Analysis of static stiffness fluctuation in radially loaded ball and roller bearings

The radial stiffness of rolling bearings is the basis for analyzing the dynamic performance of bearing-rotor systems. The changes of rolling element position may cause continuous change of radial stiffness and relative displacement of inner and outer ring during the operation of the bearing-rotor systems. As a result, the vibration of bearing-rotor systems would be aggravated. In order to accurately study the influence of the changes of rolling element position on radial stiffness, two boundary positions of the inner ring supported by even or odd number of rolling elements are considered in this paper. A mathematical method for rolling bearings modeling and stiffness calculation is proposed based on Hertz elastic contact theory. Then, the differences of radial stiffness under two boundary positions and that of rotor center displacements are studied. The results show that there exist obvious fluctuation of radial stiffness and oscillation of rotor center during the operation of bearing-rotor systems. Moreover, the effect of bearing structure parameters including internal clearance, number of rolling elements on the fluctuation of radial stiffness and oscillation of rotor center has been systematically investigated for ball and roller bearings. Consequently, this paper not only proposes an effective method for the radial stiffness, load distribution and the displacement of rotor center calculation of radially loaded rolling bearings, but also provides a direction for the design of bearing-rotor systems to eliminate vibration.