Examining the Impact of Pad Flexibility on the Rotordynamic Coefficients of Rocker-Pivot-Pad Tilting-Pad Journal Bearings

Measured and predicted static and dynamic load characteristics are provided for a three-pad, rocker-pivot, tilting-pad journal bearing in the load-between-pad orientation. The bearing has the following characteristics: 3 pads, .50 pad pivot offset, 0.6 L/D ratio, 60.69 mm (2.4 in) pad axial length, and 0.0762 mm (0.003 in) radial clearance. Three interchangeable pad configurations were tested with pad thicknesses of 8.5 mm (0.33 in), 10 mm (0.39 in), and 11.5 mm (.45 in). Tests were performed on a test bearing floating about a rigid rotor design with unit loads ranging from 172 to 1,724 kPa (25 to 250 psi) and speeds from 6 to 12 krpm. Cold and hot clearances were taken to measure the nominal and operating, respectively, radial bearing clearance. The cold clearance was taken at room temperature while the hot clearance was taken for each operating speed immediately after the rig was shut down. The hot bearing clearance shows a 23 – 34% decrease in radial bearing clearance. As the operating speed increased, the operating temperature in the bearing increased. The increase in operating temperatures caused the bearing and pads to expand and reduced the radial bearing clearance. Static load tests were performed once the test rig reached steady-state conditions. The maximum measured eccentricity ratio was over one for each pad configuration. As pad flexibility increased, the static eccentricity ratio decreased. The eccentricity ratio predictions agreed well with the measured results in the loaded direction. The measured attitude angles were as high as approximately 10°. The attitude angles remained fairly constant at low rotational speeds for tp = 8.5 mm and tp = 10 mm and decreased as unit load increased for tp = 11.5 mm. XL_TPJB© predicted attitude angles that had a smaller magnitude than the measured results for all rotational speed and unit load conditions and were negative. The temperatures did not vary greatly across pad configurations. The predictions agreed well with the measured values at low speeds and low unit loads. As the operating speed and unit load increased, the predictions were lower than the measured values. Pad flexibility was characterized as the change in the pad’s bending stiffness or the change in pad thickness. A finite-element model (FEM) was created in SolidWorks® to predict the structural bending stiffness of each pad configuration. Once the pivot was fixed in the FEM, a uniform pressure distribution was applied to the rotor-side surface of the pad. Results from the finite-element analysis (FEA) show an increase in pad flexibility as the thickness of the pad decreased. Dynamic load tests were performed for all nominal test conditions over a range of excitation frequencies to obtain complex dynamic-stiffness coefficients as a function of excitation frequency. The real and imaginary parts of dynamic-stiffness were fitted with quadratic and linear models, respectively, with respect to excitation frequency. A constant coefficient [K][C][M] model produced frequency-independent rotordynamic coefficients. For the load-between-pad configuration, the dynamic-stiffness coefficients show significant bearing orthotropy, especially as the unit load increased. In general, the dynamic-stiffness was larger in the non-loading direction than it was in the loading direction. Negative virtual mass coefficients were commonly obtained for all pad configuration. To examine the effect of pad flexibility on the rotordynamic coefficients, the measured results were compared across each pad configuration. The measured results show that the increase in pad flexibility decreased the direct damping coefficients by 12-20% and, on average, decreased the cross-coupled damping coefficients by approximately 10%. On average, the measured results show a slight increase in the stiffness coefficients as pad flexibility increased. The direct stiffness coefficients varied from an increase of 12% at low unit loads and a decrease of 3% at high unit loads. The cross-coupled stiffness coefficients change by 0 to 12% as pad flexibility increased. In general, the direct virtual mass coefficients decreased by approximately 29% as pad flexibility increased. The average change for the cross-coupled coefficients is an increase in Mxy and Myx by 2% as pad flexibility increased. XL_TPJB© was used to predict the performance of the tilting-pad bearing tested in this work. XL_TPJB© accounts for pad and pivot flexibility. The predictions using XL_TPJB© agreed well with the measured values for direct stiffness coefficients. For a given pad set, the predictions agreed well with the measured results for one operating speed case and were either lower or higher than the measured results for the remaining speed cases for Cxx. The predicted values were generally higher than the measured values for Cyy at low unit loads and were lower than measured values at high unit loads. The measured values had a smaller magnitude than the predictions for the direct virtual-mass coefficients at lower speeds. At higher speeds, the predictions had a lower magnitude than the measured direct virtual-mass coefficients. All cross-coupled-coefficient predictions were nearly zero and, the measured values were typically non-zero and negative. A non-dimensional pad flexibility parameter αflex was used to relate the pad flexibility of multiple bearings of different sizes. The parameter related the average deflection across the pad surface to the pad’s arc length. XL_TPJB© was used to predict the percent change in direct damping coefficients for a rigid pad, flexible pivot and flexible pad, flexible pivot for a surface speed of 54 m/s and a unit load of 783 kPa. The results show the pads tested in this thesis are extremely flexible compared to pads used in industry. Results show that the pad’s structural bending stiffness or flexibility is important when predicting the bearing’s dynamic performance. Damping is consistently over-predicting when excluding pad flexibility, and this could have a significant impact in predicting the bearing’s stability characteristics. In general, all codes should account for pad flexibility, as well as pivot flexibility, to properly predict the performance of a tilting-pad journal bearing