Deformation behavior and load distribution in deep groove ball bearings with variable clearance under axial, radial, and moment loads

This study presents a comprehensive analytical and numerical investigation of load distribution in deep groove ball bearings with variable radial clearance under combined axial, radial, and moment loading conditions. Unlike previous models that assume constant clearance, the proposed approach incorporates an elliptical outer race geometry to simulate realistic clearance variation. An analytical model based on Hertzian contact theory and the Newton–Raphson iterative method is developed to estimate ball deformation, load sharing, and contact angle variation. The influence of ball angular position and outer race orientation on internal load behavior is systematically analyzed. A 3D finite element model is also constructed to validate the analytical findings. Results demonstrate that the proposed design reduces the peak load on the most heavily loaded ball by approximately 3.5% compared to conventional constant-clearance bearings. The finite element analysis confirms a peak stress of 1337 MPa and a maximum inner race deformation of 0.0426 mm. These findings highlight the potential of variable clearance designs in enhancing load distribution, and reducing stress concentrations in high-load and precision applications.