C D R Computational and Theoretical Problems in Modern Rapid Prototyping Mark R. Cutkosky Stanford Center for Design Research

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Computational and Theoretical Problems in

Modern Rapid Prototyping

Mark R. Cutkosky

Stanford Center for Design Research

http://cdr.stanford.edu/interface

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NAS Math. Modeling Forum 5/10/99 -mrc 2

Outline

• Introduction to Layered Manufacturing– Commercial and research processes

– Enabling factors (why now)

• Capabilities and opportunities– (Almost) arbitrary geometry

– Functionally graded materials

– Integrated assemblies, “smart parts”

• Computational challenges– Huge design space

– Analysis

– Process planning and control

• Summary

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Traditional manufacturing:a sequential process of shaping and assembly

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Layered Manufacturing: commercial example

Laser UV curableliquid elevator

Formedobject

Photolithography processschematic Sample prototype (ME210

power mirror for UT Auto)http://me210.stanford.edu

http://me210.stanford.edu/




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Almost arbitrary 3D Geometries

Loop Tile -- dense tiling of 3D space. (Carlo Sequin, U.C.B.)

Minimum toroidal saddle surface(C. Sequin)

Tilted frames (RPL)

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From RP and CNC to . . .

2000

1970

1990Shape Deposition Manufacturing ( SDM)

RP CNC

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Deposit (part)

Shape

EmbedDeposit (support)

Shape

Part

Embedded Component

Support

Shape Deposition Manufacturing (CMU/SU)

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SDM#1: Injection mold tooling (SU RPL)

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SDM #2: Frogman (CMU)

• Example of polymer component with embedded electronics

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SDM #3: Ceramic parts (RPL)

Alumina vane

Silicon nitride pitch shaft

Alumina turbine wheels

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SDM for integrated assemblies

Motor

Leg links

Shaft

Shaft coupling

Body frame Lift pot

Knee pot

Hip pot

Abduct pressuresensor

Lift pressuresensor Extend pressure

sensor

Gears

ActuatorsMotivation: Building smallrobots with prefabricatedcomponents is difficult...and results are not robust.

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Designer composes the design from library of primitives, including embedded components

Steel leaf spring

Piston

Outlet for valve

Valve Primitive

Circuit Primitive

Inlet port primitive

Part Primitive

SDM #4: Robot leg with embedded components (http:cdr.stanford.edu/biomimetics)

http://cdr.stanford.edu/biomimetics









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Internal components are modeled in the 3D CAD environment.

Steel leaf-spring

Piston

Sensor and circuit

Spacer

Valves

Components are prepared with spacers, etc. to assure accurate placement.

Robot Leg design (cont’d.)

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The output of the software is a sequence of 3D shapes and toolpaths.

Robot Leg: compacts

Support

Part

Embedded components

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A snapshot just after valves and pistons were inserted.

Steel leaf-spring

Piston

Sensor and circuit

Valves

Robot Leg: embedded parts

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Finished parts ready for testing

Robot Leg: completed

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Layered Manufacturing: is it a new manufacturing paradigm?

Photo-sculpturestudio (1860)

Laminated manufacturing(1892-1940s)

Laser-based photolithography (1977)

[Source: Beaman 1997]

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A process enabled by computing...

3D solid model

CAD

slicingtrajectory planning

material addition process

process planner fabrication machine

data exchange format

motion control trajectories

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Summary of layered manufacturing processes

Commercial• Photolithography

• Fused deposition

• Laser sintering

• Laminated paper

Research• Selective laser sintering

(UT Austin)

• 3D printing (MIT)

• Shape deposition manufacturing (CMU/Stanford)

“Look and feel” prototypeComplex 3D shapesdirect from CAD model

Engineering materials (metals,ceramics, strong polymers)Graded materialsEmbedded componentsNot quite direct from CAD model...

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Layered manufacturing results in a huge space of possible designs:

• Ability to create arbitrary 3D structures with internal voids

• Ability to vary material composition throughout the structure

• Ability to embed components such as sensors, microprocessors, structural elements.

What kind of design environment will help designers to understand and exploit the potential of layered manufacturing?

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Ability to create arbitrary 3D structures with internal voids (homogeneous materials)

Shape optimization example:Find the minimum-weight shelf structure, bounded by box B, that supports load W without failing.

B

W

Space within B is divided into N cells, each of which can be filled or empty. Number of unique designs 2N

Rapid Prototyping Workshop 5/99 -mrc

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Ability to vary material composition

Support structure

depositionheads

Deposition heads can be controlled to deposit varying amounts of each material* as the part is built. Total material composition varies throughout the part.

Volume fractions always add to unity*

*void, or empty space, is treated as a special case of material

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Material composition: product space

Product Space: )!1(!

)!1(

1

1

mr

mr

m

mrC

urethane

glass

void

teflon

m = number of materials (including void)

vi = volume fraction of each material

r = deposition mixture resolution

11

m

iiv

Example: urethane, glass fibers, teflon, and void, controlled to a

resolution of 10% volume fraction 286 unique mixtures possible.

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Design space with arbitrary geometry and heterogeneous materials (E3 Tm)

Shape + material optimization:Assume m possible materials,(including void) with a mixture resolution of r.B

W

Space within B is discretized into N cells, each of whichcan be filled with a unique mixture of materials.

Number of unique designs

1

1

m

mrC

N

Example: 101010 cells, 4 materials, 10% mixture resolution

2861000 designs!

Rapid Prototyping Workshop 5/99 -mrc

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Toward a design environment for layered manufacturing

• The design space is huge.• But there are significant constraints

associated with the manufacturing processes.• Therefore, provide an environment that

combines manufacturing analysis, design rules, and design libraries to help designers explore the full potential of layered manufacturing.

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Computational issues #1:Process Planning

• Process constraints• Manufacturability• Support structures

• Deposition method• Deposition parameters• Path planning

• Machining method• Tool selection • Machining parameters• Path planning

Decompose Deposit Machine

Decompose Deposit MachineInput

(source: J.S. Kao SU RPL)

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Decomposition into ‘compacts” and layers

CompletePart

Compacts Layers Tool Path

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(1)

(2)

(3)

(4)

primary material

support material

Decomposition based on process sequence

(5)

(6)

(7)

(8)

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29NAS Math. Modeling Forum 5/10/99 -mrc

Definitions: Compact [Merz et al 94]

• 3-D volume with no overhanging features• Rays in growth direction enter only once• Compacts correspond to SDM cycles

Build Axis(c) OK(a) no good (b) OK

x y z z z x y z a z z z1 2 1 2, ,

z1

z2

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Decomposition algorithms

Locate silhouette edges, split surfaces

(a) (b) (c)Extrude concave loops Merge compacts(source: J.S. Kao SU RPL)

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Deposition Process Planning (RPL)

6”

3/8”

laser beam

metal powder•Thermal Stresses Develop due to:•Temperature gradients•Differences in expansion coefficient

•Thermal Stresses Cause:•Part inaccuracy•Delamination

cooling

deflection•Solutions

•Develop optimal deposition path and process parameters to minimize thermal stresses•Tailor alloy to maintain desirable properties while minimize thermal expansion coefficient

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Problems with automated process planning

• finite thickness of support material• finish on unmachined surfaces• warping and internal stresses• decomposition depends on geometry, not on intended function

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Design by Composition (M. Binnard)

Users build designs by combining primitives with Boolean operations– Primitives have high-level manufacturing plans

– Embed components and shapes as needed

Primitivesmerged by designer

Manufacturing plansmerged by algorithm

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Decomposed Features

SFF/SDM VLSIBoxes, Circles, Polygons and Wires

SFF/SDM Design Rules Mead-Conway Design Rules

Wc/ >= 2

Minimum gap/rib thickness

d d

d

(top view)a)

Generalized 3D gap/rib

d

(side view)b)

d

Minimum feature thickness

d(m1,m2,m3)

(side view)e)

m1 m2 m3

d(m1,m2,m3,)

m1 m2 m3

Toward a mechanical MOSIS?

Primitive = Compact Set + Precedence Graph

• Set of valid compacts• No intersections• Fills the primitive’s projected

volume

Primitive Compact set Compact precedence graph

• Acyclic directed graph• Link for every non-

vertical surface

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36NAS Math. Modeling Forum 5/10/99 -mrc

Merging Algorithm Example

intersection compacts

non-intersecting compacts

A B

+ =

A B C=A B

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CAD MODEL

CAD MODEL

DESIGNDECOMPOSITION

DESIGNDECOMPOSITION

DESIGN BYCOMPOSITION

DESIGN BYCOMPOSITION

LIBRARY: Decomposed Designs & primitives

COMPACT SET

CPG

SEQUENCE&

TOOL PATH PLANNING

SEQUENCE&

TOOL PATH PLANNING

re-analysis(if needed)

Combining composition and decomposition

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A need for integrated mechanical, thermal and electrical analysis

VuMan (CMU) mechanical, thermal analysis

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Summary

Emerging layered manufacturing processes such as SDM:– are made feasible by recent advances in desktop

computing and solids modeling

– afford a huge design space (E3 Tm)

– provide a rich area for geometric reasoning and process planning

– present formidable challenges in analysis, process planning and control to achieve consistent, high-quality parts

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Acknowledgements

Thanks to the members of the Center for Design Research and the Stanford Rapid Prototyping Lab for

their work in generating the results and ideas described in this presentation.

This work has been supported by theNational Science Foundation (MIP-9617994)

and by the Office of Naval Research (N00014-98-1-0669)

Documents

C D R Computational and Theoretical Problems in Modern Rapid Prototyping Mark R. Cutkosky Stanford Center for Design Research