VIBRATION

1. A Brief Introduction to Vibration Analysis of Process Plant Machinery (I)
Basic Concepts I
Machinery Vibration is Complex
Vibration of a machine is not usually simple
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Many frequencies from many malfunctions
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Total vibration is sum of all the individual vibrations
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Unfiltered overall amplitude indicates overall condition
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Displacement amplitude is not a direct indicator of vibration severity unless combined
with frequency
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Velocity combines the function of displacement and frequency
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Unfiltered velocity measurement provides best overall indication of vibration severity
Characteristics of Vibration
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Vibration is the back and forth motion of a machine part
One cycle of motion consists of
Movement of weight from neutral position to upper limit
Upper limit back through neutral position to lower limit
Lower limit to neutral position
The movement of the weight plotted against time is a sine wave
Simple Spring- Mass system
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Movement plotted against time
Free and Forced Vibration
When a mechanical system is subjected to a sudden impulse, it will vibrate at its natural
frequency.
Eventually, if the system is stable, the vibration will die out
Forced vibration can occur at any frequency, and the response amplitude for a certain
force will be constant

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Relationship between Force and Vibration
Forces that cause vibration occur at a range of frequencies depending on the
malfunctions present
These act on a bearing or structure causing vibration
However, the response is not uniform at all frequencies. It depends on the Mobility of
the of the structure.
Mobility varies with frequency. For example, it is high at resonances and low where
damping is present
Various Amplitudes of a Sine Wave
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A = Zero to Peak or maximum amplitude – used to measure velocity and acceleration
2A = Peak to Peak = Used to measure total displacement of a shaft with respect to
available bearing clearance
RMS = Root Mean Squared amplitude - A measure of energy - used to measure
velocity and acceleration – mainly used in Europe
Average value is not used in vibration measurements
Characteristics of Vibration (2)
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Time required to complete one cycle is the PERIOD of vibration
If period is 1 sec then the number of cycles per minute (CPM) is 60
Frequency is the number of cycles per unit time – CPM or C/S (Hz)

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Peak to peak displacement is the total distance traveled from one extreme limit to the
other extreme limit
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Velocity is zero at top and bottom because weight has come to a stop. It is maximum
at neutral position
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Acceleration is maximum at top an bottom where weight has come to a stop and
must accelerate to pick up velocity
Root Mean Squared Amplitude
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RMS amplitude will be equal to 0.707 times the Peak amplitude if, and only if, the signal
is a sine wave (single frequency)
If the signal is not a sine wave, then the RMS value using this simple calculation will not
be correct
Displacement, Velocity & Acceleration
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Displacement describes the position of an object
Velocity describes how rapidly the object is changing position with time
Acceleration describes how fast the velocity changes with time
If Displacement d = x = A sin (wt) , then
Velocity = rate of change of displacement
v = dx / dt = Aw cos wt = Aw sin (wt + 90o)
Acceleration = rate of change of velocity
a = dv /dt = - Aw2 sin wt = Aw2 sin (wt + 180o)

4. A Brief Introduction to Vibration Analysis of Process Plant Machinery (II)
Basic Concept II
Concept of Phase
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Weight “C” and “D” are in “in step”
These weights are vibrating in phase
Weight “X” is at the upper limit and “Y” is at neutral position moving to lower limit
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These two weights are vibrating 90 deg “out of phase”

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Weight “A” is at upper limit and weight
“B” is at lower limit
These weights are vibrating 180 deg
“out-of-phase”
Displacement, Velocity and Acceleration Phase Relationship
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Velocity leads displacement by 90o; that is, it
reaches its maximum ¼ cycle or 90obefore
displacement maximum
Acceleration leads displacement by 180o.
Acceleration leads velocity by 90o
Small yellow circles show this relationship clearly

6. Units of Vibration Parameters
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Displacement
Metric
- Micron
= 1/1000 of mm
English
- Mil
= 1/1000 of Inch
Velocity
Metric
- mm / sec
English
- inch / sec
Acceleration
Metric
- meter / sec2
English
- g = 9.81 m/sec2 =
English Metric Unit Conversion
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Displacement
1 Mil = 25.4 Micron
Velocity
1 inch/sec = 25.4 mm/sec
Acceleration
Preferable to measure both in g’s because g is directly related to force
Conversion of Vibration Parameters Metric Units
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Displacement, Velocity and acceleration are related by the frequency of motion
Parameters in metric units
D = Displacement in microns (mm/1000)
V = Velocity in mm/sec
A = Acceleration in g’s
F = Frequency of vibration in cycles /minute (CPM)
V = D x F / 19,100
A = V x F / 93,650
Therefore, F = V / D x 19,100
Conversion of Vibration Parameters English Units
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Displacement, Velocity and acceleration are related by the frequency of motion
Parameters in English units
D = Displacement in mils (inch / 1000)
V = Velocity in inch/sec
A = Acceleration in g’s
F = Frequency of vibration in cycles /minute (CPM)
V = D x F / 19,100 – same as for metric units
A = V x F / 3,690 – metric value / 25.4
Relative Amplitude of Parameters
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V = D x F / 19,100 in metric units

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This means that velocity in mm/sec will be equal to displacement in microns at a
frequency of 19100 CPM.
At frequencies higher than 19,100 CPM velocity will be higher than displacement
A = V x F / 93,650
This means that acceleration in g’s will be equal to velocity in mm/sec at a frequency of
93,650 CPM.
At frequencies higher than 93,650 CPM acceleration will be higher than velocity
Selection of Monitoring Parameters
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Where the frequency content is likely to be low (less than 18,000 CPM) select
displacement
Large, low speed, pumps and motors with sleeve bearings
Cooling tower fans and Fin fan cooler fans. Their gear boxes would require a higher
frequency range
For intermediate range frequencies ( say, 18,000 to 180,000 CPM) select Velocity
Most process plant pumps running at 1500 to 3000 RPM
Gear boxes of low speed pumps
For higher frequencies (> 180,000 CPM = 3 KHz) select acceleration.
Gear boxes
Bearing housing vibration of major compressor trains including their drivers
Larger machines would require monitoring more than one parameter to cover the entire
frequency range of vibration components
For example, in large compressor and turbines
The relative shaft displacement is measured by permanently installed eddy current
displacement probes.
This would cover the frequency range of running speed, low order harmonics and
subharmonic components
To capture higher stator to rotor interactive frequencies such as vane passing, blade
passing and their harmonics, it is necessary to monitor the bearing housing acceleration
Monitoring one parameter for trending is acceptable
However, for detailed analysis, it may be necessary to measure more than one
parameter
Example in Selecting Units of Measurement
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Amplitude measurement units should be selected based upon the frequencies of interest
Following 3 plots illustrate how measurement unit affects the data displayed. Each of the
plots contain 3 separate component frequencies of 60 Hz, 300 Hz and 950 Hz.
Displacement
This data was taken using displacement. Note how the lower frequency at 60 Hz is
accentuated

8. Velocity
The same data is now displayed using velocity. Note how the 300Hz component is more
apparent
Acceleration
The same data is now displayed using acceleration. Note how the large lower frequency
component is diminished and the higher frequency component accentuated

9. A Brief Introduction to Vibration Analysis of Process Plant Machinery (III)
Basic Concepts III
Forced Vibration
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Exciting Force = Stiffness Force + Damping Force + Inertial Force
Stiffness
Stiffness is the spring like quality of mechanical elements to deform under load
A certain force of Kgs produces a certain deflection of mm
Shaft, bearing, casing, foundation all have stiffness
Viscous Damping
Encountered by solid bodies moving through a viscous fluid
Force is proportional to the velocity of the moving object
Consider the difference between stirring water versus stirring molasses
Inertial Forces
Inertia is the property of a body to resist acceleration
Mainly weight
Physical Concept of Vibration Forces
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Stiffness determines the deflection of a rotor by centrifugal forces of unbalance
Determined by the strength of the shaft
Damping force is proportional to velocity of the moving body and viscosity of the fluid
Damping is provided by lube oil
Inertial forces are similar to those caused by an earthquake when acceleration can be
very high.
Acceleration is related to the weight of the rotor
It can cause distortion of structures
Physical Concept of Vibration Parameters
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Displacement
Displacement is independent of frequency
Displacement is related to clearances in machine
If displacement exceeds available clearances, rubbing occurs.
Velocity
Velocity is proportional to frequency
Velocity is related to wear
In machines higher the velocity, higher the wear
Acceleration
Proportional to square of frequency
Acceleration is related to force
Excessive acceleration at the starting block can strain an athlete’s leg muscle
Acceleration is important for structural strength
Stiffness Influence
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Stiffness is measured by the force in Kgs required to produce a deflection of one mm.
Stiffness of a shaft is
Directly proportional Diameter4 and Modulus of Elasticity

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Directly proportional to Modulus of Elasticity
Inversely proportional to Length3
Typical Stiffness values in pounds / inch
Oil film bearings – 300,000 to 2,000,000
Rolling element bearings – 1,000,000 to 4,000,000
Bearing Housing, horizontal – 300,000 to 4,000,000
Bearing housing, vertical – 400,000 to 6,000,000
Shaft 1’ to 4” diameter – 100,000 to 4,000,000
Shaft 6” to 15” diameter – 400,000 to 20,000,000
Damping Influence
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Damping dissipates energy
Rotor instability can be related to lack of damping
System Damping controls the amplitude of vibration at critical speed.
With low damping there is poor dissipation of energy and amplitude is high
Amplification factor Q through resonance is an indicator of damping
Relationship between Displacement, Velocity and Acceleration (For
British Units)

11. Acceleration Varies as the Square of Frequency
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Acceleration is negligible at low frequencies.
It predominates the high frequency spectrum
Measure displacement at low frequency, velocity at medium frequencies and
acceleration at high frequencies

12. A Brief Introduction to Vibration Analysis of Process Plant Machinery (IV)
Basic Concepts IV
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Basic Rotor and Stator System
Forces generated in the rotor are transmitted through the bearings and supports to the
foundation
Displacement probe is mounted on the bearing housing which itself is vibrating. Shaft
vibration measured by such a probe is, therefore, relative to the bearing housing
Bearing housing vibration measured by accelerometer or velocity probe is an absolute
measurement
Type of Rotor Vibration
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Lateral motion involves displacement from its central position or flexural deformation.
Rotation is about an axis intersecting and normal to the axis of rotation
Axial Motion occurs parallel to the rotor’s axis of rotation
Torsional Motion involves rotation of rotor’s transverse sections relative to one another
about its axis of rotation
Vibrations that occur at frequency of rotation of rotor are called synchronous vibrations.
Vibrations at other frequencies are nonsynchronous vibrations

13. The Relationship Between Forced and Vibration
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Forces generated within the machine have may different frequencies
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The mobility of the bearings and supports are also frequency dependent. Mobility =
Vibration / Force
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Resultant Vibration = Force x Mobility
Alternative Measurements on Journal Bearings
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Relative shaft displacement has limited frequency range but has high amplitude at low
frequencies – running speed, subsynchronous and low harmonic components
Accelerometer has high signal at high frequencies – rotor to stator interaction
frequencies – blade passing, vane passing
Types of Machine Vibration

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Casing Absolute is measured relative to space by Seismic transducer mounted on
casing
Shaft relative is measured by displacement transducer mounted on casing
Shaft Absolute is the sum of Casing Absolute and Shaft Relative.
Shaft Versus Housing Vibration
Shaft Versus Housing Vibration
(Selecting the Right Parameter)
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Shaft vibration relative to bearing housing
Machines with high stator to rotor weight ratio ( For example in syngas comp the ratio
may exceed 20)
Machines with hydrodynamic sleeve bearings
Almost all high speed compressor trains
Bearing housing vibration
Machines with rolling element bearings have no shaft motion relative to bearing housing.
Rolling Element bearings have zero clearance
Shaft vibration is directly transmitted to bearing housing
Shaft absolute displacement
Machines with lightweight casings or soft supports that have significant casing vibration
Bearing Housing Vibration
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Shaft-relative vibration provides
Machinery protection
Low frequency (up to 120,000 CPM) information for analysis
Many rotor- stator interactions generate high frequency vibrations that are transferred to
the bearing housing
Vane passing frequency in compressors
Blade passing frequency in turbines

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These frequencies provide useful information on the condition and cleanliness of blades
and vanes
These vibrations are best measured on the bearing housing using high-frequency
accelerometers.
Periodic measurements with a data collector.
Shaft Rotation and Precession
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Precession is the locus of the centerline of the shaft around the geometric centerline
Normally direction of precession will be same as direction of rotation
During rubbing shaft may have reverse precession
IRD Severity Chart
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Values are for filtered readings only – not overall
Velocity is expressed in peak units (not RMS units)
Severity lines are in velocity

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Displacement severity can be found only with reference to frequency.
In metric units
Very rough > 16 mm/sec
Rough
> 8 mm/sec
Slightly rough > 4 mm/sec
Fair
- 2 – 4 mm/sec
Good
- 1 – 2 mm/sec
A Brief Introduction to Vibration Analysis of Process Plant Machinery (V)
Basic Concept V
Vibration Transducers
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Transducer is a device that converts one form of energy into another.
Microphone - sound (mechanical) to electrical energy
Speaker - electrical to mechanical energy
Thermometer - thermal to electrical energy
Vibration is mechanical energy
It must be converted to electrical signal so that it can easily be measured and analyzed.
Commonly used Vibration Transducers
Noncontact Displacement Transducer
Seismic Velocity Transducer
Piezoelectric Accelerometer
Transducers should be selected depending on the parameter to be measured.
Proximity Displacement Probes
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Proximity probes measure the displacement of shaft relative to the bearing housing
They observe the static position and vibration of shaft
By mounting two probes at right angles the actual dynamic motion (orbit) of the shaft
can be observed
Non Contact Displacement Probes
(Eddy Current Proximity Probe)
Measures the distance (or “lift off”) of a conducting surface from the tip of the probe
Measures gap and nothing else.
Coil at probe tip is driven by oscillator at around 1.5 MHz
If there is no conducting surface full voltage is returned
Conducting surface near coil absorbs energy
Therefore, voltage returned is reduced
Proximitor output voltage is proportional to gap

17. Eddy Current Proximity Probe System
Eddy Current Proximity Probe System Calibration
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Eddy current “lift off” output is parabolic – not linear
Proximitor has a nonlinear amplifier to make the output linear over a certain voltage
range
For a 24 Volt system the output is linear from 2.0 to 18.0 volts
Proximity Probe Advantages
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Measures shaft dynamic motion
Only probe that can measures shaft position – both radial and axial
Good signal response between DC to 90,000 CPM
Flat phase response throughout operating range
Simple calibration
Rugged and reliable construction
Suitable for installation in harsh environments
Available in many configurations
Multiple machinery applications for same transducer – vibration, position, phase, speed
Proximity Probe DisAdvantages

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Sensitive to measured surface material properties like conductivity, magnetism and
finish
Scratch on shaft would be read as vibration
Variation in shaft hardness would be read as vibration
Shaft surface must be conductive
Low response above 90,000 CPM
External power source and electronics required
Probe must be permanently mounted. Not suitable for hand-holding
Machine must be designed to accept probes – difficult to install if space has not been
provided
Seismic Velocity Pick-Up IRD 544
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Permanent magnet is attached to the case. Provides strong magnetic field around
suspended coil
Coil of fine wire supported by low-stiffness springs
Voltage generated is directly proportional to velocity of vibration
When pick up is attached to vibrating part magnet follows motion of vibration
The coil, supported by low stiffness springs, remains stationary in space
So relative motion between coil and magnet is relative motion of vibrating part with
respect to space
Faster the motion higher the voltage
Velocity Pick-Up - Suspenped Magnet Type
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Coil fixed to body, magnet floating on very soft springs
All velocity pick ups have low natural frequency (300 to 600 CPM)
Therefore, cannot measure low frequencies in the resonant range.
Their useful frequency range is above - 10 Hz or 600 CPM

19. Advantages of Velocity Pick-Up
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Measures casing absolute motion
It is a linear self generator with a high output
IRD 544 pick up – 1080 mv 0-pk / in/sec= 42 mv / mm/sec
Bently pick up – 500 mv 0-pk / in/sec = 19.7 mv / mm/sec
High voltage Output
Can be read directly on volt meter or oscilloscope
Therefore, readout electronics is much simplified
Since no electronics needed in signal path, signal is clean and undistorted. High signal
to noise ratio
Good frequency response from 600 to 90,000 CPM
Signal can be integrated to provide displacement
Easy external mounting, no special wiring required
Disadvantages of Velocity Pick-Up

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Mechanically activated system. Therefore, limited in frequency response – 600 to
90,000 CPM
Amplitude and phase errors below 1200 CPM
Frequency response depends on mounting
Large size. Difficult to mount if space is limited
Potential for failure due to spring breakage.
Limited temperature range – usually 120oC
High temperature coils available for use in gas turbines but they are expensive
High cost compared to accelerometers
Accelerometer cost dropping velocity pick up increasing
Note - Velocity transducers have largely been replaced by accelerometers in most
applications.
Basic Concept VI
Piezoelectric Accelerometers
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Piezoelectric crystal is sandwiched between a seismic mass and outer case.
Preload screw ensures full contact between crystal & mass
When mounted on a vibrating surface seismic mass imposes a force equal to mass x
acceleration
Charge output of piezo crystal is proportional to applied force
Since mass is constant, output charge is proportional to acceleration

21. Piezoelectric Accelerometers
Converting Charge to Voltage
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The output of accelerometers is charge. Usually expressed as picocoulomb / g (pc/g)
Electronic charge amplifier is required to convert charge signal to voltage signal
Impedance of accelerometer is high. Cannot be connected directly to low impedance
instruments
Charge amplifier has high input impedance and low output impedance so that long
cables can be used.
Charge amplifier can be external or internal
In bigger accelerometers amplifier can be located inside
In small, high frequency units amplifier is located outside
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Also located outside in high temperature accelerometers
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Accelerometers Mounting
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Mounted resonance of accelerometer drops with reduction in mounting stiffness.
This causes a reduction in the upper frequency range
Ideal mounting is by threaded stud on flat surface
Maximum stiffness, highest mounted resonance
Resonant frequency 32 KHz. Usable range 10 KHz.
Magnet mounting simpler but lower response
Resonant frequency drops to 7 Khz. Usable range 2 KHz
Handheld probe convenient but very low frequency response
Due to low stiffness of hand resonant frequency < 2 KHz
Frequency response < 1 KHz
Accelerometers Resonance & Frequency Response
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Frequency response depends on resonance frequency
Higher the resonance frequency, higher the useful range
Maximum useable frequency range is 1/3rd of resonance
Resonance frequency, however, depends on mounting

22. Frequency Response - Screw Mount
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Screw mount has the highest resonance and, therefore the highest frequency response
This film of silicon grease improves contact.
Make sure bottom of accelerometer contacts measured surface
Frequency Response - Magnet Mount
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Weight of magnet determines the mounted resonance
Smaller the magnet higher the frequency response
Use the smallest magnet that holds the accelerometer without slipping. Use a machined
surface for the best grip
Frequency Response Hand Held
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Poor high frequency response - < 1 KHz
Response may change with hand pressure
Repeatability is poor when high frequencies are present

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Hand holding accelerometers should be avoided except for low frequency work
Filtering Necessary for Accelerometers
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Any high frequency vibration in the resonant range will be highly amplified.
Amplification can be up to 30 dB or almost 1,000 times
Filtered amplitudes will be highly distorted
Resonant frequency highly depends on mounting
By previous example – 32 KHz for screw mount. Only 2 KHz for handholding
Therefore, resonance range should be filtered out
For screw mount low pass filter should be set at 10 KHz
For hand holding filter should be set at 1 KHz.
Analyst must know frequency response of accelerometer used for different mounting
conditions.
Filtering can be done in FFT Analyzer by setting maximum frequency correctly.
Advantages of Accelerometers
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Measures casing or structural absolute motion
Rugged and reliable construction
Easy to install on machinery, structures, pipelines
Small size, easiest to install in cramped locations
Good signal response from 600 to 600,000 CPM
Low frequency units can measure down to 6 CPM
High freq units can reach 30 KHz (1,800,000 CPM)
Operates below mounted resonance frequency
Flat phase response throughout operating range
Internal electronics can be used to convert acceleration to velocity – Bently Velometer
Units available from a cryogenic temperature of minus 200oC to a high temperature of >
600oC
Disadvantages of Accelerometers
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Sensitive to mounting and surface conditions
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Unable to measure shaft vibration or position
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Not self generating – Need external power source
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Transducer cable sensitive to noise, motion and electrical interference
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Low signal response below 600 CPM (10 Hz)
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Temperature limitation of 120oC for ICP Acceleroms

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Double integration to displacement suffers from low frequency noise – should be
avoided
Signal filtration required depending on mounting
Difficult calibration check
Machine With Both Shaft and Bearing Housing Vibration Monitoring
Refferensi Book
1.
Machinery Malfunction Diagnosis and Correction – Robert C Eisenmann –
Prentice Hall
2.
Fundamentals of Rotating Machinery Diagnostics – Donald E. Bently –
Bently Pressurized Bearing Press
3. Vibration Vector
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5. • A vibration vector plotted in the transducer response plane
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1x vector is 90 mic pp /220o
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Zero reference is at the transducer angular location
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Phase angle increases opposite to direction of rotation
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12. Polar Plot
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15. • Polar plot is made up of a set of vectors at different speeds.
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Vector arrow is omitted and the points are connected with a line
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Zero degree is aligned with transducer location
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Phase lag increases in direction opposite to rotation
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23. • 1x uncompensated Polar Plot shows location of rotor high spot relative to
transducer
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This is true for 1x circular orbits and approximately true for 1x elliptical orbits
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32. 8/06/2011
33.
Shaft Orbit Plots (II)
34. Not- 1X Compensation of an Orbit
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36. • At Left orbit is the uncompensated orbit
37. • At right is the same orbit with the 1X component removed
38. • The remaining vibration is primarily 1/2X from a rub
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26. 40.
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42. Measurement of peak-to-peak amplitude of an Orbit
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44. X transducer measurement axis is drawn together with perpendicular lines that are
tangent to maximum and minimum points on the orbit
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47. Direction of Precession in Orbits
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49. • In the orbit plot shaft moves from the blank towards the dot. In the plot on left the
inside loop is forward precession
50. • In the right orbit the shaft has reverse precession for a short time at the outside
loop at bottom

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54. Effect of Radial Load on Orbit Shape
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56. • Orbits are from two different steam turbines with opposite rotation. Both
machines are experiencing high radial loads
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Red arrows indicate the approximate direction of the applied radial load.
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Red arcs represent the probable orientation of the bearing wall
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62. Deflection Shape of Rotor Shaft
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64. • When keyphasor dots of simultaneous orbits at various bearings along the
length of the rotor are joined an estimate of the three dimensional deflection shape of
the rotor shaft can be obtained
65. * This is a rigidly coupled rotor system
66.
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28. 70. 8/05/2011
71.
Shaft Orbit Plots (I)
72. The
Orbit
73. • The orbit represents the path of the shaft centerline within the bearing clearance.
74. • Two orthogonal probes are required to observe the complete motion of the shaft
within.
75. • The dynamic motion of the shaft can be observed in real time by feeding the
output of the two orthogonal probes to the X and Y of a dual channel oscilloscope
76. • If the Keyphasor output is fed to the Z axis, a phase reference mark can be
created on the orbit itself
77. • The orbit, with the Keyphasor mark, is probably the most powerful plot for
machinery diagnosis
78.
79. Precession
80.
81. Once a gyroscope starts to spin, it will resist changes in the orientation of its spin
axis. For example, a spinning top resists toppling over, thus keeping its spin axis
vertical. If atorque, or twisting force, is applied to the spin axis, the axis will not turn
in the direction of the torque, but will instead move in a direction perpendicular to it.
This motion is called precession. The wobbling motion of a spinning top is a simple
example of precession. The torque that causes the wobbling is the weight of the top
acting about its tapering point. The modern gyroscope was developed in the first half
of the 19th cent. by the
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84. Construction of an Orbit
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86. • XY transducers observe the vibration of a rotor shaft
87. • A notch in the shaft (at a different axial location) is detected by the Keyphasor
transducer.
88. • The vibration transducer signals produce two time base plots (middle) which
combine into an orbit plot (right)
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92. Probe Orientation and the Orbit Plot

29. 93.
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95. • On the left side, when the probes are mounted at 0o and 90oR, the orbit plot and
oscilloscope display show the same view.
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On the right, when the probes are mounted at 45oL and 45oR, the orbit plots are
automatically rotated
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The oscilloscope, however, must be physically rotated 45oCCW to
display the correct orbit orientation
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110.

30. 111.
Examples of 1X and Subsynchronous Orbits
112.
113.
• Orbit at left shows subsynchronous fluid-induced instability. Note the
multiple keyphasor dots because the frequency is not a fraction of the running speed
114.
• The orbit at right is predominantly 1X. The keyphasor dots appear in a
small cluster indicating dominant 1X behavior
115.
116.
117.
118.
Slow Roll Vector Compensation of 1X Filtered Orbit
119.
120.
• Slow roll vector compensation can considerably change the amplitude
and phase of the orbit
121.
122.
•
Slow roll vectors of X= 1.2 mil pp /324oand Y= 1.4 mil pp /231o
123.
124.
125.
126.
127.
128.
129.
130.
Slow roll Waveform Compensation of a Turbine Orbit
131.
Note how compensation makes the orbit (right) much clearer

31. 132.
133.
134.
135.
136.
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137.
8/04/2011
138.
Full Spectrum Plots
139.
Full Spectrum
140.
141.
• Half Spectrum is the spectrum of a WAVEFORM
142.
• Full Spectrum is the spectrum of an ORBIT
143.
• Derived from waveforms of two orthogonal probes
144.
– These two waveforms provide phase information to determine direction of
precession at each frequency
145.
– For phase accuracy they must be sampled at same time
146.
• Calculated by performing a FFT on each waveform
147.
• These FFT’s are subjected to another transform
148.
– Data converted to two new spectra – one for each direction of precession
– Forward or Reverse
149.
– Two spectra are combined into a single plot
150.
Forward to the right, Reverse to the left
151.
152.
Calculation of Full Spectrum Plot

32. 153.
154.
155.
156.
157.
158.
159.
First
Waveform and its half spectrum
160.
161.
162.
Second
Waveform and its half spectrum
163.
164.
Combined orbit and its full spectrum

33. 165.
166.
Circular Orbits and Their Full Spectra
167.
168.
Forward Precession
169.
Spectrum on forward side of plot
170.
171.
<-- Reverse Precession
172.
Spectrum on reverse side of plot
173.
Direction of rotation – CCW
174.
175.
<-- Forward Precession
176.
Spectrum on forward side of plot
177.
Direction of rotation – CW
178.
179.
<-- Reverse Precession
180.
Spectrum on reverse side of plot
181.
Direction of rotation - CW
182.
183.
184.
185.
Full Spectrum of Elliptical Orbit

34. 186.
187.
Orbit is generated by two counter rotating vectors
188.
189.
Forward spectrum length is twice the length of forward rotating vector
190.
191.
Reverse spectrum length is twice the length of reverse rotating vector
192.
193.
Major axis of ellipse = a +b
194.
Minor axis of ellipse = a - b
195.
196.
Original orbit cannot be reconstructed from full spectrum because there is no
phase information.
197.
198.
3 possible orbits are shown
199.
200.
201.
Circular & Elliptical 1x Orbits

35. 202.
203.
• Direction of precession is indicated by dominant line of “Forward” and
“Reverse” components.
204.
205.
•
Flatness of ellipse is determined by the relative size of forward and reverse
components
206.
207.
•
When orbit is circular there is only one spectrum line
208.
209.
•
When orbit is a line the spectrum components are equal.
210.
211.
•
Therefore, the smaller the difference between components, the more
elliptical the orbit.
212.
213.
Orbit and Spectrum of a ½x Rub
214.
215.
• Orbit and spectrum of a steam turbine with a ½ x rub
216.
•
Full spectrum clarifies the complex orbit which is a sum of ½ x, 1x and their
harmonics.
217.
•
From the ratio of forward ad reverse components
218.
•
1x is the largest, forward and mildly elliptical
219.
•
½ x and 2x orbits are nearly line orbits
220.
•
Small component of 3/2 x is third harmonic of ½ x fundamental

36. 221.
222.
223.
Half and Full Spectrum Display of a ½ x Rub
224.
225.
226.
227.
Differentiating ½ x Rub and Fluid Instability from Full Spectrum Plots
228.
• Half and full spectrum display of a ½ x rub (red data) and fluid induced
instability (blue data)
229.
• Note similarity in appearance of the two half spectrum plots
230.
• The full spectrum plots clearly show the difference in the subsynchronous
vibration
231.
– The ½ x rub orbit is extremely elliptical – small difference between forward
and reverse components
232.
– The fluid induced instability orbit is forward and nearly circular – large
difference between forward and reverse 1x and ½ x components.
233.
• The unfiltered orbits are at the bottom
234.
Full Spectrum Cascade Plot of Machine Start Up

37. 235.
236.
• Horizontal axis represents precession frequency
237.
238.
•
Rotor speed is to the left and amplitude scale is on the right
239.
240.
•
Order lines drawn diagonally from the origin show vibration frequencies that
are proportional to running speed
241.
242.
243.
244.
245.
246.
247.
248.
249.
250.
251.
•
•
•
•
•
•
•
Display of spectra plots taken at different speeds during start up
Base of each spectrum is the rotor speed at which the sample was taken
Diagonal lines are “Order” lines. Usually 1x, 2x and ½ x are plotted
Resonances and critical speed can be seen on 1x diagonal line
Sudden appearance of ½ x indicates rub which can produce harmonics.
Phase relationships cannot be seen on cascade plot.
Many harmonics at low speed usually due to scratches on shaft

38. 252.
253.
254.
Horizontal ellipse shows rub second balance resonance (critical)
255.
256.
Vertical ellipse shows ½ x rub frequency is almost equal to first critical. Slight
shift to right is due to stiffening of rotor system from rub contact.
257.
258.
259.
260.
261.
262.
Full Spectrum Waterfall Plot
263.
264.
• Displays spectra with respect to time
265.
266.
• Used for correlating response to operating parameters
267.
268.
•
Time on left and Running Speed on right. Amplitude scale is at extreme right
269.
270.
•
Plot of compressor shows subsynchronous instability whenever suction
pressure is high (red). 1x component is not shown on plot.
271.

39. 272.
•
Full spectrum shows subsynchronous vibration is predominantly
forward.
273.
274.
275.
276.
277.
Waterfall of Motor with Electrical Noise Problem
278.
279.
280.
281.
282.
283.
284.
285.
286.
287.
288.
289.
290.
•
High vibration at mains frequency (60 Hz) during start up (red). 1x is low.
•
Vibration reduces when normal speed and current are reached (green)
•
When motor is shut down (blue) 60 Hz component disappears suddenly.
•
1x component reduces gradually with speed.
291.
Summary
292.
293.
• Conventional spectrum is constructed from the output waveform of a single
transducer
294.
• Full Spectrum is constructed from the output of a pair of transducers at right
angles.
295.
– Displays frequency and direction of precession
296.
– Forward precession frequencies are shown on right side
297.
– Reverse Precession frequencies are shown on left side
298.
• Full spectrum is the spectrum of an orbit
299.
– Ratio of forward and reverse orbits gives information about ellipticity and
direction of precession
300.
– However, there is no information about orientation of orbit

40. 301.
•
spectra
302.
Cascade and Waterfall plots can be be constructed either from half or full
303.
304.
305.
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306.
8/03/2011
307.
Half Spectrum Plots
308.
Spectrum Plot-1
309.
• Machines can vibrate at many different frequencies simultaneously 1x,
2x, 3x, vane passing etc.
310.
• Timebase and orbit have frequency information but only a couple of
harmonics can be identified – impossible to identify nonsynchronous frequencies
311.
• Using an analog tunable analyzer the amplitude and phase at each
individual frequency can be identified but only one at a time.
312.
– All frequencies cannot be seen simultaneously.
313.
– Trend changes in individual frequencies cannot be followed
314.
– Each frequency sweep may take one minute during which short duration
transient events may be missed
315.
• A Spectrum Plot by a FFT Analyzer shows all frequencies
instantaneously.
316.
317.
Spectrum Plot-2
318.
• Spectrum plot is the basic display of a Spectrum Analyzer. It the most
important plot for diagnosis
319.
• Spectrum plot displays the entire frequency content of complex vibration
signals in a convenient form.
320.
– It has frequency on X-axis and amplitude on Y-axis
321.
– It is constructed from sampled timebase waveform of a single transducer –
displacement, velocity or acceleration
322.
• Fast Fourier Transform (FFT) calculates the spectrum from the sample
record which contains a specific number of waveform samples
323.
• Spectrum plots can be used to identify harmonics of running frequency,
rolling element bearing defect frequencies, gear mesh frequencies, sidebands
324.
Periodic motion with more than one frequency
325.

41. Above waveform broken up into a sum of harmonically related sine waves
326.
327.
328.
Illustration of how the previous signal can be described in terms of a
frequency spectrum.
329.
Left
- Description in time domain
330.
Right
- Description in frequency domain
331.
332.
333.
334.
335.
Spectrum Frequency as a Function of Pulse Shape
336.
337.
Construction of Half Spectrum Plot - 1
338.
• Raw timebase signal (red) is periodic but complex.
339.
•
Fourier transform is equivalent to applying of a series of digital filters
340.
•
Filtered frequency components are shown as sine waves (blue)
341.
•
Phase for each signal can be measured with respect to trigger signal
342.
•
We can see components’ amplitude, frequency and phase

42. 343.
344.
Construction of Half Spectrum Plot - 2
345.
• If we rotate the plot so that the time axis disappears we see a two
dimensional spectrum plot of amplitude v/s frequency
346.
•
Component signals now appear as series of vertical lines.
347.
•
Each line represents a single frequency
348.
•
Unfortunately, the phase of the components is now hidden.
349.
•
It is not possible to see phase relationships in spectrum plot.
350.
351.
352.
353.
These plots show why it is impossible to guess the frequency content from the
waveform.
354.
Vertical lines in top plot show one revolution
355.
It is clear that 2x and higher frequencies are present
356.
But 3x and 6x could not be predicted from the waveform.
357.
A Fourier spectrum shows all the frequencies present

43. 358.
359.
360.
Linear and Logarithmic Scaling
361.
• Amplitude scaling can be Linear or Logarithmic
362.
• Logarithmic scaling is useful for comparing signals with very large and
very small amplitudes.
363.
– Will display all signals and the noise floor also
364.
• However, when applied to rotating machinery work
365.
– Log scale makes it difficult to quickly discriminate between significant and
insignificant components.
366.
• Linear scaling shows only the most significant components.
367.
– Weak, insignificant and low-level noise components are eliminated or
greatly reduced in scale
368.
• Most of our work is done with linear scaling
369.
370.
371.
372.
373.
374.
375.
376.
377.
378.
379.
380.
381.
Illustration of Linear and Log scales
•
Log scale greatly amplifies low level signals
•
It is impossible to read 1% signals in linear scale
•
It is very easy to read 0.1% signals on the log scale
Limitations of Spectrum Plots
• FFT assumes vibration signal is constant and repeats forever.
• Assumption OK for constant speed machines .
– inaccurate if m/c speed or vibration changes suddenly.
• FFT calculates spectrum from sample record

44. 382.
– Which has specific number of digital waveform samples
383.
– FFT algorithm extends sample length by repeatedly wrapping the signal
on itself
384.
– Unless number of cycles of signal exactly matches length of sample there
will be discontinuity at the junction
385.
– This introduces noise or leakage into the spectrum
386.
• This problem is reduced by “windowing”
387.
– Forces signal smoothly to zero at end points
388.
– Hanning window best compromise for machinery work
389.
390.
Effect of Windowing
391.
392.
393.
394.
395.
396.
397.
• Figure shows a timebase plot with a mixture of 1/2x and 1x frequencies.
Two examples of half spectrum plots are shown below
•
•
Without window function the “lines” are not sharp and widen at the bottom
This “leakage” is due to discontinuity at sample record ending
398.
• When “Hanning” window is applied to the sample record 1/2x spectral line
is narrower and higher
399.
•
Noise floor at base is almost gone.

45. Half Spectrum Plots
Spectrum Plot-1
•
Machines can vibrate at many different frequencies simultaneously 1x, 2x, 3x, vane
passing etc.
•
Timebase and orbit have frequency information but only a couple of harmonics can be
identified – impossible to identify nonsynchronous frequencies
• Using an analog tunable analyzer the amplitude and phase at each individual frequency
can be identified but only one at a time.
– All frequencies cannot be seen simultaneously.
– Trend changes in individual frequencies cannot be followed
– Each frequency sweep may take one minute during which short duration transient
events may be missed
•
A Spectrum Plot by a FFT Analyzer shows all frequencies instantaneously.
Spectrum Plot-2
•
Spectrum plot is the basic display of a Spectrum Analyzer. It the most important plot for
diagnosis
•
Spectrum plot displays the entire frequency content of complex vibration signals in a
convenient form.
– It has frequency on X-axis and amplitude on Y-axis
– It is constructed from sampled timebase waveform of a single transducer –
displacement, velocity or acceleration
•
Fast Fourier Transform (FFT) calculates the spectrum from the sample record which
contains a specific number of waveform samples
•
Spectrum plots can be used to identify harmonics of running frequency, rolling element
bearing defect frequencies, gear mesh frequencies, sidebands
Periodic motion with more than one frequency
Above waveform broken up into a sum of harmonically related sine waves

46. Illustration of how the previous signal can be described in terms of a frequency spectrum.
Left
- Description in time domain
Right
- Description in frequency domain
Spectrum Frequency as a Function of Pulse Shape
•
•
•
•
•
Construction of Half Spectrum Plot - 1
Raw timebase signal (red) is periodic but complex.
Fourier transform is equivalent to applying of a series of digital filters
Filtered frequency components are shown as sine waves (blue)
Phase for each signal can be measured with respect to trigger signal
We can see components’ amplitude, frequency and phase

47. •
•
•
•
•
Construction of Half Spectrum Plot - 2
If we rotate the plot so that the time axis disappears we see a two dimensional spectrum
plot of amplitude v/s frequency
Component signals now appear as series of vertical lines.
Each line represents a single frequency
Unfortunately, the phase of the components is now hidden.
It is not possible to see phase relationships in spectrum plot.
These plots show why it is impossible to guess the frequency content from the waveform.
Vertical lines in top plot show one revolution
It is clear that 2x and higher frequencies are present
But 3x and 6x could not be predicted from the waveform.
A Fourier spectrum shows all the frequencies present
Linear and Logarithmic Scaling

48. •
•
•
Amplitude scaling can be Linear or Logarithmic
Logarithmic scaling is useful for comparing signals with very large and very small
amplitudes.
Will display all signals and the noise floor also
However, when applied to rotating machinery work
Log scale makes it difficult to quickly discriminate between significant and insignificant
components.
Linear scaling shows only the most significant components.
Weak, insignificant and low-level noise components are eliminated or greatly reduced in
scale
Most of our work is done with linear scaling
•
•
•
Illustration of Linear and Log scales
Log scale greatly amplifies low level signals
It is impossible to read 1% signals in linear scale
It is very easy to read 0.1% signals on the log scale
–
•
–
•
–
•
•
–
•
–
–
–
–
•
–
–
Limitations of Spectrum Plots
FFT assumes vibration signal is constant and repeats forever.
Assumption OK for constant speed machines .
inaccurate if m/c speed or vibration changes suddenly.
FFT calculates spectrum from sample record
Which has specific number of digital waveform samples
FFT algorithm extends sample length by repeatedly wrapping the signal on itself
Unless number of cycles of signal exactly matches length of sample there will be
discontinuity at the junction
This introduces noise or leakage into the spectrum
This problem is reduced by “windowing”
Forces signal smoothly to zero at end points
Hanning window best compromise for machinery work
Effect of Windowing

49. •
Figure shows a timebase plot with a mixture of 1/2x and 1x frequencies.
Two examples of half spectrum plots are shown below
•
•
Without window function the “lines” are not sharp and widen at the bottom
This “leakage” is due to discontinuity at sample record ending
•
When “Hanning” window is applied to the sample record 1/2x spectral line is narrower
and higher
Full Spectrum Plots
Full Spectrum
•
•
•
–
–
•
•
–
–
Half Spectrum is the spectrum of a WAVEFORM
Full Spectrum is the spectrum of an ORBIT
Derived from waveforms of two orthogonal probes
These two waveforms provide phase information to determine direction of precession at
each frequency
For phase accuracy they must be sampled at same time
Calculated by performing a FFT on each waveform
These FFT’s are subjected to another transform
Data converted to two new spectra – one for each direction of precession – Forward or
Reverse
Two spectra are combined into a single plot
Forward to the right, Reverse to the left
Calculation of Full Spectrum Plot

50. First
Waveform and its half spectrum
Second
Waveform and its half spectrum
Combined orbit and its full spectrum

51. Circular Orbits and Their Full Spectra
Forward Precession
Spectrum on forward side of plot
<--
Reverse Precession
Spectrum on reverse side of plot
Direction of rotation – CCW
<-- Forward Precession
Spectrum on forward side of plot
Direction of rotation – CW
<-- Reverse Precession
Spectrum on reverse side of plot
Direction of rotation - CW
Full Spectrum of Elliptical Orbit

52. Orbit is generated by two counter rotating vectors
Forward spectrum length is twice the length of forward rotating vector
Reverse spectrum length is twice the length of reverse rotating vector
Major axis of ellipse = a +b
Minor axis of ellipse = a - b
Original orbit cannot be reconstructed from full spectrum because there is no phase
information.
3 possible orbits are shown
Circular & Elliptical 1x Orbits

53. •
Direction of precession is indicated by dominant line of “Forward” and “Reverse”
components.
•
Flatness of ellipse is determined by the relative size of forward and reverse
components
•
When orbit is circular there is only one spectrum line
•
When orbit is a line the spectrum components are equal.
•
Therefore, the smaller the difference between components, the more elliptical
the orbit.
Orbit and Spectrum of a ½x Rub
•
•
•
•
•
•
Orbit and spectrum of a steam turbine with a ½ x rub
Full spectrum clarifies the complex orbit which is a sum of ½ x, 1x and their
harmonics.
From the ratio of forward ad reverse components
1x is the largest, forward and mildly elliptical
½ x and 2x orbits are nearly line orbits
Small component of 3/2 x is third harmonic of ½ x fundamental

54. Half and Full Spectrum Display of a ½ x Rub
•
•
•
–
–
•
Differentiating ½ x Rub and Fluid Instability from Full Spectrum Plots
Half and full spectrum display of a ½ x rub (red data) and fluid induced instability
(blue data)
Note similarity in appearance of the two half spectrum plots
The full spectrum plots clearly show the difference in the subsynchronous vibration
The ½ x rub orbit is extremely elliptical – small difference between forward and
reverse components
The fluid induced instability orbit is forward and nearly circular – large difference
between forward and reverse 1x and ½ x components.
The unfiltered orbits are at the bottom
Full Spectrum Cascade Plot of Machine Start Up

55. •
Horizontal axis represents precession frequency
•
Rotor speed is to the left and amplitude scale is on the right
•
Order lines drawn diagonally from the origin show vibration frequencies that are
proportional to running speed
•
•
•
•
•
•
•
Display of spectra plots taken at different speeds during start up
Base of each spectrum is the rotor speed at which the sample was taken
Diagonal lines are “Order” lines. Usually 1x, 2x and ½ x are plotted
Resonances and critical speed can be seen on 1x diagonal line
Sudden appearance of ½ x indicates rub which can produce harmonics.
Phase relationships cannot be seen on cascade plot.
Many harmonics at low speed usually due to scratches on shaft

56. Horizontal ellipse shows rub second balance resonance (critical)
Vertical ellipse shows ½ x rub frequency is almost equal to first critical. Slight shift to
right is due to stiffening of rotor system from rub contact.
Full Spectrum Waterfall Plot
•
Displays spectra with respect to time
•
Used for correlating response to operating parameters
•
Time on left and Running Speed on right. Amplitude scale is at extreme right
•
•
Plot of compressor shows subsynchronous instability whenever suction pressure is
high (red). 1x component is not shown on plot.
Full spectrum shows subsynchronous vibration is predominantly forward.
Waterfall of Motor with Electrical Noise Problem

57. •
High vibration at mains frequency (60 Hz) during start up (red). 1x is low.
•
Vibration reduces when normal speed and current are reached (green)
•
When motor is shut down (blue) 60 Hz component disappears suddenly.
•
1x component reduces gradually with speed.
Summary
•
•
–
–
–
•
–
–
•
Conventional spectrum is constructed from the output waveform of a single
transducer
Full Spectrum is constructed from the output of a pair of transducers at right angles.
Displays frequency and direction of precession
Forward precession frequencies are shown on right side
Reverse Precession frequencies are shown on left side
Full spectrum is the spectrum of an orbit
Ratio of forward and reverse orbits gives information about ellipticity and direction of
precession
However, there is no information about orientation of orbit
Cascade and Waterfall plots can be be constructed either from half or full spectra
Vibration Vector
•
A vibration vector plotted in the transducer response plane
•
1x vector is 90 mic pp /220o
•
Zero reference is at the transducer angular location
•
Phase angle increases opposite to direction of rotation

58. Polar Plot
•
Polar plot is made up of a set of vectors at different speeds.
•
Vector arrow is omitted and the points are connected with a line
•
Zero degree is aligned with transducer location
•
Phase lag increases in direction opposite to rotation
•
1x uncompensated Polar Plot shows location of rotor high spot relative to transducer

59. •
This is true for 1x circular orbits and approximately true for 1x elliptical orbits
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8/06/2011
Shaft Orbit Plots (II)
Not- 1X Compensation of an Orbit
•
At Left orbit is the uncompensated orbit
•
At right is the same orbit with the 1X component removed
•
The remaining vibration is primarily 1/2X from a rub
Measurement of peak-to-peak amplitude of an Orbit
X transducer measurement axis is drawn together with perpendicular lines that are
tangent to maximum and minimum points on the orbit

60. Direction of Precession in Orbits
•
In the orbit plot shaft moves from the blank towards the dot. In the plot on left the inside
loop is forward precession
•
In the right orbit the shaft has reverse precession for a short time at the outside loop at
bottom
Effect of Radial Load on Orbit Shape
•
•
Orbits are from two different steam turbines with opposite rotation. Both machines are
experiencing high radial loads
Red arrows indicate the approximate direction of the applied radial load.

61. •
Red arcs represent the probable orientation of the bearing wall
Deflection Shape of Rotor Shaft
•
When keyphasor dots of simultaneous orbits at various bearings along the length of the
rotor are joined an estimate of the three dimensional deflection shape of the rotor shaft
can be obtained
* This is a rigidly coupled rotor system
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8/05/2011
Shaft Orbit Plots (I)
The Orbit
•
The orbit represents the path of the shaft centerline within the bearing clearance.
•
Two orthogonal probes are required to observe the complete motion of the shaft within.

62. •
The dynamic motion of the shaft can be observed in real time by feeding the output of
the two orthogonal probes to the X and Y of a dual channel oscilloscope
•
If the Keyphasor output is fed to the Z axis, a phase reference mark can be created on
the orbit itself
•
The orbit, with the Keyphasor mark, is probably the most powerful plot for machinery
diagnosis
Precession
Once a gyroscope starts to spin, it will resist changes in the orientation of its spin axis.
For example, a spinning top resists toppling over, thus keeping its spin axis vertical. If
atorque, or twisting force, is applied to the spin axis, the axis will not turn in the direction
of the torque, but will instead move in a direction perpendicular to it. This motion is called
precession. The wobbling motion of a spinning top is a simple example of precession.
The torque that causes the wobbling is the weight of the top acting about its tapering
point. The modern gyroscope was developed in the first half of the 19th cent. by the
Construction of an Orbit
•
XY transducers observe the vibration of a rotor shaft
•
A notch in the shaft (at a different axial location) is detected by the Keyphasor
transducer.
•
The vibration transducer signals produce two time base plots (middle) which combine
into an orbit plot (right)

63. Probe Orientation and the Orbit Plot
•
On the left side, when the probes are mounted at 0o and 90oR, the orbit plot and
oscilloscope display show the same view.
•
On the right, when the probes are mounted at 45oL and 45oR, the orbit plots are
automatically rotated
•
The oscilloscope, however, must be physically rotated 45oCCW to display the correct
orbit orientation

64. Examples of 1X and Subsynchronous Orbits
•
Orbit at left shows subsynchronous fluid-induced instability. Note the multiple keyphasor
dots because the frequency is not a fraction of the running speed
•
The orbit at right is predominantly 1X. The keyphasor dots appear in a small cluster
indicating dominant 1X behavior
Slow Roll Vector Compensation of 1X Filtered Orbit

65. •
•
Slow roll vector compensation can considerably change the amplitude and phase of the
orbit
Slow roll vectors of X= 1.2 mil pp /324oand Y= 1.4 mil pp /231o
Slow roll Waveform Compensation of a Turbine Orbit
Note how compensation makes the orbit (right) much clearer

66. Posted by Fajar at 12:49 PM 0 comments
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8/04/2011
Full Spectrum Plots
Full Spectrum
•
Half Spectrum is the spectrum of a WAVEFORM
•
Full Spectrum is the spectrum of an ORBIT
•
Derived from waveforms of two orthogonal probes
–
These two waveforms provide phase information to determine direction of precession at
each frequency
–
For phase accuracy they must be sampled at same time
•
Calculated by performing a FFT on each waveform
•
These FFT’s are subjected to another transform
–
Data converted to two new spectra – one for each direction of precession – Forward or
Reverse
–
Two spectra are combined into a single plot
Forward to the right, Reverse to the left
Calculation of Full Spectrum Plot

67. First
Waveform and its half spectrum
Second
Waveform and its half spectrum
Combined orbit and its full spectrum

68. Circular Orbits and Their Full Spectra
Forward Precession
Spectrum on forward side of plot
<--
Reverse Precession
Spectrum on reverse side of plot
Direction of rotation – CCW
<-- Forward Precession
Spectrum on forward side of plot
Direction of rotation – CW

69. <-- Reverse Precession
Spectrum on reverse side of plot
Direction of rotation - CW
Full Spectrum of Elliptical Orbit
Orbit is generated by two counter rotating vectors
Forward spectrum length is twice the length of forward rotating vector
Reverse spectrum length is twice the length of reverse rotating vector
Major axis of ellipse = a +b
Minor axis of ellipse = a - b
Original orbit cannot be reconstructed from full spectrum because there is no phase
information.

70. 3 possible orbits are shown
Circular & Elliptical 1x Orbits
•
Direction of precession is indicated by dominant line of “Forward” and “Reverse”
components.
•
Flatness of ellipse is determined by the relative size of forward and reverse components
•
When orbit is circular there is only one spectrum line
•
When orbit is a line the spectrum components are equal.
•
Therefore, the smaller the difference between components, the more elliptical the
orbit.

71. Orbit and Spectrum of a ½x Rub
•
Orbit and spectrum of a steam turbine with a ½ x rub
•
Full spectrum clarifies the complex orbit which is a sum of ½ x, 1x and their harmonics.
•
From the ratio of forward ad reverse components
•
1x is the largest, forward and mildly elliptical
•
½ x and 2x orbits are nearly line orbits
•
Small component of 3/2 x is third harmonic of ½ x fundamental
Half and Full Spectrum Display of a ½ x Rub

72. Differentiating ½ x Rub and Fluid Instability from Full Spectrum Plots
•
Half and full spectrum display of a ½ x rub (red data) and fluid induced instability (blue data)
•
Note similarity in appearance of the two half spectrum plots
•
The full spectrum plots clearly show the difference in the subsynchronous vibration
–
The ½ x rub orbit is extremely elliptical – small difference between forward and reverse
components
–
The fluid induced instability orbit is forward and nearly circular – large difference between
forward and reverse 1x and ½ x components.
•
The unfiltered orbits are at the bottom
Full Spectrum Cascade Plot of Machine Start Up
•
Horizontal axis represents precession frequency
•
Rotor speed is to the left and amplitude scale is on the right
•
Order lines drawn diagonally from the origin show vibration frequencies that are proportional
to running speed

73. •
Display of spectra plots taken at different speeds during start up
•
Base of each spectrum is the rotor speed at which the sample was taken
•
Diagonal lines are “Order” lines. Usually 1x, 2x and ½ x are plotted
•
Resonances and critical speed can be seen on 1x diagonal line
•
Sudden appearance of ½ x indicates rub which can produce harmonics.
•
Phase relationships cannot be seen on cascade plot.
•
Many harmonics at low speed usually due to scratches on shaft
Horizontal ellipse shows rub second balance resonance (critical)
Vertical ellipse shows ½ x rub frequency is almost equal to first critical. Slight shift to right is
due to stiffening of rotor system from rub contact.

74. Full Spectrum Waterfall Plot
•
Displays spectra with respect to time
•
Used for correlating response to operating parameters
•
Time on left and Running Speed on right. Amplitude scale is at extreme right
•
•
Plot of compressor shows subsynchronous instability whenever suction pressure is high
(red). 1x component is not shown on plot.
Full spectrum shows subsynchronous vibration is predominantly forward.

75. Waterfall of Motor with Electrical Noise Problem
•
High vibration at mains frequency (60 Hz) during start up (red). 1x is low.
•
Vibration reduces when normal speed and current are reached (green)
•
When motor is shut down (blue) 60 Hz component disappears suddenly.
•
1x component reduces gradually with speed.
Summary
•
Conventional spectrum is constructed from the output waveform of a single transducer
•
Full Spectrum is constructed from the output of a pair of transducers at right angles.
–
Displays frequency and direction of precession
–
Forward precession frequencies are shown on right side
–
Reverse Precession frequencies are shown on left side

76. •
Full spectrum is the spectrum of an orbit
–
Ratio of forward and reverse orbits gives information about ellipticity and direction of
precession
–
However, there is no information about orientation of orbit
•
Cascade and Waterfall plots can be be constructed either from half or full spectra
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8/03/2011
Half Spectrum Plots
Spectrum Plot-1
•
Machines can vibrate at many different frequencies simultaneously 1x, 2x, 3x, vane
passing etc.
Timebase and orbit have frequency information but only a couple of harmonics can be
identified – impossible to identify nonsynchronous frequencies
•
•
Using an analog tunable analyzer the amplitude and phase at each individual frequency
can be identified but only one at a time.
–
All frequencies cannot be seen simultaneously.
–
Trend changes in individual frequencies cannot be followed
–
Each frequency sweep may take one minute during which short duration transient events
may be missed
•
A Spectrum Plot by a FFT Analyzer shows all frequencies instantaneously.
Spectrum Plot-2
•
Spectrum plot is the basic display of a Spectrum Analyzer. It the most important plot for
diagnosis
•
Spectrum plot displays the entire frequency content of complex vibration signals in a
convenient form.
–
It has frequency on X-axis and amplitude on Y-axis
–
It is constructed from sampled timebase waveform of a single transducer – displacement,
velocity or acceleration

77. •
Fast Fourier Transform (FFT) calculates the spectrum from the sample record which
contains a specific number of waveform samples
•
Spectrum plots can be used to identify harmonics of running frequency, rolling element
bearing defect frequencies, gear mesh frequencies, sidebands
Periodic motion with more than one frequency
Above waveform broken up into a sum of harmonically related sine waves
Illustration of how the previous signal can be described in terms of a frequency spectrum.
Left
- Description in time domain
Right
- Description in frequency domain
Spectrum Frequency as a Function of Pulse Shape

78. Construction of Half Spectrum Plot - 1
•
Raw timebase signal (red) is periodic but complex.
•
Fourier transform is equivalent to applying of a series of digital filters
•
Filtered frequency components are shown as sine waves (blue)
•
Phase for each signal can be measured with respect to trigger signal
•
We can see components’ amplitude, frequency and phase
Construction of Half Spectrum Plot - 2
•
•
If we rotate the plot so that the time axis disappears we see a two dimensional spectrum
plot of amplitude v/s frequency
Component signals now appear as series of vertical lines.

79. •
Each line represents a single frequency
•
Unfortunately, the phase of the components is now hidden.
•
It is not possible to see phase relationships in spectrum plot.
These plots show why it is impossible to guess the frequency content from the waveform.
Vertical lines in top plot show one revolution
It is clear that 2x and higher frequencies are present
But 3x and 6x could not be predicted from the waveform.
A Fourier spectrum shows all the frequencies present
•
Linear and Logarithmic Scaling
Amplitude scaling can be Linear or Logarithmic
•
Logarithmic scaling is useful for comparing signals with very large and very small
amplitudes.
–
Will display all signals and the noise floor also

80. •
–
•
–
•
However, when applied to rotating machinery work
Log scale makes it difficult to quickly discriminate between significant and insignificant
components.
Linear scaling shows only the most significant components.
Weak, insignificant and low-level noise components are eliminated or greatly reduced in
scale
Most of our work is done with linear scaling
Illustration of Linear and Log scales
•
Log scale greatly amplifies low level signals
•
It is impossible to read 1% signals in linear scale
•
It is very easy to read 0.1% signals on the log scale
Limitations of Spectrum Plots
•
FFT assumes vibration signal is constant and repeats forever.
•
Assumption OK for constant speed machines .
–
inaccurate if m/c speed or vibration changes suddenly.
•
FFT calculates spectrum from sample record
–
Which has specific number of digital waveform samples

81. –
FFT algorithm extends sample length by repeatedly wrapping the signal on itself
–
Unless number of cycles of signal exactly matches length of sample there will be
discontinuity at the junction
–
This introduces noise or leakage into the spectrum
•
This problem is reduced by “windowing”
–
Forces signal smoothly to zero at end points
–
Hanning window best compromise for machinery work
Effect of Windowing
•
Figure shows a timebase plot with a mixture of 1/2x and 1x frequencies.
Two examples of half spectrum plots are shown below
•
•
Without window function the “lines” are not sharp and widen at the bottom
This “leakage” is due to discontinuity at sample record ending
•
When “Hanning” window is applied to the sample record 1/2x spectral line is narrower
and higher

82. Shaft Orbit Plots (I)
The Orbit
•
The orbit represents the path of the shaft centerline within the bearing clearance.
•
Two orthogonal probes are required to observe the complete motion of the shaft within.
•
The dynamic motion of the shaft can be observed in real time by feeding the output of
the two orthogonal probes to the X and Y of a dual channel oscilloscope
•
If the Keyphasor output is fed to the Z axis, a phase reference mark can be created on
the orbit itself
•
The orbit, with the Keyphasor mark, is probably the most powerful plot for machinery
diagnosis
Precession
Once a gyroscope starts to spin, it will resist changes in the orientation of its spin axis.
For example, a spinning top resists toppling over, thus keeping its spin axis vertical. If
atorque, or twisting force, is applied to the spin axis, the axis will not turn in the direction
of the torque, but will instead move in a direction perpendicular to it. This motion is called
precession. The wobbling motion of a spinning top is a simple example of precession.
The torque that causes the wobbling is the weight of the top acting about its tapering
point. The modern gyroscope was developed in the first half of the 19th cent. by the
Construction of an Orbit
•
XY transducers observe the vibration of a rotor shaft
•
A notch in the shaft (at a different axial location) is detected by the Keyphasor
transducer.
•
The vibration transducer signals produce two time base plots (middle) which combine
into an orbit plot (right)

83. Probe Orientation and the Orbit Plot
•
On the left side, when the probes are mounted at 0o and 90oR, the orbit plot and
oscilloscope display show the same view.
•
On the right, when the probes are mounted at 45oL and 45oR, the orbit plots are
automatically rotated
•
The oscilloscope, however, must be physically rotated 45oCCW to display the correct
orbit orientation

84. Examples of 1X and Subsynchronous Orbits
•
Orbit at left shows subsynchronous fluid-induced instability. Note the multiple keyphasor
dots because the frequency is not a fraction of the running speed
•
The orbit at right is predominantly 1X. The keyphasor dots appear in a small cluster
indicating dominant 1X behavior
Slow Roll Vector Compensation of 1X Filtered Orbit

85. •
•
Slow roll vector compensation can considerably change the amplitude and phase of the
orbit
Slow roll vectors of X= 1.2 mil pp /324oand Y= 1.4 mil pp /231o
Slow roll Waveform Compensation of a Turbine Orbit
Note how compensation makes the orbit (right) much clearer

86. Not- 1X Compensation of an Orbit
•
•
•
At Left orbit is the uncompensated orbit
At right is the same orbit with the 1X component removed
The remaining vibration is primarily 1/2X from a rub
Measurement of peak-to-peak amplitude of an Orbit
X transducer measurement axis is drawn together with perpendicular lines that are
tangent to maximum and minimum points on the orbit

87. Direction of Precession in Orbits
•
•
In the orbit plot shaft moves from the blank towards the dot. In the plot on left the inside
loop is forward precession
In the right orbit the shaft has reverse precession for a short time at the outside loop at
bottom
Effect of Radial Load on Orbit Shape
•
•
•
Orbits are from two different steam turbines with opposite rotation. Both machines are
experiencing high radial loads
Red arrows indicate the approximate direction of the applied radial load.
Red arcs represent the probable orientation of the bearing wall

88. Deflection Shape of Rotor Shaft
•
When keyphasor dots of simultaneous orbits at various bearings along the length of the
rotor are joined an estimate of the three dimensional deflection shape of the rotor shaft
can be obtained
* This is a rigidly coupled rotor system
Bode and Polar Plot
Vibration Vector
•
•
•
•
A vibration vector plotted in the transducer response plane
1x vector is 90 mic pp /220o
Zero reference is at the transducer angular location
Phase angle increases opposite to direction of rotation
Polar Plot

89. •
Polar plot is made up of a set of vectors at different speeds.
•
Vector arrow is omitted and the points are connected with a line
•
Zero degree is aligned with transducer location
•
Phase lag increases in direction opposite to rotation
•
1x uncompensated Polar Plot shows location of rotor high spot relative to transducer
•
This is true for 1x circular orbits and approximately true for 1x elliptical orbits
Bode Plot and Polar Plot Show the Same Detail
•
•
Bode’ Plot displays the same “vibration vector data” as the Polar Plot
Vibration amplitude and phase are plotted separately on two plots
with speed on the
horizontal axis.

90. Effect of Slow Roll Compensation
•
•
•
Slow roll compensation removes slow roll runout from filtered vibration
What remains is mainly the dynamic response
Compensated vector has zero amplitude at the compensation speed
Detecting Resonance with Bode & Polar Plots
•
In a Bode plot balance resonance is indicated by peak amplitude and sharp, significant
change of phase at the frequency of the peak.
On Polar plot rotor modes will produce large, curving loops.Small system resonances
are more easily visible as distinctive small loops