GE Oil & Gas

Rotordynamics
What is vibration? Customer Training

Vibration is simply the motion of a machine or machine

part back and forth from its position of the rest.

Input Output
Mechanical
Structure

(Force F, Frequency ω in) (Motion X, Frequency ω out)

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Introduction Customer Training

‰ A steel structure or, in particular, a turbo machine rotor is

characterized by certain typical frequencies that are strictly
related to its structure and can be excited by many sources
‰ These typical frequencies are the Natural frequencies are
the Natural frequencies

The first objective of the Rotor Dynamic is

to identify the Natural Frequencies present
in a rotor and design it around them

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What is vibration? Customer Training

The cause of vibration must be a force which

is changing either its direction or its amount.
amount

The resultanting characteristics will be

determined by the manner in which the force
is generated and by the system’s elastic
properties.
properties

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What is vibration? Customer Training

The vibration’s analysis is used during

development phase of mechanical project.
Once the system is in operation, by
monitoring the vibration trend is possible to
know the “health status” of unit.

High vibration = mechanical part

degraded

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 Customer Training

Some definitions …

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Some definitions … Customer Training

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Some definitions … Customer Training

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Some definitions … Customer Training

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Some definitions … Customer Training

(Hz)

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Some definitions … Customer Training

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 Orbit diagram Customer Training

Two non contacting probes, typically

eddy current transducers, measure the
displacement of a surface relative to the
probe mounting location.
For each probe the result is a waveform
that can be observed on an oscilloscope
in the time domain.
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Orbit diagram Customer Training

The time-base data are combined to

create a single plot showing the
precession motion of the shaft centerline

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Spectrum plot Customer Training

The time-base signal is in general a complicated periodic function that can

be mathematically transformed in a sum of harmonic sine waves.
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Spectrum plot Customer Training

Spectrum Plot is a fundamental

tool to easily analyze the
vibration pattern of a rotating
equipment.

The presence of significant

components with a frequency
different from rotation
(asynchronous) is normally the
symptom of an anomaly.

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 Mechanical behavior Customer Training

The measure of the mechanical behavior of a

compressor is given by the amplitude and frequency of
the rotor vibrations.

The rotor vibration amplitude must not cause:

Vibration Hazards
9 contact between rotor and stator

9 dry gas seals overloading

9 fatigue in the bearings

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 Customer Training

Vibrations classification

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Vibrations classification Customer Training

The typical vibrations of the centrifugal compressors can

be generally classified with reference to the frequency
and the nature of the vibration cause. According to the
first classification (frequency) the vibration may be:

Synchronous
¾ The vibration frequency corresponds to the machine rotation

Asynchronous
¾ The vibration frequency is different from the machine rotation

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Synchronous vibrations Customer Training

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Asynchronous vibrations Customer Training

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Asynchronous vibrations Customer Training

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Asynchronous Vibrations Customer Training

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Oil Whip Instability Customer Training

Oil whip occurs on those machines subject to oil whirl

when the oil whirl frequency coincides with and becomes
locked into a system’s natural frequency (often a rotor
balance or critical speed frequency).For example, refer to
Figure 1.
When the rotor speed increased to just above 9,200 RPM,
its speed increased to 2X its first balance natural
frequency. At this time the oil whirl which was
approximately 43 percent of RPM, was brought into
coincidence with this critical speed. The oil whirl was
suddenly replaced by oil whip - a lateral forward
precessional sub-harmonic vibration of the rotor. At this
point, the oil whip frequency remains the same,
Figure 1. Development of Oil Whirl
independent of the rotor RPM. Note that the oil whip Just After Startup; Followed by Oil
frequency never changed even though the machine Whip from 9,200 to 12,000 RPM 3

continued up in speed to 12,000 RPM. When a shaft goes

into oil whip, its dominant dynamic factors become mass
and stiffness in particular; and its amplitude is limited only
by the bearing clearance. Left uncorrected, oil whip may
cause destructive vibration resulting catastrophic failure –
often in a relatively short period of time.
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Vibrations Customer Training

Possible causes of vibrations

e
nc
re
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Amplitude

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0.1-0.2ωr 0.4-0.5ωr ωr 2ωr Frequency (Hz)

Subsynchronous Supersynchronous
Rotor speed 24
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Vibration classification Customer Training

According to the second classification (nature of the

vibration cause) the vibration may be:

• free

• forced

• self excited

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Free Vibrations Customer Training

The system is described by an homogeneous equation whose solution is a

periodic response with natural frequency.
Damping dissipates vibration energy reducing amplitude with time and
causing a reduction of the natural frequency.
These impulses may be due to the following causes:

• electrical short circuit

• internal rubs
• loose rotor-system components
• surge

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Forced Vibrations Customer Training

The system is described by an equation with a non homogenous term (the

exciting force). The frequency of forced vibration is the same as the
excitation frequency.
A resonance occurs when the excitation frequency coincides with the
system natural frequency. The most common sources of excitations
are:
•unbalance in the rotor system
•rotor bow
•coupling misalignment
•cross coupling forces

The excitations due to rotor unbalance and to coupling misalignment are not
affected by the compressor operating pressure. Aerodynamic effects, on the
contrary, have an increased intensity when the actual density of the gas increases.
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Self-Excited Vibrations Customer Training

The system is represented by an homogeneous equation whose solution

is a periodic response with natural frequency and increasing amplitude.
The energy supply to sustain and excite the vibration is acting through
the homogenous terms.
Resulting forces have components which are perpendicular to shaft
motion and, under certain conditions, may balance the system damping
capability causing the rotor to vibrate at the first natural frequency
(INSTABILITY).
Compressor parts where these phenomena may take place are:
•journal bearings
•oil seals rings
•gas labyrinth seals
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 Customer Training

What are the problems with

vibrations?

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What are the problems with vibrations?
Customer Training

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Resonance Customer Training

Excitation frequency = Natural frequency

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How we can avoid this problem? Customer Training

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Amplification Factor Customer Training

To determine the field operation speed has been defined the

AMPLIFICATION FACTOR,
FACTOR an index of maximum vibration displacement.

The value of AF shows HOW DANGEROUS IS THE ROTOR

VIBRATION MODE

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Amplification Factor Customer Training

Amplification Factor determine:

9 System Stability

9 Amount of System
dampening needed

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API 617 Customer Training

NC1 = Rotor first critical, center frequency, cycles per minute

Ncn = Critical speed, n th
Nmc = Maximum continuous speed, 105 percent
N1 = Initial (lesser) speed at 0,707 x peak amplitude (critical)
N2 = Final (greater) speed at 0,707 x peack amplitude (critical)
N2 – N 1 = Peak width at the half-power point
AF = Amplification factor
Nci
= ________
N2 – N1
SM = Separation margin
CRE = Critical response envelope
Ac1 = Amplitude at Nci
Aca = Amplitude at Ncn
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Critical Speeds Customer Training

When the rotor amplification factor is greater than or equal

to 2.5, the corresponding frequency is called a critical
frequency, and the corresponding shaft rotational frequency
is called a critical speed.

Amplification Factor ≥ 2.5

Critical frequency Critical Speed

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AF < 2.5 Customer Training

If the AF is less than 2.5, the response is considered critically

dumped and no SM is required.

Amplification Factor < 2.5

“Critically dumped” NO Safety Margin

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3.55 > AF > 2.5 Customer Training

If the AF is 2.5 to 3.55, a SM of 15% above the maximum

continuous speed and 5% below the minimum operating speed
is required.

3.55 < Amplification Factor < 2.5

15% Safety Margin

above the maximum continuous speed
Safety Margin
5% Safety Margin
below the minimum operating speed

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AF > 3.55 Customer Training

Amplification Factor > 3.55

the critical response peak is the critical response peak is

below the MOS above the trip speed

SM=100-[84+6/(AF-3)] SM=[126-6/(AF-3)]-100

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Critical Speed Reduction Customer Training

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Rotor Mode Shapes Customer Training

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 Main Calculation Tools Customer Training

Rotor Drawing

Bearing
Equivalent Shaft Characteristic

Laby / HC Seals Oil Seals

Characteristic (*) Characteristic (*)

• Critical Speeds Map 1,7x10

1,6x10
1,5x10
-4

-4

-4

-4
1,4x10
-4
1,3x10

Amplitude [mm]
-4
1,2x10

• Rotor Response 1,1x10

1,0x10
9,0x10
-4

-4

-5

-5
8,0x10
-5
7,0x10
-5

• Stability Analysis:
6,0x10
-5
5,0x10
-5
4,0x10
-5
3,0x10
-5
2,0x10
-5
1,0x10
0,0
400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

(*) Depending on RPM

Application Log. Dec. δ Calculation

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Damping – Journal Bearing Customer Training

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Damping Efficiency Customer Training

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Journal Bearing Stiffness Customer Training

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SWIRL BRAKES Customer Training

The fact that the gas tangential velocity at the labyrinth entrance influences the
destabilising forces has led to the development of SWIRL BRAKES and SHUNT HOLES.

This device uses an array of axial

vanes at the seal inlet to reduce
the inlet tangential velocity.

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SHUNT HOLES Customer Training

It consists in a line taking gas from the

compressor discharge and injecting
Shunt Holes flow into one of the early cavities of
the balance piston labyrinth. The gas
enters the seal with zero tangential
velocity and does not acquire much
tangential velocity as it proceeds
through the labyrinth.

Honeycomb Seals

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Honeycomb seals Customer Training

Balance Piston Honeycomb

Honeycomb seal is a powerful tool

to enhance the stability of a
machine. Even though cross
coupling stiffness is larger if
compared with a labyrinth seal, a
much higher damping and direct
stiffness lead to a large effective
damping.
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Labyrinth Seal-Gas Instability
Customer Training

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Special phenomena affecting stability
Customer Training

Fluid-dynamic excitation due to oil seals or journal bearings (oil

whirl) is peculiar to high pressure oil seals, in this application at
low pressure and with tilting pad bearings is not present.

Rubbing at impellers location:

this non linear effect reveals itself during the high speed balancing
of some large rotors : they behave as flexible rotors.

Rotating stall causes asynchronous vibrations related to

pulsating pressure.

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Design Management of Vibration
Phenomena Customer Training

Synchronous vibrations
The manifesting of synchronous vibration is not of particular
concern since the revision of bearings clearances and rotor
balancing is often the solution of the problem.

Sub-synchronous vibrations
Unstable behaviour begins with a peak of sub-synchronous
vibration corresponding to the first critical speed, suddenly the
peak increases rapidly to destroying the labyrinth seals.
In few other cases the sub-synchronous peak remain of limited
amplitude, it causes no harm from operating point of view.

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Rotordynamics - Testing Customer Training

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Probes mounting Customer Training

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Torsional Behaviour Customer Training

Torsional analysis scope :

evaluate vibration that can occur the entire compression drive train
system as singular unit.

The analysis is performed on the complete train and the results is the
calculation of compressor’s train critical speed.

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Campbell diagram Customer Training

Definition:
Campbell Diagram — A mathematically
constructed diagram used to check for
coincidence of vibration sources (i.e. 1 x
imbalance, 2 x misalignment) with rotor
natural resonance. The form of the
diagram is like a spectral map (frequency
versus rpm), but the amplitude is
represented by a rectangular plot, the
larger the amplitude the larger the
rectangle.

The diagram reports the

calculated torsional critical
speed, potential excitation
frequencies and the
operating speed range

Intersections between the critical speeds and exciting frequencies within

the operating speed range determine resonance conditions.
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