Stability analysis of a rotor–bearing system with time-varying bearing stiffness due to finite number of balls and unbalanced force

Previous investigations have indicated that the finite number of balls can cause the bearing stiffness to vary periodically. However, effects of unbalanced force in a rotor–bearing system on the bearing stiffness have not received sufficient attention. The present work reveals that the unbalanced force can also make the bearing stiffness vary periodically. The parametric excitations from the time-varying bearing stiffness can cause instability and severe vibration under certain operating conditions. Therefore, the determination of the operating conditions of parametric instability is crucial to the design of high speed rotating machinery. In this paper, an extended Jones–Harris stiffness model is presented to ascertain the stiffness of the angular contact ball bearing considering five degrees of freedom. Stability analysis of a rigid rotor–bearing system is performed utilizing the discrete state transition matrix (DSTM) method. The effects of unbalanced force, bearing loads and damping on the instability regions are discussed thoroughly. Investigations mainly show that the time-varying bearing stiffness fluctuates sinusoidally due to finite number of balls and unbalanced force. The locations and widths of the instability regions caused by these two parametric excitations differ distinctly. Unbalanced force could change the widths of the instability regions, but without altering their central positions. The axial and radial loads of the bearing only change the positions of the instability regions, without affecting their widths. Besides, damping can reduce the widths of the instability regions.