basic vibration theory
TRANSCRIPT
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