ASME GT2009-59315

Luis San AndrésMast-Childs Professor

Fellow ASME

Measurements of Structural Stiffness and Damping Coefficients in a Metal

Mesh Foil Bearing

Measurements of Structural Stiffness and Damping Coefficients in a Metal

Mesh Foil Bearing

June, 2009

ASME Turbo Expo 2009: Power for Land, Sea, and Air

ASME GT2009-59315

Supported by TAMU Turbomachinery Research Consortium

accepted for journal publication

Thomas Abraham ChirathadamResearch Assistant

Tae-Ho KimResearch Associate

Texas A&M University

ASME GT2009-59315

Metal mesh foil bearings

Metal mesh ring and top foil assembled inside a bearing cartridge.

Hydrodynamic air film will develop between rotating shaft and top foil.

Metal mesh resilient to temperature variations Damping from material hysteresis Stiffness and viscous damping

coefficients controlled by metal mesh material, size (thickness, L, D), and material compactness (density) ratio.

Potential applications: ACMs, micro gas turbines, turbo expanders, turbo compressors, turbo blowers, automotive turbochargers, APU

ASME GT2009-59315

MMFB Assembly

BEARING CARTRIDGE

METAL MESH RING TOP FOIL

Simple construction and assembly procedure

ASME GT2009-59315

TAMU past work on Metal Mesh Dampers

Zarzour and Vance (2000) J. Eng. Gas Turb. & Power, Vol. 122

Advantages of Metal Mesh Dampers over SFDsCapable of operating at low and high temperaturesNo changes in performance if soaked in oil

Al-Khateeb and Vance (2001) GT-2001-0247

Test metal mesh donut and squirrel cage( in parallel)MM damping not affected by modifying squirrel cage stiffness

Choudhry and Vance (2005) Proc. GT2005

Develop design equations, empirically based, to predict structural stiffness and viscous damping coefficient

METAL MESH DAMPERS proven to provide large amounts of damping. Inexpensive. Oil-free

ASME GT2009-59315

Recent Patents: gas bearings & systems

A metal mesh ring is a cheap replacement for a “porous foil”

‘Air foil bearing having a porous foil’Ref. Patent No. WO 2006/043736 A1

Turbocharger with hydrodynamic foil bearingsRef. Patent No. US7108488 B2

Foil JournalBearings

Thrust foilBearing

ASME GT2009-59315Metal Mesh Dampers for Hybrid Bearings

Ertas &Luo (2008) ASME J. Gas Turbines Power., 130, pp. 032503-(1-8)

MM damper force coefficients not affected by shaft eccentricity ( or applied static load)

Ertas (2009) ASME J. Gas Turbines Power, 131 (2), pp. 022503-(1-11)

Two metal mesh rings installed in a multiple pad gas bearing with flexural supports to maximize load capacity and damping. Bearing stiffness decreases with frequency & w/o external pressurization; and increases gradually with supply pressure

Ertas et al. (2009) AIAA 2009-2521

Shape memory alloy (NiTi) shows increasing damping with motion amplitudes. Damping from NiTi higher than for Cu mesh (density – 30%) : large motion amplitudes (>10 um)

Recent work by OEM with MM dampers to maximize load capacity and to add damping in gas bearings

ASME GT2009-59315

Metal Mesh Foil Bearings (+/-)

No lubrication (oil-free). NO High or Low temperature limits.

Resilient structure with lots of material damping.

Simple construction ( in comparison with other foil bearings)

Cost effective

Metal mesh tends to sag or creep over time

Damping NOT viscous. Modeling difficulties

ASME GT2009-59315

MMFB dimensions and specifications

Dimensions and SpecificationsBearing Cartridge outer diameter, DBo(mm) 58.15

Bearing Cartridge inner diameter, DBi(mm)

Bearing Axial length, L (mm) 28.05

Metal mesh ring outer diameter, DMMo (mm) 42.10

Metal mesh donut inner diameter, DMMi(mm) 28.30

Metal mesh density, ρMM (%) 20

Top foil thickness, Ttf (mm) 0.076

Metal wire diameter, DW (mm) 0.30

Young’s modulus of Copper, E (GPa), at 21 ºC

110

Poisson’s ratio of Copper, υ 0.34

Bearing mass (Cartridge + Mesh + Foil), M (kg)

0.3160 ±

PICTURE

Bearing cartridge

Top foil

Donut shaped metal mesh

Rotating shaft

Gas film

Ω

ASME GT2009-59315

Static load test setup

Lathe tool holder moves forward and backward : push and pull forces on MMFB

Lathe chuck holds shaft & bearing during loading/unloading cycles.

Lathe tool holder

Eddy Current sensor Load cell

Test MMFB

Stationary shaft

ASME GT2009-59315

-150

-100

-50

0

50

100

150

200

-0.12 -0.08 -0.04 0 0.04 0.08 0.12Displacement [mm]

Sta

tic

Lo

ad

[N

]

Push load

Pull load

Push load

Pull load

Static Load vs bearing displacement

3 Cycles: loading & unloading

Nonlinear F(X)

Large hysteresis loop : Mechanical

energy dissipation

MMFB wire density ~ 20%

Displacement: [-0.12,0.12] mmLoad: [-120, 150 ]N

Start

ASME GT2009-59315

0

0.5

1

1.5

2

2.5

3

-0.12 -0.08 -0.04 0 0.04 0.08 0.12

Displacement [mm]

Sti

ffn

es

s [

MN

/m]

Push loadPull load

Push load

Pull load

MMFB wire density ~ 20%

Derived MMFB structural stiffness

During Load reversal : jump

in structural stiffness

Max. Stiffness ~ 2.5 MN/m

Lower stiffness values for

small displacement

amplitudes

ASME GT2009-59315

Dynamic load tests

Motion amplitude controlled mode

Electrodynamic shaker

MMFB Accelerometer Force transducer

Test shaft FixtureTest shaftEddy Current sensors

MMFB motion amplitude (1X) is dominant

Waterfall of displacement

12.7, 25.4 &38.1 μm

Frequency of excitation :

25 – 400 Hz (25 Hz interval)

0

20

40

60

80

100

120

140

0 100 200 300 400

Frequency [Hz]

Dis

pla

cem

ent

[um

]

Increasing Frequency

400 Hz

25 Hz

1 X

ASME GT2009-59315

0

10

20

30

40

50

60

0 50 100 150 200 250 300 350 400

Frequency [Hz]

Dyn

amic

Loa

d [N

]

12.7 um25.4 um38.1 um

Around bearing natural frequency, less force needed to maintain same motion amplitude

Dynamic load vs excitation frequency

Dynamic load decreases around

bearing natural frequency, but increases with

further increase in excitation

frequency.

Dynamic load decreases with increasing motion

amplitudes

38.1 μm

25.4 μm 12.7 μm

Motion amplitude decreases

ASME GT2009-59315

Parameter identification model

( )tM x K x C x F

Equivalent Test System

Meq

Keq

Ceq

Fext

x Lf =244 mm Lf =221 mm L= 248 mm

F(t)

X(t)

1-DOF equivalent mechanical system

ASME GT2009-59315

Harmonic force & displacements

Impedance Function

MaterialLOSS FACTOR

Viscous Dissipationor Hysteresis Energy

( ) i tx t X e ( ) i tF t F e

2( )F

Z K M i CX

2

disE K X

2

disE C X

Parameter identification (no shaft rotation)

KC

1

ImF

K X

ASME GT2009-59315

Model of metal mesh damping material

As force increases, more stick-slip joints among wires are freed, thus resulting in a greater number of spring-damper systems in series.

Stick-slip model (Al-Khateeb & Vance, 2002)

Stick-slip model

arranges wires in series connected by dampers and

springs.

ASME GT2009-59315

Design equation: MMB stiffness/damping

Functions of equivalent modulus of elasticity (Eequiv), hysteresis coeff. (Hequiv), axial length (L), inner radius (Ri), outer radius (Ro), axial compression ratio (CA), radial interference (Rp), motion amplitude (A), and excitation frequency (ω)

, ,equiv o i A pK E f L R R f C f R f A f

, ,equiv o i A pC H g L R R g C g R g A g

2/325 21 4 10 1 2.96 10 1pA

equiv k ko i o i o i

RCL AK E

R R L R R R R

3/ 2 2/325 21 8.7 10 1 1.8 10 1

cpA

equiv co i o i o i n

RCL AC H

R R L R R R R

Empirical design equation for stiffness and equivalent viscous damping coefficients (Al-Khateeb & Vance, 2002)

ASME GT2009-59315

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 100 200 300 400Frequency [Hz]

Rea

l par

t o

f Im

ped

ance

F/X

[M

N/m

] 12.7 um25.4 um38.1 um

K - Mω 2

Real part of (F/X) decreases with increasing motion amplitude

Real part of (F/X) vs excitation frequency

Natural frequency of test system

Frequency of excitation :

25 – 400 Hz ( 25 Hz step)

12.7 μm

25.4 μm

38.1 μm

Motion amplitude increases

ASME GT2009-59315

0

0.5

1

1.5

2

2.5

0 100 200 300 400Frequency [Hz]

Str

uctu

ral s

tiffn

ess

[MN

/m]

12.7 um25.4 um38.1 um12.7 um Prediction25.4 um Prediction38.1 um Prediction

Al-Khateeb & Vance model : reduction of stiffness with force magnitude (amplitude dependent)

MMFB structural stiffness vs frequency

At low frequencies (25-100 Hz), stiffness

decreases

At higher frequencies, stiffness

gradually increases

MMFB stiffness is frequency and

motion amplitude dependent

Frequency of excitation :

25 – 400 Hz (25 Hz step)

12.7 um

25.4 um38.1 um

Motion amplitude increases

ASME GT2009-59315

0

0.2

0.4

0.6

0.8

1

0 100 200 300 400Frequency [Hz]

Imag

inar

y pa

rt o

f Im

peda

nce

F/X

[MN

/m]

12.7 um25.4 um38.1 um

Im(F/X) decreases with motion

amplitude

Imaginary impedance (F/X) vs frequency

Frequency of excitation :

25 – 400 Hz ( at 25 Hz interval)C K

12.7 μm

25.4 μm

38.1 μm

Motion amplitude increases

ASME GT2009-59315

10

100

1000

10000

100000

0 100 200 300 400Frequency [Hz]

Equi

vale

nt v

isco

us d

ampi

ng [N

s/m

]

12.7 um25.4 um38.1 um12.7 um Prediction25.4 um Prediction38.1 um Prediction

Predictions vs. test data: Damping

Amplitude increases

12.7 μm

25.4 μm38.1 μm

MMFB equiv. viscous damping

decreases as the excitation

frequency increases and

as motion amplitude increases

Predicted equivalent viscous damping coefficients in good agreement with measurements

ASME GT2009-59315

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 100 200 300 400Frequency [Hz]

Str

uc

tura

l Lo

ss

Fa

cto

r

12.7 um25.4 um38.1 um

Loss factor nearly similar for all motion amplitudes

Loss factor vs excitation frequency

Structural damping or loss

factor is the largest around the MMFB natural frequency

Frequency of excitation :

25 – 400 Hz ( at 25 Hz step)

12.7 μm

25.4 μm

38.1 μm

ASME GT2009-59315

Conclusions

Static and dynamic load tests on MMFB show large mechanical energy dissipation and (predictable) structural stiffness

MMFB stiffness and damping decreases with amplitude of dynamic motion

MMFB equivalent viscous damping decreases with motion amplitude, and more rapidly with excitation frequency

Large MMFB structural loss factor ( ) around test system natural frequency

Predicted stiffness and equivalent viscous damping coefficients are in agreement with test coefficients: Test data validates design equations

ASME GT2009-59315

Thanks to

TAMU Turbomachinery Research Consortium

Honeywell Turbocharging Technologies

Acknowledgments

Questions ?

Learn more at http://phn.tamu.edu/TRIBGroup

ASME GT2009-59315

Current work

ASME GT2009-59315MMFB rotordynamic test rig

(a) Static shaft

Max. operating speed: 75 krpmTurbocharger driven rotorRegulated air supply: 9.30bar (120 psig)

Test Journal: length 55 mm, 28 mm diameter , Weight=0.22 kg

Journal press fitted on Shaft Stub

TC cross-sectional viewRef. Honeywell drawing # 448655

Twin ball bearing turbocharger, Model T25, donated by Honeywell Turbo Technologies

MMFB

ASME GT2009-59315

Positioning (movable) table

Torque arm

Calibrated spring

MMFB

Shaft (Φ 28 mm)

String to pull bearing

Static load

Eddy current sensor

Force gauge

Top foil fixed end

Preloading using a rubber band

5 cm

Test Rig: Torque and Lift-Off Measurements

Thermocouple

ASME GT2009-59315

Rotor speed and torque vs time

Rotor starts

Constant speed ~ 65 krpm

Valve open

Valve close

3 N-mm

Rotor stops

Applied Load: 17.8 N

Manual speed up to 65 krpm, steady state operation, and

deceleration to rest

Startup torque ~ 110 Nmm

Shutdown torque ~ 80 Nmm

Once airborne, drag torque is ~ 3 % of startup

‘breakaway’ torque

Top shaft speed = 65 krpm

Iift off speed

Lift off speed at lowest torque : airborne operation

WD= 3.6 N

ASME GT2009-59315

Varying steady state speed & torque

Rotor starts

61 krpm

Rotor stops

50 krpm

37 krpm

24 krpm

2.5 N-mm

57 N-mm 45 N-mm

2.4 N-mm 2.0 N-mm 1.7 N-mm

Manual speed up to 65 krpm, steady state operation, and

deceleration to rest

Drag torque decreases with step wise reduction in

rotating speed until the journal starts rubbing the

bearing

Shaft speed changes every 20 s : 65 – 50 – 37 - 24 krpm

Side load = 8.9 N

WD= 3.6 N

ASME GT2009-59315

Bearing drag torque vs rotor speed

Lift-off speed

8.9 N (2 lb)

17.8 N (4 lb)

26.7 N (6 lb)

35.6 N (8 lb)

Max. Uncertainty ± 0.35 N-mm

Rotor accelerates

Bearing drag torque increases with increasing rotor speed and increasing applied static loads. Lift-Off speed increases almost linearly with static load

0

20

40

60

80

0 5 10 15 20 25 30Time [sec]

Sp

ee

d [

krp

m]

0

50

100

0 5 10 15 20 25 30Time [sec]B

ea

rin

g t

orq

ue

[N

-mm

]