30079_23b - Differentiating and integrating networks are...

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Differentiating and integrating networks are not satisfactory over many octaves of frequency. Fortunately, displacement information is usually only needed over a range such as 5-100 Hz, so integrating components are chosen for best accuracy in that region. Acceleration data are usually needed above about 50 Hz; when velocity pickups are used, differentiating components are selected for best operation from 50 to perhaps 2000 Hz. Serious inaccuracies result from use beyond the frequencies indicated in Table 23.2. Table 23.2 gives typical tolerances for the vibration meter only, not including the velocity pickup or accelerometer. 23.4 ACCELERATION MEASUREMENT Let us now take up the subject of accelerometers—units whose instantaneous output voltage is proportional to the instantaneous value of acceleration. Most vibration and shock measurements are even more true today than in 1986 are made with accelerometers. At high frequencies, accelerometers generate a larger signal than do velocity pickups. This may be shown by calculating the peak velocity that would exist if the peak acceleration were Ig at a frequency of 2000 Hz: English units: v ^ A 0.0162/ V = 0.031 in./sec (peak) SI units: V= 0.000 642/ V = 0.78 mm/sec (peak) Let us assume that a velocity pickup has a sensitivity of 105 mV/in. sec. It will generate about 3.22 mV (peak) or about 2.28 mV (rms). (At 200 Hz, Ig, the velocity would be 10 times greater, of course, and so would be the voltage.) A signal of only 2 or 3 mV rms is difficult to measure under some conditions. We will show that accelerometers built for these higher frequencies have a number of advantages; one advantage is higher output signal at higher test frequencies found in modern vibration tests and field measurements. A reasonable sensitivity figure for a crystal accelerometer is 10 mV (peak) per g (peak); this sensitivity is relatively constant up to, say, 10,000 Hz. In the situation discussed above (Ig at 2000 Hz) the accelerometer would generate 10 mV (peak) or 7.07 mV rms. This is about three times as much signal as the velocity pickup generates. This advantage would double with each doubling of frequency (octave). Accelerometers always operate below their natural frequencies. Thus the natural frequency must be high; the useful "flat" range is to about one-fifth of the natural frequency, where the sensitivity is about 4% higher than it is at low frequencies. A 50-kHz unit thus permits operation to 10 kHz. How might we build an instrument that would sense acceleration? The automobile enthusiast senses acceleration by "feeling" his or her body sink into the seat cushions. As the car and seat gain a high velocity (accelerate), a deflection proportional to the intensity of acceleration is noted. His or her body has inertia and tends to keep its former velocity. If we could measure the amount of deflection, we would have a crude accelerometer. In Fig. 23.27 we see a crude accelerometer and how acceleration could be measured on a meter. A cantilever beam supports a weight W. On the top and bottom are cemented strain gages, elements that change resistance when stretched or compressed.
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