A comprehensive study on the off-diagonal coupling elements in the stiffness matrix of the angular contact ball bearing and their influence on the dynamic characteristics of the rotor system

This paper not only presents the details of the composition form and classification method of the elements in bearing stiffness matrix, but also reveals the effects of the off-diagonal stiffness items in bearing stiffness matrix on the rotor dynamic characteristics. First, the complete expression of bearing stiffness matrix is derived based on the improved model of ball bearing, and the change rules of the different categories of the stiffness elements with the rotating speeds and loads are given. Then, both the quantitative and qualitative analysis methods for the rotor-bearing systems supported by a pair of the angular contact ball bearings are presented, and the effects of the off-diagonal bearing stiffness elements on the rotor supporting stiffness and natural frequencies are given and discussed. The results show that, when the rotor system is subjected to a radial load or moment load, the additional loads from ball bearings are generated due to the off-diagonal stiffness elements in bearing stiffness matrix, and the rotor with the O-configuration has higher supporting stiffness and resonance frequencies than the rotor with the X-configuration.