Time Domain Resolution
The resolution in the time domain depends on the sampling rate of the D/A converter in the analyzer - the higher the sampling rate, the greater the resolution. The FFT requires that the sampling rate be 2.56 times the maximum frequency being analyzed. Therefore, a span of 5000 Hz will set the A/D converter to 5000 x 2.56 = 12,800 samples per second. If our time record length is 1/25 second, then the time resolution is 1/25th of 12,800, or 512 samples in the time record. This means we will get 512 “snapshots” of the gear in one revolution. Since there are 13 teeth on the pinion in question, our 512 samples per revolution will produce for us 512/13 or about 39 snapshots of each tooth. This is more than adequate to examine each tooth in the averaged waveform.
On the other hand, had we used 250 Hz at 10 lines of resolution, we would have only 250 x 2.5 = 640 samples per second, and 1/25 second will only contain about 25 samples, or about 2 samples per tooth of the gear, which would probably not be adequate to examine the gear in enough detail.
This same basic setup can be used to examine the driven gear rather than the pinion. If it is not possible to put a tachometer on the shaft of the large gear, a frequency divider can be placed in the tachometer output, and if its division ratio is 13:31, its output pulses will coincide with each revolution of the large gear. Then, the time-averaged waveform will show the teeth of the driven gear rather than the pinion. The setup is shown in the figure below:
Since the driven gear is running slower than the pinion, the analyzer must be set up to acquire a time record length corresponding to a little more than 1 revolution of the large gear.
If the averaged waveform were also subjected to a frequency analysis with the analyzer, the predominant frequency in the spectrum would be 13X, which is the gear mesh frequency, as in the previous case with the pinion.
The technique can be applied to gearboxes with multiple gears as long as the numbers of teeth on each gear are known, and the frequency divider has the capability of performing the proper ratio multiplication.
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