# Research on Dynamic Modeling and Vibration Characterization of Integrated Bearings
## 1 Dynamic Modeling of Integrated Bearing Systems
### Specialized Structure of Integrated Bearings
[17] proposed a coupled dynamic model of the rolling bearing-rotor system, seamlessly integrating the rotor's detailed finite element model with the bearing dynamic model. They also introduced a variable-step numerical integration algorithm for solving the system. [PERSON] et al. [18] considered the effects of sliding and developed a dynamic model of the DGB 6205 bearing, which incorporates the radial motion of the inner race, the rotation of the cage, and the rotation of the balls. They investigated the impact of time-varying loads on the vibration characteristics of the bearing system. [PERSON] et al. [19] proposed a dynamic modeling method for deep-groove ball bearings with waviness defects. [PERSON] et al. [20] considered outer race defects and inner race misalignment, proposing a transient displacement excitation model based on piecewise functions. They solved this model to obtain the vibration response of the bearing. The study by [PERSON], [PERSON] et al. [21] investigated the impact of raceway defects on the motion of deep-groove ball bearings using a six-degrees-of-freedom dynamic model. [PERSON] et al. [22] developed a dynamic model to predict the vibrations of deep-groove ball bearings, taking into account the masses of the shaft, raceway, balls, and bearing housing. [PERSON], [PERSON] et al. [23] established a dynamic model for deep-groove ball bearings that incorporates a flexible cage, analyzingthe impact of cage flexibility on the bearings' dynamics. [PERSON], [PERSON] et al. [24; 25] proposed a six-degrees-of-freedom dynamic model for deep-groove ball bearings that considers both distributed and localized defects. The study examined the effects of clearance on the natural frequencies and vibrations of the bearing system. The current research predominantly addresses conventional ball bearings, leaving a significant gap in the study of integrated bearings with distinct structural features. Addressing this gap, the study develops a dynamic model for integrated bearings through the dynamic analysis of integrated bearings. This study seeks to clarify the vibrational properties of integrated bearings and examine how structural parameters influence vibration behavior. The findings will provide a theoretical foundation for the selection of structural parameters in integrated bearings. Integrated bearings consist of a spindle, outer ring, cage, and balls. Their design and analysis methods differ significantly from deep-groove ball bearings due to the lack of an inner ring structure. Unlike conventional deep-groove ball bearings, integrated bearings directly machine the inner raceway onto the spindle, resulting in a smaller center diameter, higher rotational speeds, and reduced installation errors, thereby offering improved precision and dynamic performance. Since integrated bearings combine the inner ring with the spindle, analyses must consider the characteristics of both components. It is essential to account for the interaction between the balls and the spindle while also analyzing the external environment in contact with the spindle. To facilitate research, the interaction with the external environment can be transformed into constraints on the degrees of freedom of the spindle.