PERFORMANCE CHARACTERISTICS OF METAL MESH FOIL BEARINGS: PREDICTIONS VS. MEASUREMENTS

Transcription

1 ASME Turbo Expo 213 GT213 June 3-7, 213, San Antonio, Texas, USA PERFORMANCE CHARACTERISTICS OF METAL MESH FOIL BEARINGS: PREDICTIONS VS. MEASUREMENTS Luis San Andrés Fellow ASME Texas A&M University Thomas Chirathadam Southwest Research Institute, San Antonio, TX ASME Paper GT accepted for journal publication This material is based upon work supported by the TAMU Turbomachinery Research Consortium, Prof. Luis San Andrés incentive fund and software development funds

2 Gas bearing technology Self acting, hydrodynamic bearings Gas film acts in series with elastic layer to provide load support Surface coatings required for reducing friction at start-up & shut-down No lubrication required, Less system part count (less weight) Low load capacity. Not easily scalable. Often need custom design Source: foilbearing.ru Source:Miti Source: nasa.gov/oil-free

3 Gas foil bearing applications High-efficiency oil-free gasturbine (max 1 kw) Source: Organic Rankine cycle (ORC) turbine generator Source: APPLICATIONS: APUs, ACMs, micro gas turbines, turbo expanders, turbo compressor, blowers etc. + Ideal for low load, high speed, low number of startup and shutdown cycles, corrosive and high temp. applications - Not suitable for low speed, high load, high endurance use, and with no thermal management for high temp operation

4 Metal Mesh Foil Bearing (MMFB) MMFB COMPONENTS: Bearing cartridge, metal mesh ring and top Foil MMFB assembly Hydrodynamic air film develops between rotating shaft and top foil. Metal mesh pads hysteretic + dry friction damping Heat treated steel strip Compressed metal mesh pad Bearing cartridge (Wire EDM machined)

5 Past work: Metal mesh foil bearings (29-21) San Andrés et al. (29) J. Eng. Gas Turb. & Power, 132 (3) MMFB structural stiffness and damping are frequency and amplitude dependent. Good correlation between MMFB structural force coefficients and predictions using empirical expressions for metal mesh damper (ring shape) MMFB evidences creep or sag after multiple dismantling and reassembly San Andrés et al. (21) J. Eng. Gas Turb. & Power, 132 (11) Once airborne, MMFB drag torque increases with speed and applied static load Top foil surface coating necessary during start-up and shut-down for reducing top foil and rotor surface damages

6 Past work: Metal mesh foil bearings (21-211) San Andrés and Chirathadam (211) J. Eng. Gas Turb. & Power, 133 San Andrés and Chirathadam (211) J. Eng. Gas Turb. & Power, 133(12) MMFB dynamic stiffness and damping decrease with increasing motion amplitudes With rotation, ie when gas film is in series with metal mesh layer, MMFB stiffness and damping slightly decreases MMFB loss factor not significantly affected by motion amplitude, rotor speed or applied static load MMFB is structurally soft compared to typical GFB designs. Falls in the low range of ROT (DellaCorte, 21)

7 Past work: Metal mesh foil bearings (212) San Andrés and Chirathadam (212) J. Eng. Gas Turb. & Power, 134 Hysteresis curve shows that MMFB has 2-3 times larger energy dissipation ability than a generation I bump foil bearing (BFB) Airborne friction factor (~.3) similar for MMFB and BFB. Gas film separates the surfaces in relative motion MMFB and BFB show little cross-coupled coefficients MMFB and BFB dynamic force coefficients show dissimilar trends Lee & Kim (212) J. Eng. Gas Turb. & Power, 134(1) MMFB stiffness and material loss factor increases with metal mesh density MMFB dissipates more energy compared to a similar sized BFB Hydrodynamic cross-coupled forces are small

8 MMFB operation Non spinning shaft supported on top foil At start-up, the rotor slides on top foil inner surface. Further, a thin gas film is generated between the shaft and the top foil The air film applies pressure on the top foil and deflects the metal mesh. After lift-off, no rubbing contact between the surfaces Exaggerated clearance

9 Geometry and coordinate system Load, W R+c Rotor Nomenclature: Circumferential coordinate e : Journal eccentricity R e e X Y e Y t Top foil h Φ Bearing cartridge l Section of metal mesh X Gas film thickness h ce cos( ) e sin( ) w X t Y t t Perturbation e e e e X X X e e e e Y Y Y it it it hh ex cos( ) ey sin( ) e e w e w e h ce cos( ) e sin( ) w X Y X X Y Y it

10 Hydrodynamic pressure Reynolds equation 3p 3 p ( ph) ( ph) ph ph 6 R 12 x x y y x t Assumptions: Isothermal Isoviscous Ideal gas Nomenclature: p Gas film pressure h : Gas film thickness Viscosity Ω Rotor speed R : Radius Perturbation of pressure and top foil deflection it ww wxex wyey e i t p p e p e p e X X Y Y w w w( p ) p i t w i t X exe py eye p p w pp pp w w w( p ), wx p X w Y p Y p p, pp pp

11 Numerical solution method a) Finite element modeling of top foil and metal mesh Unwrap top foil and metal mesh Y z y x y= y=l/2 y=-l/2 z M xy y x Q x 1 X M xx M yy M yx 4 Q y Qy Q+ y dy y Pressure difference (p-p a ) 2 M yx M yx+ dy y M yy M yy+ dy y K m w: metal mesh reaction force per unit area 3 M xx M xx+ dx x Qx Q+ x dx x M xy M xy+ dx x Rectangular shell elements represent top foil. Curvature effects neglected. Metal mesh layer produces reaction force

12 Numerical solution method b) Control volume scheme with exact advection model (Ref: Faria & San Andres, 2) Solution of partial differential equations Pressure field Integration of pressure fields over top foil surface Forces L t FX cos p pa Rddy F Y sin l Integration of viscous shear stress Drag torque L 2 l L t t h p R T Rddy Rddy Rd h l Integration of perturbed pressure components Dynamic Force coefficients K+iωC= L t KXX icxx KXY icxy px cos py cos Rddy K ic K ic p sin p sin YX YX YY YY X Y l

13 Predictions vs. experimental data Following predictions compared against limited experimental data from two metal mesh bearings (L=D=28 mm, L=38,D=36.5) 1. Static structural deflection vs applied load 2. Bearing friction factor (drag torque) vs. rotor speed for increasing applied static loads 3. Bearing dynamic stiffness and damping coefficients vs excitation frequency

14 Test bearing specifications Experiments from two metal mesh bearings (L/D ~ 1) Parameter MMFB #1 MMFB #2 Bearing cartridge OD, D Bo [mm] Bearing cartridge ID, D Bi [mm] Bearing axial length, L [mm] Journal diameter, D [mm] Metal mesh OD, D MMo [mm] Metal mesh ID, D Mmi [mm] Metal mesh thickness [mm] Metal mesh density (%) ~2 ~2 Top foil thickness, t f [mm] Top foil elastic modulus, E [GPa] Wire diameter, d W [mm].3.3 Bearing mass, M B [kg] Nominal radial clearance, c [mm] ~ 2 ~75 Metal mesh stiffness,k m [N/m/m 2 ] 2.8 x x 1 9 Compliance factor, a=p a /c/k m a) MMFB 1 x cm b) MMFB 2 5 cm

15 Load vs MMFB structural deflection Measurements vs predictions MMFB prototype 1 MMFB prototype LOAD 6 4 Static Load [N] UNLOAD LOAD UNLOAD PREDICTION Displacement [m] Approximate structural stiffness value and nominal clearance estimated (or assumed) from the load-deflection measurements Force [N] m Top foil resisting load Displacement [mm]

16 Measured friction coeff. vs Speed Measurements f = (Torque/Radius)/(Net static load) Ref: San Andres et al. (29) Friction coefficient [-] f ~.1 Rotor accelerates Rotor speed [krpm] 12.2 kpa 23.2 kpa 34.3 kpa 45.7 kpa) Friction coefficient ( f ) decreases with increasing static load f rapidly decreases initially, and then gradually raises with increasing rotor speed Dry sliding Airborne (hydrodynamic)

17 Friction coeff. vs Stribeck number Measurements vs predictions Friction coefficient, f [-] kpa 23.2 kpa 34.3 kpa 45.7 kpa 12.2 kpa Pred 23.2 kpa Pred 34.3 kpa Pred 45.7 kpa Pred PREDICTION MEASUREMENTS Friction coefficient proportional to rotor speed and viscosity (Petrov s law) µw /LD) [-] Friction factor depends on specific load and rotor speed. In the full film hydrodynamic regime, the predictions match well with the measurements

18 MMFB eccentricity vs specific load Eccentricity [m] krpm 4 krpm 5 krpm 6 krpm Nominal clearance 3 krpm 4 krpm 5 krpm Specific load, W/LD [kpa] 6 krpm EX [m] Load direction EY [m] Φ Predictions Since metal mesh structure is soft, journal eccentricity exceeds nominal clearance value Clearance circle For all loads and speeds, journal attitude angle < krpm 4 krpm 5 krpm 6 krpm

19 Min. film thickness vs specific load Predictions Min. film thickness (hmin/c) krpm 4 krpm 3 krpm 4 krpm 5 krpm 6 krpm 5 krpm 3 krpm Specific load,w/ld [kpa] Min. film thickness indicates bearing load carrying capacity Rotor starts rubbing the top foil when min. film thickness equals the average surface roughness Min. film thickness increases with speed and decreases with specific load.

20 Journal attitude angle vs sp. load Predictions Journal attitude angle [deg] krpm 3 krpm 4 krpm 5 krpm 6 krpm 6 krpm journal 3 krpm 4 krpm Specific load,w/ld [kpa] Rotor speed has little effect on attitude angle Journal attitude angle is relatively small for loads up to 45 kpa With increasing specific load, journal attitude angle decreases

21 Estimation of force coefficients Rubber straps Ad-hoc static loading mechanism REF: San Andres and Chirathadam (21) wire Electromagnetic shaker Rotor speed 5 krpm Freq. identification range: 2 to 4 Hz Rotor speed direction X Y Squirrel cage support Motion amplitudes : m, 25 m & 3 m Squirrel cage positioning table Dynamic load : N

22 Identification model EOM: MS a X X CS v X X KS X C X XX CXY x KXX KXY x FX M a C v K Y C C y K K y F SY Y SY Y SY YX YY YX YY Y K XX, C XX K YY, C YY Y Shaker force, F Y KXY, CXY K S,C S : soft SQ stiffness and damping M S : effective mass K ij,c ij : test bearing stiffness and damping Bearing Ω Journal X Shaker force, F X K SY, C SY Soft Support structure K SX, C SX K YX, C YX

23 MMFB stiffness Measurements vs predictions Stiffness [MN/m] 1-1 X K XX K YY KYX K XY K K KYX K XX XY YY Frequency [Hz] Y Stiffness [MN/m] 22 N Static load 1.5 KYY KXX KXY KYX -.5 kxx kxy kyx kyy Frequency [Hz] Predictions and measurements show comparable magnitudes in 2-35 Hz range. Predictions show constant stiffness magnitude with frequency

24 MMFB damping Measurements vs predictions X Y Eq. viscous damping [Ns/m] CXX CYY CXY CYX C C C C XX XY YX YY Frequency [Hz] 22 N Static load Eq. viscous damping [Ns/m] CXX CYY CXY CYX Cxx Cxy Cyx Cyy Frequency [Hz] Measurements show direct damping increasing with frequency. However, predictions show a gradual decay of damping with frequency. Discrepancy mainly due to the large dynamic load in experiments

25 Effect of metal mesh stiffness Predictions Film thickness/clearance [-] Increasing structural stiffness 1 GN/m3 2 GN/m3 3 GN/m3 4 GN/m Structural defl./clearance [-] GN/m3 2 GN/m3 3 GN/m3 4 GN/m3 Increasing structural stiffness Specific load, W/LD [kpa] Specific load, W/LD[kPa] Min. film thickness increases with increasing structural stiffness and decreases with applied specific load. Softer bearings deflects more with applied specific load

26 Effect of metal mesh stiffness Predictions Eccentricity/clearance [-] GN/m3 2 GN/m3 3 GN/m3 4 GN/m3 Increasing structural stiffness Specific load, W/LD [kpa] Attitude angle [deg] Increasing structural stiffness 1 GN/m3 2 GN/m3 3 GN/m3 4 GN/m Specific load, W/LD [kpa] Journal eccentricity decreases with increasing metal mesh stiffness. The journal attitude angle increases with metal mesh stiffness. For very high metal mesh stiffness, the bearing behaves like a rigid surface bearing

27 Rule of thumb (ROT) Rule-of-thumb (ROT) model (Dellacorte, 21) stiffness coeff. K~ 2,5-7,5 (Lx D) lb/in 3 damping coeff. C~.1-1 (L xd) lb-s/in 3 MMFB stiffness coeff. K~ 93-1,86 (Lx D) lb/in 3 [25-5 MN/m 3 ] damping coeff. C~ (L xd) lb-s/in 3 [ MN/m 3 ] MMFB structurally soft with large damping ( =1.68), with average K=.55 MN/m

28 Conclusions ASME Paper GT a) Model predictions validated against limited published test data. Predicted drag friction factors ( ~.1 to.2) for Stribeck numbers 2 to 15 agrees well with measurements. b) Minimum film thickness and journal attitude angle decrease with increasing applied load. Performance characteristics depend on metal mesh structural stiffness c) Predicted force coefficients have magnitudes comparable with measurements, but show different trends with frequency (especially damping) d) For thorough validation of the analytical model, more experimental data from multiple bearings required. The predictive code will aid in the engineered design of MMFBs

29 Acknowledgments/ Thanks to Honeywell Turbocharging Technologies Turbomachinery Research Consortium Questions (?)

30 Extra slides - >

31 Past work: Metal mesh foil bearings (28) San Andrés et al. (21) J. Eng. Gas Turb. & Power, 132(3) Assembled the first prototype MMFB (L=D=28 mm). Large structural damping.7) Structural stiffness [ MN/m] m Amplitude increases 38.1 m 12.7 um 25.4 um 38.1 um 12.7 um Prediction 25.4 um Prediction 38.1 um Prediction 25.4 m E q uivalent viscous dam p in g [ Ns/m] Amplitude increases 12.7 um 25.4 um 38.1 um 12.7 um Prediction 25.4 um Prediction 38.1 um Prediction 12.7 μm 25.4 μm 38.1 μm Frequency [Hz] Frequency [Hz] San Andres et al., 21, ASME J. Eng. Gas Turbines Power, 132 (3) Al-Khateeb & Vance model

32 Summary of past work: MMFB year Computational modeling- Prediction of force coefficients and performance characteristics. High temperature experiments measurement of rotor and bearing temperature with increasing rotor temperature and operating speed. Prediction and response of rotor response to speeds up to 5 krpm. 211 Comparison of static and dynamic performance of similar size MMFB and Generation I Bump Type Foil Bearing (BFB). MMFB has 2-3 times BFB damping. Airborne friction factor ~.3 for both bearings Identification of Rotordynamic coefficients using two orthogonally positioned electromagnetic shakers for varying rotor speeds (4-5 krpm), displacement amplitudes ( 2-3um), static load ( N). Estimated loss factor ~ Demonstrated operation to 45 krpm with early rotor lift off. Educated undergraduate students. Further start and shut down operation, measurement of torque and lift-off speed. Low friction factor ~.1 at high speed 6 krpm. Estimation of rotordynamic coefficients from unidirectional impact loads Assembled the first prototype MMFB (L=D=28 mm). Load vs Deflection with hysteresis shows large structural damping (g~.7). Frequency dependent stiffness agree with predictions.

33 Bearing components MMFB BFB Top Foil Metal mesh pad Bearing cartridge (+top foil+ metal mesh) Top Foil Bump foil Bearing cartridge (+top foil+ bump foil)