Gear tooth failure detection Vibration analysis has an old antecedent inmonitoring and fault diagnosis of machinery. The gears and gearboxes are mostlyused for special purposes in industry. Therefore, their fault diagnostics andmonitoring techniques have been improved quickly. Various kinds of processingtechniques can be grouped into five major categories: 1) raw signals, 2) timesynchronous signal averaging, 3) residual signal, 4) difference signal and 5)band pass mesh signal.Localized gear defects have been extensivelystudied, since gear faults are mostly initiated by localized defects.Fatigue fracture and cracks are two samples oflocalized gear faults. In this paper, two methods of fault detection in gearboxes– the resonance demodulation technique and the instantaneous power spectrum arestudied and compared.

Mostly, defects alter the amplitude and phaseof the gear vibration. Therefore, vibration monitoring for gearbox faultdetection using different methods have been improved.  The sensitivity of the phase and amplitude modulationtechniques and wavelet transform were studied. The results show that the betaKurtosis factor is a reliable tool for gear diagnostic. Smoothed Pseudo WignerVille distribution of an acoustic signal was used as a tool for local faultdetection in gearboxes by Baydar and Ball.

They suggested the acoustic signalas an effective tool for gearbox diagnostics in the early stages of faultgeneration. Mohanty and Kar studied the motor current wave form as a tool inthe fault detection of multistage gearbox. They used the decomposed frequencydemodulated current of the induction motors, which drives the gearbox, tomonitor different frequency levels in the gearbox.A full review of vibration processingtechniques for gear fault detection such as time frequency analysis wasperformed by Dalpiaz et al. 5 and the results have been compared to cestrumanalysis and time synchronous averaging analysis results for different depth ofcrack. Moreover, the effects of different positioning places of transducer onthe gear box case were shown.

In this paper, the residual signal anddemodulation techniques were suggested as a well-known tool for diagnosisdepending on a proper filtering. Another complete review of diagnostic methodsfor helicopter transmission systems is presented by Samuel and Pines. Theirstudy covers a broad range of methods in Health and Usage Monitoring (HUM)systems like statistic criteria, time frequency distribution methods, Waveletanalysis as a joint time frequency distribution, neural networks, andmathematical modeling of vibration data. They also included the performanceassessment of presented diagnostic techniques and suggested more improvement inthe field of waveform modeling and sensor development as well as signalprocessing methods.Defects in the gear affect the instantaneousenergy and frequency components in the modulation process. As the frequencyincreases, defects will appear in the frequency spectrum as sidebands, but notin 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 mateswith another tooth in a gearbox, it produces modulation effects and sidebands.

The interval of the sidebands and their amplitude mostly indicates a faultycondition. It is difficult to detect a localized fault in the spectral analysismethod, due to difficulties in detecting corresponding fault sidebands in thepresence of several gears in pair and other mechanical components, which alsoproduce extra sidebands. Therefore, other vibration analysis methods aresuggested for gear fault detection, such as time synchronous averaging, timefrequency distribution, signal modeling techniques, cestrum and statisticalmethods.In the time domain analysis, time synchronousaveraging of the raw vibration signal removes periodic events related to theno-fault gears and also reduces the noise effects.

Therefore, processingtechniques of the time averaging method, such as the extraction of the residualsignal, amplitude and phase modulation of a tooth meshing harmonics, have beenimproved for early detection of gear damages. Consequently, because of theimpacts produced by local faults in mating tooth, the vibration signal of thefaulty gearbox is considered as a no stationary signal.Thus, the methods which are based on theanalysis of stationary signals are not suitable for gear fault detections.On the other hand, the application of timefrequency distribution methods, such as wavelet transform, is useful in thetime localizing of events and detecting cracks in a special gear. Halim et alcombined two methods of time synchronous averaging and wavelet transformation,and presented a new method called time domain averaging across all scales. Heverified that removing noise and periodic events from the characteristicvibration signal of a faulty gearbox is an effective step in fault detection,and this method facilitates this feature by capturing dynamic characteristicsof 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 frequenciesand its harmonics. Due to the impact feature of gear faults in a complete revolutionin a faulty gear, higher order sidebands spread over a wide range offrequencies around high order mesh harmonics.

For the purpose of faultdetection, the signal should be averaged. This averaging reduces the noiseeffect and removes regular gear meshing harmonics. If the gear meshingharmonics are removed from the averaged signal, the result is the residualsignal. The residual signal involves some information about faults. Impactresonate the structure of the gear and this resonance plays an amplifying rolefor weak defects. Sidebands around low order mesh harmonics are generated dueto signal leakage and geometrical errors of gear and should not be taken intoaccount.

Therefore, in a frequency spectrum of a faulty gear, sidebands arounda high order mesh harmonic are of great concern. Then stop band filtering, andthen the residual signal is attained. This residual signal is then transformedinto time space and squared, where the Kurtosis factor of this squared signalis determined. Taking into account that the Kurtosis value higher than 4indicates the faulty condition, the fault could be estimated. A phase diagram indicatesthe angular position of a faulty tooth. Further in the paper, a mathematicalmodel is simulated for gear vibration and using this model, the theoreticalbasis of the method is developed extensively.Another method, which is used in this study, isa type of “Cohen class” of “quadratic time frequency distribution”, which iscalled the instantaneous power spectrum (IPS).

The application of this methodis simpler than the RD technique, but, as will be seen, this method does nothave 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 timeand frequency on the IPS contour plots. This method was first applied and thenwas completed by Levin; According to the above facts, and considering that inearly stages of fault generation the energy level is not comparable to noiseenergy, the prediction of fault presence in this stage is not simple.

To apply thismethod, similar to R.D. technique, the signal should be averaged and, then, thetwo autocorrelation function should be added to each other over the averagedcycle. After that, this sum should be normalized and weighted. For weightingfunctions, window functions such as Kaiser Window are used, knowing that theIPS is not sensitive to window parameters such as type and length.

Theendpoints of windows are not deleted in this technique. The FFT of the weighted autocorrelation sum isknown as the IPS. The position of the fault also is available in the IPS contourplots. 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 inthe gearbox and the same fault severity percentage.

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