## 5 Conclusions  
The severity of bearing failure will affect its dynamic characteristics and crack extension pattern. The rotational speed, stress variation, and crack extension trend in cylindrical roller bearings under different failure sizes are discussed in this paper and some conclusions are summarized as follows:  
1. Impact of fault severity on rolling element speed: As the severity of bearing faults increases, the impact on the rotational speed of rolling elements becomes significantly more pronounced when passing through the fault. At a fault severity of 1.25 mm, a maximum slip ratio of 6.04% is observed, indicating the occurrence of noticeable macroscopic slip. During macroscopic slip, the rotational speed of the rolling elements exhibits substantial fluctuations throughout the entire rotation process. Furthermore, the material properties influence the onset of macroscopic slip under fault conditions.
2. Crack propagation direction and speed: The direction of crack propagation aligns with the rotation direction of the inner ring. With microscopic slip, the crack propagation speed increases with fault severity. Macroscopic slip causes fluctuations in maximum shear stress, affecting the crack propagation speed.
3. Principal stresses and crack bifurcation: In the X direction, a combined tensile-compressive stress region emerges, with the tensile stress reaching a maximum of 227 MPa, which facilitates crack branching along the X direction. The crack branching rate exhibits a progressively increasing trend as fault severity intensifies. Conversely, the Y and Z directions predominantly experience compressive stresses, exerting an inhibitory effect on crack branching to a certain extent.
4. Correlation with stress trends: The slip degree of the rolling elements is consistent with the trends in maximum shear stress and the three principal stresses. This mutual verification reflects changes in bearing performance and crack propagation trends under different fault severities. The findings provide a theoretical basis for understanding crack propagation and dynamic performance changes in rolling bearings.  
Future work will aim to incorporate system-specific factors such as lubrication regimes, operational load distributions, and environmental influences into the model. These enhancements are expected to improve the model's predictive accuracy and applicability in real-world scenarios, thereby extending the insights gained from this study. Additionally, considering surface topography, such as roughness and machining marks, will provide a more comprehensive understanding of how fault dynamics are influenced by contact conditions, stress distribution, and crack propagation under varying operating scenarios.  
**Author Contributions:** L.Z.: conceptualization, supervision, funding acquisition, writing--review and editing. Z.X.: methodology, software, formal analysis, writing--original draft. H.Z.: formal analysis, writing--original draft. W.L.: formal analysis, software. C.H.: data curation. T.Q.: methodology. C.W.: funding acquisition, writing--review and editing. J.L.: conceptualization, methodology, writing--review and editing. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported by the Natural Sciences of Jiangxi Province (grant no. 20224 ACB204017), the Science and Technology Project of China State Railway Group Co., Ltd. (grant no. N2023J042), and National Key Laboratory Autonomous Projects (grant no. HIGZ2022202 and grant no. HIGZ2022208).  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author due to privacy.  
**Conflicts of Interest:** The authors declare that this study received funding from China State Railway Group Co., Ltd. The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article or the decision to submit it for publication.