11

Luis San AndrésMast-Childs Professor, Fellow ASMETexas A&M University

Research sponsored by BorgWarner Turbo Systems

Prediction of Gas Thrust Foil Bearing Performance for Oil-Free Automotive Turbochargers

Keun RyuAssistant Professor

Hanyang University

Paul DiemerDirector of Engineering

BorgWarner Turbo Systems

Recommended for Journal Publication

Proceedings of ASME Turbo Expo 2014: Turbine Technical Conference and Exposition, June 16-20, 2014, Düsseldorf, Germany

ASME GT2014-25940

2

Gas bearing for turbochargers

In support of OIL-FREE systems eliminate lubrication systems and seals No oil coking and seal failure! reduce overall system weight, complexity. extend maintenance intervals. increase system efficiency due to low drag power losses. Higher ICE efficiency and lesser emissions.Green technology

http://www.aeronautics.nasa.gov/oil_free.htm

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Oil-free turbochargers: NASA & Miti & BorgWarner

• In early 1999, NASA & Miti & BorgWarner (Schwitzer) demonstrated oil-free turbocharger with gas foil bearings.

• The revamped S410 turbocharger was installed on the gas stand and operated at temperatures over 650°C and shaft speeds to 120 krpm.

• NASA Glenn Research Center spearheaded the oil-free turbocharger project with foil bearings from Mohawk Innovative Technologies (MiTi®) and turbocharger technology from BorgWarner (Schwitzer).

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• Series of corrugated foil structures (bumps) assembled within a bearing sleeve.

• Integrate a hydrodynamic gas film in series with one or more structural layers.

Current Applications: ACMs, micro gas turbines, turbo expanders.

Reliable Tolerant to misalignment and

debris, also high temperature. Damping from dry-friction and

operation with limit cycles. Excessive drag and wear during

rotor startup and shutdown . Need coatings to reduce friction.

Gas foil bearings – Bump typehttp://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110011144.pdf

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Overview: Foil thrust bearings

Iordanoff (1998): Established limit of GFTB operation at high speeds.

Somaya et al. (2009): Analysis and testing of thrust bearings with viscoelastic supports.

Dykas (2006), Dickman (2010), Stahl (2012): Experimental results on static load and drag torque.

Lee and Kim (2011): Prediction and measurements for TFBs enhanced by hydrostatic pressurization.

Lee et al. (2008 - 2013): GFTBs integrated into turbo compressors and turbochargers. Report on-going analyses and test data.

Heshmat et al (1983): Coupled gas film pressure field to elastic surface deformation field via a simplified uniform stiffness model.

Zhou et al. (2012): Introduced novel TFB punching dimples on the top foil to act as the underspring element.

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Year Topic2011-12 Thrust Foil Bearings: Computational modeling – Prediction of

dynamic force coefficients, performance characteristics (load capacity, drag power loss etc.)

2008-13 Metal Mesh Foil Bearings: construction, verification of lift off performance and load capacity, identification of structural stiffness and damping coefficients, identification of rotordynamic force coefficients

2008-10 Performance at high temperatures, temperature and rotordynamic measurements. Extend nonlinear rotordynamic analysis

2007-09 Thermoelastohydrodynamic model for prediction of GFB static and dynamic forced performance at high temperatures

2005-07 Effect of feed pressure and preload (shims) on stability of FBS. Measurements of rotordynamic response.Rotordynamic measurements: instability vs. forced nonlinearity?

2005-06 Model for ultimate load capacity, Isothermal model for prediction of GFB static and dynamic forced performance

2004-09 Measurement of static load capacity, Identification of structural stiffness and damping coefficients. Ambient and high temperatures

TAMU research on foil bearings

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Objective & Tasks

To develop predictive tool to perform the engineering design of thrust foil bearings for automotive turbochargers.

Implement FE model of top foil and integrate to gas film analysis.

Validate predictions from model with limited published test data.

Predict static and dynamic forced performance of gas thrust foil bearings for PV turbochargers.

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Model for foil thrust bearings

9

Thin film gas flow analysis

3 31 0

12 2 12h P h Prh r h

r r r r r t

Structural analysis performed off-line, prior to computations coupling the structure to thin gas flow (Reynolds equation)

Reynolds eq: Laminar flow and isothermal conditions

Film thickness (h)

,

,

0 1T e rT

T P e r

h h h w

h h w

Top foil deformation

( , ) ( , )( ), ,r r a B TFw f P P K D

3

212 1 TF

TF TFTF

E tD

Top foil rigidity

T P

r

W (Load)

he

hi h

Film thickness

Rotor collar

Top foilUnder springwith stiffness KB

gas film

X

Y

Schematic front view of thrust foil bearing

Supportdisk

Bearing pad with top foil and underspring

Line weld

Direction of rotorSpinning,

r

X

Y

Schematic front view of thrust foil bearing

Supportdisk

Bearing pad with top foil and underspring

Line weld

Direction of rotorSpinning,

r

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Top foil: 2D Finite Elements

- Neglect curvature: Small ratio of top foil deflection to its radius (~0.001)- Negligible interactions between bumps

- 2D flat SHELL (thin plate) finite element, Anisotropic material (No membrane stresses)

x

zy

Bump foil

Fixed edge

Smooth Top Foil Finite element

r : rotor surface peed

r

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Analysis for force coefficients

pads

O

N

k

tiZZkaZ zeZFrdrdPPF )(

TFB reaction force

Mechanical impedance: z z zZ K i C

Exact advection model to solve the partial differential equations (PDEs) for the pressure fields in the gas film.

Control volume method for numerically stable and accurate solution at arbitrary operating conditions.

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MODEL VALIDATIONfor foil thrust bearings

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Validation: TFB Geometry

NO available reference with enough description of TFB to benchmark any predictive tool.

Number of pads, NPAD 6Outer diameter, Do 0.1016 mInner diameter, Di 0.0510 mPad arc extent, ΘP 45o

Pad taper extent, ΘT 15o

Pad taper, ∆h 0.050 m*Top foil material Inconel X-750

Thickness, tTF 0.150 mmBump foil material Inconel X-750

Thickness, tBF 0.102 mmPitch, s0 5.00 mm*

Half length, l0 1.60 mm*Height, hBF 0.500 mm*

Friction coefficient, μf 0.10*Bump stiffness/area, KB 6.44 N/mm3

Structural loss factor, γ 0.20*

* Assumed value based on the authors’ practical experience

Dickman, J. R., 2010, “An Investigation of Gas Foil Thrust Bearing Performance and its Influencing Factors,” MS Thesis, Case Western Reserve University, Cleveland, OH.

s0

tt

tb

l0

hbα

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Validation: Drag torque vs. speed

Good correlation => Validates model for prediction of bearing static load performance.

Load = 40N (W/AreaTB=0.06 bar [0.95 psi])

Dra

g to

rque

[Nm

]

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Validation: Drag torque vs. load

Model predictions agree well with test data for loads < ~120 N (2.85 psi)

Largest difference& Sudden increase

in torque due to rubbing contact

Dra

g to

rque

[Nm

]

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Prediction: Min. film thickness vs. Load

As load increases, the min. film thickness decreases exponentially as the top foil deformation increases linearly.

Large speed number (696) and compliance factor (αc up to 5.25) denote large compressibility effects and a very soft underspring.

26))((

e

O

a hR

P

Be

ac Kh

P

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Prediction: Film thickness & pressure, foil deformation

50 N

180 N

Drop towards ambient

Typical for low speed number,

Λ=24 (small fluid compressibility

effect)

Min. film ~3 μm

Large top foil deformation

Sags

Predicted film thickness is too small at highest load. Surface roughness effects must play an important role in the generation of drag torque and dissipation power.

26))((

e

O

a hR

P

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Prediction: Stiffness and damping vs. load

Both stiffness and damping coefficients increase with load since the film thickness decreases.

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Prediction: Force coefficient ratio vs. load

(CzΩ/Kz) γ=0.2 Apparent at large load or high speed.

γ=0.2

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Prediction of Performance for Thrust Foil Bearing in OIL-FREE TURBOCHARGER

Outer diameter, Do 0.054 mInner diameter, Di 0.026 m

Structural loss factor, γ(design) 0.32

*TFB configuration is proprietary*

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Axial load vs. shaft speed

Axial load on GTFB (normalized with respect to maximum load) versus shaft speed (normalized with respect to maximum shaft speed).

Load from balance of

thrust loads generated in

the back of the turbine and

compressor wheels

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Min. film thickness vs. axial load

Surface roughness is

important

As the shaft speed and thrust load increase, the minimum film thickness decreases.

Operation at a higher temperature leads to a larger film thickness, gas viscosity increases with temperature!

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Max. foil deformation vs. axial load

As shaft speed and thrust load increase, the maximum elastic deformation of the top foil increases linearly.

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Drag power loss vs. speed

Drag power increases with shaft speed (and load) and with gas temperature (higher viscosity).

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Friction factor vs. speed

Small friction factor makes the gas TFB an extremely attractive support for an oil-free TC. Nearly frictionless!

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Stiffness vs. axial load

Stiffness increases linearly with applied load, a typical condition for a soft TFB. Bearing compliance factor (αc) 0.12 ~ 0.50

Be

ac Kh

P

Stiffness normalized

with respect to max. stiffness

at 250°C

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Damping vs. axial load

Bearing damping is most affected by temperature at the lowest load (and shaft speed) condition, while at high speed the damping coefficient is the largest

Damping normalized

with respect to max. damping

at 250°C

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Force coefficient ratio vs axial load

Nearly constant CzΩ/Kz independent of gas temperature or load condition, structural damping is vital for mechanical energy dissipation.

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Stiffness vs. frequency

250oC

As frequency increases, the TFB stiffness hardens (increases) by ~50% at the low speed (low load) condition, and ~16% for the high speed (high load).

Stiffness normalized

with respect to max. stiffness

at 250°C

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Damping vs Frequency ratio

250oC

Damping is largest for low speed and low load conditions Very small at γ=0 & vanishing quickly as frequency

increases. Dry-friction as a loss factor determines the magnitude of damping!

Damping normalized

with respect to max. damping

at 250°C

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Force coefficient ratio vs. frequency

z

z

CK

The success of foil bearing technology relies on the selection of a metal underspring structure that offers the largest mechanical energy dissipation.

γ=0.32

250oC

(Czω/Kz) is lowest at the highest shaft

speed (and applied load) due to large

speed number (gas compressibility

effect)

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While airborne, the drag friction factor for the bearing is small, ranging from 0.009 to 0.015, thus demonstrating the advantage of an air bearing technology over engine oil lubricated bearings. The largest drag occurs at the highest temperature since the gas viscosity is also highest. The synchronous speed axial stiffness increases with operating speed and load, whereas the axial damping coefficient remains nearly invariant. The operating gas temperature plays an insignificant role on the variation of the force coefficients with excitation frequency.

ConclusionsGTFB designed for use in an oil-free turbocharger

ASME GT2014-25940

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The operating speed and the ensuing applied thrust load determine the largest change in the TFB force coefficients. As an excitation frequency increases, a TFB axial stiffness that hardens and an axial damping coefficient that decreases rapidly. The most important finding is that CzΩ/Kz ≈ γ = the material loss factor for the bearing.

Conclusions

Predictive tool validated & benchmarked to (limited) test data!

GTFB designed for use in an oil-free turbocharger

ASME GT2014-25940

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AcknowledgmentThanks to the support of• BorgWarner Turbo Systems

Learn more http://rotorlab.tamu.edu

Questions (?)

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Shell finite element

Governing differential equations of first-order shear deformation theory for isotropic top foil material (Reddy, 1993)

Resultant shear forces (Q) and

bending moments (M) for distributed

load q=P-Pa in a shell element.

0

)( ayx PPyQ

xQ

0yxxx

MM Qx y

0yx y

y

M MQ

x y

z, w

y, v

x, uOA

BC

q xyxy

MM dx

x

xx

MM dx

x

yy

MM dy

y

yxyx

MM dy

y

xM

xyM yxM

yM

xQ

yQ

yy

QQ dy

y

xx

QQ dx

x

dx

dy

z, w

y, v

x, uOA

BC

q xyxy

MM dx

x

xx

MM dx

x

yy

MM dy

y

yxyx

MM dy

y

xM

xyM yxM

yM

xQ

yQ

yy

QQ dy

y

xx

QQ dx

x

dx

dy

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Shell FE & Underspring connections

[KG] : global FE stiffness matrix[ek] : top foil FE stiffness matrix[ks] : spring FE stiffness matrix

Assembly of structural stiffness matrix

4-node shell FE and linear spring

x

yr

4

Linear spring

Finite element

1

3

22x

y

z

xy

z

lr

lc= r

ht

kl2

4

1 3

2

node

lr

lc= r*

0e

l B rk K s l

' 1B BK K i Structural loss factor (γ)

1

Nem

e

e

G sK k +k

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Global stiffness matrix decomposition

KG : global FE stiffness matrix, FG : external force vectorUG : displacement vector, L : lower triangular matrix

DECOMPOSITION Performed off-line, prior to computationscoupling structure to thin gas flow (Reynolds equation)

Computational efficiency greatly enhanced

Cholesky Decomposition Forward/backward substitutions

G G GK U = F

TG G GK L L

LG x =FG

LTUG=x