Model-Based Analysis of Spur Gears’ Dynamic Behavior in the Presence of Multiple Cracks

Abstract

Early detection of tooth cracks is crucial for effective condition-based monitoring and decision making. The scope of this work was to bring more insight into the vibration behavior of spur gears in the presence of single and multiple simultaneous tooth cracks. The investigation was conducted in both time and frequency domains. A finite element analysis was performed to determine the variation in stiffness with respect to the angular position for different combinations of crack lengths. A simplified nonlinear lumped parameter model of a one-stage gearbox with six degrees of freedom was then developed to simulate the vibration response of faulty external spur gears. Four different multiple-crack scenarios were proposed and studied. The performances of various statistical fault detection indicators were considered and investigated. The simulation results obtained via MATLAB indicated that, as the severity of a single crack increases, the values of the time domain statistical indicators increase also, but at different rates. Moreover, the number of cracks was found to have a negative effect on the values of all the performance indicators, except for the RMS. The number and amplitude of the sidebands in the frequency spectrum were also considered, while assessing the severity of the faults in each scenario. It was observed that, in the case of consecutive tooth cracks, the number of spectrum peaks and the number of cracks were consistent in the frequency range of 4-5 kHz. The main finding of this study was that the peak spectral amplitude was the most sensitive indicator of the number and severity of cracks.