correlation and error localization

1/31Correlation and Error Localization

Correlation and Error LocalizationAnalytical versus Experimental Dynamicsof a Large Structural AssemblyThesis presentation, Herman Marquart, 2013

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Content

• Introduction• Theory• Methodology• Results• Discussion• Conclusion• Recommendations

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Department at ASML

• Structural Dynamics• Component

• Well defined modeling process

• Largely automated in software

• Assembly• Less defined modeling process

• Requires more subjective interferences

Mechanical Analysis

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Assignment from ASML

“Improve the correlation (process) of analytical and experimental structural assembly models”

•Procedure• First understand the current process

• Determine typical properties of a structural assembly

• Determine applicability of correlation tools

• Determine typical errors made during modeling

• Define specific research problem• Propose methodology

Formulated as…

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General development processSystem, subsystem, …, component level

Functional requirements Realized functions

System

design

Subsystem

design

Component

designRea

lizat

ion,

inte

grat

ion

and

Specification, decomposition and

definitionTimeline

System

assembly

Subsystem

assembly

Component

production

Feedback loops

valid

atio

n

Experimental

modelsAnalytical models

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Typical high tech case

• Assembly: set of many integrated components

ASML lithography machine

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Typical high tech case

• Typical properties of such an assembly• Complex base structure (master structure)

• Thin walled box structure

• Many thin ribs and spacers

• Many holes

• Many components attached (slave structures)• Several large components

• Many small components

• Cables, wires, pipes, channels, …

Positioning module

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General modeling processSystem, subsystem, …, component level

Analytical approach

Eigensolution computation

Spatial

M C K

Modal

Φ Λ

Response

H

Modal parameter identification

Experimental approach

1

1

T

T

- -

- -

=

=

M Φ Φ

K Φ ΛΦ

( )1 TH Φ Λ Ω Φ

-= -

102

103

10-2

100

102

FREQUENCY [Hz]

MA

GN

ITU

DE

[kg

]

TP.V09 FRFS

102

103

10-2

100

102

FREQUENCY [Hz]

MA

GN

ITU

DE

[kg

]

TP.V09 FRFS

102

103

10-2

100

102

FREQUENCY [Hz]

MA

GN

ITU

DE

[kg

]

TP.V09 FRFS

102

103

10-2

100

102

FREQUENCY [Hz]

MA

GN

ITU

DE

[kg

]

TP.V09 FRFS

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Analytical approach

• Substructure assembly into components• Natural approach• Enables parallel engineering• Possibly more attention to details• More flexible to local modifications

• Reduce each substructure• Approximation• Speeds up computation of eigensolutions• Easy reuse and exchange of components

• Assemble reduced substructures

Assembly

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• Setup• Structure• Suspension• Hammer• Accelerometer• Amplifiers• Data acquisition module• Computer

• Procedure• Roving hammer method

Experimental approach

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Theory discussion

• Practical issues• Many small components• Lots of effort required to perform such detailed analysis• Simpler models could be sufficient• Limited amount of time available

• Practical solutions• Omission of slave structures• Omission of structural dynamics of slave structures• Simplification of connections

• However, assumptions are not always valid…

Theory versus application

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Research problemFormulated as…

“What is the influence of a relatively lightweight resonating slave structure on the global structural dynamic behaviour of the master structure? How

could you find the location of an unmeasured resonating slave structure with existing correlation

tools and validation procedures, when multiple components are suspicious?”

“What is the influence of a relatively lightweight resonating slave structure on the global structural

dynamic behaviour of the master structure? How could you find the location of an unmeasured resonating slave structure with existing correlation tools and validation

procedures, when multiple components are suspicious?”

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Methodology… influence …

• Simulation• Create simplified structural assembly

• Master structure

• Slave structures

• Multiple non-resonating

• One resonating

• Compare and correlate models; observe typical effects• Intended design versus realized design

• Multiple positions of the resonating slave structure• Validation

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MethodologyDesign structural assembly

• Master structure• Plate

• Linear elastic material

• Out of plane dynamics

• Asymmetric

• Mounting positions

• Simple to manufacture• f1 ≈ 200 Hz

• Slave structures• 1 Sprung mass• 9 Unsprung masses

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MethodologyDesign slave structure

• Sprung mass• Linear elastic material• Out of plane vibration• Single mount• Simple to manufacture• f1 ≈ 500 Hz

• Unsprung mass• f1 > 2000 Hz

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… influence …

Intended design10 unsprung masses

• Compare and Correlate• Frequencies [Hz]

Mode Realized

design

Intended

design ∆ [%]

1 184 185 0.5 2 222 220 -0.8 3 425 433 0.3 4 432 454 8.3 5 549 607 0.4 6 605 624 -8.0 7 679 827 -5.0 8 870 971 -1.1 9 982 1203 0.7

10 1194 1242 0.7 11 1233 1350 -0.9 12 1362 1488 1.7 13 1463 1522 1.0 14 1507 1766

Results

Realized design1 sprung mass + 9 unsprung

masses

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• Compare and Correlate• Frequencies [Hz]• Mode shapes

Results… influence …

Realizeddesign

Intendeddesign

Realized design1 sprung mass + 9 unsprung

masses

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TP.V21

TP.V

21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

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18

19

20

EXP.PLATE.FP001.ASS.V02

TP.V

21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1

2

3

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5

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8

9

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20

• Compare and Correlate• Frequencies [Hz]• Mode shapes

• MAC

Results… influence …

Inte

nded d

esi

gn

2Tr s

rs T Tr r s s

MAC φ φ

φ φ φ φ

%%

% %% %

Intended designRealized design

Realized design1 sprung mass + 9 unsprung

masses

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• Compare and Correlate• Frequencies [Hz]• Mode shapes

• MAC

• FRFs

Results… influence …

Intended design

Realized design

Magnit

ude [

kg-1]

Magnit

ude [

kg-1]

Frequency [Hz]

Frequency [Hz]

Realized design1 sprung mass + 9 unsprung

masses

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“What is the influence of a relatively lightweight resonating slave structure on the global structural dynamic behaviour of the master structure? How

could you find the location of an unmeasured resonating slave structure with existing correlation

tools and validation procedures, when multiple components are suspicious?”

Research problemFormulated as…

“What is the influence of a relatively lightweight resonating slave structure on the global structural

dynamic behaviour of the master structure? How could you find the location of an unmeasured resonating slave structure with existing correlation tools and validation

procedures, when multiple components are suspicious?”

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Methodology… localization…

• Systematically correct intended design• Known (approximately)

• Additional resonance frequency

• Slave structure mass

• Connection stiffness

• Unknown• Location

• Define objective functions to quantify model correlation• Localize the resonating slave structure with objective

function

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MethodologyProposed approach

• Isolate the master structure• Add the small slave structures as mass-spring-systems• Vary the connection stiffness of each slave structure

one by one• Recalculate the eigensolutions• Compute objective values

• Eigenfrequencies

• Mode shapes

• Weighted summation

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ResultsOne slave structure

owJωo Jφ●J‒R

Obje

ctiv

e

valu

e

Model

variant

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1P043

MODEL VARIANT

OBJ

ECTI

VE

VA

LUE

Stiffness value

Obje

ctiv

e v

alu

e

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ResultsAll slave structures

Obje

ctiv

e v

alu

e

Stiffness value

1 2 3 4 5 6 7 8 9 10

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1 2 3 4 5 6 7 8 9 10

ResultsAll slave structures

Obje

ctiv

e v

alu

e

Stiffness value

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ResultsAll slave structures

Obje

ctiv

e v

alu

e

Stiffness value

1 2 3 4 5 6 7 8 9 10

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1 2 3 4 5 6 7 8 9 10

ResultsAll slave structures

Obje

ctiv

e v

alu

e

Stiffness value

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Discussion

• Requirements• Validated master structure• Accurate measurements and mode shape identification

• Fortunate properties• No additional measurements required• Entire process performed with ANSYS and MATLAB• Clear systematic approach

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Conclusion

• The proposed procedure may help localizing the resonating component, when typical structural dynamic correlations as presented, are encountered during the monitoring of the assembly process

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Recommendations

• Research extension to more complex slave structures• Application to a case with multiple resonating slave

structures

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Questions?

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