1. 1/31 Correlation and Error Localization Analytical versus Experimental Dynamics of a Large Structural Assembly Thesis presentation, Herman Marquart, 2013

2. 2/31 Correlation and Error Localization Content Introduction Theory Methodology Results Discussion Conclusion Recommendations

3. 3/31 Correlation and Error Localization 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

4. 4/31 Correlation and Error Localization 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…

5. 5/31 Correlation and Error Localization General development process System, subsystem, …, component level Functional requirementsRealized functions System design Subsystem design Component design Realization, integration and Specification, decomposition and definition Timeline System assembly Subsystem assembly Component production Feedback loops validation Experimental models Analytical models

6. 6/31 Correlation and Error Localization Typical high tech case Assembly: set of many integrated components ASML lithography machine

7. 7/31 Correlation and Error Localization 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

8. 8/31 Correlation and Error Localization General modeling process System, subsystem, …, component level Analytical approach Eigensolution computation Spatial M C K Modal Φ Λ Response H Modal parameter identification Experimental approach

9. 9/31 Correlation and Error Localization 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

10. 10/31 Correlation and Error Localization Setup Structure Suspension Hammer Accelerometer Amplifiers Data acquisition module Computer Procedure Roving hammer method Experimental approach

11. 11/31 Correlation and Error Localization 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

12. 12/31 Correlation and Error Localization Research problem Formulated 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?”

13. 13/31 Correlation and Error Localization 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

14. 14/31 Correlation and Error Localization Methodology Design structural assembly Master structure Plate Linear elastic material Out of plane dynamics Asymmetric Mounting positions Simple to manufacture f 1 ≈ 200 Hz Slave structures 1 Sprung mass 9 Unsprung masses

15. 15/31 Correlation and Error Localization Methodology Design slave structure Sprung mass Linear elastic material Out of plane vibration Single mount Simple to manufacture f 1 ≈ 500 Hz Unsprung mass f 1 > 2000 Hz

16. 16/31 Correlation and Error Localization … influence … Intended design 10 unsprung masses Compare and Correlate Frequencies [Hz] Results Realized design 1 sprung mass + 9 unsprung masses

17. 17/31 Correlation and Error Localization Compare and Correlate Frequencies [Hz] Mode shapes Results … influence … Realized design Intended design Realized design 1 sprung mass + 9 unsprung masses

18. 18/31 Correlation and Error Localization Compare and Correlate Frequencies [Hz] Mode shapes MAC Results … influence … Intended design Realized design 1 sprung mass + 9 unsprung masses

19. 19/31 Correlation and Error Localization Compare and Correlate Frequencies [Hz] Mode shapes MAC FRFs Results … influence … Intended design Realized design Magnitude [kg -1 ] Frequency [Hz] Realized design 1 sprung mass + 9 unsprung masses

20. 20/31 Correlation and Error Localization “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 problem Formulated 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?”

21. 21/31 Correlation and Error Localization 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

22. 22/31 Correlation and Error Localization Methodology Proposed 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

23. 23/31 Correlation and Error Localization Results One slave structure o wJ ω o J φ ●J ‒R Objective value Model variant Stiffness value Objective value

24. 24/31 Correlation and Error Localization Results All slave structures Objective value Stiffness value 12345678910

25. 25/31 Correlation and Error Localization 12345678910 Results All slave structures Objective value Stiffness value

26. 26/31 Correlation and Error Localization Results All slave structures Objective value Stiffness value 12345678910

27. 27/31 Correlation and Error Localization 12345678910 Results All slave structures Objective value Stiffness value

28. 28/31 Correlation and Error Localization 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

29. 29/31 Correlation and Error Localization 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

30. 30/31 Correlation and Error Localization Recommendations Research extension to more complex slave structures Application to a case with multiple resonating slave structures

31. 31/31 Correlation and Error Localization Questions?

32. 32/31 Correlation and Error Localization