Tooth Crack Severity Assessment in the Early Stage of Crack Propagation Using Gearbox Dynamic Model

Localized tooth crack in gearboxes may be reflected in impulse components of gearbox vibration signals. Crack induced impulses have been used for crack detection and fault diagnosis. In reported studies, researchers have used statistical indicators of the identified impulses, such as root mean square (RMS) and kurtosis, to track the growth of crack. These reported statistical indicators are only effective when crack levels are high and they are unable to detect tooth crack and assess crack severity in the early stage of crack propagation. In addition, no reported studies have focused on studying how tooth crack level affects crack induced impulses. Specifically, what the dominant segments of crack induced impulses are and which segment is affected more by crack growth within a certain crack level range. This paper uses dynamic modeling to study how crack level affects crack induced impulses. First, impulses are generated with a spur gearbox dynamic model under constant working conditions. Second, an exponentially damped sinusoidal model is utilized to fit the impulses and the Matrix Pencil Method is used for model parameter estimation. Finally, relationships between crack level and impulses are studied based on the obtained model parameters. The results have shown that the segments in the fifth and the sixth frequency bands of impulses are two dominant segments, while other segments have little contribution, for the gearbox system under investigation. Within a certain crack level range, there exists an impulse segment which is more affected by the crack level. In terms of the early stage of crack propagation, the segment in the sixth frequency band of the impulse is more affected by crack growth. On this basis, three new statistical indicators have been developed with the segment in sixth frequency band of the impulse and have shown their effectiveness for tooth crack severity level assessment in the early stage of crack propagation. These results have good potential for detection and severity assessment of early tooth cracks in gearboxes.