The Art of Practical and Precise Strain Based ... - Webprofile.info

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