Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth

a b s t r a c t
Gear tooth crack will cause changes in vibration characteristics of gear system, based on
which, operating condition of the gear system is always monitored to prevent a presence
of serious damage. However, it is also a unsolved puzzle to establish the relationship
between tooth crack propagation and vibration features during gear operating process.
In this study, an analytical model is proposed to investigate the effect of gear tooth crack
on the gear mesh stiffness. Both the tooth crack propagations along tooth width and crack
depth are incorporated in this model to simulate gear tooth root crack, especially when it is
at very early stage. With this analytical formulation, the mesh stiffness of a spur gear pair
with different crack length and depth can be obtained. Afterwards, the effects of gear tooth
root crack size on the gear dynamics are simulated and the corresponding changes in statistical
indicators – RMS and kurtosis are investigated. The results show that both RMS and
kurtosis increase with the growth of tooth crack size for propagation whatever along tooth
width and crack length. Frequency spectrum analysis is also carried out to examine the
effects of tooth crack. The results show that sidebands caused by the tooth crack are more
sensitive than the mesh frequency and its harmonics. The developed analytical model can
predict the change of gear mesh stiffness with presence of a gear tooth crack and the corresponding
dynamic responses could supply some guidance to the gear condition monitoring
and fault diagnosis, especially for the gear tooth crack at early stage.

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