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Computational and Theoretical Problems in Modern Rapid Prototyping

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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

- 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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UV curable

liquid

Laser

elevator

Formed

object

Photolithography process

schematic

Sample prototype (ME210 power mirror for UT Auto)

http://me210.stanford.edu

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Tilted frames (RPL)

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

Minimum toroidal saddle surface

(C. Sequin)

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Shape Deposition Manufacturing ( SDM)

RP

CNC

1970

1990

2000

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Embedded Component

Part

Support

Deposit (part)

Shape

Shape

Deposit (support)

Embed

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- Example of polymer component with embedded electronics

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Alumina vane

Silicon nitride pitch shaft

Alumina turbine wheels

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Shaft coupling

Shaft

Motor

Leg links

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

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(http:cdr.stanford.edu/biomimetics)

Steel leaf spring

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

Piston

Part Primitive

Outlet for valve

Valve Primitive

Circuit Primitive

Inlet port primitive

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Robot Leg design (cont’d.)

Steel leaf-spring

Internal components are modeled in the 3D CAD environment.

Piston

Sensor and circuit

Spacer

Valves

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

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Robot Leg: compacts

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

Embedded components

Part

Support

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Steel leaf-spring

Piston

Sensor and circuit

Valves

A snapshot just after valves and pistons were inserted.

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Robot Leg: completed

Finished parts ready for testing

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Laminated manufacturing

(1892-1940s)

Photo-sculpture

studio (1860)

Laser-based photolithography (1977)

[Source:Beaman 1997]

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3D solid model

slicing

trajectory planning

material addition process

data exchange format

motion control trajectories

CAD

process planner

fabrication machine

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Commercial

Photolithography

Fused deposition

Laser sintering

Laminated paper

Research

Selective laser sintering (UT Austin)

3D printing (MIT)

Shape deposition manufacturing (CMU/Stanford)

Engineering materials (metals,

ceramics, strong polymers)

Graded materials

Embedded components

Not quite direct from CAD model...

“Look and feel” prototype

Complex 3D shapes

direct from CAD model

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- 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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W

Shape optimization example:

Find the minimum-weight shelf structure, bounded by box B,

that supports load W without failing.

B

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

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

deposition

heads

Support structure

Volume fractions always add to unity*

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

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m = number of materials (including void)

vi= volume fraction of each material

r = deposition mixture resolution

Product Space:

Example: urethane, glass fibers, teflon, and void, controlled to a resolution of 10% volume fraction 286 unique mixtures possible.

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W

Shape + material optimization:

Assume m possible materials,

(including void) with a mixture resolution of r.

B

Space within B is discretized into N cells, each of which

can be filled with a unique mixture of materials.

Number of unique designs

N

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

2861000designs!

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Rapid Prototyping Workshop 5/99 -mrc

- 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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Decompose

Input

Deposit

Machine

Decompose

Deposit

Machine

- Process constraints
- Manufacturability
- Support structures

- Deposition method
- Deposition parameters
- Path planning

- Machining method
- Tool selection
- Machining parameters
- Path planning

(source:J.S. Kao SU RPL)

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Complete

Part

Compacts

Layers

Tool Path

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Decomposition based on process sequence

(5)

(6)

(7)

(8)

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

z2

z1

Build Axis

(a) no good

(b) OK

(c) OK

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Locate silhouette edges, split surfaces

Merge compacts

Extrude concave loops

(source:J.S. Kao SU RPL)

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Deposition Process Planning (RPL)

- Thermal Stresses Develop due to:
- Temperature gradients
- Differences in expansion coefficient

- Thermal Stresses Cause:
- Part inaccuracy
- Delamination

- 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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- 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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Users build designs by combining primitives with Boolean operations

- Primitives have high-level manufacturing plans
- Embed components and shapes as needed

Primitives

merged by designer

Manufacturing plans

merged by algorithm

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a)

(top view)

b)

(side view)

d

d

d(a1,a2)

d(a1,a2)

l

2l

Dd

Minimum gap/rib thickness

Generalized 3D gap/rib

e)

(side view)

2l

l

d(m1,m2,m3)

d(m1,m2,m3,a1,a2)

Wc/l >= 2

m1

m2

m3

m1

m2

m3

Minimum feature thickness

SFF/SDM

VLSI

Boxes, Circles,

Polygons and Wires

Decomposed Features

SFF/SDM Design Rules

Mead-Conway Design Rules

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Primitive

Compact set

Compact precedence graph

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

- Acyclic directed graph
- Link for every non-vertical surface

A

B

+

=

A

B

C=A È B

intersection compacts

non-intersecting compacts

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CAD

MODEL

re-analysis

(if needed)

DESIGN

DECOMPOSITION

DESIGN BY

COMPOSITION

LIBRARY:

Decomposed Designs &

primitives

COMPACT

SET

CPG

SEQUENCE

&

TOOL PATH PLANNING

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VuMan (CMU) mechanical, thermal analysis

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

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

This work has been supported by the

National Science Foundation (MIP-9617994)

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

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