**5. Conclusions**

In order to clarify the fault mechanism of inter-shaft bearings, a 4-DOF local defect inter-shaft bearing of a dynamic model is established in this paper, which considers EHL and TVDE. A piecewise function is used in this model to describe the TVDE of the local defect on the surface of the inter-shaft bearing. At the same time, the influence of the oil film is considered to improve the accuracy of the fault dynamic simulation. In this paper, the frequency distribution of the fault evolution process is simulated and analyzed by the established model. The relationship between defect width, external load and rotating speed and fault CP is studied. The main conclusions of this paper are summarized as follows.


In summary, an effective dynamic model of the inter-shaft bearing is established in this paper to accurately simulate the dynamic characteristics of the inter-shaft bearing with local defects. This study provides useful insights for the use of dynamic models to inspect and monitor the health of inter-shaft bearings of aeroengines.

**Author Contributions:** Conceptualization, F.Z.; Data curation, Z.W.; Methodology, J.T.; Software, X.A.; Validation, Y.C.; Writing—review & editing, C.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China (Grant No.12172231), Natural Science Foundation of Liaoning Province of China (Grant No. 2020-BS-174), Liaoning province Department of Education fund (Grant No. JYT2020019) and Research Start-up Funding of Shenyang Aerospace University (Grant No.19YB38). The authors would like to thank them.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.
