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Solitary waves have been reported in many applications in physics and engineering. While these waves are of relatively simple shape, the mechanisms that control them are highly nonlinear and often not completely understood. In this study a flexible disk spinning against a stationary base plate and interacting with the surrounding air-field exhibits both harmonic as well as solitary waves and this, depending on the spin rate of the disk. Preliminary experimental results indicate that-in contrast with harmonic waves, the speed with which the solitary waves propagate does not depend upon the spin rate of the disk. This appears to be a lock-in phenomenon that is characteristic of well known nonlinear fluid-structure interaction problems. Furthermore, and despite the presence of dispersion in the fluid/disk medium, all solitary waves propagate with the same speed. While a full model capable of predicting these solitons has yet to be developed, a discussion is presented on both the linear model that is currently accepted in the literature, as well as on the nonlinear mechanisms that may control such interesting waves.

The wavelet transform has the ability to extract global information as well as localized small features from a given signal. This property makes it very well suited to the study of time-varying vibration signals generated by the operation of faulty gears. For a healthy and properly designed gear set, the vibration signal consists mainly of the gear meshing frequency component and its harmonics. Developing fatigue cracks introduce short-time transients that modulate both the amplitude and phase of the otherwise steady vibration signal. These transients are often difficult to detect with the traditional time-only or frequency-only techniques. Being a joint time-frequency distribution, the Wavelet transform allows one to look at the evolution in time of a signal’s frequency content. It thus appears to be the ideal tool to detect the localized transients. In this study, we use both the amplitude and phase maps of the wavelet transform to assess the condition of an instrumented gear test rig. With the proposed technique, simulated cracks as small as 20% of the tooth width at the root are easily detectable.

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