| The instantaneous phase modulation pattern of tooth meshing harmonics in the measured vibratory excitation of gearboxes has been suggested as an observable parameter for the detection of bending fatigue cracks in gear teeth. The application of Hilbert transform based phase demodulation in the detection of bending fatigue damage has been explored by a number of researchers, but the scope of this research has been limited to diagnostics. This thesis presents a methodology for using this demodulation technique in a prognostic application to obtain statistically qualified predictions of time to tooth failure, incorporating a state space adaptive-predictive feature tracking approach using a Kalman filter. To implement this approach, analytical means are developed to estimate the measurement error covariance of the instantaneous phase resulting from various error sources, and a feature is developed from the instantaneous phase parameter with improved correlation to the tooth bending fatigue failure mode.; The approach is validated for application to tooth bending fatigue using data sets simulating progression of the failure mode. This methodology is then applied to experimental data sets recording the progression of a commercial gearbox from a healthy state to tooth loss. The resulting interval predictions of time to tooth failure, with the probability of failure qualified by appropriate confidence intervals, are consistent with the observed failure trajectories, accommodating the differing degrees of measurement noise between data sets. The results demonstrate the viability of applying this approach to real world systems. Bias errors in the predictions resulted from the limitations of the second order linear kinematic process model used with the Kalman filter in tracking an exponential failure trajectory, as well as from the effect of apparent latent settling of undetermined mechanical parameters following load cycling. |
