Gear In this paper, two methods of fault

Gear tooth failure detection

 

Vibration analysis has an old antecedent in
monitoring and fault diagnosis of machinery. The gears and gearboxes are mostly
used for special purposes in industry. Therefore, their fault diagnostics and
monitoring techniques have been improved quickly. Various kinds of processing
techniques can be grouped into five major categories: 1) raw signals, 2) time
synchronous signal averaging, 3) residual signal, 4) difference signal and 5)
band pass mesh signal.

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Localized gear defects have been extensively
studied, since gear faults are mostly initiated by localized defects.

Fatigue fracture and cracks are two samples of
localized gear faults. In this paper, two methods of fault detection in gearboxes
– the resonance demodulation technique and the instantaneous power spectrum are
studied and compared.

Mostly, defects alter the amplitude and phase
of the gear vibration. Therefore, vibration monitoring for gearbox fault
detection using different methods have been improved.  The sensitivity of the phase and amplitude modulation
techniques and wavelet transform were studied. The results show that the beta
Kurtosis factor is a reliable tool for gear diagnostic. Smoothed Pseudo Wigner
Ville distribution of an acoustic signal was used as a tool for local fault
detection in gearboxes by Baydar and Ball. They suggested the acoustic signal
as an effective tool for gearbox diagnostics in the early stages of fault
generation. Mohanty and Kar studied the motor current wave form as a tool in
the fault detection of multistage gearbox. They used the decomposed frequency
demodulated current of the induction motors, which drives the gearbox, to
monitor different frequency levels in the gearbox.

A full review of vibration processing
techniques for gear fault detection such as time frequency analysis was
performed by Dalpiaz et al. 5 and the results have been compared to cestrum
analysis and time synchronous averaging analysis results for different depth of
crack. Moreover, the effects of different positioning places of transducer on
the gear box case were shown. In this paper, the residual signal and
demodulation techniques were suggested as a well-known tool for diagnosis
depending on a proper filtering. Another complete review of diagnostic methods
for helicopter transmission systems is presented by Samuel and Pines. Their
study covers a broad range of methods in Health and Usage Monitoring (HUM)
systems like statistic criteria, time frequency distribution methods, Wavelet
analysis as a joint time frequency distribution, neural networks, and
mathematical modeling of vibration data. They also included the performance
assessment of presented diagnostic techniques and suggested more improvement in
the field of waveform modeling and sensor development as well as signal
processing methods.

Defects in the gear affect the instantaneous
energy and frequency components in the modulation process. As the frequency
increases, defects will appear in the frequency spectrum as sidebands, but not
in lower frequencies 1.

In detecting the defects by vibration analysis,
two important parameters are tooth meshing frequency (including its harmonics)
and the sidebands. When a localized fault, such as a crack in a tooth mates
with another tooth in a gearbox, it produces modulation effects and sidebands.

The interval of the sidebands and their amplitude mostly indicates a faulty
condition. It is difficult to detect a localized fault in the spectral analysis
method, due to difficulties in detecting corresponding fault sidebands in the
presence of several gears in pair and other mechanical components, which also
produce extra sidebands. Therefore, other vibration analysis methods are
suggested for gear fault detection, such as time synchronous averaging, time
frequency distribution, signal modeling techniques, cestrum and statistical
methods.

In the time domain analysis, time synchronous
averaging of the raw vibration signal removes periodic events related to the
no-fault gears and also reduces the noise effects. Therefore, processing
techniques of the time averaging method, such as the extraction of the residual
signal, amplitude and phase modulation of a tooth meshing harmonics, have been
improved for early detection of gear damages. Consequently, because of the
impacts produced by local faults in mating tooth, the vibration signal of the
faulty gearbox is considered as a no stationary signal.

Thus, the methods which are based on the
analysis of stationary signals are not suitable for gear fault detections.

On the other hand, the application of time
frequency distribution methods, such as wavelet transform, is useful in the
time localizing of events and detecting cracks in a special gear. Halim et al
combined two methods of time synchronous averaging and wavelet transformation,
and presented a new method called time domain averaging across all scales. He
verified that removing noise and periodic events from the characteristic
vibration signal of a faulty gearbox is an effective step in fault detection,
and this method facilitates this feature by capturing dynamic characteristics
of one period of the vibration signal.

In the frequency spectrum of a no-fault gearbox,
low order modulation sidebands are appearing around low order mesh frequencies
and its harmonics. Due to the impact feature of gear faults in a complete revolution
in a faulty gear, higher order sidebands spread over a wide range of
frequencies around high order mesh harmonics. For the purpose of fault
detection, the signal should be averaged. This averaging reduces the noise
effect and removes regular gear meshing harmonics. If the gear meshing
harmonics are removed from the averaged signal, the result is the residual
signal. The residual signal involves some information about faults. Impact
resonate the structure of the gear and this resonance plays an amplifying role
for weak defects. Sidebands around low order mesh harmonics are generated due
to signal leakage and geometrical errors of gear and should not be taken into
account. Therefore, in a frequency spectrum of a faulty gear, sidebands around
a high order mesh harmonic are of great concern. Then stop band filtering, and
then the residual signal is attained. This residual signal is then transformed
into time space and squared, where the Kurtosis factor of this squared signal
is determined. Taking into account that the Kurtosis value higher than 4
indicates the faulty condition, the fault could be estimated. A phase diagram indicates
the angular position of a faulty tooth. Further in the paper, a mathematical
model is simulated for gear vibration and using this model, the theoretical
basis of the method is developed extensively.

Another method, which is used in this study, is
a type of “Cohen class” of “quadratic time frequency distribution”, which is
called the instantaneous power spectrum (IPS). The application of this method
is simpler than the RD technique, but, as will be seen, this method does not
have the ability of fault detection in the early stages of fault generation.

This method indicates to the presence of fault as a criterion of energy concentration.

In fact, the faults are revealed by cumulating energy spots on a specific time
and frequency on the IPS contour plots. This method was first applied and then
was completed by Levin; According to the above facts, and considering that in
early stages of fault generation the energy level is not comparable to noise
energy, the prediction of fault presence in this stage is not simple. To apply this
method, similar to R.D. technique, the signal should be averaged and, then, the
two autocorrelation function should be added to each other over the averaged
cycle. After that, this sum should be normalized and weighted. For weighting
functions, window functions such as Kaiser Window are used, knowing that the
IPS is not sensitive to window parameters such as type and length. The
endpoints of windows are not deleted in this technique.

The FFT of the weighted autocorrelation sum is
known as the IPS. The position of the fault also is available in the IPS contour
plots. The mathematical basis of this method is explained in the next section.

The results of two methods should demonstrate the same position of the fault in
the gearbox and the same fault severity percentage.