Angled Injection—Hydrostatic Bearings Analysis and Comparison to Test Results

1997 ◽  
Vol 119 (1) ◽  
pp. 179-187 ◽  
Author(s):  
Luis San Andres ◽  
Dara Childs

Hydrostatic/hydrodynamic (hybrid) journal bearings handling process liquids have limited dynamic stability characteristics and their application as support elements to high speed flexible rotating systems is severely restricted. Measurements on water hybrid bearings with angled orifice injection have demonstrated improved rotordynamic performance with virtual elimination of cross-coupled stiffness coefficients and null or negative whirl frequency ratios. A bulk-flow model for prediction of the static performance and force coefficients of hybrid bearings with angled orifice injection is advanced. The analysis reveals that the fluid momentum exchange at the orifice discharge produces a pressure rise in the hydrostatic recess which retards the shear flow induced by journal rotation, and thus, reduces cross-coupling forces. The predictions from the model are compared with experimental measurements for a 45 deg angled orifice injection, 5 recess, water hydrostatic bearing operating at 10.2, 17.4, and 24.6 krpm and with supply pressures of 4, 5.5 and 7 MPa. The correlations include recess pressures, flow rates, and rotordynamic force coefficients at the journal centered position. An application example for a liquid oxygen hybrid bearing also demonstrates the advantages of tangential orifice injection on the rotordynamic coefficients and stability indicator for forward whirl motions, and without performance degradation on direct stiffness and damping coefficients.

Author(s):  
Luis San Andrés ◽  
Joshua Norsworthy

High speed rotors supported on bump-type foil bearings (BFBs) often suffer from large subsynchronous whirl motions. Mechanically preloading BFBs through shimming is a common, low cost practice that shows improvements in rotordynamic stability. However, there is an absence of empirical information related to the force coefficients (structural and rotordynamic) of shimmed BFBs. This paper details a concerted study toward assessing the effect of shimming on a first generation BFB (L = 38.1 mm and D = 36.5 mm). Three metal shims, 120 deg apart, are glued to the inner surface of the bearing cartridge and facing the underside of the bump foil strip. The shim sets are of identical thickness, either 30 μm or 50 μm. In static load tests, a bearing with shims shows a (nonlinear) structural stiffness larger than for the bearing without shims. Torque measurements during shaft acceleration also demonstrate a shimmed BFB has a larger friction coefficient. For a static load of 14.3 kPa, dynamic loads with a frequency sweep from 250 Hz to 450 Hz are exerted on the BFB, without and with shims, to estimate its rotordynamic force coefficients while operating at ∼50 krpm (833 Hz). Similar measurements are conducted without shaft rotation. Results are presented for the original BFB (without shims) and the two shimmed BFB configurations. The direct stiffnesses of the BFB, shimmed or not, increase with excitation frequency, thus evidencing a mild hardening effect. The BFB stiffness and damping coefficients decrease slightly for operation with rotor speed as opposed to the coefficients when the shaft is stationary. For frequencies above 300 Hz, the direct damping coefficients of the BFB with 50 μm thick shims are ∼30% larger than the coefficients of the original bearing. The bearing structural loss factor, a measure of its ability to dissipate mechanical energy, is derived from the direct stiffness and damping coefficients. The BFB with 50 μm thick shims has a 25% larger loss factor—average from test data collected at 300 Hz to 400 Hz—than the original BFB. Further measurements of rotor motions while the shaft accelerates to ∼50 krpm demonstrate the shimmed BFB (thickest shim set) effectively removes subsynchronous whirl motions amplitudes that were conspicuous when operating with the original bearing.


1996 ◽  
Vol 118 (1) ◽  
pp. 190-200 ◽  
Author(s):  
Luis San Andres

The thermal analysis of flexure-pivot tilting-pad hybrid (combination hydrostatic-hydrodynamic) bearings for cryogenic turbopumps is presented. The advantages of this type of bearing for high speed operation are discussed. Turbulent bulk-flow, variable properties, momentum and energy transport equations of motion govern the flow in the bearing pads. Zeroth-order equations for the flow field at a journal equilibrium position render the bearing flow rate, load capacity, drag torque, and temperature rise. First-order equations for perturbed flow fields due to small amplitude journal motions provide rotordynamic force coefficients. A method to determine the tilting-pad moment coefficients from the force displacement coefficients is outlined. Numerical predictions correlate well with experimental measurements for tilting-pad hydrodynamic bearings. The design of a liquid oxygen, flexure-pad hybrid bearing shows a reduced whirl frequency ratio and without loss in load capacity or reduction in direct stiffness and damping coefficients.


Author(s):  
Joel Harris ◽  
Dara Childs

Static performance characteristics and rotordynamic coefficients were experimentally determined for a four-pad, spherical-seat, 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 functions of the excitation frequency. A frequency-independent [M]-[C]-[K] model did a good job of fitting the measurements. Test conditions included speeds from 4 to 12 krpm and unit loads from 0 to 1896 kPa (0 to 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 diameter of 101.78 mm (4.0070 in). Measurements indicated significant bearing crush with a radial bearing clearance of 99.63 μm (3.92 mils) in the axis 45° counterclockwise from the loaded axis and 54.60 μm (2.15 mils) in the axis 45° clockwise from the loaded axis. The pad length is 101.60 mm (4.00 in), giving L/D = 1.00. The pad arc angle is 73°, and the pivot offset ratio is 65%. Testing was performed using a test rig described by Kaul [1], and rotordynamic coefficients were extracted using a procedure adapted from Childs and Hale [2]. A bulk-flow Navier-Stokes model was used for predictions, using adiabatic conditions for the fluid in the bearings. 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 lower than predicted. Attitude angles varied from 6° to 39° and decreased with load. Power loss was well-predicted, with a maximum value of 25 kW (34 hp). The maximum detected pad temperature was 71°C (160°C) while the temperature rise from inlet to exit was over-predicted by 8°C (14°F). Direct stiffness and damping coefficients were significantly over-predicted, but the addition of a simple pivot-stiffness in series with the measured stiffness and damping values vastly improved the agreement between theory and experiment. Direct added masses were negative to a higher degree for Myy (y load direction) at low speeds and increased with speed. With the exception of Myy at zero load, they became positive before reaching 8,000 rpm. Although significant cross-coupled stiffness terms were present, they always had the same sign, producing a whirl frequency ratio of zero and netting unconditional stability over all test conditions.


Author(s):  
Dara Childs ◽  
Joel Harris

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 95.3 μm (3.75 mils). However, measurements indicated significant bearing crush with a radial bearing clearance of 99.6 μm (3.92 mils) in the axis 45 deg counterclockwise from the loaded axis and 54.6 μm (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.


Author(s):  
Yong Qin ◽  
Yanping Song ◽  
Fu Chen ◽  
Ruoyu Wang ◽  
Huaping Liu

The underlying physics of the endwall synthetic jet in improving the aerodynamic performance of a high-speed compressor stator cascade is investigated in this paper. The effects of both injected momentum and actuation frequency are discussed in detail. In the investigations, the injected momentum is controlled by either changing the maximum jet velocity or modifying the tube diameter. Numerical results demonstrate that the streamwise momentum addition and flow mixing enhancement are the key factors of the endwall synthetic jet in improving the cascade performance. The high momentum fluid injected into the flow field can reenergize the passage flow, and the generated streamwise jet vortex contributes to the strengthening of flow mixing. Consequently, the momentum exchange between the low momentum fluid region and the main flow is enhanced and boundary layer separation on the blade suction surface is delayed. The loss characteristic in the corner region is improved as well. The intensified flow mixing will also increase the total pressure loss in the near-endwall region, which as a result will worsen the cascade performance, and hence the total effect of the endwall synthetic jet depends on the sum of its impacts. Moreover, the injected momentum and the actuation frequency have strong influences on the flow control effect. With the momentum coefficient and the reduced frequency being Cµ = 0.131% and F+ = 1.0, the reduction in total pressure loss coefficient and the increment in pressure rise coefficient are 7.3% and 3.3%, respectively.


1993 ◽  
Vol 115 (2) ◽  
pp. 277-284 ◽  
Author(s):  
Luis San Andres ◽  
Zhou Yang ◽  
Dara W. Childs

A numerical thermohydrodynamic model for solution of the nonlinear differential equations describing the turbulent flow of a single-phase, cryogenic liquid annular seal is presented. A perturbation method is used for calculation of the zeroth and first-order flow solutions to determine the seal steady-state response and dynamic force coefficients. Numerical predictions for a high speed liquid oxygen seal with a roughened stator surface show that, relative to an isothermal-barotropic fluidmodel, the adiabatic THD solution presents a significant temperature-rise with a profound effect on the liquid material properties and seal performance characteristics. The calculations show the onset of two-phase flow conditions at moderate eccentricities despite the large pressure differential across the seal. Comparisons of the static performance characteristics for the reference seal show excellent agreement between the approximate analytical solution developed in Part I and the full numerical results.


Author(s):  
Luis San Andrés ◽  
Joshua Norsworthy

High speed rotors supported on bump-type foil bearings (BFBs) often suffer from large sub synchronous whirl motions. Mechanically preloading BFBs through shimming is a common, low cost practice that shows improvements in rotordynamic stability. However, there is absence of empirical information related to the force coefficients (structural and rotordynamic) of shimmed BFBs. This paper details a concerted study towards assessing the effect of shimming on a first generation BFB (L=38.1 mm, D =36.5 mm). Three metal shims, 120° apart, are glued to the inner surface of the bearing cartridge and facing the underside of the bump foil strip. The shim sets are of identical thickness, either 30 μm or 50 μm. Static load tests show that shimming produces nonlinear static load vs. deflection curves leading to a larger structural stiffness than for the bearing without shims. Torque measurements during shaft acceleration also demonstrate a shimmed BFB has a larger friction coefficient. For a static load of 14.3 kPa, dynamic loads with a frequency sweep from 250 Hz to 450 Hz are exerted on the BFB, without and with shims, to estimate its rotordynamic force coefficients while operating at ∼50 krpm (833 Hz). Similar measurements are conducted without shaft rotation. Results are presented for the original BFB (without shims) and the two shimmed BFB configurations. The direct stiffnesses of the BFB, shimmed or not, increase with excitation frequency thus evidencing a mild hardening effect. The BFB stiffness and damping coefficients decrease slightly for operation with rotor speed as opposed to the coefficients when the shaft is stationary. For frequencies above 300 Hz, the direct damping coefficients of the BFB with 50 μm thick shims are ∼ 30% larger than the coefficients of the original bearing. The bearing structural loss factor, a measure of its ability to dissipate mechanical energy, is derived from the direct stiffness and damping coefficients. The BFB with 50 μm thick shims has a 25% larger loss factor — average from test data collected at 300 Hz to 400 Hz — than the original BFB. Further measurements of rotor motions while the shaft accelerates to ∼50 krpm demonstrate the shimmed BFB (thickest shim set) effectively removes sub synchronous whirl motions amplitudes that were conspicuous when operating with the original bearing.


Author(s):  
Zhi Fang ◽  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng

Abstract Annular damper seals, such as hole-pattern seals, are widely used to control leakage and enhance rotordynamic stability in turbomachinery, especially for the balance-piston seal in the straight-through compressor, and the center seal in the back-to-back compressor. To avoid or minimize negative static stiffness, annular grooves on seal stator have been used to increase direct static stiffness of hole-pattern seals by dividing one long seal to several shorter seal sections. However, few literatures are available for understanding the influences of annular grooves on seal static and rotordynamic characteristics. To understand the comprehensive effects of grooves on the static and rotordynamic characteristics of annular seals, a proposed three-dimensional (3D) transient CFD-based method was used for predictions of rotordynamic characteristics of hole-pattern seals, based on the multi-frequency one-dimensional rotor oscillating model and mesh deformation technique. Moreover, a 3D steady CFD-based method based on the mesh deformation technique was also utilized to predict static characteristics of hole-pattern seals. The accuracy and reliability of the present transient CFD-based method were demonstrated with experimental data of frequency-dependent rotordynamic coefficients of an experimental hole-pattern seal (HPS) at three inlet preswirl conditions (μ0 = −0.2441, 0, 0.598). The leakage flow rates, static and rotordynamic force coefficients were computed for three types of HPS (one without grooves - HPS, one with annular grooves on stator - HPS-AG, and one with pocket grooves on stator – HPS-PG) with three axial locations of grooves (20%, 40%, 60% of seal axial length) at zero and positive inlet preswirl conditions. The effects of groove types (annular and pocket grooves) and groove locations on the static and rotordynamic coefficients of HPS were numerically discussed. Numerical results show that the annular groove and pocket groove on the seal stator both produce a significantly increase in static stiffness, and the HPS-PG seal possesses relatively optimal static stiffness. The annular groove and pocket groove both result in slight increase (less than 5%) in leakage flow rate. The annular groove will significantly weaken the seal dynamic stiffness capability but weakly influence the seal net damping capability. However, the pocket groove shows weakly influences on the dynamic stiffness and damping characteristics. This suggests that the pocket groove is a more suitable design to improve the static and rotordynamic characteristic. The rotordynamic force coefficients show strong dependence on the annular groove location for the HPS-AG seal, but are insensitive to the pocket groove location for the HPS-PG seal. The optimal location of annular groove is strongly related to the inlet preswirl conditions. The increasing swirl velocity induced by the annular groove results in the decrease in stiffness and damping of the HPS-AG seal.


Author(s):  
Bugra H. Ertas ◽  
Huageng Luo

The present work focuses on the dynamic characterization of oil-free wire mesh dampers. The research was aimed at determining nonlinear stiffness and damping coefficients while varying the excitation amplitude, excitation frequency, and static eccentricity. Force coefficients were extracted using a forced response method and also a transient vibration method. Due to the nonlinearity of the dampers, controlled amplitude single frequency excitation tests were required for the forced excitation method, whereas the transient response was analyzed using a Hilbert transform procedure. The experimental results showed that eccentricity has minimal influence on force coefficients, whereas increasing excitation amplitude and frequency yields decreasing stiffness and damping trends. In addition to the parameter identification tests, a rotating test was performed demonstrating high-speed damping capability of the oil-free wire mesh dampers to 40,000 rpm, which was also simulated using a nonlinear rotordynamic response to imbalance analysis.


Author(s):  
Bugra Ertas ◽  
Huageng Luo

The present work focuses on the dynamic characterization of oil-free wire mesh dampers. The research was focused on determining nonlinear stiffness and damping coefficients while varying the excitation amplitude, excitation frequency, and static eccentricity. Force coefficients were extracted using a forced response method (FRM) and also a transient vibration method. Due to the nonlinearity of the dampers, controlled amplitude tests were required for the forced excitation method, whereas the transient response was analyzed using a Hilbert Transform procedure. The testing using both methods showed that eccentricity has minimal influence on force coefficients, whereas increasing excitation amplitude and frequency yield decreasing stiffness and damping trends. In addition to the parameter identification tests, a rotating test was performed demonstrating high-speed damping capability of the oil-free wire mesh dampers to 40,000 rpm, which was also simulated using an nonlinear rotordynamic response to imbalance analysis.


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