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)(tFxkxcxm

xmamF 1

xcvcF 2

xkF 3

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

• Mat foundation (Soil supported)

• Pile / Caisson foundations

Fan Foundation

• Modal Analysis

• Response Analysis

Types of Analysis

Forced vibration of a damped system

ω: Operating frequencyωn: Natural frequency

τ : Damping ratio

m: Mass of the system

k: Stiffness of the system DAF : Dynamic Amplification Factor

Stiffness (k) Mass (m)Damping (c)

m

kn

DAF

• 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.

Vibration Acceptance Criteria (Commonly used) (Vendor’s requirement and SCS Standards)

MODAL ANALYSIS

RESPONSE ANALYSIS

Wheel unbalance (Sensitivity check)

F = m e ω2

in

slbxm

2

386

1

16

1

m = 1 oz.

1 oz of wheel

unbalance

e=50 in

ω = 2 π f

f = 900 rpm

Hz1560

900

F = 72 lb

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

XY

ZInches Pounds

Foundation/Soil Members in GTSTRUDL Combined Model

X

Y

Z

Foundation/Soil Dynamic Properties

X

Y

Z

6 Members = 6 DOF’s for stiffness and damping

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

Y

Z

TYPICAL MODES

OF CONCERN

Isometric view

X

Y

Z

Longitudinal Sliding(X Translation)

X

Y

Z

Vertical(Y Translation)

Y

ZX

Lateral Sliding(Z Translation)

Z

X

Y

Rocking(X Rotation)

X

Y

Z

Yawing(Y Rotation)

X

Y

Z

Pitching(Z Rotation)

X

Y

Z

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

Vibration Testing

• In-situ testing to measure vibration for acceptance

• Use In-situ testing results to validate the math model

Thank you

Questions ?