Measurement and Analysis Why Analysis Spectrum or Overall Level Filters Linear vs. Log Scaling Amplitude Scales Parameters The Detector/Averager Signal vs. System analysis
The Measurement Chain Transducer Preamplifier Filter(s) Detector/ Averager Output
Why Make a Analysis B C A Amplitude Time Amplitude A B C D E D E
Analysis Acc. Level
Spectrum or Overall Level Transducer Preamplifier Filter(s) Detector/ Output Averager Overall Level Spectrum
Spectrum or Overall Level Spectrum 5 4 3 2 1 Overall Level 1 2 3 4 5 Fan 5 4 3 2 1 Date 1 2 3 4 5 Gearbox Date
Presenting the Data Linear vs. Log Scaling Amplitude in db? Linear and Logarithmic Scales Decades Octaves
Linear vs Logarithmic Scales 0 1/2 1 Empty Full 0 0.25 0.5 0.75 1 0 1/10 1/5 1/2 1 Full 0.05 0.1 0.2 0.5 1
Linear vs Logarithmic Scales 0 10 20 30 40 50 60 70 80 90 100 0.01 0 0.1 0.5 1 1 Decade 1 Decade Linear 1 2 5 10 20 50 100 1 2 5 10 25 50 0.01 0.1 1 10 100 1 Decade 1 Decade 1 Decade 1 Decade 1 2 5 10 20 50 100 Logarithmic
Linear vs Logarithmic Scales Level 120 Hz 50 Hz 0 200 400 600 800 1K 1,2K 1,4K 1,6K 1,8K 2K Hz Linear Level 20 50 100 200 500 1K 2K 5K 10K 20K Logarithmic
Bandpass Filters and Bandwidth 0 B Ideal filter Bandwidth = f 2 f 1 Centre = f 0 f 1 f 0 f 2 0 Ripple Area = Area - 3 db Real filter and definition of 3 db Bandwidth Real filter and definition of Noise Bandwidth f 1 f 0 f 2 f 1 f 0 f 2
Filter Types Constant Bandwidth B = x Hz Constant Percentage Bandwidth or Relative Bandwidth B = y% = y f 0 100 Linear 0 20 40 60 80 50 70 100 150 200 B = 31,6 Hz B = 10 Hz B = 3,16 Hz Logarithmic B = 1 octave B = 1/3 octave B = 3%
Constant Bandwidth Filtering Bandwidth = 400 Hz Linear Axis 0 1k 2k 3k 4k 5k 6k 7k 8k 9k 10k Logarithmic Axis 1 2 5 10 20 50 100 200 500 1k 2k 5k 10k
Constant Percentage Bandwidth Filters Bandwidth = 1/1 octave = 70% of Centre Linear Axis 0 1k 2k 3k 4k 5k 6k 7k 8k 9k 10k, Hz Logarithmic Axis 1 2 5 10 20 50 100 200 500 1k 2k 5k 10k 125 8k, Hz
Linear vs Logarithmic Scales Level 120 Hz 50 Hz 0 200 400 600 800 1K 1,2K 1,4K 1,6K 1,8K 2K Hz Linear Level 20 50 100 200 500 1K 2K 5K 10K 20K Logarithmic
Selecting Bandwidth Filter width Level Spectrum Level
Most important in Analysis B = bandwidth T = time BT 1 (often called the Uncertainty Principle)
Linear scale Linear vs Logarithmic Amplitude Scales 1000 1000 Linear Logarithmic 3.16 900 amplitude amplitude 316 800 3.16 3.16 700 100 3.16 600 500 400 300 200 100 0 Advantages of logarithmic amplitude scale Constant factor changes are equally displayed for all levels Optimal way of displaying a large dynamic range 3.16 3.16 3.16 3.16 31.6 10 3.16 1 Logarithmic scale
The db Scale Acceleration db re. 10-6 m/s 2 60 Acceleration m/s 2 1000 2 a ( db) = 10log 10 = 20log 2 a N 10 a ref ref a 50 40 30 20 316 100 31.6 10 100 = 40 db 3.16 = 10 db Logarithmic amplitude 3.16 = 10 db 10 3.16 10 = 20 db 3.16 = 10 db 1 1
Transmission of Input Forces System + Response = (Mobility) 8 db + = 8 db Forces caused by Imbalance Shock Friction Acoustic Structural Parameters: Mass Stiffness Damping Parameters: Acceleration Velocity Displacement
Real World Levels ms -2 db 1 000 000 240 1000 180 1 120 0.001 60 0.000 001 0
Parameters Relative Amplitude 100 000 10 000 1000 100 10 1 10 100 1000 10 000 100 000 0.1 1 10 100 1 k 10 khz Acceleration Velocity Displacement
Which Parameter to Choose Measurement A Acc. Vel. Disp. Measurement B Acc. Vel. Disp. Measurement C Acc. Vel. Disp. Choose Displacement Choose Velocity Choose Acceleration
The Detector/Averager RMS Peak Peak- Peak Level Peak-Peak Hold Peak-Peak Time Peak RMS Time
Averaging Time Level (Peak) Averaging Time = 10 s Averaging Time = 1 s Time Time
Signal vs. System Analysis Signal Analysis System Analysis signal Excitation (Input) Response (Output)
Conclusion This lecture should provide you with sufficient information 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
Literature for Further Reading Shock and Handbook (Harris and Crede, McGraw-Hill 1976) 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)