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
During design, operation and maintenance of power plants, we encounter the following forms of vibration.
Machinery vibration includes 1. Induced or Forced Draft Fan, 2. Cooling Tower Fan Deck, 3. Turbine generator Foundations
Piping vibration includes 1. Flow induced, 2. Water hammer, 3. Acoustic resonance

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
Operation and Maintenance: To prevent forced outages; Not to do maintenance more often than necessary.

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

5. Equation of motion
Inertial force, Damping force and Stiffness resistance

6. Types of Vibration When F = 0 (Free vibration)
F = F0sinωt (Forced Vibration)
c = 0 (Undamped system)
c ≠ 0 (Damped system)
During design, operation and maintenance of power plants, we encounter the following forms of vibration

7. 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
During design, operation and maintenance of power plants, we encounter the following forms of vibration

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

9. Types of Analysis
Modal Analysis
Response Analysis

10. Single Degree of Freedom
Vibration modes are analogous to DOF in a node
m: Mass of the system
k: Stiffness of the system
c: Damping

11. Forced vibration of a damped system
Damping (c)
Mass (m)
Stiffness (k)
DAF
Vibration modes are analogous to DOF in a node
m: Mass of the system
k: Stiffness of the system DAF : Dynamic Amplification Factor
ω: Operating frequency
ωn: Natural frequency
τ : Damping ratio

12. Vibration Acceptance Criteria (Commonly used)
(Vendor’s requirement and SCS Standards)
MODAL
ANALYSIS
Natural freq away from ± 20% of operating freq
Bearing Housing disp ≤ 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 ≥ x 106 lb/in per support.
RESPONSE
ANALYSIS
Typically there are four acceptance criteria that are required to be met. To meet the first criteria we need to carry out a Modal analysis. The next three criteria requires Response analysis.

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

14. 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
Vibration modes are analogous to DOF in a node

15. Trial sizing criteria

16. Foundation Plan
This is the plan of the foundation showing the locations of the 12 caissons.

17. Foundation/Soil Links to GTSTRUDL Combined Model

18. Foundation/Soil Members in GTSTRUDL Combined Model

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

20. Vibration Modes Y Longitudinal Sliding (Translation in X) 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
Vibration modes are analogous to DOF in a node

21. Isometric view X Y Z
The plant is spending approximately $400 million the SCR program (SCR = Selective Catalytic Reduction)
-- an environmental control system that will reduce Nox emissions -- a key ingredient in the formation of ozone. These NOX emissions will be reduced by approximately 85%.
Last year’s User’s Group meeting…
Scott Lange, SCS Atl -- SCR project at Bowen -- Steel structure supporting precipitator ductwork and the two SCR boxes
Ed Marshal -- modifications to the boiler house.

22. Longitudinal Sliding (X Translation)Y Z X

23. Vertical (Y Translation)X Z

24. Lateral Sliding (Z Translation)Y X Z

25. Rocking (X Rotation) Y Z X

26. Yawing (Y Rotation) Y X Z

27. Pitching (Z Rotation) Y X Z

28. 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
The addition of the SCR system means that the existing ID fan output must increase to handle the additional pressure drop of the SCR system. This required the ID fan be replaced.

29. Vibration Testing In-situ testing to measure vibration for acceptance
Use In-situ testing results to validate the math model
The addition of the SCR system means that the existing ID fan output must increase to handle the additional pressure drop of the SCR system. This required the ID fan be replaced.

30. The addition of the SCR system means that the existing ID fan output must increase to handle the additional pressure drop of the SCR system. This required the ID fan be replaced.

31. The addition of the SCR system means that the existing ID fan output must increase to handle the additional pressure drop of the SCR system. This required the ID fan be replaced.

32. The addition of the SCR system means that the existing ID fan output must increase to handle the additional pressure drop of the SCR system. This required the ID fan be replaced.

33. The addition of the SCR system means that the existing ID fan output must increase to handle the additional pressure drop of the SCR system. This required the ID fan be replaced.

34. Thank you
Questions ?
The addition of the SCR system means that the existing ID fan output must increase to handle the additional pressure drop of the SCR system. This required the ID fan be replaced.

35. Thank you
Questions ?
The addition of the SCR system means that the existing ID fan output must increase to handle the additional pressure drop of the SCR system. This required the ID fan be replaced.
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Madhavan Mahendra\Vibration Presentation_Anniston