Context:

Health monitoring for gears is traditionally based on vibration analysis. It is generally assumed in both the literature and within the community that gear vibrations can be modelled (at least in their amplitude modulation component) by the following multiplicative model [1].

where  is a reference shaft angle,  represents the gearmesh, and  and  are the modulating effects of the two gears and represent the variability of the engagement due to imperfections in the gear teeth. All components in this model are considered to be multi-harmonic with fundamental frequencies  respectively.

According to this model, the spectrum of the signal  should be characterized by a series of peaks at the gearmesh harmonics , each with modulation sidebands  and .

Experimental investigation:

The established model may be an interesting approximation at first sight but our experimental investigation has shown several inconsistencies.

First, there are sidebands present in the spectrum at the crossed frequency . This is actually justified by the fact that a model 

is more physically rigorous, i.e. the combined effect of the two gears must have a periodicity which corresponds to the event of the same two teeth meshing again.

Secondly, all the experimental spectra show that the ratio between the sidebands of different gearmesh harmonics is not constant, even after a precise order-tracking using an encoder with a high number of pulses. There are several hypotheses regarding the explanation for this difference.

• The transfer function.

The transfer function between excitation and actual measurement is the obvious suspect for this distortion. However, even after applying a cepstral long-pass lifter (aimed at removing the transfer function “scaling” of the spectrum), the differences between sideband patterns remain strong.

• Simultaneous effect of tooth stiffness and geometric profile error

A more subtle hypothesis instead involves the consideration of two effects resulting in the modulation of the gearmesh. Under this hypothesis, tooth-stiffness-induced vibrations (load dependent) and vibrations induced by profile error (independent of load) are acting as two parallel models, with different carriers and modulations, but coincident frequencies. Under this assumption the gearmesh harmonics show different combined patterns of sidebands because of the additive effect of two different gearmesh carriers and modulations.

Different operating conditions and test-rig layouts will be used in this paper to validate these assumptions and identify modelling limitations.

[1] C. Capdessus, “Aide au diagnostic des machines tournantes par traitement du signal (Aid to the diagnosis of rotating machines by signal processing),” 1992.