Calculation of ball bearing speed-varying stiffness

• The bearing speed-varying stiffness has been studied and explained.
• An analytic method is proposed to accurately calculate speed-varying stiffness.
• Comparisons with other theoretical and experimental results have been illustrated.

Dynamic properties of ball bearing (or any rolling bearing) are varying during operation, especially the stiffness which mostly depends on rotating speed and loads applied. Therefore, in this paper, the notion of rolling bearing speed-varying stiffnesses introduced and explained by studying the relations of load-deflection through the bearing dynamic model which is based on Jones & Harris's efforts. After the acquisition of load-deflection relations, two common numerical (linearization) methods are provided to calculate bearing stiffness, which turned out to be too unstable to get satisfied results. To improve the method of calculating speed-varying stiffness, an analytic model based on the differentiation of implicit function is proposed to calculate the speed-varying stiffness. The comparisons between the results from the numerical method and the proposed method have been made to validate the proposed method. In addition, the results calculated by the proposed method are compared with those which appeared in other literatures or experiments.