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Order-Tuned Vibration Absorbers for Systems with Cyclic Symmetry

Order-Tuned Vibration Absorbers for Systems with Cyclic Symmetry. with Applications to Turbomachinery. MOTIVATION & BACKGROUND. Motivation. Bladed Disk Assemblies. Motivation. Engine Order Excitation. Motivation. Resonance Structure / Conditions for Resonance. Motivation.

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Order-Tuned Vibration Absorbers for Systems with Cyclic Symmetry

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  1. Order-Tuned Vibration Absorbers for Systems with Cyclic Symmetry with Applications to Turbomachinery

  2. MOTIVATION & BACKGROUND

  3. Motivation Bladed Disk Assemblies

  4. Motivation Engine Order Excitation

  5. Motivation Resonance Structure / Conditions for Resonance

  6. Motivation Order-Tuned Absorbers

  7. Motivation Vibration Reduction via Order-Tuned Absorbers

  8. Motivation Vibration Reduction via Order-Tuned Absorbers Sleeves Tuned Dampers Chamber & End Caps

  9. Motivation Vibration Reduction via Order-Tuned Absorbers

  10. Motivation Vibration Reduction via Order-Tuned Absorbers

  11. Motivation Goals of this Work • Quantify/understand underlying linear resonance structure; • Design absorbers to eliminate/reduce blade vibrations; and • Generalize to include effects of nonlinearity. • How does Campbell diagram representation change when order-tuned absorbers are present? • Exploit underlying linear resonance structure for linear absorber design. • Can nonlinearity be exploited to further improve the linear design?

  12. Outline • Motivation and Background Frequency- and Order-Tuned Absorbers Cyclic Systems Theory of Circulants / Mathematical Preliminaries Engine Order Excitation • The Linear Analysis Model / Formulation Modal Analysis / Forced Response Linear Resonance Structure / Absorber Tuning Effects of Damping • The Nonlinear Analysis Mathematical Model / Path Selection Formulation: Scaling / Averaging Traveling Wave Forced Response / Stability Nonlinear Absorber Tuning • Conclusions Recommendations for Absorber Design Summary of Contributions Directions for Future Work

  13. Background Engine Order Excitation

  14. Background Engine Order Excitation

  15. Background Engine Order Excitation

  16. Background Engine Order Excitation

  17. Background Engine Order Excitation

  18. Mathematical Model and THE LINEAR ANALYSIS Model / Formulation Modal Analysis / Forced Response Linear Resonance Structure / Absorber Tuning Effects of Damping Summary

  19. Mathematical Model Bladed Disk Assembly with Absorbers

  20. Mathematical Model Linearized System Model

  21. Modal Analysis Block Decoupling the EOM

  22. Modal Analysis Steady-State Modal Response

  23. Modal Analysis Steady-State Modal Response

  24. Special Cases1 • Blades Locked, Absorbers Free • Gives Linear Absorber Tuning Order • Blades Free, Absorbers Locked • A Benchmark to evaluate absorber performance • Single Isolated Sector, Blade/Absorber Free • Demonstrates the essential features of the full coupled system

  25. Special Cases1 ( ) Blades Locked, Absorbers Free

  26. Special Cases2 ( ) Blades Free, Absorbers Locked

  27. Special Cases2 ( ) Blades Free, Absorbers Locked

  28. Special Cases3 ( ) Single Isolated Sector, Blade/Absorber Free

  29. Special Cases3 ( ) Single Isolated Sector, Blade/Absorber Free

  30. Special Cases3 ( ) Single Isolated Sector, Blade/Absorber Free

  31. Special Cases3 ( ) Single Isolated Sector, Blade/Absorber Free

  32. Special Cases3 ( ) Single Isolated Sector, Blade/Absorber Free

  33. Special Cases3 ( ) Single Isolated Sector, Blade/Absorber Free

  34. Linear Resonance Structure N = 10 Sectors, Blades/Absorbers Free

  35. Linear Resonance Structure The Effects of Detuning: No-Resonance Gap

  36. Linear Forced Response

  37. Linear Forced Response Absorbers Free

  38. Linear Forced Response Absorbers Free

  39. The Effects of Damping

  40. Linear Absorber Design Summary

  41. Linear Absorber Design Summary • Absorbers are effective • No-resonance zone* • Ideal tuning (Complete reduction of blade motions**) • Slight undertuning (Good reduction of blade motions and no resonances over full range of rotor speeds) * Persists in the presence of sufficiently small damping ** No absorber damping, independent of blade damping

  42. Linear Absorber Design Summary • Absorbers are effective • No-resonance zone* • Ideal tuning (Complete reduction of blade motions**) • Slight undertuning (Good reduction of blade motions and no resonances over full range of rotor speeds) Recommendation * Persists in the presence of sufficiently small damping ** No absorber damping, independent of blade damping

  43. THE NONLINEAR ANALYSIS Mathematical Model / Path Selection Formulation: Scaling / Averaging TW Forced Response / Stability NL Absorber Tuning Summary

  44. Mathematical Model Nonlinear Sector

  45. Mathematical Model Absorber Path

  46. Formulation Scaled Sector Models

  47. Formulation Linear Resonance Structure of the Scaled System

  48. Formulation Linear Resonance Structure of the Scaled System

  49. Formulation Averaged Sector Models

  50. Formulation Averaged Sector Models

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