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Strain-Based Measurement Introduction:Figures 1-22 and 1-23 illustrate how even small parameter inputs, at or nearresonance, can produce high-level ringing of the sensor output.FIGURE 1-22. A Complex Input to the Sensor Transfer Function:Magnitude+1g0g-1g+10 gComponent 1: ± 10g at 100 HzComponent 2: ± 1g at 1000 HzTime-10 g+11 gPhysical Input toAccelerometerSummed WaveformTime-11 gMagnitudedB+40 dBCalibration FrequencyResonant Peak0 dB100 HzComponent 11000 HzComponent 2Sensor Transfer Function (Magnitude)Resonance Frequency = 1000HzCalibration at 100 Hz = 1mV/gSensor Range = 10 gSensor Overrange = 100gLog FrequencyCHAPTER 1-42 The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999
Applications Note 1-7:The 100-Hz (±10 g peak) input may be the input of interest where the 1,000-Hz(±1g peak) input is of secondary interest and may be due to bearing chatter or gearmeshingcomponents. In this case, the 10-g range accelerometer shows a sensitivityof 1 mV/g, as calibrated at 100 Hz, with an undamped resonant frequency of1,000 Hz showing a maximum response of +40 db (= 20 log V o /V cal , where V cal isthe calibrated sensitivity of the sensor at a much lower frequency within the ÒflatÓfrequency response range of the sensor). It would be reasonable for the accelerometerto show a maximum overhang tolerance of ±100 g before mechanical damageis suffered. The net accelerometer output is as shown in Figure 1-23.As shown, the 10-g input component will produce a ±10 millivolt output componentat 100 Hz, however, the situation is dramatically different for the ±1g, 1000-Hz component. Since the 1,000-Hz component exists at the resonant frequency ofthe device, the accelerometer will mechanically amplify the ±1g input by the +40dB mechanical gain at resonance, which, when multiplied by the 1mV/g sensitivity,will result in a ±10 mV output component at 1,000 Hz as shown. The net outputwaveform shows massive ringing at 1000 Hz where the information of interestis marginally evident as the modulated envelope of the response shown. Frequencyfiltering of the output of the sensor would help to filter out the 1,000-Hz component,however, the 100-g maximum over-range of the accelerometer means that thesubject sensor is, in all likelihood, broken! If the maximum allowable overrange is100 g, this figure is given as being valid within the useful frequency range of thesensor and not at resonance. The ±1 g input at resonance could, therefore, be quitesufficient to cause overrange destruction of the device. The moral of this story isthat we must be aware of all components present within an input signal and assessthe potential impact of each component with respect to the transfer function of thesensor.The Fourier Series is not just a Òmathematically-elegantÓ method of expressing the inputwaveform but, more importantly, a valuable means of determining the power spectral density(the energy that exists within each of the Fourier components), and of visualizing thecomponents of the input and output separately. -JPThe Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999 CHAPTER 1-43
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The Art of Practical andPrecise Str
Page 3 and 4: Special Credits:Mrs. Helen Pierson,
Page 5 and 6: Table of ContentsBy James G. Pierso
Page 8 and 9: ContentsApplications Note 4-10:Lead
Page 10: ContentsCHAPTER 8Electrical Conside
Page 13 and 14: CHAPTER 1Strain-BasedMeasurementInt
Page 15 and 16: Applications Note 1-1: Introduction
Page 17 and 18: Applications Note 1-1: Introduction
Page 19 and 20: Applications Note 1-2:The Art of Ap
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Page 25 and 26: Applications Note 1-4:The measureme
Page 27 and 28: Applications Note 1-4:uncertainty i
Page 29 and 30: Applications Note 1-5:All strain-ba
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Page 33 and 34: Applications Note 1-6:ical size of
Page 35 and 36: Applications Note 1-6:and where:j i
Page 37 and 38: Applications Note 1-6:5. millivolts
Page 39: Applications Note 1-6:.Electrodynam
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