# Gear Wear Process Monitoring Using a Sideband Estimator Based on Modulation Signal Bispectrum
## 1 Introduction  
Gears are critical mechanical components for power transmission systems and are widely used in automobiles, helicopters, and industrial power trains. Gear wear is a progressive material loss from contacting tooth surfaces, which is an inevitable phenomenon in the service lifetime of gears [1]. When gear wear reaches a certain degree of severity, it can lead to the occurrence of gear failures such as surface pitting, scuffing, and broken teeth. Therefore, the subject of gear wear monitoring and diagnosis is receiving a lot of attention from the field of condition monitoring (CM). Wear debris analysis is popularly used for gear wear monitoring [1,2]. However, wear particles analysis cannot reveal changes in gear transmission dynamic features in a timely fashion, which can be used to examine if the gears are still working properly. In contrast, the vibro-acoustic signals can reflect the gear dynamic features at the measured instant, thus could be used to assess the effects of wear on gears in real-time. Acoustic signals in conjunction with modulation signal bispectrum (MSB) signals processing methods have been used to monitor the gear wear process [3]. It was found that the meshing frequency components and the associated shaft modulating components can indicate tooth wear. The acoustic signature is a sequence of pressure waves that propagate through a compressible media; this mediais often heavily contaminated by various noises from the surrounding environment and by nearby machines. Therefore, heavy noise content means that fault diagnosis by analysing airborne sound signals is difficult and unreliable, as such great care has to be taken when interpreting the information content [4]. As one of the mainstream techniques of CM, vibration-based methods are relatively easy to implement and to process the results. The influence of wear on gear dynamic features has already been investigated theoretically [5], but was not validated physically. Therefore, measuring the vibration signal for gear wear assessments is presented in this article. Gear wear will usually result in a deviation from the intended tooth profile and alter the gear meshing excitations [6], which will produce a nonlinear coupling phenomenon that will present small sidebands, a variance of the meshing frequency and shaft rotational frequency; these phenomena are distributed around the meshing frequency and its harmonics. In gear fault diagnosis, the amplitudes of these small sidebands are useful for both detection and diagnosis. As these sidebands are usually influenced by random noise, in order to obtain more accurate results, many signal processing methods have been tried in many of the latest studies. The traditional methods--such as fast Fourier transform, power spectrum and cepstrum analysis [7]--are primarily based on stationary signals, and have difficulty in analysing nonlinear phenomenon and in suppressing noise. Therefore, many researchers have investigated alternative signal analysis methods such as smoothed pseudo-Wigner Ville distribution [8], time synchronous averaging (TSA) [2; 9], cyclo-stationary analysis [10], empiric mode decomposition (EMD) [11], ensemble empirical mode decomposition (EEMD) [12], wavelet analysis [13], and combined methods [1] to analyse vibration signals for a more accurate feature extraction. Although these efforts have shown promising results, they may be still lacking because these signal analysis methods possess limited noise reduction capability. Bispectrum analysis is a useful signal processing tool that has shown significant benefits over traditional spectral analyses due to its unique properties of nonlinear system identification, Gaussian noise elimination, and phase information retention [14; 15; 16; 17; 18; 19; 20; 21]. Conventional bispectrum (CB) was applied to vibration signals for the detection of different degrees of tooth breakage of a two-stage helical gearbox and tooth crack [15]. [PERSON] et al.