Dynamic analysis of double-row self-aligning ball bearings due to applied loads, internal clearance, surface waviness and number of balls

Abstract In this paper, a three degrees of freedom (dof) model was established for a double-row self-aligning ball bearing (SABB) system, and was applied to study the dynamic behavior of the system during starting process and constant speed rotating process. A mathematical model was developed concerning stiffness and damping characteristics of the bearing, as well as three-dimensional applied load, rotor centrifugal force, etc. Balls and races were all considered as nonlinear springs, and the contact force between ball and race was calculated based on classic Hertzian elastic contact deformation theory and deformation compatibility theory. The changes of each ball׳s contact force and loaded angle of each row were taken into account. In order to solve the nonlinear dynamical equilibrium equations of the system, these equations were rewritten as differential equations and the fourth order Runge–Kutta method was used to solve the equations iteratively. In order to verify accuracy of the dynamical model and correctness of the numerical solution method, a kind of SABB-BRF30 was chosen for case studies. The effects of several important governing parameters, such as radial and axial applied loads, normal internal, inner and outer races waviness, and number of balls were investigated. These parametric studies led to a complete characterization of the shaft-bearing system vibration transmission. The research provided a theoretical reference for new type bearing design, shaft-bearing system kinetic analysis, optimal design, etc.

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