A new approach to time-domain vibration condition monitoring : gear tooth fatigue crack detection and identification by the Kolmogorov–Smirnov test

Abstract

This paper introduces a new technique for early identification of spur gear tooth fatigue cracks, namely the Kolmogorov–Smirnov test. This test works on the null hypotheses that the cumulative density function (CDF) of a target distribution is statistically similar to the CDF of a reference distribution. In effect, this is a time-domain signal processing technique that compares two signals, and returns the likelihood that the two signals have the same probability distribution function. Based on this estimate, it is possible to determine whether the two signals are similar or not. Therefore, by comparing a given vibration signature to a number of template signatures (i.e., signatures from known gear conditions) it is possible to state which is the most likely condition of the gear under analysis. It must be emphasised that this is not a moment technique as it uses the whole CDF, instead of sections of the cumulative density function. In this paper, this technique is applied to the specific problem of fatigue crack detection. Here, it is shown that this test not only successfully identifies the presence of the fatigue cracks but also gives an indication related to the advancement of the crack. Furthermore, this technique identifies cracks that are not identified by popular methods based on the statistical moment analysis of the vibration signature. This shows that, despite its simplicity, the Kolmogorov–Smirnov test is an extremely powerful method that effectively classifies different vibration signatures, allowing for its safe use as another condition monitoring technique.