Gear is the most common part in mechanical equipment, and its running condition directly affects the performance of finishing table equipment. The fault mechanism and vibration characteristics of gears are summarized and analyzed. The methods of gear vibration signal analysis and fault diagnosis are introduced in detail, and the fault vibration signal of gears is processed by wavelet packet denoising. The vibration signal of gear failure is non-stationary, and the conventional Fourier analysis method can not achieve good results. Wavelet analysis method can analyze signals from both time domain and frequency domain at the same time, which is very suitable for gear fault diagnosis. Wavelet packet analysis theory is a fault signal diagnosis method developed rapidly in recent years, and it has been successfully applied in image processing, communication and geophysical research. Wavelet packet transform is an upgrade of wavelet transform, which together constitutes wavelet analysis. In this paper, the application of wavelet transform and wavelet packet transform in gearbox fault diagnosis is verified theoretically and experimentally, and wavelet packet analysis method is applied to the field of gear fault diagnosis. The main coverage is as follows: 1. From two aspects of diagnosis theory and fault signal characteristics, it is shown that wavelet packet analysis of fault signal is the inherent requirement of diagnosis. 2. Secondly, the theoretical basis of wavelet analysis and wavelet packet analysis is studied, and the noise reduction principle and model are analyzed theoretically. 3. The practical application of wavelet packet analysis in signal denoising is studied, and the signal is decomposed and denoised by wavelet packet, which has achieved good results. 4. The practical application of wavelet packet in frequency band decomposition feature extraction is studied, and the example analysis shows that this method can extract feature information well and diagnose faults. Based on the high-resolution decomposition and reconstruction ability of wavelet packet, the signal is decomposed into different frequency bands, and then the effective frequency band is selected to reconstruct the fault signal and separate the fault information. By denoising and decomposing the gear fault signal, it shows that this method can effectively remove the noise interference, extract the fault characteristic signal, and diagnose the gear fault.