Structural and Rotordynamic Force Coefficients of a Shimmed Bump Foil Bearing: an Assessment of a Simple Engineering Practice

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1 Proceedings of ASME Turbo Expo 2015: Turbine Technical Conference and Exposition, June 15-19, 2015, Montreal, Canada Paper GT Structural and Rotordynamic Force Coefficients of a Shimmed Bump Foil Bearing: an Assessment of a Simple Engineering Practice Luis San Andrés Mast-Childs Chair Professor Texas A&M University Joshua David Norsworthy Engineer, Borg-Warner Turbo Research funded by the Turbomachinery Research Consortium

2 Bump-Type Foil Bearings (BFBs) A gas film in series with a top foil and an under-spring element is a proven support for microturbomachinery (<200kW). Typically the top foil and shaft are coated to minimize wear & reduce friction. Applications: ACMs, micro gas turbines, turbo expanders, turbo compressors, turbo blowers, soon in automotive turbochargers Issues: Expensive & highly engineered element Nonlinear substructure: prone to show rotor sub synchronous whirl motions Thermal management advised LOW load capacity (compared to oil lubricated bearings) 2

3 Example subsynchronous whirl motion Ruddloff, L., Arghir, M., et al., 2011, Experimental Analysis of a First generation foil Bearing. Start-Up Torque and Dynamic Coefficients, ASME GT Unloaded FB: Self-Excited whirl motions at speed 30 krpm (500 Hz) with whirl frequency=165 Hz (WFR=0.33) 3

4 Original and shimmed GFB Thin foil Θ l Structural bump Θ l Ω Ω Journal Y Journal Y g Housing Θ p Θ s t s Shim X (a) Gas Original foil bearing GFB Original GFB X (b) Gas foil Shimmed bearing with GFBthree shims Shimmed GFB Inserting metal shims underneath bump strips introduces a preload (centering stiffness) at low cost a typical industrial practice. 4

5 Literature Review BFB supported rotors often show large amplitude sub synchronous whirl motions. Kim and San Andrés (2009) Trib. Trans., 52 Sim et al. (2012) J.Tribol., 134 Oil free turbocharger on shimmed foil bearings. Sim et al. (2014) ASME Turbo Expo Three pad BFB. Schiffmann & Spakovszky (2013) J. Tribol., 135 Impractical Selective Shimming Guidelines for Improved Stability. Prior art: A shimmed BFB increases the onset speed of rotor instability and reduces the amplitude of sub synchronous whirl motions

6 ORIGINAL BEARING Kim and San Andrés (2009) Trib. Trans., 52 Rotor deceleration from 50 krpm, side pressure of 0.34 bar Amplitude [ ìm] [μm] Amplitude [um] Original GFB Free end, vertical direct ion 2 krpm 25 krpm g Θ l Ω Journal X (a) Gas foil bearing Thin foil Structural bu Y Housing krpm Frequency [Hz] [Hz] Large amplitude subsynchronous motions (27 krpm 50 krpm) Whirl frequency: 120 Hz Hz 1X 6

7 SHIMMED BEARING Kim and San Andrés (2009) Trib. Trans., 52 Rotor deceleration from 50 krpm, side pressure of 0.34 bar Amplitude [microns] [ ìm] Amplitude [μm] krpm 25 krpm Frequency [Hz] [Hz] Small amplitude subsynchronous motions (38 krpm 50 krpm) Shimmed GFB Whirl frequency: 140 Hz Hz 1X Y g l bump Θ p Θ l Θ s 50 krpm Ω Journal t s X 7 Shim Delay ~ 11 krpm the threshold rotor speed for onset of subsynchronous whirl motions. 25 μm (1 mil) thick shims Y

8 Objective Experimentally characterize the effect of shimming on a bump-type foil bearing: frequency dependent stiffness & damping force coefficients; and transient rotor speed during start up events: drag torque (friction coefficient), peak startup airborne operation X Y

9 BFB and shims Bearing dimensions L= 38.1 mm, D = 36.5 mm (L/D~ 1.0) Shims with adhesive surface. Shim pushes bumps towards rotor. Thickness =30 µm,50 µm Shims placed 120 o apart, stretch axially through bearing. FB radial clearance, c nom = ½ (D I -D s ) = mm

10 BFB Specifications Parameters Bearing cartridge outer diameter, D O Bearing cartridge inner diameter, D I Bearing axial length, L Top foil (Inconel X750) thickness t T foil length, 2πD I Magnitude mm mm mm 0.1 mm 110 mm Number of bumps, N B 26 Bump foil (Inconel X750) thickness, t pitch, s 0 length, l B mm 4.3 mm 2.1 mm height, h Shim (AISI 4140) length 0.50 mm 38.1 mm 2c nom D i L Thickness, t s 30 & 50 µm width 7.87 mm Angular extent 12 D o Shaft diameter, D s Measured inner diameter of FB (assembled) 36.5 mm mm Nominal FB radial clearance, c nom =½(D I -D s ) mm Weight of bearing and cartridge 1.1 kg (10 N)

11 Clearance of shimmed BFB Clearance profile: t s 1 c( ) 1 cnom ts cos NS 1 p 2cnom 2 c nom : Nominal bearing clearance t S : Shim thickness N S : Number of shims θ : Angular coordinate θ p : Angular distance between consecutive shims θ 1 : Angular coordinate of the first shim The clearance of a shimmed bearing is periodic, as that of a tri-lobe or three pad bearing. The bearing clearance reduces at shim locations.

12 Static load vs. BFB deflection 4 cycles of push and pull Load directed 90 degrees to top foil fixed end A third order polynomial fits regions with bump compression Bearing reaction force: F K 0 K 1 x K 3 x 3 Small BFB hysteresis loop: little mechanical energy dissipation Regions of low load (<25 N) show diametral clearance region

13 Estimated BFB Structural Stiffness BFB structural stiffness: F K( x) K1 3K3x x 2 Bearing with 100µm shims K 0 at x=0 : assembly interference fit (no clearance) Bearing stiffness increases with bearing deflection and shim thickness.

14 Rotordynamic test rig Bearing TC cross-sectional view Max. operating speed: 80 krpm Turbocharger driven rotor Journal diameter:36.5 mm Journal press fitted on shaft stub Model T25, donated by Honeywell Turbo Technologies

15 Drag Torque Accelerate to 60 krpm, steady state operation, and deceleration to rest. Lift off speed occurs at the lowest torque: airborne operation

16 Break-away drag torque (dry friction) f Torque RW Peak friction factor during start up Drag torque and rotor lift off speed increase with specific load. f ~ 0.50 f ~ 0.31 Friction factor of shimmed BFB increases with shim thickness. f decreases with specific load (W/(LD)).

17 Friction factor from start up to airbone f Torque RW Friction factor [-] Original bearing Dry friction (rubbing) Bearing with 30 µm shims Airborne operation Rotor speed [krpm] Original 30 µm shims 50 µm shims W/(LD)~20 kpa Bearing with 50 µm shims f ~ 0.05 f is low for BFB (with or w/o shims) when airborne and above >50 krpm.

18 Rotordynamic test rig Dynamic load : 1000 N or 250 N Rotor speed: up to 75 krpm Load cell Test identification range: Up to 450 Hz Electromagnetic shaker X W Y Positioning table X Y Test bearing

19 Dynamic loads: sine-sweep Shaft speed: 50 krpm (833 Hz) Displacement amplitude: 20 µm Specific load W/(LD):14.3 kpa Test frequency range: 200 Hz- 450 Hz Dynamic load: up to 250 N

20 Rotordynamic test rig Oil inlet TC center housing Eddy current sensor Static load Journal BEARING Air outlet BEARING X Shaft stub Accelerometer Oil outlet Turbine Squirrel housing Thermocouple cage (Soft Static load elastic (force gauge) support) Stinger connection to shaker Y Load sensor Accelerometer Thermocouple 5 cm Starting at ambient temperature, after a 30s test, bearing cartridge temperature raised 30 C.

21 Parameter Identification Apply: sine sweep load excitations ( Hz), amplitude controlled (20 µm). Measure: bearing absolute accelerations and displacements relative to journal System EOM: CS K X SX 2 XX XX XY XY x FX MS A X j ( ) ( ) X( ) y CS K K Y SY YX j CYX KYY j CYY ( ) F Y M A ( ) S 2 Y Y j ( ) K j C K j C Frequency domain analysis yields stiffness and damping coefficients. K S,C S : soft SQ stiffness & damping M S : effective mass K ij,c ij : test bearing stiffness & damping

22 BFB stiffnesses, K W/(LD)=14.3 kpa Shaft speed 50 krpm (833 Hz) (a) Original Bearing (b) BFB with 30 µm shims (c) BFB with 50 µm shims X Y 14.3 kpa specific load Uncertainty:±0.08 MN/m BFB direct stiffnesses increase with excitation frequency, not affected by shims.

23 BFB Damping, C W/(LD)=14.3 kpa Shaft speed 50 krpm (833 Hz) (a) Original Bearing (b) BFB with 30 µm shims (c) BFB with 50 µm shims Damping C XX, along static load (X), decreases with excitation frequency. Direct damping increases a little for shimmed BFB. Max. variability: ±100 Ns/m

24 Force coefficients comparison Static load direction 14.3 kpa specific load X Y BFB direct stiffnesses increase with excitation frequency, not affected by shims. Damping C XX decreases with excitation frequency. Direct damping increases little for shimmed BFB. Original 30 µm shims 50 µm shims

25 BFB loss factor, X Proportional structural damping model C K Y From viscous energy dissipation (E v ) = structural material energy dissipated (E m ) Loss factor (frequency dependent for circular orbits) (textbook) C K XX XX C K YY YY Average loss factor from 300 Hz (ω 1 ) to 400 Hz (ω 2 )

26 BFB loss factor, Loss factor [-] Loss factor [-] Bearing with 30 µm shims Original Bearing Frequency [Hz] Bearing with 50 µm shims 0 krpm Original Bearing Frequency [Hz] 50 krpm increases for BFB with shims. Large scatter when operating at 50 krpm Loss factor decreases by ~ 10%-20% for operation with journal speed. Original 30 µm shims 50 µm shims

27 Average loss factor 300 Hz (ω 1 ) to 400 Hz (ω 2 ) range Loss Bearing Configuration Factor, Standard deviation σ Original krpm 30 m shims m shims Original krpm 30 m shims m shims Bearing with 50 μm shims has the largest loss factor; however it also has the larger standard deviation.

28 TC vibration measurements Original bearing Bearing with 30 µm shims Rotor on shimmed BFB does not show sub synchronous whirl motions. Bearing with 50 µm shims

29 FB post test inspection

30 Conclusion Shimmed (50 μm) BFB shows LARGEST DRY friction coefficient (f ~ ). Once airborne, drag friction factor for BFB is low [ f ~0.05]. Rotordynamic coefficients: shim thickness does not affect BFB stiffnesses; however, it increases a little the damping coefficients. The bearing with 50 μm shims has an average loss factor γ~0.62, 30% higher than γ~0.47 with original bearing. The standard deviation is higher, however. Other tests demonstrate improved rotordynamic performance of a shaft supported on a shimmed BFB.

31 Thanks to the Turbomachinery Research Consortium for its support. Questions(?) Learn more at Some material reproduced with permission from 2014 Int. IFToMM Conference on Rotordynamics, Milano, IT. 31