www.bksv.com Brel & Kjr Sound & Vibration Measurement A/S. Copyright Brel & Kjr. All Rights Reserved.
Introduction to Order Analysis
www.bksv.com, 2
IntroductionContents
Sources of Machine Vibration
Principles of Order Analysis
Various Methods of Order Analysis FFT based Order Tracking
Order Analysis.
Vold-Kalman Order Tracking Filter Technique
Additional tools Auto-Tracking, no tacho signals available
DC Speed Ramp signal
Signal enhancement
www.bksv.com, 3
Machines have been designed to perform certain tasks
Merits of Machines
However, due to design and/or manufacture flaws, wear/tear, machines
vibrate and make noise.Lets have a look at the sources of this
noise and vibration
www.bksv.com, 4
Energy Transfer in Machines
1Vibration excitation
due to imperfections in rotating parts
2Transfer of energy
to other parts of the machine through
the machine structure
4 and emission
of noise
3. causing
vibration in all parts of the
machine
www.bksv.com, 5
Measure on the Outside to Learn about the Inside
we can get information about what
happens inside the machine
and measurement of noise near the machine
From measurement of vibration on the
outside of the machine
www.bksv.com, 6
Moving and Fixed Parts in MachinesLets have a look at what a machine contains..
During operation these moving parts are themain causes of noise and vibration
A machine contains one or several rotating and reciprocating parts like shafts, gears, and pistons.
When the frequency of this vibration coincides with one of the resonance frequencies of the fixed parts (structural resonances) the structure will amplify the vibrations.
in addition, the machine contains a large number of fixed parts whichvibrate when excited by the vibration generated by the rotating parts.
www.bksv.com, 7
Forces and Vibration
891875
Vibration+ =InputForcesSystem
Response(Mobility)
Forces caused byImbalanceShockFrictionAcoustic
StructuralParameters:MassStiffnessDamping
+ =
VibrationParameters:AccelerationVelocityDisplacement
Frequency Frequency Frequency
www.bksv.com, 8
Sources of Machine VibrationThe moving parts of machines create vibration at different frequencies.
Frequency, Hz
Vibrationlevel
Vibration at the rotational frequency (1st order) of the main shaft, caused by unbalance
Extra high level of 6th harmonic/order due to imperfect fan with 6 blades
Vibration (suborders at 42-48% of RPM) caused by oil film whirl or whip in journal bearing
Vibrations at 50 or 60 Hz (incl. harmonics) caused by electromagnetic forces or electric
noise picked up from power cablesVibration caused by worn gear
12th
Vibration amplified by structural resonances in the machine structure
NOISE, i.e., vibrations causedby other machines or ambience
e.g., wind excitation or acoustic excitationHarmonics of speed of main shaft caused by
misalignment
Misalignment of the shaft causes vibration at lower harmonics = orders
(rotational frequency 1, 2, 3,)
2nd 3rd 4th 5th 6th 7th 8th 9th1st(Frequency, Hz)Order
www.bksv.com, 9
When we remove the colors used in the previous example
The Frequency Spectrum
We will therefore now demonstrate how we can identify and analyze different frequency components using
Order Analysis
it becomes very difficult to tell which vibration component account for which
property/defect!
Vibrationlevel
(Frequency, Hz)Order
www.bksv.com, 10
Principle of Order Analysis
The key to sound and vibration analysis on rotating machines ismeasurement of the rotational speed of the machine
simultaneously with measurement of sound and vibration.
The speed is normally measured with a Tacho probe giving one (or more) tacho pulse(s) for each revolution of the rotating part (shaft).
Order Analysis or Order Tracking(Rotational speed = RPM = Revolutions/minute = 1st order)
When the analysis is related to the rotational speed it is called
Vibration
MachineSound
Tacho
Speed = RPM = 1/T
T
www.bksv.com, 11
Older Analog Analysis techniques
Analog tracking filter and Analog recording
www.bksv.com, 12
Older Analog Analysis techniques
Analog tracking filter and Analog recording
www.bksv.com, 13
Storage of Spectra (Method 1)
Storage of Slices (Method 2)
+ Tags Speed values from Tachometer Average Speed values from Analyzers Time Process parameter (Overall level)
Tags
#
##
#
AverageSpeed 2
SpectraFFT, Order,
1/n Octave, etc...Slices
Order, Frequency bandOverall L,A,B,C levels
#
##
##
Time
#
##
##
Speed 1
#
##
#
Speed 2
#
##
#
AverageSpeed 1
Todays numerical method - Storage in Multi-buffers
#
##
#
Overalllevel
(based upon speed interval, time interval,..)
www.bksv.com, 14
Frequency [Hz]
1800
1400
1000
[RPM]Speed
0
5
10Vibration level
[m/s2]
Vibrationlevel[m/s2]
0
5
10
1000
1800160014001200
[RPM]Speed
Frequency [Hz]
Principle of Order TrackingTo investigate the machine during operation, e.g., during a run-up, we measure vibration spectra at certain RPM intervals. Since each spectrum is tagged with the actual RPM, we can show Waterfall plot and Contour plots of the vibration spectra as a function of RPM (z-axis).Notice how the contour plot makes it very easy to separate spectral components related to the speed of the machine from other components, e.g., structural resonances.
www.bksv.com, 15
From the plots we can extract just the information we want: Order or Structural Resonance slices.
Principle of Order Analysis
These slices can be viewed during the measurement or extracted from the stored spectral information after the measurement as post-processed slices.
Speed [RPM]
[m/s2]
05
10 1st order
Speed [RPM]
[m/s2]
05
106th order
Speed [RPM]
[m/s2]
05
10Structural
Resonance
Frequency [Hz]
1800
1400
1000
[RPM]Speed
0
5
10Vibration level
[m/s2]
www.bksv.com, 16
Mlt UP FFT spectrum(Vibration Z)Working : Input : Order Run-up : FFT Analyzer
0 40 80 120 160 200 240 280 320 360 400
0
1
2
2k
3k
4k
5k
[Hz]
[m/s]
[RPM] (Speed Tacho 1)
Mlt UP FFT spectrum(Vibration Z)Working : Input : Order Run-up : FFT Analyzer
0 40 80 120 160 200 240 280 320 360 400
0
1
2
2k
3k
4k
5k
[Hz]
[m/s]
[RPM] (Speed Tacho 1)
Analysis Methods of Order Analysis
FFT based Order Tracking (Real Time) Only lower orders are of interest Orders are well separated Rotational speed variation is limited
Digital Re-sampling Order Analysis (Real Time) High orders are of interest Rotational speed variation is wide and/or fast
Vold-Kalman Order Tracking (Post processing) Measurement situations are difficult
Crossing orders Very fast RPM change (high slew rate) Gear shift
Order waveform is wanted for playback
Order waveform of 1. and 3. order
3. order1. order
www.bksv.com, 17
Speed processing for FFT and Order analysis
Tacho processing method
Pulse train, n pulse per revolution
Auto Tracking, no Tacho signal
DC Voltage ramp
AB
www.bksv.com, 18
1- FFT based Order Tracking
FFTAnalyzer
Tacho-meter
Use: RPM tagging Extraction of
order slices
TimeSignals
TachoSignals
FFTSpectra
Analysis based on ordinary FFT spectrum analysis.FFT spectra and slices, shown as function of RPM measured by the tachometer.
Orderand
FrequencySlices
www.bksv.com, 19
Mlt UP FFT spectrum(Vibration Z)Working : Input : Order Run-up : FFT Analyzer
0 40 80 120 160 200 240 280 320 360 400
0
1
2
2k
3k
4k
5k
[Hz]
[m/s]
[RPM] (Speed Tacho 1)
Mlt UP FFT spectrum(Vibration Z)Working : Input : Order Run-up : FFT Analyzer
0 40 80 120 160 200 240 280 320 360 400
0
1
2
2k
3k
4k
5k
[Hz]
[m/s]
[RPM] (Speed Tacho 1)
Simple Contour plot and waterfallWaterfall and Contour plot of the same run-up test of the Vibration-Z sensor.
FFT based water fall analysis.
The contour plot has a delta order cut cursor at an oblique angle used to make slice cut of key orders vs RPM.
Mlt UP FFT spectrum(Vibration X) - sliceWorking : Input : Order Run-up : FFT Analyzer
1.2k 1.6k 2k 2.4k 2.8k 3.2k 3.6k 4k 4.4k 4.8k 5.2k
0
400m
800m
1.2
1.6
2
2.4
2.8
3.2
3.6
4
[RPM] (Nominal Values)
[m/s] Mlt UP FFT spectrum(Vibration X) - sliceWorking : Input : Order Run-up : FFT Analyzer
1.2k 1.6k 2k 2.4k 2.8k 3.2k 3.6k 4k 4.4k 4.8k 5.2k
0
400m
800m
1.2
1.6
2
2.4
2.8
3.2
3.6
4
[RPM] (Nominal Values)
[m/s]
www.bksv.com, 20
FFT based Order Tracking
Advantage: Low cost
(more channels for a given processing power) On-line analysis Slice extraction with multiple tacho references
Limitation: Smearing of higher orders Only for lower, well separated orders over a
limited RPM range and relatively slow run-up.
www.bksv.com, 21
2- Order Analysis (re-sampling)
OrderAnalyzer
Tacho-meter
The Sampling rate of an Order Analyzer changes in accordance with the rotational speed of the machine under investigation (tracking). The result is that individual orders remain on the same order line on the plot and smearing is avoided.With this technique close orders and very high orders can be identified and analysed.
Use: Tracking
reference RPM tagging Extraction of
order slices
TimeSignals
TachoSignal
OrderSpectra
OrderSlices
www.bksv.com, 22
FFT based vs. Order based: Whats the Difference?a) Original signal
b) Fixed sampling frequency (FFT Based) FFT Spectrum (no tracking)
Samples analyzed
Order Spectrum (tracking)c) Sampling according to tacho (Order Based)
Samples analyzed
fmax
fs = 2,56 fmax
Example: fs = 8 ffundamental
Frequency
4 Orders321Revolutions(periods)
Time
Time
810110/1
www.bksv.com, 23
Run-up/down Tests with re-sampling
Constant Frequency Curves
f = 50 Hz
RotationalSpeedRPM
Order No
3000
2400
1800
1200
600
1 2 3 4 5 6 7 8 9 10
f = 100 Hz
f = 150 Hz
880491
www.bksv.com, 24
Constant Frequency cursor in Order Contour Plots
White cursor line indicates a resonance in an Order based contour plot.
www.bksv.com, 25
Tacho GearingRatio 1:2
A
Probe
Factor
N pulses / rev
Factor = N, ex: 32 or 64ppr
Combined gearing = N Ratio
Ratio =Speed A
Speed B
23
17
AteethBteeth
= =
AB
B
A
Probe
www.bksv.com, 26
Order Analysis
Advantage: Accurate identification of higher orders, no smearing Analysis of high orders over a wide RPM range Analysis of close orders On-line analysis Fast runup can be handled with accurate Tacho (ex:60ppr)
Limitation: Depends on a reliable and accurate Tachometer No frequency slices
www.bksv.com, 27
Order Tracking Analysis
Time: When ?Referenced to the revolution of the shaft[Rev]
Order spectrum: How often?[per revolution]
Frequency Analysis
Time: When ?Referenced to the clock[sec]
Frequency spectrum: How often? [per second]
Order Tracking Analysis
Revolutions [Rev]
Harmonics [Order][per revolution]
Signal
Spectrum
Frequency Analysis
Time [sec]
Frequency [Hz][per sec]
FFT based vs. Order based: Whats the Difference?
www.bksv.com, 28
Time signals for FFT and Order analyzersRev (Vibration X)
W orking : Input : Input : Sync Avg Order Analyzer
0 1 2 3 4 5 6 7 8 9
-8
-6
-4
-2
0
2
4
6
8
[Revolution]
[m/s] Rev (Vibration X)W orking : Input : Input : Sync Avg Order Analyzer
0 1 2 3 4 5 6 7 8 9
-8
-6
-4
-2
0
2
4
6
8
[Revolution]
[m/s]
Time(Vibration X) - InputWorking : Input : Input : FFT Analyzer
0 10m 20m 30m 40m 50m 60m 70m 80m 90m 100m 110m 120m
-6
-4
-2
0
2
4
6
[s]
[m/s] Time(Vibration X) - InputWorking : Input : Input : FFT Analyzer
0 10m 20m 30m 40m 50m 60m 70m 80m 90m 100m 110m 120m
-6
-4
-2
0
2
4
6
[s]
[m/s]
On the left:
Time trace from and Order analyzer with an horizontal axis showing revolutions
On the right:
Time trace from and FFT analyzer with an horizontal axis showing seconds.
www.bksv.com, 29
Analysis without and with re-sampling
With tracking
Analysis of a vibration signal from a machine
with slightly varying speed
Without tracking
www.bksv.com, 30
Comparison of Order vs. FFT Analysis
www.bksv.com, 31
Order Analysis - with or without re-sampling
Run-up/down tests using frequency spectra, i.e. without re-sampling:
Advantages: Fast Orders referenced to different
speeds can be extracted from the same spectra
Easy to identify resonances (fixed frequencies) from contour plot
Easily understood
Disadvantages: Smearing of components High no. of FFT lines if wide RPM
and frequency range is required
Run-up/down test using order spectra, i.e. with re-sampling:
Advantages: No smearing Identification of higher harmonic
orders Low no. of lines in the spectra Wider slew rate Time data in crank domain
Disadvantages: More processing power required Accurate tacho required
www.bksv.com, 32
Vold Kalman Filtering
www.bksv.com, 33
TimeSignals
Vold-Kalman Order Tracking Filtering
RPMprofile
extraction
Vold-Kalman
Filter
Order waveform of 1. and 3. order
3. order
1. orderTime and tacho signalscaptured using
Time Capture Analyzer
OrderLevels
OrderWaveforms
for playback
1. order
Magnitude of 4 selected orders
9. order
3. order
10. order
Two step post-process on captured data:Step 1: Extraction of accurate RPM profile.Step 2: Filter out orders according to the
RPM profile.
TachoSignals
PCMemory
www.bksv.com, 34
Gear Shift Event: RPM Profiles
Light truck, V-8 engine light load condition
Gear shifting events first, second, third and forth
gear engaged Engine and drive-shaft RPM
profiles
Gear shifting event analyzed from second to third gear
RPM profiles raw and curvefitted RPM two hinge points
www.bksv.com, 35
Editing of single orders: Waveform extraction
Removal or attenuation of orders in run up/downmeasurements
Total signal
9th order waveform
9th order removedor attenuated
Sound Quality synthesis studies
www.bksv.com, 36
Vold-Kalman Order Tracking Filtering*
Advantage: Can handle complicated situations like:
Crossing orders Gear shifts Tacho drop-out
Unlimited slew rate/speed variation Useful for Sound Quality work
Limitation: Off-line analysis More time consuming
* For a detailed description see Sound and Vibration, April 1999, p. 34 - 44:Characteristics of the Vold-Kalman Order Tracking Filter
www.bksv.com Brel & Kjr Sound & Vibration Measurement A/S. Copyright Brel & Kjr. All Rights Reserved.
AutotrackingFunctionality in PULSE LabShop and Reflex
Order tracking without direct access to the rotating parts of the machine
Tacho Processing - AutoTracking
www.bksv.com, 38
Introduction Rotating Machinery
Knowing the RPM of the rotating parts is important for analysis and diagnostics
Order Analysis
Limitations of the Tacho Solution Requires direct access to
rotating parts and dedicated sensors Mounting is time consuming and difficult
(compact engines, safety requirement)
Benefits of Autotracking Indirect measurements
Accelerometers, Microphones Order Analysis
Tacho signal not available or difficult to get
Applications Drivetrain, Turbocharger, Turbine, Engine
01
www.bksv.com, 39
Autotracking Basic Idea
An frequency tracking method where the fundamental frequency is indirectly extracted from the measured vibration or acoustic signal rather
than directly from a tacho probe
Method based on Bayesian statistics, where the posterior distribution of the fundamental frequency is computed
conditioned on the measured data and a harmonic model of the signal
where d: measured signal; I: prior knowledge in the estimation model;
n: record index; N: Number of previous records
Idp Nnnnnn ,,,,,, 03020100
03
www.bksv.com, 40
How to select harmonics, 1 ?
Acoustic signal from 5 cylinder engine
Expected harmonics:2.5, 5, 7.5 etc.
Pretest Inspection
Experimental data
09
5
2.5 2
7.5
www.bksv.com, 41
3 Cylinder engine exampleFFT waterfall showing the key
orders = 1 and 1.5
Speed versus time for regular tach pulse signal (blue) and AutoTracking generated speed siignal (orange). The two are identical until the end of the run down.
Order analysis waterfall using the AutoTracking Tacho signal
www.bksv.com, 42
Autotracking Benefits State-of-the-art solution
Based on Bayesian statistical methods using measured dataharmonic structure and tracking profile
Supplement to current Tachometer
No need for direct access to rotating parts A direct tacho signal may not be available
The tacho signal may be of bad quality
No need for dedicated tacho probes and tacho channels Less and inexpensive equipment (indirect meas using accs and mics)
Reduced channel count (use existing channels)
No problems with e.g. ground loops
Ease-of-use No time-consuming and difficult mounting (compact engines)
Reduced safety requirements
19
www.bksv.com, 43
Tacho Processing DC RampFeature introduced in Pulse 11
Order Spectrum Fourier Phase is independent of the RPM
Tracking using Aux.Signal Input [V/rpm] as tracking reference
The DC speed signal can come from the CAN bus.
www.bksv.com, 44
Signal EnhancementSpectrum Enhancement
Special for Order Analysis Advance feature
www.bksv.com, 45
Signal Enhancement
Applications Wave form analysis Reduce background noise Enhance orders Separaton of mechanical and
electrical vibrations
Signal enhancement or Synchronous time domain averaging
Extraction of a periodically repeating signalfrom additive contaminating noise
www.bksv.com, 46
Application Example
Signal enhancement in machine analysis Vibration measurement on a machine shop floor
ContaminatingBackground Vibration
MachineVibration
Accelero-meter
VibratingMachine
TachoProbe
Vibration
www.bksv.com, 47
Traditional Average vs. Signal Enhancement
Time
FFT
FFT
TimeTime
FFT FFT
FFT
Time
Time
Time Time
Average
Average
Traditional SpectrumAveraging
Signal Enhancement
www.bksv.com, 48
Time Averaging vs. Synchronous Time Averaging
Time averaging i.e. no trigger
Time synchronous averaging i.e. trigger
Averages to zero Extracts waveform
)t(a1
)t(a2
)t(a jN1
+
...
)t(a1
)t(a2
)t(a jN1
+
...
www.bksv.com, 49
Enhancement Order specturm
Sync Order spectrum(Vib 1)Working : Input : Input : Sync Order Analyzer
16 18 20 22 24 26 28 30 32 34 36 38 40
-80
-70
-60
-50
-40
-30
-20
-10
0
[Order]
[dB/1.00 in/sec] Sync Order spectrum(Vib 1)Working : Input : Input : Sync Order Analyzer
16 18 20 22 24 26 28 30 32 34 36 38 40
-80
-70
-60
-50
-40
-30
-20
-10
0
[Order]
[dB/1.00 in/sec]
Order spectrum data with and without Time Synchronous averaging after 50 averages only.
www.bksv.com, 50
Literature for Further Reading
Time Capture Type 7705(Brel & Kjr Lecture Note BA 7653-11:)
Vold-Kalman Order Tracking Filter (Brel & Kjr Lecture Note BA 7645-11:)
Frequency Analysis by R.B.Randall(Brel & Kjr Theory and Application Handbook BT 0007-11)
Order Tracking Analysis by by S. Gade, H. Herlufsen, H. Konstantin-Hansen, J. Wismer(Brel & Kjr Technical Review No. 2, 1995)
Non-stationary Signal Analysis using Wavelet Transform, Short-time Fourier Transform and Wigner-Ville Distribution by S. Gade, Klaus Gram-Hansen(Brel & Kjr Technical Review No. 2, 1996)
www.bksv.com Brel & Kjr Sound & Vibration Measurement A/S. Copyright Brel & Kjr. All Rights Reserved.
Annual Sound & Vibration ConferenceDetroit, MI
September 24-26, 2013
Dont miss the chance to register early for our upcoming Sound & Vibration Conference.
Please visit us on the web at www.bksv.com to learn more about the conference and to register early.
www.bksv.com, 52
Questions?