Condition based‐monitoring: an overview

Time

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Emiliano Mucchi – University of Ferrara – Italy emiliano.mucchi@unife.it

Maintenance…. an efficient way to assure a satisfactory level of reliability during the useful lifeof a physical asset.

• breakdown maintenance (also called unplanned maintenance, or run‐to‐failure maintenance): takes place only at breakdowns.

• time‐based preventive maintenance (also called planned maintenance): sets aperiodic interval to perform preventive maintenance regardless of the healthstatus of a physical asset. Usually the “period intervals” depend on energyconsumption, distance, operational time, etc.

• condition‐based maintenance (CBM): is a maintenance program thatrecommends maintenance actions based on the information collected throughcondition monitoring. CBM attempts to avoid unnecessary maintenance tasksby taking maintenance actions only when there is evidence of abnormalbehaviours of a physical asset. A CBM program, if properly established andeffectively implemented, can significantly reduce maintenance costs byreducing the number of unnecessary scheduled preventive maintenanceoperations.

MaintenanceA CBM program consists of three key steps:• 1. Data acquisition step (information collecting), to obtain data relevant to system health.

• 2. Data processing step (information handling), to handle and analyse the data or signals collected in step 1, for better understanding and interpretation of the data.

• 3. Maintenance decision‐making step (decision‐making), to recommend efficient maintenance policies.

Diagnostics and PrognosticsDiagnostics and Prognostics are 2 important aspects in a CBM program. • Diagnostics deals with fault detection, isolation and identification when it occurs. Fault detection is a task to indicate whether something is going wrong in the monitored system; fault isolation is a task to locate the component that is faulty; and fault identification is a task to determine the nature of the fault when it is detected. 

• Prognostics deals with fault prediction before it occurs. Fault prediction is a task to determine whether a fault is impending and estimate how soon and how likely a fault will occur.

Monitoring and diagnostics techniques• Noise and vibration• Visual inspection• Termography• Ultrasonic measurement• Acoustic emission• Power consumption• Quality control

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What is vibration

Vibration analysis• It is one of the most common techniques for CBM of 

machines• Basic idea

– After the running in the vibration level remains constant– The vibration level increases due to an incipient fault– When the vibration level exceeds a first threshold level  alarm– When the vibration level exceeds a second threshold level 

stop 

Vibrationlevel Alarm

Stop

time

Vibration measurementWhat to measure?• Displacement: large machines having slow motion

• Velocity: intermediate

• Acceleration :it is sensible to low vibration levels at high frequencies

Analysis techniques• Time domain

– Probability function– Mean– RMS– Variance– Standard deviation– Skewness– Kurtosis– Autocorrelation and correlation 

function– Time synchronous average– Envelope analysis

• Frequency domain– Autospectrum, Spectrum, 

crosspectrum

– FRF– Higher order spectra

• Quefrency domain– Cepstrum

• Time frequency domain– Short Time Fourier Transform 

(STFT)– Wavelet Transform

• Cyclostationary analysis

11

Time domain

12

Time domain

Kurtosis and Skewness

Kurtosis = 3 for Gaussian distributionKurtosis > 3 for sharper distributionKurtosis < 3 for smoother distributionSkewness =0 for Gaussian distribution

ExampleBall bearings‐signal 1‐signal 2

Signal 1 Signal 2

Mean ‐0,0166 ‐0,0170

Stand.Dev

0,0619 0,1137

RMS 0,0641 0,1150

Skewness 0,0159 0,001

Kurtosis 3,0410 3,7765

Monitoring and diagnostics of GEARS

16

A number of different gears

17

Causes of malfunctions and faults

Failure

• Wear

• Surface fatigue (pitting)

• Plastic flow

• Spalling

• Cracking

• Breakage

Description

• Loss of gear tooth surface metal

• Failure of a material as a result of repeated surface or subsurface stresses

• Surface deformation resulting from yielding of surface metal under heavy loads

• Breakaway of relatively large bits of tooth surface, typically in the case hardened gears

• Failure due to the propagation of microscopic flaws in the material under cyclic loading; more common in hardened gears

• Fracture of an entire gear tooth or a substantial portion of it

Causes

• Inadequate lubrication

• Heavy load producing repeated stresses above the endurance limit of the material

• Heavy loads, expecially impact loads

• Too abrupt a transition between hard case and soft material underneath; local metallurgical defects; development of pitting

• Generally it results from incorrect processing - grinding, queching -and usually leads to breakage

• Overstress, fatigue

18

Trouble

• Eccentricity

• Looseness of gears or bearings on the shaft

• Misalignment

• Excessive backlash

• Machining signs

Description

• Wheel and shaft geometrical centres not coincident; out-of-roundness of the gear.

• Excessive backlash between gear and shaft or between bearings and shaft.

• Axes of mating gears not parallel (cylindrical gears) or coplanar (bevel gears).

• Excessive distance between the non-working flanks of two meshing gears.

• Gear tooth profile shaped like a broken line envelopping an involute curve.

Causes

• Manufacturing errors.

• Manufacturing errors.

• Manufacturing or assembly errors.

• Manufacturing or assembly errors.

• Manufacturing methods.

19

Transducer best location

• Radial direction for spur gears• Axial direction for helical gears• As close as possible to the gears under study• No on flexible casing• Yes on rigid casing

20

Meshing stiffness• It depends on the contact point location along the involute• It is larger when two meshing contacts occurs• Due to the meshing stiffness, the force acting on the meshing teeth is

variable during the meshing. Thus, the transmisison ratio is variable

21

Transmission error• It is the difference between the driven gear angular position

without deflection (rigid behaviour) and the actual angular location• Causes of the transmission error

– Main causes: meshing stiffness– Other causes: machining, wear, eccentricity, gear errors

0 90 180 270 360

Rotation degrees

-0.10

-0.05

0.00

0.05

0.10

Tran

smiss

ion e

rror [

degr

ees]

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Transmission error• The figure shows the transmission error• There are oscillations with same periodicity as the meshing

stiffness (i.e. 1 pitch, high frequency waves) and low frequencyoscillations (i.e. due to gear eccentricy)

0 90 180 270 360

Rotation degrees

-0.10

-0.05

0.00

0.05

0.10

Tran

smiss

ion e

rror [

degr

ees]

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Meshing stiffness

fmeshing = z1 f1,rot = z2 f2,rot

z1, z2 tooth numberf1,rot, f2,rot rotational frequency of gears

• The transmission error in not a perfect sinusoidal signal. It hashigher harmonics (not only the fundamelatal one)

• The meshing forces will excite casing vibration• The vibration signal measured on the casing will have the

meshing frequency as well as the higher harmonics.

24

Modulation Effects• Gears are usually affected by eccentricity due to machining

errors, bending shaft, etc. • Eccentricity determines «amplitude modulation» of the meshing

forces and thus of the the casing vibration (which are measured).

In the frequency domain, the spectrum of the casingvibration has peaks at the meshing frequency and itshigher harmonics with sidebands

The sidebands are spacedof the rotational frequencyof the two gears.

The sidebands can be due also to «phase modulation»

Phase modulation can be due acceleration and deceleration of the gearscaused by backlash or gearfaults.

0 500 1000 1500 2000Frequency Hz

Ampl

itude

fg=416.5 Hz

2fg=833 Hz

3fg=1249.5 Hz

4fg=1666 Hz

0

Frequency Hz

Ampl

itude

750 800 850

833 Hz

808.5 Hz 857.5 Hz

825.

4 H

z

840.

6 H

z

0

(Z1=17; Z2=55; n1=1470 rpm)

1470/60=24.5Hz rot freq gear 1

24.5*(17/55)=7.5Hz rot freq gear 2

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Amplitude modulation• Eccentricity, spalling, crack teeth can determine amplitude

modulation effects in gears• The amplitude modulation signal x(t) is:

x t A a t ftm( ) ( ) ( ) 1 2sin

where:A = signal amplitudef = signal frequency (or carrier frequency) (e.g. meshing frequency) = signal phaset = time1+am(t) = amplitude modulation function

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Amplitude modulation

)2(sin)(1)( fttaAtx m

where:Am= modulation amplitudefm = modulation frequency

• In the simplest case, the amplitude modulation function is sinusoidal (as for eccentricity):

)2(sin)2(sin1)( fttfAAtx mm

0.000 0.025 0.050 0.075 0.100Time [s]

Ampl

itude

0

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Amplitude modulation

The sidebands are spaced with respect to the meshing frequencyof a quantity equal to the rotationalfrequency

• The figure shows a modulationamplitude effect

– The fundamental frequency is f = 612.5 Hz, which is the meshing frequency (Z=25, N=1470 rpm).

– The modulation frequency is fm = 24.5 Hz, which is the gearrotational frequency.

0.000 0.025 0.050 0.075 0.100Time [s]

Ampl

itude

0

0 200 400 600 800Frequency [Hz]

Ampl

itude

0

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Amplitude modulation (local fault)

• A local fault (crack at the tooth root) determines a modulation signal different w.r.t. eccentricity.

• The vibration effect of a local fault involves a short time and it determines a larger number of sidebands but of reduced amplitude.

0.00 0.01 0.02 0.03 0.04Time [s]

Ampl

itude

0

0 200 400 600 800 1000 1200 1400Frequency [Hz]

Log

Ampl

itude

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Phase modulation

Where:bm(t) = phase modulation functionA = signal amplitudef = signal frequency (or carrier frequency) (e.g. meshing frequency) = signal phaset = time

• The meshing frequency and its higher harmonics can be modulatedin phase as well. The phase modulated signal x(t) is

Effect of the phasemodulation in time domain

x t A ft b tm( ) ( ( ) ) sin 2

0 .0 0 0 0 .0 2 5 0 .0 5 0 0 .0 7 5 0 .1 0 0T im e [s ]

Ampl

itude

0

30

Phase modulation

• In the simplest case, the phase modulation function is sinusoidal:

x t A ft b tm( ) ( ( ) ) sin 2

x t A ft A f tm m( ) ( ( ( ) ) sin sin2 1 2

0 .0 0 0 0 .0 2 5 0 .0 5 0 0 .0 7 5 0 .1 0 0T im e [s ]

Ampl

itude

0

where:Am= modulation amplitude fm = modulation frequency

Effect of the phasemodulation in time domain

31

Phase modulation (local fault)

• A local fault (crack at the tooth root) can reduce the meshing stiffness .

• This reduction can also determine angular rotational speed variation.

• Thus, in the vibration signal, phase modulation effects are present at the defect frequency.

• This phase modulation effect involves a short time interval. Thus in the spectrum a large number of sidebands of little amplitude will appear.

0.00 0.01 0.02 0.03 0.04Time [s]

Ampl

itude

0

0 350 700 1050 1400Frequency [Hz]

Log

Ampl

itude

32

Amplitude and phase demodulation

• Amplitude demodulation

0 50 100 150 200 250 300 350-6

-4

-2

0

2

4

6

Wheel rotation [deg]

0 50 100 150 200 250 300 3500

1

2

3

4

Wheel rotation [deg]0 50 100 150 2

-1

-0.5

0

0.5

1

Wheel rotatio

Phase demodulation

33

A Crack in a tooth

• The crack produces a reduction in the meshing frequency and thus amplitude and phase modulation in the vibration signal

0.000 0.025 0.050 0.075 0.100Time [s]

Ampl

itude

0

0 625 1250 1875 2500Frequency [Hz]

Ampl

itude

0

Time and spectral effect of a cracked tooth

34

Broken tooth• A broken tooth determines a

not continuous transmission ratio with variable contact forces (impulse).

• In the frequency domain, high amplitude sidebands appear.

• The impulse of the contact forces can excited casing resonance frequency (Fn = 233 Hz in the Figure)

0 400 800 1200 1600Frequency [Hz]

Ampl

itude

f n1=2

33 H

z

fg=416.5 Hz

0

Spectral effect of a broken tooth (Z1=17; Z2=55; n1=1470 rpm)

35

Spalling (Pitting)• Spalling is due to the pitting

effect on the tooth surface. This occurs after a large number of cycle of work.

• The tooth surface is damageand flakes of material are removed.

• The spalling consists in impact at the rotationalfrequency.

• The vibration signal is modulated and it shows lowfrequency components at the rotational frequency and higher harmonics.

0 500 1000 1500 2000Frequency [Hz]

Ampl

itude

0

Spectral effects of spalling on teeth

36

Example

• Data– Z1 = 20 Z2 = 21– rpm1 = 1000– Rotational frequency of

gear 1:fR1 = rpm1/60 = 16.66 Hz

– Rotational frequency of gear 2:fR2 = rpm2/60 = 15.87 Hz

– Meshing frequency:fg = fR1*Z1 = fR2*Z2 = = 333.33 Hz

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Spectral analysis: Sound gears

• No sidebands occur aroundthe meshing frequency and harmonics

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18-30

-20

-10

0

10

20

30

Time [s]

0 200 400 600 800 1000 1200 1400 1600 1800 20000

2

4

6

8

10

12

Frequency [Hz]

200 300 400 500 600 700 8000

0.1

0.2

0.3

0.4

0.5

Frequency [Hz]

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Spectral analysis : gear 1 has a fatigue crack in a tooth

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18-30

-20

-10

0

10

20

30

Time [s]

0 200 400 600 800 1000 1200 1400 1600 1800 20000

2

4

6

8

10

12

Frequency [Hz]

200 300 400 500 600 700 800 90

0.1

0.2

0.3

0.4

0.5

Frequency [Hz]

• Sidebands occur around the meshing frequency and itsharmonics .

39

Cepstrum ( “quefrency» domain)

• Modulation determines sidebands• The frequency distance between sidebands is the rotational

frequency of the two gears. • Thus, a periodicity in the spectrum exists, due to the sidebands.

Complex CepstrumX(f) is the spectrum of the time signal x(t)X(f) = FFT{x(t)} c F log X fc

-1

•CEPSTRUM is a sort of a spectrum of a spectrum. It is used in order to determine periodicity in the spectrum, i.e. the presence of a family of harmonics.

40

Cepstrum analysis

• Sound gears

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.1

0.2

0.3

0.4

Quefrency [s]

Gear 1 hasa fatiguecrack in a tooth

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.1

0.2

0.3

0.4

Quefrency [s]

0.06 s

0.12 s

• Rotational period of gear 1 (ramonics of gear 1)TR1 = 60/rpm1 = 1/fR1 = 0.06 s

• Rotational period of gear 2 (ramonics of gear 2)TR2 = 60/rpm2 = 1/fR2 = 0.063 s

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Cepstrum analysis

Gears 1 and 2 havea fatiguecrack in a tooth

Gear 2 hasa fatiguecrack in a tooth

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.1

0.2

0.3

0.4

Quefrency [s]

0.063 s

0.126 s

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.1

0.2

0.3

0.4

Quefrency [s]

0.06 s

0.12 s0.063 s

0.126 s

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Monitoring and diagnostics of bearings

43

(Single-row ballbearing)

(Angular contactball bearing)

(Double‐rowself‐aligningball bearing)

(Ball thrust bearing)

(Cylindrical roller bearing) 

(Barrel‐shapedroller bearing )

(Tapered roller bearing) 

(Needle bearing)

Ball bearings

44

Main defects in bearings

• The contact between balls and rings (outer and inner) is characterized by high contact pressure. Fatigue phenomena can occur on the ring surfaces. The main defects regard the surface of balls and rings.

• Pitting is the most common defect.

Pitting wear is due to surface failure of a material as a result of fatigue stresses

45

Other defects

– Bachlash between shaft and inner ring or between outer ring and the house

– Bad lubrication – Excessive axial load

46

Conseguence

• Each time that a ball runinto a surface defect, an impact occurs

The impacts determine train of impusiveforces which cause vibration and noise. 

47

Vibration signal characteristics

• Each localized defect is charachterized by a proper fundamentalfrequency, proportional on the rotational speed of the shaft.

• This frequency is the frequency of the impacts between ballsand the defects and depends on:– Geometrical characteristics of the bearings– Number of balls– Type of defect (on the inner, on the outer ring, ...)

• The train of impacts is periodic.• The vibrations are generally measured on the external casing• The frequency content of the measured vibration signal is

related to:– The impact frequency at low frequency (till 3 kHz)– The structural resonance of the casing, at high frequency

(more than 8-10 kHz).

The vibration analysis for monitoring and diagnostics isgenenrally carried out at high frequency.

48

Characteristic frequency of bearings

– Fundamental Train Frequency

– Ball Pass Frequency Inner

– Ball Pass Frequency Outer

– Ball Spin Frequency

Expression of the frequency [Hz]

FTF n dD

n dDi o

1120

1 1cos cos

Bearing component

BPFI Z n n dDi o

120

1 cos

BPFO Z n n dDi o

120

1 cos

BSF Dd

n n dDi o

1120

12

cos

49

Procedure• The impacts can excite the natural frequencies of the casing (high

frequency range) • The time vibration signal measured on the casing is a train of peaks with

damped oscillations at the natural frequency of the casing• The bearing defect is analysed in the resonance zone of the casing (high

frequency range)

Vibration Responce to the train of impacts Vibration Responce to the train of impacts

50

Amplitude Demodulation• The impact periodicity

(related to defect type) can be found be demodulationtechniques. The procedure is:

– Band pass filter around the natural frequency of the casing (high freq. range)

– Envelope of the filtered time signal

– The spectrum of the envelope shows the fundamental frequency of the defect

0 10 20 30

Unfiltered time signal

Time [ms]0 5000 10000

Spectrum of the Unfiltered time signal

Frequency [Hz]

0 10 20 30

Filtered time signal

Time [ms]0 5000 10000

Spectrum of the Filtered time signal

Frequency [Hz]

0 10 20 30

Envelope

Time [ms]0 500 1000 1500 2000

Spectrum of the Envelope

Frequency [Hz]

51

Example- Experimental signal

Schematic of rolling bearing shaft

• This is the test bench. A and B are the two bearings. B is the tested bearing with defects. A radial load of 500N is applied.

• Shaft rotational frequency: 26.67 Hz (about 1600 rpm) • Outer race defect frequency: 129.8 Hz (1 / 7.70 ms)• Inner race defect frequency: 190.2 Hz (1 / 5.26 ms)• Rolling element defect frequency: 133.7 Hz (1 / 7.48 ms)• Cage rotational frequency: 10.8 Hz (1 / 92.60 ms)

52

• Sound condition

0 0.02 0.04 0.06 0.0-100

-50

0

50

100

Time [s]

[m/s

^2]

Normal Condition

Outer race defect frequency       

(1 / 7.70 ms)

0 0.02 0.04 0.06 0-100

-50

0

50

100

Time [s]

[m/s

^2]

Outer Race Defect

Time domain analysis

53

• Sound condition

Time domain analysis

0 0.02 0.04 0.06 0.-100

-50

0

50

100

Time [s][m

/s^2

]

Normal Condition

Inner race defect frequency      (1 / 5.26 ms)

0 0.02 0.04 0.06 0.0-100

-50

0

50

100

Time [s]

[m/s

^2]

Inner Race Defect

54

Statistical analysisSound condition Outer race defect Inner race defect

Mean –0.2265 –0.4543 –0.2861

Standard 12.0008 20.8323 19.6452

Skewness 0.0242 0.1948 –0.0163

Kurtosis 3.0728 4.4206 4.9670

RMS 12.0030 20.8372 19.6473

Dev. 

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• Sound condition

Outer race defect frequency 129.8 Hz

Spectral analysis – low frequency range

0 50 100 150 20

1

2

3

Frequency [Hz]

Ampl

itude

[m/s

^2]

Normal Conditio

0 50 100 1500

1

2

3

Frequency [Hz]

Ampl

itude

[m/s

^2]

Outer Race Defe

56

• Sound condition

Outer race defect frequency 129.8 Hz

Spectral analysis – at the first resonance frequency (high freq range)

1500 2000 250

2

4

6

8

Frequency [Hz]

Ampl

itude

[m/s

^2]

Normal Condition

1500 2000 250

2

4

6

8

Frequency [Hz]

Ampl

itude

[m/s

^2]

Outer Race Defec

57

• Sound condition

Outer race defect frequency   (1 / 7.70 ms)

Demodulation: envelope

0 0.02 0.04 0.06-20

0

20

40

60

80

Time [s]

Enve

lope

Normal Condition

0 0.02 0.04 0.06-20

0

20

40

60

80

Time [s]

Enve

lope

Outer Race Defec

58

• Sound condition

Outer race defect frequency 129.8 Hz

Demodulation: envelope spectrum

0 100 2000

1

2

3

Frequency [Hz]

Enve

lope

spe

ctru

m

Normal Condition

0 100 2000

5

10

Frequency [Hz]

Enve

lope

spe

ctru

mOuter Race Defec