A general model for preload calculation and stiffness analysis for combined angular contact ball bearings

The combined angular contact ball bearings are widely used in automatic, aerospace and machine tools, but few researches on the combined angular contact ball bearings have been reported. It is shown that the preload and stiffness of combined bearings are mutual influenced rather than simply the superposition of multiple single bearing, therefore the characteristic calculation of combined bearings achieved by coupling the load and deformation analysis of a single bearing. In this paper, based on the Jones quasi-static model and stiffness analytical model, a new iterative algorithm and model are proposed for the calculation of combined bearings preload and stiffness, and the dynamic effects include centrifugal force and gyroscopic moment have to be considered. It is demonstrated that the new method has general applicability, the preload factors of combined bearings are calculated according to the different design preloads, and the static and dynamic stiffness for various arrangements of combined bearings are comparatively studied and analyzed, and the influences of the design preload magnitude, axial load and rotating speed are discussed in detail. Besides, the change rule of dynamic contact angles of combined bearings with respect to the rotating speed is also discussed. The results show that bearing arrangement modes, rotating speed and design preload magnitude have a significant influence on the preload and stiffness of combined bearings. The proposed formulation provides a useful tool in dynamic analysis of the complex bearing-rotor system.