Vibration analysis for tooth crack detection in a spur gear system with clearance nonlinearity

This paper concentrates on the gear tooth crack detection by investigating the effects of tooth crack on the vibration behaviors of a nonlinear spur gear system. Firstly, an analytical tooth crack model is used to calculate the gear mesh stiffness for different crack sizes. Then, a 3 DOF spur gear pair model is developed with consideration of tooth backlash and bearing clearance nonlinearity. The nonlinear frequency responses based on several statistical indicators are obtained to assess the vibration behaviors and fault conditions for the gear system. In addition, the vibration responses in time and frequency domains are also analyzed. Results show that peak and crest factor are the optimal indicators for tooth crack detection. Whereas, the kurtosis hardly works in most cases due to the presence of clearance nonlinearity. Besides, the vibration response characteristics such as time histories, phase diagrams, Poincare maps, FFT spectrums and sidebands, could present indications reflecting the tooth crack propagation to some extent. Therefore, the developed model is capable of predicting the mesh stiffness and vibration behaviors of a cracked gear system, and the corresponding vibration analysis could provide references aiding the tooth crack detection for researchers and engineers.