MECH 251 Session 2

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A Process Planning and Optimization System for

Laminated Object Manufacturing Application

byAnthony PANG

IEEM Dept.,

Hong Kong University of Science & echno!ogy

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Presentation Outline1. Problem Description

2. Geometric Algorithm for Solid Level Process Planning

a. Convex Cover of the Build Part

b. Part Orientation Determination

c. Cutting Plane Generation

d. Internal Octree-based Grid Generation

3. Optimization of Layer level Cutting Path

a. Genetic Algorithmb. Genetic Algorithm with 3-opt

c. ATSP-Assign Iteration (Tuckers formulation)

4. Operation Sequence for Proposed System

5. System Architecture

6. Conclusion

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LOM Process Description

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Problem Description

Build object Traditional Hatcing !rids

Max. Section Area Layer Lowest Section Layer

Problems"

#a$ %asted effort in cutting atc grids

#b$ %asted time due to poor pat planning

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Solid Model Le&el Optimization

'on&e( 'o&er 'utting Plane !eneration

Cutting Plane

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)inding !ood Parting Planes

*+ Orient te part on te macine

,+ )ind te -best. parting line

/+ )ind te parting planes

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Part Orientation Determination

0ertical Orientation #assumed as gi&en$

Depends on surface finis considerations

Horizontal Orientation

Metod"Te minimum projection 1idt algoritm

Algoritm"

Project on 23 Plane

4otating 'aliper on 'H#projection$%min%min

2

53

feed roll

pic67up

roll

paper ad&ance

271idt

PA4T

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'utting Plane Determination

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'utting Plane Determination

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Parting Line Determination

#a$ )lattest Parting Line

&*

&,

&/

&8

&9&:

&;

&nside te 'on&e( Hull" Octree cuts

Object

?numeration Octree

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Te !eometric Planning Se@uence

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Solid Model Le&el Process Planning

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Solid Model Le&el Process Planning

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Performance 'omparison

Surface Area Part 'on&e(Hull

BoundingBo(

'uttingPlane

!rids Total 4eduction

SL

0

Test'ase

Traditional

'H 1it 4ect

'H 1it Octree

88;+=,

8/

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Laser Pat Planning )or ?ac Layer

1

2

3

4

5

6

78

9

10

11

12

13

14

15

1 2

3

4

5

89

1011

1213

14

6

7

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T1o decisions at eac step"*+ %ic is te next arcto be macined

,+ %at is te senseof dra1ing arci

7 using t1o &ariables to depict tese decisions"

"iC * if start &erte( of arciis vi# if start &erte( of arciis vi$

%iC * if te i7t arc dra1n is arc oter1ise

'learlyE all"i' s and %i' s can eiter be E or *

Laser Pat Planning )or ?ac Layer ++

Prob!e( )escription

cur&ei

cur&ej

&j,

&j*

&i*

&i,

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Laser Pat Planning )or ?ac Layer +++

Problem formulation

cur&ei

cur&ej

&j,

&j*

&i*

&i,

aij

dijbij

cij=

+n

*"*"%*

** F$*#G

=

+n

n *"*"%*

* F$*#G

$#*

* * *E*

= = =

+

n

i

n

n

t

ttii+%%

&tt&&tt&&tt&&tt&&t )""c""b""*""+ $*$#*#$*#$*# +++=

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!enetic Algoritm Basics

*+ !enerate a large number of random solutions population

,+ 4an6E Sort populations based on performance of te solutions

/+ Iill a fraction of te 1orst solutionE e+g+ %orst ,

8+ Mate te better solutions randomly to create ne(t generation

9+ 4epeat Step ,78 until an acceptable solution performance obtained

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!A Metodology

T1o7cromosome organismJ 27cromosome and 37cromosome

?ac cromosome as te same number of genesE nArcs+

>nput " nArcsarcsE eac 1it t1o #possibly coincident$ &erticesE v1and v2+

Setup of te genes "

27cromosome " permutation of G*++nArcsF

J ithgene = Kimplies itcur&e to be macined by te tool is cur&eK+

37cromosome " array of GE*F

J if Yi= 0E ten te i7t cur&e macined from &*++to++&,

J if Yi= 1E ten tat cur&e macined from &,++to++&*+

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Layer Le&el 'utting Pat Optimization

!enetic Algoritm ?(ample 4esults "Kai&e pat #Traditional$* , / 8 9 : ; < = * ** *, */ *8 *9 *: *; *< *= , ,* ,,

Kon7cutting distance

*8+;98; units

>teration Time sec

!A pat* , / 8 9 : ; = < ** *8 *, */* *= *: *; *< *9, ,* ,,

Kon7cutting distance

**+,teration Time

*,+< seconds for * iterations

4eal7time -optimization. can be done

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>mpro&ing te !A+

!A

,7Optp@

b

d

c

a

e*e,

GcurrentF

pa bc d@

G,7opt optionsF

pa bd c@

pb ac d@

pb ad c@

pc ad b@

pc bd a@

pd bc a@

pd ac b@

Nump7distances"

*

/

,

8

*

2

3

8p@

bd

c

a

e*e,e/

f

e

!A

/7Opt

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Anoter 1ay to do te pat planning

Assume" Start &erte( of eac 'ur&e is gi&en

C Asymmetric Tra&eling Salesman Problem

Assume" Te Se@uence of &isiting eac 'ur&e is fi(ed

C Assignment problem

Strategy" >terate bet1een te ATSP and te Assignment

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*

,

/

8

*

,

/

8

Te ATSP

= =

=*

* *

n

i

n

&

i&i&D%+

GTuc6erF i7 j p%ijp7*E i C *+++n j C *n i j

iE

jarbitraryE p C ma( no of arcs &isited by tool

ni%n

i

i& EE*E**

===

n&%

n

&

i&

EE*E**==

=

minimize"

subject to"

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Te Assignment Problem

arct arct* arct,

( Dt1x

t1 + D

t2x

t2 + D

t3x

t3 + D

t4x

t4)

t=1

n1

xt1 + x t2 + xt3 + x t4 = 1

xt1

+ xt3

+ xt+11 + xt+1 2 1

xt2

+ xt4

+ xt+1 3 + xt+1 4 1

minimize

s+t+

P t*

P t H ,,

P t H ,*

P t H *,

P t H **

P t,

2 t *

2 t H * 8

2 t H * /

2 t H * ,

2 t H * *

2 t 8

2 t /

2 t ,

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Performance comparisons

Toy planeE ,9: layers

)ull partE #!A performance$ Total Numping Distance

Traditional metod ,=

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Operation se@uence for proposed system-per*tion Seence /!o0ch*rt1

LoadQDesign te /D solid model in te system

'alculate te con&e( ull of te part

Determine te optimal parting direction

!enerate te partingQcutting planes

Slice te object 1it all te artifacts into layers

!enerate te internal Octree7based 1aste grids

Optimize te laser cutting operation for eac layer by /7Opt !A algoritm

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System Arcitecture

Rser

Solid Model

AP>.s

Tessellation #STL$

Surface Model

Artifacts

Build direction

Slice data

#uniform$

or

Slice data

#adapti&e$

'AD

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System Arcitecture

!eometry ?ngine

'on&e( Hull

Minimum bo( co&er

Spline Appro(imation

+++

Optimization ?ngine

!enetic Algoritm

+++

'AD system

Design

+++

Tessellation

Slicing

Object Transformations

Artifact Planning

Macine 'ontrol Planning

Slice Planning

Tool Motion Planning

Application Layer 'ore Rtilities

Macine 'ontrol Data

Part model

)eature7based Model

STL

Part Le&el Artifacts

Layer !eometry

Tool Motion Data

Data )lo1

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'onclusion

Main )eatures"

Accomplisments"De&eloped anProcess P!*nningE-pti(i2*tion3DrivenE

'ADQ'AM support system for4*(in*te) -bect M*nf*ctring

1. Geometric Base

2. !euce "aste cut

#. $%timi&e laser cutting motion

'. $%en(Architecture system

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PublicationsNournal"

Antony PangE Iatta !+ MurtyE Ajay NonejaE Leung 'i 'iuE oo! P*th -pti(i2*tion in 4*yere)

M*nf*ctring,5>>? TransactionsE /8#8$"//97/8;E April ,,+Antony PangE Ajay NonejaE Da&id '+'+ LamE Matte1 3uen, 6A 7AD87AM syste( for process

p!*nning *n) opti(i2*tion in 4-M,5 >>? TransactionsE //#8$" /897/99E April ,*

Ajay NonejaE Antony PangE Da&id LamE Matte1 3uen, 6A 7AD87AM syste( for vector3b*se) !*yere)

(*nf*ctring syste(s,5 >nt+ N+ of 'omputer >ntegrated ManufacturingE ,E &ol+ */E no+ 9E /ntl 'onference on 4P and MfgE TsingHua Rni&E BeijingE

Nuly ,*7,/E *==

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)uture %or6

*+ LOM metods impro&ement" multiple parts

,+ ?(tension to oter 4P tecnologies #SLS$

/+ >mpro&ed disassembly metod #Automated Disassembly 'ec6ing$

8+ Konlinear programming optimization for te pat planning

problem

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Some tougts on Direct Slice )ormats

V*

* +*

V,

#L* #L,$EL/ #L8$E L9E L:$

V/

VL*

+;9 8+,9 /+,9 8+,9

/+,9 8+,9 /+,9 :+9

/+,9 :+9 +;9 :+9

+;9 :+9 +;9 8+,9VL,

*+;9 8+9 ,+;9 8+9

,+;9 8+9 ,+;9 9+9

,+;9 9+9 *+;9 9+9

*+;9 9+9 *+;9 8+9

VL/

+;9 *+;9 /+;9 *+;9

* * ,+,9 *+;9 /+;9 *+;9 +;9 *+;9

VL8

*+;9 ,+ /+,9 ,+

/+,9 ,+ /+,9 ,+;9

/+,9 ,+;9 *+;9 ,+;9 *+;9 ,+;9 *+;9 ,+

VL9

* * 9+,9 /+;9 /+;9 /+;9 /+;9 /+;9

VL:

/+;9 *+,9 :+;9 ,+9

:+;9 ,+9 :+;9 *+,9

:+;9 *+,9 /+;9 *+,9

'orresponding +DSL )ileSample Slice !eometry

ttp"QQiesu9+ust+6QdfacultyQajayQprojectsQrp+tml

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Te TsingHua Macine

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4esult of te tested sample parts

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>llustration of te Tuc6er.s formulationGTuc6erF

i7

j p%

ijp7*E i C *+++n j C *n i j

iE jarbitraryE p C ma( no of arcs &isited by tool

Assume cutting !*ten go to !,

*U

, /%

*,,

,U

* /%

,*,

*U

/ /%

*/,

/U

* /%

/*,

,U

/ /%

,/,

/U

, /%

/,,

%*,C *

*U

,7*

%,*

*

,U

*7*

Assume cutting !*ten go to !, and finally go to !/

%*,C * W %,/C * *U ,7* W ,U /7*

If %/*

C *

/,W ,*

/U

*7*

*

/ )ontraictory conition

!*

!/

!,

Documents

MECH 251 Session 2