Dynamic Analysis of Fan Foundation Mahendra Madhavan

1. Dynamic Analysis of Fan Foundation Mahendra Madhavan

2. Potential Power Plant Problems Requiring Dynamic Analysis • Machinery Vibration • Piping Vibration • Heavy-load drops • Tornado missile impact • Dry cask accidents

3. Need for Vibration Analysis • Meet the vendor’s performance criteria • Industry guidelines or SCS standards • Operation / Maintenance • Vibration not generated or transmitted to other areas • Foundation is free from structural resonance • Vibration not annoying to people

4. Four basic components of Vibration • Mass (m) • Stiffness (k) • Damping (c) • Forcing Function (F)

5. Equation of motion

6. How to quantify vibration components? • Mass from Machine and Foundation drawings • Stiffness and Damping from DYNA5 (pile-soil interaction) • Force from vendor or make an estimate F

7. Fan Foundation • Mat foundation (Soil supported) • Pile / Caisson foundations

8. Types of Analysis • Modal Analysis • Response Analysis

9. Forced vibration of a damped system Damping (c) Mass (m) Stiffness (k) DAF m: Mass of the system k: Stiffness of the systemDAF: Dynamic Amplification Factor ω: Operating frequency ωn: Natural frequency τ: Damping ratio

10. Vibration Acceptance Criteria (Commonly used) (Vendor’s requirement and SCS Standards) MODAL ANALYSIS • Natural freq away from ± 20% of operating freq • Bearing Housing disp ≤ 0.125 mils pk-pk for 1 oz of wheel unbalance at outer radius (Sensitivity check) • Shaft velocity ≤ 0.1 in/sec (balancing grade) • Dynamic stiffness of the foundation should be ≥ 11.987 x 106 lb/in per support. RESPONSE ANALYSIS

11. Wheel unbalance (Sensitivity check) F = m e ω2 e=50 in m = 1 oz. 1 oz of wheel unbalance ω = 2π f The resulting displacement measured at Bearing Housing ≤ 0.125 mils pk-pk f = 900 rpm Peak to Peak F = 72 lb

12. How to Prevent Vibration? • Trial sizing criteria • Single or two degree of freedom models • Detailed analysis using GTStrudl and Dyna5 • GTStrudl for modal analysis and estimating the natural frequency • Dyna5 is used to estimate soil-structure spring stiffness and damping

13. Trial sizing criteria

14. Foundation Plan

15. Foundation/Soil Links to GTSTRUDL Combined Model

16. Foundation/Soil Members in GTSTRUDL Combined Model

17. Foundation/Soil Dynamic Properties 6 Members = 6 DOF’s for stiffness and damping

18. Y Vibration Modes • Longitudinal Sliding (Translation in X) • Vertical (Translation in Y) • Lateral Sliding (Translation in Z) • Rocking (Rotation about X) • Yawing (Rotation about Y) • Pitching (Rotation about Z) X Z TYPICAL MODES OF CONCERN

19. Y X Z Isometric view

20. Longitudinal Sliding(X Translation) Y Z X

21. Vertical(Y Translation) Y X Z

22. Lateral Sliding(Z Translation) Y X Z

23. Rocking(X Rotation) Y Z X

24. Yawing(Y Rotation) Y X Z

25. Pitching(Z Rotation) Y X Z

26. Recent Analyses • Wansley 1 and 2(Rock Foundation ) • Single DOF, Using Hand calc • Bowen 3 and 4(Pile Foundation over rock) • GTStrudl and Static pile stiffness • Bowen 1 and 2(Pile Foundation over rock) – changing soil properties (density, shear waves, poisson etc.) • GTStrudl and DYNA5

27. Vibration Testing • In-situ testing to measure vibration for acceptance • Use In-situ testing results to validate the math model

32. Thank you Questions ?