Page 55 - Prosig Catalogue 2005

SOFTWARE PRODUCTS
FREQUENCY, HERTZ & ORDERS

is unlikely that the frequencies in Hz will map exactly onto integer values
in Orders. This means then grouping several order lines to form an rms
value.
Thus in dealing with signals from rotating machinery synchronous
sampling is preferable but regrettably converting to synchronous sampling
is difficult in practice. It is impossible to sample synchronously with
some data acquisition equipment, in particular those with sigma-delta Figure 5 Synchronously Sampled Car Vibration
type ADCs must sample at regular time steps. Successive approximation be ‘smeared’ over several frequencies.
ADCs as used in the Prosig P8000 series do not have this restriction. This Training & Support
however is not always of practical significance as usually it is difficult Figure 6 below shows the Order analysis where it is quite clear that the
enough to get a reliable once/rev tacho pulse let alone N pulses per rev. energy is mostly at first order with some side bands and also some small
The solution is to use signal processing to digitally resample the data. contributions at the second and third orders.
Again we note the implication of Shannon’s Sampling Theorem that if
we sample at least twice as fast as the highest frequency present then
we have all the information about the signal. With the correct signal
processing algorithms we can then resample the initial equi speed time
increment data into equi spaced angle increment data. We will not go
into this theory and the relevant equations here except to note that the
resampling is based on the (sin x)/x function, which is called appropriately
a sinc function. This resampling algorithm can be used just to change the
sampling rate from say 20000 samples/second to 44100 samples/second
for sound replay. When being used for resampling to achieve equal angle Figure 6 Order Analysis of Car Data
it is clear that a once per rev tacho signal is also required. This provides Condition Monitoring
the relationship between time and the total ‘angle’ travelled. An even more revealing analysis is to analyze a simple swept sinewave
The DATS module ATOSYNC uses a once per rev tacho to convert a such as shown below.
regular time series to a synchronous time series. To illustrate its use we
will resample the mixed sinewave signal used earlier. A tacho signal which
matched the 60 Hz component was used, that is first order will correspond
to the 60 Hz signal. Thirty two points/rev were used. A section of the new
synchronous signal is shown in Figure 3 below. It looks identical to the
original regular time sampled data except that the x axis is now in terms
of the total angular distance travelled in Revs.
Figure 7 Swept Sine from 30 Hz to 100 Hz
Software
If we analyze this as a standard time history we get the expected spectrum
from 30 Hz to 100 Hz as shown in Figure 8.

Figure 3 Two Sinewaves Synchronously Sampled

The FFT of the synchronous signal is shown below

Figure 8 FFT of Swept Sine
Hardware
Now if we synchronously sample the swept sine using itself as its own
once/rev signal and frequency analyze then we get the synchronous
signal as shown in Figure 9.

Figure 4 FFT of Synchronous Signal

This is identical, as expected, to the FFT of the original time history
except that the x axis is now marked with units of Orders, not Hz. The
two responses are at exactly one and three orders as expected. The
mathematics has not changed, just the interpretation and our frame of
reference.
As a further observation sampling is sometimes carried out as a function Figure 9 Synchronously Sampled Swept Sine
of distance. For example a vibrating beam could be measured at equi
spaced points along the beam at one instant in time. The increment is
then in steps of metres. If we Fourier transformed that signal then we The entire signal is now concentrated entirely at the first order. The System Packages
would have a frequency axis in units of wavelength. This option however amplitude is the half amplitude and the phase jump is 270° . If we look at
the synchronously sampled signal, which is shown in Figure 10, then the
is not available in DATS. ‘swept sinewave’ is now just a ‘constant sinewave’. We have a constant
The more complex signal shown below comes from a steady state run on number of points per revolution and all evidence of the change in speed
a vehicle. There is clearly some beating going on. The vehicle speed was has gone
not constant so if one analyzed in the time domain the amplitudes would

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