In this study, the steady-state vibration response of a gearbox with gear tooth faults is investigated. Based on the analytical expression of the position-dependent mesh stiffness of the gear with perfect gear teeth derived with the potential energy method and the characteristics of involute gear teeth, expressions of the mesh stiffness of a gear with tooth faults such as tooth chip, tooth crack, and tooth breakage are derived. Using a coupled lateral and torsional vibration model of a one-stage spur gear pair, we have numerically solved a set of nonlinear equations and obtained typical vibration response diagrams of the gear pair with perfect gears and gears with tooth faults. This study reveals the relationship between the waveforms of the vibration and the types of local faults of the gear. These results are useful for identification of vibration signatures when there are these types of tooth faults.

In this paper, we combine independent component analysis in the frequency domain (ICA-FD) and Morlet wavelet filtering for gearbox fault diagnosis. Collected vibration signals from a gearbox are separated into two components with ICA-FD. Morlet wavelet filtering is then applied to the separated components. The optimal shape parameter p of the basic Morlet wavelet is obtained by minimizing the wavelet entropy. Better diagnosis results are obtained with this combination than using wavelet filtering alone.