Ball Bearing Dynamic Stiffness Prediction Considering an Uncertain Position of Rolling Elements

Abstract This paper considers the challenge of calculating accurate ball bearing stiffness, which is attributed to the uncertainty in the rolling element positions; and it solves that issue based on the simultaneous consideration of these positions and the physical effects of the rotating components. The novelty of the paper consists of the suggested methodology to resolve the uncertainty of the rolling element circumferential position when calculating bearing stiffness. The problem is solved through various formulations of dry and lubricated contact and validated based on the consideration of the finite-element (FE) model. The algorithms presented in the paper allow for the calculation of the resulting stiffness based on the stiffness values evaluated through different ball bearing positions. The approach presented in the paper is validated based on the experimental data. For this purpose, the model of the rotor in ball bearings is built, along with further calculation of the rotor dynamics. The comparison of the critical speeds calculated for the rotor in bearings, which have stiffness evaluated by the proposed approach with the measurements for the real machine, indicates a high accuracy of the suggested method in comparison with the methods that consider the single position of the rolling element when estimating their stiffness. In the paper, further recommendations for the use of the presented method are given, which will be useful for engineers in the field of turbomachinery dynamics.