## 1 Introduction
However, existing research primarily focuses on the impact of bearing fault severity on its dynamic characteristics. On the other hand, the fault severity also influences the crack propagation direction in bearings. Additionally, material properties further affect the crack propagation rate and trend. The existing body of research indicates that numerous studies have extensively examined the effects of individual factors on the rotational speed of rolling elements or crack propagation in faulty bearings. However, crack propagation is typically the result of the combined influence of multiple factors, and investigations into the mutual interactions between these characteristics are notably rare. In the context of this study, for instance, an increase in fault severity directly affects both crack propagation and fluctuations in the rolling element speed. However, the subsequent impact of speed fluctuations on crack propagation is often overlooked. Analyzing the interactions between multiple characteristics offers valuable insights for more accurately reproducing the complex operational behavior of bearings. To address the above limitations, the influence of the fault degree on the dynamic characteristics and crack propagation for rolling bearings is investigated in this paper. First, cylindrical roller bearings are selected as the research subject. Then, a dynamic model of the bearing, both under fault-free conditions and with varying fault sizes on the outer ring, was established by considering the actual working conditions of rolling bearings. Meanwhile, the reliability of the dynamic model is verified theoretically and experimentally. After that, the study examined the slip behavior of rolling elements, the variation trends in the maximum shear stress and principal stresses on the outer ring, and the direction of crack propagation under different fault severities. The main contributions of this paper include the following: (1) With the increase in fault severity, the slip ratio of rolling elements passing through the fault position gradually increases. Once the fault severity reaches a critical level, the slip transitions from microscopic to macroscopic. A comparative analysis of GCr15 and AISI304 materials reveals that the material properties influence the onset of macroscopic slip. (2) Analyzing the maximum shear stress at the entry and exit points of the fault reveals that the crack propagation direction aligns with the rotational direction of the inner ring. As fault severity increases, the crack propagation speed also accelerates. The occurrence of macroscopic slip in the rolling elements causes fluctuations in the maximum shear stress, which subsequently affects the crack propagation speed. (3) An analysis of the three principal stresses shows that only the first principal stress (in the X direction) exhibits tensile stress. The crack will branch in the direction of the first principal stress, and the crack branching speed increases with fault severity. The rest of this paper is organized as follows: Section 2 introduces the establishment of the finite element model and relevant parameters. Section 3 presents the experimental setup used to validate the effectiveness of the established finite element model. Section 4 discusses the degree of slipping and maximum stress. Finally, Section 5 concludes the study.