Identification of SFD force coefficients Large Clearance Open Ends - PowerPoint PPT Presentation

32 nd Turbomachinery Research Consortium Meeting Identification of SFD force coefficients Large Clearance Open Ends SFD TRC-SFD-01-2012 Luis San Andrés Mast-Childs Professor May 2012 TRC Project 32513/1519FB 1 Linear Nonlinear Force Coefficients for SFDs

SFD with a central groove oil inlet Pressurized lubricant anti-rotation lubricant flows film pin Feed through a central groove shaft groove to fill the journal squeeze film ball lands. bearing  housing Dynamic pressures in the film lands generate reaction forces Typical squeeze film damper (SFD) with a central groove aiding to damp excessive amplitudes of Conventional knowledge regards a groove is rotor whirl indifferent to the kinematics of journal motion, motion. thus effectively isolating the adjacent film lands. 2

P&W SFD test rig Isometric view Static loader Shaker assembly Shaker assembly ( Y direction) ( X direction) Top view Static loader Shaker in Y direction Shaker in X direction SFD test bearing 3

Test rig description Static loader Static loader shaker Y shaker X Shaker Y Shaker X Y X SFD SFD Static loader Y Y Support rods support rods base Base X X 4

SFD Test Rig – cut section Test rig main features Journal diameter: 5.0 inch Piston ring seal Film clearance: 9.9 mil Test Journal (location) Film length: 2 x 1 inch Bearing Cartridge Support stiffness: 100 klbf/in Supply orifices (3) Circumferential groove Flexural Rod (4, 8, 12) Main support rod (4) Journal Base Pedestal in 5

Lubricant flow path Oil inlet in ISO VG 2 oil 6

Objective & tasks Evaluate dynamic load performance of SFD with a central groove. Dynamic load measurements: circular orbits (centered and off centered) and identification of test system and SFD force coefficients Y Y static load e S e 45 o X X r c centered and off- centered circular orbits 7

Structure static stiffness • Pull test using static loader to determine static structure stiffness 1780 400 F Y static radial load (lbf) static radial load (N) 1335 300 X 890 200 445 100 K S ~ 100 klb f /in 0 0 0.5 1 1.5 2 2.5 3 3.5 4 (101.6 μ m) e S static radial eccentricity, (mil) 8

Structural parameters • Dry test system • Circular Centered Direct Orbits XX YY • Frequency 50-210 Hz US SI US SI 107 klb f /in 19 MN/m 120 klbf/in 21 MN/m Stiffness K s 8 lb f -s/in 1.4 kN-s/m 9 lbf-s/in 1.6 kN-s/m Damping C s -4 lb -2 kg -3 lb -1 kg Mass M 48 lb 22 kg 48 lb 22 kg System Mass M BC f ns 148 Hz 156 Hz Natural frequency ξ s 4% 4% Damping ratio 9

SFD dimensions & operating conds. • Maximum static load 324 lb f • Centered and off-centered, e S = 1, 2, and 3 mil • Frequency range: 50-210 Hz, Orbit amplitude r = 0.5 mil ISO VG 2 Oil Oil in, Q in Viscosity at 73 o F [cPoise] 3.10 Journal ( D) Oil out, Q t Density [kg/m 3 ] 785 End groove Inlet pressure [psig] 1.6 Bearing c Central L Cartridge groove ½ L Outlet pressure [psig] 0 End groove L Radial Clearance [mil] 9.9 Oil out, Q b Journal Diameter [inch] 5.0 Oil collector Central groove length [inch] 0.500 Oil out & depth 0.375 Base Support rod Land length, L [inch] 1.0 x 2 Total Length [inch] 2.5 10

SFD force coefficients Y IVFM parameter identification method 45 o e s X c Difference between lubricated SFD system and dry system (baseline) coefficients DRY system parameters K s = 100 klbf/in C SFD =C lubricated - C s M BC = 48 lb C s = 8-9 lbf-s/in Nat freq = 148-156 Hz M SFD =M lubricated - M BC Damping ratio = 4% K SFD =K lubricated - K s 11

SFD force coefficients - theory Centered journal ( e s =0), no lubricant cavitation Two film lands separated by a plenum: central groove has no effect on squeeze film forces.     L tanh 3     R   D       * * * 2 12 π 1 Damping    C C C L  XX YY    L c  D     L tanh  3 π   Inertia LR   D      * * * 2 1 M M M   XX YY L c   D Y Stiffness K XX = K YY = K XY =K YX = 0 X 12

SFD force coefficients - theory     L tanh 3   Damping   R   D       * * * 2 12 π 1    C C C L  XX YY    L c  D c= 5.5 mil C * = 7,121 N.s/m (40.7 lb f .s/in) c= 9.9 mil C * = 1,255 N.s/m (7.16 lb f .s/in)     L tanh  3 π   Inertia LR   D      * * * 2 1 M M M   XX YY L c   D c= 5.5 mil M * = 2.98 kg (6.58 lb m ) Y c= 9.9 mil M * = 1.67 kg (3.69 lb m ) X 13

Experimental SFD damping coeffs. Y • Open ends SFD • Circular orbits (r = 0.5 mil) 45 o e s X c SFD (1 inch land lengths) Damping coefficients (lb f -s/in) 31.5 kNs/m 180 C SFD 160 C YY c= 5.5 mil 140 120 C XX c= 5.5 mil 100 80 60 classical theory (40.6 lbf.s/in) C YY c= 9.9 mil 40 20 C XX c= 9.9 mil classical theory (7.1 lbf.s/in) 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 (89 μ m) static eccentricity, e S (mil) 14

Experimental SFD inertia coeffis. Y • Open ends SFDs 45 o • Circular orbits (r = 0.5 mil) e s X c SFD (1 inch land lengths) Added mass coefficients (lb) 80 36 kg M SFD 70 M XX c= 5.5 mil 60 M YY c= 5.5mil 50 40 M YY c= 9.9 mil 30 20 M XX c= 9.9 mil 10 classical theory (3.7 - 6.6 lb) 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 89 μ m static eccentricity, e S (mil) 15

Pressure sensors in bearing Top view: Sensors around bearing circumference Top view: Sensors around bearing circumference Pressure sensor locations Pressure sensor locations and and 25.4 mm 25.4 mm Pressure Pressure Top Land Top Land sensor sensor Pressure Pressure Central Central sensor sensor 12.7 mm 12.7 mm groove groove Bottom Land Bottom Land 25.4 mm 25.4 mm , , and and 63.5 mm 63.5 mm Pressure Pressure sensor sensor Central Central groove groove Side view: Sensors located at Side view: Sensors located at middle plane of film lands middle plane of film lands 16 BC BC

Dynamic pressures: films & groove Whirl frequency 130 Hz ASME GT2012-68212 film lands psi 10 0.69 bar Top and bottom pressure (psi) 5 film lands show 0 0  similar pressures. 5 -0.69 bar  10 0 1 2 3 4 time (-) Number of periods top land (120 deg) bottom land (120 deg) groove Dynamic pressure 4 0.28 bar psi pressure (psi) 2 in the groove is 0 0 not zero!  2  4 -0.28 bar 0 1 2 3 4 Number of periods time (-) groove (165 deg) groove (285 deg) 17 e s =0, circular orbit r =0.5 mil. Groove pressure P G = 0.72 bar

Peak-peak lubricant pressures Piezoelectric pressure sensors (PCB) location P-P dynamic pressure (psi) 207 (kPa) 30 30 Top land (120) Top land (240) Bearing Lands Bottom land (120) Cartridge Bottom land (240) Groove (165) (top & bottom) groove 20 Groove (285) 20 top land bottom land 10 10 groove 0 0 0 100 200 100 200 Mid- plane c =5.5 mil Frequency (Hz) 18

Peak-peak lubricant pressures Piezoelectric pressure sensors (PCB) location P-P dynamic pressure (psi) 15 15 Top land (120) Bearing Top land (240) Bottom land (120) Cartridge Bottom land (240) groove Groove (165) groove 10 Groove (285) 10 top land bottom land 5 5 lands (top & bottom) 0 0 0 100 200 100 200 Mid- plane c =9.9 mil Frequency (Hz) 19

Ratio of groove/film land pressures 4 Top land (120) Groove Top land (240) P-P pressure ratios generates groove 3 large lands (top) hydrodyna mic 2 pressures! 1 1.0 0 0 0 100 200 100 200 c =5.5 mil Frequency (Hz) 3/8”~70 c 1 “ 0.5” 1” 20

Ratio of groove/film land pressures 4 Top land (120) Groove Top land (240) P-P pressure ratios generates groove 3 larger lands (top) hydrodyna mic 2 pressures!! Larger than 1 1.0 in the film! 0 0 100 200 100 200 Frequency (Hz) c =9.9 mil 3/8”~35 c 1 “ 0.5” 1” 21

Model SFD with a central groove SFD geometry and nomenclature Use effective depth Lubricant in d  =1.6 c Bearing orifice Lubricant in Lubricant in d o d G L c : clearance groove L G recirculation recirculation separation line separation line End seal film land zone zone streamline streamline Lubricant out d  d  Journal Effective groove depth Effective groove depth Lubricant out Lubricant out z D, diameter Solve modified Reynolds equation (with fluid inertia)           2 P P h h      12 3 3 2     h h h       2     R R z z t t 22

Example predicted pressure field Feed hole (3 x 120 deg) Feed hole (3 x 120 deg) Static groove groove groove pressure at 0.60 0.60 0.5-0.6 0.5-0.6 groove shows 0.4-0.5 0.4-0.5 0.50 0.50 circumferenti 0.3-0.4 0.3-0.4 0.2-0.3 0.2-0.3 al variation Pressure Pressure Inner Film Inner Film 0.40 0.40 0.1-0.2 0.1-0.2 0.0-0.1 0.0-0.1 due to feed Pressure Pressure (bar) (bar) 0.30 0.30 holes spacing land land 0.20 0.20 1 1 9 9 17 17 25 25 0.10 0.10 33 33 41 41 49 49 57 57 circ coordinate (node #) circ coordinate (node #) 65 65 0.00 0.00 73 73 3/8”~35 c S1 S1 81 81 S8 S8 axial axial 89 89   coordi coordi 1 “ 0.5” 1” nate nate z z 23