Static Performance Characteristics and Rotordynamic Coefficients for a Four-Pad Ball-in-Socket Tilting Pad Journal Bearing

Static performance characteristics and rotordynamic coefficients were experimentally determined for a four-pad, ball-in-socket, tilting-pad journal bearing in load-between-pad configuration. Measured static characteristics include journal static equilibrium position, estimated power loss, and trailing-edge pad temperatures. Rotordynamic coefficients were determined from curve-fits of measured complex dynamic-stiffness coefficients as a function of the excitation frequency. Aside from the cross-coupled damping coefficients, a frequency-independent [M]-[C]-[K] model did a good job of fitting the measurements. The added-mass coefficient was frequently dropped, leaving only a frequency-independent stiffness and damping coefficient. Test conditions included speeds from 4000 rpm to 12,000 rpm and unit loads from 0 kPa to 1896 kPa (0–275 psi). The bearing uses cool inlet oil to decrease the pad operating temperatures and increase the bearing’s load and speed capacity. The bearing has a nominal radial clearance of $95.3μm$ (3.75 mils). However, measurements indicated significant bearing crush with a radial bearing clearance of $99.6μm$ (3.92 mils) in the axis 45 deg counterclockwise from the loaded axis and $54.6μm$ (2.15 mils) in the axis 45 deg clockwise from the loaded axis (assuming counterclockwise rotation). The pad length is 101.60 mm (4.00 in.), giving $L/D=1.00$⁠. The pad arc angle is 73 deg, and the pivot offset ratio is 65%. Testing was performed using a test rig described by Kaul (1999, “Design and Development of a Test Setup for the Experimental Determination of the Rotordynamic and Leakage Characteristics of Annular Bushing Oil Seals,” MS thesis, Texas A&M University, College Station, TX), and rotordynamic coefficients were extracted using a procedure adapted from the work of Childs and Hale (1994, “A Test Apparatus and Facility to Identify the Rotordynamic Coefficients of High-Speed Hydrostatic Bearings,” ASME J. Tribol., 116, pp. 337–344). A bulk-flow Navier–Stokes model was used for predictions, using adiabatic conditions for the fluid in the bearing. However, the model assumes constant nominal clearances at all pads, and an average clearance was used based on measured clearances. Measured static eccentricities and attitude angles were significantly higher than predicted. Attitude angles varied from 6 deg to 39 deg and decreased with load. Power loss was underpredicted at low speeds and very well predicted at high speeds, with a maximum value of 25 kW (34 hp). The maximum detected pad temperature was $71°C$$(160°F)$ while the temperature increase from inlet to maximum pad temperature location was overpredicted by 10–40%. Direct stiffness and damping coefficients were significantly overpredicted, but the addition of a stiffness-in-series correction vastly improved the agreement between theory and experiment. Direct added masses were zero or negative at low speeds and increased with speed up to a maximum of about 50 kg; they were normally greater in the $x$ (unloaded) direction. Although significant cross-coupled stiffness terms were present, they always had the same sign, and the bearing had a whirl frequency ratio of zero netting unconditional stability over all test conditions.