Spider DSA User’s Manual
264
The vibration signal is sampled by an ADC that runs at a constant 102.4 kHz
sample rate and is protected by a fixed-frequency anti-aliasing filter. The
bandwidth of this filter, F
span
, is selected such that …
F
span
>RPM
max
x O
span
/ 60
… where RPM
max
is the maximum machine shaft speed to be analyzed and O
span
is the maximum order of shaft rotation to be analyzed. The sample-rate, f
s
, is set
to a deliberately high value with regard to the input filter.
The resulting highly over-sampled digital time history is passed to the input
memory of a digital reconstruction (amplitude-interpolation) filter. While this
filter updates at the input sample rate, the output of this low-pass filter is sampled
at a fixed number of times per shaft revolution. These sample times are not
uniformly spaced in time. Rather, each sample is taken at a time corresponding to
a shaft rotation of R from its predecessor. These fixed-angle sample times are
computed from the successive periods of the tachometer signal.
The tachometer pulse train is applied to a precise timing circuit which measures
the period between adjacent pulses. The two most recent periods are sent to
curve-fitting and interpolation modules which compute the appropriate times at
which to sample the interpolation filter’s output. The sample times are computed
based upon the assumption that the shaft experiences a constant angular
acceleration between adjacent tachometer pulses. This real-time process accepts
input (n) and output (N) pulse-per-revolution sampling constants, allowing the
use of one or more equally spaced tachometer pulses per shaft rotation.
The resulting digital angle-history is presented for subsequent FFT and average
processing. The interpolation filter introduces a processing delay between ADC
input and the presentation of the angle-history. However, this delay affects all
channels identically and the process proceeds in real-time without compromise.
After data re-sampling, a discrete Fourier transform (DFT) algorithm can convert
the angle-history into the order domain. While many competitive systems employ
“power-of-two” FFTs that restrict block size to be a binary number, Crystal
Instruments utilizes a more flexible algorithm that allows this dimension to be a
product of prime numbers (i.e. 1, 2, 5). This allows selecting “nice numbers” for
resolution and span in all domains.
Tachometer Processing and RPM Measurement
A tachometer converts the angular velocity of a rotating shaft into an electrical
signal, typically a voltage. Tachometers with a DC proportional to speed output
are totally unsuitable for order analysis. A far more precise device generating
pulses on an equal-angle spacing is required. While it is possible (subject to
restrictions) to analyze the orders of a rotating shaft based upon a once-per-turn
tachometer pulse such as that generated by a keyway-viewing proximeter (a key-
phasor probe), a stable multiple pulse-per-revolution signal provides far better
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