Feature extraction is a key step of intelligent bearing fault diagnosis. However, bearing vibration signals are usually nonlinear, non-stationary signal with strong noises. Extracting the effective status feature of bearing is challenging. Thus, a new rolling bearing status feature extraction method based on variational mode decomposition (VMD) and improved envelope spectral entropy (IESE) is proposed in this paper. First, the bearing vibrational signals are decomposed into different intrinsic mode functions (IMF) by VMD. Then, the envelope spectral entropy of each IMF is calculated and the IESE is obtained by reconstructing the envelope spectral entropy to build original feature sets. Finally, the original feature set is fused by the joint approximate diagonalization eigen (JADE) to obtain a new one. The new feature set is trained and tested by using SVM to identify the bearing status. The feasibility of the proposed method for feature extraction is verified by three experimental cases. Compared with several methods, the performance of this proposed method is better than those of other methods.

Bearing is the key part of mechanical equipment, which can support the rotating machinery running. It is crucial to diagnose bearing fault in time to ensure mechanical equipment working well. Effective feature extraction is an essential step in bearing fault diagnosis. However, the bearing vibration signals collected from the equipment usually contain interference, such as heavy noise. It is difficult to extract effective feature from bearing vibration signals due to the interference. To overcome this issue, a new feature extraction method for rolling bearing faults diagnosis is proposed based on hierarchical improved envelope spectrum entropy (HIESE). First, hierarchical decomposition is used to divide the bearing vibration signal into several hierarchical components. Second, the original feature set is obtained by calculating the improved envelope spectrum entropy (IESE) of each hierarchical component. Then, joint approximate diagonalization of eigenmatrices (JADE) is introduced to fuse the original features into a new one. Finally, support vector machines (SVM) is taken to identify the bearing status. Two cases are used to test the proposed method. In case 1, the bearing vibration signals composed of different fault degrees and different fault types under two speeds are used to verify the proposed method. The recognition rate achieves 100%. In case 2, the bearing vibration signals, which consist of different fault types under three operation conditions, are analyzed. The recognition rate also achieves 100% in this case. Experimental results illustrated that the proposed method has good performance in feature extraction, which can provide a new method for feature extraction of rolling bearing.

Data-driven based fault diagnosis methods play an increasingly important role in rotating machinery. Among these methods, deep learning is widely concerned due to its strong nonlinear feature learning ability, wherein ResNet is a very powerful model. However, the diagnostic performance of the model depends on sufficient labeled data samples, which is extremely difficult to achieve under actual complex working conditions. In this paper, a multidimensional normalized ResNet is proposed for fault diagnosis of cross-working conditions under limited label samples. Firstly, the collected vibration data under different conditions are preprocessed by computed order tracking to reduce the distribution differences. Secondly, batch normalization and group normalization are fused together to enhance the feature extraction ability of ResNet. Moreover, the rectified linear unit is replaced by the gaussian error linear unit to improve the robustness of the trained model. Then, the model is trained by source domain samples, and the obtained parameters will be transferred to the target domain. Finally, the transferred model is fine-tuned through limited samples in the target domain and applied for cross conditions fault diagnosis. Two kinds of datasets are analyzed by the proposed method and existing models to demonstrate its superiority.

Intelligent machine fault diagnosis technique has recently exploded interest in digital health, energy power, and industrial maintenance. Collecting machine fault data in engineering practice is usually costly, causing big challenges in the intelligent diagnosis of most fresh-from-the-factory machines that are missing fault data. Inspired by the main idea of the digital twin, in this article, we propose a dynamic model-embedded intelligent machine fault diagnosis framework. Specifically, a machine dynamic modeling and parameter identification approach is introduced for building the machine digital model. The digital model is used to predict machine fault data from the measured healthy vibration signals. Furthermore, a parameterized convolutional neural network structure is designed for learning optimization features and recognizing the machine's healthy state. Experimental investigation demonstrates the effectiveness of the framework. The results show that the proposed framework enables intelligent machine fault diagnosis without fault data. The diagnosis effect outperforms supervised, unsupervised, and small-sample learning approaches and can be generalized to another load and speed with acceptable accuracy.

Aiming at the nonlinear vibration problem caused by the dynamic misalignment of rolling bearings in the rotating machinery, a rotor dynamic model with bearing dynamic misalignment is established, and the effects of the dynamic misalignment of single and two bearings and the phase relationship of two dynamic misalignment bearings on the rotor vibration characteristics are researched. The effects of bearing clearance, raceway curvature radius, the ball number and radial load on the nonlinear vibration response of the dynamic misalignment bearing-unbalance rotor system are further analyzed. The results show that the dynamic misalignment of the bearing can excite the vibration at twice the rotor frequency, raise the resonance speed and enhance the hardening-type nonlinearity characteristics of the rotor. The influence of dynamic misalignment under two bearings with out-of-phase on rotor resonance is greater than that of the in-phase. The stability of the system can be improved by decreasing the bearing clearance and increasing the curvature radius coefficient. The vibration caused by bearing dynamic misalignment can be reduced by selecting the bearing with more balls and appropriately increasing the bearing load.

Taking the effect of actual surface topography under elastohydrodynamic lubrication (EHL) conditions on the contact state of gear pairs into consideration, a combination model with the analytical sliced method and two-dimensional (2D) EHL model is proposed to characterize the three-dimensional (3D) meshing characteristics of spur gears. Firstly, the surface topology of gears is tested by a surface profiler, which reflects that the topography of tooth surface accords with fractal characteristics. Thus, by adopting the Weierstrass–Mandelbrot (W-M) fractal function, the gear surface is characterized. Secondly, the numerical 2D EHL model with fractal roughness is established, and distributions of oil film pressure (OFP) and oil film thickness (OFT) at different meshing positions are obtained. Finally, considering the different topography distributions in the direction of face width, time-varying mesh stiffness (TVMS) is calculated based on the analytical sliced method. Thus, the influence of 3D surface topography can be considered. The Hertz contact stiffness is substituted by the time-varying lubricating oil film stiffness (OFS). The influences of tooth surface topography and lubricant film characteristics on meshing characteristics are investigated. The results show that the 3D rough tooth surface may be well characterized by a fractal function with random phase. Moreover, there is a great difference in the distribution of OFP and OFT between rough and smooth surfaces, which certainly influences the gear meshing characteristics.