FAULT IDENTIFICATION AND MONITORING
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Condition monitoring Topics: • Introduction • Types of Condition Monitoring • Different types of predictive Maintenance • Vibration Condition Monitoring 2
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 7
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Maintenance Regimes
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Issues of Monitoring
• Criticality of inspected part/machine/process • Offline inspections / online inspections • Sensitivity of faults – parameter to monitor • Optimum inspection interval
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Techniques for Fault Detection
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Visual inspection Cost effective Optical assistance Low 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 13
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 14
Surface and Internal Defect detection • Eddy Current testing • Electrical Resistance Testing • Magnetic Particle Testing • Dye Penetration Testing • Resonance Testing • Ultrasonic Testing • Visual Examination
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Wear Debris Analysis
EARLY BIRD??
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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 22
Why Vibration Monitoring? • 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 23 • Non-intrusive, nondestructive.
• 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 26
Vibration criterion chart - VDI 2956/1964
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 frequency
T – large machines with operating speeds above the foundation natural 27 e.g., turbomachinery
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 35
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 peak (or maximum) value peak to peak value average absolute value RMS (root mean square) value
T
x average
1 = ∫ x dt T 0
T
x RMS
1 2 = x (t )dt38 ∫ T 0
Vibration criterion chart - VDI 2956/1964
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
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Other time domain measurements • Kurtosis: indicates impulsiveness of the signal k=
1
∞
4 ( x − x ) f ( x )dx ∫
σ 4 −∞ f(x) is the probability density function of the x 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 kurtosis 40 k < 3.5 good bearing k>3.5 bad bearing
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, unbalance43
Decomposition of time domain periodic signal in frequency domain 1.2
1.0
Amplitude
0.8
0.6
0.4
0.2
0.0 0
10
20
30
40
50
60
Frequency (Hz)
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Fourier Analysis
¾ To find different frequency components ¾ Amplitudes of different components
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Frequency domain measurement •
Frequency Domain measurements picks up fault symptoms early
Just 16% increase in peak to peak amplitude
100% increase in high frequency amplitude
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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
Comparing the two vibration spectra High frequency region reveals problem in one of the gear boxes 52
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 55 signal by reducing broadband noise
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Bearing Fault Identification
HFRT with ALE
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TSA – Time Synchronous Average
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
EFFECTIVENESS AND SENSITIVITY OF VIBRATION PROCESSING TECHNIQUES FOR LOCAL FAULT DETECTION 58 IN GEARS by G. Dalpiaz, A. Rivola And R. Rubini Mechanical Systems and Signal Processing (2000) 14(3), 387}412
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Gear Teeth Mesh Forces
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Second gear teeth mesh
First gear teeth mesh
Gear blank digs into pinion and withdraws once in one rotation
xcos(ωt)
xacos(ωat)
Time for 1 revolution of gear Time for 1 revolution of gear
Time (sec)
x (t ) = [ x + xa cos(ω a t )] cos ωt
Time (sec)
First gear teeth mesh
Time for 1 revolution of gear
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Amplitude Modulation in Gear Pair x(t ) = [ x] cos ωt
With perfect gearing condition
modulation frequency i.e., rotational speed of the gear - ωa carrier frequencies i.e.,gear mesh frequency - ω
x(t ) = [ x + x a cos(ω a t )] cos ωt
With imperfect gearing condition
x(t ) = [ x cos ωt + xa cos ωt cos(ωa t )] = x cos ωt +
xa x cos(ω − ωa )t + a cos(ω + ωa )t 62 2 2
ωa = 25 Hz ω = 750Hz x(t ) = x cos ωt +
xa x cos(ω − ωa )t + a cos(ω + ωa )t 2 2
ωa , 2ωa , 3ωa ,.... ω , 2ω , 3ω SPECTRUM
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• Cepstrum is defined as inverse Fourier transform of the logarithm of the power spectrum
c(τ ) = F −1{log S X (ω )} • If one or more periodic structures appear in a spectrum, each one appear as a distinct peak in cepstrum 64
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 F (k ) = N
N −1
∑f
2πnk −j ( n )e N
n =0
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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 73
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 highfrequency information 74
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 •
Morlet Wavelet
⎛
2 ⎞
ψ (t ) = e −t cos⎜⎜ π t ⎟⎟ ln 2 ⎝ ⎠ 2
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
∫
ψ (t )dt = 0
−∞
∞
•
It is square integrable, i.e., it has finite energy
∫
| ψ (t ) | 2 dt < ∞
Mother Wavelet
−∞
Scaling & shifting Son/daughter wavelets 76
Wavelets Signals 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
Ensures energy stays same for all s&b Sum over all time of the signal multiplied by scaled and shifted versions of the wavelet 78
Relation between scale & frequency Fc Fa = sΔ Fa = pseudo frequency ( for the scale value s ) Δ = sampling time s = Scale Fc = central frequency of mother wavelet in Hz. Central frequency of the Morlet wavelet is 0.8125Hz It is the freq. that maximizes the FFT of the wavelet or is the leading dominant frequency of the wavelet 79 Matlab Help Module
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Case Studies a) 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 Signals NO RUB RUB
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PARTIAL/INTERMITTENT RUB NO RUB
Partial RUB 84
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 87
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 depth97
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 98
Gear Fault detection using Wavelets Difficult 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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Experimental study conducted by Dalpiaz
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 in100 most of the cross-sections.
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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AE Technique – useful for detecting fault initiation 104
M.Tech. Thesis– Akhil Agrawal (NTPC), ITMMEC, IITDelhi 2006
Rotor Faults & Typical Vibration Features Misalignmment: 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-stator Rub: 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.
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Rotor Faults & Typical Vibration Features Crack: 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
1X response
Yes
Yes
No
No
Sub-harmonics
No
No
No
½X, ⅓X, ⅔X, & even lower
Mainly 2X; other higher harmonics
2X & 3X
Only 2X
2X, 3/2X , 3X, & even higher
Resonance at ½ & ⅓ of critical speed
Resonance at ½, & ⅓ of critical speed
Resonance at ½ of critical speed
Highly unstable
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
Multi lobed with external loops
Multi lobed with internal loops
Two loops at subharmonic resonances
Backward whirling orbit
lateral-torisonal
Yes
Yes
No
Yes
lateral-axial
Yes
Yes
No
No
torsional-axial
No
Yes
No
No
Steady state response
Super-harmonics
Transient response
Instability zones
Orbital behaviour Coupled vibrations
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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); Crack and Darpe (2002) 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 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)
Wavelet time-frequency maps for the cracked Crack and rub rotor are different from the cracked rotor with rubbing.
Prabhakar (2002)
Crack and misalignment
Investigators
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 the bearing condition. 110
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. 111
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 (2) Shock Pulse Method: Impacts in the bearings initiate damped oscillations in the transducer at its resonant frequency. (3) Acoustic Based: (a) Sound pressure measurement (b) Sound intensity measurement (c) Acoustic emission (AE) measurement
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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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Vibration Monitoring • •
•
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 the static load with the friction forces. These forces accompany the rotor selfoscillations in the bearings. The rotor self-oscillations in the journal bearings are very much alike the pendulum oscillations of the rotor in relation to the equilibrium position in the lowest point of the bearing. The rotor is shifted from the equilibrium position by the friction forces and is returned in it by the gravity force. The reason of this unstable equilibrium is the nonlinear dependence of the friction forces from the thickness of the lubrication layer that grows while the rotor position deviates from the equilibrium position. The self-oscillation frequency is the lesser the larger is the gap in the bearing, i.e. the more is the bearing's wear. 115
Vibration Monitoring •
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.
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Vibration Monitoring • "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. 117
• 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. 118
The transducer of the shock pulse meter (SPM) is a piezoelectric accelerometer tuned mechanically and electronically to a resonant frequency around 32 kHz. The shock wave is propagated through the bearing housing, and when the shock pulse hits the transducer, damped oscillations are initiated at the resonant frequency of the transducer. The amplitude increase of the damped resonant oscillation gives an indication of the condition of the rolling element bearings. The transducer signal is processed electronically to filter out low frequency vibrations such as inbalance, misalignment and other structurerelated vibrations. The decibel (dB) unit is used to measure the shock value to accommodate a large range of shock values of good and damaged bearings.
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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 with rolling elements. The shock pulse value generated by good bearings due to surface roughness has been found empirically to be dependent upon the bearing bore diameter and speed. This value, called initial value (dBi), is subtracted from the shock value of the test bearing to obtain a ‘normalized shock pulse value’ (dBN). The digital shock pulse meter gives the reading directly in dBN. The shock pulse meter gives two values namely the ‘maximum shock value’ (dBM) and the ‘carpet value’ (dBC), as shown in Figure 5.8.
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The maximum shock value is a measure of low rate (LR) impacts, and the carpet value is a measure of high rate (HR) impacts. HR impacts may exceed 1000 impacts per second and LR impacts may exceed 25 impacts per second. An increase in dBM value 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 and dBC. 121
Pumps Topics: • Causes of excessive vibration • Types of forces • Measures 122
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. 123
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) r (t)
MODEL BASED DIAGNOSIS r0(t) : previously measured undamaged system vibration 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 132
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 133
Heuristic Methods
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Definition of Expert System • A computing system capable of representing and reasoning about some knowledge rich domain, which usually requires a human expert, with a view toward solving 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 model of the domain. 135
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 136 is provided.
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Frequency Domain Signal
138 Fig.6 Screen Snapshot of Frequency Domain Signal
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Schematic 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 Domain Frequency Domain Trend Orbit Waterfall
Analysis:
Expert System Diagnosis Signal Processing
Assistance:
Demo Help
Backup Data Loader
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Expert System Each 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. 148
Vibrations of Bearings
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Roller bearings • Force impulse when rolling element passes • Roughness will increase contact forces • Modulation due to varying transfer path • Slip 150
Defect roller bearing
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Defect roller bearing
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Roller bearings Fundamental 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. 155
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: Disadvantages: • Quick • Detects fewer faults • Simple • Detects faults later, close to • Low capital outlay failure • Single number result 157
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 Comparison Advantages: • 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 Analysis Envelope 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 Analysis The 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 detection Demodulation
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Vibration of Gears
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Healthy Gears • Gear tooth profile • Fluctuating tooth meshing force • Tooth mesh frequency and harmonics • Modulations give sidebands • Several stages – many frequencies 166
Healthy Gears
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Typical defects • Localised surface damage • Wear or inadequate lubrication • Tooth root cracks, missing tooth • Pitch error • Eccentricity
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Defective gears
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Defective gears
172
Signal analysis methods • Time domain methods • Spectral methods • Parametric spectral analysis • Time-Frequency domain • Cepstral methods 173
Synchronised time domain averaging STDA • Extract signal components cyclic with shaft rotation • Equal number of samples per revolution • Resample if necessary • Multistage gearboxes – Repeat STDA 174
175
176
Residuals • Remove expected (healthy) signal components • Suitable for gears
177
Parametric spectral analysis • AR-model prediction • Extract AR-model • Use AR-model as prediction filter • AR-model residual
178
Machine condition indicators • RMS-value • Peak-value • Kurtosis • Defect Severity Index
179
180
Example • Surface damage on gear in truck gearbox
181
Upper: Healthy Lower: Defect
182
Synchronised time domain averaging
183
Extract Residual
184
AR-model prediction filter
185
• Kurtosis > 3
Kurtosis = 3.0
Kurtosis = 4.7 186
Summary • Gear meshing frequency • Sidebands • Synchronous time domain averaging • Residuals • Defect enhancement: AR-models etc • Defect severity 187
SOME OTHER COMMON ROTOR FAULTS
FATIGUE TRANSVERSE CRACK MISALIGNMENT ROTOR RUB
188
BREATHING OF CRACK
189
STIFFNESS VARIATION OF CRACKED ROTOR DUE TO BREATHING
190
191
EQUATIONS OF MOTION a) Uncracked Rotor
(
)
m(ξ&& − 2ωη& − ω 2ξ ) + c ξ& − ωη + kξ = mεω 2 cos β − mg cosθ m(η&& + 2ωξ& − ω 2η ) + c(η& + ωξ ) + kη = mεω 2 sin β + mg sin θ
b) Asymmetric Rotor
(
)
m(ξ&& − 2ωη& − ω 2ξ ) + c ξ& − ωη + kξ ξ = mεω 2 cos β − mg cosθ m(η&& + 2ωξ& − ω 2η ) + c(η& + ωξ ) + kηη = mεω 2 sin β + mg sin θ
c) Cracked Rotor
(
)
m(ξ&& − 2ωη& − ω 2ξ ) + c ξ& − ωη + kξ ξ + kξηη = mεω 2 cos β − mg cosθ m(η&& + 2ωξ& − ω 2η ) + c(η& + ωξ ) + kηξ ξ + kηη = mεω 2 sin β + mg sin θ192
ESTABLISHED VIBRATION SYMPTOMS OF A CRACK
Frequency content
Subharmonic Resonance Instability for deeper cracks, for lightly damped rotors.
193
Waterfall Plot (a)
ωcr
1/2ωcr 1/3ωcr
Lateral Vibration Response
194
Torsional Vibration (b)
1/2ωtor
1/3ωtor
(c)
1/4ωtor 1X
2X 3X
1/6ωtor
4X
195
NEED: A reliable detection strategy !!
Transient response analysis Coupling of Vibrations Full Spectrum Analysis
196
PEAK RESPONSE VARIATION
197
1/5th critical speed
Frequency spectra Asymmetric Rotor
1/3rd critical speed
1/2 critical speed
198
1/5th critical speed
Frequency spectra Cracked Rotor
1/3rd critical speed
1/2 critical speed
199
Directionality of higher harmonic components for cracked rotor
Stiffness variation characteristic due to breathing is responsible for unique directionality of crack vibration response 200
COUPLING OF LONGITUDINAL AND BENDING VIBRATIONS
(
)
m(ξ&& − 2ωη& − ω 2ξ ) + c ξ& − ωη + kξ ξ + kξηη + kξu u = mεω 2 cos β − mg cosθ m(η&& + 2ωξ& − ω 2η ) + c(η& + ωξ ) + kηξ ξ + kηη + kηu u = mεω 2 sin β + mg sin θ mu&& + cu& + k uξ ξ + k uηη + k u u = 0
To exploit Non-linearity due to crack breathing & Coupling between Bendinglongitudinal-Torsional vibrations 201
RESPONSE OF CRACKED ROTOR TO FOUR IMPULSES/ROTATION
202
CRACKED ROTOR: UNBALANCE RESPONSE, NO TORSIONAL EXCITATION
4e-6
Amplitude
vertical response, y (m)
5e-6 -1.36e-4
-1.40e-4
-1.44e-4
(a)
3e-6
2ω 2e-6 1e-6
-1.48e-4 5e-6
(b)
3ω
0e+0 5e-6
Horizontal
4e-6
Amplitude
horizontal response, z (m)
Vertical
ω
0e+0
(c)
3e-6
ω
2e-6
2ω
1e-6
-5e-6
3ω
(d)
0e+0 1e-7
Axial
8e-8
Amplitude
axial response, u (m)
0e+0
-1e-7
(e)
2ω 0e+0 1e-7 8e-8
Amplitude
torsional response, θ (rad)
4e-8 2e-8
-2e-7 2e-7
0e+0
(g)
ω
6e-8
(f)
Torsional
ω 2ω
6e-8 4e-8 2e-8
(h)
4ω
0e+0
-2e-7 0
360
Angle of rotation (degrees)
720
10
20
30
40
50
Frequency (Hz)
203 Figure 8. Unbalance response of a cracked rotor (a/D=0.3) without torsional excitation. ω=22rad/sec.
.
60
CRACKED ROTOR: UNBALANCE RESPONSE TO TORSIONAL EXCITATION ω0
-1.30e-4
Amplitude
vertical response, y (m)
-1.25e-4
-1.35e-4 -1.40e-4 -1.45e-4
ω0-2ω
ω0+ω ω0+2ω
(b)
Horizontal
ω0
2e-5 1.5e-5 1e-5 0e+0 -1e-5
1.0e-5 5.0e-6
-2e-5
(c)
-3e-5
ω 2ω
ω0-2ω
3ω
ω0-ω
ω0+ω
(d)
ω0+2ω
0.0e+0
0.0e+0
6.0e-8
-4.0e-8
Amplitude
axial response, u (m)
ω0-ω
2ω
0e+0 2.0e-5
Amplitude
horizontal response, z (m)
-1.55e-4 3e-5
Vertical
ω
(a)
-1.50e-4
-8.0e-8 -1.2e-7
Axial
ω
4.0e-8
2ω
ω ω0+ω ω0-2ω ω0-ω 0 ω0+2ω
2.0e-8
(e)
-1.6e-7
0.0e+0 0.10
0.15 0.10 0.05 0.00 -0.05 -0.10
(g)
-0.15
0.06 0.04 0.02
(h)
0.00 0
360
Angle of rotation (degrees)
720
(f)
Torsional
ωe
0.08
Amplitude
torsional response, θ (rad)
5e-6
10
20
30
Frequency (Hz)
40
50 204
60
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 205
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 206
Proximeter
Flexible coupling
A/D Card
Computer
Proximity Probe
Non-rotating Bearing Guide
Bearing Pedestal Stopper
Motor
Exciter
Disk
Motor Controller
Oscillator
Power Amplifier
Test rig with instrumentation 207
Horizontal
Vertical 0.02
0.02
(b)
(a) 0.01
Amplitude (mm)
z
0.00
-0.01
-0.01
-0.02 0.010
-0.02 0.010
(c)
1x
0.008 0.006 0.004
5x
0.002
0
10
20
30
40
50
0.04
0.006 0.004 0.002
0
10
0.02
0.00
0.00
z
0.02
-0.02
-0.02
-0.04
-0.04
0.020
0.020
40
50
3x
60
(ii) 1/3rd critical 3x
(h)
1x
0.015
1x
30
(f)
Amplitude (mm)
(g) 0.015 0.010
20
0.04
(e)
y Amplitude (mm)
5x
1x
0.008
60
0.010 0.005
0.005
0.000
0.000 0
10
20
30
40
50
0
60
(j)
0.06
10
20
30
40
50
60
(k)
0.06
0.03
z
0.03
0.00
0.00
-0.03
-0.03
-0.06
-0.06
0.05
0.05
(l)
0.04
Amplitude (mm)
y
(i) 1/5th critical (d)
0.000
0.000
Amplitude (mm)
TIME & FREQUENCY DOMAIN RESPONSE FOR CRACKED ROTOR
0.00
Amplitude (mm)
y
0.01
2x
0.03 0.02
1x
0.01
(iii) 1/2 critical 2x (m)
0.04 0.03 0.02
1x
208
0.01 0.00
0.00 0
10
20
30
40
Frequency (Hz)
50
60
0
10
20
30
40
Frequency (Hz)
50
60
Rotating condition
0.04
0.025
0.02
0.020
0.00 -0.02
100
200 300 Time (msec)
400
0
(c)
0.04
0.025
0.02
0.020
0.00 -0.02
200 300 Time (msec)
400
40 50 60 70 Frequency (Hz)
80
90 100
(d)
ω
0.010
ω0 0
0.04
0.025
0.02
0.020
0.00 -0.02
10
20
30
40 50 60 70 Frequency (Hz)
80
90 100
0.030
(a) Amplitude
Rotor vibration (mm)
30
0.015
500
(b)
ω
Vertical
0.015 0.010
ω0
0.005
-0.04 -0.06
0.000 0
100
200
300
400
0
500
Time (msec)
0.06
0.030
(c)
0.04
0.025
0.02
0.020
Amplitude
Rotor vibration (mm)
20
0.000 100
0.06
0.00 -0.02
10
20
30
40 50 60 70 Frequency (Hz)
80
ω
90 100
(d)
0.015 0.010
ω0
0.005
-0.04
0.000
-0.06 0
100
200
300
Time (msec)
.
10
0.005
-0.04 0
Vertical
ω0
0.030
-0.06
Uncracked rotor: with excitation
0.010
500
Amplitude
Rotor vibration (mm)
0.06
Horizontal
0.015
0.000
-0.06
Vertical
(b)
ω
0.005
-0.04 0
Uncracked rotor: without excitation
0.030
(a)
Amplitude
Horizontal
Rotor vibration (mm)
0.06
400
500
0
10
20
30
40
50
60
Frequency (Hz)
70
80
209
90 100
Figure 11. Time domain and frequency domain response of the uncracked shaft with axial excitation (ωΙ=ω0). a,b - horizontal, c,d - vertical.
Rotating condition
0.020
(a)
0.015 0.02 0.00 -0.02
3ω
ω0
0.000 100
200
300
400
0
500
Time (msec)
0.06
-0.02
30
200
300
400
90 100
ω0
3ω
0
500
10
20
30
40
50
60
70
80
90 100
Frequency (Hz)
0.030
(a)
0.06
ω0
0.025
(b)
0.04 Amplitude
Rotor vibration (mm)
80
0.000 100
0.08
0.02 0.00 -0.02
0.020 0.015
ω
0.010
2ω
-0.04
3ω
0.005
-0.06
0.000
-0.08 0
100
0.06
200 300 Time (msec)
400
0
500
0.04
0.025
0.02
0.020
0.00 -0.02
20
30
40
50
60
0
100
200
300
Time (msec)
400
500
80
90 100
(d)
ω
0.015
ω0
2ω
0.010
3ω
210
0.000
-0.06
70
Frequency (Hz)
0.005
-0.04
10
0.030
(c) Amplitude
Rotor vibration (mm)
70
2ω
0.010
Time (msec)
Cracked rotor: with excitation
60
ω
0.005
0
Vertical
50
-0.04 -0.06
Horizontal
40
(d)
0.015 0.00
20
Frequency (Hz)
0.04 0.02
10
0.020
(c) Amplitude
Rotor vibration (mm)
2ω
0.010
-0.04 0
Cracked rotor: without excitation
ω
0.005 -0.06
Vertical
(b)
0.04 Amplitude
Horizontal
Rotor vibration (mm)
0.06
0
10
20
30
40
50
60
Frequency (Hz)
70
80
90 100
Stress Monitoring • For detection of crack, rotor needs to be stress monitored • Additional external excitation is useful for unambiguous detection
211
Misalignment symptom
At rotational speed – 1/3rd of critical speed 212
Misalignment symptom
At rotational speed – 1/2 of critical speed 213
Misalignment Vs Crack – similar symptoms -6
1.4
x 10
1.2
Amplitude [m]
1 0.8 0.6 0.4 0.2 0 -80
-60
-40
-20 0 20 Frequency [Hz]
40
60
80
214
Procedure to get full spectrum
215
Full Spectrum of uncracked rotor x 10
-6
-6
1.4
1.2
1.2
1
1 Amplitude [m]
Amplitude [m]
1.4
0.8 0.6
0.6 0.4
0.2
0.2
-60
-40
-20 0 20 Frequency [Hz]
40
60
0 -80
80
3.5
3
3
2.5
2.5 Amplitude [m]
Amplitude [m]
x 10
2 1.5
-40
-20 0 20 Frequency [Hz]
40
60
80
x 10
at 1/2 critical speed
2 1.5 1
1
0.5
0.5 0 -80
-60
-6
-6
3.5
at 1/3rd critical speed
0.8
0.4
0 -80
x 10
-60
-40
-20 0 20 Frequency [Hz]
40
60
80
0 -80
-60
-40
-20 0 20 Frequency [Hz]
40
60
80
216
Full Spectrum of cracked rotor -6
2.5
-6
x 10
7
x 10
6 2 Amplitude [m]
Amplitude [m]
5 1.5
1
4
Depth 30%
3 2
0.5 1 0 -80 3.5
x 10
-60
-40
-20 0 20 Frequency [Hz]
40
60
0 -80
80
-6
1
x 10
-60
-40
-20 0 20 Frequency [Hz]
40
60
80
-5
3 0.8 Amplitude [m]
Amplitude [m]
2.5 2 1.5
Depth 40%
0.6
0.4
1 0.2 0.5 0 -80
-60
-40
-20 0 20 Frequency [Hz]
P = 1/3
40
60
80
0 -80
-60
-40
-20 0 20 Frequency [Hz]
P = 1/2
40
60
80
217
Residual Crack vibration After removing unbalance 1.6
x 10
-6
7
1.4
5 Amplitude [m]
Amplitude [m]
-6
6
1.2 1 0.8 0.6
4 3 2
0.4
1
0.2 0 -80
x 10
-60
-40
-20 0 20 Frequency [Hz]
P=1/3
40
60
80
0 -80
-60
-40
-20 0 20 Frequency [Hz]
p=1/2
40
60
80
218
Spectrum Cascade for Cracked Rotor Strong +2X frequency
1X 2X
-1X
3X 1138 RPM
In cracked rotor, vibration excitations are forward in nature. Presence of weak backward 1X frequency component along with the strong 219 forward 1X frequency component is due to crack only
Types of misalignment
Angular misalignment
Parallel misalignment
220
Elementary Misalignment Models Angular Misalignment
Parallel Misalignment
These models are more hypothetical than actual and could not 221 conclusively tell the misalignment behavior.
Coupled rotor system Rotor 2
Rotor 1
0.25m
0.7m
0.7m
C Fmisal
222
Misalignment effect is taken care by misalignment forces at coupling location.
At rotational speed – 1/3rd of critical speed
At rotational speed – 1/2 of critical speed
223
ω = ωcr / 4 = 12.4Hz 4X
Effect of parallel
ω = ωcr / 3 = 16.87Hz 3X
ω = ωcr / 2 = 24.8Hz 2X
misalignment (dy = 0.67e-03m)
Presence of –nx spectral components along with +nx components 224 is typical to misalignment
Experimentation set-up
Rotor - 2
First bending natural frequency = 48Hz
Proximity probes Rotor - 1
225
Full spectra of misaligned coupled rotors (ω = ωcr / 3) - Experimentation Rotor - 1 Rotor - 2
Without misalignment
With parallel misalignment (0.32mm)
226
Misalignment excites ‘-nx’ spectral components
Full spectra of misaligned coupled rotors (ω = ωcr / 3) - Experimentation Rotor - 2 Rotor - 1 Without misalignment
With angular misalignment (1.5°)
227
Misalignment excites ‘-nx’ spectral components
my&& + cy& + kyy y + kyz z = Fy ( y, z) + muω2 cos(ωt +φ) − mg ROTORmz&& + cz& + kzy y + kzz z = Fz ( y, z) + muω2 sin(ωt +φ)
STATOR RUB
Cracked shaft stiffness:
⎡ k yy ⎢k ⎣ zz
k yz ⎤ k −1 ⎡ ξ =T ⎢ ⎥ k zy ⎦ ⎣ kηξ
kξη ⎤ T ⎥ kη ⎦
Rubbing Forces: (e − δ ) k s ⎪⎧ Fy ⎪⎫ = − ⎨ ⎬ e ⎪⎩ Fz ⎪⎭
ψ f μ ⎤ ⎧ y⎫ ⎡ 1 ⎢ ⎥⎨ ⎬ − ψ μ 1 ⎢⎣ f ⎥⎦ ⎩ z ⎭
⎧−1 for ωR + vt > 0 ⎪ ⎛ y⎞ ⎛z⎞ ψ f = ⎨ 0 for ωR + vt = 0 and vt = z& ⎜ ⎟ − y& ⎜ ⎟ ⎝ e⎠ ⎝e⎠ ⎪ 1 for ωR + v = 0 t ⎩
e=
y2 + z2 228
Rotor Parameters: mass of the disk, m = 4 kg; unbalance eccentricity, u = 1E-05m; stator stiffness, = 60E+06 N/m; coefficient of friction,= 0.2.
shaft stiffness, = 2.275E+05 N/m; damping ratio, ζ = 0.05; clearance, δ = 1.735E-04 m Natural frequency = 2277 rpm (38Hz)
Vibration response of uncracked rotor without rub
229
Cascade full spectrum of rotor-stator rub Strong subharmonics
Pseudo Resonance
Bending critical speed Aperiodic response
230
-1X increases more in comparison with +1X
-nX is stronger in comparison to +nx
Backward whirl just before pseudo resonance was not reported before
231
Cascade full spectrum for cracked rotor without rub Strong +2X frequency
1X 2X
-1X
3X 1138 RPM
In cracked rotor, vibration excitations are forward in nature. Presence of weak backward 1X frequency component along with the strong 232 forward 1X frequency component is due to crack only
Cascade full spectrum for uncracked rotor with rub 1X -1X -2X
-½X
½X
2X
3X 1138 RPM
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 components233 are almost equal in magnitude.
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 234
