1. Layered Manufacturing of Thin-Walled Parts Sara McMains, Jordan Smith, Jianlin Wang, Carlo Séquin UC Berkeley

2. Is Layered Manufacturing really Rapid Prototyping? How can we speed up these manufacturing technologies? 3.5”, 20hrs3.0”, 25 hrs2.5”, 15hrs

3. Raster Scan Technologies Example: 3D Printing Speed of roller limits the process Build time = z-height Speed up: pack build volume in xy with many parts

4. Vector Scan Technologies Example: FDM (Fused Deposition Modeling) Build time = volume scanned (material used) Our Goal: create a sturdy part that is visually equivalent but uses less material, so that it builds faster

5. Building Solid Parts with QuickSlice Software interface to Stratasys 1650 FDM Machine Input: STL boundary representation Slices model into z-layer contours (SSL) Builds support structure Builds roads (nozzle fill path) (SML) FDM Roads SML 3D B-Rep STL SupportSlicer QuickSlice SSL

6. QuickSlice Fast Build Builds a semi-hollow version of the solid n solid offset rings Center filled with a loose crosshatch pattern FDM Roads SML 3D B-Rep STL SupportSlicer QuickSlice SSL Fast

7. Fast Build Limitations Structurally conservative Only applied to slice layers whose center area is completely covered by slices above and below it Gradually sloping surfaces prevent its application Worst case example z

8. Can Approach Be More Aggressive? Our Goal: –Create an automated process –Input: the boundary representation of a desired solid geometry –Output: a sturdy, physical part that is visually equivalent while using less material –Benefits: faster build times and material conservation Our Assets: –QuickSlice software as a black box –Specifically the loose fill crosshatched roads option SML 3D B-Rep FDM Automated Process?

9. Idea #1: 3D Offset Pipeline Solid-fill the volume between the input and the offset surfaces Crosshatch-fill the volume within the offset surface Polyhedron Offset FDM Quick Slice SML 3D B-Rep STL Unfortunately, the 3D offset is Assume we have true 3D offset surface at the desired distance inward Difficult to implement robustly Too aggressive: slicing can produce gaps near gradually sloping walls z

10. Idea #2: Approximate 3D Offset Key ideas: –Offsetting is much simpler in 2D than in 3D –The manufacturing process eventually represents the part as a stack in z of layers of 2D contours Start: slice polyhedron into desired set of 2D contours End: input SSL to QuickSlice to build support and roads SML Slices 3D B-Rep Slicer FDM RoadsSupportSlicer QuickSlice SSL

11. 2D Contour Offset Data: layers of 2D contours Offset the 2D contours inward by a specified distance = n layer thicknesses Near vertical walls, this is the correct 3D offset Approximation degrades as the walls approach horizontal Slices 3D B-Rep Offsets Slicer Contour Offset SML SSL FDM RSS QuickSlice

12. 2½D Polyhedron Offset Data: layers of 2D contours and offsets Adjust the loose fill areas in regions where the vertical coverage above or below is less than n layers thick –Perform 2D boolean (CSG) combinations of the contours and offsets of the ith layer with the n layers above and below it –We use OpenGL for the 2D booleans SML SSL Slices 3D B-Rep Offsets 2½D CSG Slicer FDM Contour Offset RSS QuickSlice

13. Regularized Boolean Operations Unregularized: op  { , , - } Regularized: op*  {  *,  *, -* } A op* B = Closure( Interior( A op B ) ) If A & B are 2D areas and C = A op* B then C is a non-degenerate 2D area or  B A  * B A A  B

14. 1-Layer Thick 2½D Offset z

15. z

16. z

17. n-Layer Thick 2½D Offset z

18. z

19. z

20. Results: the Bolt Part QuickSlice Fast Build –Time: 504 min (8:24) –Filament used: 22.1 m 2½D Offset Method –Time: 232 min (3:52) –Filament used: 7.6 m QuickSlice took 2.71 times as long and used 2.9 times as much filament

21. Conclusion We have implemented a robust 2D contour offsetting program. We have conservatively approximated the 3D polyhedron offset using 2D contour slices, 2D offsets, and 2½D boolean operations. We have demonstrated a novel approach to speeding up FDM manufacturing. –Our approach decomposes the desired geometry into a thin sturdy outer shell with a loosely filled center volume. –Our approach saves time and material as compared to the built-in QuickSlice solution.

22. Thanks to our Sponsors NSF –CyberCut –CADRE: MOSIS++: A Distributed Manufacturing Resource (EIA-9905140) Ford Motor Co.

23. 2D Contour Offset Implementation Difficulties arise from global interactions Robust approach based on Voronoi diagram –Generalization of the approach described by M. Held 1991 InputOffset 0.1Offset 0.2

24. Voronoi Diagram of a Contour Input sites are both Vertices and directed Edge Segments VD divides the plane into zones s.t. every point in a zone is closest to the corresponding input site than to any other site Vertices of VD have an associated signed distance VD is a signed distance function

25. Voronoi Mountain Create a height field by raising the vertices of VD in z by their signed distance Offsetting by n is the same as slicing the mountain with the plane z = n z z = 0

26. Offset Slicing z-monotone parabolic VD edges for each unvisited VD edge if VD edge  z = n Crawl VD CCW around peak CW around each VD face

27. Dragon Curve Example InputVoronoi DiagramOffset