After the synchronous solution becomes unstable, the system experiences self-excited vibration, which can be described by the same set of equations, but with unbalance forces neglected. The solution can be found in the form of harmonic oscillations with unknown frequency of self-excited vibration, . When whirl occurs, the bearing stiffness has primary influence on the instability response. This leads to a whip instability. In practice, we never really have an infinitely stiff bearing.
Whip occurs when the shaft stiffness provides the primary influence over the instability response.
This indicates a predominantly rigid-body mode of response, typical for whirl. In other words, the bearing stiffness tends to dominate the instability response. This is precisely why the SFCB eliminates whirl problems because bearing stiffness K B can be increased independent of damping to raise the threshold of instability above operating rotative speeds, precluding whirl from ever occurring. The bearing is designed initially with proper stiffness to locate the instability threshold above operating speeds. If conditions change for some reason, the bearing stiffness can be raised in the field by raising the fluid supply pressure, further increasing the threshold of stability.