Order Analysis Basics

www.bksv.com Brel & Kjr Sound & Vibration Measurement A/S. Copyright Brel & Kjr. All Rights Reserved.

Introduction to Order Analysis

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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

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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

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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

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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

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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.

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Forces and Vibration

891875

Vibration+ =InputForcesSystem

Response(Mobility)

Forces caused byImbalanceShockFrictionAcoustic

StructuralParameters:MassStiffnessDamping

+ =

VibrationParameters:AccelerationVelocityDisplacement

Frequency Frequency Frequency

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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

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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

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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

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Older Analog Analysis techniques

Analog tracking filter and Analog recording

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Older Analog Analysis techniques

Analog tracking filter and Analog recording

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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,..)

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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.

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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]

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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)


0 40 80 120 160 200 240 280 320 360 400

0

1

2

2k

3k

4k

5k

[Hz]

[m/s]


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

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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

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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

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0 40 80 120 160 200 240 280 320 360 400

0

1

2

2k

3k

4k

5k

[Hz]

[m/s]



0 40 80 120 160 200 240 280 320 360 400

0

1

2

2k

3k

4k

5k

[Hz]

[m/s]


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]

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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.

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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

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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

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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

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Constant Frequency cursor in Order Contour Plots

White cursor line indicates a resonance in an Order based contour plot.

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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

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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

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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?

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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.

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Analysis without and with re-sampling

With tracking

Analysis of a vibration signal from a machine

with slightly varying speed

Without tracking

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Comparison of Order vs. FFT Analysis

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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

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Vold Kalman Filtering

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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

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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

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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

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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


AutotrackingFunctionality in PULSE LabShop and Reflex

Order tracking without direct access to the rotating parts of the machine

Tacho Processing - AutoTracking

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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

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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

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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

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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

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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

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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.

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Signal EnhancementSpectrum Enhancement

Special for Order Analysis Advance feature

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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

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Application Example

Signal enhancement in machine analysis Vibration measurement on a machine shop floor

ContaminatingBackground Vibration

MachineVibration

Accelero-meter

VibratingMachine

TachoProbe

Vibration

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Traditional Average vs. Signal Enhancement

Time

FFT

FFT

TimeTime

FFT FFT

FFT

Time

Time

Time Time

Average

Average

Traditional SpectrumAveraging

Signal Enhancement

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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

+

...

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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.

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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)


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Dont miss the chance to register early for our upcoming Sound & Vibration Conference.

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