Hydrodynamic Fluid Film Bearings and Their Effect on the Stability of Rotating Machinery

The lecture introduces the basic principles of hydrodynamic lubrication and the fundamental equation of Classical Lubrication Theory. The analysis proceeds to derive the static and dynamic performance characteristics of short length cylindrical journal bearings, with application to the dynamic forced performance of a rigid rotor supported on plain bearings. In a radial bearing, the Sommerfeld number defines a relationship between the static load and the journal eccentricity within the bearing. This design parameter shows the static performance of the bearing as rotor speed increases. Rotordynamic force coefficients are introduced and their effect on the stability of a rotor-bearing system thoroughly discussed. Cross-coupled force coefficients are solely due to journal rotation, and the magnitude and sign of the cross-stiffness determines rotordynamic stability. The whirl frequency ratio WFR relates the whirl frequency of subsynchronous motion to a threshold speed of instability. The desired WFR is null however, plain cylindrical bearings show a whirl ratio of just 0.50, limiting the operation of rotating machinery to shaft speeds below twice the system first critical speed. The analysis concludes with a review of practical in use journal bearing configurations with highlights on their major advantages and disadvantages, including remedies to reduce or entirely avoid subsynchronous whirl instability problems.