Stability and the oil whirl frequency of a rigid rotor in journal bearings

This paper investigates the relationship between the stability and the oil whirling frequency of a rigid rotor supported on two symmetric journal bearings. The relation between the critical stable speed and the critical whirling frequency is derived according to the linear theory and compared with average whirl frequency from the simulated whirl trajectories considering both linear and nonlinear bearing forces. The nonlinear bearing forces are directly obtained from the bearing pressure distribution which is solved from the Reynolds equation at each journal position. The transient whirl frequency is expressed by an explicit mathematical formula. It is found that the critical stable speed is closely related with the critical whirling frequency. Typical whirling trajectories under position perturbation, synchronous unbalance excitation and harmonic excitation are simulated and presented to explain the stable, critical and unstable phenomena. The whirl displacement signals are also transformed to the frequency domain, and their whirling frequencies are analysed according to their frequency characteristics.