Vibration response demodulation, shock model and time tracking

A reliable monitoring of a rotating machine needs amplitude and phase demodulation over well-chosen frequency bands. Although often applied, the behaviour of this estimator is not so well established in such a context and particularly for earlier and accurate fault detection. In attempt to provide keys for the understanding of vibration measures, this paper proposes a vibration signal model of a faulty gearbox. More attention is given to the amplitude modulation function to better model the shocks created by local tooth defects and incurred by all the meshing frequency harmonics. The proposed shock model is defined as the response of a mechanical system excited by a Dirac function assuming that the fault does not evolve during the measure. Parameters of resulting response models, exponentially periodic waves, are set to fit as much as possible to a sequence of signals to model the time evolution of the GOTIX bench during a fatigue test. All signals are processed by AStrion, an automatic and data-driven spectral monitoring approach. Interestingly, setting various fault model parameters, damping factors, amplitude modulation rates, frequency modulation indexes, fault location and number, helps for the understanding of the modulation phenomenon and illustrates the intrinsic limits of the demodulation approach.