Vibration
Measurement and
Analysis
l Why Frequency Analysis
l Spectrum or Overall Level
l Filters
l Linear vs. Log Scaling
l Amplitude Scales
l Vibration Parameters
l The Detector/Averager
l Signal vs. System analysis
The Measurement Chain
Transducer Preamplifier Detector/
Averager
Filter(s) Output
Why Make a Frequency Analysis
D
E
VibrationA
B C
Amplitude
Time
Frequency
A B CD E
Amplitude
Frequency Analysis
Acc.
Level
Frequency
Frequency Spectrum or Overall Level
Overall Level
Frequency Spectrum
Transducer Preamplifier Detector/ Output
Averager Filter(s)
Frequency Spectrum or Overall Level
Fan
Gearbox
Date 1 2 3
4 5
1 2 3 4 5 Frequency
Vibration Vibration
1 23 4 5
1 2 3 4 5
Date Frequency
Frequency Spectrum Overall Level
Presenting the Data
l
Linear vs. Log Scaling
l
Amplitude in dB?
l
Linear and Logarithmic Frequency Scales
–
Decades
–
Octaves
Linear vs Logarithmic Scales
0 1/2 1
Empty Full
0 0.25 0.5 0.75 1
0 1/5 1
Full
0.05 0.1 0.2 0.5 1
1/10 1/2
Linear vs Logarithmic Scales
0 10 20 30 40 50 60 70 80 90 100
0 0.1 0.5 1
Linear
1 Decade
1 Decade 0.01
0.01 0.1 1 10 100
1
2 5
10 2550
1 Decade 1 Decade 1 Decade 1 Decade 1
1
2
2
5
5
10
10 20
20
50
50
100
100
Logarithmic
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
Linear Frequency
Logarithmic Frequency 0
Vibration Level Vibration Level
Bandpass Filters and Bandwidth
B 0
0 - 3 dB
Frequency Frequency
Frequency Ideal filter
Real filter and definition of 3 dB Bandwidth
Ripple f1 f0 f2
f f f
=
Bandwidth = f
2– f
1Centre Frequency = f
0f f f
Real filter and definition of
Noise Bandwidth
Area Area
Filter Types
B = x Hz
B = 31,6 Hz B = 10 Hz
B = 3,16 Hz
B = 1 octave B = 1/3 octave B = 3%
Constant Bandwidth Constant Percentage Bandwidth or Relative Bandwidth
B = y% = y × f
0100
0 20 40 60 80 50 70 100 150 200
Linear Frequency
Logarithmic Frequency
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
Linear Frequency Axis
Logarithmic Frequency Axis
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 10k Frequency, Hz Frequency, Hz
Bandwidth = 1/1 octave = 70% of Centre Frequency
Linear Frequency Axis
Logarithmic Frequency Axis
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
Linear Frequency
Logarithmic Frequency 0
Vibration Level Vibration Level
Selecting Bandwidth
Vibration Level
Frequency Vibration
Level
Frequency
Filter width
Frequency Spectrum
Frequency Frequency
Most important in Frequency Analysis
(often called the Uncertainty Principle) B = bandwidth
T = time
BT ≥ 1
Linear vs Logarithmic Amplitude Scales
1000
1000× 3.16
Frequency
× 3.16
× 3.16
Logarithmic amplitude
× 3.16
× 3.16
× 3.16
× 3.16
× 3.16
316 100
31.6 10
3.16 1
900 800 700 600 500 400 300 200 100 0
Linear amplitude
Linear scale Logarithmic scale
Advantages of logarithmic amplitude scale
l Constant factor changes are equally displayed for all levels
l Optimal way of displaying a large dynamic range
The dB Scale
Acceleration dB
re. 10-6 m/s2
Acceleration m/s
2×××× 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
÷÷ø ö ççè æ
÷÷ø = ççè ö
= æ
ref
a
refa a
dB a
N
2 102
10
20 log
log 10 )
(
Frequency
Transmission of Vibration
Vibration
+ =
Input Forces
System Response
(Mobility)
Forces caused by
l Imbalance
l Shock
l Friction
l Acoustic
Structural Parameters:
l Mass
l Stiffness
l Damping
+ =
Vibration Parameters:
l Acceleration
l Velocity
l Displacement Frequency
8 dB
Frequency Frequency
8 dB
“Real World” Vibration Levels
1 000 000
1000
1
0.001
0.000 001
240
180
120
60
0
ms
-2dB
Vibration Parameters
0.1 1 10 100 1 k 10 kHz
Frequency 10
1 Relative Amplitude
Acceleration
100 1000 10 000 100 000
Velocity
Displacement 100 000
10 000 1000 100 10
Which Parameter to Choose
Acc.
Choose Displacement
Measurement A
Vel.
Disp.
Choose Velocity
Measurement B
Acc.
Vel.
Disp.
Choose Acceleration
Measurement C
Acc.
Vel.
Disp.
Vibration Level
The Detector/Averager
Time RMS Peak Peak-
Peak Time
RMS Peak Peak-Peak Hold Peak-Peak Vibration
Averaging Time
Time
Time Averaging Time = 10 s
Averaging Time = 1 s Vibration
Level (Peak) Vibration
Signal vs. System Analysis
Vibration signal
Excitation (Input)
Vibration Response (Output)
Signal Analysis System Analysis
Conclusion
This lecture should provide you with sufficient information to:
l
Choose the right vibration parameters to measure
l
Present the measured data in a suitable way
l
Understand the basic filter and analysis parameters and limitations
l
Understand the difference between signal and
system analysis
Literature for Further Reading
l
Shock and Vibration Handbook
(Harris and Crede, McGraw-Hill 1976) lFrequency Analysis
(Brüel & Kjær Handbook BT 0007-11)l
Structural Testing Part 1 and 2
(Brüel & Kjær Booklets BR 0458-12 and BR 0507-11) l
