Rotordynamic Coefficients Measurements Versus Predictions for a High Speed Flexure-Pivot Tilting-Pad Bearing (Load-Between-Pad Configuration)
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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.
