fault identification and monitoring in rolling element bearing
DESCRIPTION
fault identification by using vibration analysisTRANSCRIPT
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FAULT IDENTIFICATION AND MONITORING
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Condition monitoring
Topics:
• Introduction
• Types of Condition Monitoring
• Different types of predictive Maintenance
• Vibration Condition Monitoring
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Introduction
• Approximately “half of all operating costs” in most processing
and manufacturing operations can be attributed to maintenance.
• Machine condition monitoring and fault diagnostics
– the field of technical activity in which selected physical
parameters, associated with machinery operation, are observed for
the purpose of determining machinery integrity.
• The ultimate goal in regard to maintenance activities is to
schedule only what is needed at a time, which results in
optimum use of resources.
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Need of Monitoring
• Demand for economic design, higher power density
• Lighter flexible designs – highly stressed machinery
• Cost of Downtime enormous
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Maintenance Regimes
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Types of Maintenance
• Periodic preventive maintenance
• Predictive maintenance
• Proactive maintenance
• Reactive maintenance
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Introduction
Predictive
Condition Monitoring
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Maintenance Regimes
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• Criticality of inspected part/machine/process
• Offline inspections / online inspections
• Sensitivity of faults – parameter to monitor
• Optimum inspection interval
Issues of Monitoring
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Techniques for Fault Detection
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Visual inspection
Cost effectiveOptical assistanceLow cost aides, e.g. Borescope, Fibrescope etc.Dye penetrant (for surface crack)
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Infrared Thermography
• Faults – accompanied by unexpected change in temperature
• E.g. overhauling of coupling, motor bearings, electrical connections
• Temperature changes much before perceptible physical damage
• Thermal imaging of the system
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Infrared Thermography• One state Electricity Board in India – using for power transmission
Lines (thermal imaging cameras (29 nos)• Railways – use for monitoring of overhead power lines along railway
tracks (overhead line switch)• Many transmission authorities in the West use helicopter patrolling to
patrol thousands of joints in transmission lines.• High voltage/high current system: I2R effect• 31 systems are recently ordered to a European company by Power
Transmission division of Korea.• Used for Boiler Insulation wear & erosion/blocking of boiler tubes.• One European electrical traction railway operator uses thermal energy
system to monitor condition of overhead lines to detect overheating clamped connections – preventive maintenance.
• Detection of single fault paid for cost of camera
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• Eddy Current testing
• Electrical Resistance Testing
• Magnetic Particle Testing
• Dye Penetration Testing
• Resonance Testing
• Ultrasonic Testing
• Visual Examination
Surface and Internal Defect detection
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EARLY BIRD??
Wear Debris Analysis
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Wear Debris Analysis
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• Vibration Monitoring– Time domain (waveform) measurements– Frequency domain representation of vibration signal– Waterfall plots, Spectrum Cascade, Full Spectrum– Quefrency Domain Signal Analysis and other signal
representation formats • Wavelet Transforms
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• Almost all faults show themselves up in a changed vibration behavior
• For most structural and rotor parts….gears, bearings, rotors, belts, cracks, couplings etc
• Vibration is very sensitive to fault severity• Machine never required to shut down,
stopped and inspected….• The process of vibration measurement is
online…. continuous and convenient • Non-intrusive, nondestructive.
Why Vibration Monitoring?
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• Vibration or Process Parameter Monitoring???
• Offline inspections• Most faults show up in vibration response• Vibration Monitoring: convenient and most
suitable to online diagnostics
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Vibration based methods
Convenient & on-line
For most structural and rotor parts
Fault Detection through variety of signals analysis: e.g., TD, FD, Cepstrum, Wavelet, HFRT etc.
For gears, bearings, rotors, belts, cracks, couplings etc.
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Waterfall, Trend Plot, Spectrum Cascade, Wavelet Transform, chaos
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Machines are classified into four groups:
K – small machines upto 15kW
M – medium machines upto 75 kW or upto 300kW on special foundations
G – large machines with speeds below the foundation natural frequency
T – large machines with operating speeds above the foundation naturalfrequency e.g., turbomachinery
Vibration criterion chart - VDI 2956/1964
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Quality judgment of vibrations severity of large machines
(ISO/IS3945)
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General Machinery Vibration Severity Chart
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Waterfall, Trend Plot, Acoustic Emission, Wavelet Transform
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Time domain techniques:
sometimes useful information from raw data
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Time domain information:mostly rich in content, little in information
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Various parameters quantifying the waveform
dtxT
xT
average ∫=0
1dttx
Tx
T
RMS ∫=0
2 )(1
peak (or maximum) value
peak to peak value
average absolute value
RMS (root mean square) value
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Machines are classified into four groups:
K – small machines upto 15kW
M – medium machines upto 75 kW or upto 300kW on special foundations
G – large machines with speeds below the foundation natural frequency
T – large machines with operating speeds above the foundation natural frequency
e.g., turbomachinery
Vibration criterion chart - VDI 2956/1964
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• Kurtosis: indicates impulsiveness of the signal
f(x) is the probability density function of the instantaneous amplitude, x(t), at time t,
is the mean value and σ is the standard deviation of x(t).
• Useful for faults such as spalling on balls/rollers and cracked races in rolling element bearings leading to impulses in time domain waveforms that can be picked up by large values of the kurtosisk < 3.5 good bearing k>3.5 bad bearing
Other time domain measurements
∫∞
∞−
−= dxxfxxk )()(1 44σ
x
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Spike energy measurement system
Mainly used for measurement of bearing faults
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Envelop Analysis
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Shaft orbit
Faults such as misalignment, bearing stability, unbalance
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Decomposition of time domain periodic signal in frequency domain
Frequency (Hz)
0 10 20 30 40 50 60A
mpl
itude
0.0
0.2
0.4
0.6
0.8
1.0
1.2
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Fourier Analysis
To find different frequency componentsAmplitudes of different components
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Frequency domain measurement• Just 16% increase
in peak to peak amplitude
100% increase in high frequency amplitude
Frequency Domain measurements picks up fault symptoms early
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Spectral analysis of response of misaligned rotor system
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Case studies Compressor of a process industry
Casing vibration from velocity pickup
Using frequency domain data in different directions for fault identification
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Case studies… contd.Process High Speed Air Compressor
vibration spectrum
High frequency range
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Process Air Compressor vibration spectrum
Low frequency range
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Two identical speed increasing Gear Boxes
High frequency region reveals problem in one of the gear boxes
Comparing the two
vibration spectra
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Axial flow air compressor
vibration frequency spectrum
Diagnosis of fault: Stator blades of some stages curved in.
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Spectral analysis of geared rotors to assess faulty gears
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High Frequency Resonance Technique (Shiroishi et al.)
MFRT utilizes the fact that much of the energy resulting from a defect impact manifests itself in the higher resonant frequencies of the system. Defect frequency if periodic, presents in the spectra of the enveloped signal. ALE enhances the spectrum of enveloped signal by reducing broadband noise
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HFRT with ALEBearing Fault Identification
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TSA – Time Synchronous Average
EFFECTIVENESS AND SENSITIVITY OF VIBRATION PROCESSING TECHNIQUES FOR LOCAL FAULT DETECTION IN GEARS by G. Dalpiaz, A. Rivola And R. Rubini Mechanical Systems and Signal Processing (2000) 14(3), 387}412
By synchronizing the sampling of the vibration signal with the rotation of a particular gear and evaluating the ensemble average over many revolutions with the start of each frame at the same angular position, a signal called time-synchronous average (TSA) is obtained, which in practice contains only the components which are synchronous with the revolution of the gear in question. As a matter of fact, this process strongly reduces the effects of all other sources, including other gears, and the noise
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Gear Teeth Mesh Forces
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First gear teeth mesh
Second gear teeth mesh
Time (sec)
Time for 1 revolution of gear
xcos(ωt)Gear blank digs into pinion and withdraws once in one rotation xacos(ωat)
Time (sec)
Time for 1 revolution of gear
First gear teeth mesh
Time (sec)
Time for 1 revolution of gear
ttxxtx aa ωω cos)]cos([)( +=
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Amplitude Modulation in Gear Pair
ttxxtx aa ωω cos)]cos([)( +=
txtxtxttxtxtx aa
aa
aa )cos(2
)cos(2
cos)]cos(coscos[)( ωωωωωωωω ++−+=+=
carrier frequencies i.e.,gear mesh frequency - ω
modulation frequency i.e., rotational speed of the gear - ωa
txtx ωcos][)( = With perfect gearing condition
With imperfect gearing condition
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txtxtxtx aa
aa )cos(
2)cos(
2cos)( ωωωωω ++−+=
Hz750 Hz 25 == ωωa
ωωωωωω 3 ,2 , ,....3 ,2 , aaa
SPECTRUM
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• Cepstrum is defined as inverse Fourier transform of the logarithm of the power spectrum
• If one or more periodic structures appear in a spectrum, each one appear as a distinct peak in cepstrum
{ })(log)( 1 ωτ XSFc −=
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Cepstrum of gear box vibration signal
Cepstrum for Spectrum Quefrency for Frequency Rahmonics for Harmonics Gamnitude for Magnitude
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Example of cepstrum of gear box vibration signal
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Quefrency domain analysis
Mechanical Vibrations: S S Rao
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CONCLUSIONS .. Contd…
• Spectral analysis of gear faults gives a rather confusing picture
• Cepstrum analysis is better suited in such type of faults and gives a clearer picture
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Other signal representation formats
Waterfall plot
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Trend plots
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Wavelet Transform
• Signal Analysis of Vibration Data – KEY for Fault Detection & Monitoring
• Time Domain & Fourier Analysis has some inherent disadvantages
• Wavelet Transforms scores over traditional techniques for transient signals
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Fourier Analysis
Breaking down a periodic signal into its constituent sinusoids of different frequencies
∑−
=
−=
1
0
2
)(1)(N
n
Nnkj
enfN
kFπ
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Short Time Fourier Transform
Analyzing a small section of the signal at a time with Fourier Transform
Same Basis Functions (sinusoids) are used
Window size is fixed (uniform) for all frequencies
so all spectral estimates have same (constant) bandwidth
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Can we have something better?
• NEED?– Varying window size
• To determine more accurately either time or frequency
Wavelet Analysis – A windowing technique with variable sized regions
Allows use of long time intervals where we need more precise low-frequency information
& use of shorter regions where we want high-frequency information
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Wavelet Transform Fourier Transform –
signal broken into sinusoids
that are global functions
Wavelet Transform –
signal broken into a series of local basis functions
called wavelets, which are scaled and shifted versions of the original (or Mother) wavelet
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• Wavelet means a small wave
• The function that defines a wavelet integrates to zero
• It is local in the sense that it decays to zero when sufficiently far from its center
• It is square integrable, i.e., it has finite energy
Wavelet
∫∞
∞−
= 0)( dttψ
∫∞
∞−
∞<dtt 2|)(|ψ Mother Wavelet
Morlet Wavelet
Scaling & shifting
Son/daughter wavelets
⎟⎟⎠
⎞⎜⎜⎝
⎛= − tet t
2ln2cos)(
2
πψ
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WaveletsSignals with sharp sudden changes could be better
analyzed with an irregular wavelet than with a smooth sinusoid
In other words, local features can be better captured with wavelets which have local extent
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Continuous Wavelet Transform
Sum over all time of the signal multiplied by scaled and shifted versions of the wavelet
Ensures energy stays same for all s&b
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Relation between scale & frequency
Fa = pseudo frequency ( for the scale value s )Δ = sampling times = ScaleFc = central frequency of mother wavelet in Hz.
Central frequency of the Morlet wavelet is 0.8125HzIt is the freq. that maximizes the FFT of the wavelet or is the
leading dominant frequency of the wavelet
Δ=
sF
F ca
Matlab Help Module
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Case Studiesa) Rotor Stator Rub
•
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Rotor-Stator Rub Test Setup
Rotor-stator arrangement
Rotor Disc Casing (Stator)
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Experimental Results
NO RUB
RUB
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CWT of the SignalsNO RUB
RUB
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PARTIAL/INTERMITTENT RUB
Partial
RUB
NO RUB
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CWT of Partial Rub
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ROTOR RUB DETECTION
• Localized (in time) rubbing is detected using wavelet transform
• Intermittent rub is better detected• High frequency components are also
localized in a cycle of rotation
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Case Studies - b) Rotor Crack
Breathing behaviour of crack
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Finite Element Model
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Cross coupled Stiffness Variation
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Response of Cracked Rotor w/o Torsional Excitation
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Response of Cracked Rotor with Transient Torsional Excitation at ϕ=00 during 5th cycle
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CWT of the Torsional Vibration
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CWT of Lateral Response of Cracked Rotor with Transient Torsional
Excitation
at ϕ=00
during 5th cycle
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Response of Cracked Rotor with Transient Torsional Excitation at ϕ=1800 during 5th cycle
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CWT of Lateral Vibration Response
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CWT of Lateral Vibration Response
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Sensitivity of CWT coefficients to crack depth
5% crack depth
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Novel way to detect crack
• Short duration transient excitation can be applied so that the rotor is not stressed
• Good use of the advantages of Wavelet Transform for bringing out transient response features of crack
• Good use of nonlinear nature of crack breathing making the detection foolproof
• Highly sensitive to depth of crack
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Gear Fault detection using WaveletsDifficult to evaluate the spacing and evolution of sideband families
Several gear pairs other mechanical components Contribute to the overall vibration.
Local faults in gears produce impacts transient modifications in vibration signals.
Signals have to be considered as non-stationary
Most of the widely used signal processing techniques are based on the assumption of stationarity and globally characterize signals.
Not fully suitable for detecting short-duration dynamic phenomena.
Wavelet transform (WT) is better suited in such situations.
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From the above WT map of TSA vibration, it is possible to clearly distinguish the transient effects introduced by the cracked tooth.
Moreover, such a procedure makes it possible to localize the damage in most of the cross-sections.
Experimental study conducted by Dalpiaz
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WAVELET TRANSFORM
• Wavelet Transform is an excellent tool for detection of non-stationary vibration signals
• Features that are obscured during Fourier Transformation are revealed with better clarity
• Time information is preserved
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Acoustic Emission Technique
AE is the phenomena of transient elastic wave generation due to a rapid release of strain energy caused by a structural alteration in a solid material under mechanical or thermal stresses. The most commonly measured AE parameters are peak amplitude, counts and events of the signal.
Some studies indicate that Acoustic emission measurements are better than vibration measurements and can detect a defect even before it appears in vibration acceleration.
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Results on test rig simulating very slow speed rolling bearings of Air Preheater (1.3-1.4rpm)
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M.Tech. Thesis– Akhil Agrawal (NTPC), ITMMEC, IITDelhi 2006
AE Technique – useful for detecting fault initiation
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Rotor Faults & Typical Vibration FeaturesMisalignmment:
Strong 1X and 2X component along with the other higher harmonics of the rotating speed is the typical characteristic of misalignment.
Subharmoic resonance at ½ & ⅓ of critical speeds.
Lateral-torsional & Lateral-axial coupled vibrations.
Multi lobed orbits, with outer loops.
Rotor rubbing can exhibit very rich form of the periodic, quasi-periodic and chaotic vibrations.
Subharmonics chiefly at 1/2X, 1/3X, and 2/3X along with the higher harmonics mainly at 2X, 3/2X and 3X of rotor speed is observed.
Rubbing result in to backward whirling orbits.
Instability zones at 1/2, 1/3, 2/3, 1, 3/2, and 2 of the critical speeds.
Rotor-stator Rub:
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Rotor Faults & Typical Vibration FeaturesCrack:
Steady state response mainly with components 2X and 3X of the rotating speed, but sometimes, 5X is also observed.
Subharmonic resonances at ½ & ⅓ of ωcr during cost up or down.
Lateral-torsional-axial coupled vibrations.
Inner looped and multi lobed orbits near the fraction of the critical speeds.
Instability zones at 1/3, 1/2, 1 and 2 of the critical speeds. Asymmetry:
Steady state response with frequency component 2X of the rotating speed is observed.
Subharmonic resonances at only ½ of ωcr during cost up or down.
Orbits with two inner loops at subharmonic resonance.
Instability zones at 1/2, 1 and 2 of the critical speeds.
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Vibration Characteristics Misalignment Crack Asymmetry Rub
Steady state response
1X response Yes Yes No No
Sub-harmonics No No No ½X, ⅓X, ⅔X, & even lower
Super-harmonics Mainly 2X; other higher harmonics 2X & 3X Only 2X 2X, 3/2X , 3X, &
even higher
Transient responseResonance at ½ & ⅓ of critical
speed
Resonance at ½, & ⅓ of critical
speed
Resonance at ½ of critical speed Highly unstable
Instability zones No at ⅓, ½, 1 & 2 of the critical speeds
at ½, 1, 3/2, & 2 of the critical
speeds
at ⅓, ½, ⅔, 1, 3/2, & 2 of the critical
speeds
Orbital behaviour Multi lobed with external loops
Multi lobed with internal loops
Two loops at subharmonic resonances
Backward whirling orbit
Coupled vibrations
lateral-torisonal Yes Yes No Yes
lateral-axial Yes Yes No No
torsional-axial No Yes No No
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Multi fault identification
Investigators Faults investigated Fault separating feature/method
Muszynska (1989)
Crack and misalignment
Inner looped orbits for crack and outer looped orbits for misalignment
Imam (1989) Crack and misalignment
For crack, changes in magnitude of 2X vibrations and phase is more compared to the other components.
Chan (1995); Darpe (2002)
Crack and asymmetry
For crack, subharmonic resonances at ½ and ⅓ of the critical speed observed. Whereas for asymmetric shaft subharmonic resonance at only ½ the critical speed is observed.
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Multi fault identification
Investigators Faults investigated Fault separating feature/method
Darpe (2002) Crack and asymmetry
In the plot of peak of the response with unbalance angle, cracked rotor shows only one maxima and one minima, whereas asymmetric rotor shows two maxima and two minima.
Wen (2004) Crack and rubWavelet time-frequency maps for the cracked rotor are different from the cracked rotor with rubbing.
Prabhakar (2002)
Crack and misalignment
Continuous wavelet transform is more sensitive to the misalignment compared to crack.
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Fault Detection in Rolling Element Bearing Techniques:
(1) Vibration Based Methods:(a) Time Domain: Though parameters such as overall RMS level, crest
factor, probability density and kurtosis. Among these, kurtosis is the most effective.
(b) Frequency Domain: The direct vibration spectrum from a defective bearing may not indicate the defect at the initial stage. Some signal processing techniques are therefore, used. The high-frequency resonance technique is the most popular of these.
(2) Shock Pulse Method:The shock pulses caused by the impacts in the bearings initiate damped
oscillations in the transducer at its resonant frequency. Measurement of the maximum value of the damped transient gives an indication of the condition of rolling bearings. The maximum normalized shock value is a measure of thebearing condition.
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Fault Detection in Rolling Element Bearing
(3) Acoustic Based:(a) Sound pressure measurement(b) Sound intensity measurement(c) Acoustic emission (AE) measurement
AE is the phenomena of transient elastic wave generation due to a rapid release of strain energy caused by a structural alteration in a solid material under mechanical or thermal stresses. The most commonly measured AE parameters are peak amplitude, counts and events of the signal.
Acoustic emission measurement is proved to be better compared to other two methods in the group. Some studies indicate that these measurements are better than vibration measurements and can detect a defect even before it appears in vibration acceleration.
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Fault Detection in Rolling Element Bearing Techniques:
(1) Vibration Based Methods:(a) Time Domain: Though parameters such as overall RMS level, crest
factor, probability density and kurtosis. Among these, kurtosis is the most effective.
(b) Frequency Domain: The direct vibration spectrum from a defective bearing may not indicate the defect at the initial stage. Some signal processing techniques or trendings are therefore, used.
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Fault Detection in Rolling Element Bearing
(3) Acoustic Based:(a) Sound pressure measurement(b) Sound intensity measurement(c) Acoustic emission (AE) measurement
(2) Shock Pulse Method:Impacts in the bearings initiate damped oscillations
in the transducer at its resonant frequency.
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Vibration Monitoring• There is a strong negative correlation between the overall vibration level for a
bearing, and the expected life of that bearing.
• Put simply, the higher the overall vibration level to which the bearing is subjected,
then the shorter the expected life of the bearing.
• Second, it should be recognised that bearing vibration can be induced by applying
cyclical forces from two sources, either:
• From forces originating within the bearing (e.g. those due to impending bearing
failure), or
• From forces applied to the bearing from external effects.• Misalignment• Improper bearing installation• Rotor imbalance• Pump cavitation• Flow induced vibration, Etc.
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• Journal Bearings• Besides the forces of kinematic origin and friction forces in the journal
bearings, the forces act hat are the results of nonlinear interaction of thestatic load with the friction forces. These forces accompany the rotor self-oscillations in the bearings.
• The rotor self-oscillations in the journal bearings are very much alike thependulum oscillations of the rotor in relation to the equilibrium position inthe lowest point of the bearing. The rotor is shifted from the equilibriumposition by the friction forces and is returned in it by the gravity force. Thereason of this unstable equilibrium is the nonlinear dependence of thefriction forces from the thickness of the lubrication layer that grows whilethe rotor position deviates from the equilibrium position. The self-oscillationfrequency is the lesser the larger is the gap in the bearing, i.e. the more is thebearing's wear.
Vibration Monitoring
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• As a rule the rotor self-oscillation frequency changes abruptly from the RPM to
1/2 RPM but sometimes, with increasing the wear, to 1/3 RPM.
• The reason of the rotor self-oscillation can be not only its wear, but also the
decreased quality of lubricant or failure in feed lubrication.
• The self-oscillation can appear also in the rolling element bearings but only with
large wear.
• The frequency of the rotor self-oscillation in the rolling element bearings as a rule
coincides with the second order of the rotating frequency of the cage.
• The shock forces that act in the journal bearings can be of two types. A "dry"
shock with the disruption of the lubrication layer is very dangerous but it appears
very seldom and is accompanied with significant growth of high frequency
vibration.
Vibration Monitoring
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• "Hydraulic" shock does not disrupt the lubrication layer, but because of uneven
wear of the bearing in the loaded zone, where the thickness and the velocity of the
lubrication flow jump, the turbulent breakaway of the flow occurs. The moment of
the breakaway of the flow is sensed by the measuring system as a shock,
accompanied by an impulse increase of the high frequency vibration. Such shock
does not lead to fast destruction of the bearing but it is a cause of fast uneven wear.
• The friction forces in the journal bearing are rather stronger than in the rolling
element bearings but as the high frequency bearing vibration, when there is no
turbulence of the lubrication flow, is activated only by the boundary friction, the
random vibration of the journal bearing is significantly lower than in the rolling
element bearings.
Vibration Monitoring
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• Shock Pulse Analysis (SPA)• The SPA technique has been specifically developed for the
condition monitoring of rolling element bearings. The technique is based on the fact that any damage in rolling element bearings will cause mechanical impacts that will generate ultrasonic shock waves. The magnitude of these impacts is a measure of the condition of the bearings. The magnitude of impacts depends on impact velocity, which depends on defect size and bearings speed and size.
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The transducer of the shock pulse meter (SPM) is apiezoelectric accelerometer tuned mechanically andelectronically to a resonant frequency around 32kHz. The shock wave is propagated through thebearing housing, and when the shock pulse hits thetransducer, damped oscillations are initiated at theresonant frequency of the transducer. The amplitudeincrease of the damped resonant oscillation gives anindication of the condition of the rolling elementbearings. The transducer signal is processedelectronically to filter out low frequency vibrationssuch as inbalance, misalignment and other structure-related vibrations. The decibel (dB) unit is used tomeasure the shock value to accommodate a largerange of shock values of good and damagedbearings.
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• The bearing race surfaces will always have a certain degree of roughness. So,when a bearing rotates, this surface roughness causes mechanical impacts withrolling elements. The shock pulse value generated by good bearings due tosurface roughness has been found empirically to be dependent upon thebearing bore diameter and speed. This value, called initial value (dBi), issubtracted from the shock value of the test bearing to obtain a ‘normalizedshock pulse value’ (dBN). The digital shock pulse meter gives the readingdirectly in dBN. The shock pulse meter gives two values namely the‘maximum shock value’ (dBM) and the ‘carpet value’ (dBC), as shown inFigure 5.8.
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The maximum shock value is a measure of low rate (LR) impacts, and the carpetvalue is a measure of high rate (HR) impacts. HR impacts may exceed 1000 impactsper second and LR impacts may exceed 25 impacts per second. An increase in dBMvalue without an increase in dBC value is an indication of damaged bearings.Increase in both dBM and dBC value is an indication of lubrication problems.Manufacturers of SPM instruments supply a diagnostic table based on dBM anddBC.
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Pumps
Topics:
• Causes of excessive vibration
• Types of forces
• Measures
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Causes of excessive vibration
• Rotor unbalance (new residual impeller/rotor unbalance or
unbalance caused by impeller metal removal, wear)
• Shaft (coupling) misalignment
• Liquid turbulence due to operation too far away from the
pump best efficiency flow rate.
• Cavitations due to insufficient NPSH margin.
• Pressure pulsations from impeller vane – casing tongue (cut
water) interaction in high discharge pumps.
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Pumps vibration measurements
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Parameters of Condition monitoring
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Frequency ranges
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Diagnostic Paradigm
• Signal Based Diagnosis• Model Based Diagnosis
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r0(t) : previously measured undamaged system vibration
MODEL BASED DIAGNOSIS
r(t) : vibrations of the damaged system r(t)=r0(t)+Δr(t)
β: Vector representing fault parameters such as type, magnitude, location of the fault
e.g., for a transverse crack, β represents depth a and location n of the crack
Thus a fault induced change in the vibrational behavior is represented by virtual forces on the undamaged system
r0(t)r (t)
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Residual vibrations representing fault in the system is given as
Δr=r(t)-r0(t)
The equivalent (virtual) loads induce the change in the dynamic behavior of the undamaged linear model
If the vectorial difference Δr is found out, from the known system matrices, ΔF can be found, wherefrom the fault can be estimated.
To identify fault parameters, the difference between the virtual forces from measured data and theoretical fault model is minimised using the least square method
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Heuristic Methods
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Definition of Expert System
• A computing system capable of representing andreasoning about some knowledge rich domain, whichusually requires a human expert, with a view towardsolving problems and/or giving advice.– The level of performance makes it “expert.”– Some also require it to be capable of explaining its
reasoning.– Does not have a psychological model of how the
expert thinks, but a model of the expert’s modelof the domain.
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Expert System Developed in IIT Delhi• OLES (online expert system)• OSBUDD (operator support and backup data
display).• Uses knowledge base compiled by john S
Sohre.• Continuous online vibration and process data
can be acquired from any machine.• The diagnosis of the fault is almost
instantaneous.• The important vibration data be trended over
any interval of time.• Orbit plot, waterfall plot, can be plotted.• An integrated signal analysis toolbox is
provided.
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138Fig.6 Screen Snapshot of Frequency Domain Signal
Frequency Domain Signal
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141
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142Schematic of the system
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OSBUDD (Operator Support and Back Up Data Display)
Displays processed data in various format
Trend of important vibration parameters
Expert system diagnostic results
Provision of reviewing past data
Demo and Help for operator assistance
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Plots: Time DomainFrequency DomainTrend OrbitWaterfall
Analysis: Expert System DiagnosisSignal Processing
Assistance: DemoHelp
Backup Data Loader
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Expert SystemEach fault produces a typical frequency pattern (signature)
Sohre’s Database as knowledge base
Direction and type (shaft/brg) of predominant vibration taken into account
Expert system estimates probability of each fault, lists five most probable ones.
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• Advanced turbine fault diagnostics system:• Detection of eccentricity change in coupling,• Blade failure,• Bearing instability,• Steam whirl,• Rotor crack,• Rotor rubbing,• Temporary rotor bow,• Loose bearing pedestal,• Inclined position of bearing,• Electrical run-out,• Mechanical run-out,• Loose stator core in generator,• Change of imbalance at shutdown,• Radial bearing damage,• Inter turn short circuit in generator rotor, etc.
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Vibrations of Bearings
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• Force impulse when rolling element passes• Roughness will increase contact forces• Modulation due to varying transfer path• Slip
Roller bearings
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Defect roller bearing
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Defect roller bearing
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Roller bearingsFundamental frequencies
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Roller bearing spectrum
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B&K Application note:Detecting Faulty Rolling Element Bearings
Why do they fail?Rolling element bearings fail because of: manufacturing errors; improper assembly, loading, operation, or lubrication; or because of too harsh an environment.
How do they fail? Most failure modes for rolling element bearings involve the growth of discontinuities on the bearing raceway or on a rotating element.
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Vibration spectrum measured at a motor six weeks before a rolling element bearing burnt out.
Increase in two high frequency bands
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Measurement of overall vibration level
Measuring RMS acceleration lvel over a range of high frequencies (e.g. 1,000 Hz to 10,000 Hz) gives best results.
By plotting the measurement results over time the trend in vibration can be followed and extrapolated.Advantages:
• Quick • Simple • Low capital outlay • Single number result
Disadvantages: • Detects fewer faults • Detects faults later, close to failure
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Measurement
of crest factor
Advantages: • Quick • Simple • Low capital outlay
Disadvantages:• Prone to interference from other vibration sources • Does not detect as wide a range of faults as
Spectrum comparison
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Spectrum ComparisonAdvantages: • Detects a wide range of machine faults • Provides frequency information that can be used for fault diagnosis
• Same equipment can usually be used to do further fault diagnosis
Disadvantages: • Larger capital outlay
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Envelope AnalysisEnvelope spectrum showing a harmonic series of fout
(Outer race defect)
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Zoom Analysis
Zoom spectrum showing harmonics corresponding to the ball-pass frequency outer race. When the bearing was stripped down, eight months after the fault was first detected, a spall was discovered on
the outer race.
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Cepstrum AnalysisThe family of harmonics shows up in the cepstrum as a distinct peak whose quefrency corresponds to the frequency spacing of the harmonics. A number of rahmonics
are also present.
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Amplitude modulation
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Envelope detectionDemodulation
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Vibration of Gears
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• Gear tooth profile• Fluctuating tooth meshing force• Tooth mesh frequency and harmonics• Modulations give sidebands• Several stages – many frequencies
Healthy Gears
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Healthy Gears
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• Localised surface damage• Wear or inadequate lubrication• Tooth root cracks, missing tooth• Pitch error• Eccentricity
Typical defects
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169
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Defective gears
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Defective gears
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• Time domain methods• Spectral methods• Parametric spectral analysis• Time-Frequency domain• Cepstral methods
Signal analysis methods
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• Extract signal components cyclic with shaft rotation• Equal number of samples per revolution• Resample if necessary• Multistage gearboxes – Repeat STDA
Synchronised time domain averaging STDA
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• Remove expected (healthy) signal components• Suitable for gears
Residuals
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• AR-model prediction• Extract AR-model• Use AR-model as prediction filter• AR-model residual
Parametric spectral analysis
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• RMS-value• Peak-value• Kurtosis• Defect Severity Index
Machine condition indicators
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180
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• Surface damage on gear in truck gearbox
Example
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Upper: Healthy Lower: Defect
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Synchronised time domain averaging
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Extract Residual
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AR-model prediction filter
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• Kurtosis > 3
Kurtosis = 3.0
Kurtosis = 4.7
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• Gear meshing frequency• Sidebands• Synchronous time domain averaging• Residuals• Defect enhancement: AR-models etc• Defect severity
Summary
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SOME OTHER COMMON ROTOR FAULTS
FATIGUE TRANSVERSE CRACK
MISALIGNMENT
ROTOR RUB
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BREATHING OF CRACK
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STIFFNESS VARIATION OF CRACKED ROTOR DUE TO BREATHING
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( ) sinsin)()2(
coscos)2(
22
22
θβεωηωξηηωξωη
θβεωξωηξξωηωξ
mgmkcm
mgmkcm
+=+++−+
−=+−+−−
&&&&
&&&&
a) Uncracked Rotor
EQUATIONS OF MOTION
b) Asymmetric Rotor
( ) sinsin)()2(
coscos)2(
22
22
θβεωηωξηηωξωη
θβεωξωηξξωηωξ
η
ξ
mgmkcm
mgmkcm
+=+++−+
−=+−+−−
&&&&
&&&&
c) Cracked Rotor( )
sinsin)()2(
coscos)2(
22
22
θβεωηξωξηηωξωη
θβεωηξωηξξωηωξ
ηηξ
ξηξ
mgmkkcm
mgmkkcm
+=++++−+
−=++−+−−
&&&&
&&&&
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ESTABLISHED VIBRATION SYMPTOMS OF A CRACK
Instability for deeper cracks, for lightly damped rotors.
Frequency content
Subharmonic
Resonance
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Waterfall Plot
ωcr
1/2ωcr
1/3ωcr
(a)
Lateral Vibration Response
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Torsional Vibration
1/3ωtor
1/4ωtor
1/6ωtor
1/2ωtor(b)
(c)
1X 2X
3X
4X
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NEED: A reliable detection strategy !!
Transient response analysis
Coupling of Vibrations
Full Spectrum Analysis
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PEAK
RESPONSE
VARIATION
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Frequency spectra
Asymmetric Rotor
1/5th critical speed
1/3rd critical speed
1/2 critical speed
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Frequency spectra
Cracked Rotor
1/5th critical speed
1/3rd critical speed
1/2 critical speed
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Directionality of higher harmonic components for cracked rotor
Stiffness variation characteristic due to breathing is responsible for unique directionality of crack vibration response
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( )
0
sinsin)()2(
coscos)2(
22
22
=++++
+=+++++−+
−=+++−+−−
ukkkucum
mgmukkkcm
mgmukkkcm
uuu
u
u
ηξ
θβεωηξωξηηωξωη
θβεωηξωηξξωηωξ
ηξ
ηηηξ
ξξηξ
&&&
&&&&
&&&&
COUPLING OF LONGITUDINAL AND BENDING VIBRATIONS
To exploit
Non-linearity due to crack breathing
&
Coupling between Bending-longitudinal-Torsional vibrations
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RESPONSE OF CRACKED ROTOR TO
FOUR IMPULSES/ROTATION
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203Figure 8. Unbalance response of a cracked rotor (a/D=0.3) without torsional excitation. ω=22rad/sec.
Angle of rotation (degrees)
0 360 720
tors
iona
l res
pons
e,
θ (r
ad)
-2e-7
0e+0
2e-7
axia
l res
pons
e,
u (m
)
-2e-7
-1e-7
0e+0
Ampl
itude
0e+0
2e-8
4e-8
6e-8
8e-8
1e-7
Frequency (Hz)
10 20 30 40 50 60
Am
plitu
de
0e+0
2e-8
4e-8
6e-8
8e-8
1e-7
Am
plitu
de
0e+0
1e-6
2e-6
3e-6
4e-6
5e-6
horiz
onta
l res
pons
e,
z (m
)
-5e-6
0e+0
5e-6
verti
cal r
espo
nse,
y
(m)
-1.48e-4
-1.44e-4
-1.40e-4
-1.36e-4
Am
plitu
de
0e+0
1e-6
2e-6
3e-6
4e-6
5e-6
ω
2ω
ω 2ω
3ω
ω
2ω
ω2ω
4ω
3ω(a) (b)
(c) (d)
(e) (f)
(g) (h)
CRACKED ROTOR: UNBALANCE RESPONSE, NO TORSIONAL EXCITATION
Vertical
Horizontal
Axial
Torsional
.
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204
Ampl
itude
0e+0
5e-6
Angle of rotation (degrees)
0 360 720
tors
iona
l res
pons
e,
θ (r
ad)
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
axia
l res
pons
e,
u (m
)
-1.6e-7
-1.2e-7
-8.0e-8
-4.0e-8
0.0e+0
Ampl
itude
0.0e+0
2.0e-8
4.0e-8
6.0e-8
Frequency (Hz)
10 20 30 40 50 60
Ampl
itude
0.00
0.02
0.04
0.06
0.08
0.10
Ampl
itude
0.0e+0
5.0e-6
1.0e-5
1.5e-5
2.0e-5
horiz
onta
l res
pons
e,
z (m
)
-3e-5
-2e-5
-1e-5
0e+0
1e-5
2e-5
3e-5
ω
2ω
ω0
ω0+ω
ω0+2ω
ω0-ωω0-2ω
ω 2ω
ω0
ω0+ωω0-ω
ω
2ω
ωe
ω0ω0+ω
ω0+2ωω0-ωω0-2ω
ω0+2ωω0-2ω3ω
(a) (b)
(c) (d)
(e) (f)
(g) (h)
verti
cal r
espo
nse,
y
(m)
-1.55e-4
-1.50e-4
-1.45e-4
-1.40e-4
-1.35e-4
-1.30e-4
-1.25e-4
CRACKED ROTOR: UNBALANCE RESPONSE TO TORSIONAL EXCITATION
Vertical
Horizontal
Axial
Torsional
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COUPLING OF VIBRATIONS
CRACK INDICATORS
Resonance conditions: natural frequency component
Interaction between external excitation frequency and rotational frequency and its harmonics
- presence of sum and difference frequencies
- Horizontal component (natural freq.) - stronger
Sensitive to crack depth
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EXPERIMENTATION
Transient Response through Critical Speed
Variation of peak response
Unbalance phase
Slotted and fatigue cracked rotor
Response through subharmonic resonances
Response to impulse axial excitation
Presence of the coupling mechanism
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207Test rig with instrumentation
Proximeter A/D Card Computer
MotorController
Motor
Flexiblecoupling
Proximity Probe
Disk
BearingPedestal
Stopper
Non-rotating Bearing Guide
Exciter
Oscillator PowerAmplifier
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z
-0.06
-0.03
0.00
0.03
0.06
0 10 20 30 40 50 600.000
0.002
0.004
0.006
0.008
0.010
0 10 20 30 40 50 600.000
0.002
0.004
0.006
0.008
0.010
Frequency (Hz)0 10 20 30 40 50 60
0.00
0.01
0.02
0.03
0.04
0.05
Frequency (Hz)0 10 20 30 40 50 60
Ampl
itude
(mm
)
0.00
0.01
0.02
0.03
0.04
0.05
0 10 20 30 40 50 600.000
0.005
0.010
0.015
0.020
0 10 20 30 40 50 60
Ampl
itude
(mm
)
0.000
0.005
0.010
0.015
0.020
z
-0.02
-0.01
0.00
0.01
0.02
y
-0.02
-0.01
0.00
0.01
0.02
y
-0.04
-0.02
0.00
0.02
0.04
z
-0.04
-0.02
0.00
0.02
0.04
y
-0.06
-0.03
0.00
0.03
0.06
Ampl
itude
(mm
)Am
plitu
de (m
m)
Ampl
itude
(mm
)
Ampl
itude
(mm
)
(l) (m)
(d)(c)
(g) (h)
(a) (b)
(e) (f)
(j) (k)
Vertical Horizontal
1x
5x
1x5x
1x 3x
1x3x
1x
2x
1x
2x
(i) 1/5th critical
(ii) 1/3rd critical
(iii) 1/2 critical
TIME & FREQUENCY DOMAIN RESPONSE FOR CRACKED ROTOR
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Horizontal
Vertical
Uncracked rotor: without excitation
Time (msec)0 100 200 300 400 500
Roto
r vib
ratio
n (m
m)
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
Frequency (Hz)0 10 20 30 40 50 60 70 80 90 100
Ampl
itude
0.000
0.005
0.010
0.015
0.020
0.025
0.030Time (msec)
0 100 200 300 400 500
Roto
r vib
ratio
n (m
m)
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
Frequency (Hz)0 10 20 30 40 50 60 70 80 90 100
Ampl
itude
0.000
0.005
0.010
0.015
0.020
0.025
0.030
Time (msec)
0 100 200 300 400 500
Roto
r vib
ratio
n (m
m)
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
Frequency (Hz)
0 10 20 30 40 50 60 70 80 90 100
Ampl
itude
0.000
0.005
0.010
0.015
0.020
0.025
0.030Time (msec)0 100 200 300 400 500
Roto
r vib
ratio
n (m
m)
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
Frequency (Hz)0 10 20 30 40 50 60 70 80 90 100
Ampl
itude
0.000
0.005
0.010
0.015
0.020
0.025
0.030
(a) (b)
(c) (d)
(a) (b)
(c) (d)
Figure 11. Time domain and frequency domain response of the uncracked shaft with axial excitation (ωΙ=ω0). a,b - horizontal, c,d - vertical.
ω
ω0
ω
ω0
ω
ω0
ω
ω0
Vertical
Horizontal
Uncracked rotor: with excitation
Vertical
Rotating condition
.
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Time (msec)
0 100 200 300 400 500
Rot
or v
ibra
tion
(mm
)
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
Frequency (Hz)
0 10 20 30 40 50 60 70 80 90 100
Ampl
itude
0.000
0.005
0.010
0.015
0.020
0.025
0.030Time (msec)
0 100 200 300 400 500
Rot
or v
ibra
tion
(mm
)
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
Frequency (Hz)0 10 20 30 40 50 60 70 80 90 100
Ampl
itude
0.000
0.005
0.010
0.015
0.020
0.025
0.030(a) (b)
(c) (d)
ω
ω0
ωω02ω
3ω
2ω3ω
Time (msec)
0 100 200 300 400 500
Rot
or v
ibra
tion
(mm
)
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
Frequency (Hz)
0 10 20 30 40 50 60 70 80 90 100
Ampl
itude
0.000
0.005
0.010
0.015
0.020Time (msec)
0 100 200 300 400 500
Rot
or v
ibra
tion
(mm
)
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
Frequency (Hz)
0 10 20 30 40 50 60 70 80 90 100
Ampl
itude
0.000
0.005
0.010
0.015
0.020(a) (b)
(c) (d)
ω
ω0
ω
ω0
2ω
3ω
2ω
3ω
Horizontal
Cracked rotor: without excitation
Vertical
Horizontal
Cracked rotor: with excitation
Vertical
Rotating condition
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Stress Monitoring
• For detection of crack, rotor needs to be stress monitored
• Additional external excitation is useful for unambiguous detection
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Misalignment symptom
At rotational speed – 1/3rd of critical speed
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Misalignment symptom
At rotational speed – 1/2 of critical speed
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Misalignment Vs Crack – similar symptoms
-80 -60 -40 -20 0 20 40 60 800
0.2
0.4
0.6
0.8
1
1.2
1.4 x 10-6
Frequency [Hz]
Am
plitu
de [m
]
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Procedure to get full spectrum
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Full Spectrum of uncracked rotor
-80 -60 -40 -20 0 20 40 60 800
0.5
1
1.5
2
2.5
3
3.5 x 10-6
Frequency [Hz]
Am
plitu
de [m
]
-80 -60 -40 -20 0 20 40 60 800
0.5
1
1.5
2
2.5
3
3.5 x 10-6
Frequency [Hz]
Am
plitu
de [m
]
-80 -60 -40 -20 0 20 40 60 800
0.2
0.4
0.6
0.8
1
1.2
1.4 x 10-6
Frequency [Hz]
Am
plitu
de [m
]
-80 -60 -40 -20 0 20 40 60 800
0.2
0.4
0.6
0.8
1
1.2
1.4 x 10-6
Frequency [Hz]
Am
plitu
de [m
]
at 1/3rd critical speed
at 1/2 critical speed
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Full Spectrum of cracked rotor
-80 -60 -40 -20 0 20 40 60 800
0.5
1
1.5
2
2.5 x 10-6
Frequency [Hz]
Am
plitu
de [m
]
-80 -60 -40 -20 0 20 40 60 800
1
2
3
4
5
6
7 x 10-6
Frequency [Hz]
Am
plitu
de [m
]
-80 -60 -40 -20 0 20 40 60 800
0.5
1
1.5
2
2.5
3
3.5 x 10-6
Frequency [Hz]
Am
plitu
de [m
]
-80 -60 -40 -20 0 20 40 60 800
0.2
0.4
0.6
0.8
1 x 10-5
Frequency [Hz]
Am
plitu
de [m
]
Depth 30%
Depth 40%
P = 1/3 P = 1/2
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Residual Crack vibration
-80 -60 -40 -20 0 20 40 60 800
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6 x 10-6
Frequency [Hz]
Am
plitu
de [m
]
-80 -60 -40 -20 0 20 40 60 800
1
2
3
4
5
6
7 x 10-6
Frequency [Hz]
Am
plitu
de [m
]
After removing unbalance
P=1/3 p=1/2
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Spectrum Cascade for Cracked Rotor1X
2X
3X-1X
Strong +2X frequency
1138 RPM
In cracked rotor, vibration excitations are forward in nature.
Presence of weak backward 1X frequency component along with the strong forward 1X frequency component is due to crack only
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Types of misalignment
Angular misalignment
Parallel misalignment
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Angular Misalignment Parallel Misalignment
Elementary Misalignment Models
These models are more hypothetical than actual and could not conclusively tell the misalignment behavior.
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Coupled rotor system
CmisalF
Misalignment effect is taken care by misalignment forces at coupling location.
Rotor 2 Rotor 1
0.7m 0.7m0.25m
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At rotational speed – 1/3rd of critical speed
At rotational speed – 1/2 of critical speed
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Effect of parallel
misalignment
(dy = 0.67e-03m)
4X 3X
2X
ω = ωcr / 4 = 12.4Hz ω = ωcr / 3 = 16.87Hz
ω = ωcr / 2 = 24.8Hz
Presence of –nx spectral components along with +nx components is typical to misalignment
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Experimentation set-up First bending natural frequency = 48Hz
Rotor - 2 Rotor - 1Proximity probes
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Full spectra of misaligned coupled rotors (ω = ωcr / 3) - ExperimentationRotor - 1 Rotor - 2
Without misalignment
With parallel misalignment
(0.32mm)
Misalignment excites ‘-nx’ spectral components
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Rotor - 1 Rotor - 2
Without misalignment
With angular misalignment
(1.5°)
Misalignment excites ‘-nx’ spectral components
Full spectra of misaligned coupled rotors (ω = ωcr / 3) - Experimentation
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ROTOR-
STATOR RUB
2( , ) cos( )yy yz ymy cy k y k z F y z mu t mgω ω φ+ + + = + + −&& &
2( , ) sin( )zy zz zmz cz k y k z F y z mu tω ω φ+ + + = + +&& &
1yy yz
zz zy
k k k kT T
k k k kξ ξη
ηξ η
−⎡ ⎤ ⎡ ⎤= ⎢ ⎥ ⎢ ⎥
⎣ ⎦⎣ ⎦
Cracked shaft stiffness:
Rubbing Forces:
1( )1fy s
fz
F ye kzeF
ψ μδψ μ
⎡ ⎤⎧ ⎫ ⎧ ⎫−⎪ ⎪ = − ⎢ ⎥⎨ ⎬ ⎨ ⎬−⎪ ⎪ ⎩ ⎭⎢ ⎥⎩ ⎭ ⎣ ⎦
2 2e y z= +
1 00 01 0
t
f t t
t
for R vy zfor R v and v z ye e
for R v
ωψ ω
ω
− + >⎧⎪ ⎛ ⎞ ⎛ ⎞= + = = −⎨ ⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠⎪ + =⎩
&&
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Vibration response of uncracked rotor without rub
Rotor Parameters:
mass of the disk, m = 4 kg; shaft stiffness, = 2.275E+05 N/m; unbalance eccentricity, u = 1E-05m; damping ratio, ζ = 0.05; stator stiffness, = 60E+06 N/m; clearance, δ = 1.735E-04 mcoefficient of friction,= 0.2. Natural frequency = 2277 rpm (38Hz)
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Cascade full spectrum of rotor-stator rub
Pseudo Resonance
Bending critical speed
Strong subharmonics
Aperiodic response
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-1X increases more in comparison with +1X
-nX is stronger in comparison to +nx
Backward whirl just before pseudo resonance was not reported before
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1X2X
3X-1X
Cascade full spectrum for cracked rotor without rub
In cracked rotor, vibration excitations are forward in nature.
Presence of weak backward 1X frequency component along with the strong forward 1X frequency component is due to crack only
Strong +2X frequency
1138 RPM
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1X
-1X
-2X 2X 3X½X-½X
Cascade full spectrum for uncracked rotor with rub
Spectrum shows forward whirling 1X response with substantial -1X frequency component.
Spectrum rich in superharmonics is typical rub indicator. However, these harmonics are weak in magnitude and +ve and –ve frequency components are almost equal in magnitude.
1138 RPM
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SUMMARY• Single sided FFT may not give full information• Can not pinpoint the fault among the probable
faults with similar symptoms• Transient vibration response reveals more
information• Stress monitoring useful particularly for crack
detection• Full Spectrum analysis is found very useful for
pinpointing faults with similar symptoms