Correlation and Error Localization

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

2. Content • Introduction • Theory • Methodology • Results • Discussion • Conclusion • Recommendations

3. Department at ASML Mechanical Analysis • Structural Dynamics • Component • Well defined modeling process • Largely automated in software • Assembly • Less defined modeling process • Requires more subjective interferences

4. Assignment from ASML Formulated as… “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

5. General development process System, subsystem, …, component level Functional requirements Realizedfunctions Feedbackloops Systemdesign Systemassembly validation Subsystemdesign Subsystemassembly Specification, decomposition and definition Realization, integration and Componentdesign Componentproduction Analytical models Timeline Experimental models

6. Typical high tech case ASML lithography machine • Assembly: set of many integrated components

7. Typical high tech case Positioning module • 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, …

8. General modeling process System, subsystem, …, component level

9. Analytical approach Assembly • 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

10. Experimental approach • Setup • Structure • Suspension • Hammer • Accelerometer • Amplifiers • Data acquisition module • Computer • Procedure • Roving hammer method

11. Theory discussion Theory versus application • 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…

12. 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?” “What is the influenceof 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. 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. Methodology Design 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

15. Methodology Design slave structure • Sprung mass • Linear elastic material • Out of plane vibration • Single mount • Simple to manufacture • f1≈ 500 Hz • Unsprung mass • f1> 2000 Hz

16. Results … influence … • Compare and Correlate • Frequencies [Hz] Realizeddesign 1 sprung mass + 9 unsprung masses Intended design 10 unsprung masses

17. Intended design Realized design Results … influence … • Compare and Correlate • Frequencies [Hz] • Mode shapes Realizeddesign 1 sprung mass + 9 unsprung masses

18. Results … influence … Intended design Realized design • Compare and Correlate • Frequencies [Hz] • Mode shapes • MAC Intended design Realizeddesign 1 sprung mass + 9 unsprung masses

19. Results … influence … Realizeddesign • Compare and Correlate • Frequencies [Hz] • Mode shapes • MAC • FRFs Magnitude [kg-1] Frequency [Hz] Intended design Magnitude [kg-1] Realizeddesign 1 sprung mass + 9 unsprung masses Frequency [Hz]

20. Research problem Formulated as… “What is the influenceof 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 influenceof 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. 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. 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. Results One slave structure • wJω • Jφ • J • R Objective value Objective value Model variant Stiffness value

24. Results All slave structures Objective value Stiffness value

25. Results All slave structures Objective value Stiffness value

26. Results All slave structures Objective value Stiffness value

27. Results All slave structures Objective value Stiffness value

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

31. Questions?