Theoretical method to reduce the non-repetitive run-out (NRRO) of angular contact ball bearings

As ultra-precision index of bearings, the value of non-repetitive run-out (NRRO) directly influences the rotation precision of rotating mechanism of complex mechanical system. However, the value of NRRO is very difficult to predict and control due to various causes. This paper develops a mathematical model to study the constrictive relationship between the geometrical errors and the NRRO of an angular contact ball bearing based on Hertzian contact theory and solution method of dimensional chain, so as to reduce the NRRO by optimizing the manufacturing process of bearing components. Firstly, based on the motion relationship of parts in bearings and the dimensional chain theory, a kinematic model is built with taking into account the regularities of variation of contact angle under different axial load. In the model, the geometrical errors of rings raceway and balls are described through superposition of sinusoidal function. Secondly, the nonlinear equations of force balance of balls are built based on Hertzian contact theory. Finally, by solving nonlinear equations, the trajectory of rotation center is calculated to quantitatively analyze the NRRO of bearings caused by the geometrical errors of rings raceway and balls. Findings of this paper provide theoretical supports to reduce the NRRO by optimizing manufacturing process of bearing components.