Spur gear crack modelling and analysis under variable speed conditions using variational mode decomposition

Cracks in gear are the most common mode of failure. The presence of cracks leads to a reduction in the time-varying mesh stiffness and eventually affects the vibration properties of the gear system. The non-stationarities induced due to the speed variation complicate the fault diagnosis process. A gear tooth crack model for spur gear with a simplified crack profile is proposed to mimic the natural path of crack propagation. The vibration response simulated using a six-degrees of freedom lumped parameter model is exploited with Short-Time Fourier Transform and the Variational Mode Decomposition. The effectiveness of the Variational Mode Decomposition method to filter out the non-stationarities in the signals subjected to low and very low amplitude speed fluctuations is addressed. A new state feature (Side-band Power Index) that does not require the measured speed profile (using tacho pulse input) is proposed for severity level classification. A feature importance study based on the Random Forest classifier is performed to prove the effectiveness of the proposed state feature amongst the conventional state features. The simulation model is validated with several experiments. The article aims to provide a complete diagnostic solution for the spur gear systems subjected to variable speed conditions.