An Introduction to Bearing Instability

Hydrodynamic bearings operating at high speeds encounter instability problems of oil whirl and whip. Instability may ruin not only the bearings but the entire machine. It is well-known that hydrodynamics bearings play an important role in determining and controlling the vibrations of a rotating machinery, because of the springs and dampers, and bearings strongly influence the critical speed and imbalance response. Under certain conditions, the bearings can create rotor instability which results in significant self-excited vibrations.

The types of stability here are for a balanced journal and are mentioned below. If, as time increases, the trajectory of the journal center goes to a point of the clearance circle and remains there indefinitely, then the bearing is considered to exhibit “point stability,” Fig. 1(a). If, as time increases, the trajectory does not go to a point, as shown in Fig. 1(b) and (c), then the bearing, is considered to exhibit “point instability”. Two types of instability are shown in Figure 1. In Fig 1(b) the trajectory continues to increases without bound, ultimately reaching the limit of the clearance circle, therefore, this case is called “unbounded “. As time increases eases, if the trajectory closes on itself forming a limit cycle, as shown in Fig 1(c), then the trajectory can be said to be “orbitally stable”.

Satisfactory dynamic characteristics are essential to good bearing design. Hence it is very important for the designers to predict the journal center motion trajectories. AxSTREAM Bearing™ is used to calculate the hydrodynamic characteristics based on the mass-conserving mathematical model by applying the finite difference method with the successive over-relaxation (SOR) algorithm.

The numerical analysis of dynamic behavior of hydrodynamic bearings requires that the rotational speed and the additional forces be taken into account. Although the current numerical analysis is used for determining the stability, characteristics have mainly relied on linearized methods applied to the equilibrium position of a balanced or unbalanced rotor. A linearized approach can be used to predict the threshold stability. It can provide more insight into the dynamic behavior of rotor-bearing systems and determines if a system is stable or not.

In the following plots, the stability results are presented. In this case, the rotor transient operation quickly settles into a steady state elliptic orbit. The trajectory of the journal bearing was obtained over a range of operation, and the values were plotted against the steady state eccentricity. The points at which the trajectory was obtained, and the resulting stability curves are given in Fig. 2

Choice of Bearings

Bearing stiffness and damping, which are important in controlling or suppressing the critical speed vibrations of the rotor, are also greatly influenced by bearing scheme. Many factors should be considered when deciding on the bearing type to be used in a specific application. These include minimum oil film thickness, maximum operating temperatures, power loss, oil flow requirement, stability and response to dynamic forces. A summary of various profiles is provided below as a useful guide.

1. Cylindrical bore: The simplest bearing; use wherever possible; poor stability, but grooving can be used to give some improvements.
2. Lemon bore: Better stability than the cylindrical bore with little additional manufacturing complexity; vertical stiffness and damping are very good, but horizontal is rather poor; load capacity is good; suggested maximum preset 0.6; presets up to 0.7 quite common for increased stability but then suffers increasingly from poor horizontal characteristics and high oil flow requirement.
3. Offset halves: Extremely good stability characteristics and high stiffness and damping; careful choice of preset and manufacturing tolerances can give essentially equal direct coupled stiffnesses; high oil flow requirement, which can be an advantage at high speeds or when large heat soak into the bearing is expected; load capacity is good if loaded into or near to the crown, but avoid loading towards step; only suitable for one direction of rotation; suggested maximum preset is 0.6.
4. Three-lobe, symmetrical: Good for high speed applications with high stability and stiffness and damping; difficult to use satisfactorily where (for assembly reasons) bearings have to be in halves; suggested maximum preset is 0.8-0.85.
5. Three-lobe, tilted: Improved stability over the symmetrical 3-lobe; high oil pumping characteristic allows for high speeds, or operation with heat soak into the bearings; some reverse rotation possible depending on amount of tilt used, but certainly not a bi-directional bearing; suggested maximum preset is 0.8-0.85.

Reference:

1. Hydrodynamic Journal Bearings Optimization Considering Rotor Dynamics Restrictions, Proceedings of ASME Turbo Expo, June 11 -15, 2018 | Oslo, Norway.
2. Hydrodynamic Journal Bearing Optimization Based on Multidisciplinary Analysis of the Rotor-Bearing System for the Induction Motor, Proceedings of ELROMA, September 14-15, 2017, Mumbai, India.
3. Stability of profile bore bearings: influence of bearing type selection. Tribology International, Volume 13, Issue 5, October 1980, Pages 204-210.