New Gear-Fault-Detection Parameter by Use of Joint Time-Frequency Distribution

Abstract

A new gear-fault-detection parameter called NP4 is introduced. This fault-detection parameter utilizes the properties of the joint time-frequency analysis given by the Wigner-Ville distribution (WVD) and kurtosis. With the WVD, the instantaneous power of the gear-vibration signature for one complete rotor revolution can be obtained. The presence of single-gear-tooth damage can be manifested by the existence of an instantaneous power distribution with a peakedness larger than the normal distribution. The normalized kurtosis, a fourth-order statistical parameter calculated for the instantaneous power distribution, provides the gear-fault-detection parameter NP4. The developed fault-detection parameter NP4 is sensitive to gear-tooth damage, especially for damage in a single tooth. The application of this NP4 fault-detection parameter was demonstrated by experimental data obtained from a gear test rig. The results showed that the NP4 parameter, used with the WVD, can provide an accurate fault identi cation of gear-tooth damage. The parameter NP4 would be of help to the practitioners in the eld of machine health monitoring. NomenclatureC = positive real constant E = total energy of the signal f = frequency in hertz h(t ) = window function j = complex number L = length of the data window N = number of data points NK = normalized kurtosis NP4 = normalized kurtosis of instantaneous signal power n, i = index corresponding to the data point P(t ) = instantaneous signal energy or signal power P = mean value of signal power P(t ) s(t ) = analytic signal, complex function T = time sampling interval t = time in seconds W x x (t , f ) = Wigner-Ville distribution, a function of both time and frequency X ( f ) = energy density spectrum x ¤ (t ) = complex conjugate of the analytic signal x(t) x(t ), y(t ) = acquired vibration signal l (t ) = weighting function r = standard deviation r t = positive real constant s = time in seconds

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