Experimental dynamic force coefficients are presented for a flexure-pivot-tilting-pad (FPTP), bearing in load-between-pad (LBP) configuration for a range of rotor speeds and bearing unit loadings. The bearing has the following design parameters: 4 pads with pad arc angle 72° and 50% pivot offset, pad axial length 0.0762 m (3 in), pad radial clearance 0.254 mm (0.010 in), bearing radial clearance 0.1905 mm (0.0075 in), preload 0.25 and shaft nominal diameter of 116.84 mm (4.600 in). Measured dynamic coefficients have been compared with theoretical predictions using an isothermal analysis for a bulk-flow Navier-Stokes model. Predictions from two models — the Reynolds equation and a bulk-flow Navier-Stokes (NS) equation model are compared with experimental, complex dynamic stiffness coefficients (direct and cross-coupled) and show the following results: (i) The real part of the direct dynamic-stiffness coefficients is strongly frequency dependent because of pad inertia, support flexibility, and the effect of fluid inertia. This frequency dependency can be accurately modeled for by adding a direct added mass term to the conventional stiffness/damping matrix model. (ii) Both models underpredict the identified added-mass coefficient (∼32 kg), but the bulk-flow NS equations predictions are modestly closer. (iii) The imaginary part of the direct dynamic-stiffness coefficient (leading to direct damping) is a largely linear function of excitation frequency, leading to a constant (frequency independent) direct damping model. (iv) The real part of the cross-coupled dynamic-stiffness coefficients shows larger destabilizing forces than predicted by either model. The direct stiffness and damping coefficients increase with load, while increasing and decreasing with rotor speed, respectively. As expected, a small whirl frequency ratio (WFR) was found of about 0.15, and it decreases with increasing load and increases with increasing speed. The two model predictions for WFR are comparable and both underpredict the measured WFR values. Rotors supported by either conventional tilting PAD bearings or FPTP bearings are customarily modeled by frequency-dependent stiffness and damping matrices, necessitating an iterative calculation for rotordynamic stability. The present results show that adding a constant mass matrix to the FPTP bearing model produces an accurate frequency-independent model that eliminates the need for iterative rotordynamic stability calculations.

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Experimental dynamic force coefficients are presented for a four pad flexure-pivot tilting-pad bearing in load-between-pad configuration for a range of rotor speeds and bearing unit loadings. Measured dynamic coefficients have been compared to theoretical predictions using an isothermal analysis for a bulk-flow Navier-Stokes (NS) model. Predictions from two models—the Reynolds equation and a bulk-flow NS equation models are compared to experimental, complex dynamic stiffness coefficients (direct and cross-coupled) and show the following results: (i) The real part of the direct dynamic-stiffness coefficients is strongly frequency dependent because of pad inertia, support flexibility, and the effect of fluid inertia. This frequency dependency can be accurately modeled for by adding a direct added-mass term to the conventional stiffness/damping matrix model. (ii) Both models underpredict the identified added-mass coefficient (∼32kg), but the bulk-flow NS equation predictions are modestly closer. (iii) The imaginary part of the direct dynamic-stiffness coefficient (leading to direct damping) is a largely linear function of excitation frequency, leading to a constant (frequency-independent) direct damping model. (iv) The real part of the cross-coupled dynamic-stiffness coefficients shows larger destabilizing forces than predicted by either model. The frequency dependency that is accounted for by the added mass coefficient is predicted by the models and arises (in the models) primarily because of the reduction in degrees of freedom from the initial 12 degrees (four pads times three degrees of freedom) to the two-rotor degrees of freedom. For the bearing and condition tested, pad and fluid inertia are secondary considerations out to running speed. The direct stiffness and damping coefficients increase with load, while increasing and decreasing with rotor speed, respectively. As expected, a small whirl frequency ratio (WFR) was found of about 0.15, and it decreases with increasing load and increases with increasing speed. The two model predictions for WFR are comparable and both underpredict the measured WFR values. Rotors supported by either conventional tilting-pad bearings or flexure-pivot tilting-pad (FPTP) bearings are customarily modeled by frequency-dependent stiffness and damping matrices, necessitating an iterative calculation for rotordynamic stability. For the bearing tested and the load conditions examined, the present results show that adding a constant mass matrix to the FPTP bearing model produces an accurate frequency-independent model that eliminates the need for iterative rotordynamic stability calculations. Different results may be obtained for conventional tilting-pad bearings (or this bearing at higher load conditions).

A gas windback seals is similar to a labyrinth seal except the cavity is one continuous channel which winds around the shaft like a screw thread. One application is in gas compressors to isolate lubrication oil from the gas flow paths. A CFD based study of clearance, pressure ratio, and shaft speed has been performed. One seal geometry was experimentally studied to provide verification of the CFD accuracy. An empirical model for the leakage rate has been developed which fits the data with a standard deviation of 0.8%. The effects of pressure ratio and shaft speed upon the leakage rate are independent of each other. Analysis of the CFD results indicate that the kinetic energy carry over coefficient is substantially less for the windback seal operating at low differential pressures and gas densities than for a labyrinth seal operating under typical conditions.

Test results are presented for laminar-flow seals that are representative of buffered-flow oil seals in centrifugal compressors. The seals are short (L∕D≅0.21), with a diameter of 117mm and a clearance-to-radius ratio 0.0007. A smooth seal, a seal with one central groove, and a seal with three grooves were tested. Groove geometries employed are representative of industrial practice for compressors with a groove-depth to clearance ratio on the order of 6. Tests were conducted at 4000, 7000, and 10,000rpm shaft speed with delta pressures across the seals of 21, 45, and 69bars. For all cases, the flow was laminar. The seals were tested from a centered position out to an eccentricity ratio of 0.7. Static data included leakage and equilibrium loci for a range of loads. Direct and cross-coupled stiffness and damping coefficients and direct mass coefficients were determined from dynamic tests. For the smooth seal, comparisons between measurements and predictions were reasonable for the direct and cross-coupled stiffness and damping coefficients; however, measured added mass coefficients were roughly ten times larger than predicted. Predictions for the grooved seals from a “deep-groove” model that assumed zero pressure oscillations in the grooves greatly over predicted the influence of the grooves. In a centered position, smooth and grooved seals had comparable leakage performance. At higher eccentricity ratios, the grooved seals leaked modestly more. For eccentricity ratios less than approximately 0.3, the grooved seals and the smooth seal had qualitatively similar static and dynamic characteristics. In terms of cross-coupled stiffness coefficients, the grooved seals were less stable than the smooth seal at eccentricity ratios greater than approximately 0.5 but had significantly lower cross-coupled coefficients at reduced eccentricity ratios between zero and 0.3. A grooved centered seal is more stable than a smooth centered seal. The smooth seal had higher damping than the grooved seals and had moderately better centering capabilities.