Fault Identification and Monitoring in rolling element bearing

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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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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

158

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

159

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

160

Envelope AnalysisEnvelope spectrum showing a harmonic series of fout

(Outer race defect)

161

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.

162

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.

163

Amplitude modulation

164

Envelope detectionDemodulation

165

Vibration of Gears

166

• Gear tooth profile• Fluctuating tooth meshing force• Tooth mesh frequency and harmonics• Modulations give sidebands• Several stages – many frequencies

Healthy Gears

167

Healthy Gears

168

• Localised surface damage• Wear or inadequate lubrication• Tooth root cracks, missing tooth• Pitch error• Eccentricity

Typical defects

169

170

171

Defective gears

172

Defective gears

173

• Time domain methods• Spectral methods• Parametric spectral analysis• Time-Frequency domain• Cepstral methods

Signal analysis methods

174

• 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

175

176

177

• Remove expected (healthy) signal components• Suitable for gears

Residuals

178

• AR-model prediction• Extract AR-model• Use AR-model as prediction filter• AR-model residual

Parametric spectral analysis

179

• RMS-value• Peak-value• Kurtosis• Defect Severity Index

Machine condition indicators

180

181

• Surface damage on gear in truck gearbox

Example

182

Upper: Healthy Lower: Defect

183

Synchronised time domain averaging

184

Extract Residual

185

AR-model prediction filter

186

• Kurtosis > 3

Kurtosis = 3.0

Kurtosis = 4.7

187

• Gear meshing frequency• Sidebands• Synchronous time domain averaging• Residuals• Defect enhancement: AR-models etc• Defect severity

Summary

188

SOME OTHER COMMON ROTOR FAULTS

FATIGUE TRANSVERSE CRACK

MISALIGNMENT

ROTOR RUB

189

BREATHING OF CRACK

190

STIFFNESS VARIATION OF CRACKED ROTOR DUE TO BREATHING

191

192

( ) 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

+=++++−+

−=++−+−−

&&&&

&&&&

193

ESTABLISHED VIBRATION SYMPTOMS OF A CRACK

Instability for deeper cracks, for lightly damped rotors.

Frequency content

Subharmonic

Resonance

194

Waterfall Plot

ωcr

1/2ωcr

1/3ωcr

(a)

Lateral Vibration Response

195

Torsional Vibration

1/3ωtor

1/4ωtor

1/6ωtor

1/2ωtor(b)

(c)

1X 2X

3X

4X

196

NEED: A reliable detection strategy !!

Transient response analysis

Coupling of Vibrations

Full Spectrum Analysis

197

PEAK

RESPONSE

VARIATION

198

Frequency spectra

Asymmetric Rotor

1/5th critical speed

1/3rd critical speed

1/2 critical speed

199

Frequency spectra

Cracked Rotor

1/5th critical speed

1/3rd critical speed

1/2 critical speed

200

Directionality of higher harmonic components for cracked rotor

Stiffness variation characteristic due to breathing is responsible for unique directionality of crack vibration response

201

( )

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

202

RESPONSE OF CRACKED ROTOR TO

FOUR IMPULSES/ROTATION

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

.

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

205

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

206

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

207Test rig with instrumentation

Proximeter A/D Card Computer

MotorController

Motor

Flexiblecoupling

Proximity Probe

Disk

BearingPedestal

Stopper

Non-rotating Bearing Guide

Exciter

Oscillator PowerAmplifier

208

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

209

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

.

210

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

211

Stress Monitoring

• For detection of crack, rotor needs to be stress monitored

• Additional external excitation is useful for unambiguous detection

212

Misalignment symptom

At rotational speed – 1/3rd of critical speed

213

Misalignment symptom

At rotational speed – 1/2 of critical speed

214

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

]

215

Procedure to get full spectrum

216

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

217

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

218

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

219

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

220

Types of misalignment

Angular misalignment

Parallel misalignment

221

Angular Misalignment Parallel Misalignment

Elementary Misalignment Models

These models are more hypothetical than actual and could not conclusively tell the misalignment behavior.

222

Coupled rotor system

CmisalF

Misalignment effect is taken care by misalignment forces at coupling location.

Rotor 2 Rotor 1

0.7m 0.7m0.25m

223

At rotational speed – 1/3rd of critical speed

At rotational speed – 1/2 of critical speed

224

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

225

Experimentation set-up First bending natural frequency = 48Hz

Rotor - 2 Rotor - 1Proximity probes

226

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

227

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

228

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

− + >⎧⎪ ⎛ ⎞ ⎛ ⎞= + = = −⎨ ⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠⎪ + =⎩

&&

229

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)

230

Cascade full spectrum of rotor-stator rub

Pseudo Resonance

Bending critical speed

Strong subharmonics

Aperiodic response

231

-1X increases more in comparison with +1X

-nX is stronger in comparison to +nx

Backward whirl just before pseudo resonance was not reported before

232

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

233

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

234

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