GE Oil & Gas

Understanding Dynamic Response

Extract from Bently Nevada Machinery Diagnostics Training

Transient Vibration Data Formats

• Amplitude and Phase displayed together

• Slow roll runout vector• Heavy/high spot location• Rotor and structural resonances• Rotor mode shape “1st critical”

Bode’ and Polar Plots

Bode' Plot

Polar Plot• Typical “synchronous rotor response”.Phase lag angle increases with machine speed.Amplitude increases to a max. at “critical” speed, then reduces

Dynamic Stiffness – Simple Model

K D

M

Dynamic Unbalance Force

F(t) = m.r. W2 = U. W2

DampingSpring

MassDisplacementFrom rest

d (t)

Equation of Motion: dMdDdKF t )(ti

t ed )(let:

dieid ti

deid ti 222then:

and:

dMdDidKF 2

DiMKd

F 2

Simple Dynamic Stiffness:

Direct

displacement accelerationvelocity

Quadrature

Dynamic Stiffness at Low Speed

K

Synchronous Dynamic Stiffness

f = 20 D.W

M.W2

At low speeds, dominant factor is “Spring Stiffness”

Dynamic Stiffness at Resonance

K

Synchronous

Dynamic Stiffness f = 90

D.W

M.W2

At resonance, dominant factor is “Damping Stiffness”

This is also known as “Quadrature Stiffness”

2MK

At Resonance:

M

Kres

Resonant Frequency:

Dynamic Stiffness at High Speed

K

Synchronous Dynamic Stiffness f = 150

D.W

M.W2

At high speeds, dominant factor is “Mass Stiffness” – i.e: Inertial

effect

Synchronous Vibration Response – Low Speed

M.W2

K

D.W

At low speeds, displacement is in same direction as

unbalance force

Unbalance

Unbalance Force = U.W2

Dynamic response (displacement) = Force / Dynamic Stiffness

Displacement

M.W2

K

D.W

At resonance, displacement has a 90 degree phase lag from

unbalance force

Unbalance Force = U.W2

Dynamic response (displacement) = Force / Dynamic Stiffness

Displacement

f = 90

Synchronous Vibration Response – Resonance

Unbalance

M.W2

K

D.W

At high speeds, displacement vector is almost opposite the unbalance

force

Unbalance Force =

U.W2

Locus of displacement vectors through the whole speed range

Dynamic response (displacement) = Force / Dynamic Stiffness

Displacement

Synchronous Vibn Response – High Speed

Unbalance

1X (Synchronous) Response

0°

90°

180°

270°

ROTN

Probe

Heavy Spot

WR = System Resonance Frequency

W

WWR

High Spot

Angle of Heavy Spot

fu

f

0

90°

180°

Ph

ase L

ag

1X

Am

plitu

de |

A|

A

Transient Vibration Analysis

• Reveals information on whether Dynamic stiffness has changed from run to run. Confirms integrity of the rotor.

• Shows symptoms caused by increased system stiffness – like seal rubs

• Indicates where we should add our trial balance weights

• Gives clues about why the machine behaves this way – ie: might be running near a natural resonance…

Questions?