Stiffness analysis of bearings in multi-bearing system of tilting table at different attitude

At present, the studies of bearings stiffness in multi-bearing system focus on symmetric structures, such as spindle. However, the previous methods are not suitable for the supporting bearings of the CNC (computer numerical control) tilting rotary table which has complex rotary part and suffers gravity force and cutting forces. In this paper, a method was proposed to analyze the bearings static stiffness in the multi-bearing system of the tilting table. The finite element model of the rotary part was condensed with the substructure method and the shafts were represented by beam elements. The beam elements and condensed finite element model were connected by rigid coupling constrain equations. Then the static equivalent equations of the system were achieved with the stiffness model of angular contact ball bearings. And the equations were solved with the iteration algorithm to get the actual loads and stiffness of the bearings. Take a system supported by four bearings for example, the load and stiffness of the bearings were got by the commercial software and the theoretical method respectively. The difference is less than 1% and the method proposed is verified. Finally, it is found that the stiffness of the four bearings of the tilting table vary greatly with the tilting angle when gravity force is considered.