On the Force Coefficients of a Flooded, Open Ends Short Length Squeeze Film Damper: From Theory to Practice (and Back)

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Luis San Andrés ◽  
Sean Den ◽  
Sung-Hwa Jeung
Keyword(s):  
Large Amplitude ◽  
Small Amplitude ◽  
Forced Response ◽  
Short Length ◽  
Theory And Practice ◽  
Squeeze Film ◽  
Squeeze Film Damper ◽  
Force Coefficients ◽  
Deep Groove ◽  
Large Amplitude Motions

Gas turbine aircraft engine manufacturers push for simple squeeze film damper (SFD) designs, short in length, yet able to provide enough damping to ameliorate rotor vibrations. SFDs employ orifices to feed lubricant directly into the film land or into a deep groove. The holes, acting as pressure sources (or sinks), both disrupt the film land continuity and reduce the generation of squeeze film dynamic pressure. Overly simple predictive formulations disregard the feedholes and deliver damping (C) and inertia (M) force coefficients not in agreement with experimental findings. Presently, to bridge the gap between simple theory and practice, the paper presents measurements of the dynamic forced response of an idealized SFD that disposes of the feedholes altogether. The short-length SFD, whose diameter D = 127 mm, has one end submerged (flooded) within a lubricant bath and the other end exposed to ambient. ISO VG 2 lubricant flows by gravity through the film land of length L = 25.4 mm and clearance c = 0.122 mm. From dynamic load tests over excitation frequency range 10–250 Hz, experimental damping coefficients (CXX, CYY) from the flooded damper agree well with predictions from the classical open ends model with a full film for small amplitude whirl motions (r/c ≪ 1), centered and off-centered. Air ingestion inevitably occurs for large amplitude motions (r/c > 0.4), thus exacerbating the difference between predictions and tests results. For reference, identical tests were conducted with a practical SFD supplied with lubricant (Pin = 0.4 bar) via three orifice feedholes, 120 deg apart at the film land midplane. A comparison of test results shows as expected that, for small amplitude (r/c ∼ 0.05) orbits, the flooded damper generates on average 30% more damping than the practical configuration as the latter's feedholes distort the generation of pressure. For large amplitude motions (r/c > 0.4), however, the flooded damper provides slightly lesser damping and inertia coefficients than the SFD with feedholes whose pressurized lubricant delivery alleviates air ingestion in the film land. The often invoked open ends SFD classical model is not accurate for the practical engineered design of an apparently simple mechanical element.

On the Force Coefficients of a Flooded, Open Ends Short Length Squeeze Film Damper: From Theory to Practice (and Back)

2017 ◽  
Author(s):  
Luis San Andrés ◽  
Sean Den ◽  
Sung-Hwa Jeung
Keyword(s):  
Large Amplitude ◽  
Small Amplitude ◽  
Forced Response ◽  
Short Length ◽  
Theory And Practice ◽  
Squeeze Film ◽  
Squeeze Film Damper ◽  
Force Coefficients ◽  
Deep Groove ◽  
Large Amplitude Motions

Gas turbine aircraft engine manufacturers push for simple squeeze film damper (SFD) designs, short in length, yet able to provide enough damping to ameliorate rotor vibrations. SFDs employ orifices to feed lubricant directly into the film land or into a deep groove. The holes, acting as pressure sources (or sinks), both disrupt the film land continuity and reduce the generation of squeeze film dynamic pressure. Overly simple predictive formulations disregard the feedholes and deliver damping (C) and inertia (M) force coefficients not in agreement with experimental findings. Presently, to bridge the gap between simple theory and practice, the paper presents measurements of the dynamic forced response of an idealized SFD that disposes of the feedholes altogether. The short-length SFD, whose diameter D = 125 mm, has one end submerged (flooded) within a lubricant bath and the other end exposed to ambient. ISO VG 2 lubricant flows by gravity through the film land of length L = 25.4 mm and clearance c = 0.122 mm. From dynamic load tests over excitation frequency range 10–250 Hz, experimental damping coefficients (CXX, CYY) from the flooded damper agree well with predictions from the classical open ends model with a full film for small amplitude whirl motions (r/c << 1), centered and off-centered. Air ingestion inevitably occurs for large amplitude motions (r/c > 0.4) thus exacerbating the difference between predictions and tests results. For reference, identical tests were conducted with a practical SFD supplied with lubricant (Pin = 0.4 bar) via three orifice feedholes, 120° apart at the film land mid plane. A comparison of test results shows as expected, that for small amplitude (r/c ∼ 0.05) orbits, the flooded damper generates on average 30% more damping than the practical configuration as the latter’s feedholes distort the generation of pressure. For large amplitude motions (r/c > 0.4), however, the flooded damper provides slightly lesser damping and inertia coefficients than the SFD with feedholes whose pressurized lubricant delivery alleviates air ingestion in the film land. The often invoked open ends SFD classical model is not accurate for the practical engineered design of an apparently simple mechanical element.

Forced Response of a Squeeze Film Damper and Identification of Force Coefficients From Large Orbital Motions

2004 ◽  
Vol 126 (2) ◽  
pp. 292-300 ◽  
Author(s):  
Luis San Andre´s ◽  
Oscar De Santiago
Keyword(s):  
Excitation Frequency ◽  
Air Entrainment ◽  
Forced Response ◽  
Effective Length ◽  
Single Frequency ◽  
Squeeze Film ◽  
Inertia Force ◽  
Damping Force ◽  
Squeeze Film Damper ◽  
Force Coefficients

Experimentally derived damping and inertia force coefficients from a test squeeze film damper for various dynamic load conditions are reported. Shakers exert single frequency loads and induce circular and elliptical orbits of increasing amplitudes. Measurements of the applied loads, bearing displacements and accelerations permit the identification of force coefficients for operation at three whirl frequencies (40, 50, and 60 Hz) and increasing lubricant temperatures. Measurements of film pressures reveal an early onset of air ingestion. Identified damping force coefficients agree well with predictions based on the short length bearing model only if an effective damper length is used. A published two-phase flow model for air entrainment allows the prediction of the effective damper length, and which ranges from 82% to 78% of the damper physical length as the whirl excitation frequency increases. Justifications for the effective length or reduced (flow) viscosity follow from the small through flow rate, not large enough to offset the dynamic volume changes. The measurements and analysis thus show the pervasiveness of air entrainment, whose effect increases with the amplitude and frequency of the dynamic journal motions. Identified inertia coefficients are approximately twice as large as those derived from classical theory.

On the Effect of the Gap of End Seals on Force Coefficients of a Test Integral Squeeze Film Damper: Experiments and Predictions

2020 ◽  
Author(s):  
Luis San Andrés ◽  
Xueliang Lu ◽  
Bonjin Koo ◽  
Scott Tran
Keyword(s):  
Theory And Practice ◽  
Squeeze Film ◽  
Test Element ◽  
Inlet Temperature ◽  
Dynamic Force ◽  
Virtual Mass ◽  
Squeeze Film Damper ◽  
Force Coefficients ◽  
Rotor Bearing ◽  
Bearing System

Abstract An integral squeeze film damper (ISFD) offers the advantages of a lower number of parts, a shorter axial span, a lighter weight, a split manufacturing and high precision on its film clearance construction. An ISFD does not only add damping to reduce shaft vibration amplitudes and to enhance the stability of a rotor-bearing system but also can be used to tune a rotor-bearing system natural frequency, and thus increasing the operational safety margin between the running shaft speed and the system critical speed. In spite of the numerous commercial applications, the archival literature is scant as per the experimental quantification of force coefficients for ISFDs. This paper details the results of an experimental and analytical endeavor to quantify and to predict the dynamic force coefficients of an ISFD, hence bridging the gap between theory and practice. With an axial length of 76 mm, the test damper element has four arcuate film lands, 73° in arc extent at a diameter of 157 mm, and each with a clearance (c) equaling to 0.353 mm. As is customary, the damper has its axial ends sealed with end plates produced by a set of installed shims giving an axial gap (d) equal to 1.5c, 1.21c, and 0.8c. A baseline configuration, namely open ends, is also tested without the end seals in place. In the test rig, the ISFD and its housing are flexibly mounted while the rotor is rigid and stationary (no spinning). The lubricant is an ISO VG46 oil supplied at a low pressure, 1 to 2 bar(g) and ∼ 47 °C inlet temperature, typical of compressor applications. The test procedure applies static loads on the ISFD and records the bearing static offset or eccentricity to verify the structure stiffness, and meanwhile, individual hydraulic shakers deliver dynamic loads along two orthogonal directions to produce motions over a set frequency range, 10 Hz to 160 Hz. The ISFD produces direct damping and inertia that increase with the journal static eccentricity albeit at a lower rate than predictions from a computational squeeze film flow model that includes lubricant compressibility. The end seals are effective in significantly raising the damping coefficient while reducing the oil through flow rate. The damper with the tightest sealed ends (d = 0.8c) shows nearly 20 times more damping that the open ends ISFD albeit also revealing a significant stiffness hardening (negative virtual mass) as the excitation frequency increases. On the contrary, the open ends ISFD and the sealed ends configurations with gaps d = 1.21c and 1.5c produce a (positive) virtual mass that exceeds the test element physical mass and thus softens the test element direct dynamic stiffness. For the configurations with loose end seals (d = 1.21c or larger to open ends), the model predicts well the damping coefficients but under predicts the added masses by 50% or more. Note this virtual mass coefficient, largely ignored in practice, can make the test element either extremely stiff as with the sealed damper configuration with the smallest gap d = 0.8c, or very soft as with the ISFD with end seals gap = 1.21c or 1.5c. Hence, designers are cautioned not to pursue overly tight end sealed dampers as the mineral lubricant, nearly incompressible though always having a small amount of entrapped gas, may behave distinctly when confined to a squeezed film volume and having no adequate routes to escape or flow through.

Experimental Performance of an Open Ends, Centrally Grooved, Squeeze Film Damper Operating With Large Amplitude Orbital Motions

2014 ◽  
Vol 137 (3) ◽  
Author(s):  
Luis San Andrés ◽  
Sung-Hwa Jeung
Keyword(s):  
Large Amplitude ◽  
Gas Turbines ◽  
Mechanical Energy ◽  
Forced Response ◽  
Dynamic Loads ◽  
Squeeze Film ◽  
Radial Clearance ◽  
Force Coefficients ◽  
Squeeze Film Dampers ◽  
Static Eccentricity

Aircraft engines customarily implement squeeze film dampers (SFDs) to dissipate mechanical energy caused by rotor vibration and to isolate the rotor from its structural frame. The paper presents experimental results for the dynamic forced performance of an open ends SFD operating with large amplitude whirl motions, centered and off-centered. The test rig comprises of an elastically supported bearing with a damper section, 127 mm in diameter, having two parallel film lands separated by a central groove. Each film land is 25.4 mm long with radial clearance c = 0.251 mm. The central groove, 12.7 mm long, has a depth of 9.5 mm (38c). An ISO VG 2 lubricant flows into the groove via three 2.5 mm orifices, 120 deg apart, and then passes through the film lands to exit at ambient condition. Two orthogonally placed shakers apply dynamic loads on the bearing to induce circular orbit motions with whirl frequency ranging from 10 Hz to 100 Hz. A static loader, 45 deg away from each shaker, pulls the bearing to a static eccentricity (es). Measurements of dynamic loads and the ensuing bearing displacements and accelerations, as well as the film and groove dynamic pressures, were obtained for eight orbit amplitudes (r = 0.08c to ∼0.71c) and under four static eccentricities (es = 0.0c to ∼0.76c). The experimental damping coefficients increase quickly as the bearing offset increases (es/c → 0.76) while remaining impervious to the amplitude of whirl orbit (r/c → 0.51). The inertia coefficients decrease rapidly as the orbit amplitude grows large, r > 0.51c, but increase with the static eccentricity. A comparison with test results obtained with an identical damper but having a smaller clearance (cs = 0.141 mm) (San Andrés, L., 2012, “Damping and Inertia Coefficients for Two Open Ends Squeeze Film Dampers With a Central Groove: Measurements and Predictions,” ASME J. Eng. Gas Turbines Power, 134(10), p. 102506), show the prior damping and inertia coefficients are larger, ∼5.0 and ∼2.2 times larger than the current ones. These magnitudes agree modestly with theoretical ratios for damping and inertia coefficients scaling as (c/cs)3 = 5.7 and (c/cs) = 1.8, respectively. In spite of the large difference in depths between a groove and a film land, the magnitudes of dynamic pressures recorded at the groove are similar to those in the lands. That is, the groove profoundly affects the dynamic forced response of the test damper. A computational physics model replicates the experimental whirl motions and predicts force coefficients spanning the same range of whirl frequencies, orbit radii, and static eccentricities. The model predictions reproduce with great fidelity the experimental force coefficients. The good agreement relies on the specification of an effective groove depth derived from one experiment.

On the Effect of the Gap of End Seals on Force Coefficients of a Test Integral Squeeze Film Damper: Experiments and Predictions

2021 ◽  
Vol 143 (1) ◽  
Author(s):  
Xueliang Lu ◽  
Luis San Andrés ◽  
Bonjin Koo ◽  
Scott Tran
Keyword(s):  
Theory And Practice ◽  
Squeeze Film ◽  
Test Element ◽  
Inlet Temperature ◽  
Dynamic Force ◽  
Virtual Mass ◽  
Squeeze Film Damper ◽  
Force Coefficients ◽  
Rotor Bearing ◽  
Bearing System

Abstract An integral squeeze film damper (ISFD) offers the advantages of a lower number of parts, a shorter axial span, a lighter weight, a split manufacturing, and high precision on its film clearance construction. An ISFD does not only add damping to reduce shaft vibration amplitudes and to enhance the stability of a rotor-bearing system but also can be used to tune a rotor-bearing system natural frequency, and thus increasing the operational safety margin between the running shaft speed and the system critical speed. In spite of the numerous commercial applications, the archival literature is scant as per the experimental quantification of force coefficients for ISFDs. This paper details the results of an experimental and analytical endeavor to quantify and to predict the dynamic force coefficients of an ISFD, hence bridging the gap between theory and practice. With an axial length of 76 mm, the test damper element has four arcuate film lands, 73 deg in arc extent at a diameter of 157 mm, and each with a clearance (c) equaling to 0.353 mm. As is customary, the damper has its axial ends sealed with end plates produced by a set of installed shims giving an axial gap (d) equal to 1.5c, 1.21c, and 0.8c. A baseline configuration, namely, open ends, is also tested without the end seals in place. In the test rig, the ISFD and its housing are flexibly mounted while the rotor is rigid and stationary (no spinning). The lubricant is an ISO VG46 oil supplied at a low pressure, 1 to 2 bar(g) and ∼47 °C inlet temperature, typical of compressor applications. The test procedure applies static loads on the ISFD and records the bearing static offset or eccentricity to verify the structure stiffness, and meanwhile, individual hydraulic shakers deliver dynamic loads along two orthogonal directions to produce motions over a set frequency range, 10 Hz to 160 Hz. The ISFD produces direct damping and inertia that increase with the journal static eccentricity albeit at a lower rate than predictions from a computational squeeze film flow model that includes lubricant compressibility. The end seals are effective in significantly raising the damping coefficient while reducing the oil through flow rate. The damper with the tightest sealed ends (d = 0.8c) shows nearly 20 times more damping that the open ends ISFD albeit also revealing a significant stiffness hardening (negative virtual mass) as the excitation frequency increases. On the contrary, the open ends ISFD and the sealed-ends configurations with gaps d = 1.21c and 1.5c produce a (positive) virtual mass that exceeds the test element physical mass and thus softens the test element direct dynamic stiffness. For the configurations with loose end seals (d = 1.21c or larger to open ends), the model predicts well the damping coefficients but under predicts the added masses by 50% or more. Note this virtual mass coefficient, largely ignored in practice, can make the test element either extremely stiff as with the sealed damper configuration with the smallest gap d = 0.8c, or very soft as with the ISFD with end seals gap = 1.21c or 1.5c. Hence, designers are cautioned not to pursue overly tight end sealed dampers as the mineral lubricant, nearly incompressible though always having a small amount of entrapped gas, may behave distinctly when confined to a squeezed film volume and having no adequate routes to escape or flow through.

Experimental Performance of an Open Ends, Centrally Grooved, Squeeze Film Damper Operating With Large Amplitude Orbital Motions

2014 ◽  
Author(s):  
Luis San Andrés ◽  
Sung-Hwa Jeung ◽  
Gary Bradley
Keyword(s):  
Large Amplitude ◽  
Mechanical Energy ◽  
Groove Depth ◽  
Forced Response ◽  
Dynamic Loads ◽  
Squeeze Film ◽  
Radial Clearance ◽  
Force Coefficients ◽  
Static Eccentricity ◽  
Physics Model

Aircraft engines customarily implement Squeeze Film Dampers (SFDs) to dissipate mechanical energy caused by rotor vibration and to isolate the rotor from its structural frame. The paper presents experimental results for the dynamic forced performance of an open ends SFD operating with large amplitude whirl motions, centered and off-centered. The test rig comprises of an elastically supported bearing with a damper section, 127 mm in diameter, having two parallel film lands separated by a central groove. Each film land is 25.4 mm long with radial clearance c = 0.251 mm. The central groove, 12.7 mm long, has a depth of 9.5 mm (38c). An ISO VG 2 lubricant flows into the groove via three 2.5 mm orifices, 120 degrees apart, and then passes through the film lands to exit at ambient condition. Two orthogonally placed shakers apply dynamic loads on the bearing to induce circular orbit motions with whirl frequency ranging from 10 Hz to 100 Hz. A static loader, 45° away from each shaker, pulls the bearing to a static eccentricity (es). Measurements of dynamic loads and the ensuing bearing displacements and accelerations, as well as the film and groove dynamic pressures, were obtained for eight orbit amplitudes (r = 0.08c to ∼0.71c) and under four static eccentricities (es = 0.0c to ∼0.76c). The experimental damping coefficients increase quickly as the bearing offset increases (es/c→0.76) while remaining impervious to the amplitude of whirl orbit (r/c→0.51). The inertia coefficients decrease rapidly as the orbit amplitude grows large, r>0.51c, but increase with the static eccentricity. A comparison with test results obtained with an identical damper but having a smaller clearance (cs = 0.141 mm) [1], show the prior damping and inertia coefficients are larger, ∼5.0 and ∼2.2 times larger than the current ones. These magnitudes agree modestly with theoretical ratios for damping and inertia coefficients scaling as (c/cs)3 = 5.7 and (c/cs) = 1.8, respectively. In spite of the large difference in depths between a groove and a film land, the magnitudes of dynamic pressures recorded at the groove are similar to those in the lands. That is, the groove profoundly affects the dynamic forced response of the test damper. A computational physics model replicates the experimental whirl motions and predicts force coefficients spanning the same range of whirl frequencies, orbit radii and static eccentricities. The model predictions reproduce with great fidelity the experimental force coefficients. The good agreement relies on the specification of an effective groove depth derived from one experiment.

Extended Finite Element Analysis of Journal Bearing Dynamic Forced Performance to Include Fluid Inertia Force Coefficients

2012 ◽  
Author(s):  
Luis San Andrés
Keyword(s):  
Finite Element ◽  
Test Data ◽  
Small Amplitude ◽  
Forced Response ◽  
Inertia Force ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Force Coefficients ◽  
Reaction Forces ◽  
Bearing Stiffness

Reynolds equation governs the generation of hydrodynamic pressure in oil lubricated fluid film bearings. The static and dynamic forced response of a bearing is obtained from integration of the film pressure on the bearing surface. For small amplitude journal motions, a linear analysis represents the fluid film bearing reaction forces as proportional to the journal center displacements and velocity components through four stiffness and four damping coefficients. These force coefficients are integrated into rotor-bearing system structural analysis for prediction of the system stability and the synchronous response to imbalance. Fluid inertia force coefficients, those relating reaction forces to journal center accelerations, are routinely ignored because most oil lubricated bearings operate at relatively low Reynolds numbers, i.e., under slow flow conditions. Modern rotating machinery operates at ever increasing surface speeds to deliver more power in smaller size units. Under these operating conditions fluid inertia effects need to be accounted for in the forced response of oil lubricated bearings, as recent experimental test data also reveal. The paper presents a finite element formulation to predict added mass coefficients in oil lubricated bearings by extending a basic formulation that already calculates the bearing stiffness and damping force coefficients. That is, a small amplitude perturbation analysis of the lubrication flow equations keeps the temporal fluid inertia effects and develops a set of equations to obtain the bearing stiffness, damping and inertia force coefficients. The method does not impose on the cost of the original formulation which makes it very attractive for ready implementation in existing software. Predictions of the computational model are benchmarked against archival test data for an oil-lubricated pressure dam bearing supporting large compressors. The comparisons show fluid inertia effects cannot be ignored for operation at high rotor speeds and with small static loads.

On the Experimental Dynamic Force Performance of a Squeeze Film Damper Supplied Through a Check Valve and Sealed With O-Rings

2021 ◽  
Author(s):  
Luis San Andrés ◽  
Bryan Rodríguez
Keyword(s):  
Dynamic Pressure ◽  
Excitation Frequency ◽  
Check Valve ◽  
Forced Response ◽  
Single Frequency ◽  
Squeeze Film ◽  
Dynamic Force ◽  
Viscous Damping ◽  
Test Rig ◽  
Force Coefficients

Abstract In rotor-bearing systems, squeeze film dampers (SFDs) assist to reduce vibration amplitudes while traversing a critical speed and also offer a means to suppress rotor instabilities. Along with an elastic support element, SFDs are effective means to isolate a rotor from its casing. O-rings (ORs), piston rings (PRs) and side plates as end seals reduce leakage and air ingestion while amplifying the viscous damping in configurations with limited physical space. ORs also add a centering stiffness and damping to a SFD. The paper presents experiments to quantify the dynamic forced response of an O-rings sealed ends SFD (OR-SFD) lubricated with ISO VG2 oil supplied at a low pressure (0.7 bar(g)). The damper is 127 mm in diameter (D), short in axial length L = 0.2D, and the film clearance c = 0.279 mm. The lubricant flows into the film land through a mechanical check valve and exits through a single port. Upstream of the check valve, a large plenum filled with oil serves to attenuate dynamic pressure disturbances. Multiple sets of single-frequency dynamic loads, 10 Hz to 120 Hz, produce circular centered orbits with amplitudes r = 0.1c, 0.15c and 0.2c. The experimental results identify the test rig structure, ORs and SFD force coefficients; namely stiffness (K), mass (M) and viscous damping (C). The ORs coefficients are frequency independent and show a sizeable direct stiffness, KOR ∼ 50% of the test rig structure stiffness, along with a quadrature stiffness, K0∼0.26 KOR, demonstrative of material damping. The lubricated system damping coefficient equals CL = (CSFD + COR); the ORs contributing 10% to the total. The experimental SFD damping and inertia coefficients are large in physical magnitude; CSFD slightly grows with orbit size whereas MSFD is relatively constant. The added mass (MSFD) is approximately four-fold the bearing cartridge mass; hence, the test rig natural frequency drops by ∼50% once lubricated. A computational physics model predicts force coefficients that are just 10% lower than those estimated from experiments. The amplitude of measured dynamic pressures upstream of the plenum increases with excitation frequency. Unsuspectedly, during dynamic load operation, the check valve did allow for lubricant backflow into the plenum. Post-tests verification demonstrates that, under static pressure conditions, the check valve does work since it allows fluid flow in just one direction.

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