Critical Journal Mass and Critical Whirl Speed
Usually, the bearing damping coefficients are symmetric whereas stiffness coefficients lack the symmetry because k23 is not equal to k32. This asymmetry of the stiffness coefficients causes an unstable behavior of the rotor in the bearing. At a particular speed, the static equilibrium position of the journal is no longer dynamically stable, and rotor starts to whirl in a small orbit around the equilibrium position. The whirl frequency usually coincides with the lowest natural frequency of the system, and the ratio of the whirl frequency to rotational frequency is typically around 0.5.
Linearized coefficients cannot be used for predicting the behavior of the system beyond the threshold speed. But due to a rapid growth of the whirl speed, a threshold speed based on the linearized coefficients can be considered as the limiting speed for a safe operation. The threshold speed also depends on the rotor properties and its connection to the bearing. Thus, an analysis of the full system is needed to calculate the actual threshold speed of a system. However, to get some basic ideas and to compare the bearings with each other, a threshold speed based on a symmetric and rigid rotor is very useful. A critical journal mass based on this assumption is given by
where
and
where ω is the instability whirl speed. Subscripts 2 and 3 denote the local y direction and the local z direction, respectively. Since the dynamic coefficients are functions of the journal speed, a threshold speed for the instability is the speed at which the critical journal mass becomes equal to the actual journal mass. The critical whirl speed and the critical journal mass are available as <phys>.<feat>.omega_c and <phys>.<feat>.m_c, respectively.