Analytical determination of the nonlinear stiffness characteristics of the combined angular contact ball bearings under various configurations

Abstract As a typical nonlinear mechanical system, the combined angular contact ball bearing (C-ACBB) is widely used in various fields, but the theoretical studies on its nonlinear stiffness characteristics are rarely involved. This paper proposed a general mathematical model for the C-ACBB under different configuration forms based on the load-deformation coordination analysis under the multi-coordinate systems, and then a multi-layer nested algorithm based on the homotopy method and Newton-Raphson method for the efficient solution of the nonlinear equilibrium equations of the proposed model is presented. Besides, the complete expressions of the stiffness matrices for the C-ACBB under different configurations are analytically derived, and the relationships between the integral C-ACBB and multiple SR-ACBBs is presented. On the basis, and effects of both the rotating speed and axial preload on the C-ACBB under 5 different configurations and 3 different load conditions are analyzed. The results show that, the C-ACBB under different configurations present various and complex piecewise nonlinear stiffness characteristics, which is affect by both the rotating speed and initial preload. Besides, the axial stiffness variation of the C-ACBB under asymmetric configuration shows obvious directionality, the radial stiffness variation of the C-ACBB is symmetrical and related to the load action point.