1 Identification of structural stiffness and material loss factor in a shimmed (generation one) bump type foil bearing Luis San Andrés Mast-Childs Professor May 2013 Joshua Norsworthy Graduate Research Assistant TRC-B&C rd Turbomachinery Research Consortium Meeting TRC Project 32513/1519 FB Metal Mesh Foil Bearings: Operation at high temperatures

2 Bump-type foil bearing (BFB) BFB components: bearing cartridge, bump Foil strip (compliant), and top foil Hydrodynamic air film pressure develops between the rotating shaft and the top foil Bearing Cartridge Top Foil Bump Foil Top Foil Fixed End Bump Foil Applications: ACMs, micro gas turbines, turbo expanders, turbo compressors, turbo blowers, soon in automotive turbochargers Adequate load capacity provided by the bump foil strip (compliant) Frictional damping (due to relative motion of bump foils) dominates Tolerant to misalignment Bearing Cartridge

Issues with foil bearings Endurance: performance at start up & shut down Little test data for rotordynamic force coefficients Thermal management for high temperature applications (gas turbines, turbochargers) Prone to subsynchronous whirl and limit cycle operation –

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) Example s ubsynchronous motions

5 Original GFB Shimmed GFB Original GFB Inserting metal shims underneath bump strips introduces a preload (centering stiffness) at low cost – typical industrial practice. Preload produces centering stiffness at small loads Original and shimmed GFBs Kim, T.H., and San Andrés, L., 2009, Trib. Trans.

Test BFB specifications L DoDo DiDi 2c nom ParametersMagnitude Bearing cartridge outer diameter, D O mm Bearing cartridge inner diameter, D I mm Bearing axial length, L38.10 mm Top foil thickness (Inconel X750), t T 0.1 mm foil length, 2πD I 110 mm Number of bumps, N B 26 Bump foil (Inconel X750) Thickness, t B mm Pitch, s mm Length, l B 2.1 mm Height, h B 0.50 mm Shim (AISI 4140) length Length 38.1 mm Thickness, t s 50 µm Width7.87 mm Angular extent11.8° Shaft diameter, D s 36.5 mm Measured inner diameter of the FB (assembled) mm Nominal FB radial clearance, c nom =(D I -D s )/ mm Weight of test bearing and outer cartridge1.1 kg (10 N) L/D = 1.03

7 Top Foil Bump Foil Metal Shim Bearing Cartridge Shimmed bump-type foil bearings Shimmed bumps are pressed closer to the rotor than other bumps Shims are added at discrete locations circumferentially and stretch axially The shims have an adhesive glue layer on the bottom

8 Clearance in a shimmed BFB Clearance profile: 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 (all angular coordinates taken from the middle of the shim)

Eddy current sensor Lathe saddle Test bearing Shaft affixed in lathe chuck Load cell Lathe chuck Lathe tool holder Eddy Current sensor Load cell Test bearing Stationary shaft Lathe chuck holds shaft & bearing during loading/unloading cycles. Static load test rig Dr. Chirathadam, TRC 31 st (2011)

10 Load-deflection results for original BFB Region of bump compression Bearing reaction force: Regions of low load (<50 N) evidence the diametral clearance region Regions with bump compression are fitted to a third order polynomial 4 cycles of push and pull loads directed 90 o to top foil fixed end Nonlinear F(X) Small BFB hysteresis loop : little mechanical energy dissipation

11 Load vs. deflection – compare Original and Shimmed BFBs show nonlinear force behavior. Shims effectively reduce bearing clearance. Applied load vs BFB deflection

12 Bearing with 100μm shims Push/Pull Original bearing Push/Pull Bearing with 50μm shims Push/Pull Bearing stiffness increases with bearing deflection and shimthickness Bearing structural stiffness: Estimated bearing structural stiffness K ≠0 at x =0: assembly interference fit (no clearance) Bearing with 100 µm shims

13 BFB with 100µm shims Loss factor estimation Loss factor Bearing Configuration 45º Original µm shims µm shims º Original µm shims µm shims0.053 Largest loss factor for the 50µm shim bearing due to increased sliding friction

14 Predictions (90º orientation) Stiffness Load vs BFB deflection Original 50 µm shims 100 µm shims Predictions from a simple model agree well with experimentalresults for all test configurations

Shimmed BFB (without an assembly interference fit) shows larger energy dissipation than original BFB. Bearing structural stiffness increases with increasing shim thickness and hardens with bearing displacement. The loss factor for the test (generation one) BFB is small. Highest loss factor  ~0.20 for bearing with 50 µm shims due to increase in sliding of foil strips wit bearing cartridge. Predictions from model agree well with experimental results. Conclusions

a)Install and test the original and shimmed BFB in a rotordynamic test rig. b)Conduct dynamic load tests to determine force coefficients over a range of excitation frequencies c)For increasing static loads, conduct rotor speed start-up and shut down tests and record drag torque and lift-shaft speed. Proposal to TRC (1 year) Objective: Quantify rotor lift off and shut down events for shimmed BFBs, as well as determine force coefficient

17 Effect of Shimming on the Rotordynamic Force Coefficients of a Bump-type Foil Bearing Luis San Andrés Mast-Childs Professor May 2013 Joshua Norsworthy Graduate Research Assistant New Proposal

TRC budget Year I Support for graduate student (20 h/week) x $ 2,050 x 12 months$ 24,600 Fringe benefits (0.6%) and medical insurance ($185/month)$ 2,378 Travel to (US) technical conference$ 1,200 Tuition three semesters ($362 credit hour x 24 h/year)$ 8,688 Supplies for test rig (machine parts $1,000 + portable data storage $140) $ 1,140 $ 37,996 Research will characterize, qualitatively and quantitatively, shimming as a cheap and effective way of improving rotordynamic performance of rotors supported on BFBs.The work is important for manufactures of turbochargers, turboexpanders and micro gas turbines Shimmed bump foil bearings