BA 7676-12, 1
VibrationMeasurement
andAnalysis
� Why Frequency Analysis� Spectrum or Overall Level� Filters� Linear vs. Log Scaling� Amplitude Scales� Vibration Parameters� The Detector/Averager� Signal vs. System analysis
BA 7676-12, 2
The Measurement Chain
Transducer Preamplifier Detector/Averager
Filter(s) Output
BA 7676-12, 3
Why Make a Frequency Analysis
DE Vibration
A
B C
Amplitude
Time
Frequency
AB CD E
Amplitude
BA 7676-12, 4
Frequency Analysis
Acc.Level
Frequency
BA 7676-12, 5
Frequency Spectrum or Overall Level
OverallLevel
FrequencySpectrum
Transducer Preamplifier OutputDetector/Averager
Filter(s)
BA 7676-12, 6
Frequency Spectrum or Overall Level
Fan
Gearbox
Date
12 3
4 5
1 2 3 45
FrequencyVibration
Vibration
12345
12345
DateFrequency
Frequency Spectrum Overall Level
BA 7676-12, 7
Presenting the Data
� Linear vs. Log Scaling� Amplitude in dB?� Linear and Logarithmic Frequency Scales
– Decades– Octaves
BA 7676-12, 8
Linear vs Logarithmic Scales
0 1/2 1
Empty Full
0 10.25 0.5 0.75
0 1/5 1
Full
0.05 10.1 0.2 0.5
1/10 1/2
BA 7676-12, 9
Linear vs Logarithmic Scales
0 10 20 30 40 50 60 70 80 90 100
0 0.1 0.5 1Linear
1 Decade
1 Decade0.01
0.01 0.1 1 10010
1 2 5 10 25 50
1 Decade 1 Decade 1 Decade 1 Decade
1
1
2
2
5
5
10
10 20
20
50
50
100
100
Logarithmic
BA 7676-12, 10
Linear vs Logarithmic Frequency Scales
200 400 600 800 1K 1,2K 1,4K 1,6K 1,8K 2K Hz
120 Hz 50 Hz
20 50 100 200 500 1K 2K 5K 10K 20K
LinearFrequency
LogarithmicFrequency
0
VibrationLevel
VibrationLevel
BA 7676-12, 11
Bandpass Filters and BandwidthB
0
0
- 3 dB
Frequency Frequency
Frequency
Ideal filter
Real filter anddefinition of3 dB Bandwidth
Ripple
f1 f0 f2
f1 f0 f2
=
Bandwidth = f2 – f1Centre Frequency = f0
f1 f0 f2
Real filter anddefinition ofNoise Bandwidth
Area Area
BA 7676-12, 12
Filter Types
B = x Hz
B = 31,6 HzB = 10 Hz
B = 3,16 Hz
B = 1 octaveB = 1/3 octave
B = 3%
Constant Bandwidth Constant Percentage Bandwidthor Relative Bandwidth
B = y% =y × f0100
0 40 8020 60 20010050 70 150LinearFrequency
LogarithmicFrequency
BA 7676-12, 13
Constant Bandwidth Filtering
1 2 5 10 20 50 100 200 500 1k 2k 5k 10k
0 1k 2k 3k 4k 5k 6k 7k 8k 9k 10k
Bandwidth = 400 Hz
LinearFrequencyAxis
LogarithmicFrequencyAxis
BA 7676-12, 14
Constant Percentage Bandwidth Filters
0 1k 2k 3k 4k 5k 6k 7k 8k 9k 10k
1 2 5 10 20 50 100 200 500 1k 2k 5k 10k125 8k
Frequency, Hz
Frequency, Hz
Bandwidth = 1/1 octave = 70% of Centre Frequency
LinearFrequencyAxis
LogarithmicFrequencyAxis
BA 7676-12, 15
Linear vs Logarithmic Frequency Scales
200 400 600 800 1K 1,2K 1,4K 1,6K 1,8K 2K Hz
120 Hz 50 Hz
20 50 100 200 500 1K 2K 5K 10K 20K
LinearFrequency
LogarithmicFrequency
0
VibrationLevel
VibrationLevel
BA 7676-12, 16
Selecting Bandwidth
VibrationLevel
Frequency
VibrationLevel
Frequency
Filterwidth
Frequency Spectrum
Frequency
Frequency
BA 7676-12, 17
Most important in Frequency Analysis
(often called the Uncertainty Principle)
B = bandwidthT = time
BT ≥ 1
BA 7676-12, 18
Linear vs Logarithmic Amplitude Scales
1000 1000× 3.16
Frequency
× 3.16
× 3.16
Logarithmicamplitude
× 3.16
× 3.16
× 3.16
× 3.16
× 3.16
316
100
31.6
10
3.16
1
900800700600500400300200100
0
Linearamplitude
Line
ar s
cale
Loga
rithm
ic s
cale
Advantages of logarithmic amplitude scale� Constant factor changes are equally displayed for all levels� Optimal way of displaying a large dynamic range
BA 7676-12, 19
The dB ScaleAcceleration
dBre. 10-6 m/s2
Accelerationm/s2
×××× 100= 40 dB
×××× 10= 20 dB
× 3.16 = 10 dB
× 3.16 = 10 dB
× 3.16 = 10 dB
1000
316
100
31.6
10
3.16
1
Logarithmic amplitude
60
50
40
30
20
10
1
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10 log20log10)(
Frequency
BA 7676-12, 20
Transmission of Vibration
891875
Vibration+ =InputForces
SystemResponse(Mobility)
Forces caused by� Imbalance� Shock� Friction� Acoustic
StructuralParameters:� Mass� Stiffness� Damping
+ =
VibrationParameters:� Acceleration� Velocity� Displacement
Frequency
8 dB
Frequency Frequency
8 dB
BA 7676-12, 21
“Real World” Vibration Levels
1 000 000
1000
1
0.001
0.000 001
240
180
120
60
0
ms-2 dB
BA 7676-12, 22
Vibration Parameters
0.1 1 10 1 k100 10 kHzFrequency
101
Relative Amplitude
Acceleration
1001000
10 000100 000
Velocity
Displacement100 000
10 0001000
10010
BA 7676-12, 23
Which Parameter to Choose
Acc.
Choose Displacement
MeasurementA
Vel.
Disp.
Choose Velocity
Measurement B
Acc.
Vel.
Disp.
Choose Acceleration
Measurement C
Acc.
Vel.
Disp.
BA 7676-12, 24
VibrationLevel
The Detector/Averager
Time
RMSPeak Peak-
Peak
TimeRMS
Peak
Peak-PeakHold
Peak-Peak
Vibration
BA 7676-12, 25
Averaging Time
Time
Time
Averaging Time = 10 s
Averaging Time = 1 s
VibrationLevel(Peak)
Vibration
BA 7676-12, 26
Signal vs. System Analysis
Vibrationsignal
Excitation(Input)
VibrationResponse(Output)
Signal Analysis System Analysis
BA 7676-12, 27
Conclusion
This lecture should provide you with sufficientinformation to:
� Choose the right vibration parameters to measure� Present the measured data in a suitable way� Understand the basic filter and analysis parameters
and limitations� Understand the difference between signal and
system analysis
BA 7676-12, 28
Literature for Further Reading
� Shock and Vibration Handbook (Harris and Crede, McGraw-Hill 1976)
� Frequency Analysis (Brüel & Kjær Handbook BT 0007-11)
� Structural Testing Part 1 and 2(Brüel & Kjær Booklets BR 0458-12 and BR 0507-11)
� Brüel & Kjær Technical Review– No.2 - 1996 (BV 0049-11)
– No.2 - 1995 (BV 0047-11)
– No.2 - 1994 (BV 0045-11)
– No.1 - 1994 (BV 0044-11)
– No.1 - 1988 (BV 0033-11)
– No.4 - 1987 (BV 0032-11)