The stiffness characteristics analysis of the duplex angular contact ball bearings based on a comprehensive multi-degree-of-freedom mathematical model

Abstract

Although the duplex angular contact ball bearings (DACBBs) are widely used in industry, the published mathematical model of DACBBs is sparse. To analyze the stiffness characteristics of DACBBs, this paper proposes a comprehensive multi-degree-of-freedom (multi-DOF) mathematical model for the DACBBs in three traditional configurations. The implicit differential method is adopted to derivate the analytical stiffness matrix formulation of DACBBs. The geometrical constraints and interactions inside the DACBBs are presented based on the vector-and-matrix method. The detailed iterative algorithm with two layers for solving the presented model is given based on the Newton-Raphson method. A systematic study for evaluating the impacts of angular misalignment on the stiffness characteristics of DACBBs has been carried out under three typical load conditions: the pure axial load condition, the pure radial load condition, and the combined-loaded condition. The results indicate that the angular misalignment remarkably affects the stiffness characteristics of DACBBs. Under the pure axial and radial load conditions, the stiffness curves of DACBBs can be divided into two segments according to the value of misalignment angle, and the angular misalignment will be the predominant factor when the angular misalignment is great. Under the combined-loaded condition, the mode (single or combined angular misalignment) and the direction of angular misalignment significantly influence the stiffness characteristics of DACBBs. Also, the angular misalignment effects depend on the radial load. The proposed model can also analyze the mechanical performance of double-row angular contact ball bearings.