# Study on Ring Deformation and Contact Characteristics of Thin-Walled Bearing for RV Reducer
## 1 Introduction  
The RV reducer finds extensive applications within industrial robotics [1]. A pair of thin-walled angular contact ball bearings are installed on the pin gear housing and planetary frame to bear the full external load of the reducer. The main bearing and pin gear housing are usually thin-walled structures, which are prone to elastic deformation, resulting in changes in bearing contact characteristics. Consequently, it is critical to develop a bearing model incorporating structural elastic deformation considerations and analyze the effect of various factors on the ring deformation and flexible contact characteristics. The traditional bearing analysis theory is based on the rigid ring hypothesis, which holds that elastic deformation primarily takes place within the ball-raceway contact area, while the overall shape of the ring does not change [2]. This hypothesis provides an excellent approximate method for bearing analysis with large ring thicknesses. For instance, [PERSON] et al. [3] proposed a critical criterion for the ball-raceway separation. They indicated that the ball separates from the inner raceway and only contacts the outer raceway due to the inertial effect, which causes the difference in the contact state between the ball and the inner raceway in the static and quasi-static models under the same load condition. [PERSON] et al. [4] studied the influences of load conditions and structural parameters on the moment rigidity and rotation accuracy of the main bearings for the RV reducer. [PERSON] et al. [5] analyzed the force state of the main bearings for the RV reducer under extremeload conditions. Regarding carrying capacity, allowable contact stress [6], fatigue life [7; 8], deflection, and elliptical truncation [9] are usually used to characterize the carrying capacity. [PERSON] et al. [10] propose a method for computing the axial carrying capacity in cases where the contact ellipse fails to surpass the raceway rib, but their method only applies to purely axial force conditions. [PERSON] et al. [11] improved this method and applied it to arbitrary working conditions, then studied the influences of geometric parameters and radial force on the carrying performance of the bearing. [PERSON] et al. [12] explored the influence of the elliptical truncation rate on the bearing contact characteristics. The findings indicate that elliptical truncation leads to a relocation of the ball-raceway maximum contact stress position from the contact center to the raceway edge, and a 10% elliptical truncation would lead to a 50% reduction in fatigue life. [PERSON] et al. [13] used the maximum contact stress to characterize the carrying capacity. They compared the sensitivity of different structural parameters influencing the carrying capacity. [PERSON] et al. [14] investigated how the mesh size of the finite element model impacted the carrying capacity. Their findings indicate that for simulation results closest to theoretical predictions, the mesh size should not exceed half of the short semi-axis length of the Hertzian contact ellipse. However, previous researchers only studied the carrying capacity of bearings under rigid conditions, with little attention paid to the effect of ring deformation on carrying capacity. Contemporary advanced bearing technology toward the direction of thin walls and component integration, and some studies indicate that ring deformation can change the bearing contact characteristics [15; 16]. [PERSON] et al. [17] were the first to consider the influence of ring deformation. They used the outer ring two-point support condition to study planetary gear bearings. They found that the ring deformation worsens the ball-raceway contact state, significantly reducing bearing fatigue life. [PERSON] et al. [18] described the ring deformation based on the Roark formula and introduced it into the bearing balance equation. They found that structural deformation causes the expansion of the loaded zone and a decrease in maximum contact stress. [PERSON] et al.