## 1 Introduction  
The rolling bearing is one of the critical components in rotating machinates, in which the cage acts as a core tool to space apart and guide rollers, and to keep rollers under both uniform and alternating load conditions. Dimensional deviations in the cage pockets may alter the amplitude of cage motion, affecting the stress and load distribution across various bearing components, leading to increased wear, noise generation, and even premature bearing failure. Traditional bearing cage models often idealize the pocket dimensions, failing to account for the impact of pocket dimensional deviations on the bearing's dynamic characteristics. In the research field of bearing dynamics, [PERSON] [1] established a dynamic model of full degrees of freedom in bearing parts and obtained the dynamic performance of bearings, changing over time, by integral solution of the dynamic equation. However, there were problems such as the strict selection of initial values and long solving time. Based on Hertzian contact theory, [PERSON] [2] proposed a calculation formula and an experimental study of the stiffness damping matrix of ball bearings using a dynamic model. [PERSON] [3] established a four-degree-of-freedom dynamic equation of rolling bearings, considering the clearance, and conducted a dynamic analysis of bearing stiffness changes under different working conditions. [PERSON] and [PERSON] [4] employed the ADAMS software to construct a dynamic model of the cylindrical roller bearing cage and carried out dynamic simulations to analyze the motion of the cage's center of mass and the stress conditions. [PERSON] et al. [5] utilized the ADAMS system to develop a rigid-flexible multi-body dynamic analysis program for angular contact ball bearings and analyzed the dynamic performance of the high-speed angular contact ball bearing cage. Additionally, they [6] established the differential equations of the dynamics of high-speed cylindrical roller bearings. The differential equations were solved by combining the fine integration method and the predictive correction Adams-Bashforth-Moulton multistep method. Theoretical analyses were conducted on the dynamic characteristics of the cage. In terms of research on bearing cage pockets, [PERSON] [7] proposed a comprehensive dynamic model for analyzing the stability, skidding degree, ball-cage collision, wear distribution, and wear rate of four types of cage pocket. [PERSON] [8] studied the cage's motion with different pocket shapes, such as spherical, square, and cylindrical, with an angular contact ball bearing under different operating conditions. [PERSON] [9] established the dynamic models of spherical and cylindrical pocket cages, and studied the effect of cage pocket shape on the dynamics of angular contact ball bearings with different pocket clearances. [PERSON] [10] conducted experiments on cage motion and wear to investigate the influence of clearance on ball bearings. [PERSON] [11] experimentally investigated the stability of six cages with different pocket shapes and obtained the influence patterns of pocket shapes on cage stability. [PERSON] [12] analyzed the influencing factors for different amounts of friction consumption at various structural sizes of the cage, and revealed the effects of these structural sizes on friction consumption. [PERSON] [13] simulated the vibration response of the bearing-rotor system. In the research field of bearing cage motion, [PERSON] [14] experimented on cage motion and wear to investigate the influence of clearance on ball bearings. [PERSON] [15] et al. explored the dynamic characteristics of the cage during the acceleration and deceleration of angular contact ball bearings under different radial loads through experiments, found that acceleration and deceleration significantly affected the dynamic characteristics of the cage, and proposed a model to measure the relationships between the cage sliding ratio, acceleration, and radial load.