Dynamical signatures of gearbox vibrations

Citation

Zaremba, Slawomir M. (1998) Dynamical signatures of gearbox vibrations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ab9t-b513. https://resolver.caltech.edu/CaltechETD:etd-02082008-160817

Abstract

The applicability of a dynamical systems approach to the analysis of gearbox vibration signatures is investigated. The signal acquired from a standard one-step helical gearbox is analyzed and the existence of the low-dimensional nonlinear and chaotic behavior is examined. For this purpose, the criteria of broadband spectrum, sensitivity to initial conditions, positive Lyapunov exponents, and short-term dynamical predictability are applied. The largest Lyapunov exponent is also used to quantify the predictability of the measured time series and a surrogate data test is performed to confirm that the analyzed signal is unlikely to correspond to a linear stochastic time-invariant model. To confirm the applicability of a dynamical systems approach, forecasts of the gearbox time series are produced, using various predictors in the state space. Several methods of dynamical signal separation are also discussed. Finally, a family of statistics is proposed, on the basis of geometric features of the system dynamics in the state space, to serve as dynamical monitoring tools for observing changes in the operating conditions. These are tested using several models of dynamical systems which exhibit behavior similar to that observed in the actual gearbox. The most promising monitoring statistics are recommended for additional studies of gearboxes.

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