Stability analysis of conical whirl of aerostatic journal bearing rotor systems based on a nonlinear trajectory model

Whirl instability is the main problem encountered for aerostatic bearings, limiting their applications. Although extensive research has focused on the stability analysis of translational whirl, little attention has been paid to the conical whirl instability. In this study, a stability analysis of the conical whirl of an aerostatic bearing-rotor system is conducted based on a nonlinear trajectory approach. A nonlinear model is first developed, coupling the transient Reynolds equation with equations of conical motion, to simulate the trajectory of the rotor. Simulations indicate the existence of a stability boundary for the initial angular position. When the initial angular position is within the stability boundary, the system is stable. Conversely, if the initial angular position is outside the boundary, the system becomes unstable. If the initial angular position is on the boundary, the system exhibits marginal stability. Then, the algorithm to determine the stability boundary is proposed, and the effects of various parameters on the stability are analyzed. Finally, the instability mechanism of the conical whirl is discussed from the viewpoint of the variation of the area of stability boundaries. Two or more threshold values for the variables are found between the stable and unstable states of the rotor. Besides, the instability is observed as a half-frequency whirl, characterized by the rotor axis whirling in a conical mode at a frequency equal to or slightly less than half of the rotor's rotational frequency. This study can provide new insight into the conical whirl motions and guidance for designing aerostatic bearing-rotor systems.