The gear transmission system is an important part of the mechanical system, so it is essential to judge its running state accurately. To solve the difficult problem of identifying the components of coupling faults, this paper derives the calculation method of gear time-varying mesh stiffness for coupling faults of pitting and cracking based on the energy method and considering the coupling between teeth, establishes the dynamics model of two-stage gear transmission system with coupling faults and studies the influence of coupling faults on gear time-varying mesh stiffness and dynamic characteristics. The accuracy of the proposed method is verified by experiments. The results show that both pitting and cracking can lead to a reduction in mesh stiffness. The stiffness of pitting will fluctuate irregularly due to the influence of pitting on the tooth surface, while the stiffness of cracked teeth is relatively smooth. The coupling fault stiffness is dominated by more serious faults. By analyzing the periodic impact components in time domain and the sideband components around the harmonics in frequency domain the faulty gears in the transmission system can be distinguished. It provides an effective reference for the diagnosis of faulty gears.

Gearboxes operate in challenging environments, which leads to a heightened incidence of failures, and ambient noise further compromises the accuracy of fault diagnosis. To address this issue, we introduce a fault diagnosis method that employs singular value decomposition (SVD) and graph Fourier transform (GFT). Singular values, commonly employed in feature extraction and fault diagnosis, effectively encapsulate various fault states of mechanical equipment. However, prior methods neglect the inter-relationships among singular values, resulting in the loss of subtle fault information concealed within. To precisely and effectively extract subtle fault information from gear vibration signals, this study incorporates graph signal processing (GSP) technology. Following SVD of the original vibration signal, the method constructs a graph signal using singular values as inputs, enabling the capture of topological relationships among these values and the extraction of concealed fault information. Subsequently, the graph signal undergoes a transformation via GFT, facilitating the extraction of fault features from the graph spectral domain. Ultimately, by assessing the Mahalanobis distance between training and testing samples, distinct defect states are discerned and diagnosed. Experimental results on bearing and gear faults demonstrate that the proposed method exhibits enhanced robustness to noise, enabling accurate and effective diagnosis of gearbox faults in environments with substantial noise.

A gearbox compound fault intelligent diagnosis method based on the period group sparse model is proposed for the problem that the fault features are coupled with each other and the fault components are superimposed on each other and difficult to be separated in the gearbox compound fault signal. Firstly, a binary sequence is constructed to embed the fault pulse period as a priori knowledge into the group sparse model to decouple and separate the composite fault signal while maintaining the amplitude and sparsity of the extracted features. Secondly, the wavelet packet energy features of the decoupled signals are extracted to improve the data quality while enhancing the characterization ability of the dictionary in the classification model. Finally, the wavelet packet energy features are imported into the sparse dictionary classification model, and the fault diagnosis is completed by outputting the fault categories using the self-driven characteristics of the data. The results show that the fault identification accuracy using the proposed method is 97%. In addition, the experimental validation under different states and working conditions with different rotational speeds allows the superiority and effectiveness of the algorithm in this paper to be tested and has the feasibility of a practical application in engineering.