J. Antoni Research Associate R. B. Randall Professor School of Mechanical and Manufacturing Engineering, The University of New South Wales, Sydney 2052, Australia Differential Diagnosis of Gear and Bearing Faults This paper deals with the vibration-based diagnosis of rolling element bearings in the presence of strong interfering gear signals, such as is typical of helicopter gearboxes. The key idea consists in recognizing gear signals as purely periodic, whereas bearing signals experience some randomness and are close to cyclostationary, i.e. with a periodic bivari- ate autocorrelation function. This assertion is demonstrated by introducing a comprehen- sive model for the vibration generating process of bearing faults: distinctions are made between localized and distributed faults, between cyclostationary and pseudo- cyclostationary processes, and between additive and multiplicative interactions with gear signals. Finally, an original diagnostic procedure is proposed and its performance illus- trated using simulated, experimental and actual cases. DOI: 10.1115/1.1456906 Introduction Gears and rolling element bearings are critical elements in com- plex machinery to which predictive maintenance is often applied. The benefit of using vibration analysis for their monitoring and diagnosis has been demonstrated to be successful since the early 70’s 1. Since then, a number of ad hoc vibration-based tech- niques have been developed and perfected, and are nowadays well accepted. Some conventional established techniques for the diag- nosis of gears include spectral analysis, cepstral analysis and de- modulation analysis 2,3. Techniques for the diagnostics of bear- ings include statistical analysis, spectral analysis, envelope analysis High Frequency Resonance analysis, etc. 4,5. These techniques work perfectly well for simple systems, where either the effects of the gears or bearings predominate over all other mechanisms, at least in some frequency range. However, this may no longer be the case with more complex systems. In high-speed gearboxes, such as helicopter gearboxes, the gear-related vibrations extend into the high frequency range where also bearing faults manifest themselves, thus showing a mixture of the two types of signal over the whole frequency range. In the simplest case the mixture is found to be additive, but cases have been encountered where the bearing fault modulates the gear signal, due to the close physical connection of the gear and bear- ing elements. Under these circumstances, the ad hoc techniques for the diagnosis of gear or bearing signals are not guaranteed to apply any more. This paper deals with the diagnostics of bearings in the pres- ence of strong interfering gear signals, such as typically found in helicopter gearboxes. A strong emphasis is placed on how to dis- tinguish between gear and bearing faults where the two signals may interact in a complex way, as in multiplicative mixtures. The key idea is based on recognizing gear signals as being purely periodic, whereas bearing signals experience some randomness and are approximately 2 nd order cyclostationary, i.e. with a peri- odic bivariate autocorrelation function. One original contribution of this paper is to support the afore- mentioned assertion, by introducing a refined model for the vibra- tion generating process of a bearing fault. From first principles, this model is shown to produce cyclostationarity or pseudo- cyclostationarity, under conditions which are discussed in detail. These results finally lead to the proposal of a new detection scheme, specifically dedicated to bearing faults in the presence of gear signals with which they are associated multiplicatively. Vibration Signals Induced by Gears The vibration signal arising from the operation of gears is typi- cally modelled as a summation of phasors, each one related to a gearmesh frequency or one of its multiples. In turn, the amplitude and phase of each individual phasor is modulated by the shaft speeds. For a machine operating at constant speed, the resulting vibration signal is to a first approximation perfectly periodic, with a period which can actually be very long since all the shafts in the system share it. However a finite value always exists. Typical faults affecting gears are pitting, spalls and, more seri- ously, cracks. It is believed that these faults, at least in their early stages, do not affect the periodic nature of the signal, because they contact periodically with exactly the same matching surfaces. Rather, only the strength and shape of the modulations are af- fected in a deterministic fashion. Indeed, this is the major asser- tion which makes cepstral techniques so powerful for detecting spalls, for example 2. This assertion was verified in extensive experiments run on a test-rig in the Acoustics and Vibration Laboratories at the Univer- sity of New South Wales UNSW. The rig consists of a parallel shaft spur gear pair with interchangeable wheels, operating with a 1 to 1 ratio and which was equipped with accelerometers and a shaft encoder. One of the wheels had a simulated crack at the root of one tooth 5 mm0.5 mm across the whole width and generated by spark erosion. An example of a measured vibration signal is displayed in Fig. 1, along with the synchronous average taken over 25 cycles and the residual signal signal with synchronous average removed on the first cycle. Since the synchronous aver- age captures all the periodic components in the signal, these fig- ures clearly reveal that most of the energy in the signal was dis- tributed over periodic components, despite the fault. Similar results were obtained over various sets of speeds and loads. In practice, actual gear signals may experience some departure from exact periodicity due to speed fluctuations in the machine. If so, order tracking—resampling on an angular rather than a tem- poral basis—can be used to compensate for these variations. Vibration Signals Induced by Bearings The vibration signal arising from the operation of a rolling el- ement bearing is not as straightforward as for gears. A distinction should be made between the signal coming from a bearing in good condition or from a faulty bearing. Our concern herein is only for the latter. Most frequent rolling element bearing faults include damage of the inner race, the outer race and/or the rolling elements. Gener- ally, during the early stages of the fault, the surface is only locally affected and vibrations are generated as a result of the repetitive impacts of the moving components on the defect. Therefore the Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 2001; revised December 2001. Associate Editor: M. I. Friswell. Copyright © 2002 by ASME Journal of Vibration and Acoustics APRIL 2002, Vol. 124 Õ 165