Vibration AnalysisBasic Concepts

What is Vibration ?

Vibration is a pulsating motion of a machine or a

machine part from its original position of rest and

can be represented by the formula :

Vibration Amplitude Response = Dynamic ForceDynamic Resistance

Force Balance

M

CK

1. The Exciting Force ‘F’ such as Unbalance

2. The mass of vibrating system ‘M’

3. The stiffness of vibrating system ‘K’

4. The damping characteristics ‘C’

Vibration Characteristics

Amplitude

Frequency

Phase

Direction

Vibration Characteristics

Amplitude

Frequency

Phase

Direction

Vibration Displacement

MD

ISP

LA

CE

ME

NT

Time

Minimum Displacement

Max Displacement

Pk-P

k

Amplitude Units

Displacement Pk-Pk mils or microns

Vibration Velocity

M

Ve

locity

Minimum Velocity

Max Velocity

RM

S

RMS of a Sinusoidal Wave

T = 1__f

Where T = period of one cycle of the vibration

v = instantaneous velocity

t = the variable time

i

Amplitude Units

Displacement Pk-Pk mils or microns

Velocity RMS in/sec or mm/sec

Vibration Acceleration

M

Acce

lera

tio

n

Minimum Acceleration

Max Acceleration

Pk

Amplitude Units (Metric)

Displacement Pk-Pk microns

Velocity RMS mm/sec

Acceleration Pk g’s

Amplitude Units (Imperial)

Displacement Pk-Pk mils

Velocity Pk in/sec

Acceleration RMS g’s

Comparison of Amplitude Units

Displacement

Velocity

Acceleration

What do they measure?

Displacement How far it moves

Mils or Microns

Velocity How fast it moves

in/sec or mm/sec

Acceleration How quickly velocity changes

g or in/sec2 or mm/sec2

How Much is too Much ?

Manufacturers specified limits

End User limits

Comparison with identical machines

Same Load, Mounting, Temp, Pressure

Standards specific to type

BS 4999 part 142 Electric Motors

General Standards

BS-4675 (ISO-2372), VDI - 2056

Historical Data

Conversion of Parameters

METRIC UNITS

Where: D=Peak-To-Peak Displacement (µm Pk-Pk)

V=Peak Velocity (mm/sec Pk)

A=Peak Acceleration (g’s-Pk)

F=Frequency (CPM)

V = DF

19,100

V = 3690 A

F

A = DF2

70,470,910

D = 9,100V

F

A = VF

3690

D = 70,470,910

F2

Conversion of Parameters

ENGLISH UNITS

Where: D=Peak-To-Peak Displacement (Mils Pk-Pk)

V=Peak Velocity (in/sec Pk)

A=Peak Acceleration (g’s-Pk)

F=Frequency (CPM)

V = DF

19,100

V = 93640 A

F

A = DF2

1,790,000,000

D = 19,100V

F

A = VF

93,640

D = 1,790,000,000

F2

Velocity RMS - MM/Sec

RMS - root mean square, appears at 0.707 the value of the amplitude

Gives a good overall picture, of the vibration in our machine

Acceleration - G-s

Value from the base line to the peak amplitude

Looks a force generated in our machine (High frequency domain)

Displacement - microns

Total movement, value is from Peak to Peak

Ignores all high frequencies and looks at the low frequency

Amplitude Units

Vibration Characteristics

Amplitude

Frequency

Phase

Direction

Vibration Frequency

Vibration Frequency is simply a measure of the

numbers of complete cycles that occur in a

specified period of time such as ‘Cycles per

Second’ or ‘Cycles per Minute’. Frequency is

related to the period of vibration by this simple

formula :

Frequency = 1 / Period

Vibration Frequency

MD

ISP

LA

CE

ME

NT

Time, mili sec0.5 1.0

Time Period = 1.0 mili sec

Frequency = 1 / Time Period

Frequency = 1 / 10-3 CPS

Frequency = 1000 CPS or Hz

Frequency = 1000*60 CPM

Frequency = 60 kCPM

Significance of Frequency

The forces that cause vibration are usually

generated through the rotating motion of the

machine parts. These forces change in direction or

amplitude according to rotational speed of the

machine components, most vibration problems will

have frequencies that are directly related to the

rotational speeds.

Vibration Frequency is an Analysis or Diagnostic Tool

Vibration Frequency & Likely CausesFrequency InTerms of RPM

Most Likely Cause Other Possible Causes and Remarks

1 X RPM Unbalance 1. Eccentric Journals2. Misalignment or bent shaft if High Axial Vibration3. Bad belts if RPM of belt4. Resonance5. Reciprocating Forces6. Electric Problems

2 X RPM MechanicalLooseness

1. Misalignment if high axial vibration2. Reciprocating Forces3. Resonance4. Bad belts if 2 X RPM of belt

3 X RPM Misalignment Usually a combination of misalignment and excessive axialclearances (looseness)

Less than 1 X RPM Oil Whirl (Less than ½ RPM) 1. Bad Belt Drives2. Background Vibration3. Sub-Harmonic Resonance4. Beat Vibrations

Synchronous ACLine Frequency

Electrical Problems Common Electrical Problems include broken rotor bars, unbalancedphases in poly-phase system, unequal airgap

2 X SynchronousLine Frequency

Torque Pulses Rare as a possible unless resonance is exited

Many Times RPMHarmonically Related

Bad GearsAerodynamic ForcesHydraulic ForcesMechanical LoosenessReciprocating Forces

1. Gear Teeth times RPM if bad gear2. Number of fan blades times RPM3. Number of impeller vanes times RPM4. May occur 2,3,4 and sometimes higher harmonics if severe

looseness

High FrequencyNot Harmonically Related

Bad Anti Friction Bearings 1. Bearing Vibration2. Cavitation, recirculation and flow turbulance cause random, high

frequency vibration3. Improper lubricationof journal bearing (friction exciting vibration4. Rubbing

Comparison of Parameters

F (CPM)

60

600

6,000

60,000

600,000

D (um)

100.00

10.00

1.00

0.10

0.01

V (mm/s)

0.314

0.314

0.314

0.314

0.314

A (g)

0.0002

0.002

0.020

0.201

2.012

LOG

AMPLITUDE

(um, mm/s, g)

LOG FREQUENCY (CPM)

Displacement

Velocity

Acceleration

Force Indicator

Fatigue Indicator

Stress Indicator

60 600 6K 120K 600K

10 um

.314 mm/s

.002 g

.20 g

.314 mm/s

.1 um

Vibration Characteristics

Amplitude

Frequency

Phase

Direction

What is Phase ?

The angular reference … at a given frequency …

at one instance in time … of a moving part … to a

fixed point

The angular reference … at a given frequency …

at one instance in time … of two moving parts …

to a fixed point

Vibration Phase

Phase is simply a convenient means of

determining the relative motion of two vibrating

parts of machines. It is measured in degrees or

clocks.

Vibration Phase

Phase Relationship as Used With Machinery Vibration

Phase - Phase Vs Amplitude Units What we are going to see now is the significant difference between

the phase relationships of the three different amplitude units.

This is governed by the laws of physics

– Using Displacement as the base unit, then readings taken in Velocity will lead Displacement by 90°. Acceleration will lead Velocity by 90°, therefor leading Displacement by 180°.

It is important to understand the phase shifts with different amplitude units, especially when comparing new data to previous data if the units are different.

Velocity Waveform

+90° +90°

Displacement Waveform

Acceleration Waveform

Phase - Acquiring Phase Data

How does the cross channel collect phase data, if ‘phase’ is the relationship between the peak value and the 1x Ts Pulse?

Cross channel uses the first transducer as a reference point, and the second transducer as the comparison.

– Taking the peak value from both waveforms over the same period of time and calculating the difference in the same way as before

Cross Channel Phase

Phase - Acquiring Phase Data

Single Channel Phase Acquisition - How it Works!

The Phase Angle is calculated using the formula:

As stated earlier phase data can be acquired by two means:

– Single Channel

– Dual Channel

Single Channel Phase

Phase Angle =(Difference in Time)

(Time of 1 Revolution)X 360°

Phase - Amplitude Characteristics

In basic vibration training you were introduced to the three units to measure amplitude:

– Velocity

• The most common unit used for trending data

• Defined as the ‘Rate of Movement’

– Acceleration

• Used for high speed machinery were impacting is common - Gears, Trouble Shooting Bearings, Peakvue

• Defined as ‘Change in Velocity over a period of time’

– Displacement

• Mainly used when looking at relative motion or slow speed machines

• Defined as ‘Total movement from a reference point ’

Phase - Amplitude Characteristics

Basic vibration also introduced to the effects each unit has on the spectral data

– Velocity

• Gives you a good overall level of vibration of both high frequency and low frequency data

– Acceleration

• Accentuates the high frequencies and ignores the low frequencies. Good for looking at impacts.

– Displacement

• Looks at the low frequency data (relative motion) and ignores the high frequency impacting

As expected, the amplitude units effect the time domain much in the same way they do the frequency domain

Phase - Amplitude Characteristics Displacement

The spectral plot displays no high frequency data.

This is also apparent in the waveform by the lack of noise riding on the sinusoidal shape 40 - Dust Filter Fan No.2 C/Mill

M7292 -F1H Fan Inboard Horiz ontal

ROU TE SPECTRU M

18-Apr-02 18:04:29

OVERALL= 5.46 V-DG

P-P = 94.27

LOAD = 100.0

RPM = 1418.

RPS = 23.63

0 30 60 90 120

0

30

60

90

120

Frequency in kCPM

P-P

Dis

p in

Mic

ron

s

ROU TE WA VEFOR M

18-Apr-02 18:04:29

P-P = 87.38

PK (+) = 55.85

PK (-) = 54.21

CR ESTF= 1.81

0 1 2 3 4 5

-60

-40

-20

0

20

40

60

80

Revolution Number

Dis

pla

ce

me

nt

in M

icro

ns

40 - Dust Filter Fan No.2 C/Mill

M7292 -F1H Fan Inboard Horiz ontal

ROU TE SPECTRU M

18-Apr-02 18:04:29

OVERALL= 5.46 V-DG

RMS = 5.44

LOAD = 100.0

RPM = 1418.

RPS = 23.63

0 30 60 90 120

0

1

2

3

4

5

6

7

Frequency in kCPM

RM

S V

elo

cit

y in

mm

/Se

c

ROU TE WA VEFOR M

18-Apr-02 18:04:29

RMS = 4.84

PK (+) = 15.15

PK (-) = 12.86

CR ESTF= 3.13

0 1 2 3 4 5

-15

-10

-5

0

5

10

15

20

Revolution Number

Ve

loc

ity

in m

m/S

ec

Phase - Amplitude Characteristics Velocity

Viewing the same data linearly across the spectra displays high and low frequency data that was not apparent with ‘Displacement’.

The waveform displays an underlying sinusoidal waveform, but is carrying the high frequency data as well - noisier waveform

40 - Dust Filter Fan No.2 C/Mill

M7292 -F1H Fan Inboard Horiz ontal

ROU TE SPECTRU M

18-Apr-02 18:04:29

OVERALL= 5.46 V-DG

RMS = 1.50

LOAD = 100.0

RPM = 1418.

RPS = 23.63

0 30 60 90 120

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Frequency in kCPM

RM

S A

cc

ele

rati

on

in G

-s

ROU TE WA VEFOR M

18-Apr-02 18:04:29

RMS = 1.55

PK (+) = 6.64

PK (-) = 5.96

CR ESTF= 4.29

0 1 2 3 4 5

-8

-6

-4

-2

0

2

4

6

8

Revolution Number

Ac

ce

lera

tio

n in

G-s

Phase - Amplitude Characteristics Acceleration

The spectra displays a lot of high frequency data, raised noise floor level.

Waveform displays very distinct impacting, common to the high frequency data

Amplitude units also effect ‘phase readings

Limitations

There are a few disadvantages to using Single Channel Phase analysis:

– You have to have direct line of sight from the tachometer to the shaft (which is not always possible)

– Reflective tape needs to be on the shaft (This becomes a problem if the machine is running and no tape is fitted?)

– Direct sunlight or excessive vibration can cause error between the tachometer reading and the analyzer.

Where to take Readings

Before we take any phase data it is important to understand why we would want to collect phase data, and what can it tell us?

Common terminology used when analyzing phase data are:

– In Phase (0°)- Meaning the relationship between the two points are moving uniformly in the same direction.

– Out of Phase (180°) - Meaning the relationship between the two points are moving in different directions

Phase data is a diagnostic tool and is most commonly used to confirm a suspect fault, such as:

– Imbalance

– Misalignment

– Looseness

– Resonance

Where to take Readings

We need to acquire phase data in a methodical way to enable us to distinguish certain fault types, (which will be discussed in other topics)

Next take an end-end Horizontal Phase reading. Again note down the phase and amplitude results

Starting with the ‘Driver’ take and end-end Vertical Phase reading. Note down the Phase and Amplitude results

When taking phase data, there is a lot of information we need to remember (amplitudes, in or out of phase and phase angle). To make things easier there is a simple method to follow:

Precautions!

There are a few precautions to consider when collecting and analyzing phase data. These are:

– 1) Transducer Direction

– 2) Observation Errors

Transducer Direction!

– The orientation of a transducer is very important and is the most common cause of interpretation error (more common in the axial direction)

180°

Data taken across a coupling shows 180° phase difference.

– Are these ‘in’ or ‘out’ of phase?

Phase - Transducer Polarity The selection of different amplitude units is just one source of

hardware induced phase shifts.

Another source of induced phase shift is ‘Transducer Polarity’ This is to do with the internal wiring of the transducer.

– Two identical transducers can be wired the opposite way round to each other causing a 180° phase shift between readings. (Only associated with ‘Cross Channel Phase’

A B

Place the two transducers side by side and acquire a phase reading.

The phase angle should be

0° if it is 180° then this should be deducted from all

phase readings thereafter

Phase Summary

It is important to understand phase as it is a useful tool for doing ‘Investigative’ vibration analysis.

Phase data is a useful tool for finding many common machine faults

– Imbalance

– Misalignment

– Looseness / Soft Foot

It also helps the analyst to visualise the actual movement of the machine

– Like a basic ODS.

Be careful of ‘Transducer Polarity’ and ‘Transducer Direction’ as each can effect the phase angle

Allow a 30° tolerance across all phase data

Vibration Characteristics

Amplitude

Frequency

Phase

Direction

Vibration Direction

Vibration is measured in three direction

– Horizontal

– Vertical

– Axial

Motor Pump

M1H

M1V

M1A

M2H

M2V

M2A

P1H

P1V

P1A

P2H

P2V

P2A

OB IB OBIB

Measurement Points

Vibration Spectrum

The term ‘FFT’ stands for ‘Fast Fourier Transform’

It is named after an 18th century mathematician called Jean Baptiste Joseph Fourier.

He established:

– Any periodic signal could be represented as a series of sines and cosines. Meaning if you take a time waveform and mathematically calculate the vibration frequency along with their amplitudes, we can convert this in to a more familiar frequency format.

Fast Fourier Transform

TimeAmplitude

TimeAmplitude FrequencyAmplitude

Complex waveform changes to a simple waveform

The waveform is

converted to an

amplitude/frequency

domain

This is called a

spectrum

Fast Fourier Transform

Before we learn how to diagnose potential faults within a spectrum, we need to understand the units of measurement.

However there are a few considerations we need to take into account first.

As well as the frequency scale and units

The vibration data that is converted from the waveform by the FFT process can be seen very clearly

The amplitude scale and the amplitude units are important

Spectrum

Energy in Spectrum

Synchronous energy - related to turning speed.

All the other peaks are harmonics off, which means they are related to the first peak

We can see from the spectrum that the first peak is at 1 Orders (which means it is 1 x turning speed)

Examples of synchronous energy:

1) Imbalance 2) Misalignment 3) Gearmesh

Synchronous Energy

Non-synchronous energy -not related to turning speed

We can see from the spectrum that the first peak is at 10.24 Orders. This is not related to turning speed.

• Examples of non-synchronous energy:

• Bearings Multiples of belt frequency Other Machine Speeds

Non- Synchronous Energy

Sub-synchronous energy -Less than turning speed

The spectrum shows the first impacting peak below 1 Order. This is sub-synchronous energy

Examples of sub-synchronous energy are:

Belt Frequencies

Other Machine Speeds

Cage Frequencies

Sub-Synchronous Energy

Lines of Resolution

Lines of Resolution (LOR) determine how clear the peaks(data) are defined within our spectrum.

The more lines we have over the same F-max (Maximum frequency scale). The more accurate our data will be

Example.

– The diagram below shows data that has been collected using 400 LOR. Notice how the top of the peaks are capped. When the LOR are increased the data becomes more accurate.

L2 - TA 16

TA 16 -M1H Motor Outboard H orizontal

A nalyze Spectrum

13-Mar-01 09:13:53

PK = .7078

LOA D = 100.0

R PM = 1496.

R PS = 24.94

0 400 800 1200 1600

0

0.1

0.2

0.3

0.4

0.5

Frequency in H z

PK

Ac

ce

lera

tio

n in

G-s

The spectrum shown displays data at 800 L.O.R with an Fmax of 1600 Hz

Lines of Resolution

L2 - TA 16

TA 16 -M1H Motor Outboard H orizontal

A nalyze Spectrum

13-Mar-01 09:13:53

PK = .7078

LOA D = 100.0

R PM = 1496.

R PS = 24.94

0 400 800 1200 1600

0

0.1

0.2

0.3

0.4

0.5

Frequency in H z

PK

Ac

ce

lera

tio

n in

G-s

L2 - TA 16

TA 16 -M1H Motor Outboard H orizontal

A nalyze Spectrum

13-Mar-01 09:14:16

PK = .3852

LOA D = 100.0

R PM = 1497.

R PS = 24.95

0 400 800 1200 1600

0

0.04

0.08

0.12

0.16

0.20

Frequency in H z

PK

Ac

ce

lera

tio

n in

G-s

The spectrum shown displays data at 800 L.O.R with an Fmax of 1600 Hz

The second spectrum displays the same data but with 3200 L.O.R over the same Fmax

Lines of Resolution

There are 8 LOR settings we can choose from on the analyzer. These start at 100 Lines and go up to 6400 Lines.

The average number of LOR is around 800 Lines for a typical motor/pump set up

Remember. If you double your lines of resolution you double your

data collection time.

To change the LOR settings we need to alter our parameter set.

This is done in the Database Setup program

Lines of Resolution

Questions

0.001 0.002 0.003 0.004

3

3

mil

s

sec

CPM

0.001 0.002 0.003 0.004

3

6

mil

s

sec

CPM

T= 0.002

F = 1 / T

F= 1/0.002

F= 500 Hz

F= 500 x 60 CPM

F= 30000 CPM

30000 60000 90000

Mil

s P

-P

3

0.002 0.004 0.006 0.008

3

3

In /

sec

sec

CPM

0.002 0.004 0.006 0.008

3

3

In/s

ec

sec

CPM30000 60000 90000

In /

sec

Pk

3

0.003 0.006 0.009 0.012

2

2

G’s sec

CPM

1.414

CPM10000 20000 30000

G’s

RM

S

0.003 0.006 0.009 0.012

2

2

G’s sec

0.015 0.030 0.045 0.060

11m

ils

sec

0.01 0.02 0.03 0.04

4.2

In/s

ec

sec

0.032 0.064 0.096 0.112

10

G’s

sec

Bonus : if RPM = 1000

What type of Energy is this?

Bonus : if RPM = 3000, and

Fmax = 50 x RPM, Using

LOR = 1600, Calculate

BW in CPM & Hz?

Bonus : if RPM = 3600

What type of Energy is this?

0.001 0.002 0.003 0.004

3

mil

s

sec

CPM

0.9

6

CPM30000 60000 90000

Mil

s P

-P

0.001 0.002 0.003 0.004

3

mil

s

sec

0.9

1.8

0.005 0.010 0.015 0.020

10

In /

sec

sec

CPM

4

10

CPM6000 12000 18000

In /

sec

Pk

4

24000

0.005 0.010 0.015 0.020

10

In /

sec

sec

4

B: G-s

Acceleration can be measured in which unit?

A: mm/sec B: G-s

C: Microns D: Hz

£100

C: Velocity

The unit RMS or mm/sec can equate to which amplitude measurement?

A: Acceleration B: Displacement

C: Velocity D: Peak to Peak

£200

A: Peak to Peak

Displacement measures which value of a waveform?

A: Peak to Peak B: Peak

C: RMS D: Average

£300

D: Hz CPM Order

What are the three units of Frequency?

A: Hz CPM RMS B: Hz CPM Peak

C: Peak Hz RMS D: Hz CPM Order

£500

D: Acceleration

The Peak value of a waveform relates to which amplitude measurement?

A: Velocity B: Displacement

C: Average D: Acceleration

£1,000

B: Related to 1 Order

What does Synchronous energy mean?

A: Below 1 Order B: Related to 1 Order

C: Bearing Defect D: Above 1 Order

£2000

D: Acceleration

What unit is best used to detect bearing defects?

A: Velocity B: Displacement

C: Average D: Acceleration

£4,000

D: 3 Orders

If a motor runs at 1500RPM how many orders would 4500 CPM be?

A: 1 Order B: 2 Orders

C: 2.5 Orders D: 3 Orders

£8,000

D: Above 1 Order

Sub Synchronous Data is?

A: Below 1 Order B: Equal to 1 Order

C: Up to 5 Orders

£16,000

A: Below 1 Order

D: Hz

A Spectrum is defined as:

Amplitude versus …?

A: Time B: CPM

C: Frequency

£32,000

C: Frequency

D: Outboard D/E

The measurement point P2P is taken where on the machine?

A: Inboard D/E B: Inboard ND/E

C: Outboard ND/E

£64,000

C: Outboard ND/E

D: Fan outboard axialD: Fan outboard axial

The measurement point F2A means?

A: Fan inboard axial B: Fan inboard peakvue

C: Fan inboard vertical

£125,000

D: Synchronous EnergyD: Synchronous Energy

Locating turning speed will distinguish…?

A: The Frequency Units B: Peak Amplitudes

C: The Amplitude Units

£250,000

A: Non Synchronous

Bearing Defects are…?

A: Non Synchronous B: Synchronous

C: Undetectable D: Only Detectable with Peakvue

£500,000

D: Non SynchronousD: Non Synchronous

Electrical defects are what type of energy..?

A: Synchronous B: Sub Synchronous

C: Undetectable

£1,000,000