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

���

����

�=��

�

�

��

�

�=

refref aa

aadBN 102

2

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)