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This paper takes an asymmetric support ball bearing-rotor system subjected by unbalanced force and parametric excitation (varying compliance) as the research object. Multi-modes of resonance such as natural frequency resonance region of each order, VC (varying compliance) frequency resonance region, the 1/2 sub-harmonic VC frequency resonance region, and quasi-periodic regions, and the nonlinear characteristics in these regions are analyzed. Besides, the effect of the number of balls of the ball bearing is also considered and the result shows that the parity of this parameter matters a lot. By introducing a definition of the absolute quasi-periodic frequency, the law of the occurrence of the quasi-periodic motion is demonstrated and the possible cause is given to some extent. The work provides a theoretical basis for clarifying the nonlinear characteristics of the bearing-rotor system and suppressing the nonlinear behavior of the system.

William Alexander was the official draughtsman of the Macartney Embassy. His pictures of China covered a wide range of themes. Each theme represented a certain purpose. Landscapes, architectural dr...

Fault diagnosis of rotating machinery is an important engineering problem. In recent years, fault diagnosis methods based on the Convolutional Neural Network (CNN) and Recurrent Neural Network (RNN) have been mature, but Transformer has not been widely used in the field of fault diagnosis. To address these deficiencies, a new method based on the Time Series Transformer (TST) is proposed to recognize the fault mode of bearings. In this paper, our contributions include: Firstly, we designed a tokens sequences generation method which can handle data in 1D format, namely time series tokenizer. Then, the TST combining time series tokenizer and Transformer was introduced. Furthermore, the test results on the given dataset show that the proposed method has better fault identification capability than the traditional CNN and RNN models. Secondly, through the experiments, the effect of structural hyperparameters such as subsequence length and embedding dimension on fault diagnosis performance, computational complexity and parameters number of the TST is analyzed in detail. The influence laws of some hyperparameters are obtained. Finally, via t-Distributed Stochastic Neighbor Embedding (t-SNE) dimensionality reduction method, the feature vectors in the embedding space are visualized. On this basis, the working pattern of TST has been explained to a certain extent. Moreover, by analyzing the distribution form of the feature vectors, we find that compared with the traditional CNN and RNN models, the feature vectors extracted by the method in this paper show the best intra-class compactness and inter-class separability. These results further demonstrate the effectiveness of the proposed method., Comment: 17 pages, 10 figures