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Modulation
According
to
(Eq.
3.1),
a
perfect
gear
should
only
produce
vibration
energy
at multiples of its tooth pass frequency. A gear hub crack will however create a di.erent energy of the meshing tone depending on the rotational position of the gear. Thus, gear rotation and meshing becomes modulated. This will manifest itself as modulation sidebands to the harmonics of the meshing tone, with sideband distance to the carrier equal to the shaft rotation frequency. Monitoring these frequencies will provide indications of gear web cracks,
severe
localized
damage,
and
unbalance
in
the
gear
shaft
[42].

Bearing Indicators
A crack in the inner race or outer race of a bearing will manifest itself as a pulse repeated every time a roller passes over the crack. A crack directly on the roller will generate a pulse every time the crack passes one of the races,
i.e. twice for every rotation of the roller. This gives the three fault frequencies of a bearing; ball pass frequency inner race (IR) ball pass frequency outer race
(OR)
and
ball
spin
frequency
(BF)
[35].
These
frequencies,
relative
to
the shaft rotation, are speci.c to each bearing.
Monitoring any of these frequencies directly will however not detect any faults, as repeated pulses on these frequencies will become modulate on the natural frequency of the bearing, and end up as sidebands to this frequency. As the natural frequency normally is high, and not necessarily known, looking for modulation sidebands in the expected locations is not practical.
A better approach is to demodulate the signal. The signal envelope, or Hilbert transform, will demodulate the bearing fault frequencies from the carrier and project them back to their expected locations. Calculating the DFT of the enveloped signal will thus reveal any bearing damage. Normally, an area of ±10% around each fault frequency is extracted to accomodate for roller slip.
3.3.2 Stationarity Indicators
Although the basic condition indicators provide reliable indications to change in the condition in the underlying assets, they are of little use without a comparative baseline. Rather than de.ning a baseline for each indicator, it is possible to compare each observation with the most recent ones to look for any trends in the evolution of the indicators. A simple method is to perform a linear regression of the last couple of observations, and measure the rate of incline
or
decline
over
this
segment
[33]
[21]
[22].
Alternative, it is possible to extrapolate the linear model, and estimate the time remaining before it crosses some pre-de.ned threshold. If a condition indicator is seen as a parameterization of the raw sensor signal, a stationarity indicator constitutes a second level parametrization.
　
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