Analysis of effect of clearance on static mechanical behavior for double row self-aligning ball bearing and control of clearance

Abstract: Double row self-aligning ball bearing generally consists of outer ring, inner ring, ball and sealing cover, etc. Because of its self-aligning working properties, this type of bearings have been widely used in various mechanical systems, such as agricultural machinery, engineering machinery, light industry machinery, military machinery, etc. Related rolling bearing design literatures have already analyzed the structure size and work performance of double row self-aligning ball bearings, but these literatures all ignore the effect of clearance when analyzing performance of this type of bearings. In practical conditions, bearing clearance has great influence on the bearing performance, so it must be considered. In this paper, the static mathematical model of double row self-aligning ball bearing under radial and axial combined loads has been established, based on Hertz elastic contact theory and deformation compatibility theory, also under the premise of considering of initial clearance and the change of real contact angle. In the meantime, related factors of bearing static equilibrium have been analyzed and calculated, such as load distribution, geometric deformation, principal curvatures of ball contact point, contact load, load distribution angle, etc. After analyzing the static balance equations and feasible region of unknown variables, the procedure of numerical solution based on Broyden rank 1 Quasi-Newton method has been presented. And the initial value of iteration is analyzed and optimized to reduce the iterative time. In order to verify the accuracy of the above nonlinear equilibrium equations and the solving method and to analyze the impact of clearance for double row self-aligning ball bearing static performance, as an example of double row self-aligning ball bearing BRF12, which is produced by Zhejiang Zhenhua Bearing Manufacturing Company, its non-linear static equilibrium equations are established and solved, and then analyze the influence of clearance on relative displacement of inner and outer rings, bearing axial stiffness, bearing radial stiffness, load distribution, maximum contact load, actual load distribution angle, real contact angle, etc. It can be derived from the above calculation and analysis that clearance is a key factor affecting double row self-aligning ball bearing working quality, so it should be strictly controlled. After analysis of the geometrical relationship of all kinds of clearances and contact angles, a simple calculation formula of all kinds of clearances and clearance dimension chain has been obtained, and dimension control and measuring method of clearance has been presented. The research provides a theoretical reference for designing and analyzing of the new type double row self-aligning ball bearings, such as the calculation of static load rating and dynamic load rating, the kinetic analysis, and the optimal design.