A reduced-order dynamic model, based on three-dimensional (3D) finite element model (FEM) and component modal synthesis technique (CMS), was presented for simulating the dynamic behavior of the spur gear system. The gear shaft and gear body were established via 3D elements to simulate bending and torsion of the gear system. The CMS technique was used to generate a reduced-order model of a spur gear system. A pair of mating teeth was assimilated to two different foundations (one for the pinion tooth and the other one for the gear tooth) linked in series by some independent springs, which was used to simulate the contact stiffness. The validity of the proposed model was verified by static analysis, dynamic analysis, and experimental analysis. The results show that the proposed model is an effective model. In addition, the proposed model has also been applied to analyze spur gear spalling faults. The results show that the dynamic response of the gear system is periodic vibration shock response due to the alternate meshing of single and double teeth. When the spalling fault occurs, some shock responses with significantly enhanced amplitude will be generated as the result of contact loss.

This paper presents the vibration of a transversely cracked rotor supported by anisotropic journal bearings, where the speed-dependent characteristic of bearing is considered. A 3D finite element model and the contact-based approach are employed for the shaft and crack. The governing differential equations of the whole cracked rotor-bearing system were obtained by synthesizing the equations of the cracked shaft, the breathing crack and the journal bearings. In order to solve the computational difficulties caused by the high dimensions of model, the free-interface complex component mode synthesis method (CMS) is employed to reduce the order of the model. On this basis, the eigenvalue and the steady-state forced response of the cracked rotor-bearing system are obtained by the Hill’s method. Finally, the effects of the anisotropic and speed-dependent characteristics of bearings on the vibration of the system are studied. Numerical results show that both the two characteristics can significantly affect the response of the system. The anisotropy in the bearing leads to the split of resonant peaks and influence the amplitudes of the peaks. The speed-dependent characteristic mainly affects the responses at the speeds close to the resonant regions, because the parametric excitation effect of the resonance region is greater than other speeds.

Rotating machinery is widely employed in critical industries such as petrochemical, aerospace, and rail transportation, where its operational condition is vital for ensuring system safety and reliability. However, fault diagnosis in such machinery is challenged by the limited availability of data samples in real-world applications. Traditional diagnostic methods often fail to significantly improve fault detection accuracy under these conditions. To address this issue, this paper proposes a fault diagnosis method tailored for rotating machinery with limited sample sizes, combining enhanced auxiliary classifier generative adversarial networks (EACGAN) with a multi-scale attention convolutional neural network (MSACNN). First, a continuous wavelet transform is applied to convert the one-dimensional vibration signal into a time-frequency spectrogram, generating a time-frequency sample dataset. Next, the model structure and loss function are refined to develop an EACGAN capable of generating high-quality data samples for data augmentation. Finally, a multi-scale convolutional network is introduced, and in conjunction with the dual-pooling efficient channel attention (DP-ECA) mechanism, the MSACNN is designed to enhance diagnostic recognition accuracy. Experimental results from bearing and gear datasets show that the proposed method can accurately identify multi-modal faults in rotating machinery, even with limited sample sizes, significantly improving diagnostic performance.

Gearboxes are key transmission components in rotating machinery, and their vibration signals are highly susceptible to strong background noise in practical operating environments. Such interference can obscure weak fault-related features and introduce fluctuations into adaptive thresholds generated from current feature statistics, thereby compromising the balance between noise suppression and useful feature preservation. To address this issue, this study proposes HTG-Net, an adaptive gated fault-diagnosis network for severe-noise environments. Built upon the Spatial Reconstruction Unit (SRU), the proposed method reformulates SRU from a feature-redundancy suppression module into an adaptive denoising unit for noise-aware feature screening. First, global average pooling and global maximum pooling are jointly employed to construct a multi-statistic data-driven threshold, enabling threshold estimation to account for both overall response levels and prominent local activations. On this basis, a statistics-discrepancy-aware base-threshold fusion mechanism is introduced to adaptively regulate the contributions of the data-driven threshold and a prior base threshold according to the discrepancy between the two statistics, thereby reducing excessive dependence on potentially unstable sample statistics under strong noise. Second, hard gating is adopted in the forward pass to perform discrete feature selection and avoid the continuous amplitude shrinkage associated with soft-thresholding operations, while a straight-through estimator provides surrogate gradients during back-propagation for end-to-end optimization. In addition, ConvMLP-based channel interaction and residual connections are incorporated to enhance inter-channel information exchange and mitigate information loss during gated feature screening. Experiments conducted on the Southeast University gearbox fault dataset under different signal-to-noise ratio conditions show that HTG-Net maintains stable diagnostic performance in severe-noise environments, achieving an average diagnostic accuracy of 82.60 ± 0.55% at −10 dB. These results indicate that the proposed adaptive threshold-fusion and hard-gating feature-screening mechanisms can improve the robustness of gearbox fault diagnosis under strong-noise conditions.

Deep salt–gypsum formations undergo pronounced creep under high temperature and nonuniform in situ stresses, transferring time-dependent loads through the cement sheath and causing casing ovalization. The constant viscosity of the classical Nishihara model limits its ability to simultaneously represent weakly activated and strongly nonstationary creep responses. An exponentially time-varying viscosity was therefore introduced into the Bingham viscoplastic branch and coupled with a reference-normalized Heard factor to develop a nonstationary Nishihara–Heard model. Five 8 h triaxial creep tests at a confining pressure of 30 MPa, with deviatoric stresses of 15–65 MPa and temperatures of 25–90 °C, were used for multi-condition parameter identification. The proposed model increased the pooled R² from 0.582 to 0.907 and substantially reduced systematic medium-to-late-stage residuals under strongly activated conditions while retaining the near-stationary response under weak activation. The model was implemented in Abaqus/Standard through a user material subroutine (UMAT) and coupled with a casing–cement sheath–formation finite-element model. Calibration using well X1 reproduced the measured one-year casing ovality, and fixed-parameter predictions for wells X2 and X3 yielded relative errors below 8%. These results demonstrate preliminary cross-well engineering applicability within the investigated 1–2-year observation window.