Layered Manufacturing of ThinWalled Parts Sara Mc Mains

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

Is Layered Manufacturing really Rapid Prototyping? 2. 5”, 15 hrs 3. 5”, 20 hrs 3. 0”, 25 hrs • How can we speed up these manufacturing technologies?

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

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

Building Solid Parts with Quick. Slice 3 D B-Rep STL Slicer SSL Support Roads • 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) SML FDM

Quick. Slice Fast Build 3 D B-Rep STL Quick. Slicer SSL Support • Builds a semi-hollow version of the solid • n solid offset rings • Center filled with a loose crosshatch pattern Fast Roads SML FDM

Fast Build Limitations z • 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

Can Approach Be More Aggressive? 3 D B-Rep Automated Process? SML FDM • 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: – Quick. Slice software as a black box – Specifically the loose fill crosshatched roads option

Idea #1: 3 D Offset Pipeline 3 D B-Rep Polyhedron Offset STL Quick Slice Assume we have true 3 D offset surface at the desired distance inward • Solid-fill the volume between the input and the offset surfaces • Crosshatch-fill the volume within the offset surface Unfortunately, the 3 D offset is difficult to implement robustly! SML FDM z

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

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

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

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

1 -Layer Thick 2½D Offset z

1 -Layer Thick 2½D Offset z

1 -Layer Thick 2½D Offset z

n-Layer Thick 2½D Offset z

n-Layer Thick 2½D Offset z

n-Layer Thick 2½D Offset z

Results: the Bolt Part • Quick. Slice Fast Build • 2½D Offset Method – Time: 504 min (8: 24) – Filament used: 22. 1 m – Time: 232 min (3: 52) – Filament used: 7. 6 m Quick. Slice took 2. 71 times as long and used 2. 9 times as much filament

Conclusion • We have implemented a robust 2 D contour offsetting program. • We have conservatively approximated the 3 D polyhedron offset using 2 D contour slices, 2 D 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 Quick. Slice solution.

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

2 D Contour Offset Implementation Input Offset 0. 1 Offset 0. 2 • Difficulties arise from global interactions • Robust approach based on Voronoi diagram – Generalization of the approach described by M. Held 1991

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

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

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

Dragon Curve Example Input Voronoi Diagram Offset