G 2Hz Meaning
G 2Hz Meaning
G 2Hz Meaning
Random vibration test standards and specifications usually provide spectra showing desired
vibration intensity as Power Spectral Density (PSD) or as Acceleration Spectral Density (ASD) in
rather strange units of g2/Hz vs. frequency in hertz or Hz.The following paragraphs are intended to
promote understanding of these odd PSD/ASD units and why they are necessary and useful.
Editor’s note: Wayne Tustin is one the electronics industry’s foremost experts on mechanical testing. It this first of a series, Wayne uses a
“Tom, Dick, and Harry” fable to highlight the importance of context in conducting vibration testing.
Tom’s assignment the frequency of his calibration shaker (maintaining 1-g RMS
Tom is asked to physically measure the vibration existing at some = 1.414 g peak) over a wide range of frequencies. Tom plots
physically realizable location. Tom gathers vibration-measuring his voltmeter reading (which surprisingly remains constant at
instruments similar to those in Figure 1. Temporarily, however, 1 Vrms) vs. frequency. Figure 2 shows the calibration results.
Tom bypasses the filter. In the real world, of course, the response will never be this flat.
The graph was drawn with a ruler.
Before taking measurements, Tom calibrates his measurement
system. He temporarily attaches his accelerometer to the table Something motivates Tom to introduce the bandpass filter shown
of a small electrodynamic calibration shaker that develops 1 g in Figure 1. He unbypasses the filter. He adjusts the filter center
Root Mean Square (RMS); that is, 1.414 g peak, at the arbitrarily frequency to 1000 Hz and the bandwidth to 160 Hz. Now Tom
chosen sine test frequency of 1000 Hz. Tom adjusts his “set gain” repeats the previous sweep and graph.
control so that his true RMS readout displays 1 Vrms.
Note the dramatic change in sensitivity vs. frequency depicted
What is the sensitivity of his measurement system? That is, what in Figure 3. Tom’s sensitivity is still 1 V/g but only from 920 Hz
is Tom’s transfer sensitivity from acceleration in g to volts? 1:1, to 1080 Hz. Real world responses are never this rectangular. The
right? Whenever Tom sees 1 V on the meter, he knows that his transitions at the “cutoff” frequencies are never vertical. These,
accelerometer is experiencing 1 g. Whenever Tom sees 2 V on too, were drawn with a ruler. The only reason for including Fig-
the meter, he knows that his accelerometer is experiencing 2 g ure 3 is the remote possibility that some readers might not be
and so on. familiar with bandpass filters.
But Tom has only learned the sensitivity at 1000 Hz. He needs Finally, Tom is prepared to make that measurement. Tom removes
to determine the sensitivity at other frequencies. Tom sweeps his accelerometer from the calibration shaker and attaches it at the
bypass
variable
bandpass TRMS
crystal accelerometer filter electronic
accelerometer amplifier voltmeter
set set
center bandwidth
set
frequency “B”
gain
vibration
input
motion
Figure 1
Please understand that the foregoing is fiction. It could never Equipment Reliability Institute
have happened. The concept of analysis in terms of volts2/Hz was 1520 Santa Rosa Avenue
already well established in telephony long before say 1950, when Santa Barbara, CA 93109
engineers began to measure random vibrations. A far less popular Tel: 805-564-1260
normalizing alternative is volts/root Hz. Ω Fax: 805-966-7875
E-mail: tustin@equipment-reliability.com
Wayne Tustin is president and founder of Equipment Reliability Website: www.equipment-reliability.com
Institute, a specialized Santa Barbara, Calif., engineering
school that focuses on the reliability of hardware for space,
air, sea, and land vehicles and commercial equipment. Wayne’s
courses explore the basics of vibration and shock testing,
measurement, analysis, and calibration.