PEER REVIEW
20
th
Australian International Aerospace Congress, 27-28 February 2023, Melbourne
The 20th Australian International Aerospace Congress
ISBN number: 978-1-925627-66-4
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Comparison of vibration and transmission error in gear
crack diagnostics
Zhan Yie Chin
1
, Pietro Borghesani
1
, Wade A. Smith
1
, Robert B. Randall
1
, Yuanning Mao
1
, and Zhongxiao Peng
1
1
School of Mechanical and Manufacturing Engineering, UNSW Sydney, New South Wales, 2052, Australia
Abstract
Vibration has long been established for gear diagnostics. In the literature, the study of gear-
crack induced vibration can be interpreted and divided into two main groups. The first group of
studies treat crack-induced gearmesh stiffness and tooth-specific profile deviations due to
plastic deformation (e.g., crack being permanently open) as excitations of gearbox dynamics.
The two excitations can be combined as a single component, leading to static-transmission-
error (STE). STE then passes through a certain transfer function, leading to outputs such as
measurements of transmission error (TE) and vibration. Hence, signal processing based on this
traditional interpretation of crack symptoms focuses on the first several gearmesh harmonics
and their sidebands in the low frequency range, and is valid when the system can be suitably
considered as linear-time-invariant (LTI), supported both experimentally and theoretically (i.e.,
modelling) by recent studies. The second group of studies instead look into the free-vibration-
like system impulse responses caused by the impulsive events generated by the crack at high
frequencies as abrupt changes in gearmesh stiffness and profile occur. This paper further
explores this area and compares it to TE-based diagnostics. It is shown that TE is the best
measurement to capture crack symptoms directly related to compliance and profile changes in
the low-frequency region, whereas vibration is sensitive to high-energy impulsive events in the
high-frequency range. As future work, the combination of these two measurements can be
further exploited to develop more effective strategies for gear condition monitoring.
Keywords: gear cracks, transmission error, vibration, gear diagnostics.
Introduction
Vibration has been the traditional gear diagnostic tool for decades. Among the multitude of
studies on knowledge-based signal-processing for this application, it is possible to distinguish
two main categories, based on their interpretation of the key physical phenomenon to target for
the identification of tooth crack symptoms.
A first category follows a model in which crack-induced gearmesh stiffness and profile
deviations due to crack-related plastic deformation are treated as standard “excitations” of the
gearbox dynamics. This approach has been recently linked to the concept of static-transmission-
error (STE). Under this modelling interpretation, the gearmesh compliance (inverse of stiffness)
𝑠
(
𝑡
)
and geometric error 𝜀
(
𝑡
)
combine additively to give STE, with the average load 𝐹, to act
as a weight:
