Transcript No Slide Title

Dynamic Analysis
of
Fan Foundation
Mahendra Madhavan
Potential Power Plant Problems Requiring
Dynamic Analysis
• Machinery Vibration
• Piping Vibration
• Heavy-load drops
• Tornado missile impact
• Dry cask accidents
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
Four basic components of Vibration
• Mass (m)
• Stiffness (k)
• Damping (c)
• Forcing Function (F)
Equation of motion
m x  c x  k x  F (t )
F1  m a  m x
F2  c v  c x
F3  k x
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
Fan Foundation
• Mat foundation (Soil supported)
• Pile / Caisson foundations
Types of Analysis
• Modal Analysis
• Response Analysis
Forced vibration of a damped system
Damping (c)
Stiffness (k)
Mass (m)
k
n 
m
D
A
F
ω: Operating frequency
ωn: Natural frequency
m: Mass of the system
τ : Damping ratio
DAF : Dynamic Amplification Factor
k: Stiffness of the system
Vibration Acceptance Criteria (Commonly used)
(Vendor’s requirement and SCS Standards)
• Natural freq away from ± 20% of operating freq
MODAL
ANALYSIS
• 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
Wheel unbalance
(Sensitivity check)
F = m e ω2
e=50 in
m = 1 oz.
1
1 lb s 2
m x
16 386 in
ω=2πf
f = 900 rpm
900

 15 Hz
60
F = 72 lb
1 oz of wheel
unbalance
The resulting displacement measured at
Bearing Housing ≤ 0.125 mils pk-pk
Peak to Peak
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
Trial sizing criteria
Foundation Plan
Foundation/Soil Links to
GTSTRUDL Combined Model
Foundation/Soil Members in
GTSTRUDL Combined Model
X
Foundation/Soil Dynamic Properties
Y
Z
X
6 Members = 6 DOF’s for
stiffness and damping
Y
Vibration Modes
X
• 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)
Z
TYPICAL
MODES
OF
CONCERN
Isometric view
Y
Z
X
Longitudinal Sliding
(X Translation)
Y
Z
X
Vertical
(Y Translation)
Y
Z
X
Lateral Sliding
(Z Translation)
Y
X
Z
Rocking
(X Rotation)
Y
Z
X
Yawing
(Y Rotation)
Y
Z
X
Pitching
(Z Rotation)
Y
X
Z
Recent Analyses
•
Wansley 1 and 2 (Rock Foundation )
–
•
Bowen 3 and 4 (Pile Foundation over rock)
–
•
Single DOF, Using Hand calc
GTStrudl and Static pile stiffness
Bowen 1 and 2 (Pile Foundation over rock) – changing
soil properties (density, shear waves, poisson etc.)
– GTStrudl and DYNA5
Vibration Testing
•
In-situ testing to measure vibration for
acceptance
•
Use In-situ testing results to validate the math
model
Thank you
Questions ?