Section II - Basic Vibration Theory

Vibration Analysis

Basic 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 Force

Force Balance

M

C

K

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

Vibration Characteristics



Amplitude



Frequency



Phase

Vibration Displacement

M

Amplitude Units

Vibration Velocity

M

RMS of a Sinusoidal Wave

T = __1 f

Where T = period of one cycle of the vibration v = instantaneous velocity

t = the variable time

Amplitude Units



Displacement

Pk-Pk

mils or microns

Vibration Acceleration

M

Amplitude Units (Metric)



Displacement

Pk-Pk

microns



Velocity

RMS

mm/sec

Amplitude Units (Imperial)



Displacement

Pk-Pk

mils



Velocity

Pk

in/sec

Comparison of Amplitude Units

Displacement

Velocity

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

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

Vibration Characteristics



Amplitude



Frequency



Phase

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 :

Vibration Frequency

M

DISPL

ACEM

ENT

Time, mili sec

0.5 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 Causes

Frequency In Terms of RPM

Most Likely Cause Other Possible Causes and Remarks

1 X RPM Unbalance 1. Eccentric Journals

2. Misalignment or bent shaft if High Axial Vibration 3. Bad belts if RPM of belt

4. Resonance

5. Reciprocating Forces 6. Electric Problems

2 X RPM Mechanical

Looseness

1. Misalignment if high axial vibration 2. Reciprocating Forces

3. Resonance

4. Bad belts if 2 X RPM of belt

3 X RPM Misalignment Usually a combination of misalignment and excessive axial

clearances (looseness)

Less than 1 X RPM Oil Whirl (Less than ½ RPM) 1. Bad Belt Drives

2. Background Vibration 3. Sub-Harmonic Resonance 4. Beat Vibrations

Synchronous AC Line Frequency

Electrical Problems Common Electrical Problems include broken rotor bars, unbalanced

phases in poly-phase system, unequal airgap 2 X Synchronous

Line Frequency

Torque Pulses Rare as a possible unless resonance is exited

Many Times RPM Harmonically Related Bad Gears Aerodynamic Forces Hydraulic Forces Mechanical Looseness Reciprocating Forces

1. Gear Teeth times RPM if bad gear 2. Number of fan blades times RPM 3. Number of impeller vanes times RPM

4. May occur 2,3,4 and sometimes higher harmonics if severe looseness

High Frequency

Not Harmonically Related

Bad Anti Friction Bearings 1. Bearing Vibration

2. Cavitation, recirculation and flow turbulance cause random, high frequency vibration

3. Improper lubricationof journal bearing (friction exciting vibration 4. Rubbing

Comparison of Parameters

Vibration Characteristics



Amplitude



Frequency



Phase

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 - 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

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

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)

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

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

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 Fa n No.2 C/Mill

M72 92 -F1H Fan Inboa rd Horiz ontal

ROU TE SPECTRU M 18- Apr-02 18:04 :29 OVERALL= 5.46 V- DG P-P = 94.2 7 LOAD = 10 0.0 RPM = 141 8. RPS = 23.6 3 0 30 60 90 120 0 30 60 90 120 Frequency in kCPM P -P D is p in M ic ro n s ROU TE WA VEFOR M 18- Apr-02 18:04 :29 P-P = 87.3 8 PK (+) = 55 .85 PK (-) = 54 .21 CR ESTF= 1.81 0 1 2 3 4 5 -60 -40 -20 0 20 40 60 80

Rev olution Numbe r

D is p la c e m e n t in M ic ro n s

40 - Dust Filter Fa n No.2 C/Mill M72 92 -F1H Fan Inboa rd Horiz ontal

ROU TE SPECTRU M 18- Apr-02 18:04 :29 OVERALL= 5.46 V- DG RMS = 5.4 4 LOAD = 10 0.0 RPM = 141 8. RPS = 23.6 3 0 30 60 90 120 0 1 2 3 4 5 6 7 Frequency in kCPM R M S V e lo c it y in m m /S e c ROU TE WA VEFOR M 18- Apr-02 18:04 :29 RMS = 4.8 4 PK (+) = 15 .15 PK (-) = 12 .86 CR ESTF= 3.13 0 1 2 3 4 5 -15 -10 -5 0 5 10 15 20

Rev olution Numbe r

V e lo c it y in m m /S e c

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

40 - Dust Filter Fa n No.2 C/Mill M72 92 -F1H Fan Inboa rd Horiz ontal

ROU TE SPECTRU M 18- Apr-02 18:04 :29 OVERALL= 5.46 V- DG RMS = 1.5 0 LOAD = 10 0.0 RPM = 141 8. RPS = 23.6 3 0 30 60 90 120 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Frequency in kCPM R M S A c c e le ra ti o n in G -s ROU TE WA VEFOR M 18- Apr-02 18:04 :29 RMS = 1.5 5 PK (+) = 6.6 4 PK (-) = 5.9 6 CR ESTF= 4.29 0 1 2 3 4 5 -8 -6 -4 -2 0 2 4 6 8

Rev olution Numbe r

A c c e le ra ti o 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

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

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

Vibration Characteristics



Amplitude



Frequency



Phase

Vibration Direction



Vibration is measured in three direction

–

Horizontal

–

Vertical

Motor

Pump

M1H

M1V

M1A

M2H

M2V

M2A

P1H

P1V

P1A

P2H

P2V

P2A

OB

IB

IB

OB

Measurement Points

 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.

T

im

e

Amplitude

T

im

e

Amplitude

_Amplitude

_F

_r

_e

_q

_u

_e

_n

_c

_y

 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

 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

 Nonsynchronous 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.

•

• Bearings Multiples of belt frequency Other Machine Speeds

 Subsynchronous 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

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 P K A c c e le r a t io n i n G -s

 The spectrum shown

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

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 P K A c c e le r a t io n i n 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 P K A c c e le r a t io n i n 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

 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

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

30000

60000

90000

Mi

ls

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/sec

sec

CPM

30000

60000

90000

In

/ sec

P

k

3

0.003 0.006 0.009 0.012

2

2

G’

s

_sec

CPM

1.414

CPM

10000

20000

30000

G’

s R

MS

2

2

G’

s

_sec

0.015 0.030 0.045 0.060 11

mi

ls

sec

In/s

ec

sec

G’

s

sec

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

0.001 0.002 0.003 0.004

3

mil

s

sec

CPM

0.9

6

CPM

30000

60000

90000

Mil

s

P

-P

3

mil

s

sec

0.9

1.8

0.005 0.010 0.015 0.020

10

In

/ sec

sec

CPM

4

10

CPM

6000

12000

18000

In

/ sec

P

k

4

24000

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

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

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

D: Acceleration

What unit is best

used to detect

bearing defects?

A: Velocity

B: Displacement

C: Average

D: Acceleration

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

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

D: Fan outboard axial

D: Fan outboard axial

The measurement

point F2A means?

A: Fan inboard axial

B: Fan inboard peakvue

C: Fan inboard vertical

D: Synchronous Energy

D: Synchronous Energy

Locating turning

speed will

distinguish…?

A: The Frequency Units

B: Peak Amplitudes

C: The Amplitude Units

A: Non Synchronous

Bearing Defects

are…?

A: Non Synchronous

B: Synchronous

C: Undetectable

D: Only Detectable with

Peakvue

D: Non Synchronous

D: Non Synchronous

Electrical defects are

what type of energy..?

A: Synchronous

B: Sub Synchronous

C: Undetectable