The stability during riveting is crucial; if pillar rivets bend and deform under the action of riveting pressure due to instability, it can lead to inelastic ball retention in retainers and poor rotation of bearings. Since rivets have greater flexibility in bending along the thickness direction, it is only necessary to verify the stability of the rivets in the thickness direction. For annular groove rivets, the flexibility in bending along the thinner thickness direction is represented by the formula: λ is the flexibility, μ is the height coefficient, i is the radius of gyration, and J is the moment of inertia of the rivet in the thickness direction.

During the secondary riveting process, the rivet can be considered as fixed at its lower end, with the upper end only able to translate horizontally without rotation. Due to the shorter length of the rivet, its flexibility is generally less than the flexibility of the corresponding material's yield limit, making the rivet a low flexibility rod. Therefore, the critical stress for rivet instability is the formula used for conducting a stability check on the rivet as a column. The formula includes: the actual stability safety factor during riveting, the specified stability safety factor, typically ranging from 1.8 to 3.0, and the working stress of the rivet. If the calculated results for the annular slot rivet do not meet the above conditions, it indicates that the rivet lacks stability during riveting and should be improved by increasing the rivet thickness S.

The Shao Dou Kong Lang-shaped Retainer exhibits poor overall rigidity, prone to issues such as rivet deformation and misalignment of the two halves during riveting. Therefore, when designing ring groove rivets, it is crucial to select the appropriate rivet and retainer parameters, and perform relevant calculations to avoid problems like bearing ball jamming and lack of rotation flexibility.