Rolling bearings often work under nonstationary conditions, which will lead to spectrum smearing phenomenon and the failure of traditional diagnostic methods. Order tracking is a common technique to alleviate this problem by resampling the time-domain signal using the instantaneous rotation frequency. For tacholess applications, it is of great importance to obtain accurate rotation speeds. In this paper, a tacholess order tracking method based on spectral amplitude modulation (SAM) is proposed. Based on the fact that SAM can separate frequency components with different levels of energy, an appropriate weight is selected to highlight the instantaneous frequency, which is then extracted from the time-frequency representation by peak search algorithm. Moreover, entropy is employed to evaluate the valuable information in the time-frequency representation in order to select an optimal weight adaptively. A simulated signal and experimental signals of bearing outer and inner ring faults demonstrate that the proposed method can extract instantaneous rotation frequency and detect nonstationary bearing fault characteristics effectively.

In this work, an improved computational method for the prediction of the vibration and noise of a gearbox that considers the flexibility of the shaft is developed. Based on the finite element method (FEM), a coupled dynamic model of a spur gear-shaft-bearing system is established, and the time-varying mesh stiffness (TVMS), the time-varying bearing stiffness (TVBS), and the flexibility of the shaft are considered. The Newmark integration method (NIM) is utilized to obtain the dynamic load of the bearing. Furthermore, the proposed model is validated by experiments. The bearing load is then considered to be the excitation of the housing, and the radiated noise is calculated via the finite element method/boundary element method (FEM/BEM). The effects of the shaft flexibility on the bearing response and radiated noise are discussed based on the proposed method. The results demonstrate that, when the shaft flexibility is considered, the system undergoes the bending vibration of the shaft, and the vibration amplitude and excitation frequency components of the bearing load decrease significantly. Additionally, the main resonance mode of the gearbox is changed, and the radiated noise is enhanced. The effects of the input speed and shaft stiffness on the bearing response and radiated noise are also investigated. The results provide a theoretical basis for the further development of the vibration and noise reduction of gearboxes.

Aiming at the problem that the vibration energy of shaft crack early weak fault is small and the feature extraction was difficult, the fault diagnosis method of cuckoo search, maximum correlation kurtosis deconvolution and variational mode decomposition (CS-MCKD-VMD) was proposed to diagnose the early weak fault of shaft cracks. Firstly, considering the periodic characteristics of fault signal, MCKD was used to highlight the fault signal, and the kurtosis correlation of deconvolution signal processed by MCKD were enhanced. Then, VMD could be used to decompose the harmonic signal, and VMD was used to process the deconvolution signal to generate some intrinsic mode functions (IMF), and the correlation coefficient method was used to calculate the components with the maximum correlation. At the same time, in order to improve the correlation of parameters in MCKD and VMD, CS was used to optimize the parameters to reduce the error of human selection. Thirdly, the optimal component was calculated by the fast spectral kurtosis (FSK), and the envelope spectrum was obtained by filtering the optimal component with the parameters obtained. Finally, the simulation and experimental results show that the transfer frequency and its 2 and 3 times frequency were prominent in the envelope spectrum, which was consistent with the analysis of shaft crack fault mechanism, Therefore, it was proved that the CS-MCKD-VMD method can effectively extract the early weak fault features of shaft cracks.

To analyze the vibration characteristic differences of a gear transmission system with gear and shaft cracks, an improved computational method for deriving the shaft stiffness matrix with breathing cracks is developed. Also, the three-dimensional contact model of spur gear with a crack is established via the finite element method (FEM), and its meshing stiffness is calculated. Simultaneously, considering bearing stiffness and shaft flexibility, the finite element dynamic models of two-stage gear transmission system with gear and shaft cracks are established. Based on this, different source fault vibration responses are compared and the influencing factors are explored. In addition, a novel signal processing method based on the particle swarm optimization, maximum correlated kurtosis deconvolution, variational, mode decomposition and fast spectral kurtosis (PSO-MCKD-VMD-FSK) is utilized to extract fault characteristics for the signal-to-noise ratio and uneven energy distribution problems. Results show that a system with gear cracks mainly presents periodic impact in the time domain, while in the frequency domain it impacts rotation frequency modulation near the meshing frequency and its multiple frequencies. However, the shaft crack breathing effect meant that the time domain mainly presents “simple harmonic” modulation, and the rotation frequency and its faulty shaft multiplication occurs in the low-frequency region of the frequency domain. The PSO-MCKD-VMD-FSK method extracts fault features in a strong noise environment and has good robustness. Results identify different source faults and provide a theoretical basis.

The technique for target detection based on a convolutional neural network has been widely implemented in the industry. However, the detection accuracy of X-ray images in security screening scenarios still requires improvement. This paper proposes a coupled multi-scale feature extraction and multi-scale attention architecture. We integrate this architecture into the Single Shot MultiBox Detector (SSD) algorithm and find that it can significantly improve the effectiveness of target detection. Firstly, ResNet is used as the backbone network to replace the original VGG network to improve the feature extraction capability of the convolutional neural network for images. Secondly, a multi-scale feature extraction (MSE) structure is designed to enrich the information contained in the multi-stage prediction feature layer. Finally, the multi-scale attention architecture (MSA) is fused onto the prediction feature layer to eliminate the redundant features’ interference and extract effective contextual information. In addition, a combination of Adaptive-NMS and Soft-NMS is used to output the final prediction anchor boxes when performing non-maximum suppression. The results of the experiments show that the improved method improves the mean average precision (mAP) value by 7.4% compared to the original approach. New modules make detection much more accurate while keeping the detection speed the same.