The gear is one of the important parts of a rotary gearbox. Once catastrophic gear failure occurs, it will cause a great threat to production and life safety. The crack is an important failure factor causing changes in time-varying stiffness and vibration response. It is difficult to effectively identify the vibration response and meshing stiffness changes when there is a fine crack in the gear. Therefore, it is of great importance to improve the accuracy of meshing stiffness calculation and dynamic simulations under micro-cracks. Investigations of meshing stiffness and the vibration response of a gearbox is almost all about fixed gear shape parameters. However, the actual production process of gear system needs to change gear shape parameters. In this paper, the meshing stiffness and vibration response of the dynamic simulation signals of gear teeth with different crack depths at different tooth shape parameters (the pressure angle, the modulus, and the tooth number) were calculated, respectively. The influence of cracks on the vibration response was investigated by the fault detection indicators, the Root Mean Square (RMS), the kurtosis, and the crest factor. The result shows that when the pressure angle and modulus change, the vibration response changes erratically. However, when the tooth numbers change, the vibration response changes regularly. The results could be a guide for choosing gears in different shape parameters when system stability is the aim.

This paper investigates the effect of a gear tooth peeling on meshing stiffness of involute gears. The tooth of the gear wheel is symmetric about the axis, and its symmetry will change after the gear spalling, and its meshing stiffness will also change during the meshing process. On this basis, an analytical model was developed, and based on the energy method a meshing stiffness algorithm for the complete meshing process of single gear teeth with peeling gears was proposed. According to the influence of the change of meshing point relative to the peeling position on the meshing stiffness, this algorithm calculates its stiffness separately. The influence of the peeling sizes on mesh stiffness is studied by simulation analysis. As a very important parameter, the study of gear mesh stiffness is of great significance to the monitoring of working conditions and the prevention of sudden failure of the gear box system.

The turn domain resampling (TDR) method is proposed in the paper on the basis of the existing angle domain resampling for solving the problem of non-fixed fault frequency under variable working conditions. TDR can select the appropriate sampling order according to the influence of frequency conversion, which avoided the error caused by the spline interpolation method. It can provide accurate parameters for the subsequent calculation of the equivalent frequency order. Variable multi-scale morphological filtering (VMSMF) method is proposed for the purpose of further reducing the interference of noise in resampling signal to feature extraction. VMSMF adaptively selects structural elements according to the parameter change of impact signal to make its scale more targeted. It only needs to calculate once using the optimal structural unit for a particular impact, and the filtering accuracy and operating efficiency have been greatly improved. The main steps of this article are as follows. First, the TDR is used to resample the original signal as to get the resampling signal which is still submerged by the strong noise. In the second step, VMSMF is used to filter the resampling signal to obtain the signal with less noise interference. Finally, the fault characteristics of the filtering signal was extracted and compared with the possible fault frequency calculated by the sampling parameters provided by resampling, so as to determine the fault type of the planetary gearbox. By analyzing the simulation signal and the experimental signal respectively, this method can find out the corresponding fault characteristics effectively.

Under complex working conditions with noise interference, the fault feature of planetary gearbox is difficult to be extracted and the fault mode is difficult to be identified. To tackle this problem, the technologies of Variable Multi-scale Morphological Filtering (VMSMF) and Average Multi-scale Double Symbolic Dynamic Entropy (AMDSDE) are proposed in this paper. VMSMF selects Chebyshev Window as the structural element and automatically selects the optimal scale parameters according to the signal characteristics of the planetary gearbox, which improves the filtering accuracy and calculation efficiency. AMDSDE fully considers the correlation between various state modes. Once combined with relevant knowledge of Mathematical statistics, the algorithm can effectively reduce misjudgment. Firstly, the Turn Domain Resampling (TDR) is used to transform the time domain signal of variable speed into the angle domain signal that is not affected by speed change. Secondly, the proposed VMSMF is used to de-noise the vibration signal, and the fault signal with a high signal-to-noise ratio is obtained. Finally, AMDSDE is used to extract the entropy value of the fault signal and judge the fault type. The proposed technology is verified by four kinds of signals collected from the sun gear of the planetary gearbox under non-stationary working conditions.