Research Papers

Adaptive Slicing in Additive Manufacturing Process Using a Modified Boundary Octree Data Structure

[+] Author and Article Information
Nandkumar Siraskar

Center for Global Design and Manufacturing,
Department of Mechanical and
Materials Engineering,
University of Cincinnati,
Cincinnati, OH 45221
e-mail: siraskarns@gmail.com

Ratnadeep Paul

Center for Global Design and Manufacturing,
Department of Mechanical and
Materials Engineering,
University of Cincinnati,
Cincinnati, OH 45221
e-mail: paulrp@ucmail.uc.edu

Sam Anand

Center for Global Design and Manufacturing,
Department of Mechanical and
Materials Engineering,
University of Cincinnati,
Cincinnati, OH 45221
e-mail: sam.anand@uc.edu

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received August 10, 2013; final manuscript received September 10, 2014; published online November 26, 2014. Assoc. Editor: Jack Zhou.

J. Manuf. Sci. Eng 137(1), 011007 (Feb 01, 2015) (11 pages) Paper No: MANU-13-1306; doi: 10.1115/1.4028579 History: Received August 10, 2013; Revised September 10, 2014; Online November 26, 2014

In additive manufacturing (AM) processes, the layer-by-layer fabrication leads to a staircase error resulting in dimensional inaccuracies in the part surface. Using thinner slices reduces the staircase error and improves part accuracy but also increases the number of layers and the build time for manufacturing the part. Another approach called adaptive slicing uses slices of varying thicknesses based on the part geometry to build the part. A new algorithm to compute adaptive slice thicknesses using octree data structure is presented in this study. This method, termed as modified boundary octree data structure (MBODS) algorithm, is used to convert the stereolithography (STL) file of an object to an octree data structure based on the part's geometry, the machine parameters, and a user defined tolerance value. A subsequent algorithm computes the variable slice thicknesses using the MBODS representation of the part and virtually manufactures the part using these calculated slice thicknesses. Points sampled from the virtually manufactured part are inspected to evaluate the volumetric, profile, and cylindricity part errors. The MBODS based slicing algorithm is validated by comparing it with the uniform slicing approach using various slice thicknesses for different parts. The developed MBODS algorithm is observed to be more effective in improving the part quality while using lesser number of slices.

Copyright © 2015 by ASME
Topics: Algorithms , Errors , Octrees
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Ghariblu, H., and Rahmati, S., 2014, “New Process and Machine for Layered Manufacturing of Metal Parts,” ASME J. Manuf. Sci. Eng., 136(4), p. 041004. [CrossRef]
Paul, R., Anand, S., and Gerner, F., 2014, “Effect of Thermal Deformation on Part Errors in Metal Powder Based Additive Manufacturing Processes,” ASME J. Manuf. Sci. Eng., 136(3), p. 031009. [CrossRef]
Edwards, P., O'Conner, A., and Ramulu, M., 2013, “Electron Beam Additive Manufacturing of Titanium Components: Properties and Performance,” ASME J. Manuf. Sci. Eng., 135(6), p. 061016. [CrossRef]
Paul, R., and Anand, S., 2011, “Optimal Part Orientation in Rapid Manufacturing Process for Achieving Geometric Tolerances,” J. Manuf. Syst., 30(4), pp. 214–222. [CrossRef]
Paul, R., and Anand, S., 2012, “Process Energy Analysis and Optimization in Selective Laser Sintering,” J. Manuf. Syst., 31(4), pp. 429–437. [CrossRef]
Panhalkar, N., Paul, R., and Anand, S., 2013, “Adaptive Layering in Additive Manufacturing using a k-d Tree Approach,” Proceedings of the 41st NAMRC 2013, Madison, WI, June 10–14.
Koc, B., 2004, “Adaptive Layer Approximation of Free-Form Models Using Marching Point Surface Error Calculation for Rapid Prototyping,” Rapid Prototyping J., 10(5), pp. 270–280. [CrossRef]
Ma, W. Y., But, W. C., and He, P. R., 2004, “NURBS-Based Adaptive Slicing for Efficient Rapid Prototyping,” Comput.-Aided Des., 36(13), pp. 1309–1325. [CrossRef]
Zhou, M. Y., Xi, J. T., and Yan, J. Q., 2004, “Adaptive Direct Slicing With Non-Uniform Cusp Heights for Rapid Prototyping,” Int. J. Adv. Manuf. Technol., 23(1–2), pp. 20–27. [CrossRef]
Cormier, D., Unnanon, K., and Sanii, E., 2000, “Specifying Non-Uniform Cusp Heights as a Potential Aid for Adaptive Slicing,” Rapid Prototyping J., 6(3), pp. 204–211. [CrossRef]
Zhao, Z. W., and Laperriere, L., 2000, “Adaptive Direct Slicing of the Solid Model for Rapid Prototyping,” Int. J. Prod. Res., 38(1), pp. 69–83. [CrossRef]
Hope, R. L., Roth, R. N., and Jacobs, P. A., 1997, “Adaptive Slicing With Sloping Layer Surfaces,” Rapid Prototyping J., 3(3), pp. 89–98. [CrossRef]
Sabourin, E., Houser, S. A., and Bohn, J. H., 1996, “Adaptive Slicing Using Stepwise Uniform Refinement,” Rapid Prototyping J., 2(4), pp. 20–26. [CrossRef]
Anand, S., and Knott, K., 1991, “An Algorithm for Converting the Boundary Representation of a CAD Model to Its Octree Representation,” Comput. Ind. Eng., 21(1–4), pp. 343–347. [CrossRef]
Allada, V., and Anand, S., 1992, “Manufacturing Applications of Octrees,” Comput. Ind. Eng., 23(1–4), pp. 37–40. [CrossRef]
Brunet, P., and Navazo, I., 1990, “Solid Representation and Operation Using Extended Octrees,” ACM Trans. Graphics, 9(2), pp. 170–197. [CrossRef]
Navazo, I., 1989, “Extended Octtree Representation of General Solids With Plane Faces—Model Structure and Algorithms,” Comput. Graphics, 13(1), pp. 5–16. [CrossRef]
Ayala, D., 1988, “Boolean Operations between Solids and Surfaces by Octrees—Models and Algorithm,” Comput.-Aided Des., 20(8), pp. 452–465. [CrossRef]
Samet, H., 1988, “An Overview of Quadtrees, Octrees, and Related Hierarchical Data Structures,” Theor. Found. Comput. Graphics CAD NATO ASI Ser., 40, pp. 51–68. [CrossRef]
Brunet, P., and Ayala, D., 1987, “Extended Octtree Representation of Free Form Surfaces,” Comput. Aided Geom. Des., 4(1–2), pp. 141–154. [CrossRef]
Ayala, D., Brunet, P., Juan, R., and Navazo, I., 1985, “Object Representation by Means of Nonminimal Division Quadtrees and Octrees,” ACM Trans. Graphics, 4(1), pp. 41–59. [CrossRef]
Gargantini, I., 1982, “Linear Octtrees for Fast Processing of 3-Dimensional Objects,” Comput. Graphics Image Process., 20(4), pp. 365–374. [CrossRef]
Meagher, D., 1982, “Geometric Modeling Using Octree Encoding,” Comput. Graphics Image Process., 19(2), pp. 129–147. [CrossRef]
Jackins, C., and Tanimoto, S., 1980, “Oct-Trees and Their Use in Representing 3-Dimensional Objects,” Comput. Graphics Image Process., 14(3), pp. 249–270. [CrossRef]
Samet, H., 1985, “A Top-Down Quadtree Traversal Algorithm,” IEEE Trans. Pattern Anal. Mach. Intell., 7(1), pp. 94–98. [CrossRef] [PubMed]
Samet, H., and Shaffer, C. A., 1985, “A Model for the Analysis of Neighbor Finding in Pointer-Based Quadtrees,” IEEE Trans. Pattern Anal. Mach. Intell., 7(6), pp. 717–720. [CrossRef] [PubMed]
Samet, H., and Tamminen, M., 1985, “Computing Geometric-Properties of Images Represented by Linear Quadtrees,” IEEE Trans. Pattern Anal. Mach. Intell., 7(2), pp. 229–240. [CrossRef] [PubMed]
Kulkarni, P., Marsan, A., and Dutta, D., 2000, “A Review of Process Planning Techniques in Layered Manufacturing,” Rapid Prototyping J., 6(1), pp. 18–35. [CrossRef]
Dolenc, A., and Makela, I., 1994, “Slicing Procedures for Layered Manufacturing Techniques,” Comput.-Aided Des., 26(2), pp. 119–126. [CrossRef]
Allen, S., and Dutta, D., 1998, “Wall Thickness Control in Layered Manufacturing for Surfaces With Closed Slices,” Comput. Geom. Theory Appl., 10(4), pp. 223–238. [CrossRef]
Roth, S. D., 1982, “Ray Casting for Modeling Solids,” Comput. Graphics Image Process., 18(2), pp. 109–144. [CrossRef]
Masood, S. H., and Rattanawong, W., 2002, “A Generic Part Orientation System Based on Volumetric Error in Rapid Prototyping,” Int. J. Adv. Manuf. Technol., 19(3), pp. 209–216.
Rattanawong, W., Masood, S. H., and Iovenitti, P., 2001, “A Volumetric Approach to Part-Build Orientations in Rapid Prototyping,” J. Mater. Process. Technol., 119(1–3), pp. 348–353. [CrossRef]
Navangul, G., 2011, “Stereolithography (STL) File Modification by Vertex Translation Algorithm (VTA) for Precision Layered Manufacturing,” M.S. thesis, University of Cincinnati, Cincinnati, OH.
Navangul, G., Paul, R., and Anand, S., 2011, “A Vertex Translation Algorithm for Adaptive Modification of STL File in Layered Manufacturing,” ASME Paper No. MSEC2011-50283. [CrossRef]
The American Society of Mechanical Engineers, 1995, American National Standards Institute: Dimensioning and Tolerancing for Engineering Drawings, ANSI Standard Y14.5M, ASME, New York.


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Fig. 1

(a) Example 3D object, (b) octree decomposition, and (c) tree representation

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Fig. 2

(a) Part model, (b) quadtree representation, and (c) extended quadtree representation

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Fig. 3

Cube edge and triangle facet intersection

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Fig. 4

Cube face and triangle edge intersection

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Fig. 5

Cube with intersecting triangles parallel or perpendicular to the cube faces

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Fig. 6

Rays casted in a gray cube

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Fig. 7

Test to determine if point is (a) inside the part volume or (b) outside the part volume

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Fig. 8

Determination of point with no intersections

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Fig. 9

Segments for rays originating from points lying (a) outside the part and (b) inside the part

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Fig. 10

Slice thickness calculations

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Fig. 11

Division of a cube octant into multiple regions

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Fig. 12

Redivision of octant and calculation of residual slice thickness

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Fig. 13

Cube overlapping with already fixed slice thicknesses

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Fig. 14

(a) CAD model, (b) STL file, and (c) MBODS representation for test part 1

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Fig. 15

(a) CAD model, (b) STL file, and (c) MBODS representation for test part 2

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Fig. 16

(a) Test part 3, (b) MBODS representation, and (c) sampled points on virtually manufactured surface

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Fig. 17

(a) Surface under consideration in test part 1 and (b) points sampled from virtually manufactured surface

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Fig. 18

(a) STL format of cylinder with 45 deg the Z-axis and (b) Points dataset for cylindricity evaluation



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