Layered Manufacturing of Thin-Walled Parts

Sara McMains, Jordan Smith,

Jianlin Wang, Carlo Séquin

UC Berkeley

Is Layered Manufacturing really Rapid Prototyping?

• How can we speed up these manufacturing technologies?

3.5”, 20hrs 3.0”, 25 hrs2.5”, 15hrs

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

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 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)

FDMRoadsSML

3D B-RepSTL

SupportSlicer

QuickSliceSSL

QuickSlice Fast Build

• Builds a semi-hollow version of the solid

• n solid offset rings• Center filled with a loose

crosshatch pattern

FDMRoadsSML

3D B-RepSTL

SupportSlicer

QuickSliceSSL

Fast

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

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

FDMAutomated Process?

Idea #1: 3D Offset Pipeline

• Solid-fill the volume between the input and the offset surfaces

• Crosshatch-fill the volume within the offset surface

PolyhedronOffset

FDMQuickSlice

SML

3D B-RepSTL

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

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

SMLSlices

3D B-Rep

Slicer FDMRoadsSupportSlicer

QuickSliceSSL

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

Slices3D B-Rep

Offsets

SlicerContourOffset

SML

SSL

FDMRSS

QuickSlice

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

Slices3D B-Rep

Offsets2½DCSG

Slicer FDMContourOffset

RSS

QuickSlice

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 * BA A B

11 iiii SSSSB

1-Layer Thick 2½D Offset iSA Offset

11 OffsetOffset iii SSSC CBAShell

z

11 iiii SSSSB

1-Layer Thick 2½D Offset iSA Offset

11 OffsetOffset iii SSSC CBAShell

z

11 iiii SSSSB

1-Layer Thick 2½D Offset iSA Offset

11 OffsetOffset iii SSSC CBAShell

z

n-Layer Thick 2½D Offset

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n-Layer Thick 2½D Offset

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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

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.

Thanks to our Sponsors

• NSF– CyberCut– CADRE:

• MOSIS++: A Distributed Manufacturing Resource (EIA-9905140)

• Ford Motor Co.

2D Contour Offset Implementation

• Difficulties arise from global interactions

• Robust approach based on Voronoi diagram– Generalization of the approach described by

M. Held 1991

Input Offset 0.1 Offset 0.2

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

• 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

zz = 0

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