Mechanical Systems and Signal Processing (2001) 15(5), 873}885 doi:10.1006/mssp.2001.1413, available online at http://www.idealibrary.com on USE OF THE MOVING CEPSTRUM INTEGRAL TO DETECT AND LOCALISE TOOTH SPALLS IN GEARS M. EL BADAOUI, J. ANTONI, F. GUILLET AND J. DANIE E RE Laboratoire d+Analyse des Signaux et des Processus Industriels (LASPI)~EA-3059, IUT de Roanne, 20, Avenue de Paris, 42 334 Roanne, France. E-mail: badaoui@univ-st-etienne.fr AND P. VELEX Laboratoire de Me & canique des Contacts, UMR CNRS 5514, INSA de Lyon, Ba L t. 113, 20 Avenue Albert Einstein, 69 621 Villeurbanne Cedex, France The objective of this paper is to propose a new indicator for the vibratory diagnosis of gear systems. This indicator is deduced from the power cepstrum of the accelerometer signal. A model aimed at simulating the contributions of local tooth defects such as spalls to the gear dynamic behaviour is set-up. The pinion and the gear of a pair are modelled as two rigid cylinders with all six degrees of freedom connected by a series of springs which represent gear body and gear tooth compliances on the base plane. It permits us to foresee the shape of the excitation induced by the presence of spalls. From an analytical analysis of the equa- tions of motion, a detection technique based upon the acceleration power cepstrum is proposed. The identi"cation of the spalls is provided by the fact that the power cepstrum of the excitation that it generates is strictly negative, in contrast to that of a normal excitation. A tool of detection and localisation, using this property, has been de"ned. It is "rst tested on acceleration signals simulated by numeric integration of the model, then on real signals.  2001 Academic Press 1. INTRODUCTION Rotating machine diagnosis is becoming more important because it contributes to safety in critical applications such as aeronautics but, more generally, because it reduces equipment downtime and maintenance costs. There are two main types of diagnostic techniques in use today, i.e. vibration monitoring and debris monitoring techniques, which have both had limited success in detecting gear failures. Focusing on vibration analysis, some methods use synchronously averaged signals in order to reduce random noise and contributions unre- lated to the particular gear of interest. The current tendency is to "nd techniques capable of detecting the occurrence of faults at an early stage. The simplest time domain analyses are based on statistical indicators such as kurtosis [1, 2] whose amplitude can be related to the state of the gear. More sophisticated techniques can be employed, including amplitude and phase demodulation by using Hilbert transforms [3], time}frequency transforms based on the Wigner}Ville decomposition [4], wavelet transforms [5}7], etc. Due to the lack of sensitivity of these methods for early detection, alternate methods relying on stress wave propagation (acoustic emission) have been considered [8, 9] but they are strongly dependent on the propagation path and the interfaces between the wave source and the sensors. Among the numerous available signal processing techniques used in vibration monitor- ing, it has been demonstrated in early papers [10}13] that the power cepstrum of the 0888}3270/01/050873#13 $35.00/0  2001 Academic Press