Variable amplitude Fourier series with its application in gearbox diagnosis-Part I: Principle and simulation

Vibration signal analysis has been an important method in the detection and diagnosis of gearbox faults. The vibration signals measured from a gearbox are complex multi-component signals, which include tooth meshing vibration, gear shaft rotating vibration and gearbox resonance vibrations. They are often non-stationary and time-varying. When conducting gearbox failure detection, it is not simple to interpret the results coming from traditional Fourier analysis; other signal processing methods such as short-time Fourier series (FS) and wavelet analysis are not always sufficient to exactly extract the desired frequency component for a certain gear. In this paper, a novel signal analysis method, which we named the variable amplitude FS (VAFS), is proposed. This method is based on an improvement of the traditional FS analysis and comes from the analysis of the gear meshing vibration signal model. In part I, the principle of the VAFS is introduced, and then an algorithm for calculating VAFS coefficients is presented. The performance of the VAFS is compared with that of a wavelet transform in the analysis of a numerically generated noisy chirp signal. In part II, the VAFS method is applied in the analysis of the vibration signal of a truck gearbox containing a gear in good, cracked and broken condition, and the results are compared with that of the wavelet analysis.