Crack identification in a single stage straight bevel gear system through nonlinear vibration analysis-theoretical and experimental methods

Abstract

The tooth crack identification through the effect of the tooth root crack on nonlinear vibration behaviors in a straight bevel gear (SBG) system is sought. The mesh stiffness is evaluated through an analytical method based on the potential energy and Tredgold approximation associated with tooth root crack modeling. A 10-dof model is developed for the SBG system where the backlash nonlinearity is of concern. To assess the nonlinear vibration behaviors of the SBG system, first, the dynamic response is extracted analytically with the proposed dynamic model, and experimentally with a designed setup, then the extracted response is assessed based on the different crack identification statistical factors. Results indicate that the Skewness is the most effective factor in identifying the crack in the SBG system with backlash nonlinearity, compared to other investigated factors. The nonlinear vibration response as a time history, phase diagram, Poincaré map, modal analysis, and mesh stiffness FFT spectrum is analyzed and recommended as an appropriate indicator for tooth root cracks. The modeled mesh stiffness and simulated SBG system are verified by applying FEM and the experimental method. Graphical abstract: (Figure presented.) © The Author(s), under exclusive licence to Springer Nature B.V. 2024.