Modeling Rotordynamic Effects of Angular Contact Ball Bearing in X- and O-arrangements with Full Bearing Matrix

Since ball bearings are one of the most commonly used bearing type in rotating machinery, predicting their dynamic performance is of utmost importance. The use of one-dimensional (1D) beam elements and bearing stiffness matrices with diagonal terms only is prevalent in the modeling and simulation of rotor-bearing systems. This study analyses the rotordynamic effects of angular contact ball bearings in X- and O-arrangements. A modeling method employing three-dimensional (3D) solid finite elements (FE) to model complex rotor geometries combined with a ball bearing stiffness formulation that accounts for the off-diagonal terms is presented. The case of an electric machine with an outer rotor permanent magnet design is studied with the O- and X-arrangements of the ball bearings. These arrangements are compared with the bearing stiffness matrix considering only the diagonal terms using both 3D solid FE and 1D beam element to model the rotor. The results show large variations between the natural frequencies and mode shapes of the compared models. It is observed that accounting for the off-diagonal terms in the bearing stiffness matrix in different arrangements, and using the 3D solid FE rotor model, can have a significant impact on the results. Therefore, the proposed method can improve the accuracy in the prediction of critical speeds for safe operation of the rotor-bearing system.