acetone and 3D 101. Etching was conducted through sonication at room temperature for one hour.
  • Fig. 121 Results from the etching investigation are shown in Fig. 121.
  • the test component in Fig. 121a shows the condition and dimensions of the component prior to etching. Individual components were used for each etching experiment.
  • Fig. 121b and 121c show the condition of the component after etching with acetone and 3D 101, respectively. From these results, it may be seen that neither of the two etching techniques completely removed the GSS. In each case, the GSS remained bonded to the side wall and a significant portion of GSS surrounded the unsupported column. However, while portions of the GSS were etched, so was a proportional
  • the recoating speed may be reduced from 30mm/s to lOmm/s and the exposure time may be increased from 170ms to 218ms.
  • a lower recoating speed may act to lower the minimum degree of conversion required to survive material recoating.
  • Increasing the exposure time enables a larger difference in the degree of conversion between grayscale exposure and all white exposure.
  • embodiments of the present invention may also comprise a novel technique of alternating grayscale values between successive layers was developed to minimize print-through in the GSS.
  • This technique is depicted in Fig. 119c.
  • the technique consists of alternating the grayscale values between successive layers from a high grayscale value to a low grayscale value. For instance, consider the GSS of 56% presented in Fig. 120. The high degree of conversion generated from print-through could be reduced by reducing the grayscale of every other layer within the GSS.
  • the degree of conversion When the degree of conversion is below the gel point, due to autoacceleration, for example, a lower degree of conversion has a lower corresponding polymerization rate, which is demonstrated in Fig. 117. As a result, the lower degree of conversion may act as a barrier to mediate incremental polymerization throughout the fabrication of GSS.
  • the connection of the GSS to the side wall may be removed to increase the surface area which may be developed after completion of the build.
  • the gap separation between the GSS and the side wall may be set to approximately 1mm, and 2mm of GSS may be used to surround the column in all directions.
  • Fig. 122 Results from these modifications are shown in Fig. 122.
  • the low grayscale value was held constant at 50% and the high grayscale value was investigated at 52% (b), 53% (c), 54% (d), and 56% (e).
  • a constant GSS of 50% is also shown in (a).
  • the first row shows the test components before developing with 3D101. It may be seen that the GSS appears much less viscous than GSS formed in the first trial shown in Fig. 119.
  • the second row shows the test component after rinsing with a water jet using 3D 101, which is a typical technique used to remove residual monomer. It may be seen that removal of the GSS reveals the successful fabrication of the grayscale supported test component.
  • Fig. 122a shows that a GSS of 50% may fabricate an unsupported column. This shows that alternating GSS are not necessary to fabricate unsupported features. Rather, the critical parameter was the material recoating speed. However, it is demonstrated that alternating grayscale exposure within the GSS is an effective method for fabricating unsupported geometries as well. The advantage of alternating GSS is the mitigation of "all or nothing" behavior.
  • Fig. 122 shows that alternating grayscale GSS expands the range of grayscale that may be used to fabricate the unsupported column. This is evidenced by Fig. 122e, where an alternating GSS of 50% and 56% was used. Previously, a GSS with the use of a single grayscale value at 56% was unable to be easily removed due to significant print- through. However, inserting a grayscale value of 50% every other layer within the GSS enabled the successful fabrication of the unsupported feature and easy removal of the GSS with standard development techniques. This shows the ability of alternating grayscale to mitigate residual curing from print- through. This aspect increases the reliability of fabricating unsupported geometries and may allow for more variation in build parameters.
  • One aspect of the test component which should be noted is that the height of the column.
  • the column height was designed to be 3mm, yet for each GSS, the height of the column was ⁇ 3.5mm. This may be related to print- through causing curing up to 5 layers beneath the column.
  • Grayscale exposure consumes many of the inhibitor species typically present in unexposed monomer. As a result, any additional exposure dose goes directly to polymerization, which causes the column to be longer than the design value.
  • Fig. 119d an additional design revision to the GSS may be performed, which may be seen in Fig. 119d.
  • grayscale exposure is removed from directly underneath the unsupported feature.
  • This design feature attempts to mitigate print-through, since the inhibitors in the PCMS must be consumed before curing may occur. As a result, the probability of developing additional thickness beneath the exposed layer is reduced, which could result in a more accurately built test component.
  • Results from a print- through mediated alternating GSS are shown in Fig. 123.
  • the test component shown was fabricated with alternating grayscale values of 50% and 70%.
  • Figs. 123a and 123b depict the GSS before development and the unsupported column which appears after development, respectively.
  • the difference between alternating grayscale values for the print- through mediated GSS are more disparate than the typical alternating GSS, which may be related to the volume reduction of the grayscale support. From this result, a larger gap between the base and the unsupported feature may be seen, which results in a higher accuracy in the build direction.
  • the column height was measured to be 3.2mm. This indicates that print-through develops additional thickness corresponding to two layers beneath the column in the absence of grayscale support directly beneath the column (i.e., as opposed to 5 layers when grayscale is beneath the column).
  • the GSS may be easily removed after part completion without mechanical methods, which is important for applications to LAMP.
  • Many of the unsupported geometries encountered in airfoil molds are within the internal features of the mold. This technique of grayscale support structures holds promise for successfully fabricating unsupported features within airfoil molds and thus expanding the versatility of LAMP.
  • a uniform light intensity exposure is applied to a large area, which causes anomalous defects to form during BBO.
  • One of these behaviors is "fissures,” which is shown in Fig. 124. While large-scale defects that prevent functionality of the mold for casting are not present in green bodies, fissure precursors may be seen, which are shown in Fig. 124a. Fissures formed during BBO are straight and parallel with the LAMP layers. Additionally, a periodicity of every 4, 6 and 8 layers is observed throughout the airfoil mold.
  • Fig. 124B shows the state of the mold after heating to 193°C. From this image it appears that the fissures are formed during BBO, yet before significant weight loss has occurred, corresponding to the potential fissure precursors observed in the green body, which is confirmed in Fig. 124c. For closer inspection, Fig. 124d shows an expanded view of a typical fissure with a 6 layer period.
  • the second mechanism of stress generation develops with the exposure of multiple layers, which is shown in Fig. 125b.
  • the linear contraction interacts with the preceding layer. If no boundary conditions are applied, curvature develops towards the light source.
  • Multiple layer shrinkage stress will continue to develop deeper into the build due to print- through. It is interesting to note that print-through in LAMP may penetrate approximately 6 layers, which is quite similar to the periodicity observed in the fissures. It may be hypothesized, therefore, that the fissures are the result of a stress relaxation from the accumulation of shrinkage stress across multiple layers due to print-through.
  • the average degree of conversion may decrease by more than 50% when compared to an all white exposure, as shown in Fig. 118. This indicates that the net mitigation of volumetric shrinkage may also be greater than 50%.
  • uncured or partially cured monomer is retained within the layer, which has been shown to reduce volumetric shrinkage stress through monomer migration. 9
  • this shows promise for reducing defects in the green body mold. Since the origin of fissures and delamination generally depends on the state of the green body mold, reducing defects in the green body may reduce these types of defects during BBO and sintering.
  • the test component was a hollow cylinder, which is shown in Fig. 127a.
  • the outer diameter of the cylinder was set to 22mm with a thickness of 3mm and height of 24mm to simulate nominal dimensions used in airfoil molds.
  • the hollow cylinders were fabricated with all white exposure and with three screening resolutions within the homogenous transition.
  • the screening techniques utilized were checkerboard patterns with square lengths of 170 ⁇ , 255 ⁇ and 425 ⁇ , which correspond to screening resolutions near grayscale exposure, in the middle of the homogenous transition, and near all white exposure, respectively.
  • the layers were exposed in a staggered pattern so that the exposed region was unexposed in the following layer and vice versa, which is shown in Fig. 127b.
  • Fig. 128 shows the result from fabrication of a test cylinder with all white exposure.
  • the image in (a) shows the green body mold illuminated to enhance the detection of defects.
  • the mold contained a smooth surface, but distinct defects were present in the green body.
  • Fig. 128b shows an expanded view of a section of the surface with enhanced contrast to demonstrate the fissure precursor. It may be seen that a similar periodicity to the mold shown in Fig. 124A develops in the all white test cylinder. This indicates a high probability that fissures will develop during BBO.
  • a defect related to "shuffle” may be seen, which is related to the serpentine path traversed in LAMP during large area exposure. From these defects in the green body, it may be expected that fissures will develop in the regions shown in Fig. 128b and the shuffle defect will become more apparent during BBO and sintering due to thermally initiated polymerization and subsequent shrinkage..
  • Fig. 129 shows numerous horizontal defects resulting from BBO and sintering of the all white exposure test cylinder. The brightness from these fissures is higher compared to those in the green body, which indicate a larger defect. In this sample there were 4 horizontal defects which propagated throughout the circumference of the cylinder accompanied with many localized fissures. It may be seen that fissures occur throughout the height of the test cylinder, where the severity of the defect varies, yet the spacing remains constant.
  • Fig. 128B shows the regular spacing of 4, 6, or 8 layers.
  • Fig. 130 shows the green body molds for cylinders fabricated with checkerboard exposure at square lengths of 170 ⁇ (a), 255 ⁇ (b), and 425 ⁇ (c). In each screening resolution the surface roughness increased compared to the all white cylinder. In addition, spalling is observed and portions of the outer surface were removed during development. These effects result due to the limited connectivity of the cured portions within the cylinder and the lack of a smooth outer surface. However, no fissure precursors could be discerned from the captured images. This indicates that fissures should not develop during BBO and sintering.
  • the absence of a shuffle pattern defect may also be noted.
  • vertical lines appear on the cylinder surfaces, which could lead to the formation of vertical defects during BBO and sintering.
  • the vertical features resulting from a square length of 170 ⁇ appear less straight, when compared to cylinder with a square length of 255 ⁇ and 425 ⁇ , and are irregularly spaced.
  • the spacing is substantially constant and the lines are straight and parallel to the build direction.
  • the spacing between vertical lines is larger and with higher contrast for a square length of 425 ⁇ compared to a square length of 255 ⁇ . The length of the spacing was found to be equivalent to the square length utilized in the exposure method, which indicates that the lines are a characteristic of the exposure technique.
  • Fig. 131 shows the effects of BBO and sintering on the test cylinders fabricated using a staggered checkerboard exposure with square length of 170 ⁇ (a), 255 ⁇ (b), and 425 ⁇ (c).
  • FIG. 131a shows greatest number of long range horizontal fissures. However, these were the primary horizontal defects observed, in contrast to the all white exposure in which numerous horizontal defects of smaller length were observed. When examining the screening resolution with a square length of 255 ⁇ and 425 ⁇ , no long range horizontal defects were observed.

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Abstract

L'invention concerne des systèmes et des procédés pour fabriquer des objets tridimensionnels. Le système comprend un système d'imagerie optique fournissant une source de lumière ; un support photosensible conçu pour changer d'états lors d'une exposition à une partie de la source de lumière provenant du système d'imagerie optique ; un système de commande pour commander le déplacement du système d'imagerie optique, le système d'imagerie optique se déplaçant de manière continue au-dessus du support photosensible. Le procédé consiste à déplacer un système d'imagerie optique sans masque fournissant le faisceau de lumière dans une séquence continue ; à présenter le faisceau de lumière sur une partie du support photosensible ; à abaisser une plaque sur laquelle se trouve le support photosensible ; et à appliquer une nouvelle couche du support photosensible.
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EP2917012A4 (fr) 2016-08-10
WO2014074954A3 (fr) 2015-01-29
CN105163922B (zh) 2018-11-06
EP3925761A1 (fr) 2021-12-22
JP2016501139A (ja) 2016-01-18
CN105163922A (zh) 2015-12-16
HK1218638A1 (zh) 2017-03-03
WO2014074954A2 (fr) 2014-05-15
JP6306603B2 (ja) 2018-04-04

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